Uncertainty quantification of fast sodium current steady-state inactivation for multi-scale models of cardiac electrophysiology

Abstract

Perhaps the most mature area of multi-scale systems biology is the modelling of the heart. Current models are grounded in over fifty years of research in the development of biophysically detailed models of the electrophysiology (EP) of cardiac cells, but one aspect which is inadequately addressed is the incorporation of uncertainty and physiological variability. Uncertainty quantification (UQ) is the identification and characterisation of the uncertainty in model parameters derived from experimental data, and the computation of the resultant uncertainty in model outputs. It is a necessary tool for establishing the credibility of computational models, and will likely be expected of EP models for future safety-critical clinical applications. The focus of this paper is formal UQ of one major sub-component of cardiac EP models, the steady-state inactivation of the fast sodium current, INa. To better capture average behaviour and quantify variability across cells, we have applied for the first time an ‘individual-based’ statistical methodology to assess voltage clamp data. Advantages of this approach over a more traditional ‘population-averaged’ approach are highlighted. The method was used to characterise variability amongst cells isolated from canine epi and endocardium, and this variability was then ‘propagated forward’ through a canine model to determine the resultant uncertainty in model predictions at different scales, such as of upstroke velocity and spiral wave dynamics. Statistically significant differences between epi and endocardial cells (greater half-inactivation and less steep slope of steady state inactivation curve for endo) was observed, and the forward propagation revealed a lack of robustness of the model to underlying variability, but also surprising robustness to variability at the tissue scale. Overall, the methodology can be used to: (i) better analyse voltage clamp data; (ii) characterise underlying population variability; (iii) investigate consequences of variability; and (iv) improve the ability to validate a model. To our knowledge this article is the first to quantify population variability in membrane dynamics in this manner, and the first to perform formal UQ for a component of a cardiac model. The approach is likely to find much wider applicability across systems biology as current application domains reach greater levels of maturity.

Sinusoidal Voltage Protocols for Rapid Characterisation of Ion Channel Kinetics

“…The cell-specific models outperformed a model constructed using averaged data from multiple cells/experiments, in line with the 'failure of averaging' discussed in Golowasch et al (2002) and the problems of fitting to averaged summary curves outlined in Pathmanathan et al (2015). Our inactivation protocol (Pr4) showed that it is possible for models to fit some (or all) summary curves well, without necessarily replicating the underlying current traces with less error.…”

Sinusoidal voltage protocols for rapid characterisation of ion channel kinetics

“…() and the problems of fitting to averaged summary curves outlined in Pathmanathan et al . (). Our inactivation protocol (Pr4) showed that it is possible for models to fit some (or all) summary curves well, without necessarily replicating the underlying current traces with less error.…”

Uncertainty quantification of 2 models of cardiac electromechanics

“…Such approach, which has not been pursued to date in the cardiac electromechanics community, will need an orchestrated effort between the modeling and experimental teams, as experimental data should thoroughly address and quantify the measurement error as well as the variability inherent to biological samples, and report it in terms of probability distributions that can be properly incorporated in uncertainty quantification analyses. First steps towards a UQ analysis of a cardiac electrophysiology model that follows such approach has been recently reported in Pathmanathan et al, so we expect this attempts to permeate to the electromechanical interaction in the near future, as experimental parameter data reported in probabilistic terms becomes available. Another limitation of this work is the introduction of uncertainty only in the input parameters.…”