Mesin, Luca

English

PORTO Publications Open Repository TOrino

Luca Mesin 
 LISiN, Dipartimento di Elettronica, Politecnico di Torino, Torino, Italy 
MODEL OF GENERATION OF SURFACE EMG WITH MULTI-LAYER VOLUME 
CONDUCTOR WITH VARIABLE THICKNESS OF SUBCUTANEOUS TISSUE 
Primo Congresso Nazionale di Bioingegneria, Pisa, 3-5 luglio 2008 
1. INTRODUCTION 
Acknowledgements 
3. RESULTS 
References 
                                                            Simulation of surface electromyography (EMG) found application in the estimation of physiological variables (inverse problem), the choice of the detection system, the 
design and test of algorithms for information extraction, the interpretation of experimental results. Both analytical and numerical methods have been proposed.  
The thickness of the fat layer is divided into two contributions: a constant value and a variable 
function  
[1] Mesin L, Merletti R. Farina D. and Merletti R., “A novel approach for precise simulation of the EMG signal detected by surface electrodes”, IEEE Trans. on Biomed. Eng. 48: 637 – 646, 2001. 
[2] Farina D., Mesin L., Martina S., Merletti R.,  A surface EMG generation model with multi-layer cylindrical description of the volume conductor, IEEE Trans. on Biomed. Eng. 51: 415-426, 2004. 
[3] Mesin L., Farina D., Simulation of surface EMG signals generated by muscle tissues with in-homogeneity due to fiber pinnation, IEEE Trans. on Biomed. Eng., 51: 1521-1529, 2004. 
[4] Mesin L., Joubert M., Hanekom T., Merletti R., Farina D., A Finite Element Model for Describing the Effect of Muscle Shortening on Surface EMG, IEEE Trans. on Biomed. Eng., 53: 593-600, 2006.  
Fig.3 Example of A) monopolar and B) single differential (SD) interference signal and mean ± standard deviation 
(over 10 simulated distributions of the MUs within the muscle’s cross section) of ARV, MNF and CV (between 
adjacent pairs of channels). ARV and MNF from each simulation were normalised with respect to the mean value 
across channels.  
2. METHODS 
),(),( zxfyzxG F 
Assumed smooth and of the same magnitude as  Fy
A regular perturbation expansion of the potential can be considered 
),,(),,(),,(),,( 2210 zyxzyxzyxzyx  
Assumed very small  1
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A Taylor series of the boundary condition in terms of       is also considered 
                                                      A two layer volume conductor describing subcutaneous tissue and 
muscle tissues is considered. The subcutaneous tissue is assumed isotropic, the muscle anisotropic. 
Muscle layer is a hemi-space. Subcutaneous tissue has a variable thickness. 
Fig.2 A) Volume conductor with variable thickness of the subcutaneous tissue layer. B) Cross section of 
the volume conductor. C) Volume conductor with linear variation of subcutaneous tissue layer thickness.  
Fat layer 
Muscle layer 
5 mm 
y 
x 
z 
SD channel 1 
SD channel n 
Subcutaneous layer 
Muscle layer 
Fy
),( zxf
A) B) 
C) 
NMJ 
1.4 mm 
Subcutaneous layer 
Muscle layer 
5 mm 
Muscle fibre 
Distal tendon Proximal tendon 
60 mm 
Model of the subcutaneous tissue 
2.6 mm 
25 detection electrodes 
Volume conductor considered for the simulations 
y 
z 
NMJ: neuromuscular junction 
mS /103.4 4s
Subcutaneous tissue 
mSMT /09.0s
Muscle: transversal conductivity 
mSML /4.0s
Muscle: longitudinal conductivity 
Table 1: Simulated conductivities 
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FzzFyFxxzxfyy F



 Equating the same powers in     , a hierarchic mathematical problem (each problem with solution 
depending on the solutions of all the preceding ones) is obtained.  
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First order 
Each of these problems is defined in a plane layer volume conductor. The problem of order zero 
is not homogeneous (a Dirac delta function is considered here to study the impulse response), but 
has vanishing boundary condition. The other problems are homogeneous, but have a flux term 
from the boundary. All these problems can be solved analytically transforming the x and z space 
variables (see Fig. 1) into spatial frequency kx and kz by a 2D Fourier transform. 
Fig.1 Basic steps in the development of a structure based model of generation of surface EMG signals. A) Source of the problem. B) Poisson problem for different volume conductors. C) Detection system.  
Linearly varying subcutaneous 
thickness 
Constant subcutaneous 
thickness 
-12 
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A) Monopolar signals 
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11 
IZ 
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B) SD signals 
100 ms 
0 
IZ 
12 
1.0 
1.1 
MNF (normalised) 
0.6 
0.8 
1.1 
1.2 
ARV (normalised) 
3 
4 
5 
CV (m/s) 
1.2 
Proximal 
tendon 
Distal  
tendon 
-12 
Channel number 
0 12 -12 
Channel number 
0 12 -12 
Channel number 
0.9 
1.0 
1.1 
1.2 
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0.8 
1.0 
1.2 
3 
4 
5 
IZ 
Proximal 
tendon 
Distal  
tendon 
IZ 
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tendon 
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tendon 
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A structured generation model for EMG requires to address the following issues 
k j i zz yy xx 
r r r 
s s s s    
Plane layers [1] 
k j i zz 
r r r 
s s s s qq rr    
Cylindrical layers [2] 
Pinnate Muscle [3] 
air 
fat 
muscle 
skin 
k T n zz TT nn 
r r r 
s s s s    
n 
r 
T 
r ) ( ) , , ( z z y x s s  
) ( ) , , ( r s q r s  z 
Mathematical Problem: conductivity tensor for EMG, influence of geometry, boundary conditions  Analysis of the Source  Analysis of the Detection System 
Current Source 
Current 
Source 
Current 
Sink 
Muscle fibre 
Equivalent tripole 
Poisson problem. Homogeneous Neumann’s conditions at the boundaries 
Fusiform Muscle with curvilinear fibres [4] 
A) B) C) 
IJ  )( s 0ˆ  n
Transmembrane current 
Adesive linear electrode array 
Matrix of electrodes Anal probe 
+1 -1 -1 +2 -1 -1 +4 -1 
-1 
-1 
SD DD NDD 
Single  
Differential 
Double  
Differential 
Laplacian 
                                                     A linear variation of the thickness of the subcutaneous 
tissue layer between 1.4 and 2.6 mm along the direction of the muscle fibres was 
simulated (Fig. 2C). A linear array with 25 electrodes (5 mm inter-electrode distance), 
centred over the innervation zone was simulated. Fibres were located in a range of depths 
1 – 8 mm and with transversal distances from the detection array in the range -20 mm to 
20 mm. Symmetrical muscle fibres with semi-length 60 mm were simulated. Motor unit 
action potentials (MUAP) were simulated with a spread of neuromuscular junctions and 
tendons of 8 mm. The number of fibres in the MUs was distributed as an exponential 
function, with ratio of innervation numbers 20. The distribution of conduction velocity 
(CV) of the MUs was Gaussian, with mean 4 m/s and standard deviation 0.3 m/s. 
Interference EMG signals at 80% of maximal voluntary contraction (MVC) were 
simulated in monopolar and SD configuration (Fig. 3) for 10 random distributions of the 
MUs within the muscle.  
Average rectified value (ARV) and mean frequency (MNF) were estimated from a 5 s 
portion of simulated signal for each monopolar and SD channel. CV was estimated by a 
maximum likelihood method from channel pairs. Results are shown in Fig. 3.  
Variables can be estimated reliably only far from IZ and tendons. Far from IZ and 
tendon, ARV and MNF are lower when estimated above a thicker subcutaneous tissue 
layer (about 10%, 20% variation for ARV and 10%, 5% for MNF estimated from 
monopolar-SD signals, respectively). CV was not affected by the simulated variation of 
thickness of the subcutaneous tissue layer. 
                                                       This work introduces an analytical model of simulation 
of surface EMG that, together with the other models proposed in the literature, is 
contributing to understanding the effect of particular conductivity or geometrical 
properties of the tissues on the recorded signals. Even simulating small variations of 
subcutaneous thickness, the results provided show that amplitude and spectral variables 
extracted from EMG are largely affected by the position of the detection point. On the 
other hand, CV estimated by a maximum likelihood approach from channel pairs is not 
affected by the thickness of the subcutaneous tissue in the simulated range of variation. 
Work supported by the European Community project n. 016712 “Cybernetic Manufacturing Systems (CyberManS)”.  
4. CONCLUSIONS 


A Finite Element Model for Describing the Effect of Muscle Shortening on Surface EMG,

A surface EMG generation model with multi-layer cylindrical description of the volume conductor,

Simulation of surface EMG signals generated by muscle tissues with in-homogeneity due to fiber pinnation,

Model of generation of surface EMG with multi-layer volume conductor with variable thickness of subcutaneous tissue

MESIN, LUCA

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEModel of generation of surface EMG with multi-layer volume conductor with variable thickness of subcutaneous tissue /MESIN L.. - (2008), pp. 495-496. ((Intervento presentato al convegno Primo Congresso Nazionale di Bioingegneria,tenutosi a Pisa nel 3-5 LUGLIO 2008..OriginalModel of generation of surface EMG with multi-layer volume conductor with variable thickness ofsubcutaneous tissuePublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/1919729 since:Primo Congresso Nazionale di Bioingegneria   (Congresso GNB2008)  Pisa, 3-5 luglio 2008 MODEL OF GENERATION OF SURFACE EMG WITH MULTI-LAYER VOLUME CONDUCTOR WITH VARIABLE THICKNESS OF SUBCUTANEOUS TISSUE   L. Mesin LISiN, Department of Electronics, Polytechnic of Turin, Italy    INTRODUCTION Simulation of surface electromyography (EMG) found application in the estimation of physiological variables (inverse problem), the choice of the detection system, the design and test of algorithms for information extraction, the interpretation of experimental results. Both analytical and numerical methods have been proposed in the literature [1] to simulated surface EMG. In spite of the higher flexibility of numerical methods, analytical solutions are valuable to check the accuracy of numerical methods, to reduce the computational time and to determine the theoretical dependence of the solution on specific parameters of the system.  Surface EMG can be described as a propagating wave in space invariant volume conductors. This allows reducing the simulation time and considering the detection channels as spatial filters. Recent works investigated also non space invariant volume conductors, indicating the effect of tissue inhomogeneity or complex geometry on the simulated EMG signal. Also small perturbations from space invariant volume conductors can have important effects on surface EMG and on EMG variables. Models can provide indication on the effect of a specific perturbation from the ideal space invariant volume conductor. This work introduces a new analytical model for the generation of surface EMG signals from a non space invariant volume conductor constituted by a planar muscle and a subcutaneous tissue with variable thickness.   METHODS Tissues are modelled as volume conductors in stationary conditions. The electric potential is obtained by solving an electrostatics problem with isolation condition at the surface I )(  , where   is the electric potential, I  is the source current density, and   the conductivity tensor. A two layer volume conductor describing subcutaneous tissue and muscle tissues is considered. The subcutaneous tissue is assumed isotropic with conductivity 4103.4   S/m. Muscle is anisotropic, with transversal conductivity 09.0MT  S/m and longitudinal conductivity 4.0ML  S/m. Muscle layer is a hemi-space. Subcutaneous tissue layer is placed over the muscle and has a variable thickness, described by a function ),( zxGy   (Figure 1). The thickness of the subcutaneous tissue is divided into a constant value Fy  and a function ),( zxf  (smooth and of the same magnitude as Fy ) multiplied by parameter 1 , so that small variations with respect to the constant thickness Fy  are considered. An approximate impulse response is obtained analytically by expanding the function ),( zxG  describing the subcutaneous tissue surface Fig.1 A) Volume conductor with variable thickness of the subcutaneous tissue layer. B) Cross section of the volume conductor. C) Volume conductor with linear variation of subcutaneous tissue layer thickness considered for s mulatio s. Primo Congresso Nazionale di Bioingegneria   (Congresso GNB2008)  Pisa, 3-5 luglio 2008 and the solution as a series of powers of  . A hierarchy of Poisson problems is obtained for a planar geometry, for which a solution can be found. Series truncation to a second order approximation was considered.  RESULTS AND DISCUSSION As an example of application, a linear variation of the thickness of the subcutaneous tissue layer between 1.4 and 2.6 mm along the direction of the muscle fibres was considered. A linear array with 25 electrodes (5 mm inter-electrode distance), centred over the innervation zone was simulated (Figure 1C). Fibres were located in a range of depths 1 – 8 mm and with transversal distances from the detection array in the range -20 mm to 20 mm. Symmetrical muscle fibres with semi-length 60 mm were simulated (Figure 2). Motor unit action potentials (MUAP) were simulated with a spread of neuromuscular junctions and tendons of 8 mm. The number of fibres in the MUs was distributed as an exponential function [2], with ratio of innervation numbers 20. The distribution of conduction velocity (CV) of the MUs was Gaussian, with mean 4 m/s and standard deviation 0.3 m/s. Interference EMG signals were simulated for 10 random distributions of the MUs within the muscle (80% MVC) using the model in [2].  Average rectified value (ARV) and mean frequency (MNF) were estimated from a 5 s portion of simulated signal for each monopolar and SD channel. CV was estimated by a maximum likelihood method from channel pairs (Figure 2). Variables can be estimated reliably only far from IZ and tendons. Far from IZ and tendon, ARV and MNF are lower when estimated above a thicker subcutaneous tissue layer (about 10%, 20% variation for ARV estimated from monopolar-SD signals, respectively; 10%, 5% variation for MNF estimated from monopolar-SD signals, respectively). CV was not affected by the simulated variation of thickness of the subcutaneous tissue layer.    In conclusion, this work introduces an analytical model of simulation of surface EMG that, together with the other models proposed in the literature, is contributing to understanding the effect of particular conductivity or geometrical properties of the tissues on the recorded signals. Even simulating small variations of subcutaneous thickness, the results provided show that amplitude and spectral variables extracted from EMG are largely affected by the position of the detection point. On the other hand, CV estimated by a maximum likelihood approach from channel pairs is not affected by the thickness of the subcutaneous tissue in the simulated range of variation.   REFERENCES [1] Farina D. et al.,  Med. Biolog. Eng. & Comp., 42, 467-476 (2004).  [2] Fuglevand A.J. et al., J Neurophysiol., 1993, 70:2470-2488.   ACKNOWLEDGEMENTS  Work supported by the European Community project n. 016712 “Cybernetic Manufacturing Systems (CyberManS)”.  Fig.2 Example of A) monopolar and B) single differential (SD) interference signal and mean ± standard deviation (over 10 simulated distributions of the MUs within the muscle’s cross section) of ARV, MNF and CV. ARV and MNF from each simulation were normalised with respect to the mean value across channels.  

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Model of generation of surface EMG with multi-layer volume conductor with variable thickness of subcutaneous tissue

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