No abstract

Computational models of cardiac electrophysiology hold great potential in the drug discovery process to bridge the gap between in vitro and in vivo preclinical trials. Current methods for solving inverse problems in cardiac electrophysiology are limited by their accuracy, scalability, practicality, or a combination of these. We investigate the feasibility of using kernel methods to solve the inverse problem of estimating the parameters of ionic membrane currents from observations of corresponding action potential (AP) traces. In particular, we consider AP traces generated by a cardiac cell action potential model, which mimics those obtained experimentally in measurable in vitro cardiac systems. This proof-of-concept study aims to improve existing pipelines for identifying drug effects in "heart-on-a-chip" systems by introducing a new approach to solving the inverse problem. Using synthetic training data from the 1977 Beeler-Reuter AP model of mammalian ventricular cardiomyocytes, we demonstrate our recently proposed boosted KRR solver StreaMRAK, which is particularly robust and well-adapted for high-complexity functions. We show that this method is less memory demanding, estimates the model parameters with higher accuracy, and is less sensitive to parameter identifiability problems than existing methods, such as standard KRR solvers and loss-minimization schemes based on nearest neighbor heuristics.

Kernel ridge regression (KRR) is a popular scheme for non-linear non-parametric learning. However, existing implementations of KRR require that all the data is stored in the main memory, which severely limits the use of KRR in contexts where data size far exceeds the memory size. Such applications are increasingly common in data mining, bioinformatics, and control. A powerful paradigm for computing on data sets that are too large for memory is the streaming model of computation, where we process one data sample at a time, discarding each sample before moving on to the next one.In this paper, we propose StreaMRAK -a streaming version of KRR. StreaMRAK improves on existing KRR schemes by dividing the problem into several levels of resolution, which allows continual refinement to the predictions. The algorithm reduces the memory requirement by continuously and efficiently integrating new samples into the training model. With a novel sub-sampling scheme, StreaMRAK reduces memory and computational complexities by creating a sketch of the original data, where the sub-sampling density is adapted to the bandwidth of the kernel and the local dimensionality of the data.We present a showcase study on two synthetic problems and the prediction of the trajectory of a double pendulum. The results show that the proposed algorithm is fast and accurate.