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Abstract

The pattern of action potential propagation during various tachyarrhythmias is strongly suspected to be composed of multiple re-entrant waves, but has never been imaged in detail deep within myocardial tissue. An understanding of the nature and dynamics of these waves is important in the development of appropriate electrical or pharmacological treatments for these pathological conditions. We propose a new imaging modality that uses ultrasound to visualize the patterns of propagation of these waves through the mechanical deformations they induce. The new method would have the distinct advantage of being able to visualize these waves deep within cardiac tissue. In this article, we describe one step that would be necessary in this imaging process—the conversion of these deformations into the action potential induced active stresses that produced them. We demonstrate that, because the active stress induced by an action potential is, to a good approximation, only nonzero along the local fiber direction, the problem in our case is actually overdetermined, allowing us to obtain a complete solution. Use of two- rather than three-dimensional displacement data, noise in these displacements, and/or errors in the measurements of the fiber orientations all produce substantial but acceptable errors in the solution. We conclude that the reconstruction of action potential-induced active stress from the deformation it causes appears possible, and that, therefore, the path is open to the development of the new imaging modality.