Mathematical Modeling

Our research approach emphasizes the use of mathematical modeling to understand and quantify the underlying physics that govern the assembly, properties, and responsive nature of our materials. Using this strategy, we have developed a physical and quantitative understanding of polymer-nanoparticle (PNP) hydrogel assembly (Nature Communications 2015). We have additionally developed statistical-kinetic models to describe and predict how material properties change within photoresponsive hydrogels in response to controlled light exposure (Macromolecules 2013Journal of Polymer Science Part A 2013).

Publications

Appel, E.A.*Tibbitt, M.W.*; Webber, M.J.; Mattix, B.A.; Veiseh, O.; Langer, R. "Self-assembled hydrogels utilizing polymer-nanoparticle interactionsNature Communications20156, 6295.

Tibbitt, M.W.; Kloxin, A.M.; Sawicki, L.A.; Anseth, K.S. "Mechanical properties and degradation of chain and step-polymerized photodegradable hydrogelsMacromolecules201346, 2785-2792.

Tibbitt, M.W.; Kloxin, A.M.; Anseth, K.S. "Modeling controlled photodegradation in optically thick hydrogelsJournal of Polymer Science Part A: Polymer Chemistry201351, 1899-1911.

Tibbitt, M.W.; Kloxin, A.M.; Dyamenahalli, K.U.; Anseth, K.S. "Controlled two-photon photodegradation of PEG hydrogels to study and manipulate subcellular interactions on soft materialsSoft Matter20106, 5100-5108.

Kloxin, A.M.; Tibbitt, M.W.; Kasko, A.M.; Fairbairn, J.A.; Anseth, K.S. "Tunable hydrogels for external manipulation of cellular microenvironments through controlled photodegradationAdvanced Materials201022, 61-66.

Aimetti, A.A.; Tibbitt, M.W.; Anseth, K.S. "Human neutrophil elastase responsive delivery from poly(ethylene glycol) hydrogelsBiomacromolecules200910, 1484-1489.