Models and Computations for Studying Biofluid Applications

Wednesday, June 16 at 07:45pm (PDT)
Thursday, June 17 at 03:45am (BST)
Thursday, June 17 11:45am (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS16" time block.
Note: this minisymposia has multiple sessions. The second session is MS10-MMPB (click here).

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Zhiliang Xu (Univeristy of Notre Dame, USA), Giordano Tierra (University of North Texas, USA), Shixin Xu (Duke Kunshan University)


The past decades have witnessed a rapid development of mathematical and computational models for biophysical applications. This mini-symposium is intended to provide a forum for researchers to present contributions in the broad field of modeling and computational methods for fluid related biological applications. Topics within the scope of interest include, but are not limited to: a) continuum models such as phase-field models and efficient simulation schemes; b) discrete-continuum multiscale mechanistic models and applications; c) simulations of various biofluid applications.

Rolf Ryham

(Fordham University, USA)
"Collective hydrodynamics of amphiphilic particles assembled as small unilamellar vesicles"
In this talk we study the collective hydrodynamic behavior of amphiphilic Janus particles assembled as small unilamellar vesicles (sUVs). The simulations use a hybrid approach that is shown to capture the formation of bilayers in a solvent (SIAM J Multiscale Model. Simul., vol 18, pp. 79-103). In this hybrid formulation, the non-local interactions between the coarse-grained lipid molecules are described by a hydrophobicity functional, giving rise to forces and torques (between lipid particles) that dictate the motion of both particles and the fluid flow in the viscous solvent. Both the hydrophobic and hydrodynamic interactions between the coarse-grained amphiphilic particles are formulated into integral equations, which allow for accurate and efficient numerical simulations in both two- and three-dimensions. We validate our hybrid coarse-grained model by reproducing various physical properties of a lipid bilayer membrane, and use this simulation tool to examine how a small unilamellar vesicle behaves under a planar shear flow, and investigate the collective dynamics of sUVs under a shear flow. Finally we also examine the possibility of membrane rupture by extreme flowing conditions.

Wenrui Hao

(Penn State University, USA)
"Computational models of cardiovascular disease"
In this talk, I will introduce several computational models of cardiovascular disease including both atherosclerosis and aortic aneurysm growth to quantitatively predict the long-term cardiovascular risk. These models integrate both the multi-layered structure of the arterial wall and the aneurysm pathophysiology together. The heterogeneous multiscale method is employed to tackle different time scales while the finite element method is adopted to the deformation of the hyperelastic arterial wall all the time. A three-dimensional realistic cardiovascular FSI problem with an aortic aneurysm growth based upon the patients' CT scan data is simulated to validate a medically reasonable long-term prediction.

Yiwei Wang

(Illinois Institute of Technology, USA)
"An energetic variational approach for wormlike micelle solutions: Coarse graining and dynamic stability"
Wormlike micelles are self-assemblies of polymer chains that can break and recombine reversibly. In this talk, we present a thermodynamically consistent two-species micro-macro model of wormlike micellar solutions by employing an energetic variational approach. The model incorporates a break- age and combination process of polymer chains into the classical micro-macro dumbbell model of polymeric fluids in a unified variational framework. The modeling approach can be applied to other reactive or active complex fluids. Different maximum entropy closure approximations to the new model will be discussed. By imposing a proper dissipation in the coarse-grained level, the closure model, obtained by “closure-then-variation”, preserves the thermo- dynamical structure of both mechanical and chemical parts of the original system. The same modeling approach can be applied to many active or reactive systems found in biology.

Giordano Tierra

(University of North Texas, USA)
"Energy-stable numerical schemes for fluid vesicles with internal nematic order"
Models of flows containing vesicles membranes with liquid crystalline phases have been widely studied in recent times due to its connection with biological applications. During the presentation I will present the main ideas to derive a new model to represent the interaction between flows and vesicle membranes with internal nematic order and preferential orientation of their molecules in the membrane. In fact, the dynamics of this system is determined by the dissipation of an energy that regulates the competition between different effects, through the kinetic, bending, elastic and anchoring energies. Moreover, I will introduce a new unconditionally energy-stable numerical scheme to approximate the model, and I will present several numerical results in order to show the well behavior of the proposed scheme and the dynamics of this type of vesicle membranes.

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Virtual conference of the Society for Mathematical Biology, 2021.