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,

estxczou@hust.edu.cn

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.

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