Composite Biomarkers Derived from Micro-Electrode Array Measurements and Computer Simulations Improve the Classification of Drug-Induced Channel Block

Figure 1. (A) Schematic of one well of the nine-electrode MEA device. The bidomain equations are solved in the domain Ω with homogeneous Neumann boundary conditions on ΓN: ∇ϕe·n→=0 and homogeneous Dirichlet boundary conditions on ΓD: ϕe = 0 where the ground is located. (B) Corresponding finite element mesh.

Figure 2. Experimental recording of MEA field potential. Eight biomarkers are extracted from the time series: DA, depolarization amplitude; DW, depolarization width; RA, repolarization amplitude; FPD, field potential duration; AUCr, area under repolarization curve; RC, repolarizarion center; RW, repolarization width; FPN, field potential notch.

Figure 3. Comparison between in vitro and in silico MEA FP recordings. In each case, the FPs are recorded in control conditions and for five different drug concentrations. For the in silico measurements, the drugs effects are modeled using Equation (2), which amounts to reducing gfi, gsi or gso depending on the ion channel affected by the drug. (A) Effect of flecainide (sodium antagonist drug) on experimental recordings (left) and effect of a virtual sodium antagonist drug on simulated MEA FPs (right). (B) Effect of diltiazem (assumed to be mainly calcium antagonist in this study) on experimental recordings (left) and effect of a virtual calcium antagonist drug on simulated MEA FPs (right). (C) Effect of moxifloxacin (potassium antagonist drug) on experimental recordings (left) and effect of a virtual potassium antagonist drug on simulated MEA FPs (right).

Figure 4. Steady-state analysis: the Bidomain equations are solved for 100 consecutive beats. Qualitatively, a satisfactory steady state is reached at the second beat (left). The beat-to-beat relative difference of the FP is monitored (right) and is to be compared to the relative difference between two identical solutions, each polluted by an independent noise (right).

Figure 5. Heterogeneity modeling: different APs obtained by simulating the MV model with different values of the heterogeneity parameter c. The heterogeneity parameter is a function of space and its pattern differs from one well to another (see Figure 6).

Figure 6. One sample of cell heterogeneity field c(x, y) generated using the correlation matrix method. As c ranges from 0 to 1, the cell action potential varies from that of cell type “A” to cell type “B” (see Figure 5).

Figure 7. Example of composite biomarkers weights. The three highest weights (in absolute value) are highlighted by a red dot for each composite biomarker. Note that some classical biomarkers are selected by the method: DA~ for gfi, RC~ (closely related to the FPD) for gsi and RA in the ratio (DA/RA) for gso.

Figure 8. Correlation matrix of the conductances of interest with the “classical” biomarkers (Left) and with the composite biomarkers (Right).

Figure 9. Plot of the 2,325 in silico conductances samples. Three populations of 155 virtual drugs were generated according to their ion channel targets: sodium antagonist drugs (red), calcium antagonist (blue) and potassium antagonist (green). For each drug, 5 different concentrations are considered which correspond to 5 different set of conductances. These conductances are then used as inputs to generate in silico MEA measurements using the bidomain equations.