Electrical Model of an Implantable Epimysial Electrode for EMG

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IJARCCE
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DOI 10.17148/IJARCCE.2020.91201
Copyright to IJARCCE IJARCCE 1
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Electrical Model of an Implantable Epimysial
Electrode for EMG
Joel Flores1, Patricia Lorena Ramírez2, Rita Trinidad Rodríguez3
Professor, Communications and Electronic Engineering Department (ICE), ESIME-ZAC, IPN, Mexico City, Mexico1-3
Abstract: This paper presents the development of an electrical model for an implantable electrode that allows the
detection of the most stable and precise electromyography signal (EMG) directly on a skeletal muscle in a chronic way.
Keywords: Implantable epimysial electrode, electrical activity of a skeletal muscle, electromyography (EMG), electrical
model of an implantable electrode.
I. INTRODUCTION
The development of this type of implantable electrodes has focused on the area of chronic nerve stimulation [10, 12, 13]
and on the functional stimulation of paralyzed or weak muscles [11, 14]. The implantable electrodes that have been
developed mainly are of the cuff type (on the nerve), epimysial (on nerve and muscle) and intramuscular; as shown in
Fig. 1.
Fig. 1 Implantable electrodes: a) intramuscular, b) epimysial and c) cuff
For the particular case of the recording of an electromyography (EMG) or myoelectric signal with implantable electrodes,
the attention has focused on obtaining the signals produced by a few muscle fibers belonging to mammalian muscles.
Very limited information has been published on the recording with electrodes of signals produced by most of the motor
units of a skeletal muscle. Implantable electrodes were developed because traditional surface recording techniques (for
the skin) and insertion or percutaneous electrodes (wire or needle), do not just in situ monitoring for long periods of time
[2, 3] without the stability and signal reliability is compromised. This long-term recording is used for the control of
myoelectric prosthesis [4, 5, 6, 7, 8, 9] where the stable and reliable recording of the signals of the majority of the motor
units in a muscle is an indispensable condition for the proper identification of the EMG signal. Surface electromyography
has been used to achieve this control with moderate success.
This work focuses on the development of implantable epimysial electrodes that, applied to chronic and in situ monitoring
of the electrical activity of most of the motor units of a skeletal muscle, help to reduce or avoid the problem related to
use surface and percutaneous electromyography. On the other hand, having an electrical model provides information on
the behaviour of the impedance of the implanted electrodes, without having to subsequently resort to a surgical procedure
for the implantation, and thus preventing the animal model from damaging or rejecting the implanted electrodes under
study. Excessive disturbance of the animal model is also avoided, and consequently the path of research on implantable
telemetry systems is shortened.
b)
c)
a)

IJARCCE
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DOI 10.17148/IJARCCE.2020.91201
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II. DESCRIPTION
The criteria for the construction of the implantable epimysial electrode are established in terms of design requirements
(electrode configuration involving size, shape and distance between electrode surfaces) and design elements (selection
of materials). Three different structures were made for the implantable electrodes: a) multipolar flat rectangular type
electrodes, b) multipolar round tubular type electrodes and c) bipolar flat rectangular type electrodes; some of them with
or without reference electrode. Names are assigned based on the configuration and shape of the surface on which the
sensor elements are mounted. Fig. 2 shows the three types of structures proposed for epimysial electrodes.
These epimysial electrodes must allow differential recording: bipolar type, consisting of two electrodes placed on the
muscle of interest and a third (reference) electrode placed on an adjacent muscle; of the multipolar type, with several
electrodes placed on the muscle of interest. These two types of recording are considered as the greatest amount of
information is desired from the EMG signal. Through the percutaneous connector, a means of communication is
established between the biological environment and the outside, which allows to follow the evolution of the impedance
of the electrode and to record the EMG signal. It also allows you to check the integrity and correct functioning of the
electrode during the implantation procedure.
The epimysial electrode was implanted in an animal model (young New Zealand rabbit) between the cervical and thoracic
portions of the trapezius muscle. This is because it is a large muscle that is difficult for the animal to access, thus
preventing the electrode from being pulled out once the animal is bothered by postoperative symptoms.
Fig. 2 Three structures proposed for the implantable epimysial electrode:
a) flat rectangular multipolar, b) round tubular multipolar and c) flat rectangular bipolar

IJARCCE
ISSN (Online) 2278-1021
ISSN (Print) 2319-5940
International Journal of Advanced Research in Computer and Communication Engineering
Vol. 9, Issue 12, December 2020
DOI 10.17148/IJARCCE.2020.91201
Copyright to IJARCCE IJARCCE 3
This work is licensed under a Creative Commons Attribution 4.0 International License
Once epimysial electrodes have been developed and implanted, they need to be evaluated in three main aspects:
mechanical, electrical and biological. These parameters are involved in obtaining a stable and reliable detection of
electrical activity produced by skeletal muscle, in situ and chronically.
This work focuses on the electrical aspect, which includes the evaluation of the electrical parameters of the electrode.
These parameters determine its behaviour during the implantation, through the impedance and EMG signal of the
implanted epimysial electrode. This is due to the fact that the recording of the impedance as a function of time since the
implantation gives an idea of the stability of the impedance as an indicator of the maturity period of the implanted
electrode. This is because this parameter is an indicator of the growth of fibrous tissue around the electrode. Likewise,
the impedance, as a function of frequency, provides a notion of the responsiveness to the EMG, based on a comparison
of the results under saline conditions, at the time of implantation and in the last weeks of registration. An electrical model
of the electrode is thus obtained to simulate its response as a circuit element, providing essential information for the
design of stimulation and recording systems.
Changes in the magnitude of impedance can be caused by changes in fibrous tissue, tissue fluid, muscle and the electrode
itself, during the implantation period. Major changes in impedance are present during the swelling, coagulation and
hemolysis stages. If the impedance remains constant over time, it may be an indication that the adaptation of the implanted
electrode in the biological environment has been achieved and, consequently, it becomes stable. Then it can be said that
stable and reliable physiologically tolerable or mature electrode, being appropriate for the chronic recording of EMG. To
measure the impedances of the implanted electrodes, a resistive circuit was applied, as shown in Fig. 3.
Fig. 3 Circuit applied to measure the impedance of the implanted electrodes
If: Vx = 2.5 sin ωt and: Vy = Vy sin (ωt + ϴ)
Current is given by:
)sen(
100

+= t
V
Iy
tIZ
e

sen5.2)1100( =+
Clearing for Ze:
1100
)sen(
sen250
1100
)sen(
100
sen5.2 −
+
=−
+
=




tV t
t
Vt
Z
y
y
e
If:
º
0
2
sen =A
tA

y

=+ 2
)sen( A
tA
Thus:
1100
250
1100
2
1
0
2
1
250
º
−







−=−














=


yy
eVV
Z
where: Vx = peak voltage from the generator
Vy = peak voltage at R100
f = natural frequency in Hz
tR = delay time in ms
tRF = delay time produced by the filters in ms
ω = angular frequency in rad/s

IJARCCE
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As: k ∟α = k cos (α) + j k sin (α)
So: Re = k cos (α) and: Im = k sin (α)







−+







−−=−−+−= )sen(
250
1100)cos(
250
1100)sen(
250
)cos(
250

yyyy
eV
j
VV
j
V
Z
22
)sen(
250
1100)cos(
250







−+







−−=

yy
eVV
Z
Magnitude of the electrode impedance (1)
ff 2832.62 ==

( )
1416.3
180
2832.6 −== RFRttft

( )
1802 −= RFRe tt

Electrode impedance angle (2)
Equations 3 and 4 are used to calculate the real and imaginary parts of the electrode impedance:
)cos(
eee ZR

=
(Ω) (3) y
)sen(
eee Z

=
(Ω) (4)
The input voltage signal, with amplitude of 5 Vpp (peak-to-peak voltage) and variable frequency, is produced by the
function generator. This voltage (Vx) is measured and adjusted, and its waveform is viewed on the oscilloscope through
channel 1. This signal will serve as the reference waveform. Current will flow through the entire circuit and a voltage
drop will appear across the 100 Ω resistor terminals. This voltage drop is sent through the filter and its output is measured
and viewed on channel 2 of the oscilloscope. This signal appears distorted, noisy, with reduced amplitude and delayed.
These characteristics arise because other signals are added through the electrode. The reduced amplitude is due to the
voltage drop across resistor R2, since R2 < R1. The delay is caused by the filters and capacitive components in the electrode
from their contact with the muscle.
The impedance was measured at 0.5, 1, 10, 100, 1000 y 5000 Hz under different conditions: a) before implantation with
the electrodes immersed in isotonic saline solution (unfiltered); b) at the time of implantation and c) during the period of
time that the electrode remained implanted in the animal model, daily. The magnitude and phase angle of the impedance
of the electrodes were calculated, for each frequency value, considering the peak-to-peak voltage at the filter output and
the delay time between the reference voltage and filter output.
III. RESULTS
To determine the maturity of the implanted epimysial electrode, the magnitude of the impedance was evaluated daily.
This evaluation lasted as long as the 6 electrodes remained within the animal model (bipolar: 1, 2, 3, 4; multipolar: 1 and
2). The averages of the impedance magnitudes obtained per week were calculated for each frequency, considering 5 days
of continuous recording. A second degree polynomial was fitted to the results of the averages. The fitted curve is shown
in Fig. 4 as a solid line.
The electrical model was obtained by comparison, by trial and error, the frequency response of the electrode in the last
weeks of impedance recording, with the response obtained from computer simulations. Initially, the model consisted of
two pairs of RC branches connected in parallel (R1C1 and R2C2), in series with a resistor R (R3 and R4). This structure
was later modified to indicate that an RC circuit is distributed over two electrode-electrolyte interfaces.

IJARCCE
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DOI 10.17148/IJARCCE.2020.91201
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Fig. 4 Curve fitting of the two most representative types of electrodes: Bipolar 1 and Multipolar 1, respectively
Finally, Fig. 5 shows the proposed electrical model.
Fig. 5. Electrical model of the implanted epimysial electrodes

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Resistor R4 represents the resistance of the junction between the Pt-Ir and stainless steel wires (the electrode conductors).
The parallel connection of R1 and C1 represents the charge distribution and the Helmholtz double layer at the electrode-
electrolyte interface, respectively. The double layer formed when the electrode and the electrolyte (tissue fluid) come
into contact generates a voltage E1, known as half-cell potential [1, 15, 16, 17, 18]. On the other side, the parallel branch
R2 and C2 represents the detection area formed in between the electrodes. Capacitance can be attributed to the surface of
the electrode, the separation between the electrodes, and the tissue fluid accumulated between them. The resistance is
attributed to the accumulated muscle tissue between both electrodes. R3 corresponds to the muscular and fibrous tissue
that grows around the electrodes. Table 1 shows the results obtained for these elements of the circuit from the frequency
response of the models of each of the electrodes.
TABLE 1 MAGNITUDES OF CIRCUIT ELEMENTS FOR EACH OF THE IMPLANTED EPIMYSIAL
ELECTRODES
Electrode type
Circuit elements
R1
C1
R2
C2
R3
R4
Model 1 (Bipolar 1)
1.95 k
104 μF
540
0.47 μF
353.2
8.4
Model 2 (Bipolar 2)
1.75 k
112 μF
340
1 μF
423.2
8.4
Model 3 (Bipolar 3)
1.46 k
123 μF
280
1.2 μF
241.4
9.3
Model 4 (Bipolar 4)
1.7 k
128 μF
480
0.36 μF
191.4
9.3
Model 5 (Multipolar 1)
2.7 k
64 μF
400
2.2 μF
414.6
7.7
Model 6 (Multipolar 2)
2.35 k
73.4 μF
560
0.49 μF
224.6
7.7
From these circuit elements, the magnitude of the total impedance of the electrical model between terminals A and B can
be calculated. The results are shown in Table 2 for the two most representative types of electrodes.
TABLE 2. MAGNITUDES OF IMPEDANCE AT DIFFERENT FREQUENCIES FOR THE TWO MOST
REPRESENTATIVE TYPES OF ELECTRODES
Electrode
type
Impedance magnitude ( )
Calculations for:
0.5 Hz
1 Hz
10 Hz
100 Hz
1 kHz
5 kHz
Bipolar 1
Saline solution
5844.444
4754.234
1706.911
564.482
378.579
308.974
At the time of
implantation
3983.338
2096.606
1401.029
665.620
Last month of
implant
(4 weeks)
4013.836
3090.014
2039.679
1192.587
595.473
446.037
Electric model
4086.176
3055.151
984.737
904.138
577.485
384.3
Matching
impedances
4013.835
3090.013
2039.578
1192.586
595.472
446.036
Multipolar 1
Saline solution
4782.353
4028.287
1464.187
562.377
323.490
283.450
At the time of
implantation
4822.771
2835.760
1533.803
718.447
Last month of
implant
(4 weeks)
5458.404
4325.299
2098.111
943.895
535.181
522.114
Electric model
5489.985
4265.938
1014.735
768.7
448.986
430.8
Matching
impedances
5458.403
4325.297
2098.110
943.894
535.180
522.113
If the Laplace transform is applied to the electrical model of the implanted epimysial electrode to obtain the impedance
Z(s) of the two-terminal structure, equation 5 is obtained.
34
22
2
11
1)(2
1
1
1
1
2)( RR
CR
s
C
CR
s
C
sZ ++
+
+












+
=
(5)

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To determine the real and imaginary components of the impedance of the equivalent circuit, s = jω is substituted into
equation 5. The rectangular form of Z(jω) is thus obtained.








+
+
+
+++
+
+
+
=2
2
2
2
2
2
2
2
2
1
2
1
2
1
2
1
43
2
2
2
2
2
2
2
1
2
1
2
111
2
2
11
2
)( CR
CR
CR
CR
jRR
CR
R
CR
R
Z






(6)
The behaviour of the impedance magnitude can be established considering equation 6, the equivalent circuit in Fig. 5 and
the graphs in Fig. 4. For the case of high frequencies, it can be seen in Fig. 4 that the magnitude of the resistance remains
approximately constant regardless of frequency (1 and 5 KHz). For the model in Fig. 5, the capacitive reactance
approaches zero as the frequency of the input signal between points A and B increases, producing a magnitude of
impedance equal to 2R4 + R3. It can be concluded that the behaviour magnitude impedance is mainly resistive. For the
case of low frequencies, the graphs in Fig. 4 show that the impedance is a function of the frequency of the input signal,
suggesting a capacitive behaviour in the impedance of the implantable electrodes.
IV. CONCLUSION
The maturity period of the implanted epimysial electrodes was determined as a function of the magnitude of the
impedance, when it reached its stage of stability. Periods of 15 to 20 weeks were obtained for bipolar electrodes and 15
to 35 weeks for multipolar electrodes.
Using the electrical model developed, a resistive and capacitive behaviour of the implanted epimysial electrodes was
verified. The capacitive effect is pronounced at 0.5, 1 and 10 Hz, and the resistive effect at 100, 1000 and 5000 Hz. These
effects test the instability of the impedance at low frequencies and its stability at high frequency, as well as the definition
of the elements of the circuit (resistors and capacitors) that form the electrical structure between electrode and muscle.
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BIOGRAPHY
Joel Flores Martínez received his B.Sc. in electronics and communications engineering from ESIME
Zacatenco IPN, Mexico, in 1997 and M.Sc. degree in Bioelectronics from CINVESTAV IPN, Mexico in
2000. Currently he is a Professor at the Department of Electronics and Communications engineering in
ESIME Zacatenco. His research interests are in acoustics and biomedical engineering.

IJARCCE
ISSN (Online) 2278-1021
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International Journal of Advanced Research in Computer and Communication Engineering
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DOI 10.17148/IJARCCE.2020.91201
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Patricia Lorena Ramírez Rangel received her B.Sc. in electronics and communications engineering from
ESIME Zacatenco IPN, Mexico, in 1997. Currently she is a teacher at the Department of Electronics and
Communications engineering in ESIME Zacatenco. Her research interests are in acoustics.
Rita Trinidad Rodríguez Márquez received her B.Sc. in electric engineering from ESIME Zacatenco IPN,
Mexico, in 1995. Currently she is a teacher at the Department of Electronics and Communications
engineering in ESIME Zacatenco. Her research interests are in the theory of electrical circuits.