Numerical methods in biomedical sciences

Wednesday, June 16 at 09:30am (PDT)
Wednesday, June 16 at 05:30pm (BST)
Thursday, June 17 01:30am (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS13" time block.
Note: this minisymposia has multiple sessions. The second session is MS14-DDMB (click here).

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Yifan Wang (University of California, Irvine, USA), Pejman Sanaei (New York Institute of Technology, USA)


Mathematical modeling and numerical methods play an important role in biomedical sciences nowadays. A diversity of mathematical models and techniques ranging from solving partial differential equations and stochastic modeling to applying machine learning algorithms to image and data analysis has been tackled and explored, with many interesting applications such as improving the medical imaging to identify pathological tissue better, studying patient RNA-sequencing data to facilitate disease diagnosis, computational analysis to design patient-specific treating plans to improve the treatment outcomes and so on. This mini-symposium plans to gather mathematicians and field experts with various biomedical research interests to share their modeling techniques, discuss the associated challenges, stimulate new research collaborations, and connect different applications that similar mathematical approaches may apply.

Feng Fu

(Dartmouth University, USA)
"Mathematical Modeling of Combination Cancer Immunotherapy"
It is of fundamental importance to understand the key mechanisms that govern the progression of cancer and elucidate the often-unknown factors that account for treatment failures. Immunotherapies have had a significant impact, but only in a minority of late-stage lung cancer and melanoma patients. While potentially curative immunotherapies are being rapidly developed and tested, a major barrier is the lack of quantitative models to describe and evaluate their efficacy. We investigate clinically relevant mathematical and in-silico models of cancer cell dynamics for personalized immunotherapy that boost anti-tumor activities of effector immune cells using single-agent checkpoint blockade and their potential combinations. Our work can be used to interpret lab and clinical results and to guide the design of future lab experiments and clinical trials, all with an eye toward model-informed personalized immunotherapy.

Pejman Sanaei

(Mathematical modeling in tissue engineering, USA)
"Mathematical modeling in tissue engineering"
Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this work, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the nutrient concentration as well as the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.

Yifan Wang

(University of California Irvine, USA)
"Lattice Boltzmann approach to study the evolutionary dynamics of stem-cell driven cancer"
We propose a new approach based on the Lattice Boltzmann Method to simulate tumor cell growth dynamics in the crowded intracellular system. The main advantage of this approach is that it resolves the cell-growth process at the mesoscopic level and thereby provides a more accurate and detailed description than the standard continuous approaches. It is also more computationally efficient than agent-based approaches. Moreover, our method can treat non-regular boundary surfaces efficiently and can capture the heterogeneous property of the intercellular micro-environment and the stochasticity in the tumor growth and other phenomena such as cell confinement from the tissue/extracellular matrix structure.

Min-jhe Lu

(Department of Mathematics, Illinois institute of technology, Chicago, Illinois, USA)
"Nonliner simulation of vascular tumor growth with a necrotic core and chemotaxis"
In this work, we develop a sharp interface tumor growth model to study the effect of both the intratumoral structure using a fixed necrotic core and the extratumoral nutrient supply from vasculature. We first show that our model extends the one by Cristini et al. (Cristini et al., J. Math. Biol., 2003 Mar;46(3):191-224) using linear stability analysis. Then we solve the generalized model using a spectrally accurate boundary integral method in an annular domain with a Robin boundary condition that models tumor vasculature. Our nonlinear simulations reveal the effects of angiogenesis, chemotaxisand necrosis in the development of morphological instabilities. The values of the nutrient concentration with its fluxes and the hydrostatic pressure with its gradients are solved accurately on the boundaries to better understand the balance in the controlling of the necrosis.

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Virtual conference of the Society for Mathematical Biology, 2021.