Cell-specific cardiac electrophysiology models

Abstract

The traditional cardiac model-building paradigm involves constructing a composite model using data collected from many cells. Equations are derived for each relevant cellular component (e.g., ion channel, exchanger) independently. After the equations for all components are combined to form the composite model, a subset of parameters is tuned, often arbitrarily and by hand, until the model output matches a target objective, such as an action potential. Unfortunately, such models often fail to accurately simulate behavior that is dynamically dissimilar (e.g., arrhythmia) to the simple target objective to which the model was fit. In this study, we develop a new approach in which data are collected via a series of complex electrophysiology protocols from single cardiac myocytes and then used to tune model parameters via a parallel fitting method known as a genetic algorithm (GA). The dynamical complexity of the electrophysiological data, which can only be fit by an automated method such as a GA, leads to more accurately parameterized models that can simulate rich cardiac dynamics. The feasibility of the method is first validated computationally, after which it is used to develop models of isolated guinea pig ventricular myocytes that simulate the electrophysiological dynamics significantly better than does a standard guinea pig model. In addition to improving model fidelity generally, this approach can be used to generate a cell-specific model. By so doing, the approach may be useful in applications ranging from studying the implications of cell-to-cell variability to the prediction of intersubject differences in response to pharmacological treatment.

Fig 1. Progression of GA estimation.

(A-C) The GA is initialized with 500 random individuals, i.e., model instantiations, in generation 0. Each individual is simulated according to the protocol, here a single action potential, and its error is calculated (sum of squared errors between model output and FR model target objective; Eq 2 in the Methods). Left columns show action potentials generated by three different generation 0 model instantations (traces are colored according to their error and color bar in panel F) compared to the baseline FR model (black). Right column bar graphs indicate the scaling of the nine model parameters for each individual, with a scaling of 1 representing the original FR model value. Parameters 1 through 9 correspond to: I_Na, I_CaL, I_CaT, I_K1, I_Kr, I_Ks, I_Kp, I_pCa, and J_SERCA, respectively. (D-G) With progression through the generations, individual action potentials become more similar to the optimization objective and errors decrease accordingly. At generation 100, the overall best individual and the FR model appear very similar, although the bar graph indicates differences among the parameters (E).

Fig 2. Stochastic stimulation improves parameter estimation and predictability.

(A) The stochastic stimulation optimization sequence (black) and the best fit from 10 GA runs applied to fit it (light blue dashed line) show the quality of the GA fit. (B) Zoom-in of shaded region in (A) shows fitness of closely coupled action potentials. (C) Using the stochastic stimulation optimization sequence in the objective function causes some improvement in parameter recovery (light blue circles) compared to using a single action potential (green squares), most notably for I_Kr, I_CaL, and I_Ks conductances. Symbols indicate the best individual from each of the 10 individual GA runs, error bars give the mean (black) ± standard deviation (gray), and the dashed line at parameter scaling 1 indicates the original FR model parameter values. (D) When subjected to a novel stimulation sequence, the error between the model fit based on the stochastic stimulation sequence and the FR model (light blue circles) is significantly smaller (p-value of 0.0001) than the error between FR model and the best fit based on a single action potential only (green squares), i.e., the stochastic stimulation objective leads to models with higher prediction accuracy.

Fig 3. Multi-step voltage clamp protocol.

(A) Voltage clamp protocol (blue) and current response (red). (B) Close-up of shaded region in (A) where voltage steps change rapidly. (C-G) Percentage contributions of the individual currents during particular parts of the protocol isolates I_K1 (C), I_CaL (E) and I_Ks (F and G) well.

Fig 4. Improvement of the optimization results with inclusion of voltage-clamp protocol and use of iterative optimization technique.

(A) Error reduction during optimization with combined stochastic pacing and voltage clamp objective. Circles indicate contribution to the summed error from each of the 500 individuals during stochastic pacing (blue) and voltage clamp (red), while the correspondingly colored traces give the population means. The summed error of the best individual is shown as the black trace. (B) Improvements in the parameter estimation from using stochastic stimulation (light blue circles) or voltage clamping (green squares), to using the combined stochastic pacing and voltage clamp protocol (orange diamonds), and to using the iterative optimization (magenta triangles) as visualized with estimation results centered around 1 and tighter error bars. Symbols indicate results from the individual runs; error bars give the mean (black) ± standard deviation (gray). (C) The prediction error is large for the voltage clamp protocol alone (green squares), which does not train models according to membrane potential. Adding the voltage clamp protocol to the stochastic pacing protocol (i.e., combined protocol; orange diamonds) gives better predictions compared to stochastic stimulation alone (light blue circles; p = 0.00005). The prediction error is further reduced when using the iterative optimization approach (magenta triangles; p = 0.0003).

Fig 5. GA voltage and current recovery for in vitro myocyte compared to FR model.

(A) Stochastic stimulation optimization sequence shows the difference between the experimental voltage response (red trace) and the original FR model (black trace). The GA fitted model (blue, dashed trace) matches the experimental action potentials closely. (B) The multi-step voltage clamp protocol reveals that the experimental current data is also very different from the original FR model, in particular during the first I_K1-inducing step which results in a much larger current in the experimental recording, and during I_Ks-inducing steps which trigger much larger currents in the model. Again, the experimental data is well fit by the optimized model. (C) The optimized model also predicts the response to a novel stochastic stimulation sequence well. This is reflected in the prediction error (D), which is reduced for the optimized models for all four cells (colored circles; standard deviation of the 10 best individuals for each cell falls with the circles) compared to the FR model (black circles). The data shown in (A-C) is from Cell 2. In (A) and (B) stimulus artifacts and capacitative currents were removed (see Methods), but data sets were plotted as continuous traces to ease visualization.

Fig 6. Parameter estimation for individual guinea pig left ventricular myocytes.

Estimated parameters from the four isolated myocytes (colored circles; bars give standard deviation) reveal conserved variation (e.g., I_K1, I_Ks, I_CaL) from the original FR model (dashed line) as well as cell-to-cell variability (e.g., I_Na).