Uncertainty Quantification in Simulations of Myocardial Ischemia

Abstract

Computational models of myocardial ischemia are parameterized using assumptions of tissue properties and physiological values such as conductivity ratios in cardiac tissue and conductivity changes between healthy and ischemic tissues. Understanding the effect of uncertainty in these parameter selections would provide useful insight into the performance and variability of the modeling outputs. Recently developed uncertainty quantification tools allow for the application of polynomial chaos expansion uncertainty quantification to such bioelectric models in order to parsimoniously examine model response to input uncertainty. We applied uncertainty quantification to examine reconstructed extracellular potentials from the cardiac passive bidomain based on variation in the conductivity values for the ischemic tissue. We investigated the model response in both a synthetic dataset with simulated ischemic regions and a dataset with ischemic regions derived from experimental recordings. We found that extracellular longitudinal and intracellular longitudinal conductivities predominately affected simulation output, with the highest standard deviations in regions of extracellular potential elevations. We found that transverse conductivity had almost no effect on model output.

Figure 1.

Forward solution from the synthetic dataset. Column one shows the 5 mm radius synthetic ischemic core. The black line shows the cut plane for subsequent visualization. Column two shows the forward solution using default conductivity parameters. Column three shows the PCE mean forward solution. Column four shows the PCE standard deviation due to all four parameters.

Figure 2.

Per-parameter standard deviations (mV) for the synthetic dataset. Columns one through four show the standard deviation contributions to the forward solution of extracellular longitudinal, extracellular transverse, intracellular longitudinal, and intracellular transverse ischemic tissue conductivities, respectively.

Figure 3.

Forward solution from the measured dataset. Column one shows isosurfaces of the measured ischemic regions. The black line shows the cut plane for subsequent visualization. Column two shows the measured extracellular potentials. Column three shows the forward solution using default conductivity parameters. Column four shows the PCE mean forward solution. Column five shows the PCE standard deviation due to all four parameters.

Figure 4.

Parameter standard deviations for the measured dataset. Figure arrangement is the same as Figure 2