Identifying Drug Response by Combining Measurements of the Membrane Potential, the Cytosolic Calcium Concentration, and the Extracellular Potential in Microphysiological Systems

FIGURE 1. Geometry used in the bidomain-base model simulations. The domain contains 8 × 8 evenly spaced electrodes, and the propagating wave is initiated by stimulating the lower left corner of the domain. The conduction velocity is computed between the electrodes marked as a and b, and when we plot the extracellular potential of just a single electrode, we consider the electrode marked as c.

FIGURE 2. Simulation procedure used to generate data for the inversions. In Step 1, we conduct bidomain-base model simulations, recording V, Ca and U for a number of time steps. In Step 2, we extract V and Ca data for inversion by recording the mean V and Ca over the domain at each time step and normalizing the traces to values between 0 and 1. In addition, U is recorded (in mV) in 8 × 8 electrodes at each time step during the depolarization wave.

FIGURE 3. Illustration of some of the properties included in the cost function Eq. 8. From the V-trace, we include a number of APD-values (see Eq. 9), and the integral of V above APD30 (see Eq. 11). From the Ca-trace, we include a number of CaD-values (see Eq. 10) in addition to the Ca transient time to peak, CaP (see Eq. 13). From the U data, we include the value in each time point and each electrode (see Eq. 14) and the conduction velocity computed using the time points in which U crosses 0 mV after the peak in different electrodes (see Eq. 15 and Figure 1).

FIGURE 4. Effect of perturbing I Kr, I CaL and I Na on the V, Ca and U data. For the U data, we show the extracellular potential in the electrode marked as c in Figure 1 and the time scale is zoomed in on the first 20 ms of the simulation.

FIGURE 5. Effect of perturbing I Kr, I CaL and I Na on the computed conduction velocity. The conduction velocities are computed from the U data as explained in Section 2.2.1.

FIGURE 6. Effect of perturbing I Kr, I CaL and I Na on the V, Ca and U data for three different adjustments, γ Ca, of the extracellular calcium concentration (see Section 2.3). For the U data, we show the extracellular potential in the electrode marked as c in Figure 1 and the time scale is zoomed in on the first 20 ms of the simulation.

FIGURE 7. Illustration of how including an extra extracellular calcium concentration adjustment may improve the identifiability of I Kr and I CaL. In the upper panel, we compare V and Ca for two different block combinations for the default extracellular calcium concentration (γ Ca = 0), and in the lower panel we consider the solutions for a 25% increased extracellular calcium concentration (γ Ca = 0.25). For γ Ca = 0, the two solutions are very similar, but the difference is increased for γ Ca = 0.25.

FIGURE 8. Repolarization wave in hiPSC-CM data and bidomain-base model simulations. The upper panel shows measurements of U during an action potential for three different data sets. The traces for the 64 electrodes are overlaid in the plots. In the second panel, we zoom in on the repolarization wave. The third panel shows U in three bidomain-base model simulations, and the bottom panel shows the corresponding repolarization waves. The parameters used in the simulations are given in Table 1, except for σ i and σ e which are reported in the plot titles.

FIGURE 9. Measured and simulated U data in 64 electrodes for the control case and for 10 μM Flecainide, modeled using IC50CaL = 9 μM, IC50NaL = 47 μM, IC50Kr = 1.9 μM, IC50Na = 0.2 μM, h i = 1 for i = CaL, NaL, and Kr, and h Na = 0.4. The parameters used in the simulations are given in Tables 1 and 2, and the default g Na value is increased by 45%. The stimulation location is adjusted to correspond to the propagation direction in the data.

FIGURE 10. Result of the inversion procedure applied to simulated data of twelve drugs, based on the block percentages corresponding to three times the free plasma Cmax reported in (Crumb et al., 2016).

FIGURE 11. Result of the inversion procedure applied to simulated data of the twelve drugs of Figure 10.We have here included 5% noise in the V data, 3% noise in the Ca data and 1% noise in the U data.