Sampling methods for exploring between-subject variability in cardiac electrophysiology experiments

Abstract

Between-subject and within-subject variability is ubiquitous in biology and physiology, and understanding and dealing with this is one of the biggest challenges in medicine. At the same time, it is difficult to investigate this variability by experiments alone. A recent modelling and simulation approach, known as population of models (POM), allows this exploration to take place by building a mathematical model consisting of multiple parameter sets calibrated against experimental data. However, finding such sets within a high-dimensional parameter space of complex electrophysiological models is computationally challenging. By placing the POM approach within a statistical framework, we develop a novel and efficient algorithm based on sequential Monte Carlo (SMC). We compare the SMC approach with Latin hypercube sampling (LHS), a method commonly adopted in the literature for obtaining the POM, in terms of efficiency and output variability in the presence of a drug block through an in-depth investigation via the Beeler-Reuter cardiac electrophysiological model. We show improved efficiency for SMC that produces similar responses to LHS when making out-of-sample predictions in the presence of a simulated drug block. Finally, we show the performance of our approach on a complex atrial electrophysiological model, namely the Courtemanche-Ramirez-Nattel model.

Unlocking data sets by calibrating populations of models to data density: A study in atrial electrophysiology

“…Accurate prediction of the specific shapes of the APs for SR and cAF patients is important because it suggests that the differential actions of the many ionic currents that together produce the AP are being well captured by the POMs calibrated to distributions. This is critical when it comes to using these POMs for further analysis, such as considering the response of the different members of the population to drug treatments that act on specific membrane currents ( 7 , 22 ) or identifying the differences in underlying electrophysiology that characterize the two populations. We demonstrate these aspects in the following subsection.…”

“…These calibrated POMs have been used to great effect, including suggesting modifications to existing models of rabbit ventricular ( 15 ) and human atrial cells ( 16 ) required to reproduce specific data; determining the electrophysiological properties that lead to the dangerous phenomena of alternans ( 17 , 18 ), repolarization abnormalities ( 19 ), and atrial fibrillation ( 20 ); and characterizing the sources of the differing function of failing hearts ( 21 ). The technique has also been used to explore the variable response of a population to antiarrhythmic drug treatments ( 7 , 22 , 23 ), to the onset of ischemia in rabbits ( 24 ), and to the effects of hypertrophic cardiomyopathy ( 25 ). Most relevant to our work, calibrated POMs were used by Sánchez et al ( 26 ) to explore the differences between patients exhibiting sinus rhythm (SR) or chronic atrial fibrillation (cAF).…”

“…We extend a recent statistically informed sampling technique for POM construction ( 22 ), sequential Monte Carlo (SMC), to propose a new method that produces POMs directly calibrated to data distributions. As compared to Latin hypercube sampling (LHS), the uniform sampling approach typically used for range-based calibration ( 27 ), SMC identifies regions of the parameter space that correspond to a higher density of data and generates proportionally more samples in these locations.…”

“…As compared to Latin hypercube sampling (LHS), the uniform sampling approach typically used for range-based calibration ( 27 ), SMC identifies regions of the parameter space that correspond to a higher density of data and generates proportionally more samples in these locations. It also allows the complexity of the sampling problem to be introduced in a gradual fashion, relevant also when calibrating to ranges ( 22 ). We demonstrate not only how our calibration technique generates POMs that reproduce the distributions in experimental data but also, more importantly, how this type of calibration allows additional insights to be gained from these data.…”

Humans Vary, So Cardiac Models Should Account for That Too!

“…There are multiple approaches available for generating the population of models. For example, parameters and their ranges generate high-dimensional spaces from which their values are sampled using different sampling algorithms (e.g., the Latin Hypercube, Monte Carlo method) to generate an ensemble of variant models (Drovandi et al, 2016 ). The candidate models are simulated to mimic, for example, experimental settings regarding bath solution composition, voltage protocol, and pacing rate.…”