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).

Diving into a simple anguilliform swimmer's sensitivity

“…∇ • u(x, t) = 0 (8) where u(x, t) and p(x, t)are the fluid's velocity and pressure, respectively, at spatial location x at time t. F(x, t) is the force per unit area applied to the fluid by the immersed boundary, i.e., the swimmer. These three quantities are modeled in an Eulerian framework on a fixed rectangular mesh.…”

“…Similarly, scientists investigating cellular processes, immunology, or oncology may attempt to fine tune model parameters based off experimental data available to investigate novel therapies [4,5,6]. Moreover, parameter explorations have provided insight into a number of organismal systems, including odorcapture by crabs [7] or tubular heart pumping [8]. A chief focus in each of these studies involved not only parameter exploration within a particular parameter space, but the sensitivity of model's output to the model's input parameters.…”

“…In organismal biology contexts, uncertain parameters, or fluctuations in parameters, could be viewed slightly differently than those in some population epidemiology or cellular contexts. Rather than only focusing on fine tuning model parameters to match experimental data, variations in parameters could be interpreted as biodiversity, even extending towards evolutionary contexts by exploring robustness of a performance metric to parameter sensitivities [10,11,8]. In particular, biodiversity has highlighted elegant "many-to-one mapping" solutions, where different morphologies (form) can lead to similar performance (function) [12,13].…”

Tuning a mechanical model to biological reality: A case study in the LaMSA system of the trap-jaw antStrumigenys

“…Even in the case of a simple lever system found in many vertebrate mandibles, it is possible to measure the force of a bite as well as its maximum speed, two metrics that generally form a trade-off in these systems (Westneat 2003). Trade-offs such as these are often viewed as potential drivers of speciation and thereby diversification due to creating multiple directions of selection (Taylor and Thomas 2014; Vincent 2016; Polly 2020; Waldrop et al 2020). In multi-part systems such as LaMSA systems there are a variety of potential output metrics, all of which may be important functionally, such as velocity, acceleration, power, and energy.…”

Cilia beating modulated radiating ternary nanofluids flow in a corrugated asymmetric channel with electromagnetohydrodynamic and momentum slip

“…Effective pumping mechanisms available in natural systems are the driving force to propel the physiological fluids in control manner without any contamination and provide the substances to the body, which is required for the growth and development of the parts. Several pumping mechanisms like peristaltic pumping, 1 heart pumping, 2 membrane pumping, 3 cilia‐beating motion, 4 and so forth are available in the living organs and function in transport phenomena at microlevel and macrolevel. Recently, researchers have shown their interest in the study of peristaltic flow on magnetohydrodynamic by using magnetic nanoparticles as drug carriers for targeted drug delivery 5 .…”