Olson: A Level Set Reaction Diffusion Model for Cartilage...
Feb
8
Fri 2:00 PM
When Friday, February 8, 2008
Time
2:00 PM - 3:00 PM
Where Tech M416
Contact Alvin Bayliss
847-491-7221
Group McCormick-Colloquia Engineering Sciences and Applied Mathematics
Applied Math Colloquium
Title: A Level Set Reaction Diffusion Model for Cartilage Regeneration
Speaker: Sarah Olson, North Carolina State University
Special Note: Note unusual time.
Abstract: Articular cartilage is a connective tissue that lines the surface of bones in diarthrodial joints (hips, shoulders and knees). Cartilage has a limited capacity for growth and repair of large defects due to injury or aging; therefore biomaterials such as hydrogels are being explored to provide a 3-d scaffold for cartilage regeneration. A mathematical model and numerical solutions will be presented for an interface problem that models an in-vitro experiment for regeneration of articular cartilage in a localized defect region. In this experiment, a cylindrical cartilage explant has a core region removed and replaced with a nutrient-rich hydrogel. The gel-tissue aggregate is then immersed in media for a period of several weeks. An axisymmetric reaction-diffusion model of this experiment is developed to capture coupling between cell-mediated nutrient absorption and matrix biosynthesis, and diffusive transport of nutrients and matrix constituents. The reaction governing turnover of the hydrogel to newly synthesized tissue is modeled via a level set method that captures the moving gel-tissue interface. After nondimensionalizatino, finite difference numerical solutions are employed to simulate cartilage regeneration as a function of cell mediated reaction rates in the model. Cases of external media maintained at a homeostatic nutrient concentration as well as at a higher concentration associated with the nutrient-rich hydrogel are considered. Regeneration times required to completely degrade the hydrogel are determined via a detailed parametric analysis using the model. Potential effects of local curvature along the gel-tissue interface will be briefly discussed.
Title: A Level Set Reaction Diffusion Model for Cartilage Regeneration
Speaker: Sarah Olson, North Carolina State University
Special Note: Note unusual time.
Abstract: Articular cartilage is a connective tissue that lines the surface of bones in diarthrodial joints (hips, shoulders and knees). Cartilage has a limited capacity for growth and repair of large defects due to injury or aging; therefore biomaterials such as hydrogels are being explored to provide a 3-d scaffold for cartilage regeneration. A mathematical model and numerical solutions will be presented for an interface problem that models an in-vitro experiment for regeneration of articular cartilage in a localized defect region. In this experiment, a cylindrical cartilage explant has a core region removed and replaced with a nutrient-rich hydrogel. The gel-tissue aggregate is then immersed in media for a period of several weeks. An axisymmetric reaction-diffusion model of this experiment is developed to capture coupling between cell-mediated nutrient absorption and matrix biosynthesis, and diffusive transport of nutrients and matrix constituents. The reaction governing turnover of the hydrogel to newly synthesized tissue is modeled via a level set method that captures the moving gel-tissue interface. After nondimensionalizatino, finite difference numerical solutions are employed to simulate cartilage regeneration as a function of cell mediated reaction rates in the model. Cases of external media maintained at a homeostatic nutrient concentration as well as at a higher concentration associated with the nutrient-rich hydrogel are considered. Regeneration times required to completely degrade the hydrogel are determined via a detailed parametric analysis using the model. Potential effects of local curvature along the gel-tissue interface will be briefly discussed.
