A Mathematical Model for the Detachment Profile of 10μm Polystyrene Microspheres from Collapsed PNIP

by Alexandria Brady-Mine

Submitted : Spring 2019

PNIPAAm is a thermoresponsive polymer that is currently being researched for applications in tissue engineering. In this paper, a model for the detachment profile of PS particles from PNIPAAm was mathematically derived using data extrapolated from Dr. Sanden’s Thesis. Due to the significant variability of the data, points within the margin of error were assumed to be the same point and averaged which created a graph that roughly followed a parabolic curve. The data was then used to find the average values of f’(x) and f’’(x) and integrated to find f(x), the mathematical model. The model derived can be used to estimate the adherent fraction given shear stress for shear stresses between 0 and 249. This will allow scientists working within this range to predict the adherence of cells to the collapsed PNIPAAm.

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