In silico identification of potential calcium dynamics and sarcomere targets for recovering left ventricular function in rat heart failure with preserved ejection fraction

Fig 1. 3D biventricular rat heart contraction model multi-scale map. Chosen 16 input parameters are calcium transient and sarcomere properties (green), hemodynamics properties (red) and tissue properties (blue). The output features of interest are 14 indexes (yellow) characterising the LV function and are extracted from the LV pressure and volume curves. The input parameters (Table 1) can be quantitatively be mapped to the output features (Table 2) either by running the full model or by making predictions using trained GPEs.

Fig 2. Model validation workflow. (1) The pore block model is used to calculate the fraction of blocked ion channel at a given compound concentration for each ion channel. These channels’ conductances are scaled to reflect the effect of the compound. (2) The rat myocyte electrophysiological model is run to generate perturbed calcium transients for different compound concentrations. (3) The calcium transients are used as an input for the 3D biventricular rat heart contraction model, and perturbed LV features’ values are obtained. For each LV feature, the number of perturbed values was equal to the number of input calcium curves, which corresponds to the number of tested compound concentrations. (4) Each LV feature values are plotted against the tested compound concentrations to obtain dose-response curves. (5) The qualitative trend of the LV features after in silico pharmacological modulation is compared with literature experimentally measured effects of the same compound on the same LV features for each compound under study.

Fig 3. Sobol’ first-order (S1) and total effects (ST). The contribution of each parameter (Table 1) by itself (S1) or jointly with the other parameters (ST) into explaining the total variance of each LV feature (Table 2) is expressed as Sobol’ indices ranging from 0 (no effect) to 1 (maximal effect).

Fig 4. Model validation against known CiPA compounds effects on whole-organ function. Eight CiPA compounds effects (“experiment” columns) on PeakP, maxdP and mindP are compared with model same compounds’ predicted effects on the same features (“model” columns). The effects of compounds are colour-coded as orange (feature unchanged) and green (feature decreased). None of the compounds caused an increase in the considered LV features. White/empty space means that the specific effect could not be retrieved from the examined literature studies. Model predicted effects are in agreement with the experimentally observed effects for 6 out of 8 compounds.

Fig 5. Representative SHAM and ZSF1 rat models calcium transients and pressure-volume loops. The ZSF1 rat model is created by perturbing the SHAM, healthy state. LV features which significantly changed from control to diseased animal are highlighted at the center of the PV loops sub-plot. EF showed no significant change.

Fig 6. History matching waves progression. At each wave, 128 points are simulated from the current non-implausible parameter region and the features’ values from the converging simulations are plotted as box plots coloured in blue variants for different consecutive waves. The median trend of these distributions is represented by a dashed blue line. Mean ±3 standard deviations target intervals are represented in light red-coloured shaded areas for each LV feature.

Fig 7. Best fit recovered rat heart models. For each parameter group, the last wave fitted models are compared against the target mean which the history matching aimed to match, and the best-fit model is selected according to the L2-norm. This best-fit rat model (RECOV, black thick line) is compared with the reference ZSF1 rat model (red dashed line) and with the reference SHAM rat model (blue dashed line).

Fig 8. Parameter distributions across progressing waves for the four different parameter groups. Each parameter distribution is represented as a gray box plot at each wave. Its median trend during multiple waves is highlighted in a solid black line and is compared with the ZSF1 rat model reference value for the same parameter highlighted in a dashed red line. All the plotted RECOV parameter values are given as percentages of the respective baseline ZSF1 parameter values. (A) Ca group. (B) TNF group. (C) TKF group. (D) CaMYO group.

Fig 9. Isometric force-calcium relationship and generated active tension properties from the recovered rat model parameter space. (A) Calcium sensitivity (pCa50) and Hill coefficient (h) features are extracted from the force-calcium curve, while peak tension (Tmax) and maximum rates of tension development (dT/dtmax) and decay (dT/dtmin) are extracted from the twitch transient. (B) Distributions of extracted pCa50 (blue), h (orange), Tmax (green), dT/dtmax (red), dT/dtmin (purple) values are compared with the respective ZSF1 rat model baseline values (dashed lines).