Multiscale simulations of biological fluid dynamics

Tuesday, June 15 at 05:45pm (PDT)
Wednesday, June 16 at 01:45am (BST)
Wednesday, June 16 09:45am (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS09" time block.
Note: this minisymposia has multiple sessions. The second session is MS08-MMPB (click here).

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Matea Santiago (University of California, Merced, United States), Shilpa Khatri (University of California, Merced, United States)


Biological fluid dynamics encompass a wide range of scales, from the organism to subcellular levels. The role of fluid dynamics in tissue, organ, and organism scales are of particular interest due to their providing high-level understanding of organism movement and physiology. These scales often involve solving systems of linear and non-linear partial-differential equations. Further, these biological applications typically involve complicated boundary conditions where the fluid interacts with an elastic or rigid moving structure, making these problems mathematically challenging. This has led to the development of advanced numerical methods to gain insight into these interesting problems. In this minisymposium, we present what occurs at the tissue and organ scale where there are many interesting and valuable physiological applications where the role of biological fluid dynamics is significant. For instance, modeling different components of the circulatory system can require fluid dynamics at the organ scale, heart, or at the tissue scale, blood vessel, depending on the problem being investigated. Further we will also discuss the fluid dynamics at the organism scale, specifically fluid flows around sessile and motile marine organisms. These applications can provide insight into open questions relating to marine ecology, engineering problems, and mixing dynamics.

Lindsay Waldrop

(Assistant professor, Chapman University, United States)
"The effects of circulatory resistivity on performance of transport by systems with tubular, peristaltic hearts"
During individual development and evolutionary history, the chambered hearts of vertebrate animals begin as contracting, tubular hearts that pump peristaltically. This system has been extensively studied in computational models, but typically with a simple, racetrack circulatory system. The circulatory systems of animals are often resistive, including the closed systems of vertebrates consisting of capillary beds at its smallest diameters and the semi-closed systems of tunicates which have a connected bed of very small vessels in the pharyngeal basket. We used an immersed boundary model of peristaltic pumping attached to different circulatory systems that are more resistive: a branch that divides the top of the tube into two smaller tubes, a tube that widens and contain round, fixed obstacles, and a branched system with obstacles. We varied the Womersley number, compression ratio, and compress frequency of the pumping heart for each circulatory system and analyzed the system using uncertainty quantification with generalized polynomial chaos scheme and by calculating Sobol indices to quantify global sensitivity. We found that more resistive circulatory systems resulted in a 50% drop in average flow speed and a 33% drop in average volume flow rate within the circulatory systems of greater resistivity compared to the racetrack system. The pressure differential generated by the heart increased by 4.5 times in the system with the greatest resistivity. However, the cost of transport and work of pumping did not significantly increase, and the pattern of parameter sensitivity did not change with different circulatory systems. Results suggest that heart performance (cost of transport and flow) can be maximized by operating at lower pumping frequencies and higher Womersley numbers and that the relationship between performance and parameters do not change with the addition of resistive circulatory systems.

Laura Miller

(Departments of Mathematics and Biomedical Engineering, University of Arizona, United States)
"Slow and fast airflow past Saguaro and other cacti"
The cacti of the Sonoran desert in the southwest United States must deal with temperatures on the order of 120 degrees Farenheit and monsoons with wind speeds upwards of 100 miles per hour. It has been speculated that the ridges and spines of these cacti help dissipate heat in light wings, in addition to providing protection. It is also possible that the ridges and spines reduce drag acting on the cacti during strong winds. In this presentation, we use computational fluid dynamics to quantify the airflow around Saguaro and prickly pear cacti in both light and strong winds. The effects of the ridges and spines are systematically studied by smoothing the trunk and leaves. The resulting flow structures will be discussed in the context of drag reduction and heat dissipation.

Shilpa Kharti

(Department of Applied Mathematics, University of California, Merced, United States)
"Pulsing Soft Corals"
Soft corals of the family Xeniidae have a pulsing motion, a behavior not observed in many other sessile organisms. We are studying how this behavior may give these corals a competitive advantage, especially by allowing their symbiotic algae to photosynthesize to a greater extent. We will present computational simulations of the pulsations of the coral. Direct numerical simulations of the pulsing corals and the resulting fluid flow by solving the Navier-Stokes equations coupled with the immersed boundary method will be discussed. We will present results of how the fluid flow created by the corals is modified as we vary parameters of the fluid and the pulsing motion.

Matea Santiago

(Department of Applied Mathematics, University of California, Merced, United States)
"Soft Corals: Pulsing, Mixing, and Photosynthesis"
Some species of octocorals in the family Xeniidae actively pulse their tentacles. It is hypothesized that the pulsing mixes the fluid which enhances the photosynthesis of their symbiotic algae. We will present mathematical models and numerical methods for the tentacle motion and fluid flow coupled with the photosynthesis. The numerical simulations are analyzed to understand the benefit of pulsing for mixing and photosynthesis in different parameter regimes. The fluid flow is used to build Poincaré maps, a common tool in dynamical systems, used to understand fluid transport in periodic flows. This tool is coupled with the photosynthesis simulations to understand the enhancement of photosynthesis due to the flow.

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Virtual conference of the Society for Mathematical Biology, 2021.