Equivalent Circuit Model to Simulate
the Neuromuscular Electrical Stimulation
Nerve and Muscle Stimulation with Simulation Comparison
Diego Lujan Villarreal, Dietmar Schroeder and Wolfgang H. Krautschneider
Institute of Nanoelectronics
Hamburg University of Technology
Hamburg, Germany
Abstract— In this study, an equivalent circuit model (ECM) to
simulate the Neuromuscular Electrical Stimulation (NMES) has
been developed. The ECM includes all regions from the
transcutaneous electrodes to the neuron cell membrane to
simulate the nerve stimulation with biphasic rectangular
waveform. The model was developed as a series of ‘tissue
subsystems’, hence these can be treated independently. The
frequency and current density dependency of the electrodeelectrolyte and gel-skin interfaces and the frequency dependency
of the tissues were considered. The ECM was used to simulate in
PSpice 6 strength–duration curves obtained by experimental
transcutaneous stimulation of the extensor muscles in the
forearm of one subject using two fully gelled electrodes of size
45x80 mm². To monitor muscle contraction, a three axial
accelerometer was placed on the proximal phalange of the middle
finger. The mean voltage response in the stimulation experiments
was compared with ECM simulations. The energy dissipation in
the human tissue layers was investigated using the ECM. The
correlation coefficient was used to evaluate quantitatively the
agreement between simulations and experiments.
literature. The ECM takes into account the normal tendency of
frequency and current density dependency in the electrodeelectrolyte gel-skin interfaces, the anisotropic characteristics
of the muscle and the non-linear behavior of the human skin.
The sub-threshold model of the neuron cell membrane was
incorporated to simulate the response of a single axon, and the
cell membrane potential was monitored until it reaches
threshold. Biphasic rectangular waveform was selected
because it has been used as standard shape for electrical
neurostimulation.
Keywords-neurostimutation; strength-duration curve; electrical
stimlation; skin impedance
I.
INTRODUCTION
Neuromuscular Electrical Stimulation (NMES) is used to
activate nerves and muscle fibers by applying electrical current
pulses using two electrodes with inter-electrode distance IED
placed on the skin. When the desire is to simulate the
transcutaneous stimulation of nerves and muscles, an
equivalent circuit model must be developed with components
that behave comparable to the human tissue. Almost all
equivalent circuit models (ECM) present so far only a
simplified view on tissue layers and do not include a model of
the stimulated nerve [1].
The primary objective in this study is firstly to develop a
precise equivalent circuit model including all regions from the
transcutaneous electrodes to the neuron cell membrane and
secondly to compare the voltage response across the
transcutaneous electrodes in neuromuscular stimulation and
PSpice simulations, particularly using the strength-duration
curves. The model was built as a series of ‘tissue subsystems’,
hence these can be treated independently using values of the
conductivity, permittivity and tissue thickness taken from
Figure 1. Equivalent circuit model with the subsystems included.
(Layer thicknesses not drawn to scale.)
II.
MODEL DEVELOPMENT
The impedance measurement of human tissue has several
complications due to several factors, such as the electrode-
46
electrolyte interface (EEI), the inhomogeneity of human skin
and muscle, the anisotropy of muscle fibers, the non-linear
phenomena of human skin [2], [3] and the time dependent ionic
redistribution. These factors must be taken into account to
effectively simulate the flow of current density through the
tissues.
The equivalent circuit model shown in the three
dimensional drawing (fig. 1) presents the ‘tissue subsystems’
with their components and their dependencies. The stratum
corneum, the lower layers, and the muscle were coarsely
discretized in the transverse and longitudinal directions (see
fig. 1) and modeled with lumped circuit elements indicated in
fig. 1 with subscripts t and l, respectively. This is clearly a
rather granular discretization of an inherently threedimensional flow problem, but it leads to a computationally
efficient implementation, which can serve e.g. as a realistic
load model for the development of stimulation circuits.
To determine the value of each parameter in the transverse
division of the stratum corneum, the lower layers and muscle,
the resistance was calculated with the normal equation, R =
l/σA. Where l is the thickness of the tissue, σ is the conductivity
of the tissue and A is the area of the electrodes, and the result
was divided by 2. Moreover, the capacitance was calculated
with the typical equation, C = εoεrA/l, where εo is the
permittivity of free space, εr is the permittivity of tissues, A is
the area of the electrodes and l is the thickness of the tissue,
and the result was multiplied by 2. The parameters of the
longitudinal circuit elements were obtained in the same way,
with length l now being the distance of the electrodes and area
A the product of the width of the electrodes and the thickness
of the respective layer.
Since alpha motor units synapse extrafusal muscle fibers,
the extracellular medium is represented by the equivalent
circuit of the muscle; it is connected to the equivalent circuit
model of the cell membrane.
A. Electrode-electrolyte gel-skin equivalent circuit
It is well known that the components of the EEI are
frequency and current density dependent [4]. The most typical
equivalent circuit to characterize the EEI is a parallel
arrangement of resistance and capacitance. Its dependency on
frequency can be explained by observing that the impedance is
purely resistive at low frequencies. As the frequency increases,
the value of the capacitance decreases, and the total impedance
of the parallel combination decreases. Using low current
densities, the EEI can be modeled as a linear system with an
equivalent circuit composed with linear components [5]. Care
has to be taken when the frequency or the current density is
increased.
The equivalent circuit model of the EEI and of the
electrolyte gel-skin is shown in Figure 1. It contains the halfcell potential Vhc and a parallel arrangement of a capacitance
CB and a resistance RB. The resistance RGEL of the selfadhesive gel is placed in series. Vhc can be different in each
electrode-electrolyte interface during each stimulus; the values
in the simulations have been set as to match the experimentally
observed total DC offset of 3.4 V. The electrical components
CB and RB were measured using a balance Bridge (subscript B
denotes Bridge). Physically, the unknown components were
two fully gelled electrodes 45x80 mm² (PG473, FIAB)
attached to one another, with the self-adhesive gel in-between.
A sine wave generator was used to select frequencies of 976
Hz, 1.953 kHz, 3.906 kHz and 7.812 kHz (periods ‘T’ of 1024,
512, 256 and 128 µs, respectively) and peak electric currents
ranging from 10 mA to 60 mA. Table 1 shows the values of the
electrical parameters CB and RB thus determined and used in
simulations. It should be noted that these values do not change
essentially when the experiment is repeated with a square wave
generator. They are thus considered to be valid for the
experiments described below too, where rectangular pules have
been used.
RGEL can be determined easily by attaching the electrodes
to one another as above and measuring the impedancefrequency plot relationship from 20 Hz to 500 kHz using an
LCR meter (4284A, Agilent Technologies). As the frequency is
increased, the components of the electrode-electrolyte gel
interface decrease. It can be assumed that the asymptotic at
high frequency is the impedance of the self-adhesive gel. The
impedance thus determined is purely ohmic with a value of 106
Ω. This value was also taken into account when computing CB
and RB at the lower frequencies (see above).
The interface between the electrolyte gel and the human
skin is modeled by a resistance RGS and a capacitance CGS in
parallel [7]. Both parameters, RGS and CGS, cannot be measured
unless ex vivo experimental measurements are performed.
Therefore, the values of RGS and CGS were adapted such that
the voltage response matches the response found in the
stimulation experiment.
TABLE I.
f (Hz)
VALUES OF RB AND CB IN EXPERIMENTS
976
1953
3906
7812
i (mA)
RB
(Ω)
CB
(nF)
RB
(Ω)
CB
(nF)
RB
(Ω)
CB
(nF)
RB
(Ω)
CB
(nF)
10
16
376
11
321
12
142
10
216
20
16
376
13
318
9
243
10
216
30
18
319
12
354
13
247
11
262
40
18
319
16
356
14
243
14
288
50
18
1104
16
356
14
243
14
288
60
19
2114
16
356
14
243
14
288
B. Stratum corneum equivalent circuit
The stratum corneum is the outmost layer of the epidermis
which consists of dead cells. Once the electrodes are placed on
the surface of the skin, the non-conductive stratum is between
the conductive electrode and the underneath conductive tissues
and thus generates a capacitor. This tissue is relatively nonconductive in that it includes only a few free ions which
contribute to direct current conductance. There exists a low
flow of ions that cross the stratum corneum via paracellular
pathways, and the ionic current can be described by a low
conductive property. At frequencies lower than 10 kHz, the
skin impedance is determined by this thin tissue [8] and the
electric properties of the stratum corneum dominate the
impedance.
47
The behavior of this thin layer can be represented as a
parallel RSCS circuit (Figure 1). The conductivity σS and the
relative permittivity εS were determined by evaluating the
dispersion plots in [3] at the frequencies selected in the ECM
simulation. Table 2 shows the values thus obtained, which have
been used in the simulations.
C. Lower layers equivalent circuit
Several authors have measured the impedance of the skin
when the stratum corneum is removed. Yamamoto and
Yamamoto [10] measured the variations in skin impedance
caused by stripping off the stratum corneum and remarkable
differences have been found in the electrical properties
between deeper tissues and the stratum corneum. The lower
layers have a constant and much lower resistivity ρLW, whereas
the permittivity of lower layers εLW changes greatly in
frequencies below 100 kHz [3]. Researchers [10] have
simplified the deeper tissue system by a material with
homogeneous electric properties. Therefore, we can assume
homogeneous electric properties in the rest of the epidermis,
dermis and subcutaneous fat, and model these with parallel
RLWCLW equivalent circuits (figure 1). The conductivity σLW
and the permittivity εLW were chosen by examining the
dispersion plots in [3] at the frequencies selected in the ECM
simulation. In table 2 the values used in simulations can be
seen.
TABLE II.
determined by the properties of the lipid bilayer. The
conducting plates are the intracellular and extracellular
solutions, separated by a non-conducting membrane. The
membrane resistance RMEM determines the entry of charged
ions into the axon and it is characterized by the resistivity of
the membrane at the node of Ranvier. The axoplasm resistance
RAXP is on the inside and runs longitudinally along the axon.
Equation (1) was used to calculate the membrane
resistance. Variable rrn in (1) is the radius of the node of
Ranvier and rt is the radius in the node minus the thickness b of
the cell membrane. Equation (2) calculates the membrane
capacitance. The non-conductive membrane can be described
with a dielectric constant, which includes the dielectric
constant of water and of the hydrophilic molecule’s heads
(attracted to water). The value of the dielectric constant for the
bilayer structure is found to be k = 7 [13].
The calculation of the axoplasm resistance is done using
equation (3). Table 4 shows the variables used to calculate the
electric properties of the cell membrane.
TABLE IV.
PARAMETERS USED IN THE CELL MEMBRANE EQUIVALENT
CIRCUIT
Variable
Symbol (units)
Value
df (μm)
20
ρm (MΩm)
16
rrn (μm)
4.74
Thinkness cell membrane
b (nm)
3
Nodal length
lm (μm)
20.54
Axoplasm resistivity
ρi (Ωm)
0.5
lmy (mm)
1.5
Fiber diameter
Resistivity of membrane
SKIN PARAMETERS USED IN SIMULATIONS
Nodal radius
Stratum Corneum
Lower layers
Frequency (Hz)
σ (µS/m)
ε (x103)
σ (S/m)
ε (x105)
976
27
2
0.2
2.2
1953
60
2
0.2
1.8
3906
80
1.9
0.2
1.4
7812
140
1.7
0.2
1.1
Length of myelin sheat
(1)
D. Muscle equivalent circuit
Muscle fibers contain very high salinity and water, making
the muscle a good conductor. The anisotropic behavior of the
muscle has an important characteristic which must be
considered because it exhibits a higher longitudinal electrical
conductivity σML, 0.2 to 0.8 S/m, than the transverse σMT, 0.04
to 0.16 S/m [3], [16]. The extracellular liquid is less conductive
than the cell and the conduction is easier along the length of the
fiber. Due to the properties of muscles stated above, it can be
assumed to characterize the equivalent circuit of the muscle by
just a resistance RM (figure 1). In table 3 the values used in
simulations can be seen.
TABLE III.
MUSCLE PARAMETERS USED IN SIMULATIONS
Frequency (Hz)
976
1953
3906
7812
σML (S/m)
0.24
0.25
0.3
0.34
σMT (S/m)
0.12
0.12
0.16
0.16
E. Cell Membrane Equivalent Circuit
The electric properties of the cell membrane are
characterized by a membrane capacitance CMEM, which is
(2)
(3)
The resting potential VRP in our simulations is -70 mV and
the threshold voltage is -55 mV.
The equivalent circuit of the cell membrane describes the
original cable model [16]. This linear model can explain the
electrical behavior of the axon with its capacitive behavior, and
the time when the cell membrane voltage reaches threshold.
For sub-threshold stimuli, it can be assumed that the membrane
conductance is constant during monitoring the membrane
voltage when it reaches threshold [15]. Since alpha motor units
synapse extrafusal muscle fibers, the extracellular medium is
represented by the muscle equivalent circuit.
The thicknesses of the tissues [18], [19], [20], [23] were
used as well the depth from the superficial part of the skin to
the cell membrane. From the superficial part of skin in the
48
forearm to the nerves desired to stimulate, the radial nerve has
a depth between 1.5 and 2 cm, while the depth of the median
nerve in the same region is 2.5 to 3 cm [21], [22]. Since the
muscles activated in the experiments include both of these
nerves, it is sufficient to include only the deeper lying median
nerve in the equivalent circuit, at a depth of 2.5 cm.
F. Summary
With the exception of the frequency and current density
dependent values of the electrode-electrolyte gel and
electrolyte gel-skin interfaces, the electrical parameters that
represent the tissues (stratum corneum, σS and εS; lower layers
σLW and εLW; the muscle σML and σMT) are simply frequency
dependent. The electrical properties of the cell membrane are
independent of frequency and current density.
III.
METHODS AND MATERIALS
A. Subjects for experiment In vivo
The in vivo experiments were performed under written
consent of 1 healthy subject. There was no knowledge of
neurological or orthopedic disease history; therefore it is
assumed that the involved muscle is innervated. The
experiments were conducted over six days with the same
subject.
B. Experimental Procedure
For the stimulation we used a portable stimulator developed
in our research institute [17]. For safety reasons the device is
battery powered, and it is controlled through the PC via
wireless IEEE Std. 802.15.4 interface. It can deliver analog
current stimulation pulses from a digital data stream, the
maximum output voltage is ± 100 V and the current is limited
to ± 66 mA. To contact the skin two fully gelled electrodes
45x80 mm² (PG473, FIAB) were used. In order to measure the
muscle twitch response, a three-axial accelerometer was used
(LIS344AL, ST). The data were acquired by the computer via a
National Instrument DAQ M 6289 PCI card at a sampling rate
of 100 kS/s per channel.
The subject was seated comfortably in a chair, and after
cleaning the skin surface, the electrodes were placed on the
right forearm. The reference electrode was positioned on the
elbow over the ulnar nerve and the working electrode over the
extensor muscle, with 105 mm of separation. The extensor
muscle was found by a visual inspection during the movement
of the middle finger. The forearm was fixed on the armrest of
the chair with the hand hanging in order to avoid the contact
with any surface. The pulses were symmetrical biphasic current
pulses (anodic first) without interphase. The waveform used
was rectangular pulse. The pulse widths were 128, 256, 512
and 1,024 µs. Note that the fundamental frequencies of these
pulses correspond to the frequencies used for determining the
tissue parameters in section II. The amplitudes were swept
from 7.7 to 66 mA with steps of 6.5 mA. The number of
stimuli for a complete sweep of these values was 40; each one
was repeated 5 times in order to take the average of the results,
so the total of pulses was 200 with a separation of 1.5 s. To
ensure the muscle contraction, a three axial accelerometer was
placed on the proximal phalange of the middle finger. The
accelerometer gives the acceleration in a specific direction.
Therefore, the data were converted to spherical coordinates
from which only the radius was taken, i.e. the amplitude
without direction.
A Matlab script organized the data and performed some
tasks in order to obtain the desired curves, such as the current,
the accelerometer response and voltage response in all the
samples. When the accelerometer is at rest its output is 1
gravity (g). Thus, in order to measure a muscle reaction, the
given inertial responses for the experiment was a minimum
value of 1.2 g.
C. Simulation Procedure
From the stimulation results mentioned above, strengthduration curves were put together by finding the pulse widths
and current amplitudes where the accelerometer reaction
showed the minimum response. The evaluation was done for
each single day, giving a total of six curves, and corresponding
means and standard deviations were computed.
The values of the tissue parameters in tables 2 and 3 have
been taken according to the fundamental frequency of the
actual pulses.
For the respective experimental pulse width, the
longitudinal conductivity of the muscle was varied in
simulations such that the maximum cell membrane voltage
reaches threshold (see table 3). The difference between the
minimum and the maximum longitudinal conductivity was
0.1 S/m. The influence on the voltage response waveform when
the longitudinal conductivity is changed is imperceptible.
The frequency and current density components of the
interface electrolyte gel-skin were adapted to match the peak
voltage response in the stimulation experiment. The
magnitudes of the resistances RGS and CGS thus obtained are
shown in Table 5.
The charge delivered by the stimulator was computed as the
time integral of the stimulation current. The energy delivered
by the device and the energy dissipation in the skin were
calculated by integrating the respective electrical power over
time. The correlation coefficient was obtained using a Matlab
script.
IV.
RESULTS
Figures 2 and 3 show the comparison of the voltage
response peaks (positive and negative respectively) with
biphasic rectangular pulse, as average and standard deviation of
the six days. The adaptation of the electrolyte gel-skin
impedance was done such that the error was evenly distributed
between the positive and negative peak.
Figure 4 compares and the mean response in the
experiment, the delivered current and the tissue voltage drop.
Figure 5 shows again the voltage response in the simulation,
together with the standard deviation in the experiment.
Figure 6 shows the charge delivered by the stimulator.
Figure 7 compares the total energy delivered by the device with
the simulated energy dissipation in the tissues.
The values of the impedance of the electrolyte gel-skin
interface used to match the voltage response in stimulation
experiments are shown in Table 5. It can be seen that the
49
magnitude of the impedance decreases when the pulse width
decreases, which coincides with the behavior of a charge
double layer that develops at the gel-skin interface [25]. The
variation of the impedances reflects the variability of the
contact quality on the skin when the electrodes were repeatedly
attached on the distinct days of the stimulation experiments.
TABLE V.
VALUES USED TO MATCH THE VOLTAGE RESPONSE IN
STIMULATION EXPERIMENTS.
RGS (kΩ)
CGS (nF)
│Z│(Ω)
PW (µs)
Mean
SD
Mean
SD
Mean
SD
1024
6.01
1.54
459
25.2
355
19.4
512
5.64
1.92
368
24.8
222
16.6
256
2.12
0.4
354
32.2
115
10.6
128
0.518
0.067
328
3.48
62
6.63
The correlation coefficient was used to evaluate a
quantitative relationship in the voltage response between
simulations and experiments for the respective pulse widths.
Table 6 shows the results as mean and standard deviation for
the six days.
TABLE VI.
CORRELATION COEFFICIENT RESULTS
PW (µs)
1024
512
256
128
Mean
0.995
0.994
0.991
0.990
SD
0.001
0.001
0.003
0.005
V.
DISCUSSION
The results in figures 2 to 5 express that it is possible to
simulate the voltage response of nerve and muscle stimulation
with the same researched parameters of the tissues and the
measured electrical parameters of the electrode-electrolyte gel
interface, regardless the day when the experiment is carried
out. The gel-skin interface, on the other hand, depends strongly
on the contact quality on the skin in different sessions of
stimulation. This quality is reflected by the impedance of the
interface electrolyte gel-skin. Therefore, RGS and CGS had to be
adapted in each session to match the voltage response, and the
variations of results in the voltage response shown in figures 2
and 3 are related to this variability.
While the tissues merely show a frequency dependency, the
interfaces of electrode-electrolyte gel and electrolyte gel-skin
are frequency and current density dependent. The equivalent
circuit model can produce notable results in situations when the
frequency and current density settings in stimulation are
changed. Although RGS and CGS have been fitted just to match
the peak response voltages with our model, good agreement of
the overall waveform between experiment and simulation is
demonstrated by the correlation coefficient of the voltage
responses, whose lowest mean value was 0.990 ±0.005.
Higher frequencies imply increased amplitudes of delivered
current in nerve and muscle stimulation when using the
principle of the strength-duration curve. In our stimulation
results, the mean delivered current at 128 µs pulse width
increases more than threefold of that at 1024 µs pulse width.
Further, the mean voltage response in the stimulation
experiment at 1024 µs pulse width is higher by more than 1.2fold of that at 128 µs pulse width. At the subsystems where the
impedance is purely ohmic, the voltage drop at 128 µs pulse
width in the electrolyte gel and the muscle rises more than
threefold and more than 2.5-fold, respectively, of that at 1024
µs pulse width. The importance of the impedance in the gelskin interface becomes less at higher frequencies and
amplitudes, because of increasing voltage drops in the muscle
and the gel.
The highest voltage response which was recorded in the
simulations can be seen in figure 4. Using this case as an
example, the voltage drop in the human tissue is less than 20%
of that across the electrodes. The remaining voltage drop can
be attributed to the electrode-electrolyte gel-skin interfaces.
The comparison of the positive and negative voltage peaks
show comparable outcomes for pulse widths evaluated. The
mean percentage error in the positive peak voltage response
reaches 0.4212% whereas the negative peak voltage drop is
2.092%. The maximum deviation occurs on the fifth day at
1024 µs with a difference of 0.858 V.
The conductivity and permittivity of the human tissue are
essential and must be selected accurately to develop a
meaningful equivalent circuit model. Concerning the voltage
response between the electrodes, the electrical properties of the
human tissue have a lower influence than the properties of the
electrode-electrolyte gel-skin interfaces.
The charge delivered by the stimulator contributes to the
risk of tissue damage. By analyzing figure 6, it can be
concluded that the risk of tissue damage is lower when the
nerve and muscle are stimulated with lower pulse widths.
Therefore, to minimize the possibility of tissue damage, it is
important to determine the least stimulus intensities required at
various stimulus durations to reach action potential.
Nevertheless, this does not necessarily mean that there exists a
risk of tissue damage by stimulating at high pulse widths (e.g.
1024µs).
Figure 7 shows the energy delivered by the stimulator.
Most energy-efficient stimulator devices will deliver the
minimum energy to the tissues. Furthermore, this will extend
the battery life of the device and hence reduce the costs related
to battery replacements. In our experiments, the lowest energy
to stimulate the nerve and muscle is at 256µs pulse width. The
standard deviation results at 128µs overlaps with the outcomes
at 256µs.
By analyzing figure 7 at pulse width 1024µs, we see that
the energy loss across the electrodes is higher by more than
eightfold than the energy dissipated in the tissues. The energy
consumed by the tissues remains almost constant during the
pulse widths tested.
VI.
CONCLUSION
An equivalent circuit model to simulate the NMES has
been developed including all regions from the transcutaneous
electrodes to the cell membrane.
50
2)
3)
4)
5)
6)
7)
Figures 2) to 7). 2 and 3 are the comparison with measurements of biphasic rectangular pulse for different pulse widths: 2) Positive peak voltage response, 3)
Negative peak voltage response. 4) Voltage response comparison with a 128µs biphasic rectangular pulse. The green plot corresponds to the delivered current in
stimulation and the magenta plot shows the voltage drop from the stratum corneum to the cell membrane. 5) The red plot corresponds to ECM simulation and the
blue marks show the standard deviation of the stimulation experiment. 6) Mean and standard deviation of the charge delivered by the stimulator device. 7) Mean
and standard deviation of the energy delivered by the stimulator device (red plot), and the energy dissipation in the human tissues (blue plot).
While we report here only on stimulation with biphasic
rectangular pulse waveforms, we expect that the model can be
used for other waveforms as well. The significance of the
results achieved with our model is demonstrated by a high
degree of correlation between simulation and experiment.
Despite its relatively coarse lumped-element approximation
of an inherently three-dimensional flow problem, the model is
useful as a realistic load model for the development of
stimulation circuits. It helps to obtain a fundamental
understanding concerning the magnitudes of the stimulation in
the different layers of human tissue, and to clarify basic
relationships and parameters for the development of an
advanced 3D FEM-based model.
When the aim is to develop such a comprehensive model,
special attention must been paid in the electrical properties of
the model to overcome complications that may occur. Specific
parameters could change the electrical properties of the model
such as the subject (healthy person or patient), the day of
stimulation experiment, the waveform used, the amplitude of
current density delivered to the tissues, the length of pulse
51
width (frequency) used, the thickness of the tissues, the extend
of motor unit recruitment and the time-dependent impedance
when the electrodes are placed on human skin.
REFERENCES
[1]
[2]
Agache, Pierre. Measuring the Skin. Springer, 2004.
Yamamoto T., Yamamoto Y. Non-linear electrical properties of skin in
the low frequency range. Med. & Bio. Eng. & Comput., 1981.
[3] Damijan Miklavcic, Natasa Pavselj, Hart Francis. Electric Properties of
Tissues. Wiley Encyclopedia of Biomedical Engineering, 2006.
[4] Geddes L., Mayer S., Bourland J. Faradic resistance of the
electrode/electrolyte interface. Medical & Biological Engineering &
Computing. 30, 538 – 542. 1992.
[5] Boccaletti C., Castrica F., Fabbri G., Santello M. A non-invasive
biopotential electrode for the correct detection of bioelectrical currents.
BioMED '08 Proceedings, 353-358. 2008.
[6] Holman J., Graham H. Chemistry in Context. Nelson Thornes 5th
Edition. 2000.
[7] Khandpur. Handbook of Biomedical Instrumentation. 2nd Edition. Tata
McGraw-Hill Education, 2003.
[8] Sverre Grimnes, Ørjan Grøttem Martinsen. Bioimpedance and
bioelectricity basics. Academic Press. Second Edition. 2008.
[9] Damijan Miklavcic, Natasa Pavselj. Numerical Models of Skin
Electropermeabilization taking into account conductivity changes and
the presence of local transport regions. IEEE Transactions on Plasma
Science, 2008.
[10] Yamamoto T., Yamamoto Y. Electrical Properties of the epidermal
stratum corneum. Medical and Biological Engineering, 1976.
[11] Sherwood Lauralee. Human Physiology: From Cells to Systems.
Cengage Learning, 2009.
[12] Fwu Tarng Dun. The Length and Diameter of the Node of
Ranvier. IEEE Transactions on Biomedical Engineering. 1970
[13] Hobbie R., Roth B. Intermediate Physics for medicine and biology.
Springer Science & Business Media, 2007.
[14] Uri Moran, Phillips Rob. SnapShot: Key Numbers in biology.
Weizmann Institute of Science and California Institute of Technology.
[15] McNeal D. Analysis of a model for excitation of myelinated
nerve. IEEE Transactions on Biomedical Engineering, 1976.
[16] Kuhn Andreas. Modeling Transcutaneous Electrical Stimulation. Diss.
ETH No. 17948, 2008.
[17] Mario A. Meza-Cuevas, Dietmar Schroeder and Wolfgang H.
Krautschneider. Neuromuscular Electrical Stimulation Using Different
Waveforms - Properties comparison by applying single pulses. Institute
of Nanoelectronics. Hamburg University of Technology. Hamburg,
Germany. 2012. “in press”.
[18] Ishida, Y. Body Fat and Muscle Thickness in Japanese and Caucasian
Females. American Journal of Human Biology. 711-718, 1994.
[19] Sandby-Møller J., Poulsen T., Wulf HC. Epidermal thickness at different
body sites: relationship to age, gender, pigmentation, blood content, skin
type and smoking habits. Acta Derm Venereol. 83(6):410-3, 2003.
[20] Valentin J. Basic anatomical and physiological data for use in
radiological protection: reference values: ICRP Publication 89. Annals
of the ICRP. Volume 32, Issues 3–4, September–December 2002, Pages
1–277.
[21] Regional Anesthesia: Peripheral Nerve Blockade in Adults. Wolters
Kluwer France, 2004.
[22] Kaye A. D. Essentials of Regional Anesthesia. Springer, 2012.
[23] Kuhn Andreas. Modeling Transcutaneous Electrical Stimulation. Diss.
ETH No. 17948, 2008.
[24] Chen A., Moy Vincent. Cross@Linking of cell surface receptors
enhances cooperativity of molecular adhesion. Biophysical Journal,
2000.
[25] Merlo A., Campanini I. Technical Aspects of Surface Electromyography
for Clinicians. The Open Rehabilitation Journal, 3, 98-109, 2010.
52