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