Farina, D.

Mesin, Luca

English

PORTO Publications Open Repository TOrino

 1
Const. Conductivity (7.5 mS/m) Const. Conductivity (5 mS/m)
First order expansion Second order expansion
0 5 10 15 20
-8
-6
-4
-2
0
2
Time (ms)
A.U.
-100 -50 0 50 100
1
3
5
7
mm
Variable conductivity of the fat layer considered
Const. Conductivity (7.5 mS/m)
C
on
du
ct
iv
ity
 o
f t
he
fa
t l
ay
er
 (m
S/
m
)
 
REPRESENTATIVE SIMULATION OF SINGLE FIBER ACTION 
POTENTIALS GENERATED BY THE PROPOSED MODEL IN CASE OF 
HOMOGENEOUS VOLUME CONDUCTOR AND IN CASE OF GAUSSIAN 
VARIATION OF CONDUCTIVITY OF THE SUBCUTANEOUS LAYER, 
WITH ZERO ORDER, FIRST ORDER, AND SECOND ORDER 
EXPANSIONS.  
T01: EMG modeling 
 
AN ANALYTICAL MODEL FOR SURFACE EMG GENERATION  IN VOLUME CONDUCTORS WITH 
SMOOTH VARIATION IN CONDUCTIVITY 
 
Mesin L.(1), Farina D.(2) 
(1) LISiN, Dept. of Electronics, Politecnico di Torino, Torino, Italy. (2) Center for Sensory-Motor Interaction 
(SMI), Department of Health Science and Technology, Aalborg University, Aalborg, Denmark 
 
AIMS: In this study we provide an analytical description of a non-space invariant 
volume conductor for surface EMG signal generation. The volume conductor presents 
a variation in conductivity along the direction of the muscle fibres. This may reflect 
the practical situation of tissues with different conductivity properties in different 
locations or of transitions between tissues with different properties.  
METHODS: The volume conductor comprises planar layers representing the muscle and 
subcutaneous tissues. The muscle tissue is homogeneous and anisotropic while the 
subcutaneous layer is inhomogeneous and isotropic. The inhomogeneity in the 
subcutaneous layer is modelled as a smooth variation in conductivity along the muscle 
fibre direction. The problem is studied in the two-dimensional Fourier domain with 
spatial angular frequencies corresponding to the longitudinal and perpendicular 
direction with respect to the 
muscle fibres, in planes parallel 
to the detection surface.  
Regular perturbation theory was 
applied, representing the 
solution as a series expansion. 
This leads to a set of Poisson’s 
problems, for which the source 
term in an equation and the 
boundary conditions are 
determined by the solution of 
the previous equations. This set 
of problems is solved iteratively, 
obtaining approximations of 
higher order at each step. The 
series expansion is truncated for 
the practical implementation, 
leading to an approximate 
solution.  
RESULTS: The model was 
implemented in Matlab and 
showed high convergence rate. 
A second order expansion 
indeed provided an 
approximation with negligible 
error with respect to higher 
orders (Figure). A smooth 
change in the simulated 
conductivity of the 
subcutaneous layer determined a perturbation in the shape of the surface potential in 
the direction of source propagation (Figure). The perturbation dependsed on the 
position of the source, thus the model is not space invariant.  
 
Conclusions: The proposed model constitutes a new approach for surface EMG signal 
simulation with applications related to the validation of methods for information 
extraction from this EMG signals.  


An analytical model for surface sEMG generation in volume conductors with smooth variation in conductivity

MESIN, LUCA

FARINA D.

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

05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEAn analytical model for surface sEMG generation in volume conductors with smooth variation in conductivity / MESIN L.;FARINA D. - (2006). ((Intervento presentato al convegno XVI Congresso della International Society of Electrophysiology& Kinesiology (ISEK), tenutosi a Torino, nel 29 giugno - 1 luglio 2006.OriginalAn analytical model for surface sEMG generation in volume conductors with smooth variation inconductivityPublisher: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: 11583/1919687 since: 1Const. Conductivity (7.5 mS/m) Const. Conductivity (5 mS/m)First order expansion Second order expansion0 5 10 15 20-8-6-4-202Time (ms)A.U.-100 -50 0 50 1001357mmVariable conductivity of the fat layer consideredConst. Conductivity (7.5 mS/m)Conductivity of thefat layer (mS/m) REPRESENTATIVE SIMULATION OF SINGLE FIBER ACTION POTENTIALS GENERATED BY THE PROPOSED MODEL IN CASE OF HOMOGENEOUS VOLUME CONDUCTOR AND IN CASE OF GAUSSIAN VARIATION OF CONDUCTIVITY OF THE SUBCUTANEOUS LAYER, WITH ZERO ORDER, FIRST ORDER, AND SECOND ORDER EXPANSIONS.  T01: EMG modeling  AN ANALYTICAL MODEL FOR SURFACE EMG GENERATION  IN VOLUME CONDUCTORS WITH SMOOTH VARIATION IN CONDUCTIVITY  Mesin L.(1), Farina D.(2) (1) LISiN, Dept. of Electronics, Politecnico di Torino, Torino, Italy. (2) Center for Sensory-Motor Interaction (SMI), Department of Health Science and Technology, Aalborg University, Aalborg, Denmark  AIMS: In this study we provide an analytical description of a non-space invariant volume conductor for surface EMG signal generation. The volume conductor presents a variation in conductivity along the direction of the muscle fibres. This may reflect the practical situation of tissues with different conductivity properties in different locations or of transitions between tissues with different properties.  METHODS: The volume conductor comprises planar layers representing the muscle and subcutaneous tissues. The muscle tissue is homogeneous and anisotropic while the subcutaneous layer is inhomogeneous and isotropic. The inhomogeneity in the subcutaneous layer is modelled as a smooth variation in conductivity along the muscle fibre direction. The problem is studied in the two-dimensional Fourier domain with spatial angular frequencies corresponding to the longitudinal and perpendicular direction with respect to the muscle fibres, in planes parallel to the detection surface.  Regular perturbation theory was applied, representing the solution as a series expansion. This leads to a set of Poisson’s problems, for which the source term in an equation and the boundary conditions are determined by the solution of the previous equations. This set of problems is solved iteratively, obtaining approximations of higher order at each step. The series expansion is truncated for the practical implementation, leading to an approximate solution.  RESULTS: The model was implemented in Matlab and showed high convergence rate. A second order expansion indeed provided an approximation with negligible error with respect to higher orders (Figure). A smooth change in the simulated conductivity of the subcutaneous layer determined a perturbation in the shape of the surface potential in the direction of source propagation (Figure). The perturbation dependsed on the position of the source, thus the model is not space invariant.   Conclusions: The proposed model constitutes a new approach for surface EMG signal simulation with applications related to the validation of methods for information extraction from this EMG signals.  

Mesin, L.

Farina, Dario

An analytical model for surface EMG generation in volume conductors with smooth variation in conductivity

https://iris.polito.it/retrieve/handle/11583/1919687/50993/ISEK_Conductivity_Model.pdf

An analytical model for surface sEMG generation in volume conductors with smooth variation in conductivity

Abstract

Similar works

Full text

Available Versions

PORTO Publications Open Repository TOrino

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

VBN