About Me:

I am originally from Coventry, Rhode Island and received a bachelors degree from Providence College in 2003, majoring in Biology and Mathematics. I started my graduate work in Mathematics at the University of Rhode Island, where I received a Masters degree in 2005. Currently, I am finishing my PhD in the Biomathematics Program at North Carolina State University. My advisor is Dr. Mansoor Haider and I am working in the Orthopaedic Biomaterials Group, which is part of the NSF Research Training Group on Mathematics of Materials.

Research Interests:

My research interests are mathematical modeling, applied partial differential equations, and scientific computing with applications in mathematical biology. I have experience with level set methods for moving interfaces and artificial neural network models and algorithms.

Recent Research Manuscripts:

[submitted] S. D. Olson and M. A. Haider.  A level set reaction-diffusion model for tissue regeneration in a cartilage-hydrogel aggregate.

[in preparation] S. D. Olson, D. L. Nettles,  K. Trabbic Carlson, A. Chilkoti, L. A. Setton, M. A. Haider. Predicting mechanical properties of elastin-like polypeptides using artificial neural networks.

Research:

My research is focused on studying different aspects of the cartilage regeneration process. Articular cartilage is an avascular and aneural connective tissue that lines the surfaces of bones in diarthrodial joints (hips, shoulders, knees). Cartilage covers each end of the bone, protecting these surfaces from impact stresses, and minimizes friction and wear in the joint. The structure of cartilage is due to the extracellular matrix (crosslinked network of proteoglycans and collagen) that is maintained by chondrocytes (cells) that are sparsely distributed through the matrix. Due to againg or injury, osteochondral defects will occur where the tissue has eroded away. Cartilage has a limited capacity for growth and repair, therefore biomaterials such as hydrogels are being explored to provide a 3-dimensional scaffold for cartilage regeneration. Hydrogels are comprised of natural or synthetic polymers with flexibility similar to natural tissues. Depending on the type of hydrogel, they can undergo a phase transition from liquid to gel. Elastin-like polypeptides are a type of hydrogel that undergo a phase transition at physiological temperature. At room temperature, it is in the liquid form and can be seeded with nutrients, cells, or growth factors. Upon injection into a defect site, the transition to gel occurs and the gel can fill an irregularly shaped defect.

I am working on modeling two aspects of the cartilage regeneration problem. The first problem involves modeling an in vitro experiment where a cylindrical cartilage-hydrogel aggregate evolves over the course of several weeks. A level set reaction-diffusion model is developed for axisymmetric geometry to capture interactions between matrix accumulation (cartilage regeneration), hydrogel degradation, and nutrient diffusion and absorption. The second part of my thesis research involves the development of supervised learning Artificial Neural Network algorithms to predict the structure-function relationships between the underlying biopolymer design characteristics and the mechanical properties of the hydrogel. This works involves the development of a customized compiled implementation of the Scaled Conjugate Gradient algorithm and its application to analysis of complex tissue engineering datasets. This work has been in collaboration with Dr. Lori Setton at Duke University, Department of Biomedical Engineering and Department of Surgery. For more information on my research, please see the research summary link above.