Spatial-dependent regularization to solve the inverse problem in electromyometrial imaging

Recently, electromyometrial imaging (EMMI) was developed to non-invasively image uterine contractions in three dimensions. EMMI collects body surface electromyography (EMG) measurements and uses patient-specific body-uterus geometry generated from magnetic resonance images to reconstruct uterine electrical activity. Currently, EMMI uses the zero-order Tikhonov method with mean composite residual and smoothing operator (CRESO) to stabilize the underlying ill-posed inverse computation. However, this method is empirical and implements a global regularization parameter over all uterine sites, which is sub-optimal for EMMI given the severe eccentricity of body-uterus geometry. To address this limitation, we developed a spatial-dependent (SP) regularization method that considers both body-uterus eccentricity and EMG noise. We used electrical signals simulated with spherical and realistic geometry models to compare the reconstruction accuracy of the SP method to those of the CRESO and the L-Curve methods. The SP method reconstructed electrograms and potential maps more accurately than the other methods, especially in cases of high eccentricity and noise contamination. Thus, the SP method should facilitate clinical use of EMMI and can be used to improve the accuracy of other electrical imaging modalities, such as Electrocardiographic Imaging. Graphical abstract The spatial-dependent regularization (SP) technique was designed to improve the accuracy of Electromyometrial Imaging (EMMI). The top panel shows the eccentricity of body-uterus geometry and four representative body surface electrograms. The bottom panel shows boxplots of correlation coefficients and relative errors for the electrograms reconstructed with SP and two conventional methods, the L-Curve and mean CRESO methods.