Computational Methods for Heterogeneous Soft Living Materials

West Chester University Of Pennsylvania, West Chester PA

Investigators

Abstract

Biofilms are present everywhere in the natural world and can have beneficial or adverse health effects. Through this award the principal investigator will provide a solid modeling platform and develop and analyze the computational tools that are needed for better understanding the behavior of biofilm formation and interaction with the microenvironment. For example, biofilms can be present in water systems affecting pipes and filters, and they can also be found in chronic wounds and infected prosthetic joints and heart valves, causing resistance to antibiotic use and then requiring further surgical interventions and prosthesis replacement. The computational methods developed in this research will provide an additional inexpensive and powerful method that compliments the work done by experimentalists. The computational algorithms and software tools are sufficiently general that they may be applied to other problems in science and engineering that present similar challenges. An interesting example is to better understand how bacteriophage adhere to mucus as a way to provide a nonhost-derived immunity. Improved insights provided through computational modeling have the potential to lead to the creation of new kinds of antibiotics. The principal investigator (PI) aims to develop numerical techniques for the solutions of equations that model heterogeneous soft living materials arising in biology. The focus is on biofilms and mucosal surfaces, and their interactions with surrounding fluid and biological agents, e.g. bacteria and viruses. Multiphase living materials are characterized by adhesive forces, they have viscoelastic properties and can diffuse, grow, deform or shear. The PI plans to focus on computational tools for solving the energy driven Cahn-Hilliard type equations describing phase separation and sharp diffusive interfaces, coupled with fluid flow equations. Interacting biological agents introduce heterogeneities and discontinuities into multiphase systems, highlighting the need for the design of a robust computational framework that couples continuous and discrete models. The PI aims to develop integrated methods for addressing challenges particular to heterogeneous biomaterials. He aims to combine high order discontinuous Galerkin finite element discretizations, in conjunction with time and spatial adaptivity, for analyzing the solution of the underlying systems while accounting for discontinuities, nonlinearities and moving sharp interior interfaces. Unconditionally energy stable and locally mass conservative schemes will be used to model long time dynamics. The resulting ill-conditioned nonlinear algebraic systems will be solved using efficient solvers based on multigrid techniques that exploit the specific local structure stemming from the choice of discretization. The development of computational tools that resolve these issues can lead to a better understanding of the factors that impact the evolution of soft biological systems. The efficient nonlinear and spatiotemporally adaptive solvers proposed will apply to even more general equations and will therefore advance the field of numerical nonlinear partial differential equations.