Abstract
In biophysics, gel substrates have been used to do stem-cell differentiation by utilizing the stiffness distribution in the gel. However, in the currently available designs, the stiffness range may not be large enough and there also lacks a quantitative control. In this paper, we introduce a mechanical–chemical model for a spherical gel structure which generates an inhomogeneous deformation in the gel with a stiffness distribution when it is immersed in a solvent. The solution is quantitatively computed and the influences of adjustable geometric, material, loading parameters on the stiffness range are examined in detail. A bifurcation analysis is conducted to determine the threshold of the loading parameter. As a result, a guideline is provided on how to adjust the involved parameters to generate a desirable large stiffness range without the occurrence of bifurcation. Two examples are provided in which the proper parameters are selected, leading to the stiffness ranges suitable for stem-cell differentiation for skin and thyroid tissues.
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