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New mathematical models for the large strain swelling response of biological tissues: Applications to Edema, Inflammation, and Pregnancy

Hasan Demirkoparan

CMU-Q Point of Contact

Mathematical models that describe how soft biological tissue responds to mechanical stress are an essential part of basic biomechanics. There are many useful models that have been reasonably validated by experimental procedures in order to relate current states of stress to the often large deformations that can occur in soft tissue. Longer time scale models account for the history of the tissue so as to establish useful models for the more complicated physiological processes of tissue remodeling and tissue growth. Modeling and simulation becomes more precise as increasingly powerful computers become available. Even so, at the tissue and organ level it is not possible to track the myriad cellular events in individual cells. This research addresses this issue for processes in which tissue swelling is critical. We will do so by building upon the success of our ongoing research. The success of that research justifies this renewal proposal. Our aim is to create continuum level mathematical formulations that describe the relation between swelling, deformation, stress, and key metabolic factors such as nutrients transported by the interpenetrating fluid component within a solid matrix that itself has complex fibrous microstructure. A significant feature of the modeling is that it allows for ongoing change to the fibrous microstructure of the tissue due to resorption and reassembly. For example, collagen remodeling occurs in wound healing, pregnancy, and organ growth. Ongoing work by our group has begun to provide fundamentally new applied math methods for describing the interactions that occur under swelling and tissue fiber change. In particular, we have demonstrated the applicability of our modeling in both the case of tracheal angioedema (a relatively common and often life threatening allergic reaction) as well as cervical change during pregnancy. These are complex problems, and continued excellent progress is contingent on moving forward with our recently assembled team of postdoctoral researchers. Renewal of this proposal will allow us to do so. This will enable us to progress toward more physiologically faithful simulation, especially as regards pregnancy modeling (an eventual goals is patient-specific modeling). We are also poised to begin to simulate additional inflammatory disease states, including large deformation modeling of rheumatoid arthritis and other debilitating conditions.

Project

NPRP 8-2424-1-477

Year

2017

Status

Closed

Team
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Thomas Pence

Michigan State University
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Hasan Demirkoparan

Carnegie Mellon University - Qatar