Britton; Computational study of remodeling of fibrin networks under compression

Fibrin network is one of the major structural components of both physiological blood clots and pathological thrombi. Fibrin fiber mechanics underlie clot stability and macroscopic behavior of clots. Moreover, mechanical and structural properties of fibrin network contribute to clot mechanical stability and determine its deformation under pressure from blood flow. Fibrin polymers in the model to be described in the talk are represented using the Worm-Like-Chain (WLC) approach. The Langevin equations describe the motion of individual nodes. Computational study of dynamical deformations of fibrin networks under compression demonstrate that dramatic remodeling of a clot observed in experiments [1] is based on bending and reorientation of individual fibers as well as on the fiber-fiber non-covalent linkage. Structures of the network used in model simulations are generated from the confocal microscopy images of in vitro fibrin clots. Upon network compression, non-covalent interactions between fibers result in dynamic variation of network architecture. These interactions significantly affect mechanical response of the network at high degrees of compression, ultimately resulting in clot stiffening. Simulation results match experimental data in both fiber linking rates and network densification under different compression rates. Finally, the model is used to predict how stress propagates through the network and how rearrangement and linking of fibrin fibers affects clot stiffening. Finally, the model can be extended for studying deformations of the fibrin-collagen composites [2].

Oleg V. Kim, Rustem I. Litvinov, John W.Weisel and Mark S. Alber, Structural basis for the nonlinear mechanics of fibrin networks under compression, Biomaterials 2014, 35, 6739-6749.

O.V. Kim, R.I. Litvinov, J. Chen, D.Z. Chen, J.W. Weisel and M.S. Alber [2017], Compression-induced structural and mechanical changes of fibrin-collagen composites, Matrix Biol. 2017, 61:141-156.

Samuel Britton1, Oleg Kim1,2, Rustem Litvinov2,3, John Weisel2, Mark Alber1,4

1Department of Mathematics, Center for Quantitative Modeling in Biology, University of California Riverside, Riverside, CA 92505, USA

2Department of Cell and Developmental Biology, University of Pennsylvania School of Medicine, Philadelphia, PA 19104, USA

3Department of Biochemistry and Biotechnology, Kazan Federal University, Kazan 420008, Russian Federation

4School of Medicine, University of California Riverside, Riverside, CA 92505, USA

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Chi; Squirmer suspended in (Living) Liquid Crystal

Living Liquid Crystal (LLCs) is a general class of active fluids. The suspending medium is a nontoxic liquid crystal (LC) that supports the activity of self-propelled particles, like bacteria. The non-trivial interaction between LC and active matter leads to many interesting behavior. Here is this poster, we consider a model describing active squirmer, which is a model to describe bacteria, suspended in LC based on Beris-Edwards Model. We study the long time behavior of the squirmer numerically and analytically.

This is joint work with I.S.Aronson and L.Berlyand. This work was supported by NSF Division of Physics 1707900.

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Creese; Continuum approximations to systems of interacting particles.

Collective behavior arising from interacting particles such as biological cells leads to many striking phenomena. An individual based model (IBM) for interacting particles and several continuum approximations to this IBM via truncations of the BBGKY hierarchy will be described. Specifically, the Mean Field Approximation (MFA), the Kirkwood Superposition Approximation (KSA), and a more recent truncation of the BBGKY hierarchy (Truncation Approximation - TA). Properties of these approximations are compared showing that TA is less computationally expensive than KSA. In addition these continuum approximations are compared to Monte Carlo simulations of the IBM numerically showing that TA and KSA are more accurate than MFA.

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Novack; Dimension reduction for the Landau-de Gennes model: the vanishing nematic correlation length limit

We present results regarding nematic liquid crystalline films within the framework of the Landau-de Gennes theory in the limit when both the thickness of the film and the nematic correlation length are vanishingly small compared to the lateral extent of the film. We discuss a Γ-convergence result for a sequence of singularly perturbed functionals with a potential vanishing on a high-dimensional set and a Dirichlet condition imposed on admissible functions. In addition, we demonstrate the existence of local minimizers of the Landau-de Gennes energy, in the spirit of a theorem due to Kohn and Sternberg, despite the lack of compactness arising from the high-dimensional structure of the wells. The limiting energy consists of leading order perimeter terms, similar to Allen-Cahn models, and lower order terms arising from vortex structures reminiscent of Ginzburg-Landau models.