Uncertainty analysis of biological systems: towards a digital twin of the human heart

The human heart has always been a challenge for doctors and scientists with its amazing complexity and individual variability. Owing to recent decades increase in computational power, it has been possible to develop in-silico duplicates of reality that greatly extend the possible analyses. However, such models have a main limitation: their results do not directly account for individual variability. Uncertainty Quantification (UQ) methodologies integrate elements of probability theory and statistics with machine learning techniques to investigate how uncertainties and variability impact model dynamics. In this manuscript, starting with a simplified cardiac duplicate comprising only the left chambers, UQ methodologies were applied to investigate the most relevant uncertain quantities and guide the subsequent optimisation of the model. According to the analyses performed, the activation of a healthy heart is totally dominated by fast conduction pathways (Purkinje network, internodal bundles, etc.) and fibers orientation. The model was therefore updated to account for these structures, in particular the Purkinje Network extending into the ventricles and the double orientation of ventricular fibers. In addition, fundamental elements of cardiac dynamics were included, such as the orientation of muscle fibres for both atria and ventricles, four realistic chambers, and differentiated cell models to characterise the action potentials of different parts of the heart. Importantly, this advanced cardiac model has been designed to account for a parametric variation of geometrical and physical quantities, which is essential for running UQ analyses. The flexibility of UQ techniques also allowed several partnerships with medical groups. The methodologies of classical statistics, integrated with metamodelling techniques, allowed the analysis of gastroenterological diseases. Furthermore, global sensitivity analyses coupled with Monte Carlo methods enabled studies on teaching neonatal resuscitation procedures to medical residents. These works highlighted the main challenge of UQ analyses: in applicative contexts, particularly medical ones, the information available to the investigator is limited, therefore the results are potentially biased or even incorrect. To address the necessity to perform UQ analyses even with incomplete/wrong information, we developed techniques to perform correlation analyses for error-affected databases and defined a robustness index for global sensitivity analyses (Nested UQ).