From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology

Abstract

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.

Deriving the Bidomain Model of Cardiac Electrophysiology From a Cell-Based Model; Properties and Comparisons

“…The second limitation is that convergence is obtained using a relatively coarse mesh ( x ∼ 0.25 mm, see Xie et al, 2004;Clayton and Panfilov, 2008;Niederer et al, 2011b) and thus a typical mesh block contains several hundred cardiomyocytes (see, e.g., Jaeger et al, 2021a,b). Therefore, understanding of the conduction properties (see, e.g., Henriquez, 2014;Veeraraghavan et al, 2014) close to the myocytes cannot be achieved using these models (see, e.g., Jaeger et al, 2021a).…”

“…These limitations of the homogenized (bidomain/monodomain) models are well known and several authors have developed alternatives where all individual cells are explicitly represented in the models (see, e.g., Spach et al, 2007;Jacquemet and Henriquez, 2009;Hubbard and Henriquez, 2014;Lin and Keener, 2014;Tveito et al, 2017a;Weinberg, 2017;Jaeger et al, 2019Jaeger et al, , 2021aDomínguez et al, 2021;Jaeger and Tveito, 2021). Here, we will apply the EMI model where both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model (see, e.g., Tveito et al, 2017a,b;Jaeger and Tveito, 2021), and compare properties with the homogenized bidomain model.…”

Image-Driven Modeling of Nanoscopic Cardiac Function: Where Have We Come From, and Where Are We Going?

“…Still, this problem represents a substantial computational effort. To date, very large cardiac simulations involving both classical and more recent electrodiffusion models ( Tveito et al, 2017 ; Jæger et al, 2021a ) have been performed at a similar scale (several billion computational nodes), albeit using powerful compute resources and for very brief simulation times ( Jæger et al, 2021b ). As such, approaching this computational problem is likely to require similarly substantial computational resources, thoroughly optimized numerical implementations, and well-designed simulations of relatively short duration.…”

“…The storied work of Hodgkin and Huxley (1952a , b , c , d) and Hodgkin et al (1952) gave every reason for optimism, and the same methods were quickly applied to understand cardiac electrical activation ( Noble, 1962 ). From these formalisms, continuum mathematical representations were developed to understand many aspects of macroscopic cardiac function ( Plonsey and Barr, 1987 ; Henriquez, 1993 , 2014 ; Henriquez et al, 2004 ; Roberts et al, 2008 ; Tveito et al, 2017 ; Jæger et al, 2021a ). As many of the imaging methods described above have developed, it has become apparent that nanometer scale structures and their functional dynamics make critical contributions to cardiac electrophysiology and contractile function.…”

Nano-scale solution of the Poisson-Nernst-Planck (PNP) equations in a fraction of two neighboring cells reveals the magnitude of intercellular electrochemical waves

“…We then let the model approach a resting state by letting only the K + channels be open between the intracellular and extracellular spaces on the membrane of both cells. For the initial conditions (electroneutral), ρ is zero, and φ is constant (see (6) and ( 10)).…”