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August 10, 2018
Retraction NoticeRetraction Notice: Chen L, Ke A, Zhang P, Gao Z, Zou X, He J. (2018) Bioheattransfer model of transcutaneous spinal cord stimulation-inducedtemperature changes. PeerJ 6:e4921 https://doi.org/10.7717/peerj.4921
The authors wish to Retract this article. Upon publication it was realized thatcertain research collaborators had not been appropriately notified of thepublication and therefore they had not been able to provide input into thearticle, nor to approve the final publication. All authors on this article agree tothis Retraction.
PeerJ Editorial Office. 2018. Retraction: Bioheat transfer model oftranscutaneous spinal cord stimulation-induced temperature changes. PeerJ6:e4921/retraction https://doi.org/10.7717/peerj.4921/retraction
Bioheat transfer model of transcutaneousspinal cord stimulation-inducedtemperature changes
Luyao Chen1,2,3, Ang Ke2,3, Peng Zhang2,3, Zhaolong Gao2,3,Xuecheng Zou1 and Jiping He2,3,4
1 School of Optical and Electronic Information, Huazhong University of Science and Technology,
Wuhan, China2 Neural Interface and Rehabilitation Technology Research Center, School of Automation,
Huazhong University of Science and Technology, Wuhan, China3 Collaborative Innovation Center for Brain Science, Huazhong University of Science and
Technology, Wuhan, China4Advanced Innovation Center for Intelligent Robots and Systems, Beijing Institute of Technology,
Beijing, China
ABSTRACT
Transcutaneous spinal cord stimulation (tSCS) has been extensively studied due
to its promising application in motor function restoration. Many previous studies
have explored both the essential mechanism of action and the methods for
determining optimal stimulation parameters. In contrast, the bioheat transfer
analysis of tSCS therapy has not been investigated to the same extent, despite widely
existing, and being of great significance in assuring a stable and thermally safe
treatment. In this paper, we concentrated on the thermal effects of tSCS using a finite
element-based method. By coupling the electric field and bioheat field, systematic
finite element simulations were performed on a human spinal cord model to survey
the influence of anatomical structures, blood perfusion, and stimulation parameters
on temperature changes for the first time. The results show that tSCS-induced
temperature rise mainly occurs in the skin and fat layers and varies due to individual
differences. The current density distribution along with the interactions of multiple
biothermal effects synthetically determines the thermal status of the whole spinal
cord model. Smaller stimulation electrodes have a higher risk of thermal damage
when compared with larger electrodes. Increasing the stimulation intensity will
result in more joule heat accumulation, hence an increase in the temperature.
Among all configurations in this study that simulated the clinical tSCS protocols, the
temperature rise could reach up to 9.4 �C on the skin surface depending on the
stimulation parameters and tissue blood perfusion.
Subjects Bioengineering, Neuroscience, Computational Science
Keywords Transcutaneous spinal cord stimulation, Bioheat transfer, Finite element analysis,Temperature distribution
INTRODUCTIONTranscutaneous spinal cord stimulation (tSCS) is a non-invasive and low-cost technique
that has already shown promising effects in the neuromodulation of motor control
(Gerasimenko et al., 2015a, 2015b; Krenn et al., 2015; Minassian et al., 2016). By passing
How to cite this article Chen et al. (2018), Bioheat transfer model of transcutaneous spinal cord stimulation-induced temperature
changes. PeerJ 6:e4921; DOI 10.7717/peerj.4921
Submitted 10 January 2018
Accepted 17 May 2018
Published 4 June 2018
Corresponding author
Xuecheng Zou,
Academic editor
Tjeerd Boonstra
Additional Information and
Declarations can be found on
page 21
DOI 10.7717/peerj.4921
Copyright
2018 Chen et al.
Distributed under
Creative Commons CC-BY 4.0
currents through the skin and targeting neural circuits in the lumbosacral spinal cord,
lower limb motor function could be restored to a certain extent for patients with spinal
cord injury. Despite the breakthroughs in both modeling studies and clinical experiments,
the risk of thermal damage caused by tSCS cannot be ignored. Skin burns have been
suggested to be the major obstacle for transcutaneous electrical stimulation-based
therapies according to Nadler’s retrospective questionnaire study (Nadler et al., 2003).
Thermal damage caused by continuous stimulation induced an uncomfortable sensation,
thus restricting the further application of the non-invasive therapy (Patriciu et al., 2001,
2005; Lagopoulos & Degabriele, 2008). Previous reports on the skin burns caused by
transcutaneous electrical stimulation indicated the significant role of the electrode
properties and stimulation parameters on the bioheat accumulation and transference
(Balmaseda et al., 1987; Patriciu et al., 2001; Ford et al., 2005; Satter, 2008;
Sharma et al., 2011).
Commonly, joule heat will be generated in any electrical field where electrical current
is circulating. Thus, it is inevitable that thermal energy is accumulating during tSCS as
the electrical current is delivered through the biological tissues by the electrode pairs.
Additionally, the Pennes model (Pennes, 1948) indicated that the contribution of
physiological procedures, such as the metabolic heat generation and blood perfusion,
in determining the thermal status. The synthetic and complex interaction of these internal
and external heat sources and heat sinks could result in either slight or severe temperature
rises during electrical stimulation treatments depending on the tissue properties and
stimulation parameters.
Finite element calculation is an efficient tool to explore both the electrical and
thermal field distribution with the help of accurate anatomical models. Previous
numerical studies based on spinal cord modeling have already clarified valuable
information regarding the electrical field distribution and nerve fiber response. It was
demonstrated that both the anterior and posterior root fibers can be activated by tSCS,
which covers the targeting regions of epidural spinal cord stimulation, and offers evidence
for the lower limb muscle responses induced by transcutaneous posterior root stimulation
(Ladenbauer et al., 2010). More recently, Kuck’s group concluded from their spinal
cord and axon modeling study that the current density induced by tSCS is sufficiently
strong to evoke functional modulation (Kuck, Stegeman & van Asseldonk, 2017). Those
studies showed that tSCS with proper stimulation parameters can become a promising
noninvasive modality in the rehabilitation of people suffering related neural disorders.
While most of the existing research focuses on verifying the efficacy and searching for
a proper stimulation protocol for tSCS (Ladenbauer et al., 2010; Danner et al., 2011;
Gerasimenko et al., 2015a), insufficient efforts have been put towards investigating the
bioheat transference of this promising therapy which is significant in evaluating the
safety of the treatment.
In this paper, we tested the impact of several biological and stimulation properties on
the bioheat transfer, including the thicknesses of the skin and fat layers, the blood
perfusion rate of the dermis and neural tissue, electrical stimulation intensities, and
the size of the stimulation electrode. A finite element human spinal cord model was
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 2/25
built to simulate the electrical and thermal field during continuous tSCS. Parameter
sweeping studies were used to compare the electrical field distribution and the
temperature changes during stimulation. Prior to clinical research, this work provides a
systematic description of analyzing the thermal issues related to the tSCS treatment.
MATERIALS AND METHODS
Finite element spinal cord model with transcutaneous electrodes
A three-dimensional human spinal cord model was constructed based on a model from a
previous study (Ladenbauer et al., 2010). We first constructed a two-dimensional
model including tissues such as the gray matter (GM), white matter (WM), cerebral
spinal fluid (CSF), epidural fat (EF), vertebrae (Vert), and muscles, by referring to the
geometry and size of Ladenbauer’s model. The model was then imported to COMSOL
Multiphysics (COMSOL Inc., Burlington, MA, USA), and layered cylinders were used to
represent the boundary of the fat and three-layered skin with stratum corneum (SC),
epidermis (ED), and dermis. A symmetrical three-dimensional model was finalized by
extruding the surface model as shown in Fig. 1A. In this work, to study the impact of
individual anatomical differences on temperature variance, different models with various
skin and fat layer thicknesses were formulated and simulated. It is believed that
Figure 1 Human spinal cord model and the transcutaneous electrodes. (A) Two-dimensional spinal cord model and the extruding direction to
form the three-dimensional model. (B) The three-dimensional full spinal cord model with the stimulation electrode placed on the surface of the
skin. The side length of the electrode is 1 cm. The surface highlighted in blue color is defined as the stimulation surface. (C) The spinal cord model
with the return electrode. The side length of the return electrode is 5 cm. The surface highlighted in blue color is defined as the return surface.
(D) The central cross-sectional surface of the spinal cord model across the centers of the stimulation surface and the return surface. (E) Detailed
view of the cross-sectional surface of the spinal cord. A central line across the center of the stimulation surface and the return surface is defined in
red. (F) Magnified view of the central parts of the spinal cord. Full-size DOI: 10.7717/peerj.4921/fig-1
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 3/25
the thickness of the surface skin layers outside the dermis is approximately 100 mm
and that of the SC layer varies from 10 to 40 mm. In the simulations, SC thicknesses of
10, 20, 30, and 40 mm were tested, and the corresponding ED layer was 90, 80, 70, or
60 mm in thickness, respectively. Furthermore, previous studies set the thickness of the
fat layer at 10 mm (Lv & Liu, 2007) or 4.4 mm (Xu et al., 2008) and thickness of the
dermis layer at 1.5 mm (Xu et al., 2008) or 2 mm (Lv & Liu, 2007). Therefore, we created
models with dermis thicknesses of 1, 1.5, and 2 mm, and models with fat thicknesses from
4 to 16 mm with 2 mm steps to cover the reference range. As the control model, the
thicknesses of the SC/ED/dermis/fat were set to 20/80 mm/2/10 mm, respectively. Before
tSCS, the 1 � 1 cm � 2 mm (length � width � depth) stimulation electrode was
symmetrically placed over the spine and a 5 � 5 cm � 2 mm (length � width � depth)
return electrode was fixed over the abdomen of the model as shown in Figs. 1B and 1C,
respectively. In this work, stimulation electrodes with the side lengths of 1, 1.5, and 2 cm
were made to simulate the impact of electrode size on the thermal accumulation
during tSCS.
Before starting the simulations, the spinal cord model with electrodes was meshed
using tetrahedral and swept methods. The main element size parameters used to define
the mesh settings included the maximum element size, minimum element size, maximum
element growth rate, curvature factor, and resolution of narrow regions. We first used a
free tetrahedral mesh for the stimulation and return electrodes with element size
parameters of 0.0219, 0.0016 m, 1.4, 0.4, and 0.7 corresponding to the above-mentioned
parameters, respectively. Since the structure of the SC and ED layers are characterized
by an extremely high surface area-to-thickness ratio, a prior triangular mesh with
element size parameters of 0.005, 2.67E-4 m, 1.08, 0.3, and 0.95 was applied to the skin
surfaces followed with a swept mesh for the whole volumes of the two tissue types.
The distribution properties of the swept mesh were set as a fixed number of elements, four
for the SC layer and 16 for the ED for the control model, and varied correspondingly with
the thickness of the skin layers. A finer mesh was chosen for the skin layers, while a coarser
mesh was applied to the remaining tissues using a free tetrahedral method. The
corresponding element size parameters were 0.0319, 0.00399 m, 1.45, 0.5, and 0.6
respectively. The mesh statistics of the control model are shown in Table 1. A convergence
study was conducted to determine the proper meshing sizes by tracking the peak
temperature with the total meshing elements. Consequently, a trade-off between the
computational time and accuracy was reached at a total of 0.63 million elements as
shown in Table 1. In order to illustrate and analyze the simulation results, two reference
surfaces and a reference line of the spinal cord model were defined, i.e., the skin
surface beneath the stimulation electrode as shown in Fig. 1B, the cross-sectional surface
as shown in Fig. 1D, and the red line as shown in Fig. 1E. Figure 1F shows the detailed
anatomical structure of the spinal cord.
Bioheat model during tSCS
During tSCS, the heat sources include joule heat and metabolic heat, while the heat
dissipation process consists of the blood perfusion effect and heat convection effect
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 4/25
between air and skin or electrode surface as shown in Fig. 2. Based on the Pennes
model (Pennes, 1948), we added the joule heat induced by the electrical field as an extra
heat source as expressed in Eq. (1). Furthermore, the heat convection is considered in
the SC and electrode surfaces as shown in the last term of the Eq. (1).
c�@T
@t¼ r � krTð Þ þ ~J
�
�
�
�
2=�þ QM � !b�bcb Tb � Tð Þ � h T � Textð Þ (1)
Where T, c, and ρ represent the temperature (�C), specific heat (J/kg-K), and density
(kg/m3) of a specific tissue type, respectively, and Tb, cb, ρb, and vb represent the blood
temperature (�C), blood specific heat (J/kg-K), blood density (kg/m3), and blood
perfusion rate (s-1), respectively, k is the thermal conductivity (W/m-K), t represents
stimulation time (s), J represents the current density distribution (A/m2), s is the electric
conductivity (S), QM is the metabolic heat (W/m3), h is convective heat transfer
coefficient (W/m2-K), and Text is the external air temperature (�C). Specifically, the initial
temperature of the biological tissues were set at 37 �C, Text at 25�C, and h is 1.86 and
7.9 for the skin surface (de Dear et al., 1997) and electrode surface (The Engineering
ToolBox, 2018), respectively. In the steady state, the Laplace equation, ∇·(s∇V) = 0, is used
to determine the potential distribution V (V) among the tissues, which could then be used
Table 1 The mesh statistics.
Mesh statistics parameter Value
Number of tetrahedral elements 3.1E5
Number of prism elements 3.2E5
Number of triangular elements 1.0E5
Number of Quadrilateral elements 1.2E4
Minimum element quality 0.7818
Average element quality 0.03521
Element volume ratio 9.67E-7
Element volume 0.01157 m3
Note:The stimulation electrode size is 1cm in length and width, the thickness of the tissues are: fat = 10 mm, dermis = 2 mm,epidermis = 80 mm, SC = 20 mm.
Figure 2 Bioheat transfer model during tSCS. Full-size DOI: 10.7717/peerj.4921/fig-2
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 5/25
to calculate the electric field and current density in a further step. The initial electric
condition was determined byV = 0. Note that the outer boundaries of the spinal cord were
selected as electrical insulations, where ∂V/∂n = 0. Except for the skin surface, which was
treated as a heat convective flux, other outer boundaries were thermally insulated and
defined as ∂T/∂n = 0. All the internal boundaries with two interfacing tissue layers were
treated as electrically and thermally continuous. Additionally, in this work, we treat
metabolic heat generation as zero or constant values, as listed in Table 2.
In the present simulation studies, except for the isotropic electrical properties of the
muscles and WM, all biological compartments are considered as pure resistors under
constant stimulation. The electrical and thermal properties of the tissues are listed in
Table 2. As for the stimulation intensity, we modeled the commonly used alternating
current input as an equivalent constant value under the principle that the total joule
heat energy caused by both stimulation signals during the same amount of stimulation
period are the same. Thus, a sequence of biphasic pulses repeated at fLwith an amplitude
of Ip would be equivalent to a constant current Irms as represented in Eq. (2), where
N indicates the number of the pules at a frequency of fH.
Irms ¼ Ip�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N�fL=fHp
(2)
To cover most of the parameter settings utilized in recent clinical applications, we
swept the constant current from 0 to 40 mA in this work. The total stimulation time
was set at 15 min, which was enough for the model to reach a stable peak temperature
(Chen et al., 2017; Khadka et al., 2017). The time-dependent study was chosen with a
maximum time step of 10 s under a peak relative tolerance of 0.01. A parametric sweep
was added to test the impact on the biothermal status of the blood perfusion rate
Table 2 Properties of the biological tissues.
Biological
tissues
Blood perfusion
rate v (1/s)
Metabolic heat
generation QM (W/m3)
Thermal conductivity
k (W/m-K)
Electrical conductivity
s (S/m)
SC 0 368.1 0.235 0.0025
ED 0 368.1 0.235 0.15
Dermis 0.012 368.1 0.445 1.62
Fat 0.0035 368.3 0.185 0.02383
Abdomen 0.3 180 0.52 0.0414
Muscle 0.00017 690 0.498 0.081/0.52
Vert 0.0003 368.3 0.3 0.0285
EF 0.0035 368.3 0.21 0.04
CSF 0 0 1.12 1.7
GM 0.012 10,000 0.565 0.23
WM 0.012 10,000 0.503 0.0831/0.62
Notes:1 Transversal;2 Longitudinal.Schwan & Kay (1957), Tavernier, Dierickx & Hinsenkamp (1992), Gabriel, Gabriel & Corthout (1996), Xu et al. (2008), Smith & Zhu (2010), Danner et al. (2011), Parazziniet al. (2014), and Miller et al. (2016).
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 6/25
and stimulation intensity on the control model as described in “Finite Element Spinal
Cord Model with Transcutaneous Electrodes.” The sweeping parameters were 0, 5, 10, 20,
30, and 40 mA for the stimulation intensity, 0, 0.025, 0.05, and 0.1 s-1 for the blood
perfusion rate of the dermis, and 0, 0.004, 0.008, and 0.012 s-1 for the blood perfusion
rate of the WM/GM. Simulations aimed at testing the impact of the anatomical
parameters set the stimulation intensity and the blood perfusion rate of the dermis and
WM/GM at 20 mA, 0.025, and 0.012 s-1, respectively. As for data analysis, temperature
change curves vs. stimulation time were recorded, as well as the electrical and thermal
distributions among the reference faces or line induced by the various tSCS
configurations.
RESULTS
Effects of skin or fat thickness on the temperature distribution
induced by tSCS
The thicknesses of the skin and fat layers vary by individual (Mathias & Srinivas Murthy,
2017). Figures 3A–3D, 3E–3H, and 3I–3L show the results of different SC/ED thicknesses,
dermis thicknesses, and fat thicknesses, respectively, on the temperature distribution during
tSCS at 20 mA. Peak temperatures for the skin layers, fat, abdomen, muscles, and the Vert at
the end of the stimulation varied with the changes of tissue thickness, whereas those of the
EF, CSF, and WM/GM remained the same. Figures 3B, 3F, and 3J show the temperature
distribution along the reference line defined in Fig. 1E. The results show that with an
increase in the SC layer thickness or decrease in the dermis layer thickness, the temperature
of the skin and fat layers becomes higher, which is consistent with the results shown in
Figs. 3A and 3E. The peak temperature of the whole biological model reached as high as 40.8
and 40.0 �C when the thicknesses of SC/ED/dermis were 40/60 mm/2 mm and 20/80 mm/1
mm, respectively. As for the changes of the fat thickness, no consistent pattern could be
identified for the peak temperature of the skin and fat layers from Figs. 3I–3J. In contrast,
the peak temperatures of the abdomen, muscles, and Vert decreased with an increase in the
fat thickness to 12 mm. However, for even thicker fat, the peak values remained unchanged.
We recorded the coordinates of the points with the peak temperature for each tissue type
and tracked their temperature change curves over time as shown in Figs. 3C–3D, 3G–3H,
and 3K–3L for different variables. A pattern seen across the figures, is that the temperature
of the skin and fat layers rises rapidly once the stimulation is turned on and then reaches a
plateau. The SC and ED layers share similar temperature distribution and the rising
curves of the peak temperature points almost overlapped in every simulation. With the
decrease of the SC layer thickness and increase of the dermis layer thickness, the peak
temperature points of the dermis layer were closer to those of the SC/ED layers as shown
in Figs. 3C and 3G. Similarly, the rising curves of the peak temperature points in the
muscles and Vert overlapped in each of the simulations and that of the EF, CSF, and
GM/WM overlapped in all simulations. The results revealed the significance of designing
customized stimulation protocols for individuals by considering the thicknesses of the
skin and fat layers.
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 7/25
Figure 3 Effects of the tissue thickness on the thermal status during tSCS. (A–D) The thickness of the SC layer varies from 10 to 40mm. Dermis =
2 mm. Fat = 10 mm. (E–H) The thickness of the dermis layer varies from 1 to 2 mm. SC = 20 mm. Fat = 10 mm. (I–L) The thickness of the fat layer
varies from 4 to 16 mm. SC = 20 mm. Dermis = 2 mm. (A), (E), (I) The peak temperature values of each tissue type at the end of tSCS. (B), (F), (J)
Temperature distribution at the end of tSCS along the reference line defined in Fig. 1E. Insets in (B) and (F): Magnified view of the parts across the
SC/EF/Dermis skin layers. (C–D), (G–H), (K–L) Temperature rising curves of the points with peak temperature variance for each tissue type. The
stimulation intensity is 20 mA, the stimulation electrode side length is 1 cm, and the blood perfusion rate of the dermis and WM/GM are 0.025 and
0.012 s-1, respectively. Full-size DOI: 10.7717/peerj.4921/fig-3
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 8/25
Effects of blood perfusion on the temperature distribution
induced by tSCS
It is known that blood perfusion varies with tissue temperature (Tompkinsn et al., 1994);
whether and to what extent the varied blood perfusion rate could influence bioheat
transfer and the biothermal status will be investigated in this section. In this section, the
stimulation intensity was chosen to be 20 mA and the electrode was 1 cm in side length.
Figures 4A–4B and 5A–5B show the peak temperature values of each tissue type and
temperature distribution along the reference line when the tSCS finished. The results
suggest that temperature changes induced by tSCS with different blood perfusion rate
mainly occur in the skin and fat layers, abdomen, muscles and Vert, for the dermis, and in
the Vert, EF, CSF, and WM/GM for the WM/GM.
The peak temperature of the whole biological model could reach 41.7 �C if the blood
perfusion rate of the dermis layer was set to 0. Figures 4C and 4D shows the peak
temperature rising curves of the biological tissues at the end of the stimulation. In general,
the peak temperature decreases with an increasing blood perfusion rate of the dermis,
Figure 4 Effects of the blood perfusion of the dermis layer on the thermal status during tSCS.
(A) The peak temperature values of each tissue type at the end of the electrical stimulation. (B)
Temperature distribution along the reference line at the end of tSCS. (C–D) Temperature rising curves of
the points with peak temperature variance for each tissue type. The stimulation intensity is 20 mA, the
stimulation electrode side length is 1 cm, and the blood perfusion rate of theWM/GM is 0.012 s-1. The unit
of the blood perfusion rate is s-1. Full-size DOI: 10.7717/peerj.4921/fig-4
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 9/25
consistent with previous publications (Elwassif et al., 2006; Xu et al., 2008). Specifically,
the peak temperature of the whole model is 41.7, 38.8, 38.3, and 37.9 �C when the
dermis blood perfusion rate is 0, 0.025, 0.5, and 0.1 s-1, respectively. The temperature
distribution among the reference surfaces in Fig. 6 demonstrates the influence of the
dermis blood perfusion on the thermal status after 15 min tSCS. The peak temperature of
the whole model is always located in the SC skin layer and the ED layer has a similar
temperature distribution to the SC layer. With a decrease in the dermis blood perfusion,
the difference of the peak temperature between the dermis and SC/ED becomes
smaller. Moreover, with lower blood perfusion rates, heat seems more likely to accumulate
in the deeper tissues, which may cause risk to the deep tissues, if intense stimulation
parameters are applied at the same time.
Similarly, temperature rising curves of the points with peak temperature variance for
the spine tissues are shown in Fig. 5C and the temperature distribution in the spine are
shown in Fig. 7 with different blood perfusion rate of the WM/GM. The temperature
variance of the neural tissues is about 0.2 �C for 0.012 s-1. However, without blood
perfusion of theWM/GM, the peak temperature of the tissues in the spine, which is always
located in the WM/GM, would be 37.4 �C. This may due to the fact that slower blood
perfusion in the WM/GM results in greater heat accumulates in the matters according to
the bioheat model in Eq. (1). The extra heat dissipates from the deep neural tissues to the
surrounding CSF, EF, and Vert, resulting in temperature rises in these tissues.
Effects of the electrode size on the temperature distribution
induced by tSCS
Setting the stimulation intensity at 40 mA, three models, with stimulation electrode
with a side length of 1, 1.5, or 2.0 cm, were simulated to investigate the effects of electrode
size on the temperature distribution during tSCS.
Figure 5 Effects of the blood perfusion of the WM/GM on the thermal status during tSCS. (A) The peak temperature of each tissue type at the
end of the electrical stimulation. (B) Temperature distribution along the reference line at the end of tSCS. (C) Temperature rising curves of the points
with peak temperature variance for the spine tissues. The stimulation intensity is 20 mA, the stimulation electrode side length is 1 cm, and the blood
perfusion rate of the dermis layer is 0.025 s-1. The unit of the blood perfusion rate is s-1. Full-size DOI: 10.7717/peerj.4921/fig-5
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 10/25
Theoretically, a larger contact area means smaller current density, thus less joule
heat is produced. Hence, larger-size electrodes should cause smaller temperature rises.
Figure 8 shows the current density distribution of the cross-sectional and stimulation
surfaces. The middle three figures magnify the regions near the stimulation electrode
and show relatively higher current density distribution than the deep tissues. The peak
current density of the stimulation surface using 1-cm electrode is 1.66 and 2.52 times
of that using the 1.5 and 2-cm electrode, respectively. Due to the edge effect, tissues
beneath the edges of the stimulation electrode especially attract more current density.
As for the thermal field, Fig. 9A shows the peak temperature of the biological tissues
and Fig. 9B shows the temperature distribution along the reference line using electrodes
with different sizes. Accordingly, temperature variance between the three electrodes
mainly occurred in the skin layers and fat layer. As for the abdomen, muscles, and Vert,
the peak temperature variance was relatively small and less than 0.3 �C. With the increase
of the electrode size, the peak temperature rise of the whole model caused by tSCS
decreased from 9.4 �C for the 1-cm electrode to 2.1 �C for the 1.5-cm electrode, and
becomes negligible when the side length is increased to 2 cm. For a detailed view, Fig. 10
shows the temperature distribution across the cross-sectional surface and the stimulation
Figure 6 Temperature distribution at the end of stimulation for varied blood perfusion rate of the dermis layer. (A–C) The blood perfusion
rate of the dermis is 0 s-1. (D–F) The blood perfusion rate of the dermis is 0.025 s-1. (G–I) The blood perfusion rate of the dermis is 0.05 s-1. (J–L)
The blood perfusion rate of the dermis is 0.1 s-1. (A, D, G, J) The temperature distribution on the cross-sectional surface for different perfusion rate
of the dermis layer. (B, E, H, K) The magnified view of the hot area, i.e. the skin and fat layers (circled in (A, D, G, J) respectively). (C, F, I, L) The
temperature distribution of the abdomen, muscles and the vertebrae. The stimulation intensity is 20 mA, the stimulation electrode side length is
1 cm, and the blood perfusion rate of the WM/GM is 0.012 s-1. The maximum andminimum temperature values are shown with the corresponding
color bars in each panel. Unit: �C. Full-size DOI: 10.7717/peerj.4921/fig-6
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 11/25
surface at the end of the stimulation. To exaggerate the temperature differences
induced by the electrode sizes, we magnified the specific parts circled in the first row
and separately demonstrated the temperature distribution in the abdomen, muscles, and
Vert as shown in the second and third row. The results indicate that larger electrodes deliver
weaker current density and cause smaller temperature rises, which is consistent with the
theory. It can be concluded that larger stimulation electrodes are thermally safer for
tSCS and could bear more intense stimulation when compared with smaller ones.
Effects of stimulation intensity on the temperature distribution
induced by tSCS
Unlike ESCS where the stimulation electrode is placed very close to the modulating
targets, tSCS uses electrodes on the skin surface. Consequently, to activate the nerves or
neurons locate in the WM/GM, more amount of electric power is needed to be delivered
through the layered tissues. According to Eq. (1), the input current intensity directly
affects the amount of joule heat accumulation in a square way, therefore negligible
Figure 7 Temperature distribution of the spine at the end of stimulation for varied blood perfusion
rate of the WM/GM. (A) The blood perfusion rate of the GM/WM is 0 s-1. (B) The blood perfusion rate
of the GM/WM is 0.004 s-1. (C) The blood perfusion rate of the GM/WM is 0.008 s-1. (D) The blood
perfusion rate of the GM/WM is 0.012 s-1. Tissues include vertebrae, epidural fat, CSF, WM, and GM.
The stimulation intensity is 20 mA, the stimulation electrode side length is 1 cm, and the blood
perfusion rate of the dermis is 0.025 s-1. The maximum and minimum temperature values are shown
with the corresponding color bars in each panel. Unit: �C.
Full-size DOI: 10.7717/peerj.4921/fig-7
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 12/25
Figure 8 Current density distribution of the reference surfaces for stimulation electrodes with different sizes. (A–C) The side length of the
stimulation electrode is 1 cm. (D–F) The side length of the stimulation electrode is 1.5 cm. (G–I) The side length of the stimulation electrode is 2 cm.
(A, D, G) The current density distributions on the cross-sectional surface for different electrode sizes. (B, E, H) Themagnified view of the circled area in
(A, D, G) respectively, i.e. the skin and fat layers. (C, F, I) The current density distributions on the stimulation surface. The stimulation intensity is
40 mA, and the blood perfusion rate of the dermis and WM/GM are 0.025 s-1 and 0.012 s-1 respectively. The maximum and minimum temperature
values are shown with the corresponding color bars in each panel. Unit: A/m2. Full-size DOI: 10.7717/peerj.4921/fig-8
Figure 9 Effects of the stimulation electrode size on the thermal status during tSCS. (A) The peak
temperature values of each tissue type at the end of the electrical stimulation with different electrode
sizes. (B) Temperature distribution along the reference line at the end of tSCS. The stimulation intensity
is 40 mA, and the blood perfusion rate of the dermis and WM/GM are 0.025 and 0.012 s-1, respectively.
Full-size DOI: 10.7717/peerj.4921/fig-9
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 13/25
temperature rises may occur with an increase of the input current. To verify the effects of
stimulation intensity on temperature variance, we swept the equivalent input current
from 5 to 40 mA, covering a wide range of stimulation signals with different pulse
Figure 10 Temperature distribution induced by tSCS using electrodes with different sizes. (A–D) Electrode side length = 1 cm. (E–H) Electrode
side length = 1.5 cm. (I–L) Electrode side length = 2 cm. (A, E, I) The temperature distributions on the cross-sectional surface for different electrode
sizes. (B, F, J) The magnified view of the hot area (circled in (A, E, I) respectively), i.e. the skin and fat layers. (C, G, K) The temperature distribution
of the abdomen, muscles and the vertebrae. (D, H, L)The temperature distribution on the stimulation surface. The stimulation intensity is 40 mA,
and the blood perfusion rate of the dermis andWM/GM are 0.025 s-1 and 0.012 s-1 respectively. The maximum and minimum temperature values
are shown with the corresponding color bars in each panel. Unit: �C. Full-size DOI: 10.7717/peerj.4921/fig-10
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 14/25
Figure 11 Current density distribution for different stimulation intensities. (A–C) Stimulation time = 0 mA. (D–F) Stimulation time = 5 mA.
(G–I) Stimulation time = 10 mA. (J–L) Stimulation time = 20 mA. (M–O) Stimulation time = 30 mA. (P–R) Stimulation time = 40 mA. (A, D, G, J,
M, P) The current density distribution on the cross-sectional surface for different stimulation intensities. (B, E, H, K, N, Q) the middle one is
magnified detailed view of the circled area in (A, D, G, J, M, P) respectively, i.e. the skin and fat layers. (C, F, I, L, O, R) The temperature distribution
of the vertebrae, epidural fat, CSF, WM, and GM. The stimulation electrode side length is 1 cm, and the blood perfusion rate of the dermis and
WM/GM are 0.025 s-1 and 0.012 s-1 respectively. The maximum and minimum current density values are shown with the corresponding color bars
in each panel. Unit: A/m2. Full-size DOI: 10.7717/peerj.4921/fig-11
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 15/25
Figure 12 Effects of the stimulation intensity on the thermal status during tSCS. (A) The peak temperature of each tissue type at the end
of the electrical stimulation with different stimulation intensities. (B) Temperature distribution along the reference line at the end of tSCS.
(C–D) Temperature rising curves of the points with peak temperature variance for each tissue type for stimulation intensity of 20, 30, and
40 mA. (E) Temperature rising curves of the points with peak temperature variance for each tissue type for stimulation intensity of 0, 5, and 10 mA.
The stimulation electrode side length is 1 cm, and the blood perfusion rate of the dermis and WM/GM are 0.025 and 0.012 s-1, respectively.
Full-size DOI: 10.7717/peerj.4921/fig-12
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 16/25
Figure 13 Temperature distribution at the end of stimulation for varied stimulation intensity from 0 mA to 10 mA. (A–D) The stimulation
intensity is 0 mA. (E–H) The stimulation intensity is 5 mA. (I–L) The stimulation intensity is 10 mA. (A, E, I) The temperature distributions on the
cross-sectional surface for different stimulation intensities. (B, F, J) The magnified view of the hot area (circled in (A, E, I) respectively), i.e. the skin
and fat layers. (C, G, K) The temperature distribution of the abdomen, muscles and the vertebrae. (D, H, L) Shows temperature distribution of the
vertebrae, epidural fat, CSF, WM, and GM. The stimulation electrode side length is 1 cm, and the blood perfusion rate of the dermis and WM/GM
are 0.025 s-1 and 0.012 s-1 respectively. The maximum and minimum temperature values are shown with the corresponding color bars in each
panel. Unit: �C. Full-size DOI: 10.7717/peerj.4921/fig-13
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 17/25
Figure 14 Temperature distribution at the end of stimulation for varied stimulation intensity from 20 mA to 40 mA. (A–D) The stimulation
intensity is 20 mA. (E–H) The stimulation intensity is 30 mA. (I–L) The stimulation intensity is 40 mA. (A, E, I) The temperature distributions on
the cross-sectional surface for different stimulation intensities. (B, F, J) The magnified view of the hot area (circled in (A, E, I) respectively), i.e. the
skin and fat layers. (C, G, K) The temperature distribution of the abdomen, muscles and the vertebrae. (D, H, L) Shows temperature distribution of
the vertebrae, epidural fat, CSF, WM, and GM. The stimulation electrode side length is 1 cm, and the blood perfusion rate of the dermis and WM/
GM are 0.025 s-1 and 0.012 s-1 respectively. The maximum and minimum temperature values are shown with the corresponding color bars in each
panel. Unit: �C. Full-size DOI: 10.7717/peerj.4921/fig-14
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 18/25
widths, repeated frequencies, and amplitudes used in recent clinical applications
(Gerasimenko et al., 2015a, 2015b; Krenn et al., 2015; Minassian et al., 2016), according to
Eq. (2). In addition, a simulation with stimulation intensity at 0 mA was added to show
the thermal status without tSCS. It indicates that the current density increases with the
increasing stimulation intensity as shown in the overview of the cross-sectional surface
and magnification of the layers with high current density in Fig. 11. The current density
was mainly delivered through layers of tissues into the targeted spine, and increased as
shown in the third row of Figs. 11A–11F. The shunting effect due to the larger electrical
conductivity of the CSF compared with the WM/GM was also verified as larger current
density distributed more among the CSF than the deep neural tissues.
The peak temperature of each tissue type, temperature distribution along the reference
line, and temperature change curves of points with peak temperature variance induced by
different stimulation intensities are shown in Fig. 12. Generally, temperature variance
between the groups with different stimulation intensities mainly occurred in all tissues
except the CSF and WM/GM. Input signals with an equivalent current less than 20 mA
are thermally safe for tSCS therapy. Temperature rise could be as high as 5 and 9.4 �C at
30 and 40 mA, respectively. Figure 11E indicates that the peak temperature of the SC
increases rapidly, reaches its peak value in 340, 320, and 250 s for 20, 30, and 40 mA,
respectively, and then plateaus. In comparison, the final temperature in the skin and fat
layers are lower than the initial temperature at 0 and 5 mA, and very close to 37 �C at
10 mA. This may due to the fact that the weak stimulation current-induced heat
accumulation is relatively small, while the heat convection effect of the skin surface
dissipates the heat away, lowering the temperature of the skin and fat layers. The synthetic
interaction of the heat sources and heat sinks at stimulation intensities lower than 10 mA
causes the rising curves to be different from those at higher stimulation intensities, as
shown in Fig. 12E. Detailed temperature distribution among the reference surfaces and the
spine are shown in Figs. 13 and 14. In cases of stimulation under 10 mA, the temperature
distributions are similar and the peak temperature rise of the whole model is no more than
0.2 �C. However, if the stimulation intensity is set to be more than 20 mA, the temperature of
the tissues except the EF, CSF, and WM/GM rise and will increase with the stimulation
intensity as shown in Fig. 14. Skin can be thermally damaged by a persistent heating above the
safe limit, i.e., 45 �C (Moritz & Henriques, 1947; Pearce et al., 1983; Prausnitz, 1996) or 44 �C
(Jiang et al., 2002). According to the assumptions of Henriques and Moritz (Henriques, 1947;
Jiang et al., 2002), the extent of tissue thermal damage is dependent not only on the
temperature but the exposure time and the properties of the tissues, such as frequency factor
and activation energy. Hence, the extra multiple factors are essential to be considered for a
more accurate safe threshold calculation in future work.
DISCUSSIONIn this work, the results predict that clinical tSCS protocols may induce temperature
rise of up to 9.4 �C in the skin layers which will be even larger for subjects with thicker
SC or thinner dermis. The peak temperature magnitude and temperature spatial
distribution depend on a combination of individual anatomical properties, stimulation
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 19/25
configurations, and electrode sizes. We therefore recommend paying special attention to
the individuals’ tissue thickness and blood perfusion properties when choosing proper
stimulation protocols and alternatively taking measures to accelerate heat dissipation
during tSCS clinical experiments. Our simulations with various anatomical models
and stimulation properties consistently show that temperature rises are mainly distributed
in the skin, fat, and abdomen, whereas the temperature variance of the CSF and WM/GM
remains small and stable for most of the variables considered in this work except
for the blood perfusion of the WM/GM. However, whether this change in thermal
status could contribute to the neuromodulation of the neural activity deserves further
study by referring to the thermal neuromodulation of infrared light (Wells et al., 2007;
Peterson & Tyler, 2013) or microwave (Reverter et al., 2014).
Our results suggest that smaller-sized electrodes lead to higher injected current density
and cause larger temperature rises. Similarly, in non-invasive transcranial direct current
stimulation (tDCS) therapy, temperature rises were negligible with the conventional
5 � 7 cm rectangular electrode, whereas the temperature rise could be 0.55 �C in the
brain tissues for the 4 � 1 ring electrode configuration with an electrode diameter
approximately 1.1 cm (Datta, Elwassif & Bikson, 2009). Though small-sized electrodes
may induce thermal damage, it is of great significance in neuromodulation. In clinical
applications, proper electrode size should be chosen in accordance with the anatomical
size of the subject’s and therapy’s requirement. In particular, in high-definition tSCS,
small-sized electrode arrays are necessary to achieve a better stimulation focality in the
non-invasive stimulation therapies (Nitsche et al., 2007; Dmochowski et al., 2011; Faria,
Hallett & Miranda, 2011; Sadleir et al., 2012). A trade-off should be considered between
the thermal issue and the stimulation accuracy before setting the clinical trials.
This work shows the findings that the temperature rise increases with stimulation
intensity, consistent with previous work concerning the non-invasive tDCS bioheat transfer
model (Datta, Elwassif & Bikson, 2009). Equation (2) indicates how the equivalent
stimulation intensity was computed in this work, which is a non-linear form of the detailed
stimulation parameters, such as the pulse width, pulse number, repeated frequency, and the
peak intensity. From a biothermal safety standpoint, the commonly used biphasic
stimulation waveforms may be disadvantageous despite being more efficient based on the
balanced charge delivery criterion (Elwassif et al., 2006). This is due to the fact that more
joule heat was generated by the larger equivalent intensity compared with monophasic
stimulations. On the other side, in realistic stimulations, between every two pulses of the
monophasic stimulation and during every stimulation cycle of both monophasic and
biphasic stimulations, tissues in the stimulation electrical field have a period where they can
cool, which may slow the temperature rise and delay the plateau. A better simulation
method that enables monitoring of the electrical and thermal status of the long-term pulsed
tSCS with acceptable computational consumption is necessary to investigate the
temperature variance during the stimulation-off period and its impact on the plateau.
It is worth mentioning that the bioheat model used in this work is based on the
classic Pennes equation. Although it has been widely used and proven to be valid, multiple
new models were proposed in order to overcome its limitations (Charny, 1992), by
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 20/25
considering the blood velocity field (Klinger, 1974; Wulff, 1974), dispersion and
microcirculatory perfusion (Jiji, Weinbaum & Lemons, 1984), thermoregulation
(Zolfaghari & Maerefat, 2010), or the temperature-dependent variability in tissue
perfusion (Davies, Saidel & Harasaki, 1997; Lakhssassi, Kengne & Semmaoui, 2010).
According to the simulation results of this work, in future experimental verifications, the
time-dependent blood perfusion rate and sophisticated biological effects in the neural
tissues should be considered as with the equation-unrelated factors concluded by Eugene’s
work (Wissler, 2012). Moreover, as mentioned in “Effects of Blood Perfusion on the
Temperature Distribution Induced by tSCS,” tissue burning is dependent on both the level
of heating and exposure time. The degree of burning is predicted by calculating the
fraction of necrotic tissue basing on the damage function as expressed by the
Arrhenius equation (Henriques, 1947; Jiang et al., 2002). It indicates that the first, second,
and third tissue burn occurs separately when the fraction of necrotic tissue reaches 0.411,
0.632, and 1, respectively. Future work might combine the Arrhenius model with more
sophisticated bioheat model to evaluate the exact thermal damage caused by tSCS.
Note that the model used in this work is synthetic, consisting of 11 tissue types, which is
different from reality. Actually, geometric irregularity of the spinal cord, especially the
complex structure of the Vert and neural fibers through the horns, would affect the path of
the electric field, which, in consequence, would influence temperature distribution.
Moreover, other organs such as the kidney, liver and the intestine may affect the current path
through the abdomen. This highlights the need for a more realistic biological model in future
computational tSCS studies. Furthermore, based on the results of this work, the temperature
rises during tSCS was mainly focused in the skin and fat layers which are tissues near the
electrodes. In contrast, the deep tissues are protected from thermal damages due to the sparse
effect and indirect contact with the electric sources. It is the skin’s structure that plays a
significant role in determining the overall thermal status of the biological model. This
conclusion inspires our future direction to work on amore detailed model of the skin similar
to that of Gomez-Tames et al. (2016), to obtain more accurate and reliable predicted results.
CONCLUSIONIn this work, we built a human spinal cordmodel for a bioheat analysis in tSCS, in which the
rise and spatial distribution of tSCS-induced temperature changes were monitored for 11
tissue types. Multiple factors that are thought to have an effect, including tissue thickness,
blood perfusion rate, stimulation intensity, and electrode size, were quantitatively
investigated. Systematic simulations and analysis of this work on the bioheat transfer could
provide guidance for future tSCS applications in terms of reducing risk of thermal injury.
ADDITIONAL INFORMATION AND DECLARATIONS
Funding
This work is supported by the National Natural Science Foundation of China (61233015).
The funders had no role in study design, data collection and analysis, decision to publish,
or preparation of the manuscript.
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 21/25
Grant Disclosures
The following grant information was disclosed by the authors:
National Natural Science Foundation of China: 61233015.
Competing Interests
The authors declare that they have no competing interests.
Author Contributions
� Luyao Chen conceived and designed the experiments, performed the experiments,
analyzed the data, contributed reagents/materials/analysis tools, prepared figures and/or
tables, authored or reviewed drafts of the paper, approved the final draft.
� Ang Ke contributed reagents/materials/analysis tools, authored or reviewed drafts of the
paper, approved the final draft.
� Peng Zhang analyzed the data, authored or reviewed drafts of the paper, approved the
final draft.
� Zhaolong Gao analyzed the data, authored or reviewed drafts of the paper, approved the
final draft.
� Xuecheng Zou conceived and designed the experiments, authored or reviewed drafts of
the paper, approved the final draft.
� Jiping He conceived and designed the experiments, authored or reviewed drafts of the
paper, approved the final draft.
Data Availability
The following information was supplied regarding data availability:
The raw data are provided in the Supplemental Files.
Supplemental Information
Supplemental information for this article can be found online at http://dx.doi.org/
10.7717/peerj.4921#supplemental-information.
REFERENCESBalmaseda MT Jr, Fatehi MT, Koozekanani SH, Sheppard JS. 1987. Burns in functional electric
stimulation: two case reports. Archives of Physical Medicine and Rehabilitation 68:452–453.
Charny CK. 1992. Bioengineering heat transfer. Advances in Heat Transfer 22:19–155
DOI 10.1016/S0065-2717(08)70344-7.
Chen L, Lo Y-K, Wang Y, Liu W. 2017. Thermal model of spiked electrode in Transcutaneous
Electrical Nerve Stimulation (TENS). In:Neural Engineering (NER), 2017 8th International IEEE
EMBS Conference. Piscataway: IEEE, 219–222.
Danner SM, Hofstoetter US, Ladenbauer J, Rattay F, Minassian K. 2011. Can the human lumbar
posterior columns be stimulated by transcutaneous spinal cord stimulation? A modeling study.
Artificial Organs 35(3):257–262 DOI 10.1111/j.1525-1594.2011.01213.x.
Datta A, Elwassif M, Bikson M. 2009. Bio-heat transfer model of transcranial DC stimulation:
comparison of conventional pad versus ring electrode. In: Engineering in Medicine and Biology
Society, 2009. EMBC 2009. Annual International Conference of the IEEE. Piscataway: IEEE,
670–673.
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 22/25
Davies CR, Saidel GM, Harasaki H. 1997. Sensitivity analysis of one-dimensional heat transfer in
tissue with temperature-dependent perfusion. Journal of Biomechanical Engineering 119(1):77
DOI 10.1115/1.2796068.
de Dear RJ, Arens E, Hui Z, Oguro M. 1997. Convective and radiative heat transfer coefficients for
individual human body segments. International Journal of Biometeorology 40(3):141–156
DOI 10.1007/s004840050035.
Dmochowski JP, Datta A, Bikson M, Su Y, Parra LC. 2011. Optimized multi-electrode
stimulation increases focality and intensity at target. Journal of Neural Engineering 8(4):046011
DOI 10.1088/1741-2560/8/4/046011.
Elwassif MM, Kong Q, Vazquez M, Bikson M. 2006. Bio-heat transfer model of deep brain
stimulation-induced temperature changes. Journal of Neural Engineering 3(4):306–315
DOI 10.1088/1741-2560/3/4/008.
Faria P, Hallett M, Miranda PC. 2011. A finite element analysis of the effect of electrode area and
inter-electrode distance on the spatial distribution of the current density in tDCS. Journal of
Neural Engineering 8(6):066017 DOI 10.1088/1741-2560/8/6/066017.A.
Ford KS, Shrader MW, Smith J, Mclean TJ, Dahm DL. 2005. Full-thickness burn formation after
the use of electrical stimulation for rehabilitation of unicompartmental knee arthroplasty.
Journal of Arthroplasty 20(7):950–953 DOI 10.1016/j.arth.2004.10.018.
Gabriel C, Gabriel S, Corthout E. 1996. The dielectric properties of biological tissues:
I. Literature survey. Physics in Medicine and Biology 41(11):2231–2249
DOI 10.1088/0031-9155/41/11/001.
Gerasimenko Y, Gorodnichev R, Moshonkina T, Sayenko D, Gad P, Reggie Edgerton V. 2015a.
Transcutaneous electrical spinal-cord stimulation in humans. Annals of Physical and
Rehabilitation Medicine 58(4):225–231 DOI 10.1016/j.rehab.2015.05.003.
Gerasimenko Y, Gorodnichev R, Puhov A, Moshonkina T, Savochin A, Selionov V, Roy RR,
Lu DC, Edgerton VR. 2015b. Initiation and modulation of locomotor circuitry output
with multisite transcutaneous electrical stimulation of the spinal cord in noninjured humans.
Journal of Neurophysiology 113(3):834–842 DOI 10.1152/jn.00609.2014.
Gomez-Tames J, Sugiyama Y, Laakso I, Tanaka S, Koyama S, Sadato N, Hirata A. 2016.
Effect of microscopic modeling of skin in electrical and thermal analysis of transcranial
direct current stimulation. Physics in Medicine and Biology 61(24):8825–8838
DOI 10.1088/1361-6560/61/24/8825.
Henriques JFC. 1947. Studies of thermal injury; the predictability and the significance of
thermally induced rate processes leading to irreversible epidermal injury. Archives of Pathology
43:489–502.
Jiang SC, Ma N, Li HJ, Zhang XX. 2002. Effects of thermal properties and geometrical dimensions
on skin burn injuries. Burns 28(8):713–717 DOI 10.1016/S0305-4179(02)00104-3.
Jiji LM, Weinbaum S, Lemons DE. 1984. Theory and experiment for the effect of vascular
microstructure on surface tissue heat transfer—part I: anatomical foundation and model
conceptualization. Journal of Biomechanical Engineering 106(4):331–341
DOI 10.1115/1.3138502.
Khadka N, Zannou AL, Zunara F, Truong DQ, Dmochowski J, Bikson M. 2017.Minimal heating
at the skin surface during transcranial direct current stimulation. Epub ahead of print
22 January 2017. Neuromodulation Technology at the Neural Interface DOI 10.1111/ner.12554.
Klinger H. 1974. Heat transfer in perfused biological tissue-I: general theory. Bulletin of
Mathematical Biology 36:403–415 DOI 10.1016/s0092-8240(74)80038-8.
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 23/25
Krenn M, Hofstoetter US, Danner SM, Minassian K, Mayr W. 2015. Multi-electrode array for
transcutaneous lumbar posterior root stimulation. Artificial Organs 39(10):834–840
DOI 10.1111/aor.12616.
Kuck A, Stegeman DF, van Asseldonk EHF. 2017. Modeling trans-spinal direct current
stimulation for the modulation of the lumbar spinal motor pathways. Journal of Neural
Engineering 14(5):056014 DOI 10.1088/1741-2552/aa7960.
Ladenbauer J, Minassian K, Hofstoetter US, Dimitrijevic MR, Rattay F. 2010. Stimulation of the
human lumbar spinal cord with implanted and surface electrodes: a computer simulation study.
IEEE Transactions on Neural Systems and Rehabilitation Engineering 18(6):637–645
DOI 10.1109/tnsre.2010.2054112.
Lagopoulos J, Degabriele R. 2008. Feeling the heat: the electrode-skin interface during DCS. Acta
Neuropsychiatrica 20(02):98–100 DOI 10.1111/j.1601-5215.2008.00274.x.
Lakhssassi A, Kengne E, Semmaoui H. 2010. Modifed pennes’ equation modelling bio-heat
transfer in living tissues: analytical and numerical analysis. Natural Science 2(12):1375–1385
DOI 10.4236/ns.2010.212168.
Lv YG, Liu J. 2007. Effect of transient temperature on thermoreceptor response and thermal
sensation. Building and Environment 42(2):656–664 DOI 10.1016/j.buildenv.2005.10.030.
Mathias E, Srinivas Murthy M. 2017. Pediatric thermal burns and treatment: a review of progress
and future prospects. Medicines 4(4):91 DOI 10.3390/medicines4040091.
Miller JP, Eldabe S, Buchser E, Johanek LM, Guan Y, Linderoth B. 2016. Parameters of spinal
cord stimulation and their role in electrical charge delivery: a review. Neuromodulation
Technology at the Neural Interface 19(4):373–384 DOI 10.1111/ner.12438.
Minassian K, Hofstoetter US, Danner SM, Mayr W, Bruce JA, McKay WB, Tansey KE. 2016.
Spinal rhythm generation by step-induced feedback and transcutaneous posterior root
stimulation in complete spinal cord–injured individuals. Neurorehabilitation and Neural Repair
30(3):233–243 DOI 10.1177/1545968315591706.
Moritz AR, Henriques FC Jr. 1947. Studies of thermal injury: II. The relative importance of time
and surface temperature in the causation of cutaneous burns. American Journal of Pathology
23:695.
Nadler SF, Prybicien M, Malanga GA, Sicher D. 2003. Complications from therapeutic
modalities: results of a national survey of athletic trainers. Archives of Physical Medicine and
Rehabilitation 84:849–853 DOI 10.1016/S0003-9993(02)04955-9.
Nitsche MA, Doemkes S, Karakose T, Antal A, Liebetanz D, Lang N, Tergau F, Paulus W. 2007.
Shaping the effects of transcranial direct current stimulation of the human motor cortex.
Journal of Neurophysiology 97(4):3109–3117 DOI 10.1152/jn.01312.2006.
Parazzini M, Fiocchi S, Liorni I, Rossi E, Cogiamanian F, Vergari M, Priori A, Ravazzani P.
2014. Modeling the current density generated by transcutaneous spinal direct current
stimulation (tsDCS). Clinical Neurophysiology 125(11):2260–2270
DOI 10.1016/j.clinph.2014.02.027.
Patriciu A, Member S, Yoshida K, Struijk JJ, Demonte TP, Joy MLG, Stødkilde-jørgensen H.
2005. Skin burns under surface electrodes. IEEE Transactions on Biomedical Engineering
52:2024–2031.
Patriciu A, Yoshida K, DeMonte TP, Joy MLG. 2001. Detecting skin burns induced by surface
electrodes. In: Engineering in Medicine and Biology Society, 2001. Proceedings of the 23rd Annual
International Conference of the IEEE. Piscataway: IEEE, 3129–3131.
Pearce JA, Geddes LA, Van JFV, Foster K, Allen J. 1983. Skin burns from electrosurgical current.
Medical Instrumentation 17:225–231.
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 24/25
Pennes HH. 1948. Analyiss of tissue and arterial blood temperatures in the resting human
forearm. Journal of Applied Physiology 1(2):93–122 DOI 10.1017/CBO9781107415324.004.
Peterson EJ, Tyler DJ. 2013. Motor neuron activation in peripheral nerves using
infrared neural stimulation. Journal of Neural Engineering 31(1):1713–1723
DOI 10.1109/TMI.2012.2196707.Separate.
Prausnitz MR. 1996. The effects of electric current applied to skin: a review for transdermal drug
delivery. Advanced Drug Delivery Reviews 18(3):395–425 DOI 10.1016/0169-409x(95)00081-h.
Reverter F, Prodromakis T, Liu Y, Georgiou P, Nikolic K, Constandinou T. 2014. Design
considerations for a CMOS Lab-on-Chip microheater array to facilitate the in vitro thermal
stimulation of neurons. In: Proceedings-IEEE International Symposium on Circuits and Systems.
Piscataway: IEEE, 630–633.
Sadleir RJ, Vannorsdall TD, Schretlen DJ, Gordon B. 2012. Target optimization in transcranial
direct current stimulation. Frontiers in Psychiatry 3:1–13 DOI 10.3389/fpsyt.2012.00090.
Satter EK. 2008. Third-degree burns incurred as a result of interferential current therapy. American
Journal of Dermatopathology 30(3):281–283 DOI 10.1097/dad.0b013e31816a9d4f.
Schwan HP, Kay CF. 1957. Capacitive properties of body tissues. Circulation Research
5(4):439–443 DOI 10.1161/01.RES.5.4.439.
Sharma M, Aggarwal V, Bahadur R, Gupta R. 2011. Burns secondary to improper usage of
transcutaneous electrical nerve stimulation: a case report. Punjab Journal of Orthoapedics
7:72–73.
Smith KD, Zhu L. 2010. Theoretical evaluation of a simple cooling pad for inducing hypothermia
in the spinal cord following traumatic injury. Medical & Biological Engineering & Computing
48(2):167–175 DOI 10.1007/s11517-009-0543-z.
Tavernier A, Dierickx M, Hinsenkamp M. 1992. Conductivity and dielectric permittivity of
dermis and epidermis in nutrient liquid saturation. In: Engineering in Medicine and Biology
Society, 1992 14th Annual International Conference of the IEEE. Piscataway: IEEE, 274–275.
The Engineering ToolBox. 2018. Overall heat transfer coefficients for fluids—heat exchanger
surface combinations. Available at https://www.engineeringtoolbox.com/overall-heat-transfer-
coefficients-d_284.html (accessed 5 January 2018).
Tompkinsn DT, Vanderby R, Klein SA, Beckman WA, Steeves RA, Frye DM, Paliwal BR. 1994.
Temperature-dependent versus constant-rate blood perfusion modelling in ferromagnetic
thermoseed hyperthermia: results with a model of the human prostate. International Journal of
Hyperthermia 10(4):517–536 DOI 10.3109/02656739409009355.
Wells J, Kao C, Konrad P, Milner T, Kim J, Mahadevan-Jansen A, Jansen ED. 2007. Biophysical
mechanisms of transient optical stimulation of peripheral nerve. Biophysical Journal
93(7):2567–2580 DOI 10.1529/biophysj.107.104786.
Wissler EH. 2012. 50 years of JAP Pennes’ 1948 paper revisited. Journal of Applied Physiology
85(1):35–41.
Wulff W. 1974. The energy conservation equation for living tissue. IEEE Transactions on
Biomedical Engineering BME-21(6):494–495 DOI 10.1109/TBME.1974.324342.
Xu F,Wen T, Lu T, Seffen K. 2008. Skin biothermomechanics for medical treatments. Journal of the
Mechanical Behavior of Biomedical Materials 1(2):172–187 DOI 10.1016/j.jmbbm.2007.09.001.
Zolfaghari A, Maerefat M. 2010. A new simplified thermoregulatory bioheat model for evaluating
thermal response of the human body to transient environments. Building and Environment
45(10):2068–2076 DOI 10.1016/j.buildenv.2010.03.002.
Chen et al. (2018), PeerJ, DOI 10.7717/peerj.4921 25/25