In this paper, we propose a statistical method to assess and enhance the quality of electrocardiograms (ECGs) produced by deterministic mathematical models that are used to study the physical mechanisms of electrophysiology and related pathologies. We consider a reference dataset of real ECGs and use the notion of functional data depths and quantiles to formulate a family of statistical calibration problems where the deterministic model targets selected functional quantiles of the real, reference population, properly accounting for inter-subject variability of ECG signals. The method is successfully applied to two very different models: a phenomenological model based on ordinary differential equations, and a complex biophysical model based on partial differential equations set on a three-dimensional geometry of the heart and the torso.

cardiovascular mathematics, depth measures, electrocardiograms, functional data analysis, statistical model calibration.