The shape of the cardiac action potential (AP) is often described using biomarkers: single-number quantities that can be measured experimentally and capture important AP features, for example AP duration at 90% repolarisation (APD90) or the minimum diastolic potential (MDP). These single-number summaries allow easy comparison of complex phenomena, for example expressing drug effects as a change in APD90, but they are also used to evaluate model predictions, or as part of an error function to minimise in model calibration.
To be most useful, a set of biomarkers should capture the essential information about the AP shape, while the calculation algorithms should handle a wide range of AP variation and be robust against experimental noise. We might also desire some measure of orthogonality: each new biomarker added to the set should provide new information not present in (a combination of) previous biomarkers. For model calibration, it is also desirable for calculated biomarkers to vary smoothly as model parameters are varied.
Here, we describe a geometrical approach to deriving biomarkers, based on a set of (time, voltage) coordinates which are chosen so that connecting them leads to a minimal linear representation of the AP. To avoid discontinuities in parameter space, the number of points and the way that they are chosen is determined before running the algorithm (depending on the cell type and the level of detail required), and the calculation for each cell uses a simple geometrical procedure.
We use this procedure to derive biomarker sets for ventricular, atrial, and nodal cells, and explore how these model-designed biomarkers perform on experimental data. By varying model parameters we test their robustness in pathophysiological situations, and we define and map an error function to investigate its smoothness. Finally, we discuss the benefits and drawbacks of our methods compared to conventional methods.