Patient derived organoids have emerged as robust preclinical models for screening anti-cancer therapeutics. Current 2D culturing methods do not provide physiological responses to therapeutics, therefore 3D models are being developed to better reproduce physiological responses. 3D culturing however often requires large initial cell populations and one week to one month to grow tumors ready for therapeutic testing. As a solution a 3D culturing system has been developed capable of producing physiologically relevant tumors in an expedited fashion while only requiring a small number of initial cancer cells. A bi-layer microfluidic system capable of facilitating active convective nutrient supply to populations of cancer cells facilitates expedited growth of cancer cells when starting with populations as small as 8 cells. The system has been shown to function well with adherent and non-adherent cell types by expediting cell growth by a factor ranging from 1.27 to 4.76 greater than growth under static conditions. Utilizing such an approach has enable to formation of tumors ready for therapeutic screening within 3 days and the ability to perform therapeutic screening within the microfluidic system is demonstrated. A mathematical model has been developed which allows for adjustments to be made to the dynamic delivery of nutrients inmore »
This content will become publicly available on March 1, 2023
Diffeomorphic shape evolution coupled with a reaction-diffusion PDE on a growth potential
This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that considered a static growth potential, i.e., the initial growth potential is only advected by diffeomorphisms. We focus on the mathematical study of the corresponding system of coupled PDEs describing the joint dynamics of the diffeomorphic transformation together with the growth potential on the moving domain. Specifically, we prove the uniqueness and long time existence of solutions to this system with reasonable initial and boundary conditions as well as regularization on deformation fields. In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D.
- Award ID(s):
- 1945224
- Publication Date:
- NSF-PAR ID:
- 10316563
- Journal Name:
- Quarterly of Applied Mathematics
- Volume:
- 80
- Issue:
- 1
- ISSN:
- 0033-569X
- Sponsoring Org:
- National Science Foundation
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