Himeno, Y. | bioRxiv Science

bioRxiv2023

Mathematical Analysis of Left Ventricular Elastance with respect to Afterload Change During Ejection Phase

Since the left ventricle (LV) has pressure (P{iota}{upsilon}) and volume (V{iota}{upsilon}), we can define LV elastance from the ratio between P{iota}{upsilon} and V{iota}{upsilon}, termed as "instantaneous elastance." On the other hand, end-systolic elastance (Emax) is known to be a good index of LV contractility, which is measured by the slope of several end-systolic P{iota}{upsilon} -V{iota}{upsilon} points obtained by using different loads. The word Emax originates from the assumption that LV elastance increases during the ejection phase and attains its maximum at the end-systole. From this concept, we can define another elastance determined by the slopes of isochronous P{iota}{upsilon} -V{iota}{upsilon} points, that is P{iota}{upsilon} -V{iota}{upsilon} points at a certain time after the ejection onset time by using different loads. We refer to this elastance as "load-dependent elastance." To reveal the relation between these two elastances, we used a hemodynamic model that included a detailed ventricular myocyte contraction model. From the simulation results, we found that the isochronous P{iota}{upsilon} -V{iota}{upsilon} points lay in one line and that the line slope corresponding to the load-dependent elastance slightly decreased during the ejection phase, which is quite different from the instantaneous elastance. Subsequently, we analyzed the mechanism determining these elastances from the model equations. We found that instantaneous elastance is directly related to contraction force generated by the ventricular myocyte, but the load-dependent elastance is determined by two factors: one is the transient characteristics of the cardiac cell, i.e., the velocity-dependent force drops characteristics in instantaneous shortening. The other is the force-velocity relationship of the cardiac cell. We also found that the linear isochronous pressure-volume relation is based on the approximately linear relation between the temporal differential of the cellular contraction force and the cellular shortening velocity that results from the combined characteristics of LV and aortic compliances.

biophysics↗

bioRxiv2022

The gradient-based parameter optimization to determine membrane ionic current composition of human induced pluripotent stem cell-derived cardiomyocytes

1.Premature cardiac myocytes derived from human-induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), most probably because of different expression patterns of membrane ionic currents. We aim to develop a method of determining expression patterns of functional channels in terms of the whole-cell ionic conductances (Gx) using individual spontaneous AP configurations. However, it has been suggested that apparently identical AP configurations were obtained by different sets of ionic currents in a mathematical model of cardiac membrane excitation. If so, the inverse problem of Gx estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For realistic examination, conventional cell-specific models were prepared by superimposing the model output of AP on each experimental AP record by the conventional manual adjustment of Gxs of the baseline model. Then, Gxs of 4 ~ 6 major ionic currents of the cell-specific models were randomized within a range of {+/-}5 ~ 15% and were used as initial parameter sets for the gradient-based automatic Gxs recovery by decreasing the mean square error (MSE) between the target and model output. When plotted all data points of MSE - Gx relation during the optimization, we found that the randomized population of Gxs progressively converged to the original value of the cell-specific model with decreasing MSE. To confirm the absence of any other local minimum in the global search space, we mapped the MSE by randomizing Gxs over a range of 0.1 ~ 10 times the control. No additional local minimum of MSE was obvious in the whole parameter space besides the global minimum of MSE at the default model parameter.

physiology↗