Uncertainty quantification reveals the physical constraints on pumping by peristaltic hearts

Abstract

Most biological functional systems are complex, and this complexity is a fundamental driver of diversity. Because input parameters interact in complex ways, a holistic understanding of functional systems is key to understanding how natural selection produces diversity. We present uncertainty quantification (UQ) as a quantitative analysis tool on computational models to study the interplay of complex systems and diversity. We investigate peristaltic pumping in a racetrack circulatory system using a computational model and analyse the impact of three input parameters (Womersley number, compression frequency, compression ratio) on flow and the energetic costs of circulation. We employed two models of peristalsis (one that allows elastic interactions between the heart tube and fluid and one that does not), to investigate the role of elastic interactions on model output. A computationally cheaper surrogate of the input parameter space was created with generalized polynomial chaos expansion to save computational resources. Sobol indices were then calculated based on the generalized polynomial chaos expansion and model output. We found that all flow metrics were highly sensitive to changes in compression ratio and insensitive to Womersley number and compression frequency, consistent across models of peristalsis. Elastic interactions changed the patterns of parameter sensitivity for energetic costs between the two models, revealing that elastic interactions are probably a key physical metric of peristalsis. The UQ analysis created two hypotheses regarding diversity: favouring high flow rates (where compression ratio is large and highly conserved) and minimizing energetic costs (which avoids combinations of high compression ratios, high frequencies and low Womersley numbers).