Improving cardiomyocyte model fidelity and utility via dynamic electrophysiology protocols and optimization algorithms

Abstract

Mathematical models of cardiac electrophysiology are instrumental in determining mechanisms of cardiac arrhythmias. However, the foundation of a realistic multiscale heart model is only as strong as the underlying cell model. While there have been myriad advances in the improvement of cellular-level models, the identification of model parameters, such as ion channel conductances and rate constants, remains a challenging problem. The primary limitations to this process include: (1) such parameters are usually estimated from data recorded using standard electrophysiology voltage-clamp protocols that have not been developed with model building in mind, and (2) model parameters are typically tuned manually to subjectively match a desired output. Over the last decade, methods aimed at overcoming these disadvantages have emerged. These approaches include the use of optimization or fitting tools for parameter estimation and incorporating more extensive data for output matching. Here, we review recent advances in parameter estimation for cardiomyocyte models, focusing on the use of more complex electrophysiology protocols and global search heuristics. We also discuss future applications of such parameter identification, including development of cell-specific and patient-specific mathematical models to investigate arrhythmia mechanisms and predict therapy strategies.

Figure 1. Limitations to cardiac myocyte ionic model development

Top: experimental and species variability is illustrated for a human ventricular myocyte model (the ten Tusscher et al. 2004 model). Different ionic components originate from previous modelling or experimental studies using data from a variety of species obtained at a range of temperatures. Reproduced from Niederer et al. (2009) with permission. Left: cell‐to‐cell variability in action potential for 14 myocytes isolated from the guinea pig left ventricle (following the protocol in Groenendaal et al. 2015). Bottom: manual tuning of parameters provides only poor coverage of the model parameter space (red dots represent parameter combinations tested) and may not find the best solution (the dark blue well). Right: two different sets of conductance parameters (represented by blue and red) give rise to overlapping action potentials, emphasizing that simple dynamics cause non‐uniqueness. Reproduced from Sarkar & Sobie (2010).

Figure 2. Progression of genetic algorithm parameter estimation

A–C, the genetic algorithm is initialized with 500 random individuals, i.e. model instantiations, in generation 0. Models are paced and a single action potential is recorded as its phenotype. The fitness of each individual is calculated inversely as an error (sum of squared differences) between model output and target objective action potential. Left columns show action potentials generated by three different generation 0 model instantiations (traces are coloured according to their error and colour bar in F) compared to the baseline 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 model value. Parameters 1–9 correspond to maximal conductance of the sodium current, the L‐type calcium current, the T‐type calcium current, the inwardly rectifying potassium current, I _Kr, I _Ks, the plateau potassium current, the sarcolemmal calcium pump current, and the maximal flux of the sarcoplasmic reticulum Ca²⁺‐ATPase, 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 original model are indistinguishable by eye, although the bar graph indicates differences among the parameters (E). Reprinted from Groenendaal et al. (2015).

Figure 3. Complex objectives improve parameter estimation and predictive power

A, irregular sequence of action potentials due to stochastic pacing. B, multi‐segment voltage‐clamp protocol and resulting current response. C, improvements in the in silico, genetic algorithm‐based, parameter estimation of I _Kr and I _Ks conductances by enhancing the optimization objective, from a single action potential (cyan triangles), stochastic stimulation (blue circles), or multi‐segment voltage clamp (green squares), to the combined stochastic pacing and voltage‐clamp protocol (orange diamonds). A parameter scaling of 1 indicates the baseline value to be recovered. Symbols indicate the best solution from each of 10 individual runs, differing due to the random nature of the genetic algorithm. Error bars give mean ± standard deviation. D, the ability of the optimized models to predict novel dynamics is calculated as the error in response to a novel stochastic pacing sequence (‘Prediction error’). Predictive ability is improved when using the stochastic pacing over the single action potential. The prediction error is large for the voltage‐clamp protocol alone, which does not train models according to membrane potential. Adding the voltage‐clamp protocol to the stochastic pacing protocol gives better predictions compared to stochastic stimulation alone. A second application of the genetic algorithm, allowing only fine, local, parameter changes (‘Iterative approach’, magenta triangles) results in improved parameter estimation and predictive power. Reproduced from Groenendaal et al. (2015).