Estimability Analysis and Optimal Design in Dynamic Multi-scale Models of Cardiac Electrophysiology.

We present an applied approach to optimal experimental design and estimability analysis for mechanistic models of cardiac electrophysiology, by extending and improving on existing computational and graphical methods. These models are 'multi-scale' in the sense that the modeled phenomena occur over multiple spatio-temporal scales (e.g., single cell vs. whole heart). As a consequence, empirical observations of multi-scale phenomena often require multiple distinct experimental procedures. We discuss the use of conventional optimal design criteria (e.g., D-optimality) in combining experimental observations across multiple scales and multiple experimental modalities. In addition, we present an improved 'sensitivity plot' - a graphical assessment of parameter estimability - that overcomes a well-known limitation in this context. These techniques are demonstrated using a working Hodgkin-Huxley cell model and three simulated experimental procedures: single cell stimulation, action potential propagation, and voltage clamp. In light of these assessments, we discuss two model modifications that improve parameter estimability, and show that the choice of optimality criterion has a profound effect on the contribution of each experiment.