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TRANSCRIPT
One Step Formation of Heterogeneous Tubular Biomaterials and Stimulus Responsive Hydrogels
by
Haotian Chen
A thesis submitted in conformity with the requirements for the degree of MASc – Biomedical Engineering
Institute of Biomaterials and Biomedical Engineering University of Toronto
© Copyright by Haotian Chen 2014
ii
One Step Formation of Heterogeneous Tubular Biomaterials and
Stimulus Responsive Hydrogels
Haotian Chen
MASc – Biomedical Engineering
Institute of Biomaterials and Biomedical Engineering University of Toronto
2014
Abstract
Synthetically prepared biomaterial tubular constructs have various applications including
engineered blood vessels, vascularized biomaterials as well as soft robotic actuators. Currently
there is no one-step method for the scalable preparation of perfusable tubular soft materials that
allows the tube size, morphology, composition and tensile properties to be consistently altered.
We report a scalable microfluidic approach for the consistent formation biopolymer tubes in
sodium alginate and collagen I, with outer diameters between 0.7 mm and 2.5 mm, at extrusion
velocities between 1mm/s and 20mm/s. We report the consistent formation of homogeneous
tubes with cylindrical, crimped, and corkscrew inner wall surfaces. Heterotypic tubular
constructs possess “Janus” single-layer, axial stripe patterns, and up to three concentric wall
layers. Stimulus responsive nanoparticles were incorporated as payload to induce predictive
shape transformations. This research potentially leads to high throughput construction of
complex spatially organized 3D functional soft materials and tissues.
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Acknowledgments This work is supported by the Natural Sciences and Engineering Research Council of Canada
(NSERC) and the NSERC CREATE Program in Microfluidic Applications and Training in
Cardiovascular Health (MATCH).
The authors thank Dr. Axel Guenther for project guidance, Lian Leng for teaching
microfabrication and biopolymer extrusion technique, Mark Jeronimo and Arianna McAlister for
their contribution to the work, and all group members from the Guenther lab for helping.
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Table of Contents Acknowledgments.......................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
List of Tables ................................................................................................................................. vi
List of Figures ............................................................................................................................... vii
1 INTRODUCTION AND BACKGROUND ................................................................................1
1.1 Formation of tubular constructs ...........................................................................................2
1.2 Solidification of biopolymers ..............................................................................................9
1.3 Introducing heterogeneity in biomaterials .........................................................................11
1.4 Stimulus responsive materials............................................................................................13
2 CONTRIBUTIONS ..................................................................................................................17
3 MOTIVATION .........................................................................................................................17
4 SPECIFIC AIMS .......................................................................................................................18
4.1 One-step formation of homogeneous soft material tubes ..................................................18
4.2 One-step formation of heterogeneous soft material tubes and stimulus responsive tubes ...................................................................................................................................19
4.3 Stimulus responsive hydrogel characterization and extrusion ...........................................19
5 MATERIALS AND EXPERIMENTAL...................................................................................21
5.1 Microfluidic device designs ...............................................................................................21
5.2 PDMS Device Fabrication .................................................................................................25
5.3 Homogeneous Tube Extrusion ...........................................................................................26
5.4 Multilayer Tube Extrusion .................................................................................................27
5.5 Janus Tube Extrusion .........................................................................................................28
5.6 Preparation of Stripe-Patterned Hydrogel Tubes ...............................................................28
5.7 Collagen Tube Extrusion ...................................................................................................29
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5.8 Valves Control Board Design ............................................................................................30
5.9 Labview Control Programs ................................................................................................31
5.10 Tube Dimensions Measurements .......................................................................................33
5.11 Polymer Synthesis and Hydrogel Solution Preparation .....................................................34
5.12 Stimulus Responsive Material Characterization ................................................................34
5.13 SEM Imaging of Tubular Soft Material Constructs ...........................................................35
5.14 Environmental Temperature and pH Control of Stimulus Responsive Hydrogels ............35
6 RESULTS AND DISCUSSION ...............................................................................................36
6.1 One-step formation of homogeneous soft material tube ....................................................36
6.2 Predictive control of tube dimensions................................................................................40
6.3 Soft material tubes of non-circular cross section ...............................................................46
6.4 One-step formation of heterogeneous soft material tube ...................................................50
6.5 Collagen tube formation ....................................................................................................55
6.6 Stimulus responsive tubular structures ..............................................................................58
7 SUMMARY ..............................................................................................................................68
8 REMAINING WORK AND FUTURE DIRECTION ..............................................................69
References ......................................................................................................................................70
Appendices .....................................................................................................................................75
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List of Tables Table 1. Tubular structure formation summary .............................................................................. 7
Table 2. Summary of synthetic heterogeneities in biomaterials ................................................... 13
Table 3 Recipe of stimuli-responsive particles synthesis ............................................................. 59
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List of Figures Figure 1. Microfluidic device designs. ......................................................................................... 23
Figure 2. Experimental setup of homogeneous tube extrusion. .................................................... 27
Figure 3. Experimental setup of spotted/striped tube extrusion. .................................................. 29
Figure 4. Valve control circuit. ..................................................................................................... 31
Figure 5. Labview control programs. ............................................................................................ 33
Figure 6. Device design and experimental setup. ......................................................................... 38
Figure 7. Dimension control of homogeneous tubes. ................................................................... 44
Figure 8. Homogenous tube morphologies. .................................................................................. 48
Figure 9. Heterogeneous tubular structures. ................................................................................. 53
Figure 10. Collagen tubes ............................................................................................................. 57
Figure 11. Stimuli-responsive PNIPAM-VAA nanoparticles. ..................................................... 59
Figure 12. PNIAPAM-VAA particle size and its stimuli-responsive volumetric changes. ......... 61
Figure 13. Schematic of homogeneous stimulus responsive sheet extrusion. .............................. 64
Figure 14. Homogeneous stimuli-responsive hydrogel and its response to temperature and pH. 64
Figure 15. Schematic of stimulus responsive tube assembly. ....................................................... 66
Figure 16. Temperature induced response of half-half stimulus responsive tube. ....................... 67
Figure A1. Tube extruded with no crosslinker in inner streaming fluid. ...................................... 75
Figure A2. Spotted tubes............................................................................................................... 76
Figure A3. Comparison of dimensions of single layer/Three-layer tubes. ................................... 77
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Figure A4. Heterogeneous hydrogel extrusion. ............................................................................ 80
Figure A5. Heterogeneous stimuli-responsive hydrogel sheets and their response to temperature
and pH. .......................................................................................................................................... 81
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1 INTRODUCTION AND BACKGROUND In nature, tubular structures are a common element in both plant and animal structure and
physiology. In the human body and human organs, they present in the forms of blood vessels,
airways, and ducts. Artificial biomaterial tubes were produced to mimic or replace natural
existing tubular structures. They can find applications as engineered blood vessels and micro
tissues[1], and cell-laden tubes incorporated into vascularized biomaterials [2]. Although various
efforts have been made to achieve controlled formation of tubular structures of different
materials including biomaterials, the goals of high throughput production, predictive controlled
dimensions, spatial compositional heterogeneity, flexibility of biomaterials and compatibility
with cells have not been met.
Tubular tissues in the human body exist at different scales. They can be as small as capillaries (5-
10µm in diameter) and gland ducts, and as large as the aorta (diameter approximately 30mm in
human) and bronchus (diameter approximately 25mm in human). Present approaches of
biomaterial tube formation often lack of scalability due to the small dynamic diameter range
accessible for tube formation and the inability to predictively control and maintain tube
diameters of formed tubes. Current methods are limited in terms of their compatibility with
different soft materials due to constrain on gelation time. A scalable method with precise
predictive control over dimensions of formed tubular structures, and with flexibility on material
choices, is an essential requirement towards the formation of engineered tubular tissues [1, 2].
Human tubular tissues such as bronchioles, intestinal mucosa, arteries, and blood vessels rely on
a unique spatial organization that stretches from the molecular alignments of biopolymers in the
extracellular matrix, over cells to the tubular diameter and is necessary for tissue function [3].
For instance, bronchioles and intestinal mucosa have non-circular inner walls; arteries and veins
have multiple cell layers; bronchi have gland ducts and cartilage around its circumference. This
heterogeneity in spatial composition and special morphologies cannot be mimicked by the
current tubular structure formation techniques, especially in the context of biomaterials. High
throughput formation of heterogeneous tubular structure made of biomaterials has been an
important step towards vascular graft and drug testing developments.
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To mimic biological function, nature requires that engineered tissues be responsive and adaptive
in different environments, and adjust their function accordingly. For example, blood vessels
regulate blood flow in response to temperature and several other stimuli to maintain homeostasis.
Responsive polymer materials with very similar attributes have been used in a broad range of
applications; responsive biointerfaces [4], controlled drug delivery [5], interactive coating [6]
and to mimic muscle actions [7]. They have been applied to regulate transport of ions and
molecules, alter wettability and adhesion of different species or convert between chemical
stimuli and optical, thermal and mechanical responses. Currently, the synthesis and preparation
of stimulus responsive materials involves multiple steps that are often costly and time
consuming. One-step formation of patterned soft stimulus responsive materials will improve the
production throughput significantly. Incorporating stimulus responsive material in hydrogel tube
can induce predictive stimulus response of the formed tube with known environmental changes,
and these tubes can find potential applications in controlling rate and direction of flow in
vascularized hydrogel scaffold.
1.1 Formation of tubular constructs Two approaches have been widely employed for the formation of soft material tubes: extrusion
and molding.
The Takeuchi group at the University of Tokyo demonstrated the extrusion of meter-long cell-
laden microfibers [8]. A microfluidic device with double coaxial laminar flow was used to
produce the core-shell hydrogel microfibers. This extrusion method is referred as in-plane
extrusion in my thesis because the extrusion direction is in-plane with flows in the microfluidic
device. The composition of the three co-axially flowing biopolymer solutions from inside out
was: a cell-laden biopolymer solution at the core, a fast gelling shell biopolymer solution and a
crosslinker solution. The shell biopolymer solution was ionically cross-linked while the solution
at the core was cross-liked by temperature-induced gelation. Rapid gelation produced a hydrogel
shell immediately after exiting the device with a cell-laden biopolymer solution confined in the
core. The fiber was then transferred to 37°C environment for 15 minutes for the temperature-
induced gelation of the core. Compatibility of the approach with the acid-solubilized type I
collagen, pepsin-solubilized type I collagen and fibrin as core material was demonstrated. The
extruded microfibers had cores of cell-laden collagen and shells of alginate or alginate-agarose
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interpenetrating networks. In the case of endothelial cells introduced in the core, the cells aligned
themselves to form a tubular structure. The microfibers had diameters between 92±5µm and
210±5µm.
There are several other examples demonstrating extrusion of tubular structure using an in plane
extrusion method [9-11]. Examples of predictable control of the dimensions of formed tubular
structures have been demonstrated for tubes with outer diameters from 300µm to 900µm.
However, the tubes were not made with biocompatible materials[9]. The tube materials used by
Luo’s group are polyacrylonitrile, polysulfone and polystyrene. In-plane extrusion of coaxially
arranged fluid streams was utilized and solidification was achieved due to solvent loss. This
solidification method is not suitable for hydrogel formation because hydrogels are required to
remain hydrated even after solidification. The inner diameter, outer diameter and the wall
thickness of the formed tubular structure were controlled by changing the flow rates of individual
fluid streams in the coaxial flow. Keeping the flow rates of the other fluids constant, increasing
the inner fluid flow rate resulted in increased inner and outer tube diameters. Keeping the flow
rates of the other fluids constant, increasing the outer fluid flow rate resulted in a decrease in the
tube diameters. The immiscible outer and inner fluid streams extracted the solvent from the
polymer solution contained in the middle polymer stream. An analytical model was presented
based on the Navier Stokes equations, and allowed the tube dimensions to be accurately
predicted. The model neglected the solidification of the tube wall and the associated increase in
viscosity.
Other examples demonstrating ink-jet printing of alginate based tubular structures lack
predictable tube dimensions [10, 11]. Kawakami’s group [10] demonstrated the in-plane
extrusion of homogeneous alginate tubes with outer diameters between 260µm and 310µm.
Ozbolat’s group [11] demonstrated the formation of homogeneous hydrogel tubes in alginate and
chitosan, with outer diameters between 600µm and 1300µm. In both works, the dimensions of
formed biopolymer tubes were predicted based on empirical data. Heterogeneity of spatial
composition is very difficult to achieve with in-plane extrusion of tubular structures.
Nakajima’s group demonstrated out-of-plane extrusion [12]. In this approach, the alginate tube
flowed perpendicular to the direction of alginate solution flow in a microfluidic device using a
2D array of microfabricated nozzles. The nozzles had square shapes and the center regions of the
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nozzles were solid. The alginate solution was extruded along the edge of the square nozzles. The
alginate solution was extruded into a flow of crosslinker solution that approached in a direction
perpendicular to the alginate solution flow. The alginate solution flow then changed its direction
and flowed parallel with the crosslinker flow. The outer diameter of the formed tubes was
approximately 120µm.
The off-plane tubular structure extrusion technique that is further developed in this thesis was
originally demonstrated by Arianna McAlister [13]. The designs of microfluidic devices
introduced in this thesis evolved from her device designs. Homogeneous tube extrusion was
accomplished using three layer PDMS devices; the three layers, from top down, are an inner
crosslinker solution layer of calcium chloride, an alginate matrix solution layer and an outer
calcium chloride crosslinker solution layer. The channels in the device radially feed the solutions
towards a center outlet, which directs the layered fluid towards the common extrusion outlet.
The biopolymer solution is sandwiched by the crosslinker solutions, which forms a cylindrical
wall and moves downwards. A biopolymer tube with outer diameters between 600µm and
1600µm was formed and passed through a confinement tube before entering a reservoir filled
with crosslinker solution. The dimensions of the formed alginate tubes were controlled by
changing the flow rates of the streaming solutions and the biopolymer solution. Extrusions of
bilayer tubes, Janus tubes and tubes that had secondary biopolymers incorporated as spots along
the tube circumference were demonstrated. The microfluidic device designs presented in this
thesis are further developments of the ones originally presented by Arianna McAllister. The
original device designs are more challenging to fabricate with a high yield using multilayer soft
lithography. The center extrusion outlet shared the exact diameter of the tool used for punching
the hole, requiring perfect alignment during a manual punching process. Misalignment lead to
accidental shortening of microfluidic channels around the center extrusion hole, which resulted
in an imbalance of the flow resistance around the extrusion outlet and prevented the consistent
formation of intact tubes at experimental yields exceeding 20%. An analytical model was
presented that described the tube formation process by neglecting the influences of crosslinking
and solidification of the biopolymer during extrusion process. The experimental results only to a
limited extent agreed with model predictions. Bilayer and Janus tube extrusion required more
complex device, but given the low yield of device fabrication, heterogeneous tubes could not be
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formed consistently. The formation of heterogeneous tubes and their dimensions could not yet be
consistently controlled.
The other common method of forming tubular strucutres is molding. Sacrificial materials are
commonly used to form a perfusable vascular structure inside a scaffold. In one example
demonstrated by Christopher Chen’s group, a rigid 3D filament network of carbohydrate glass
was used as sacrificial template in engineered tissues to generate vascular network [14]. The
dimension of the vasculature was defined by the sacrificial material dimensions, and the limiting
dimensions of the filament network was the nozzle size of their 3D printer. A simple model,
which did not consider coaxial flow, helped predict with reasonable accuracy the diameters of
the extruded filaments. The diameter of the filament varied between 200µm and 1100µm. A
suspension of cells in extra cellular matrix (ECM) was poured on to the filament network and
was allowed to solidify. The filament was then dissolved, leaving behind an elliptical flow
conduit within the bulk gel. The scaffold was then perfused with blood under positive pressure
pulsatile flow. An advantage of this multistep strategy is its flexibility in terms of ECM material,
as it is not limited in terms of the crosslinking time. The scaffold can also be made of agarose,
alginate, fibrin, matrigel and poly(ethylene glycol) (PEG), and a wide range of cell types can be
incorporated into the scaffold. The perfusable network was not exactly a vascular system because
the materials made of the channels are the same as the bulk gel. The cultured tissues are therefore
homogeneous in spatial composition, and cannot mimic the complex tissue interactions in natural
organisms.
In other examples, extruded endothelial cell laden alginate fibers were embedded in a collagen
scaffold [15, 16]. Fibers composed of a mixture of alginate and gelatin served as the sacrificial
material. The hydrogel fibers were produced by extrusion using the in-plane method which was
discussed above. The diameters of the fibers can be controlled to a certain extent by controlling
the size of extrusion needle and flow rate of biopolymer solution, with a range of diameters from
150µm to 1200µm. An empirical relationship between biopolymer flow rates, extrusion needle
size and hydrogel fiber diameter was presented. The produced alginate/gelatin fibers were coated
with smooth muscle cells and were embedded in collagen solution, which solidified to form a
bulk gel after thermal gelation. The alginate/gelatin fibers were dissolved by alginate lyase at the
end to leave channels in the bulk collagen gel in an approach similar to the one used by Chen’s
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group [14]. In this instance, alginate/gelatin hydrogel fibers served as a sacrificial material and a
homogenous scaffold with embedded vasculature was produced using this multi-step approach.
A technique developed by Jennifer Lewis’s group demonstrated the capability of introducing
spatial composition heterogeneity into vascularized scaffold [17]. Two types of sacrificial
materials, fugitive Pluronic F127 and gelatin methacrylate (GelMA) were used to define the
channels and were thermally gelled. A vascular network made of fugitive ink was printed with a
nozzle such that the diameter of the printed filaments could be controlled by the printing
pressure, nozzle height and nozzle movement speed. The dimensions of the printed filaments
were controlled based on empirical data. The diameter of the filaments varied from 150µm to
650µm. After the vascular network was printed, a bulk volume of GelMA ink was cast around it.
As the temperature was lowered below 4°C, the GelMA ink formed a solidified bulk gel and the
fugitive ink returned to a liquid state and was removed from the bulk gel. A perfusable vascular
network remained inside the bulk gel. A heterogeneous vascular network was created by co-
printing fugitive ink and cell-laden GelMA. A bulk GelMA ink was then cast around the printed
network. GelMA inks were then photopolymerized to form a bulk gel with an internal gelled
cell-laden vascular network. The fugitive ink was removed by reducing the temperature. At the
end, heterogeneous vascular network was formed. However, the part of network formed by cell-
laden GelMA ink was not perfusable because GelMA ink cannot be removed after
photopolymerization. This approach provides some spatial composition heterogeneity to the bulk
gel and the surroundings of the tubular structure.
The previous molding approaches produced vascularized scaffold but all involve the use of
sacrificial materials to produce a vascular network. These approaches limit the control of tubular
structure dimensions due to the limited accuracy of sacrificial layer printing. Another technique,
in which the bulk mold was produced first, effectively improved the control over vascular
network dimensions [18]. Polydimethylsiloxane (PDMS) devices containing array of channels
were produced using standard soft lithography with channel sizes between 50µm and 150µm.
The channels were then filled with fibrin/collagen solution and allowed to gel. Human umbilical
vein endothelial cells were coated at the two ends of the channels, and after 3 to 4 days of
culture, the cells were able to migrate into the gel and form capillaries. The yield of the entire
process is 50%. The major limitation of this approach is the length of tubular structure being
restricted to 1600µm.
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Table 1 summarizes the dimensions of tubular structures made by various methods, including the
ones discussed previously.
Table 1. Tubular structure formation summary
Reference Method Materials Outer
Diameters(µm)
Dimension
Control
Onoe, H., et
al. [8]
In-plane extrusion Alginate,
Alginate/Agarose
92-210 N/A
Lan, W., et
al. [9]
In-plane extrusion Polyacrylonitrile,
Polysulfon,Polystyrene
300-900 Analytical
Takei, T., et
al. [10]
In-plane extrusion Alginate 260-310 Empirical
Zhang Y.,
Y.Y.[11]
In-plane extrusion Alginate 600-1200 N/A
Hwang,
S.W., et
al.[19]
In-plane extrusion Poly(lactic co-glycolic
acid) (PLGA)
20-230 Empirical
Jeong, W., et
al. [20]
In-plane extrusion Acrylic Acid 20-90 Analytical
Choi, C.-H.,
et al. [21]
In-plane extrusion Poly(ethylene glycol)
diacrylate (PEG-DA)
55-75 N/A
Cho, S.,
T.S.,et al.
[22]
In-plane extrusion PEG-DA 70-140 N/A
Dittrich, P.S.,
et al. [23]
In-plane extrusion 1,2-dilauroyl-sn-glycero-
3-phosphocholine
3.5-20 N/A
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Hu, M., et al.
[24]
In-plane extrusion gelatin-
hydroxyphenylpropionic
acid (Gtn-HPA), poly (N-
isopropyl acrylamide)
(PNIPAAM), Alginate
111-227 Analytical
Su, J., et al.
[25]
In-plane extrusion Alginate 1-10 Analytical
Iwasaki, N.,
et al. [26]
In-plane extrusion Alginate,
Alginate/Chitosan
28.6-31.3 N/A
Cheng, Y., et
al. [27]
In-plane extrusion Alginate 40-120 N/A
Sugiura, S.,
et al. [12]
Off-plane
extrusion
Alginate 120 N/A
McAllister,
A. [13]
Off-plane
extrusion
Alginate 600-1600 Analytical
Raof, N.A.,
et al. [28]
Off-plane
extrusion
Alginate 30-300 N/A
Miller, J.S.,
et al. [14]
Molding Agarose, Alginate, Fibrin,
Matrigel, PEG
200-1100 Analytical
Sakai, S., et
al. [16]
Molding Collagen 150-1200 Empirical
Kolesky,
D.B. [17]
Molding GelMA 150-650 Empirical
Yeon, J.H., et
al. [18]
Molding Fibrin, Collagen 50-150 Analytical
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1.2 Solidification of biopolymers There are various means to trigger solidification of polymer solutions, including temperature,
pH, electric or magnetic field, catalyst, photopolymerization, solvent extraction and ionic
concentration gradient [29, 30]. These solidification processes can be reversible or irreversible.
Sol-gel transition of biomaterials is widely used in applications in tissue graft, immobilization of
biological materials and cells, and biosensor production [29, 31-33]. In the scenario of
biopolymer soft material extrusion, the extruded biomaterials should keep their mechanical
strength for a reasonably long period and should be tolerant to external environmental change to
a certain extent. Due to the need of high throughput extrusion, the reaction time for solidification
of biomaterials in extrusion process is limited. Therefore, an irreversible rapid gelation process
will be ideal for soft biomaterial extrusion.
As discussed previous, alginate is the candidate best fit in the context of soft biomaterial
extrusion process. It was used by many research groups as extrusion material for microfibers and
hydrogel tubes [34, 35]. The main advantage of using alginate is its rapid gelation process. The
sol-gel transition of alginate is induced by ionic crosslink. Rapid ion exchange kinetics results in
quick crosslink reaction. Alginates are block copolymers consist of α-L guluronic acid (G) and β-
D-mannuronic acid (M). Homopolymeric regions of M and G blocks, and interspersed regions of
alternating M and G are present in alginate. Gelation of alginates is originated from the affinity
of alginates towards divalent metal ions such as Ca2+. Calcium ions selectively bind G blocks of
two alginate chains. The process is irreversible and almost instant. The rate of gelation reaction
is dominated by relative diffusion rate of calcium ions in alginate solution [36]. Therefore, the
gelation rate can be predicted by modeling the system as diffusion limited reaction system. The
alginate gel properties strongly depend upon the length of G blocks, monomeric composition,
molecular size and concentration of alginate molecules, as well as the concentration of calcium
ions [37]. Moreover, alginates have been proved to be compatible to culture of many cell types.
They have already been widely used in applications in the fields of tissue engineering, cell
immobilization and drug delivery.
Collagen is another ECM biomaterial which is commonly used as 3D tissue culture scaffold. It is
a better material comparing to alginate in terms of mechanical strength and cell adhesion [38].
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Collagen attracts great interest from biomedical engineers for several reasons: i) Collagen is one
of the major structural materials of animal bodies. ii) It produces tissues with a wide range of
mechanical strengths based on its organizational modulation, such as bone, cartilage, tendon,
skin, intervertebral disk and ligament. iii) Load bearing structures made of collagen covers a
huge range of sizes. Blue whale Balaenoptera musculus has the length of 30m while female
Paedocypris micromegethes has the length of 0.008m. iv) Collagen-related diseases largely
impact life quality, for instance, intervertebral disk degeneration.
As discussed before, thermal gelation of collagen can only be used in molding of collagen gel
but not extrusion processes. It is because thermal gelation of collagen is a very slow process
which takes a minimum of 15 minute [8]. In hydrogel extrusion systems, the coaxial flow of
biomaterial solution and crosslinker solution cannot be maintained for such a long period.
In vivo, collagen present in the form of procollagen consisting of a right-handed helical region
which is flanked by two non-helical propeptides. The propopetides take large space around
collagen molecules and keep them apart, hence inhibit self-assembly of collagen molecules [39].
After cleaving the propetides from the tropocollagen using enzymes, spontaneous self-assembly
of highly organized fibers will start [40]. It is believed that some physical factors also exert
significant effect on fibrilogenesis via liquid crystal phasing of collagen [41]. Physicochemical
effect drives collagen fiber formation and molecular crowding plays an important role in this
process. Molecular crowding refers to volume excluded by one soluble molecule to another.
Molecular crowding produces molecule confinement such that the volume occupied by one
molecule sets a fixed boundary to another. In the crowded scenario, molecules with high aspect
ratio such as collagen tend to self-align along the long axial direction. This effect is driven by the
fact that the translational entropy gain from aligning the molecules is greater than the rotational
entropy loss [42]. The free energy of the isotropic state is therefore lower than the anisotropic
state. The system where the collagen molecules are self-assembled is more stable [43].
Molecular crowding condition can significantly accelerate the gelation of collagen therefore
reduce the gelation time. By taking advantage of the effect of molecular crowding, extrusion of
collagen gel can be achieved. Crowded solutions of PEG or hyaluronic acid (HA) can induce
molecule crowding condition to collagen solution. Using PEG or HA solutions as coaxial flow
with collagen solution can potentially shorten the time required for collagen gelation, and makes
collagen gel extrusion possible.
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1.3 Introducing heterogeneity in biomaterials Spatial composition heterogeneities usually present in natural tissues but are hardly achieved by
synthetic methods especially in the context of soft biomaterials. Current tissue engineering
technologies cannot mimic many of the complex organs with heterogeneous composition where
the organ function largely relies on interaction among different cell types. As simple as tissues,
heterogeneous structures also present. For instance, blood vessel is a multilayer tubular structure
where the layers are made of collagen and elastin respectively.
Heterogeneities can be introduced into tubular structures in the axial, radial and circumferential
directions. Axial heterogeneity refers to the compositional change along the length of the tubular
structure. Radial heterogeneity refers to multilayer tubular structure with a material difference
among layers. Circumferential heterogeneity refers to the presence of multiple materials around
the circumference of the cross section perpendicular to the length of the tube. Radial, acial and
circumferential heterogeneities individually has been demonstrated by using both extrusion and
molding methods for tubular structure formation. Incorporating all types of heterogeneities using
a single platform remains as a challenge for producing soft material tubes.
Heterogeneities have been introduced to biomaterials in various methods. The basic techniques
are similar to those producing homogeneous tubular structures discussed before. Extrusion and
molding are the two main methods.
Leng et al. have demonstrated a technique to introduce heterogeneity in biomaterials in a
continuous extrusion process[44]. A microfluidic device was used to incorporate one or multiple
secondary biopolymer solutions into a layer of a base polymer. The spatial arrangement of the
secondary biopolymer retains after leaving the microfluidic device by fast gelation of the base
polymer. Alginate solution was pumped into the microfluidic device by a syringe pump. It
formed hydrogel sheet immediately after exiting from the device and exposing to calcium
chloride solution. After exiting the device, the formed hydrogel sheet was collected by a rotating
drum. The thickness of the hydrogel sheet formed can by controlled by both the infusion rate of
the pump and the speed of the collecting drum. Computer-controlled solenoid valves initiated the
outflow of secondary biopolymers from the on-chip reservoirs. These secondary biopolymers are
loaded on the hydrogel sheet made of a primary biopolymer in the form of spots. The position
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and size of the spots can be controlled by programming the opening sequence and duration of the
solenoid valves. The heterogeneity can be formed along both lateral and axial directions.
Other examples extruding heterogeneity in hydrogel fibers have been demonstrated [22]. The
methods are based upon the stop-flow lithography technique developed by the Doyle group.
Heterogeneous poly(ethylene glycol) diacrylate (PEGDA) fibers were successfully produced
using extrusion method. Mosaic patterned microfibers were produced using a microfluidic
device. The spatial composition of the polymer solutions were controlled by microfluidic
channels prior to photo crosslink of the polymers. Fibers with width of 200µm to 1000µm and
thickness of 70µm to 140µm can be extruded. The size and aspect ratio of the fiber was
controlled by varying the fractional volume of PEGDA solution with respect to carrier liquid
flows. The carrier liquid flows were inert PEG solutions extruded from the device and enclosed
PEGDA solution from top and bottom. This method produced axial and lateral heterogeneities to
extruded fibers but cannot be directly transferred to formation of extrusion of heterogeneous
tubular structures.
An example demonstrated formation of tubular structure with heterogeneity along the radial
direction using molding [45]. Different cells were used to cover the surface of a stretched
Polydimethylsiloxane (PDMS) layer. The stretched layer was then rolled up to form a multilayer
tubular structure with different cells in different layers. The cell layers were not in direct contact
with each other due to the separation form the PDMS layer. The tube diameters can be controlled
between 100µm to 2mm. The predictive control of tube dimensions was based on empirical data.
Control over the tube diameter is based on changing the spinning speed, which determines the
thickness of PDMS layer. The tubes had finite length due to the limitation of the size of casted
PDMS layer. The multi-steps nature of the process limits the throughput of tubular structure
production.
A multilayer tubular structure has been successfully molded using collagen [46]. The
heterogeneity of the tubular structure is along the radial direction. The collagen tubular structures
were molded by using a pipe with a needle in the center. The second layer of tube was produced
by seeding endothelium on the inner wall of the formed collagen tube. The collagen tube
produced had the outer diameter of 830 µm.
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Table 2 summarizes the heterogeneities been introduced to different biomaterials, including the
ones discussed previously and some others.
Table 2. Summary of synthetic heterogeneities in biomaterials
Reference Method Structure Heterogeneity
Onoe, H., et al. [8] In-plane extrusion Fiber Radial
Dittrich, P.S., et al.
[22]
In-plane extrusion Fiber Axial, Lateral
Leng, L., et al. [44] In-plane extrusion Sheet Axial, Lateral
Cheng, Y., et al. [27] In-plane extrusion Tube Radial,
Circumferential
Yuan, B., et al. [45] Molding Tube Radial
Takei, T., et al. [46] Molding Tube Radial
1.4 Stimulus responsive materials As mentioned before, stimulus responsive materials have many valuable applications. One
example of the applications of stimulus responsive materials will be reconstructable surface
which involves formation of stimuli-responsive thin films which macromolecules are grafted
chemically to a surface at sufficiently high grafting density. The responsive behavior of these
thin films originates from the properties of the grafted polymer chains. Poly(N-
isopropylacrylamide) (PNIPAM) thin film that possess a lower critical solution temperature
(LCST) undergo a phase transition in response to temperature [47]. Polyelectrolyte thin films
respond with large conformational changes to pH [48]. Some zwitterionic thin films possess an
upper critical solution temperature changes their wetting behavior with temperature[49]. These
responsive surfaces can be used for biointerfaces and bioseparation. The possibility of switching
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adhesion between stimuli-responsive materials and proteins and cells has been explored for
control of cell and protein adhesion [50, 51].
Other common applications of stimuli-responsive materials are micro- and nano-actuators and
sensors [52]. These applications are based on the swelling and de-swelling, wetting and de-
wetting, or adsorption and desorption of organic suface layers. An example will be use internal
stresses caused by conformational transformations within thin film layers to design temperature
sensitive microcantilevers by grafting PNIPAM [53].
Moreover, stimuli-responsive materials can be used to control catalyzed chemical reaction and
drug delivery. By encapsulate catalyst particles in a thermoresponsive polymer shell, temperature
dependent swelling and shrinking of the shell can alternatively expose and hide the catalyst and
hence control chemical reaction rate [54]. Nanosized capsules could store and protect drugs and
release them inside cells after the capsule has been internalized [55]. Stimuli-responsive carries
of drugs attract a great attention because of its broad opportunities of controlled drug delivery.
Temperature and pH are common triggers of stimulus responsiveness in both nature and
synthetic materials. In the context of stimulus responsive tubular structure, a stimulus responsive
tube can regulate its diameter hence the flow rate through the tube by reacting to the pH or
temperature change of the fluid inside the tube. The working mechanism is similar to blood
vessels which regulate the flow rate of blood by changing their diameters.
Temperature responsive polymers are polymers that exhibit a drastic and discontinuous change
of their physical properties with temperature. PNIPAM is a well-known thermoresponsive
polymer. It has a LCST around 32 ̊C. The response generated by PNIPAM is due to the change
of inter and intra molecular interactions between its pendant groups and water molecules.
PNIPAM exhibits hydrophilic properties due to the hydrogen boding between the pendant group
and water molecules. When the temperature is greater than the LCST, the bonding breaks and the
polymer becomes hydrophobic [56]. The polymer collapses and thus shrinks in volume in
temperature higher than its LCST. It converts the thermal signal into a mechanical signal.
PNIPAM based particles are chosen for secondary biopolymer doping due to its excellent
responsiveness to temperature changes. Its LCST is around 32 ̊C which is in the temperature
range suitable for most biological system. The process of polymerization of PNIPAM particle is
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suitable to copolymerize many additives. Therefore the particles can be functionalized to have
more complicated stimuli-responses.
A pH responsive polymer is a material which will respond to the changes in the pH of the
surrounding medium by varying their dimensions. Many pH responsive polymers have acidic
groups which swell in basic pH [57]. As the pH in the solution increases, acidic groups such as
carboxylic group releases hydrogel ion and ionized to carry a negative charge. As the polymer
possesses many similar charged groups repelling each other, it swells and expands in
dimensions. Polymer of vinyl acetic acid (VAA) is rich in carboxylic group hence possesses pH
responsiveness. VAA group has a relatively low reaction ratio comparing to NIPAM [58].
Therefore, it can form a shell encapsulate PNIPAM when added during the polymerization of
PNIPAM. By functionalize PNIPAM particles with VAA, the resulting particle will become pH
responsive.
Stimuli-responsive materials are often patterned in order to better serve their purposes in varies
systems. For example, stimuli-responsive patterns can control the flow in microchannels as
pumps, valves, or mixers through their volumetric actuation or the change of surface properties
[59]. There are two main categories of stimuli-responsive material patterning techniques. The
first category will be photolithograph[60]. A selective UV light exposure through a photomask is
used for patterning. UV exposure selectively crosslink or cleave polymer. This technique is
usually used for making 2D patterns. For 3D patterning, multiphoton lithography can be
used[61]. This method selectively crosslink or cleave polymer on the focal spot of light.
The second category is the micromolding techniques. Replica molding makes use of thermal
crosslinking of prepolymer filling the cavity of the master mold. UV molding use UV to
crosslink prepolymer filling the cavity of the master mold[62]. Nano-imprinting technique makes
patterns by pressure-induced deformation of polymer above glass transition temperature[63].
Capillary force lithography takes advantage of capillary rise of polymer in the cavity of the
master mold [64].
These techniques can produce micro and nanoscale patterns of stimuli-responsive materials.
However, due to the requirement of photomasks or master molds, these methods can be
expensive especially for small quantity productions. As making photomasks and master molds
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are expensive and time consuming, these methods are not tolerable to frequent design changes.
They are not cost effective for prototyping and laboratory uses which produce small quantity and
are projected to frequent design changes. Moreover, as patterning process is combined with
polymerization process, the flexibility of chemistry and properties of stimuli-responsive
materials are limited due to constricted reaction conditions. The patterning process can be time
consuming because of involvement of polymerization. In my thesis, the one-step formation of
heterogeneous stimulus responsive 3D soft material can effectively reduce time cost of
patterning process.
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2 CONTRIBUTIONS The idea of off-plane extrusion and prototype designs of tube extrusion devices was first
introduced by Arianna McAlister. Arianna designed and fabricated microfluidic devices and also
conducted the initial characterization of devices and formed alginate tubes during her master’s
thesis [13].
The presented work on the one-step formation of homogeneous tubular structure was carried out
in collaboration with Mark Jeronimo, which includes modifications to microfluidic device
designs and fabrication protocol, an analytical model describing tube formation, a thorough
analysis of the operating conditions associated with the successful formation of homogeneous
alginate tubes, and the investigation of different not previously demonstrated morphologies of
homogeneous tubes, in particular, section 6.1, 6.2 and 6.3. Mark Jeronimo’s contribution is also
reflected in Figure 1, Figure 6, Figure 7 and Figure 8.
Lian Leng contributed to the designs of extrusion devices for stimulus responsive sheets shown
in Figure 13 and Figure A4.
For myself, I did the studies on heterogeneous alginate tube formation, collagen tube formation,
stimulus responsive particle synthesis and characterization of stimulus responsive hydrogels, in
particular, section 6.4, 6.5 and 6.6. I lead the research on special morphologies of homogeneous
tube in section 6.3. I also contributed to the collaborative work of microfluidic device designs
and fabrication, analytical model construction and validation, exploring operating parameter
space of tube extrusion system, in particular, section 6.1 and 6.2.
The tube formation and patterning technology demonstrated in this thesis is protected under US
Patent PCT/CA2014/050413.
3 MOTIVATION The routine formation of perfusable soft material tubes and tubular assemblies is a key
requirement for recapitulating organ structure and function in a wide range of tissue engineering
and regenerative medicine applications. Various strategies for the formation of perfusible cell-
laden tubular constructs have been demonstrated. However, the impact of these strategies is still
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limited by a lack of understanding of how heterogeneities provided by cells and their niches
impact remodeling and long-term properties of these engineered tissues. The availability of a
routine technology that allows the formation of heterotypic soft material tubes is required for
such systematic studies. Current approaches for the formation of perfusable tubular soft materials
are generally highly manual in nature, discontinuous, lack scalability, are limited in the range of
tube dimensions possible, cross-linking mechanisms, and mechanical properties produced. In
addition, the spatial heterogeneities commonly associated with the structure and function of
intact tissues and organs cannot be recapitulated achieved in present approaches.
Incorporating stimulus responsive particles into tubular hydrogels will provide additional
flexibility in the control of tube mechanical properties. The present patterning techniques of
stimulus responsive soft materials involve multiple steps which make the process lengthy and
costly. There is no technology available to introduce stimulus responsiveness into soft material
tubular structures in one-step extrusion tube formation process. Stimulus responsive
homogeneous and heterogeneous tubes should lead to new tubular structure assembly techniques
and smart tubes which predictively regulate flow rate and direction.
4 SPECIFIC AIMS
4.1 One-step formation of homogeneous soft material tubes
• Optimize the existing designs of off-plane extrusion devices to improve the yield of
device fabrication.
• Fabricate and characterize microfluidic devices for the formation of homogeneous
hydrogel tubes.
• Demonstrate successful one-step off-plane extrusion of homogeneous alginate tubes and
determine the operating envelope for successful sodium alginate tube formation.
• Develop an analytical model to predict the dimensions of extruded tubes as a function of
flow rates of crosslinker solutions and biopolymers solutions.
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• Measure the wall thickness, inner and outer diameters of formed alginate tube at different
alginate, and inner and outer streaming flow conditions.
• Compare the measured tube dimensions with expected dimensions calculated from the
analytical model.
• Demonstrate the extrusion of collagen I tube using the same system.
• Measure the dimensions of collagen tubes and compare with alginate tubes extruded with
the same conditions.
4.2 One-step formation of heterogeneous soft material tubes and stimulus responsive tubes
• Design, fabricate and test microfluidic devices that promote the formation of
heterogeneous tubes, specifically single layer “Janus” tubes, tubes with axially aligned
stripe patterns, and multilayer tubes with up to three uniform thickness layers.
• Measure the uniformity of the two halves of Janus tubes.
• Measure the thickness and uniformity of the layers in the multilayer tubes.
• Explore the relationship between the stripe width and the driving pressure of secondary
biopolymer solution.
• Measure the dimensions of Janus/multilayer/striped tubes and compare them with
homogeneous tubes extruded in the same conditions.
4.3 Stimulus responsive hydrogel characterization and extrusion
• Synthesize and characterize stimulus responsive nanoparticles which are responsive to
temperature, pH or both.
• Dope nanoparticles into alginate solution to extrude stimulus responsive hydrogel sheets.
• Characterize the formed stimulus responsive hydrogel including its responsive time,
reversibility, volume change and critical temperature/pH.
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• Demonstrate extrusion of stimulus responsive hydrogel tube using the same system as
before.
• Show stimulus responsiveness of extruded hydrogel tubes.
• Extrude heterogeneous (Janus) stimulus responsive hydrogel tube and demonstrate
stimulus induced shape transformation (bending).
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5 MATERIALS AND EXPERIMENTAL
5.1 Microfluidic device designs The feature layers of the multilayered microfluidic devices are arranged such that one or more
biopolymer matrix layers (blue color) are surrounded by layers delivering the crosslinking
solution at the top and bottom. Each layer contains the same key features: the solution, for a
given layer, was distributed evenly from a single inlet such that all channels have the same
resistance. The channels were arranged in a radial configuration around the common outlet hole.
The smallest feature size of 300µm was the width of the microchannels that radially delivered
the fluid streams to the outlet hole located at the center. All the channels in all the fluid layers
shared the same depth of 150µm. All fluid paths in a given layer had the same length and
corresponding widths and therefore identical flow resistance, causing uniform flow distribution
around the circumference of the center outlet. Within each layer there is a 1.2mm diameter pillar
feature was located in the center hole. The post was sacrificed when defining the common outlet
hole and ensured the center outlet did not collapse during device fabrication. The device design
was compliant with outlet diameters between 1.2mm (equivalent to the pillar diameter) and
4.0 mm (equivalent to the surrounded by the radially distributed channels). During device
fabrication, the outlet size should not approach the limits as the process is manually done which
carries human error. The size of the common outlet hole was 3.2mm, unless specified otherwise.
As the diameter of the outlet configuration was larger than the outlet hole, the space between the
outlet and channels allowed the liquids to distribute evenly around the outlet, even if the center
holes were not perfectly aligned. These selected device design and fabrication protocol renders
devices robust, reusable and insensitive with respect to small misalignment between layers. The
maximum tolerance of the misalignment is 800µm (while two layers are misaligned, the
maximum distance between the central points of the two layers which allows punching a 3.2mm
hole without cutting channels). In the older versions of designs made by Arianna McAllister
[13], the maximum outlet size is same as the punched hole size. Therefore, any human error such
as misalignment of layers or tilted punching will result in cutting channels, which leads to
imbalanced flow resistance around the outlet. The biopolymer containing layer only differed
from the layers carrying the inner and outer fluid (crosslinker) stream in the channel length by
2.6mm less. The footprints of different layers ensured that adjacent layers have as little channel
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overlap as possible. Overlap area of adjacent layer (matrix layer and streaming layers) is
23.3mm2.
Figure 1(a-d) show various example designs of microfluidic devices configured for preparing
different tubular structures in terms of geometry, composition and throughput. Inlets are labeled
as follows: streaming fluid inlet (1), matrix solution 1 inlet (2), matrix solution 2 inlet (3). In
Figure 1 b, all the 3 inlet of matrix solution 2 are labeled the same. However, they can be
different matrix solutions. The same conditions apply to matrix solution 1 in Figure 1d. The
solutions for the 3 matrix inlets can be different. The device in Figure 1a may be employed, for
example, for the formation of the tubular structures shown in Figure 7(c, d, e), Figure 8(a, e) and
Figure 10 a. The device in Figure 1b may be employed, for example, for the formation of the
tubular structures with spots and stripes around the circumference, shown in Figure 9(d, e) A2(a-
d). The device in Figure 1c may be employed, for example, for the formation of the tubular
structures shown in which the two halves of the tube wall made of different materials as shown
in Figure 9g. The device shown in Figure 1d was used to form three-layered tubes, for example,
for the formation of the tubular structures shown in Figure 9 (a, b).
Figure 1a shows the design of the basic device design which is used for homogeneous tube
extrusion. This device consists of 3 layers, from top down, inner streaming (Figure 1 a 2nd from
left), matrix (Figure 1 a 3rd from left) and outer streaming (Figure 1 a 4th from left). The inner
streaming and outer streaming layer mentioned below are referring to these layers. All the
devices share the same designs of inner and outer streaming layers.
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Figure 1. Microfluidic device designs. (a) Device design for homogeneous tube formation consisting of (top down): inner streaming layer (green color), matrix layer (blue color) and outer streaming layer (red color). The inner and outer streaming layers mentioned in the later captions are referring to the layers shown here. The inlets of the channels are labeled as (1) streaming
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fluid, (2) matrix solution 1 inlet, and (3) secondary matrix solution. The channels radially feed the solutions from the inlets to the center outlet. (b) Design for formation of heterogeneous tubes with at 3 equidistant locations along the circumference consisting of (top down): matrix solution feeding layer (black color), inner streaming layer, secondary biopolymer layer with 3 locations for insertion along the circumference and outer streaming layer. Secondary biopolymer solutions are fed into the biopolymer layer through the feeding layer at the locations for insertion. (c) Device design for formation of “Janus” tubes, consisting of 3 layers (top down): inner streaming layer, half-half biopolymer layer and outer streaming layer. There are two inlets feed the biopolymer layer from the two sides. (d) Device design for forming three-layered tubular structure consisting of (top down): inner streaming layer, matrix layer 1 in Figure 1a, matrix layer 2, matrix layer 3 and outer streaming layer. The center layer is matrix layer 2. The right layer is matrix layer 3.
Figure 1(b-d) serve the formation of heterogeneous tubes and are modifications to the device
design for the formation of single layer homogeneous tubes (Figure 1a). To avoid repetition,
Figure 1(b-d) only shows the additional layers that are added to the layers already shown in
Figure 1a. In each panel, the first drawing from left side corresponds to the top view of all the
layers stacked. Overlapping channels were not shown in the panels.
A single layer soft material tube accommodating three stripes of a secondary biopolymer was
produced using the configuration shown in Figure 1b. The device shown in Figure 1b is suitable
for forming tubular structures with 3 axially aligned stripes with equidistant spacing along the
tube circumference. The devices consisted of 4 feature layers from top down, formed layers
including a matrix solution feeding layer (Figure 1b 3rd from left), an inner streaming layer, an
additional matrix layer for introducing the secondary biopolymer solution at 3 locations (Figure
1b 2nd from left) and an outer streaming layer. Stripe-pattered tubes were formed by introducing
a secondary biopolymer solution from pressurized wells while supplying the primary biopolymer
at a fixed flow rate.
Figure 1c shows the device design that allows the formation of “Janus” tubes, i.e., a single-layer
tubular structure with a varying composition along its circumference. For example, one half of its
wall is composed of soft material A and the other half is composed of soft material B, with two
corresponding biomaterial inlets for each side. The corresponding microfluidic device may be
employed for forming a heterogeneous tubular structure with different compositions on each half
of the tubular structure and consists of 3 layers: a layer for the distribution of the inner fluid at
the top, the center layer distributing the two matrix streams A and B (Figure 1c 2nd from left),
and an outer fluid layer at the bottom.
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Multi-layered soft material tubes were obtained using the microfluidic device design shown in
Figure 1d. Since the microfluidic device design is modular in the vertical direction, it is possible
to incorporate multiple matrix layers and thereby obtain multi-walled tubular structures by
stacking more matrix layers in between the inner (top layer) and outer streaming layers (bottom
layer). Figure 1d shows the design of a microfluidic device for the formation of tubes with three
co-axial matrix layers. The device consists of the following layers (top down): an inner
streaming layer, a layer for biopolymer solution 1 (Figure 1a 3rd from left), a layer for
biopolymer solution 2 (Figure 1d 2nd from left), a layer for biopolymer solution 3 (Figure 1d 3rd
from left) and an outer streaming layer. The approach could be further extended towards larger
numbers of matrix layers.
5.2 PDMS device fabrication Devices were prepared using multilayer soft lithography. Transparency mask designs shown in
Figure 1 were prepared using a computer aided design program (AutoCAD version 2013,
Autodesk, San Rafael, CA, USA) and photomasks were printed at a resolution of 20,000 DPI
(CAD/ART Services, OR, USA). Masters for replica molding were prepared by rinsing
7.62mm×10.16mm glass substrates (Corning Inc., Corning, NY, USA) with isoproponol,
acetone, and then isoproponol and subsequent dehydration on a hot plate (model HP30A, Torrey
Pines Scientific, San Marcos, CA, USA) at 200ºC for 30 min. Slides were allowed to cool to
65ºC and then oxygen plasma treated for 30 s (model PDC-32G, Harrick Plasma, Ithaca, NY,
USA). A seed layer of SU-8 25 negative photoresist (Microchem, Newton, MA, USA) was spun
at 2000 rpm for 30 s (model SCS G3 spin coater, Specialty Coating Systems, Indianapolis, IN,
USA) and soft baked at 65ºC and 95ºC for a total of 10 min. The seed layer was exposed to UV
light (365 nm) for 13 s (mask aligner model 200, OAI, San Jose, CA, USA), and baked for 6 min
at 95 ºC. Feature heights of 150μm were defined by spinning two 75μm thick layers of a negative
photoresist (SU8 2050, Microchem, Newton, MA, USA) at 1900 RPM for 30 s, and soft baking
in between spins for 5 min at 65 ºC and 15 min at 95 ºC. The substrate was baked for 15 min at
65 ºC, and for 45 min at 95 ºC. The substrate was exposed through the transparency mask with
365 nm UV light at 250 J, hard baked for 20 min at 95 ºC, and developed for 10 min (SU-8
Developer, Microchem, Newton, MA, USA). The masters were rinsed with isoproponol, dried
under N2, and baked for 15 min at 80 ºC. Separate masters with the same feature layer depth
were prepared using the outlined fabrication sequence. The masters were degassed in -25 mmHg
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at room temperature for 1 hour.
To obtain reliably bonded multilayer devices, a multilayer partial curing and bonding technique
was adopted from previously established protocols [65] in combination with fully cured PDMS
layers. Pre-polymer and curing agent were mixed in a ratio of 10:1, spun onto masters at 400 rpm
for 30 s, resulting in a 200 μm thick PDMS layer. All layers except for the top layer were
prepared as described. During the preparation of the top layer, an approximately 5mm thick layer
of uncured PDMS was poured onto the master, and the layer was fully baked at 80ºC for 20 min.
The second layer was baked at 80ºC for approximately 9 min. When partially cured, the thicker
top layer was aligned over the sticky second layer and air bubbles were carefully removed. The
combined layers were baked for 18 min to ensure a strong bond. The sequence was successively
repeated until all layers were attached to each other. After bonding, inlet holes were punched for
all layers and both top. The bottom was sealed with partially cured PDMS sheets with no
features. The center outlet hole was then punched and sealed the top end.
5.3 Homogeneous tube extrusion Alginate sodium salts (Sigma Aldrich), 0.1 µm carboxylate-modified microsphere (FluoSphere,
Life Technology, ON, Canada), glycerol (Bioshop Canada, ON, Canada) and calcium chloride
(Bioshop Canada, ON, Canada) were used as received. The matrix solution was prepared by
dissolving 1 g of alginate in 30 mL of distilled water. 20 mL of glycerol was then added to the
mixture. The mixture was stirred for 10 min and then sonicated for 60 min. The streaming
solution was prepared by mixing 600mL of distilled water and 400mL of glycerol. 11.1g of
calcium chloride was then added. The concentration of Ca2+ in the streaming fluid is 100mmol. 1
L of reservoir solution was mixed with 254 mL of glycerol and 746 mL of water. The streaming
solution was prepared by mixing 20 mL of glycerol with 30 mL of water. The resulting density
of both the matrix solution and the streaming fluid was 1.12g/mL. The density of reservoir
solution was 1.08g/mL. The streaming fluid was fed to the microfluidic device by a syringe
pump (model Nemesys, Centoni, Korbussen, Germany). The inner and outer streaming fluids
were controlled independently. The matrix solution was fed by a second syringe pump (model
PHD 22/2000, Harvard Apparatus, Holliston, MA, USA). The reservoir was made of
polycarbonate sheets (thickness 1mm) and was 12cm tall, 20cm long and 15cm wide. The device
was placed horizontally within the reservoir at a distance 10 cm from the bottom. The
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confinement was 2.8cm long and was made of Tygon tubing. Figure 2 illustrates the schematic
of the experimental setup of homogeneous tube extrusion.
Figure 2. Experimental setup of homogeneous tube extrusion. The biopolymer solution (blue), inner (green) and outer (red) streaming fluids are stored in glass syringes and are driven by syringe pumps into the microfluidic device. The microfluidic device guided the solutions so they flow out from the device at the center outlet facing downwards. The solutions and extruded tube are then released into a reservoir filled up by streaming solution.
5.4 Multilayer tube extrusion Streaming and reservoir solutions were made the same way as homogeneous tube extrusion
experiment. 2%wt Alginate solutions were made the same way as before but with different 0.1
µm carboxylate-modified microspheres in solutions for the different tube layers. Alginate
solutions with different fluorescence were driven by syringe pumps with synchronized infusion
rate.
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5.5 Janus tube extrusion Streaming and reservoir solutions were made the same way as homogeneous tube extrusion
experiment. 2%wt Alginate solutions were made the same way as before but with different 0.1
µm carboxylate-modified microspheres in solutions for the two halves of the tube. Alginate
solutions with different fluorescence were driven by syringe pumps with synchronized infusion
rate.
5.6 Preparation of stripe-patterned hydrogel tubes The setup of spotted/striped tube extrusion is similar to homogeneous tubes that the inner/outer
streaming fluids and matrix feeding to the microfluidic device is the same. As the matrix layer
has additional inlets for spotting/striping materials, on-chip wells are molded on the top of the
device to contain the spotting/striping fluids. The fluids in wells can be different. A schematic
drawing of this setup is shown in Figure 3. The matrix layer of the device shown in Figure 1b
was modified such that 3 channels for the insertion of a secondary biopolymer solution were
inserted between the radially oriented channels delivering the primary biopolymer solution
equidistantly around the circumference of the center outlet. A second matrix layer served to feed
the secondary biopolymer solution and was added to the top of the device. The solutions up to
1.5mL are stored within wells that were directly attached to the top layer of the device. When
pressurized, the fluids in the well will enter the device and form spots/stripes on the extruded
tubes. The pressures in the wells are controlled independently by a magnetic valves array. The
magnetic valves array in connected to a gas pressure regulator which regulates the pressure goes
in to the valves. Head pressures varied between atmospheric pressure and a pressure level above
atmospheric pressure. When the valve is open, the pressure in the corresponding well is elevated
to the level of the gas pressure regulator output. When the valve is closed, the pressure in the
well drops to atmosphere level. The upper pressure level was adjusted with a 0-15psi digital
pressure regulator (model 3410, Marsh Bellofram, Newell, WV, USA) that was connected to
compressed house air at its inlet to individual solenoid valves hosted in a manifold (The Lee
Company, Westbrook, CT, USA) at its outlet. The solenoid valves were electronically addressed
by a and a control circuit shown in Figure 4 and a custom software program shown in Figure 5
(Labview, National Instruments, Austin, TX, USA). By activating a solenoid valve, the pressure
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in the particular well increased from atmospheric pressure to a pressure level above atmospheric
pressure the secondary biopolymer to enter from the well into the microfluidic device.
Figure 3. Experimental setup of spotted/striped tube extrusion. The primary biopolymer solution (blue), inner (green) and outer (red) streaming solutions are driven by syringe pumps into the microfluidic device. The secondary spotting/striping biopolymer solution (pink) is stored in on-chip wells. It is driven by a head pressure Ph. The pressure can be switched on/off by an array of magnetic valves where each valve controls one well.
5.7 Collagen tube extrusion Collagen I (Rat Tail, BD Science, Mississauga, ON, Canada), sodium chloride (Bioshop Canada,
ON, Canada) and PEG (Mn 35,000, Sigma Aldrich) were used as received. 100g of PEG powder
was added to 900mL of deionized (DI) water. 20g of sodium chloride was then added to the
solution. The end product is 1L of 10%wt PEG and 2%wt NaCl solution. This solution was then
used to fill up the reservoir and was used as streaming solutions. Collagen solution was used as
the biopolymer matrix solution and was infused using a syringe pump. The inner and outer
streaming fluids were controlled independently by another syringe pump. The Tygon tubing
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confinement was 18.0cm long. Collagen tubes were extruded into the reservoir and were allowed
to stay in the reservoir solution for 15min. They were then transferred to petri dish and left in
room temperature for a day for complete gelation.
5.8 Valve control board design The schematic diagram of the circuit design is shown in Figure 4a. The board layout is shown in
Figure 4b. The layout was transfer printed on to a PCB board. There are several jumpers needed
on the top of the board which is shown in Figure 4c. Two SN754410 H-bridge (Texas
Instruments) and one 74HCT04 hex inverter (NXP Semiconductors) were used to construct the
circuit. The board is powered by an external power supply of +9V. The power supply can be
switched on/off by a power switch signal which give +5V or 0V. The circuit is designed to
control up to 4 valves. There are 4 signal pins on the board that connect to a digital signal source
(0V and +5V). The digital source USB6008 (National Instrument, TX, USA) is controlled by
Labview. Each digital ping controls one valve. The circuit convert digital signal to voltage
supply to the magnetic valves. The valves are opened by +9V and are closed by -9V. The boards
reserved pins sharing power supply, power switch signal and ground between boards, so they can
be stacked to control more valves (e.g. stacking 2 boards will control 8 valves).
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Figure 4. Valve control circuit. (a) Schematic drawing of valves control circuit board. This board uses motor controllers to supply and invert the voltage to magnetic valves. SWITCH: connection to external analog input for H bridge power control. VALVEIN: voltage supply to valves. VALVEOUT: inverted voltage supply to valves. HBRIDGE: H bridge unit. INVERTER: hex inverter. SIG: connection to external digital signal which controls the valves. GND: ground. 5V: connection to external 5V power source. 12V: connection to external 12V power source. (b) PCB board blueprint of the valves control circuit board. This layout is transfer printed on the back of the circuit board. The printed wires connect the pins of the electronic components on the board. Red: wire transfer printed wire. Green: through holes on board. (c) Top view of valve control board. The wires are the jumpers used to complement connects of the printed circuit on the back of the board. Inlet for power supply and electronic components are mounted on the top of the board.
5.9 Labview control programs A Labview program was written to control the magnetic valves. Signals are sent to control board
in batches. Each batch of signals defines a status of all the valves. All the valves are switched
from one status to another when the next batch of signals is sent. The number of status and
number of valves been controlled are determined in the Step 1 of the program. The statuses of
the valves can be defined on the interface or import from a record file which is in the Step 2 of
the program. The status can be manually input in Step 3. The time frame of each status can be
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defined in this step too. Upon complete the 3 steps, the program can be launched to execute
predetermined patterns. During the execution, the signal pattern, the duration of each status and
number of repetitions of the pattern can be modified. The opening/closing durations of the valves
determines the amount of fluids goes into the spotting/striping channels and the distance between
adjacent spots/stripes. The pattern of the valve activities can be defined so the valves repeat the
pattern and produce repeating pattern on the tube. The program is designed in the way that the
variables are defined by the user in an order. Variables are disabled until the user defines the pre-
requisite variable for them. To prevent overheating of the magnetic valves, power is only
supplied to a valve when the status of the valve needs to be changed. The program can
automatically detect a change of status. At all time, the program can be stopped by pressing the
‘stop all’ button on top. All the valves will be closed and the circuit board will be disabled. The
interface of the program is shown in Figure 5a.
Another Labview program is made to control the gas pressure output of the gas pressure
regulator. The program converts gas pressure into analog signal which is sent to the pressure
regulator via control unit USB6008. The target pressure can be input in the program and can be
changed in situ. At the same time, the pressure in the regulator can be monitored. The interface
of this program is shown in Figure 5b.
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Figure 5. Labview control programs. (a) Labview interface for magnetic valves control. There are 3 preparation steps which defines the pattern of the output digital array. The program can be stopped at any time by pressing the ‘stop all’ button during operation. (b) Labview interface for gas pressure control. The output pressure of pressure regulator can be defined by set a target in the program. The chart tracks the output pressure at real time.
5.10 Tube dimension measurements 3 segments of tube of 1mm length were cut from random positions on an extruded tube. The 3
segments were transferred to Nikon A1 confocal microscope (Nikon, Japan) for imaging. All the
confocal images of tube cross sections were processed using ImageJ software. For each image,
the cross sectional area enclosed by the inner tube wall was selected. The perimeter of this area
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was measured. The inner diameter of a tube DI was calculated based on the perimeter value. The
outer diameter DO of a tube was calculated based on the perimeter of the area enclosed by the
outer tube wall. The wall thickness was calculated as (DI – DO)/2. The experiment was repeated
using tubes extruded from 3 different devices for each extrusion condition (inner/outer streaming
flow rates and biopolymer matrix solution flow rate). Total of 9 measurements were obtained for
each extrusion condition. The plotted results were the average value of the 9 measurements and
the error bars represents the standard deviation. There was error associated with manually cutting
of the tube cross sections. Cuttings may not be perfectly perpendicular to tube axial direction
therefore the tube will not stand perfectly vertical while confocal image is taking. This error is
reflected in error bars of plots and cannot be isolated or eliminated.
5.11 Polymer synthesis and hydrogel solution preparation Poly(N-isopropylacrylamide-co-vinylacetic acid) (PNIPAM-VAA) particles were synthesized by
precipitation polymerization. Ammonium persulfate (APS), N,N-methylene bisacrylamide
(MBA), sodium dodecyl sulfate (SDS) and vinyl acetic acid (VAA) were used as received
(Sigma Aldrich). NIPAM (Sigma Aldrich) was recrystalized to remove inhibitors. According to
the recipe in Table 1, NIPAM, MBA, SDS and VAA were dissolved in 150 mL of water in a
three-necked flask which was fitted with a condenser and a magnetic stirrer. The solution was
heated to 70 ºC under a nitrogen atmosphere. APS was dissolved in 10 mL water and injected to
the solution after 30 min. Polymerization was carried out for 6 hours while stirring at 250 rpm.
The solution was cooled and collected for ultracentrifugation during 45 min at 120000g. The
condensed particle solution was mixed with 1.5% wt alginate salt and sonicated (Branson 5510,
Branson, Danbury, CT, USA) for 60 min. Bubbles produced during mixing were removed by
centrifuging the solution at 3500 rpm for 15 min. The solution was further condensed by heating
to 50 ºC for 2 hours and removing water of 50% of the total volume. The resulting solution was
stirred for 10 min and sonicated for 1 hour.
5.12 Stimulus responsive material characterization The polymer solutions used for particle size characterization were collected after polymerization
and before centrifugation. The solutions were diluted for 16x before doing measurements. In the
case where Ca2+ ions were present, calcium chloride was added to the diluted solution so the
Ca2+ concentration was 100mmol. The pH of the diluted solution was controlled by titrating
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hydrochloric acid (Bioshop Canada, ON, Canada) and soldium hydroxide (Bioshop Canada, ON,
Canada). Polydispersity indexes (PDI) and hydrodynamic diameters of particles were obtained
by dynamic light scattering using Zetasizer Nano (Malvern Instruments). Stimulus responsive
sheets were used for some of the characterizations of the material. They were extruded using in-
plane extrusion method via a PDMS device. The flow rates of hydrogel solution were controlled
by a syringe pump. The extruded sheet was collected using a rotating drum. The linear speed of
the drum is controlled by computer. The shape changes of the sheets/tubes were recorded as
videos by a camera above the container of the sheets. Images were cropped from the videos for
measurements of length and curvature change of the sheets/tubes using ImageJ.
5.13 SEM imaging of tubular soft material constructs Scanning electron microscope (SEM) samples were prepared by fixing the hydrogel samples in
2% glutaraldehyde in a 0.05M sodium cacodylate buffer at pH 7.4 for 1hr at room temperature,
followed by the incremental substitution of the liquid phase with 100% ethanol. Dehydration of
the samples was achieved with liquid carbon dioxide (CO2) at 10°C in a critical point dryer.
Samples were then sputtered with gold. Samples were subsequently heated to 31°C while
increasing the pressure to 7.2MPa, transitioning the CO2 to supercritical fluid conditions. An
environmental SEM (20000X, FEI XL30 ESEM, FEI, Hillsboro, OR, USA) was used to take the
images at low vacuum mode in order to avoid charge accumulation on the sample surface.
5.14 Environmental temperature and pH control of stimulus responsive hydrogels
Temperature and pH control of the hydrogel tubes and sheets were achieved by switching water
baths, and complete stimuli-responsive shape changes were observed after maintaining a
constant environment for 15 minutes. In the case where the responsive times of the hydrogel
tubes/sheets were measured, water with different temperature and pH were flowed on the
stimulus responsive sheets. The sheet was fixed at one end in a plastic half tube. The direction of
the sheet is the same as the half tube. Water with different temperature and pH were flowed
along the direction of the sheet from the fixed end.
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6 RESULTS AND DISCUSSION 6.1 One-step formation of homogeneous soft material tube
The presented method for extruding single-layer homogeneous tubes uses a three-layer
microfluidic device, as shown in Figure 6. Figure 6a illustrates the continuous formation of a soft
tubular material in the device-normal direction (off-plane extrusion).
Biopolymer solution, inner streaming fluid and outer streaming fluid enter the microfluidic
device at well-defined flow rates and are distributed to separate device layers. Within each
device layer, the solutions are first circumferentially distributed around the common central
outlet and then radially directed to the outlet through an array of uniformly long and wide
microchannels. The three miscible fluid streams form sheath flows that meet at the 3.2mm
diameter common central outlet where the sheaths are redirected in the device-normal direction
to form concentric fluid layers that enter a confinement tube. The inner fluid stream occupies the
center region the outer fluid stream occupies the region close to the wall of the confinement tube
and the matrix fluid is confined in between. The inner diameter of the confinement tube was
identical to the diameter of the common outlet. The biopolymer occupying the coaxial matrix
layer polymerized upon contact with the inner and outer fluids, producing a continuously flowing
soft material tube.
The confining tube (Tygon, inner diameter 3.175mm, length LC=28mm, unless otherwise
specified) retains the co-axial organization of the three fluid layers while polymerization takes
place and the flowing soft material solidifies. In cases where the gelation is rapid enough, the
confinement is not necessary for successful tube formation. However it significantly extends the
operational envelope available for successful tube formation and also improves the uniformity
and predictability of tube diameters and thicknesses. The high degree of predictability is a
prerequisite for the consistent formation of tubular structures with increased geometrical
complexity. Examples are heterotypic tubes with tailored heterogeneities that predictably affect
the physicochemical properties of the produced tubes. In the case that the density of tube is
higher than the reservoir fluid, the required minimum flow rates and the minimum total flow rate
are calculated that prevent the unwanted effect of a backflow from the reservoir into the outer
fluid layer of the confinement tube. The as-produced tube exits into a reservoir that is filled with
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a cross-linker and has a density that is lower than the three fluids. The diameter of the confining
tube may be altered with the inner diameter of the common outflow hole of the microfluidic
device in order to expand the range of diameters of the formed tubes.
Figure 6b shows an example illustrating the microchannel network of a microfluidic device used
for the formation of a single layer homogeneous soft material tube. As shown in Figure 6c, the
illustrated microfluidic device consists of three feature layers: an inner streaming layer (top,
green color), an intermediate matrix layer (middle, blue color), and an outer streaming layer
(bottom, red color). Devices used for the formation of heterogeneous tubes may include
additional matrix layers. The device was fabricated using the previously discussed fabrication
sequence. The microchannel network on each layer contains the same key features: the solution
is distributed from a single inlet, circumferentially distributed around the common through a
hierarchical microchannel network with uniform flow resistance. The device architecture makes
it easy to stack additional layers during device fabrication, e.g., for creating heterogeneous
tubular constructs. For example, stacking n matrix layers in between the crosslinking layers
permits the formation of n-layered tubes with a different compatible material for each layer.
Small changes to the matrix layer design allow to introduce heterogeneities within a single layer,
e.g. to define axially aligned stripes. In addition to altering the inner, matrix and outer flow rates,
the range of addressable tube diameters can be further expanded by modifying the size of the
common exit hole and inner diameter of the confinement tube.
Figure 6d shows a photograph of the top view of a fabricated device where the fluids in the
respective channels are labeled with food color. Figure 6e shows a bright field image of the
proximity of the common outlet hole. Figure 6f shows a side view of a microfluidic device with
attached confinement while a soft material tube exits. Figure 6g shows the experimental setup.
Fluid streams may be supplied using three syringe pumps at the well-defined flow rates QI, QM,
and QO. Alternatively, the matrix solution may be supplied from on-chip wells, by controlling
the well head pressure. The produced soft material tube is collected within a liquid-filled
reservoir. The image in Figure 6d is taken from camera 1 and the image in Figure 6e is taken
from camera 2.
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Figure 6. Device design and experimental setup. (a) Schematic illustration of soft material tube formation using a multilayer microfluidic device at the extrusion hole during biopolymer through a confinement tube of length Lc. The biopolymer solution (blue), inner (green) and outer (red) streaming solution meet at the extrusion outlet at the center of the device, and change direction to flow perpendicularly downwards. (b) Top-view of microchannel network of three-layer microfluidic device consisting of inner fluid (top, green color), biopolymer (center, blue
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color) and outer fluid (bottom, red color). Scale bar: 10 mm. Inset: close-up view of region in proximity of common outlet. The bottom layer (red) overlaps with top layer (green) and cannot be seen from top. Scale bar: 2 mm (c) Exploded view of three feature layers and attached confinement. The PDMS layers are bonded to form the extrusion microfluidic device. Scale bar: 15 mm. (d) Photograph of fabricated device with dye-filled channels. Scale bar: 10 mm. (e) Bright-field photograph of resistance channels at extrusion outlet taken with top camera. The resistance channels evenly distribute the solutions around the outlet. Scale bar 1 mm. (f) Photograph taken with side view camera demonstrating continuous tube extrusion through 3.175 mm diameter confining tube, Lc=2.8 cm. The extruded tube is moving downwards into the reservoir. Scale bar: 2 mm. (g) Experimental set-up including fluidic control, the microfluidic device, confinement at extrusion outlet, a liquid filled reservoir and cameras for optical access during extrusion. Camera 1 is responsive for the image in Figure 6e. Camera 2 took the photo for Figure 6f. Scale bar 38.1 mm.
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6.2 Predictive control of tube dimensions In my thesis project, alginate was selected to demonstrate many of the utilities of the tube
extrusion system developed. It is because ionic crosslinking of alginate is a quick process which
fits well in extrusion systems. Many groups discussed above have demonstrated high throughput
extrusion of alginate tubes.
The microfluidic device used by Takeuchi’s group, Kawakami’s group and Ozbolat’s group was
designed to perform in plane extrusion such that the fluid flow inside the device was in plane
with the formed microfiber/tube [8, 10, 11]. In general in-plane extrusion of biopolymer tubes
does not provide a predictive control over the structure dimensions produced. It limits the
scalability of the biomaterial tube extrusion systems. Previous models developed for tube
extrusion in coaxial flows did not account for the fact that the tube wall solidifies during the
process [9, 13]. The increase in viscosity during the extrusion process was not described in the
models. As the inner and outer walls of the tubular structure solidify first, they tend to act as
moving walls instead of fluids. Another model is developed in this thesis which account for tube
wall solidification during the extrusion process.
The flow rates QI, QS, and QO were varied in the experiments to produce alginate tubes with
different diameters in this section. Gelation of the biopolymer solution was initiated upon contact
with the streaming fluids, i.e., at both the inner and outer tube surfaces and then further
progresses to the center of the tube wall. We divide the formation of the soft material tube into
two stages. In the initial first stage, the biopolymer solution remained in a liquid state and the
relative volumes occupied by the three fluid streams that passed through the confinement were
governed by their relative flow rates. In the second stage, after gelation was initiated at the inner
and outer tube surface, we assume a moving tube with template fluid (i.e. inner streaming
solution) at the inside and streaming at the outside.
Figure 7a shows the radial variation of the velocity profile for the 3 fluids passing through the
confinement. In the flow profile, the wall of tube is presented as blue rectangle. The center of
tube is represented as 0 on x-axis. The inner wall of confinement is located at 1 on x-axis. The
top profile shows the status where crosslinking just start when solutions meet. The light blue
region represents biopolymer solution in liquid state. The dark blue region represents the gelled
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biopolymer. The bottom profile shows the status where the tube wall is completely crosslinked.
The crosslinker solutions are assumed to be Newtonian fluids, resulting in a parabolic velocity
profile for the outer fluid layer between the hydrogel tube wall and the inner wall surface. In the
model, the moving tube can be treated as a sheath of fluid with infinitely thin thickness since
there is no relative velocity between the two sides of the tube walls. The velocity and
acceleration of the fluids at the two sides of the wall has to be continuous. As the inner streaming
fluid is completely isolated from the outer streaming fluid, the outer streaming fluid shall feel no
shear from the inner streaming. Therefore, the tube wall can be treated as the central line of fluid
moving in a circular pipe, the fluid here refers to outer streaming which should has a parabolic
flow profile. The tube wall’s velocity equals to the maximum velocity in the outer streaming
fluid. As the gradient of velocity change at maximum velocity is 0. The shear at the outside
surface of the tube wall is 0. As mention before that the inside and outside surface of the tube
wall has continuous velocity and acceleration, the gradient of velocity at the inside surface of the
tube wall is 0, so is the shear. As there is no shear around the inner streaming fluid, the inner
streaming fluid has a flat velocity profile.
The above assumptions can be validated from a view of force balance on the tube wall, while the
wall is not supported, the net force on tube wall has to be 0 (otherwise it will
accelerate/decelerate till its velocity is equal to Vm), where Vm is the radially constant fluid
velocity of the matrix stream. For the net force to be zero, either the two shears on the two side
of wall is opposite (means inner flow is flowing backwards, which is not true because it is driven
by syringe pump with positive infusion rate), or both shears are 0. So dV/dr at wall is 0 (no shear
on both sides of tube wall). V is the velocity of the tube wall.
By substituting the following boundary conditions in to Navier-Stokes equations, for r = 0, V(r)=
Vm, dVi(r)/dr = 0; for r = ri, V(r) = Vm, dV(r)/dr = 0; for r = ro, V(r) = Vm, dV(r)/dr = 0; for r = rc,
V(r)= 0. r is the radial coordination along the tube radius. V is the velocity of inner streaming
fluid at r. ri is the radius of the inner tube wall. rC is the inner radius of the confinement tube , rO
is the other radius of the formed tube.
The flow rate of the outer fluid can be expressed as
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(1)
(2)
For the flow rate of the inner stream follows
. (3)
The matrix flow rate follows as
. (4)
Figure 7b shows the parameter space available for successful tube formation for the case of ionic
cross linking of an alginate solution at a fixed flow rate of the biopolymer solution of
QM=200µL/min, while QI and QO were varied over 3 orders of magnitude. Successful tube
formation was observed over a wide range of parameters, indicating the robustness of the
platform. The outer streaming fluid flow rate has the range of 0 to 3500µL/min. We were able to
successfully form tubular structures in the absence of the outer streaming fluid. The inner
streaming fluid flow rate has the range of 20 to 3500µL/min.
By varying the flow rates, we controllably altered the tube diameter and wall thickness. We
selected a series of flow rate combinations to compare our experimental results with the
predictions from the analytical model, i.e solving for VM, ro and ri by selecting QI, QM and QO
using equation 2-4. The total flow rate of the biopolymer solution and the cross-linking solutions,
QI+QM+QO, was kept constant at 1500 µL/min while the flow rate of the biopolymer solution
remained at QM=200µL/min. We were able to produce a tube with varying diameters and wall
thicknesses along the length when varying QI and QO (Figure 7c-e). We found DI and DO
increase, wall thickness δ decrease with increasing ratio of QO/QI. The outer diameter DO varied
between 0.7 mm and 2.5 mm and δ varied between 70µm and 420µm. As shown in Figure 7f,
model predictions agreed favorably with the experimental data at most conditions except for the
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upper and lower end of considered QO/QI ratios. At high QO/QI ratios, the rapid onset of gelation
that occurred even before entering the confinement tube defined the length of the inner
circumference of the inner tube wall. The further decrease in cross sectional area occupied by
inner fluid within the confinement tube caused buckling of the already cross-linked inner wall.
Consequently, the measured mean tube wall thickness values exceeded the ones predicted by the
model. At low QO/QI ratios, the rapid gelation occurring at the outer surface of the tube wall
limited the outer diameter of the tube. Measured tube diameters were therefore smaller than the
model predictions. In order to include errors generated from device to device variance, 3 devices
were used for each extrusion condition. 3 measurements of tube dimensions at each extrusion
condition for each device were taken to eliminate anomalous measurements.
In order to support the assumption we made in our model that the inner stream acted as a
template and does not apply a stress on the inner tube wall, an experiment was conducted in
which the inner fluid contained no crosslinker. As shown in Figure 7g we found the resulting
tube dimensions to still agree with our model predictions suggesting that the inner fluid acts as a
template occupying the tube center and travels at the velocity of the tube wall. As indicated by
reconstructed confocal scans we found the tube inner wall to irregularly deform and the
operating envelope to decrease in size, if no cross linker was added to the inner fluid. For
example, at QI > 1000 µL/min successful tube formation was only possible if a cross-linker was
present in the inner fluid stream. Only one device was used for this experiment so the error
generated from device to device variance is not presented here. 3 measurements of each
extrusion conditions were taken.
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Figure 7. Dimension control of homogeneous tubes. (a) Left: Cross-sectional view of example device at outlet hole with flow rates QI, QM and QO forming soft material tube of outer diameter DO and inner diameter DI. Tubular structure flows with velocity V in direction of tube axis, x, through confinement conduit of diameter DC and length LC. Polymerization is completed at distance L. Right: Model prediction of velocity profile at device outlet prior to confinement. (b) Operating window for QI (100mmol CaCl2 solution, applies to all inner streaming solutions in this figure) and QO (100mmol CaCl2 solution, applies to all outer streaming solutions in this figure) at QM=200µL/min (2% alginate solution, applies to all biopolymer solutions in this figure) using device in Figure 2a with conditions of successful ( ) and unsuccessful tube
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formation ( ). The red line indicate the boundary between successful and unsuccessful extrusion conditions, n=1. Confocal images of homogeneous alginate tube cross sections extruded with (c) DO=1612µm and wall thickness δ=132µm, for QI=500µL/min, QM=200µL/min and Qo=800µL/min. with (d) DO=1901µm and δ=148µm for QI=650µL/min, QM=200µL/min and Qo=650µL/min. and with (e) DO=2240µm and δ=70µm, for QI=1200µL/min, QM=200µL/min and Qo=100µL/min. (scale bars (c-e) 500 µm) (f) Measured DO ( ) and corresponding model prediction (upper solid line), DI ( ) and corresponding model prediction (middle solid line) and δ ( ) along with corresponding model prediction (lower solid line) at QM = 200µL/min. The predicted results were produced by solving equation 2-4 using Vm, ri and ro as unknown variables. The experimental data points are averaged from 9 measurements. 3 cross sections were randomly chosen from a meter-long tube extruded from a microfluidic device. 3 devices hence 9 cross sections were used for measurements, n=9. (g) Measured tube dimensions as function of flow rates in absence of cross-linker in inner fluid stream at QI = 200µL/min. Measured DO with ( ) and without cross-linker added to the inner fluid ( ), DI with ( ) and without cross linker added to inner fluid ( ), δ with ( ) and without cross linker added to inner fluid ( ) for QI= 200µL/min, n=3 (3 cross sections randomly picked from extruded tubes from the same device). Data points and error bars are mean values and standard deviation of the n measurements for f and g.
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6.3 Soft material tubes of non-circular cross section The morphology of the tube inner wall may deviate from the cylindrical shape with a uniform
curvature radius, DI/2 that we have considered so far. By lowering the ratio QI/Qo to lower than
1/12, we obtained tubular constructs with a buckling inner wall and a uniform diameter
cylindrical outer wall (Figure 8a). The experimental setup remained unchanged and the device
shown in Figure 1a was used. The flow rates were separately controlled using syringe pumps.
Since locations where the inner streaming and the biopolymer matrix solutions were the least
proximal to the confinement tube, cross-linking at the inner tube already started prior to entering
the confinement. Low values of QI therefore lead to a small DI and induced buckling at the inner
wall. Cross-linking at the outer wall surface occurred while the tubular construct had already
entered the confinement. We directly compared the two cases with identical flow rates and no
cross-linked present in the inner stream. In this case, cross-linking at the inner tube wall was not
initiated prior from entering the confinement but only at a further downstream position at which
the crosslinker had diffused through the tube wall from outside. Figure A1a in appendices shows
the resulting tube that shares comparable inner and outer diameter with the tube in Figure 8a but
the inner tube wall is not folded. The inner diameter may be calculated as the hydraulic diameter
(5)
where A is the inner cross sectional area of the tube. Alternatively the calculation may be based
upon the inner perimeter of the tube inner wall
(6)
where S is the perimeter of the tube inner wall. The ratio Di,2/Di,1 is indicative of the degree of
buckling observed at the inner wall surface. Large values of Di,2/Di,1 imply a larger degree of
buckling and values equal to unity correspond to a perfectly circular inner surface. Figure 8b
suggests that with increasing QI the degree of buckling decreases.
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Tubular structures with buckled outer and inner wall surfaces (Figure 8c) can be produce by
using a confinement channel with a diameter DC = 1.59mm which is smaller than the device
central outlet (2.0mm diameter) positioned at the exit of device in Figure 1a. The flow rates were
adjusted to adapt the change of the confinement diameter. The narrower confinement resulted in
forming a tubular construct at reduced diameters and increased velocity. The diameter reduction
induced buckling in both the inner and outer wall surfaces, prior to cross-linking was complete.
The buckled tube shape was therefore retained. We used the ratio Do,1/Do,2 to quantify buckling
behavior in Figure 8d. Do,1 is the hydraulic outer diameter and Do,2 is the outer diameter
calculated based on outer tube wall perimeter. While pressurized, the tube wall will unfold
before it is stretched. The tube can be pressurized and expand without inducing strain in the tube
wall for a diameter change of up to 20%, since Do,2 is 20% larger than Do,1.
A corkscrew shaped inner wall (Figure 8e) was obtained by increasing Qi above 2500µL/min
while reducing Qo below 100µL/min, using the device shown in Figure 1a. The wavelength of
the corkscrew shape inner wall was found to decrease with increasing inner stream flow rate as
shown in Figure 8f. We attribute this shape to a similar reason as in the case of the folded inner
tube wall. As the inner tube wall formed within the device and fixed the perimeter and cross
sectional area of the inner surface before the tube entering the confinement, the only way to
accommodate the large volume of inner streaming entering the luminal side of the tube was to
increase the length of the inner tube wall. In other words, volume of inner streaming fluid equals
to the product of inner cross sectional area and length of inner tube wall. As the cross sectional
area is fixed, an increase in volume resulted in an increase in inner tube wall length. With the
limited length of tube formed, a corkscrew shape inner wall was formed to adapt the increase in
length of the inner tube wall. It also explains the effect that increasing the inner stream flow rate
lowers the wavelength of the corkscrew shape inner wall (increase inner wall length). With
higher volume of the inner streaming enters the tube, the wavelength of the corkscrew shape has
to decrease to fit more waves in a given length of tube.
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Figure 8. Homogenous tube morphologies. (a) Confocal reconstruction of cross section of tube with circumferential buckling of inner wall obtained at: QI=100µL/min (100mmol CaCl2 solution, applies to all inner streaming solutions in this figure), QM=200µL/min (2% sodium alginate, applies to all biopolymer solutions in this figure) and QO=1200µL/min (100mmol CaCl2 solution, applies to all outer streaming solutions in this figure). The tube has dimensions of: DO=1361µm, Di=484µm and δ=438µm. The inner diameter of the tube is calculated based on the cross sectional area enclosed by the inner tube wall. (scale bar 500 µm). (b) Ratio Di,1/Di,2 as
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function of inner streaming flow rate for QM=200µL/min and QTotal=1500µL/min, n=9 (3 measurements each condition for 3 devices). (c) Confocal reconstruction of tube with circumferential buckling inner and outer walls, formed at: QI=23µL/min, QM=10µL/min and QO=277µL/min. The tube has dimensions of: DO=873µm, Di=726µm and δ=74µm. The tube was extruded by a device having outlet diameter of 2.0mm. The confinement has diameter Dc=1.59mm and length Lc=2.8cm. (d) Corresponding ratio Di,1/Di,2 of crimped wall tubes for: QI=23µL/min, QM=10µL/min and QO=277µL/min (scale bar 500 µm), n=3 (from same device). (e) Corkscrew shaped inner wall tube for: QI=3500µL/min, QM=200µL/min, QO=5µL/min. (scale bar 3 mm). (f) Wavelength of corkscrew shape for varying QI, while QM=200µL/min and QO=5µL/min, n=5 (from same device). Data points and error bars are mean values and standard deviation of the n measurements for b, c and f.
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6.4 One-step formation of heterogeneous soft material tubes Incorporating spatial composition heterogeneities of materials on the radial, circumferential and
axial directions in a single system have not been demonstrated by previous in-plane extrusions.
Molding techniques using sacrificial templates also has the limitation producing spatial
composition heterogeneity. In this thesis, the off-plane extrusion was demonstrated extrusion of
biomaterial tubes with spatial composition heterogeneities on radial, circumferential and axial
directions.
In addition to the previously demonstrate continuous formation of single-walled tubular
structures, we now extend the approach towards the formation of heterotypic tubular structures.
We demonstrate the formation of different circular cross section tubes with a heterogeneous
composition as shown in Figure 9.
We first discuss soft material tubes that possess a heterogeneous wall composition in the radial
direction and homogeneous compositions in the circumferential and axial directions. Such
multilayered tubes may be obtained from microfluidic devices that possess two or more feature
layers distributing more than one biopolymer streams. Vertically stacking n biopolymer matrix
layers in between the crosslinking layers permits the formation of n-layered tubular structures
with a different compatible material for each layer. For example, using the microfluidic device
design shown in Figure 1d, a three-layered tube was extruded. Figure 9a shows a confocal
reconstruction of the tube cross-section. The 3 layer tubular structure was prepared using 2%
alginate solutions that were optically distinguished because they carried different payloads of
fluorescent microspheres. The approach may be extended to different biopolymers or payloads.
For instance, a slow gelling biopolymer may occupy the center matrix layer, surrounded on both
sides by layers of rapidly gelling biopolymers. The latter would therefore act as templates and
confine the biopolymer in the center layer while gelation takes place until a monolithic tube is
obtained. As shown in Figure 9 (b, c), the inner diameter DI, outer diameter DO and wall
thickness δ measured for three-layer tubes compare favorably with the single layer tubes
produced at similar (total) matrix and streaming flow rates. Several different combinations of
flow rates were tested and the results are shown in Figure A3 in appendices.
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The cross sectional area of each individual layer of the three-layer tube is uniform as shown in
Figure 9d. The standard deviation of the cross sectional area of the layers is 0.042mm2, which is
9.6% of the total cross sectional area. With the same flow rate of all matrix layers of 100µL/min
each, the thicknesses of the three layers decreased from the inside to the outside, compensating
for the increase in the circumference as shown in Figure 9e.
We now discuss the formation of single-layered tubes where the matrix composition is
heterogeneous in the circumferential direction and homogeneous in the radial and axial
directions. Tubular structures with two or more compatible matrix materials along their
circumference were prepared using device shown in Figure 1b. In addition to delivering primary
biopolymer solution to the outlet, microfluidic channels delivering secondary biopolymer
solutions are inserted surrounding the circumference of the center outlet. One or more matrix
solutions can be delivered independently through these microfluidic channels. The configuration
allows forming vertical tessellations within the tube wall that may predictably alter the
mechanical properties in the circumferential direction along the tube wall. Tube walls composed
of axially aligned stripes of alternating composition may be formed by introducing a secondary
biopolymer solution from a well operated at elevated head pressure Ph while delivering the
primary biopolymer solution using a syringe pump. The details of the experimental setup are
shown in Figure 3. As indicated in Figure 9h, increased (time-constant) head pressures produced
wider stripes in cases where the flow rates of the primary biopolymer solution and streaming
fluids were kept constant. In the examples shown in Figure 9(f, g), the stripes correspond to
alginate doped with payloads of different fluorescent microspheres than the primary biopolymer
(alginate). However, secondary and primary biopolymer solutions are not confined to sodium
alginate. Different tubular structures may be obtained using the same setup and microfluidic
device by varying the extrusion conditions, the base and secondary biopolymer solutions, or the
payload.
The head pressures delivering one or several of the secondary biopolymer solutions may be
altered with time, thereby periodically initiating or preventing the local incorporation of the
secondary biopolymer within the tube wall, and producing heterogeneities not only along the
tube circumference but also along its axis. The volume of the secondary biopolymer solution that
was incorporated per spot as well as the spot size was controlled by the pressure and opening
time of the inlet of the spotting channels. Figure A2(a, b) show that smaller spots were generated
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by reducing upper value of the head pressure. Each spotting channel was independently
controlled, so alternating spotting at different locations can be achieved, as illustrated in Figure
A2c. Multiple spots were produced at the same time, as shown in Figure A2d.
Figure 9i shows the cross-section of a “Janus” tube with a tube wall that has a different
composition at each half and was produced using the microfluidic device shown in Figure 1c.
This is another example of heterogeneous tube with circumferential direction heterogeneity. The
matrix flow rates of the respective halves are Qm,1 and Qm,2. The two halves were formed from
2% alginate solutions that carried different fluorescent microspheres as payloads. Since the two
sides were fed at the same flow rate, Qm,1 = Qm,2, the fraction of the circumference occupied by
the base and secondary material was very similar (Figure 9j). Figure 9(k, l) show that DI, DO, and
δ of the half-half tubes were similar to a single layer tube that was produced from the same
biopolymer solution at comparable flow rates of matrix and streaming flow rates. The application
of this type of tube can be found below while half of the tube is formed by stimulus responsive
hydrogel.
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Figure 9. Heterogeneous tubular structures. (a) Confocal image of cross section of three-layer sodium alginate tube formed at QI=650µL/min (100mmol CaCl2 solution, applies to all inner streaming solutions in this figure), Qm,1=67µL/min (2% alginate solution, applies to all biopolymer matrix solutions in this figure), Qm,2=67µL/min, Qm,3=67µL/min and Qo=650µL/min (100mmol CaCl2 solution, applies to all inner streaming solutions in this figure). (Scale bar 500
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µm). Inset shows three-layer alginate tube formed at QI=650µL/min, Qm,1=67µL/min, Qm,2=67µL/min, Qm,3=67µL/min and Qo=650µL/min. The tube has dimensions of: DO=2079µm and δ=131µm. (Scale bar 200 µm) (b) Comparison of inner and outer diameters of single layer tube (grey color) and three-layer tube (white color), n=3 (from same device). (c) Comparison of wall thicknesses between single layer tube and three-layer tube, showing them having similar dimensions while extruded with same conditions. n=3 (from same device). (d) Comparison of cross sectional area occupied by different layers, showing the layers have similar cross sectional area. The tube is formed at QI=650µL/min, Qm,1=100µL/min, Qm,2=100µL/min, Qm,3=100µL/min and Qo=650µL/min, n=3 (from same device). (e) Comparison of wall thickness of different layers, showing that outer layers are thinner than inner ones. The tube is formed at QI=650µL/min, Qm,1=100µL/min, Qm,2=100µL/min, Qm,3=100µL/min and Qo=650µL/min, n=3 (from same device). (f) Confocal reconstruction of secondary biopolymer stripe incorporated within tube wall. QI=650µL/min, Qm=200µL/min and Qo=650µL/min. Secondary biopolymer incorporated using constant head pressure of 6.89kPa. (Scale bar 500 µm) (g) Cross sectional view of second biopolymer stripes on tubular structure wall. QI=650µL/min, Qm=200µL/min and Qo=650µL/min. Head pressure Ph=13.79kPa. (Scale bar 500 µm) (h) Change of stripe width with respect to change in head pressure Ph, n=3 (from same device). The stripe width increases with increased Ph. (i) “Janus” tube formed at QI=650µL/min, Qm,1=100µL/min, Qm,2=100µL/min, and Qo=650µL/min. The tube has dimensions of: DO=2024µm and δ=118µm. (Scale bar 500 µm) (j) Circumferential length ratio evaluated for “Janus” tubes, showing the two halves have similar arc length, n=3 (from same device). (k) Comparison of inner and outer diameters of single layer tube and “Janus” tube, showing that “Janus” tubes have similar dimensions as single layer tube while extruded with same conditions. Single layer tube: grey. “Janus” tube: white, n=3 (from same device). (l) Wall thickness of single layer tube and “Janus” tube are similar when extruded with the same conditions, n=3 (from same device). Data points and error bars are mean values and standard deviation of the n measurements for b, c, d, e, h, j, k and l.
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6.5 Collagen tube formation Other suitable solidification methods include other forms of polymerization, including physical
and chemical crosslinking, are compatible with the described approach for forming tubular soft
materials. To illustrate the applicability of the approach to temperature induced gelation we now
discuss the gelation of collagen I in a case study.
The disadvantage of alginate based approach is that the shell material (alginate) is not ideal in
terms of cell adhesion. And cell migration in the shell is expected to be poor comparing with
materials like collagen. Therefore, only cell-laden fibers can be made instead of cell-laden tubes
using Takeuchi’s approach [8]. The key factor limited this approach was the slow gelation of
collagen. Alginate was essential for the process that it prevents collagen from leaking out from
the extruded fiber. Moreover, the second step of incubating extruded microfiber limited the
throughput of microfiber production. Below, a process of one-step extrusion of collagen tubes
will be demonstrated which solves the problem of slow gelation of collagen.
Homogeneous tubes were made from collagen solution that was derived from rat tail and had
dimensions that were comparable to the previously described sodium alginate tubes. During the
extrusion, collagen solution was kept at 4°C at pH3and the streaming solutions and reservoir
solution is kept at room temperature. The increase in temperature and pH induced the gelation of
collagen. The inner and outer streaming fluids and the reservoir solution contained 10% wt PEG.
Even though the gelation may be accelerated by exposing the collagen solution to PEG solutions
delivered in the inner and outer fluid streams due to molecular crowding[66], the gelation process
is still slower compared with the alginate case. As a result, a longer residence time is required
while passing through the cylindrical confinement and may be achieved in one of two ways:
either by reducing the streaming and matrix flow rates and thereby the velocity of extrusion, or
by extending the length of the confinement, LC . Both methods were tested and found to be
successful. By slowing the extrusion velocity down to 1mm/s, corresponding to
QI = QO=165µL/min and QM =70µL/min. The residence time required to pass through the Tygon
tube confinement (LC=100mm, DC=3.2mm) was 100s. The PEG solution had a density of
1.011g/mL that was greater than the density of the collagen solution, resulting in the produced
collagen tubes to float and collapse upon exiting the confinement, or to collapse even within the
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confinement, thus impact the yield of collagen I tube production. The extrusion setup is the same
as the alginate extrusion describe in Figure 6.
Collagen gelation rate was found to increase when applying shear to the gel. Therefore, it gels
faster with higher flow rates hence higher extrusion velocity. In section 6.2, an assumption of no
shear at tube wall was made. This assumption does not hold in the case of collagen I extrusion
because collagen solution remain as liquid for most of the time while in the confinement. The
tube needs to gel to the extent that it does not collapse after coming out from the confinement.
While the tube comes out too early in the crosslinking stage, the tube will collapse even when it
is submerged. To achieve this extent of gelation, as mentioned before, 100s is required for 1mm/s
extrusion velocity. On the other hand, only 45s is required for 4mm/s extrusion velocity. For an
extrusion velocity of 4mm/s that corresponded to a QI=QO=500µL/min and QM= 200µL/min. A
confinement with LC=180mm and DC=3.2mm was used, resulting in a residence time of 45s. As
the gelation process was faster at higher extrusion velocity (higher shear) and the tube exiting the
confinement was stiff enough to not collapse easily. Figure 10(a, b) show images of as produced
collagen tubes. As illustrated in Figure 10(c, d), the collagen tubes obtained at these flow rates
had smaller diameters and exhibited higher elastic moduli as compared to the alginate tube
produced with the same flow rates of fluids. The elastic modulus (evaluated in the axial
direction) of the collagen tube was 63kPa as compared with 38kPa for the alginate case (Figure
10e). The elasticity of tube segments was measured using a custom tensile tester (840LE2, Test
Resources, Shakopee, USA). Tube segments of 2cm length were pulled with speed ramp of
0.1mm/s until failure. The load cell used was 1000g.
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Figure 10. Collagen tubes (a) Collagen tubes collected in 90mm diameter petri dish. Conditions for tube formation: QI=500µL/min (10%wt PEG, 2%wt NaCl solution), Qm=200µL/min (3.7mg/mL acid-solubilized collagen I solution at pH3) and Qo=500µL/min (10%wt PEG, 2%wt NaCl solution). (b) Confocal image of collagen tube cross section shown in Figure 10a. The tube has dimensions of: DO=1738µm and δ=141µm. (c) Comparison of inner and outer diameters of single layer alginate tubes and collagen tubes. Alginate tubes were extruded at QI=500µL/min (100mmol CaCl2 solution), Qm=200µL/min (2% alginate solution) and Qo=500µL/min (100mmol CaCl2 solution). Collagen tubes were extruded at QI=500µL/min (10%wt PEG, 2%wt NaCl solution), Qm=200µL/min (3.7mg/mL acid-solubilized collagen I solution at pH3) and Qo=500µL/min (10%wt PEG, 2%wt NaCl solution). Collagen tube: white. Alginate tube: grey, n=3 (from same device). (d) Comparison of wall thicknesses between collagen and alginate tubes. The tubes were extruded at the same conditions as in Figure 10c, n=3 (from same device). (e) The elastic moduli of collagen tube and alginate tubes are in the same order. The tubes were extruded at the same conditions as in Figure 10c, n=5 (from same device). Data points and error bars are mean values and standard deviation of the n measurements for c-e.
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6.6 Stimulus responsive tubular structures There is a great interest in the applying spatially organized soft materials to undergo
programmed shape transformations. I am exploring such shape transformations in the contexts of
homogeneous and heterogeneous tubular/planar soft materials with incorporated stimulus
responsive nanoparticle payloads.
Poly(N-isopropylacrylamide-co-vinylacetic acid) (PNIPAM-VAA) particles with large swelling
ratios in response to stimuli (i.e., pH and temperature changes) are dispersed as a payload in
alginate solution before gelation. PNIPAM and PNIPAM-VAA particles were synthesized by
precipitation polymerization using the recipe in Table 3, which is a widely used synthesis
method for polymers[58]. PNIPAM is only responsive to temperature changes while PNIPAM-
VAA is responsive to both temperature and pH changes. As described in the experimental
section 5.11, the recipe can be used to synthesis 160mL of stimulus responsive nanoparticle
suspension solution. PNIPAM-VAA is used for the experiments in this section unless stated
otherwise. The stimuli-responsive microgel of PNIPAM-VAA has a NIPAM core and a
vinylacetic acid shell as indicated in Figure 11a. NIPAM formed the core because it has greater
reaction ratio than VAA. Therefore NIPAM tends to polymerize before VAA and formed a block
polymer which possess the core shell structure. The core is responsive to temperature changes as
temperature passes its LCST (Figure 11b). The shell is responsive to pH changes due to the
similar charge repulsion between carboxylic groups (Figure 11c)[67]. As the particles are doped
with a high density of 0.089g/mL, the microscopic swelling behavior of the particles will lead to
the macroscopic volume change of the hydrogel sheets. In the figure, base hydrogel refers to
alginate hydrogel. The blue and red arrows only indicate the direction of reaction. They do not
mean temperature change along the direction.
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Table 3 Recipe of stimuli-responsive particles synthesis
Poly (PNIPAM) (mol) Poly (PNIPAM-VAA) (mol)
N-Isopropylacrylamide (NIPAM) 3.5×10-3 3.5×10-3
Vinylacetic Acid (VAA) 0 6.5×10-4
Sodium Dodecyl Sulfate (SDS) 1.7×10-4 1.7×10-4
Ammonium Persulfate (APS) 4.4×10-4 4.4×10-4
N,N-Methylene Bisacrylamide (MBA) 1.24×10-2 1.24×10-2
Figure 11. Stimuli-responsive PNIPAM-VAA nanoparticles. (a) Structure and composition of PNIPAM-VAA particles and its temperature responsiveness. The particle has a VAA shell and a NIPAM core. The core swells as temperature become lower than LCST of the material and the
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reaction is reversible. (b) pH responsiveness can be induced on the shell of the particle. The shell swells as environmental pH become basic and the reaction is reversible. (c) Shape change of hydrogel sheet can be imposed by triggering volumetric change of the doped stimulus responsive particles. A
PNIPAM-VAA particles swell in basic environment and shrink in acidic environment. The
hydrodynamic diameter of PNIPAM-VAA particles are measured using dynamic light scattering
(DLS). Based on DLS measurements, the polydispersity index (PDI) of the particles is 0.012
(Figure 12a). The hydrodynamic diameter distribution of each batch is narrow even the absolute
values are different. A representative distribution is selected for illustration. Particles with PDI
less than 0.1 are considered monodisperse. The hydrodynamic diameter dh at 40 ̊C is half of dn at
room temperature (Figure 12b). The hydrodynamic diameter at pH10 db is 2 times of
hydrodynamic diameter dn at neutral at room temperature (Figure 12c). At different pH, the
LCST of the particles are different. LCST tends to shift higher at higher pH and shift lower at
lower pH (Figure 12d). As for the measurements of the normalized or absolute hydrodynamic
diameters of the particles, since the results are already obtained from average of all the particles
in the solution, there is no error bar for the plot. For each data point, the result of a single
measurement is represented because multiple DLS measurements do not change the result. The
measurements were taken from a single batch of polymer synthesis to remove human errors
(weighing ingredients). Batch to batch difference of the polymer synthesis is not studied here.
In order to crosslink alginate hydrogel, Ca2+ is required. However, it is known that Ca2+ will
cancel pH response by interconnect carboxylic groups on the particle surface [57]. In basic
environment, the particles do not swell significantly in presence of Ca2+ (Figure 12e). The
method overcomes this problem is to use pH as trigger for stimulus response of the temperature
responsive cores of the particles. In order to trigger the stimuli-responsiveness by pH, the VAA
shell is added to PNIPAM so that a change in pH will change LCST of the particles. Therefore,
by moving LCST, the state of the particles can be changed at a fixed temperature by changing
pH (Figure 12f). Though PNIPAM-VAA was synthesized and studied before, this method of
triggering its pH response have never been used. It is observed that PNIPAM-VAA particles tend
to aggregate at temperature higher than its LCST. In presence of Ca2+, the aggregation becomes
more prominent at low pH. Though this aggregation process is reversible by lowering the
temperature below LCST, no meaningful measurements of the hydrodynamic diameter of the
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particles can be obtained through DLS in presence of Ca2+ and at temperature higher than their
LCST.
Figure 12. PNIAPAM-VAA particle size and its stimuli-responsive volumetric changes. (a) DLS polydispersity measurement of PNIPAM-VAA particles. The particles are monodispersed with a PDI of 0.012. (b) Hydrodynamic diameter change of PNIPAM-VAA particles with respect to pH at room temperature. The particle size is largest at pH=10 and is smallest at pH=3. (c) Hydrodynamic diameter change of PNIPAM-VAA particles with respect to temperature at
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pH7. The LCST of the particle is at 32°C at pH 7. (d) Normalized hydrodynamic diameter change of PNIPAM-VAA particles in water for, pH3 ( ), pH7 ( ) and pH10 ( ). The particle is more sensitive (low LCST) to temperature changes at low pH and is less sensitive (high LCST) at high pH. (e) Hydrodynamic diameter change of PNIPAM-VAA particle at room temperature in water ( ) and in calcium ( ) at different pH at room temperature. The hydrodynamic diameter of the particle does not as much when Ca2+
is present. It implies that Ca2+ impedes swelling behavior of PNIPAM-VAA particle during pH change. (f) Normalized hydrodynamic diameter change of PNIPAM-VAA particles in 100mmol Ca2+ solution for pH3 ( ), pH7 ( ) and pH10 ( ). In presence of Ca2+ the particles are more sensitive to temperature at lower pH. n=1 for all measurements.
Temperature and pH can both be used as triggers of stimuli responses of the doped hydrogels.
Homogeneous stimulus responsive hydrogel tubes were successfully extruded using the same
setup for homogeneous tubes discussed before, shown in Figure 14(a, b). The outer diameter of
stimulus responsive tube extruded at QI=650µL/min, QM=200µL/min and Qo=650µL/min is
2640±230µm, while alginate tubes extruded at the same condition has outer diameters of
1920±180µm. The PNIPAM-VAA nanoparticles were concentrated in the stimulus responsive
hydrogel solution such that the nanoparticles were not fully swelled. Therefore, the nanoparticles
absorb water from environment after extrusion and result in the increase of extruded tube size.
Hydrogel sheets were extruded in order to study the stimulus responsive properties of the
material. In-plane extrusion with a PDMS device was used to obtain hydrogel sheet of 200μm
thickness and 5mm width. The outlet of the device in immersed in 100mmol Ca2+ solution made
of calcium chloride and DI water. Stimulus responsive polymer solution was pumped into the
microfluidic device and was distributed as a planar flow. Gelation happened at the outlet of the
device. Formed hydrogel sheet was collected by a rotating drum with linear velocity of 4mm/s.
The length change of stimuli-responsive hydrogel induced by temperature change at low pH can
be as high as 105%. The particle diameter change measurements agree with the hydrogel sheet
length change measurements. 3 sheets extruded at different times were used for the length
change measurements. The stimuli-response of the hydrogel is completely reversible (Figure
14c). After switching water bathes of 25 ̊C and 40 ̊C for 9 times, there is no observable change in
swelling and shrinking magnitude of the homogeneous stimuli-responsive hydrogel sheet. In
terms of responsive time, for a hydrogel sheet which is 200μm thick and 5mm wide, shrinking is
completed in 60 seconds while swelling requires 10 minutes to finish, shown in Figure 14(d, e).
It is because water is actively pumped out from the hydrogel while the hydrogel becomes
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insoluble and collapses. On the other hand, swelling requires water to penetrate the hydrogel
matrix via diffusion, which takes a much longer time
Stimuli-responsive particles are doped into the alginate solution at a high intensity (0.089g/mL
dry mass) such that the particles are closely packed in the hydrogel matrix after gelation. Stimuli-
responsive particles filled up the void spaces between alginate fibers. Figure 14f shows a
Scanning electron microscope (SEM) image of the alginate matrix produced by extrusion. My
hypothesis is that the particles and the alginate fibers are connected by interpenetration. If the
particles are trapped in alginate matrix rather than interpenetrated, shrinking of particles will
release water into the matrix but will not induce an overall volumetric change of the hydrogel.
SEM images confirmed this hypothesis (Figure 14g). The alginate fibers penetrate the particles
and form a “branches and leaves” structure, whereas alginate fibers are the branches and the
particles are the leaves. In terms of the type of connection between alginate and PNIPAM-VAA,
they are physically winded instead of ionic bonded. Experiment evidence shows that doping
PNIPAM particles will produce the same temperature responsiveness as doping PNIPAM-VAA
particles. This means Ca2+ did not establish connection between the carboxylic groups in VAA
and the carboxylic groups in alginate. In a case such connection is established, the temperature
responsiveness produced by doping PNIPAM-VAA will be stronger than doping PNIPAM.
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Figure 13. Schematic of homogeneous stimulus responsive sheet extrusion. The stimulus responsive hydrogel solution is driven by a syringe pump into a microfluidic device which evenly distributes the solution into a planar flow. The solution gels after exiting from the device and entering a bath of crosslinker solution.
Figure 14. Homogeneous stimuli-responsive hydrogel and its response to temperature and pH.. (a) Homogeneous stimuli-responsive hydrogel tube responses to temperature changes. Lc is the length of tube at room temperature. Lh is the length of tube at 40°C. Homogeneous tube was extruded at 4mm/s in 100mM Ca2+ solution. The hydrogel tube is 150μm thick and 2.4mm in outer diameter in swell state using the homogeneous tube extrusion device shown in Figure 1a at QI=650µL/min, QM=200µL/min and Qo=650µL/min. Particle density in the hydrogel solution is 0.089g/ml (dry mass) Scale bar: 2mm. (b) Length change of stimuli-responsive hydrogel material in response to pH and temperature, with the comparison with hydrodynamic diameter changes of stimuli-responsive particles. pH3 Particle Diameter, pH7 Particle Diameter, pH10
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Particle Diameter, pH3 Material Length pH7 Material Length, pH10 Material Length. The measurements in (b-g) are based on extruded sheets using the setup shown in Figure 13 using 100mmol CaCl2 crosslinking solution. The sheet was extruded at a velocity of 4mm/s. n=3 (3 hydrogel sheets extruded at different times). (c) Length change of stimuli-responsive hydrogel material in cycles of temperature change, showing the reversibility of the stimulus response. Temperature is switch from 25ºC to 40ºC back and forth, starting at 25 ºC, n=1. (d) Length changes over time while hydrogel material is swelling, n=3 (3 hydrogel sheets extruded at different times). (e) Length changes over time while hydrogel material is shrinking, n=3 (3 hydrogel sheets extruded at different times). (f) SEM image of alginate matrix. Network of alginate fibers is visible in the image. Scale bar: 2µm. (g) SEM image of alginate matrix doped with particles. Individual particles can be seen in this image. Scale bar: 2µm. Data points and error bars are mean values and standard deviation of the n measurements for b-e.
Tubular structure is one of the most commonly seen 3D structures in natural tissues and
organisms, namely vascular structure. It is a perfusable structure which allows effective deliver
of liquids. Nature uses this structure to distribute nutrition across large tissues and organisms. By
creating a stimuli-responsive tube, the flow rate of liquid can be automatically adjusted. For
example, by using a pH responsive tube which shrinks in low pH, flow rate of ions can be
automatically regulated, as the flow rate decreases at low pH and increases at high pH due to
stimuli-responsive diameter changes of the tube. Heterogeneous tubular structure made of
stimuli-responsive soft material will possess the ability of change flow direction according to the
stimuli it receives. By designing the spatial composition along the peripheral of the tube, the
bending direction of the tube can be designed for selective stimuli. Moreover, stimulus
responsive tubes can be assembled easily by shrinking one end of a tube and insert into another
tube as discussed in Figure 15.
To demonstrate the ability of assembly stimulus responsive tubes, by taking advantage of
stimulus responsiveness, the following experiment is conducted. A stimulus responsive tube is
cut into two segments. One segment is immersed in hot water bath of 50°C for 5mins. The heat
segment is shrank in diameter and then transfer to the room temperature water bath where the
other segment is residing. The swelling of the tube needs 15mins which is relatively slower than
shrinking. Therefore, there is enough time to insert the shrink tube segment into the tube segment
of the original size. After 15mins, the shrink tube is fully swelled and went back to its original
size. As the result, the inserted tube segment is sealed inside the other tube segment. Figure 15
shows a schematic diagram of the tube assembly process.
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In the case that a Janus tube is made that only half of the tube is stimulus responsive, a curvature
change can be induced by induce stimulus response using temperature change. As one side of the
tube is swelled/shrank, internal stresses are induced in the tube and the tube will bend. In the
example shown in Figure 16, the curvature of the tube is changed between 0.060mm-1 and
0.138mm-1, which is a 231% change of curvature. The concept of extruding patterned stimulus
responsive hydrogel was first validated using in-plane extrusion of heterogeneous hydrogel
sheets. Heterogeneous hydrogel sheets can be patterned such that the shape deformation is
predictable. Details of heterogeneous stimulus responsive hydrogel sheets are described in
appendices.
Figure 15. Schematic of stimulus responsive tube assembly. A homogeneous stimulus responsive tube is cut into two segments. One segment is heated and shrank so it can be inserted into the other segment which is unchanged. The tube was extruded at QI=650µL/min(100mmol CaCl2 solution,), Qm,=67µL/min(1.5% alginate, 0.087g/mL PNIPAM-VAA particle solution) and Qo=650µL/min (100mmol CaCl2 solution,)
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Figure 16. Temperature induced response of half-half stimulus responsive tube. The “Janus” tube with half of the tube stimulus responsive was extruded using the device shown in Figure 1c. Upon heating, the tube bends because of the shrinking of the stimulus responsive half. The process is reversible. QI=650µL/min(100mmol CaCl2 solution,), Qm,1=67µL/min (2% alginate solution), Qm,2=67µL/min(1.5% alginate, 0.087g/mL PNIPAM-VAA particle solution) and Qo=650µL/min (100mmol CaCl2 solution,). (Scale bars 2mm)
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7 SUMMARY Tubular constructs of engineered biomaterials increasingly gain attention as they are potential
therapeutic replacements of human tissues. In vitro, they are extensively studied as platform of
cell-cell and cell-matrix interactions. The methods described in this thesis demonstrated
continuous extrusion of hydrogel tubes using a microfluidic platform. Tubular structures were
formed through off-plane extrusion of coaxial flow of biopolymer solutions and crosslinker
streaming solutions. The developed system is robust that it operates at a wide range of flow rates
(0-3500µL/min for streaming solutions). The throughput of tube extrusion is up to 20mm/s. By
controlling the flow rates of streaming solutions, the diameters and wall thicknesses of the
extruded tubes can be tuned predictively. The produced tube outer diameter ranged from 0.7mm
to 2.5mm. Alginate and collagen I hydrogel tubes can be consistently formed by coupling with
suitable crosslinkers in the streaming solutions. The flexible and automated nature of this tube
extrusion approach should enable formation tissue constructs of many cell types at different
scales.
Tube morphologies such as crimped and corkscrew shape inner tube walls were produced by
bringing the flow rates ratio of inner and outer streaming solutions to extremes. Spatial
composition heterogeneities along radial (multilayer tube), axial (tube with stripe patterns) and
circumferential (“Janus” tube) directions were incorporated in the extruded alginate tubes using
the same system. These morphologies and heterogeneities may lead to develop tubular tissue
constructs mimic natural tissues in terms of morphologies and spatial organization of different
cells.
Homogeneous and heterogeneous stimulus responsive tubes were extruded using the same
system, by doping synthesized PNIPAM-VAA nanoparticles in alginate solution. The
nanoparticle doped alginate based hydrogel was characterized in terms of its volumetric change
in changing temperature and pH, responsive time and reversibility of the reaction. Assembly of
homogeneous hydrogel tubes using their volumetric stimulus responsive change and bending of
“Janus” stimulus responsive hydrogel tube was demonstrated. This work is an important step
towards applications such as high order hydrogel construct assembly, responsive actuators and
flow regulators.
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8 REMAINING WORK AND FUTURE DIRECTIONS As formation of homogeneous and heterogeneous tubular structures was extensively discussed in
the context of alginate, other materials need to be tested to validate the results obtained using
alginate. For example, the experiments on collagen tube formation can be explored to evaluate
operational parameters of collagen using the same system. Introducing heterogeneity in collagen
tubes was not validated and may be tested in future experiments.
Methods of fixation and perfusion of produced hydrogel tubes should be developed in order to
utilize the different types of tubular structure produced. Hosting of tubes can be achieved by
using reversible sealed microfluidic devices or cannulation. Quantitative measurements such as
elasticity of the tube wall, diffusivity of different biomaterials and magnitude of stimulus
responsiveness can be evaluated if the tubes can be hosted and perfused in a controlled manner.
Biocompatible materials were used to form these tubular structures. Culturing different cell types
in the tubular structures can be tested, in order to study properties such as viability of cells,
migration of cells and biodegradation of the tubular structures. For example, endothelial cells can
be cultured to form vascular networks. Induced pluripotent stem cell can be cultured to and
developed in to various cell types on the tubular structure. Multiple cell types can be introduced
into the heterogeneous tubular structures at the same time to study cell-cell interactions.
Moreover, methods of assembling the tubular structures into complex 3D structures as building
blocks can be developed. Perfusable scaffolds of biomaterials can be made based on the
produced tubes.
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Appendices
A.1 Tube extrusion without crosslinker in the inner stream
Alginate tubes are extruded using the setup in Figure 2. The inner streaming fluid contains no
calcium ions. The crosslinking of alginate completely relies on diffusion of calcium ions from
the outside of the tube. The gelation of the inner wall is relative slow than the case where
calcium ions are present in the inner streaming fluid. Alginate is free to move in the lumen of the
tube and hence formed the structure shown in Figure A1b.
Figure A1. Tube extruded with no crosslinker in inner streaming fluid. (a) Confocal image of tube cross section extruded at QI=100µL/min (DI water), QM=200µL/min (2% alginate soltuion) and Qo=1200µL/min (100mmol CaCl2 solution). (Scale bar 500µm) (b) Confocal image of tube cross section extruded at QI=100µL/min (DI water), QM=200µL/min (2% alginate soltuion) and Qo=1200µL/min (100mmol CaCl2 solution). (Scale bar 500µm)
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A.2 Spotted tubes
Figure A2. Spotted tubes. (a) shows a fluorescence image of large spots produced by subjecting the spotting inlet channel to a pressure of 1 Psi during a solenoid valve opening time of 100ms. QI=500µL/min (100mmol CaCl2 solution), QM=200µL/min (2% alginate soltuion) and Qo=500µL/min (100mmol CaCl2 solution). (Scale bar 500 µm) (b) shows a fluorescence image of small spots produced by 200ms opening time of spotting channel with 0.6Psi. (Scale bar 500 µm) (c) shows a fluorescence image of alternating spots produced by 100ms opening time of spotting channel with 1Psi. (Scale bar 1 mm) (d) shows a fluorescence image of 2 rows of parallel alternating spots produced by 100ms opening time of spotting channel with 1Psi. (Scale bar 1 mm).
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A.3 Comparison of dimensions of single layer/three-layer tubes
Figure A3. Comparison of dimensions of single layer/Three-layer tubes. The format of the x-axis label is QI/QM(Qm,1/ Qm,2/ Qm,3)/QO. n=3 (3 measurements from same device). The tubes are made of alginate where the streaming fluids are 100mmol CaCl2 solution and the biopolymer solution is 2% alginate solution.
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A.4 One-step formation of heterogeneous stimuli responsive hydrogels
(PNIPAM-VAA) particles with large swelling ratios in response to stimuli (i.e., pH and
temperature changes) are dispersed as a payload in alginate solution before gelation. This hybrid
hydrogel can be controllably incorporated within a base hydrogel by a microfluidic device. Both
hydrogel materials undergo gelation after leaving the microfluidic device and exposing to a
solution containing crosslinkers which are Calcium ions at room temperature. The thickness of
the hydrogel sheet can be controlled by tuning the rotation speed of the drum which guides the
sheet at the device exit. Mosaic hydrogels with different tessellations can be produced by
controlling the pressure of each inlet of the device. The schematic diagram illustrates the
extrusion process of mosaic hydrogel sheet (Figure A4a).
There are 3 devices made for simple heterogeneous stimuli-responsive hydrogel sheets. For all
the devices, the channels are designed such that the flow resistances for all channels are the same
in each device. 1) Bilayer extrusion device (Figure A4b): this device has two layers on top of
each other. Each layer has two inlets which join at a T junction in the device. Different solutions
can be flowed in each layer by controlling the pressure of each inlet. This device is aimed to
extrude a bilayer hydrogel sheet where one layer is stimuli-responsive and the other is not. 2)
Side stripes extrusion device (Figure A4d): this device is designed to extrude hydrogel sheets
which has different materials at the center and at the two sides. The width of the central region
and the side stripes can be adjusted by tuning the relative flow rates of hydrogel solutions. For
example, while the flow rate in central channels is increased, the central region of the hydrogel
sheet will become wider. The purpose of this device is to extrude hydrogel sheets that the central
region is inert while the two sides of the hydrogel sheets are stimuli-responsive. 3) Side by side
extrusion device (Figure A4f): This device has two inlets and each inlet is responsible for
extruding one side of the hydrogel sheet. Therefore, the materials on each side of the hydrogel
sheet can be different. The width of each side of the hydrogel sheet is again controlled by flow
rate in each inlet. This device was made to extrude hydrogel sheets which one side is stimuli-
responsive and the other side is not.
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Bilayer heterogeneous hydrogel sheet can bend in response to external change of temperature or
pH (Figure A4c and Figure A5a). While one layer of the sheet is contracting and the other layer
remains unchanged, stress is created between two layers and causes the hydrogel sheet to bend.
The higher degree of contraction in the stimuli-responsive layer, the higher the curvature of the
hydrogel sheet produced by stresses. The curvature of the hydrogel sheet is a function of
temperature (Figure A5b). The curvature measurements were taken from 3 separately extruded
hydrogel sheets.
Stimuli-responsive stripes at sides hydrogel sheet bends globally and form saddle-like structure
locally due to the internal stresses caused by shrinking of the stripes at the two sides (Figure A4e)
[68].
Side by side heterogeneous hydrogel sheet buckles and form a wavy structure on the side of
hydrogel which has lower elastic modulus, while one side of the hydrogel is shrinking and the
other side remains unchanged (Figure A4g and Figure A5c) [69]. This morphology is also caused
by the stress at the interface of different materials, which is a result of swelling ratio difference
between the two sides. The wavelength of the wave structure decreases as the internal stress
increases. This implies that the wavelength is a function of temperature Figure A5d).
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Figure A4. Heterogeneous hydrogel extrusion. (a) Overview of extrusion of heterogeneous hydrogel with designed stimulus responses using a microfluidic printing device. Stimulus responsive and non-responsive solutions are driven into a microfluidic device with spatially align the solutions before gelation which happens at the exit of device. The extruded sheet is collected by a rotating drum. (b) Microfluidic device for double layer hydrogel sheet formation. The red layer is on top of the blue layer. There are two inlets for each layer which allow switch of stimulus responsive and non-responsive hydrogel solution within a layer. (c) Dual layer with one
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side stimulus responsive and other side inert roll up upon heating. (d) Microfluidic device for stripes at sides hydrogel sheet formation. (e) Hydrogel sheet forms wave and saddle shape and overall bending upon triggered response. (f) Microfluidic device for side by side stripes hydrogel sheet formation. (g) Wave and spiral shape formed on one side of the sheet while response of the material is triggered.
Figure A5. Heterogeneous stimuli-responsive hydrogel sheets and their response to temperature and pH. (a) Heterogeneous stimulus responsive hydrogel sheet rolls while temperature is changed from at 25ºC to 40ºC at pH 3. The sheets used in this figure was extruded at 4mm/s. The stimulus responsive hydrogel solution consist 1.5% alginate and 0.087g/mL PNIPAM-VAA. The non-responsive hydrogel is 1.5% alginate. The crosslinker used is 100mmol CaCl2 solution. (b) Curvature change of double layer heterogeneous stimulus responsive sheets. The curvature of the sheet increases upon heating and decreases while cooled. The environment is pH 3. n=3(3 hydrogel sheets extruded at different times). (c) Side by side hydrogel sheet forms spiral shape on one side while temperature is changed from at 25ºC to 40ºC at pH 3. (d) Side by side hydrogel sheet (spiral) wavelength vs. temperature at pH 3. The wavelength decreases as the temperature increases. n=9 (3 waves was measured from each hydrogel sheet for 3 sheets extruded at different times). Data points and error bars are mean values and standard deviation of the n measurements for b and d.