Improving the accuracy of retrieved cardiac electrical conductivities

Abstract

Accurate values for the six cardiac conductivities of the bidomain model are crucial for meaningful electrophysiological simulations of cardiac tissue and are yet to be achieved. A two-stage optimisation process is used to retrieve the cardiac conductivities from cardiac potentials measured on a multi-electrode array—the first stage simultaneously fits all six conductivities, and the second stage fits a subset of the conductivities (intracellular conductivities), while holding the remainder of the conductivities (extracellular conductivities) constant. Previous studies have shown that the intracellular conductivities are retrieved to a lesser degree of accuracy than extracellular conductivities. This study tests the proposition that there exists a relationship between the extracellular and intracellular conductivities during the second stage of the optimisation that affects the accuracy of the retrieved intracellular conductivities. A measure to quantify this relationship is developed using polynomial chaos. The results show that a significant relationship does exist, and thus any errors in the extracellular conductivities are magnified in the retrieved intracellular conductivities. Thus, it is suggested that future protocols for retrieving conductivities incorporate the uncertainty in the extracellular conductivities.

References

• R. C. Aster, B. Borchers, and C. H. Thurber. Parameter Estimation and Inverse Problems. Elsevier, 2018. doi: 10.1016/C2015-0-02458-3
• W. Huberts, W. P. Donders, T. Delhaas, and F. N. van de Vosse. Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model. Int. J. Numer. Meth. Biomed. Eng. 30.12 (2014), pp. 1679–1704. doi: 10.1002/cnm.2695
• B. M. Johnston, S. Coveney, E. T. Y. Chang, P. R. Johnston, and R. H. Clayton. Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia. Med. Bio. Eng. Comput. 56.5 (2018), pp. 761–780. doi: 10.1007/s11517-017-1714-y
• B. M. Johnston and P. R. Johnston. Approaches for determining cardiac bidomain conductivity values: Progress and challenges. Med. Bio. Eng. Comput. 58 (2020), pp. 2919–2935. doi: 10.1007/s11517-020-02272-z
• B. M. Johnston and P. R. Johnston. Determining six cardiac conductivities from realistically large datasets. Math. Biosci. 266 (2015), pp. 15–22. doi: 10.1016/j.mbs.2015.05.008
• B. M. Johnston, P. R. Johnston, and D. Kilpatrick. A new approach to the determination of cardiac potential distributions: Application to the analysis of electrode configurations. Math. Biosci. 202.2 (2006), pp. 288–309. doi: 10.1016/j.mbs.2006.04.004
• A. Kamalakkannan, P. R Johnston, and B. M. Johnston. A modified approach to determine the six cardiac bidomain conductivities. In: Comput. Bio. Med. 135, 104549 (2021). doi: 10.1016/j.compbiomed.2021.104549
• I. J. Legrice, P. J. Hunter, and B. H. Smaill. Laminar structure of the heart: A mathematical model. Am. J. Physiol. Heart Circ. Physiol. 272.5 (1997), H2466–H2476. doi: 10.1152/ajpheart.1997.272.5.H2466 References C166
• R. Plonsey and R. Barr. The four-electrode resistivity technique as applied to cardiac muscle. IEEE Trans. Bio-med. Eng. 29.7 (1982), pp. 541–546. doi: 10.1109/tbme.1982.324927
• D. D. Streeter Jr, H. M. Spotnitz, D. P. Patel, J. Ross Jr, and E. H. Sonnenblick. Fiber orientation in the canine left ventricle during diastole and systole. Circ. Res. 24.3 (1969), pp. 339–347. doi: 10.1161/01.res.24.3.339
• M. Sun, N. M. S. de Groot, and R. C. Hendriks. Cardiac tissue conductivity estimation using confirmatory factor analysis. In: Comput. Bio. Med. 135, 104604 (2021). doi: 10.1016/j.compbiomed.2021.104604
• L. Tung. A Bi-Domain Model for Describing Ischemic Myocardial D-C Potentials. Thesis. Massachusetts Institute of Technology, 1978. url: http://hdl.handle.net/1721.1/16177 [13] S. Weidmann. Electrical constants of trabecular muscle from mammalian heart. J. Physiol. 210.4 (1970), pp. 1041–1054. doi: 10.1113/jphysiol.1970.sp009256
• N. Wiener. The homogeneous chaos. Am. J. Math. 60.4 (1938), pp. 897–936. doi: 10.2307/2371268
• D. Xiu and G. E. Karniadakis. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24.2 (2002), pp. 619–644. doi: 10.1137/S1064827501387826