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Bioinformatics, Computational and Systems Biology

Physics-informed modeling of living systems

An Adaptive Physics Refinement Method for Capturing Multi-Resolution Cell-Laden Flow

Friday, October 13, 2023
5:00 PM – 5:15 PM PDT
Location: 331 (Center, Level 3)
Introduction::


Explicit knowledge of migration tendencies of circulating tumor cells (CTCs) can shed light on the mechanisms driving metastasis and assist advanced treatment planning. Computational models capable of recapitulating intercellular interactions while simulating CTC movement over mm-scale and longer trajectories can serve this purpose. However, the computational burden of conventional methods limit the target domain to at most a few millimeters, even using the world’s largest supercomputers.

Using a hybrid CPU-GPU approach, we extend the advanced physics refinement (APR) method ([1]) to couple a finely-resolved region of explicitly-modeled red blood cells to a coarsely-resolved bulk fluid domain. By introducing the red blood cell (RBC) interactions to model, we enable more physiologically realistic studies as RBCs constitute 45% of human blood and therefore it is important to consider their interactions with the CTCs [2]. The insertion of RBCs within the window results in the window having a fluid viscosity corresponding to blood plasma whereas the bulk viscosity is equivalent to whole blood as there are no cells. The problem thus becomes more challenging as it requires the coupling of fluids with different viscosities along with varying resolutions as shown in Figure 1. In this work, we extend and validate the APR method by introducing multi-viscosity coupling between the domains along multi-resolution coupling to insert RBCs within the window.






Materials and Methods::


The APR algorithm is developed within HARVEY, a massively parallel computational fluid dynamics solver based on the lattice Boltzmann method (LBM) [3]. The cells are modeled as fluid-filled membranes having elasticity and bending stiffness with Skalak’s law and are coupled to the ambient fluid using immersed boundary method (IBM) [4, 5]. The APR is implemented with a hybrid CPU-GPU approach, where the bulk is solved by the CPUs and the window is assigned to the GPUs. Previously, the APR method could only perform multi-resolution coupling between the fine and coarse domains as described in [1]. To account for the viscosity changes resulting from the need of explicit modeling of RBCs within the window a discontinuity in the physical kinematic viscosity ν was considered such that the ratio of viscosities between the fine and the coarse lattices, λ = νf /νc where νf is the fine lattice viscosity identical to plasma and νc is the coarse lattice viscosity identical whole blood. The interdependence of viscosity and the relaxation time in LBM also demanded modifying the relation of the relaxation times, τ corresponding to the fine and the coarse lattices which were addressed as follows:







τf = 1/2 + nλ (τc - 1/2)




where n is the resolution ratio of coarse to fine lattice spacing.















Results, Conclusions, and Discussions::


We validated the multi-viscosity component of the APR algorithm against an analytical solution by setting up a shear flow with three fluid layers within a cubic domain of length L= 90 μm, where a zero-velocity boundary condition was applied at y=0 plane and at y=L plane U0 velocity was applied. Along y axis, the cubic domain was divided into three distinct fluid regions of 30 μm height as shown in Figure 2A. Regions 1 and 3 were modeled as coarsely-resolved bulk regions having the same viscosity μ1. In contrast, Region 2 was modeled with a finely-resolved window having viscosity μ2 such that the velocity contrast is given by λ = μ2/μ1. Spanning the values that represent the viscosity contrast between whole blood and plasma, we performed simulations with λ = 1/2, 1/3, and 1/4 [6, 7] with resolution rations, n = 2, 5, and 10 to confirm accuracy at a broader range. In Figure 2B we show the velocity profile along y-axis for the cases having a resolution ratio of 2, which showed a good agreement with the analytical solution. We also calculated the L2 error norms for each of the resolution and viscosity combinations illustrated in Figure 2C, for both the bulk and the window regions. The error was observed to range between 1-4% for all the considered cases ensuring accurate coupling between the fine and coarse domains with varying viscosities.

The multi-viscosity coupling between the coarse lattice representing whole blood and the fine lattice representing plasma will allow the insertion of RBCs within the window while maintaining physiologically relevant hematocrit and effective viscosity. The incorporation of RBCs within the APR can promote a more accurate system for tracking cancer cells over large scales with cell-laden flow using limited computational resources that is intractable using current conventional approaches.






Acknowledgements (Optional): :


An award of computer time was provided by the INCITE program. This research also used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725. Research reported in this publication was supported by the National Institutes of Health under Award Number U01-CA253511. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.






References (Optional): :


[1] D. F. Puleri, S. Roychowdhury, P. Balogh, J. Gounley, E. W. Draeger, J. Ames, A. Adebiyi, S. Chidyagwai, B. Hernández, S. Lee, et al., “High performance adaptive physics refinement to enable large-scale tracking of cancer cell trajectory,” in 2022 IEEE International Conference on Cluster Computing (CLUSTER), pp. 230–242, IEEE, 2022.
[2] R. Sharma and S. Sharma, “Physiology, blood volume,” 2018.
[3] A. P. Randles, V. Kale, J. Hammond, W. Gropp, and E. Kaxiras, “Performance analysis of the lattice Boltzmann model beyond Navier-Stokes,” in Parallel & Distributed Processing (IPDPS), 2013 IEEE 27th International Symposium on, pp. 1063–1074, IEEE, 2013.
[4] J. Gounley, E. W. Draeger, and A. Randles, “Numerical simulation of a compound capsule in a constricted microchannel,” Procedia Comput Sci, vol. 108, pp. 175–184, 2017.
[5] P. Balogh and P. Bagchi, “A computational approach to modeling cellular-scale blood flow in complex geometry,” J Comp Phys, vol. 334, pp. 280–307, 2017.
[6] A. R. Pries, D. Neuhaus, and P. Gaehtgens, “Blood viscosity in tube flow: depen- dence on diameter and hematocrit,” American Journal of Physiology-Heart and Circulatory Physiology, vol. 263, no. 6, pp. H1770–H1778, 1992.
[7] Y.-c. Fung, Biomechanics: circulation. Springer Science & Business Media, 2013.