Uncertainty Quantification in the Parameterization of Cardiac Action Potential Models Through the Singular Value Decomposition

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• Samuel Wall (Simula Research Laboratory)
• Thursday 06 June 2019, 15:30-16:00
• Seminar Room 1, Newton Institute.

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FHTW01 - Uncertainty quantification for cardiac models

Mathematical models describing cardiac action potential dynamics are highly used to understand processes that may disrupt the normal electrical activity of the heart.  However, these models, consisting of biophysical descriptions of ion flux and transport across membranes and through the cell, are heavily, heterogeneously, and non-uniquely parameterized, leading to significant uncertainty in their predictions.  Here we investigate this uncertainty, in the context of model parameterization through adjustment of the maximum conductances of the individual contributing ionic cellular currents.  It has been well described that non-unique solutions exist for given action potential dynamics using this approach, and we present a method for quantifying the uncertainty in this framework.  Our key question is this: How can the maximum conductances of a model be changed without giving appreciable changes to a given action potential? We probe this question using a method founded on the singular value decomposition of a matrix built from the contribution from all the individual ion currents over the time course of an action potential. When small singular values of this matrix are present, there exist identifiable combinations of currents that will lead to no or minimal change to the overall voltage waveform.  We test this method across a range of cardiac models, quantifying parameter uniqueness in each case, and testing whether the conclusion from linear analysis of the matrix of currents carries over to provide insight in the uniqueness of the parameters in the non-linear case.

This talk is part of the Isaac Newton Institute Seminar Series series.

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