Multi Sensing Grasper for Minimally Invasive Surgery

S.J. Fattahi, A. Zabihollah, and H. Adldoost

Sharif University of Technology, International Campus, School of Science and Engineering, Kish Island (Iran)

Abstract— In the present work, a multi sensing grasper has

been developed for minimally invasive surgery with embedded

ZnO piezoelectric and Fiber Bragg Grating sensors. In this

model, a sensing patch equipped with three FBG sensors to

sense the temperature in rage of 800 n.m and two separated

FBG in range of 1550 m.m to detect the displacement in x and

y directions. ZnO piezoelectric is highly sensitive to time and

provides a good resistance to temperature. Therefore, this

sensor is used for measuring the rate of strain and creep

coefficient. A finite element approach based on the viscous

material theory and plane displacement theory of anisotropic

materials has been utilized to obtain the compliance matrix of

muscles. The compliance matrix is then used to determine the

electromechanical coupling of ZnO piezoelectric sheet. The

optomechanical relations between strains and FBG reflected

wavelength shift have been utilized to study the static

behavior of a grasper’s jaw when grasping an object. The

interrogated reflected spectrum caused by strain displacement

in x and y directions, has been studied to find Cauchy-Green

tensor equation and Prony series coefficients. Numerical

illustrations have been presented to simulate the behavior of

three types of human muscles subject to applied grasping

load.

Index Terms—MIS, FBG, ZnO

I. INTRODUCTION

n recent years the use of piezoelectric elements are

commonly being used in smart minimally invasive

surgery (MIS) systems as both sensors and actuators. First

attempt in estimation of the contact force in MIS was

presented by Shikida et al. [4] who proposed an active

tactile sensor with capability to detect both contact force

and hardness of an object. Dragahi [5] showed the

possibility of using of polyvinylidene fluoride (PVDF)

sensors for tactile sensing system. Narayanan et al. [6]

presented the design and fabrication of a micro-machined

piezoelectric endoscopic tactile sensor to determine the

properties of tissues in minimally invasive surgery.

Determination of the compliance of sensed objects has

been designed by Sedaghati et al. [7] to determine the ratio

of force experienced by the rigid cylinder to the total force

applied to the sensor. Robotic grippers have been

investigated by Nakazawa et al. [8]. They modeled a

robotic griper to control the force based on human grasping

schemes. Recently, Seibold et al. [9] proposed an actuated

and sensitized instruments for minimally invasive robotic

surgery, which helped to increase the surgeon’s immersion

and dexterity. One of the first experimental works in this

area had been done by Dargahi et al. [10] who designed

and fabricated a tool to detect the strain and deformation of

the grasper’s tip for endoscopic tactile sensors. Bicchi et al.

[11] investigated the effects of compliance and viscoelastic

property of tissues to measure the force and angular

displacement of endoscopic graspers. Most recently, a

tactile sensor with capability to differentiate the various

complaint objects was constructed by Dario et al. [12, 13].

As it is observed the use of PVDF elements as sensors in

MIS system is quite extensive, however, using PVDF

sensors has a high influence of the electrochemical

behavior of human body and piezoelectric. The

piezoelectric materials produce a pulse voltage for any

applied force. Thus, in the present work the ZnO sheet has

been proposed to reduce the electrochemical noise. Most

importantly, in order to achieve a clear and close image of

the grasper force, the use of Fiber Bragg Grating (FBG)

sensors has been proposed to measure the normal stress

tensors and temperature. FBG sensors are quite immune to

any electromagnetic fields. Finally, to distinct different

muscles, a nonlinear optimization method based on

Cauchy-Green tensor equation and Prony series has been

utilized to determine the viscoelastic coefficients of three

different types of common human body muscles. Using

MATLAB® and ANSYS® numerical illustrations have

been presented to show the functionality and performance

of the proposed system.

II. ANALYSIS OF VISCOUS MATERIAL

Creep and stress relaxation are two characteristic behaviors of

viscoelastic materials. Creep occurs when a constant stress

applied to the material results in increasing strain. On the

other hand, stress relaxation occurs when a material is

under constant strain but the stress decreases until it

reaches some steady-state value. The one-dimensional

models of creep deformation and stress relaxation are given

as:

���� � ������

(1)

���� � ������ (2)

where J(t) is creep compliance for constant stress, ��, and

G(t) is the stress relaxation modulus for constant strain, ��.

The creep compliance and relaxation modulus are

empirically determined and describe the creep and stress

relaxation behavior of the viscoelastic material as a

I

2011 IEEE/ASME International Conference onAdvanced Intelligent Mechatronics (AIM2011)Budapest, Hungary, July 3-7, 2011

978-1-4577-0839-8/11/$26.00 ©2011 IEEE 344

function of time. The creep compliance and relaxation

modulus based on Zener [14] are given by

���� � � � �� � � ������ � (3)

���� � � � � � � ����������� � (4)

where , � are the spring constant and b is viscosity

coefficient.

III. FBG ANALYSIS

A. FBG Principal

The principle of a FBG sensor is based on the wavelength

shifting of the reflected spectrum when strain or

temperature change in the element. FBG sensors provide

advantages such as multi and continuous sensing using

only single fiber line, ease of placing and embedding in

composite, self-referencing capability independent of the

total power level of the source and the loss of coupler or

connection, electromagnetic interference immunity, high

sensitivity, and multiplexing capability.

Temperature and strain variations applied to the gratings

cause shifting in their Bragg wavelengths as:

���� � ����� � ����������� (5)

where i =1,2,…,n represent the grating written in the fiber

respectively. The thermal sensitivity,���� depends on the

thermal expansion of the fiber and, essentially, on the

thermo-optic coefficient. On the other hand, the strain

sensitivity,����, depends on the photo-elastic coefficient of

the fiber, mainly, determined by the variation of the grating

pitch due to the applied strain. The strain sensitivity

depends on the mechanical properties of the fiber. In

general, the maximum reflectivity occurs at the so-called

Bragg wavelength �� given by: ������� � � !""�� (6)

where !"" is the effective refractive index of the mode

propagating in the fiber and � is the FBG period.

B. Strain Sensing

Reflected wavelength �� is affected by any variation in the

physical or mechanical properties of the grating region.

Similarly, changes in temperature lead to change in !"" via

the thermo-optic effect and in an unconstrained fiber; � is

influenced by thermal expansion or contraction.

Stress state of a circular FBG in plane coordination [13] is

given as:

�## � �$��% (7)

�&& � '$��% (8)

where D is diameter of fiber, h is length of the FBG under

load. From Hook's law the in-plane strain can be expressed

as:

�## � � � ��( �)�##�� � �� � ��&&* (9)

���������&& � � � ��( �)�&&�� � �� � ��##*�������� (10)

Next, the wavelength shifting in x and y coordinates are

expressed as:

���# � � !""�� )�##�+ ��&&*��#��������� (11)

���& � � !""�� )�&&�+ ��##*��&��������� (12)

where, , �� is the change in Bragg wavelength �,- Pockel’s coefficient of the stress-optic tensor. The total

wavelength shifting is given by:

��� � ���# � ���&����������������� (13)

Substituting Eqs. (11) and (12) into Eq. (13), one may

achieve in Eq. (14), in which the first term gives the effect

of strain on wavelength and the second term describes the

effect of temperature.

�� �� ���� � ����� � ����� ������������������ (14)

where,���, � and � are respectively the photoelastic,

thermal expansion and thermo-optic coefficients of the

fiber, �� is the change of strain and �� is the temperature

change.

The photoelastic definition is expressed as:

� � !""�� )��+ ��.�+ ��/*�������������������� (15)

Substituting Eq. (15) into Eq. (14), the Bragg wavelength

shift with strain and temperature can be expressed as: ������ � 0� � !""�� )��+ ��.�+ ��/*1 ���

����� � ���������������� (16)

C. Temperature Sensing and Compensating

Temperature strongly affects FBG signals, thus, exact

measuring of strain can be achieved by temperature

compensating. The effects of temperature can be

compensated by using a separate FBG as a temperature

sensor in environment without any mechanical stress. The

wavelength change due to changing temperature can be

achieved by:

���������2���3��4� �� ������� ����������������� (17)

345

2��3��4� �� �� �������� �� (18)

where �� is wavelength of FBG temperature sensor and

����represents the change in wavelength due to

temperature change, thus, by subtracting ��, the

wavelength shifting due to strain is achieved.

������ � 0� � !""�� )��+ ��.�+ ��/*1 ��

������ � �� �������� ��

(19)

It can be observed that the �� changes linearity when the

applied strain changes axially.

D. Signal Interrogation using Wavelength-Division

Multiplexing

Knowing that many gratings combined on a single fiber

and addressed simultaneously, the FBG sensor has a

different Bragg wavelength. Therefore, it is possible to find

the reflected spectrum and place of related grating by using

the Wavelength Division Multiplexing (WDM) integration.

In this method a scan generator tunes the light source with

known instant wavelength and sweeping it back. When this

wavelength coincides with the Bragg wavelength of an

FBG, light is reflected back down the fiber to a photo

detector. The scan generator also supplies a timing signal,

and checks this with the spectrum. Further processing is

performed to identify the peaks in this spectrum, find their

peak positions and convert these to strain. The peak

reflected wavelength from the Bragg grating is determined

by:

�5�6� � �789�� ��:��8;�<=���>=� ?��

(20)

where � is basic wavelength, � is center of reflected

wavelength and 7��is width of the Gaussian curve. Where

the Gaussian kernel is stepped among the data set, thus, f

(�) is evaluated for varying values of 7�, and by using mean

squared error and examination between f (�) and the

received spectrum, the reflected spectrum’s peak � can be

determined, then the bragg signal is minimized.

IV. PIEZOELECTRIC ANALYZE

Under small field conditions, the constitutive relations for a

piezoelectric material are [15]:

%� � @�-�(- � A�BC �B (21)

�� � A-�D (- � E�BF �B (22)

which can be rewritten in compact form as:

G%�H � I@� ACAD EFJ�G(�H�� (23)

where vector D of size (3×1) is the electric displacement

(Coulomb/K�), � is the strain vector (6×1) (dimensionless),

E is the applied electric field vector (3 × 1) (Volt/m) and

�B is the stress vector (6 × 1) (N/K�). The piezoelectric

constants are the dielectric permittivity @�-� of size (3×3)

(Farad/m), the piezoelectric coefficients A�BC (3×6) and A-�D

(6×3) (Coulomb/N or m/Volt), and the elastic compliance LD�of size (6×6) (K�/N). The piezoelectric coefficient A-�D

(m/Volt) defines strain per unit field at constant stress and A�BC (Coulomb/N) defines electric displacement per unit

stress at constant electric field. The superscripts c and d

have been added to differentiate between the converse and

direct piezoelectric effects, though in practice, these

coefficients are numerically equal. The superscripts � and

E indicate that the quantity is measured at constant stress

and constant electric field respectively. For a sheet of

piezoelectric material, the d matrix can then be expressed

as:

A � M N N NN N NAO AO� AOON AP NA�Q N NN N NR

(24)

where the coefficients AO, AO� and AOO relate the normal

strain in the 1, 2 and 3 directions respectively to a field

along the poling direction, (O. The coefficients AP and A�Q

relate the shear strain in the 1-3 plane to the field ( and

shear strain in the 2-3 plane to the (� field, respectively. In

general, the compliance matrix of viscous material is of the

form

ESF �TUUUUVESES�ESOESQESPESWXYYYYZ �

TUUUUUV� �� �O�� ��� ��O�O �O� �OO�Q �Q� �QO�P �P� �PO�W �W� �WO

�Q �P �W��Q ��P ��W�OQ �OP �OW�QQ �QP �QW�PQ �PP �PW�WQ �WP �WWXY

YYYYZ

(25)

and the permittivity matrix is given by:

@ � [@� N NN @��� NN N @OO� \

(26)

The stress vector is written as:

� �TUUUUV����O�Q�P�WXYYYYZ�TUUUUV�����OO��O�O��XY

YYYZ

(27)

346

In the case of a sensor, where the applied external electric

field is zero, Equation (23) simplifies as:

M%%�%OR � M N N NN N NAO AO� AOO

N AP NA�Q N NN N NR TUUUUV����O�Q�P�WXYYYYZ

(28)

This equation summarizes the principle of operation of

piezoelectric sensors. A stress field causes an electric

displacement to be generated as a result of the direct

piezoelectric effect. Note that shear stress in the 1-2 plane,

�W is not capable of generating any electric response. The

electric displacement D is related to the generated charge

by the relation,

] �^_% %� %O`�MAaAa�AaOR�

(29)

where Aa, Aa� and AaO are the components of the

electrode area in the 2-3, 1-3 and 1-2 planes respectively. It

can be seen that the charge collected, q, depends only on

the component of the infinitesimal electrode area dA

normal to the displacement D. The charge q and the voltage

generated across the sensor electrodes bD are related by the

capacitance of the sensor, cd as:

bD � ]ecd (30)

Therefore, by measuring the charge generated by the

piezoelectric material, from Equations (28) and (29), it is

possible to calculate the stress in the material.

Considering only the effect of strain along the 1-direction,

from Equations (24-30) the voltage generated by the sensor

can be expressed as:

bD � AOfDgDcd h �S Ai (31)

where fD is the Young’s modulus of the piezoelectric

material.

The equation relating strain and voltage generated by the

sensor is given by:

�S � bDcdAOfDgDjD (32)

where typical piezoelectric sheet can be treated as a parallel

plate capacitor, whose capacitance is given by:

cd � �OO� jDgD�D (33)

where jD, gD and �D are length, width, and thickness of the

piezoelectric sensor respectively.

V. MUSCLE DETECTION AND EVALUATION

The muscle deformation is time-dependent, finite and

nonlinear phenomena. It can be determined by using the

constitutive equations based on the theory of hyper-

viscoelasticity. The nonlinear stress response was

characterized using a 2nd order polynomial hyperelastic

strain energy function as the following: k � c��l � m� � c��l� � m� �c�l � m��l� � m����

(34)

where l and l� are strain measured by FBG no. 2 and 3

and are invariants of Cauchy-Green tensor. Therefore, the

values of c�, c�, c can be measured by measuring

wavelength shifting by FBG no 2 and 3 the strain l and l�

can computed. These values then can be used to compute

the force applied and consequently, compared with muscle

databank to indentify the gasped object.

The data representing a time-dependent or viscoelastic

response of materials can be approximated by a Prony

series, based on a relaxation or creep. In large strain

viscoelasticity, the elastic strain energy or the stress is

expressed in terms of Prony series.

���� � � �no�O�4 �� � ���e�p� (35)

with constraints of �� > 0,�o� > 0 and G(0) = 1. A nonlinear

optimization rule was developed to curve-fit the

experimental data to extract material parameters�o, o� ,�oO

, �, ��, �O , hence by finding these parameters of muscle,

the surgeons grasper can makes a sense of tissue softness.

VI. NUMERICAL EXAMPLES

A grasper jaw integrated with FBG sensors and ZnO

piezoelectric sensors as shown in Fig. 1 has been

considered to illustrate the performance of the system. Both

the FBG sensors are mounted at the outer side of the jaw

whereas ZnO piezoelectric is at inner side of the jaw.

Material properties of the FBG and ZnO are given in Table

1 and Table 2 respectively. ANSYS software is used for

modeling the grasper (see Fig. 1) and muscle. Element type

PLANE223, a 2D 8-node coupled-field solid element,

suitable for piezoelectric modeling is used, this element has

three degrees of freedom at each node which are

displacement at x and y directions, and voltage. The

grasper jaw has been meshed with PLANE 82.

Fig.1: Grasper mode in Ansys

347

The model is meshed using

that the temperature

environment is about

wavelength �qrrN� s �Nnumber 2 and FBG

the strain in x and y direction�N�W and

computed from measur

shifting of FBGs number 2 and 3 as

and�qrrtt sstrain results in change in voltage generated by

ZnO voltage is

Stress-Strain which measured by FBG

possible to find

and compare

grasped object

and stress (Mpa) for three

Illiococcygeal, Perineal body)

coefficient of constitutive equation

coefficients,

measured by ZnO

7, respectively.

Centre wavelength

FBG length

Peak reflectivity

Strain range

Strain sensitivity

Strain resolution

Temperature sensitivity

Temperature resolution

Fibre type

MEASURED

Voltage (V/micro m)

The model is meshed using

temperature difference

environment is about

of FBGs change�N�u. Compensating this

2 and FBG number

the strain in x and y direction

and t'm s �N�W,

computed from measurement of reflected

shifting of FBGs number 2 and 3 as s �N�W, respectively

results in change in voltage generated by

voltage is summarized

Strain which measured by FBG

possible to find the viscoelastic parameters,

and compare them with muscle

grasped object. Table 4 provides

and stress (Mpa) for three

Illiococcygeal, Perineal body)

coefficient of constitutive equation

the relaxation (Creep) of these muscles is

measured by ZnO and the

respectively.

MATERIAL PROPERTIES O

Property

E1

E2

G12

�21

�12 ρ

MATERIAL PROPERTIES O

Property

Centre wavelength

FBG length

Peak reflectivity

Strain range

Strain sensitivity

Strain resolution

Temperature sensitivity

Temperature resolution

Fibre type

T

MEASURED SHEAR BY

Time step vwx (Pa)

Voltage (V/micro m)

Nq��s�N

�

The model is meshed using 2000 plane elements.

difference inside

environment is about tyC, therefore,

changes from

ompensating this difference

number 3, as shown by

the strain in x and y directions are determined as

respectively.

ement of reflected

shifting of FBGs number 2 and 3 as

respectively. Similarly, the change in

results in change in voltage generated by

summarized in Table 3.

Strain which measured by FBG number

the viscoelastic parameters,

with muscle databank

provides the result

and stress (Mpa) for three different muscles

Illiococcygeal, Perineal body). Table 5 shows the fitted

coefficient of constitutive equation.

relaxation (Creep) of these muscles is

results are shown in Table 6 and

TABLE1

ATERIAL PROPERTIES OF ZN

value

113.9 GPa

7.9856 GPa

3.138 GPa

0.0178

0.288

1480 kg/m3

TABLE2

ATERIAL PROPERTIES OF THE FBG

Value

1510 – 1590 nm

5 mm

70 %

+/- 9,000 > +/- 9,000

1.20 pm/

0.4 strain

Temperature sensitivity 11 pm/°C

Temperature resolution 0.05°C

Single Mode

TABLE 3

HEAR BY ZNO RESPECT TO TIME

z{�1 z{�2 z{ 31237 4011 6685

Nq��s�N

�

Nq|�s�N

�W Nq��

s�N�W

Nq�rs�N

�P

elements. Assum

inside the body

, therefore, the reflected

from �qrr s �N�udifference in FBG

as shown by Figs 4 and 5,

determined as ��tr These values are

ement of reflected wavelength

shifting of FBGs number 2 and 3 as �qrrmr s �NSimilarly, the change in

results in change in voltage generated by ZnO.

. Finally, by using

number 2 and 3,

the viscoelastic parameters, c� , c� ,

databank to identify the

the results of strain (

muscles (Pubovisceral

able 5 shows the fitted

For Prony series

relaxation (Creep) of these muscles is

shown in Table 6 and

NO

113.9 GPa

7.9856 GPa

3.138 GPa

3

FBG

Value

1590 nm

5 mm

70 %

9,000 strain

strain

strain

11 pm/°C

0.05°C

Single Mode

RESPECT TO TIME

z{ 4 z{ 5

9359 12033

Nq�rs�N

�P Nq�}

s�N�P

Assuming

body and

the reflected u to

in FBG

igs 4 and 5, ��tr svalues are

wavelength �N�W

Similarly, the change in

The

, by using

3, it is

, c

identify the

strain (%)

(Pubovisceral,

able 5 shows the fitted

Prony series

relaxation (Creep) of these muscles is

shown in Table 6 and

Fig.3: Reflected wavelenght for

Fig.4: Reflected wavelenght for

Fig.5: Reflected wavelenght for

Re

fle

cti

vit

yR

efl

ec

tiv

ity

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Re

fle

cti

vit

y

FIG.2: THE STRAIN

Fig.3: Reflected wavelenght for

Fig.4: Reflected wavelenght for

increasing temrature by a FBG No.2

Fig.5: Reflected wavelenght for

increasing temrature by a FBG No.3

2.548 2.5485 2.549

0

0.2

0.4

0.6

0.8

1

FBGs reflected power by increasing 4o centigrade

Re

fle

cti

vit

y

1.52 1.530

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1FBGs reflected power due to 1245 micro Strain in x Direction

Main Reflected

Strain Reflected

1.52 1.530

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1FBGs reflected power due to 463 micro strain in y direction

HE STRAIN – WAVELENGTH RELATION

Fig.3: Reflected wavelenght for 4oC increasing temrature

Fig.4: Reflected wavelenght for 1245 micro

increasing temrature by a FBG No.2

Fig.5: Reflected wavelenght for 463 micro strain tension in y direction

increasing temrature by a FBG No.3

2.549 2.5495 2.55

FBGs reflected power by increasing 4o centigrade

wavelength

1.54 1.55

FBGs reflected power due to 1245 micro Strain in x Direction

wavelength

Main Reflected

Strain Reflected

1.54 1.55

FBGs reflected power due to 463 micro strain in y direction

wavelength

WAVELENGTH RELATION IN FBG

increasing temrature by a FBG

45 micro strain tension in x direction

increasing temrature by a FBG No.2

micro strain tension in y direction

increasing temrature by a FBG No.3

2.5505 2.551 2.5515

FBGs reflected power by increasing 4o centigrade

Main Spectrum

Reflected Specrum

1.56 1.57 1.58

FBGs reflected power due to 1245 micro Strain in x Direction

1.56 1.57 1.58

FBGs reflected power due to 463 micro strain in y direction

FBG

by a FBG No.1

strain tension in x direction

micro strain tension in y direction

2.5515

x 10-7

Main Spectrum

Reflected Specrum

1.58

x 10-6

1.58

x 10-6

348

TABLE 4

MEASURED STRAIN AND STRESS BY FBGS ON THREE DIFERENT MUSCLE

Stress (Mpa) Strain (%)

Pubovisceral Illiococcygeal Perineal body

0 0 0 0

0.1 0.007 0.009 0.014

0.2 0.008 0.009 0.015

0.3 0.017 0.011 0.02

0.4 0.022 0.016 0.028

0.5 0.039 0.022 0.043

0.6 0.041 0.031 0.061

0.7 0.043 0.044 0.094

TABLE 5

CALCULATED CONSTITUTIVE EQUATIONS COEFICIENT FOR THREE

DIFERENT MUSCLE

Muscle Type C10 C01 C11

Pubovisceral -0.106 0.129 0.038

Illiococcygeal -0.2 0.244 0.069

Perineal body -0.03 0.04 0.019

TABLE 6

MEASURED SHEAR BY ZNO AND RELATED GREEP FOR THREE DIFERENT

MUSCLE WITH RESPECT TO TIME

Relaxation

Time (Sec) Pubovisceral Illiococcygeal Perineal body

0 1 1 1

0.01 0.99 0.99 0.99

0.1 0.95 0.96 0.95

0.5 0.9 0.92 0.91

1 0.7 0.79 0.72

2 0.62 0.7 0.64

3 0.6 0.68 0.6

TABLE 7

PRONY SERIES COEFICIENT FOR THREE DIFERENT MUSCLE

Muscle Type ~� ~� ~� v� v� v�

Pubovisceral 0.325 0.308 0.179 11.39 0.708 297.99

Illiococcygeal 0.25 0.265 0.19 18.4 0.907 483.47

Perineal body 0.346 0.335 0.183 15.397 0.968 357.05

VII. CONCLUSION

The multi sensing of graspers for minimal invasive surgery

with embedded ZnO piezoelectric and Fiber Bragg Grating

sensors was studied. The feature of high sensitivity in time

and good resistance to temperature of ZnO, it is used for

measuring the rate of strain of muscles and using the

electromechanical coupling of ZnO, and Prony series

coefficients determined by measuring the rate of change of

muscle’s creep. The optomechanical relations between

strains and FBG reflected wavelength shifting caused by

strain displacement in x and y directions, has been studied

to determine the Cauchy-Green tensor equation for three

different types of common body muscles. By finding Prony

series coefficients and Cauchy-Green tensor equation, three

types of common body muscles diagnosed separately.

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