Source localization in electromyography using the inverse potential problem

We describe an efficient method for reconstructing the activity in human muscles from an array of voltage sensors on the skin surface. MRI is used to obtain morphometric data which are segmented into muscle tissue, fat, bone and skin, from which a finite element model for volume conduction is constructed. The inverse problem of finding the current sources in the muscles is solved using a careful regularization technique which adds a priori information, yielding physically reasonable solutions from among those that satisfy the basic potential problem. Several regularization functionals are considered and numerical experiments on a 2D test model are performed to determine which performs best. The resulting scheme leads to numerical difficulties when applied to large-scale 3D problems. We clarify the nature of these difficulties and provide a method to overcome them, which is shown to perform well in the large-scale problem setting.

[1]  Gea Drost,et al.  Clinical applications of high-density surface EMG: a systematic review. , 2006, Journal of electromyography and kinesiology : official journal of the International Society of Electrophysiological Kinesiology.

[2]  Todd A. Kuiken,et al.  A multiple-layer finite-element model of the surface EMG signal , 2002, IEEE Transactions on Biomedical Engineering.

[3]  J. T. Stonick,et al.  Estimation and localization of multiple dipole sources for noninvasive mapping of muscle activity , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[4]  Gene H. Golub,et al.  Inexact Preconditioned Conjugate Gradient Method with Inner-Outer Iteration , 1999, SIAM J. Sci. Comput..

[5]  R. Gulrajani The forward and inverse problems of electrocardiography. , 1998, IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society.

[6]  Per Christian Hansen,et al.  Rank-Deficient and Discrete Ill-Posed Problems , 1996 .

[7]  D. Pai,et al.  Computed myography : three-dimensional reconstruction of motor functions from surface EMG data , 2008 .

[8]  H. Helmholtz Ueber einige Gesetze der Vertheilung elektrischer Ströme in körperlichen Leitern mit Anwendung auf die thierisch‐elektrischen Versuche , 1853 .

[9]  U. Ascher,et al.  Dynamic level set regularization for large distributed parameter estimation problems , 2007 .

[10]  E.F. LoPresti,et al.  Identifying significant frequencies in surface EMG signals for localization of neuromuscular activity , 1995, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society.

[11]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[12]  E. Chauvet,et al.  Inverse problem in the surface EMG: a feasibility study , 2001, 2001 Conference Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[13]  W. Rundell,et al.  Iterative methods for the reconstruction of an inverse potential problem , 1996 .

[14]  Uri M. Ascher,et al.  On level set regularization for highly ill-posed distributed parameter estimation problems , 2006, J. Comput. Phys..

[15]  Hui Huang,et al.  On Effective Methods for Implicit Piecewise Smooth Surface Recovery , 2006, SIAM J. Sci. Comput..

[16]  R. Greenblatt Probabilistic reconstruction of multiple sources in the bioelectromagnetic inverse problem , 1993 .

[17]  V. L. Stonick,et al.  Processing signals from surface electrode arrays for noninvasive 3D mapping of muscle activity , 1994, Proceedings of IEEE 6th Digital Signal Processing Workshop.

[18]  Hui Huang,et al.  Efficient reconstruction of 2D images and 3D surfaces , 2008 .

[19]  Dianne P. O'Leary,et al.  Deblurring Images: Matrices, Spectra and Filtering , 2006, J. Electronic Imaging.

[20]  A. Beardwell Electromyography , 1945 .

[21]  Dinesh K. Pai,et al.  Fast Musculoskeletal Registration Based on Shape Matching , 2008, MICCAI.

[22]  E. Haber,et al.  Preconditioned all-at-once methods for large, sparse parameter estimation problems , 2001 .

[23]  M. Murray,et al.  EEG source imaging , 2004, Clinical Neurophysiology.

[24]  Roberto Merletti,et al.  Electromyography. Physiology, engineering and non invasive applications , 2005 .

[25]  Michael P. Friedlander,et al.  Probing the Pareto Frontier for Basis Pursuit Solutions , 2008, SIAM J. Sci. Comput..

[26]  Uri M. Ascher,et al.  Multiple Level Sets for Piecewise Constant Surface Reconstruction in Highly Ill-Posed Problems , 2010, J. Sci. Comput..

[27]  R. Ilmoniemi,et al.  Interpreting magnetic fields of the brain: minimum norm estimates , 2006, Medical and Biological Engineering and Computing.

[28]  Y. Y. Belov,et al.  Inverse Problems for Partial Differential Equations , 2002 .

[29]  G. Chavent,et al.  Identification de la Non-Linearité D'Une équation Parabolique Quasilineaire , 1974 .

[30]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .