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

Abstract

The bidomain model is considered to be the gold standard for numerical simulation of the electrophysiology of cardiac tissue. The model provides important insights into the conduction properties of the electrochemical wave traversing the cardiac muscle in every heartbeat. However, in normal resolution, the model represents the average over a large number of cardiomyocytes, and more accurate models based on representations of all individual cells have therefore been introduced in order to gain insight into the conduction properties close to the myocytes. The more accurate model considered here is referred to as the EMI model since both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model. Here, we show that the bidomain model can be derived from the cell-based EMI model and we thus reveal the close relation between the two models, and obtain an indication of the error introduced in the approximation. Also, we present numerical simulations comparing the results of the two models and thereby highlight both similarities and differences between the models. We observe that the deviations between the solutions of the models become larger for larger cell sizes. Furthermore, we observe that the bidomain model provides solutions that are very similar to the EMI model when conductive properties of the tissue are in the normal range, but large deviations are present when the resistance between cardiomyocytes is increased.

Physiological accuracy in simulating refractory cardiac tissue: the volume-averaged bidomain model vs. the cell-based EMI model

“…We have conducted a comparative analysis between the conventional bidomain model and the contemporary EMI model. As of the time of writing, only one other comparison study between these models has been published [11], and the present comparison is the first to consider strength-interval curves and the refractory period of cardiac tissue. The results bring to light three notable differences between the bidomain and EMI models that can be seen in the morphology of the SI curves, the lengths of the relative refractory periods (RRPs), and the difference in their respective resting thresholds.…”

“…Ongoing developments in high-performance computing make it feasible to perform meaningful simulations at such a level of detail. Due to the relative newness of the EMI model, however, there are only a handful of studies that explore its capabilities [5,4,6,7,8,9,10,11], and only one of these studies examines it in relation to the bidomain model [11]. In the present study, we compare the bidomain model to the EMI model in the context of unipolar stimulation of refractory cardiac tissue, an application relevant to the design of pacemakers and defibrillators.…”

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

“…This limits the modeling capabilities of these models. At the level of individual cardiomyocytes (� μm), cell-based (EMI) models representing both the extracellular (E) space, the cell membrane (M) and the intracellular (I) space can be applied; see, e.g., [2][3][4][5]. The EMI models increase the modeling capabilities, allowing parameters to vary between and within individual cardiomyocytes, at the cost of significantly increased computing efforts needed to solve the equations; see, e.g., [6].…”

Arrhythmogenic influence of mutations in a myocyte-based computational model of the pulmonary vein sleeve

“…This is referred to as the EMI model since it explicitly represents the extracellular (E) space, the membrane (M) and the intracellular (I) space, and thus follows the modeling tradition represented by, e.g., 25 , 33 . The average mesh length applied in the EMI model is m whereas mm is the standard mesh length for the bidomain model; see, e.g., 28 , 32 , 34 – 38 . Consequently, the size of one mesh block is about 1 pL for the EMI model and 15600 pL for the bidomain model.…”

“…Note that since convergence of the bidomain model is achieved at the mesh size mm, further physiological details cannot be achieved by decreasing the mesh parameter using this model. Further comparisons of the bidomain model and the EMI model are found in 38 .…”