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.

在生物物理学中，凝胶底物已用于通过利用凝胶中的刚度分布来进行干细胞分化。但是，在当前可用的设计中，刚度范围可能不够大，并且也缺乏定量控制。在本文中，我们介绍了球形凝胶结构的机械化学模型，当将其浸入溶剂中时，该模型会在凝胶中产生不均匀的变形，并具有刚度分布。对该解决方案进行了定量计算，并详细研究了可调几何形状，材料，载荷参数对刚度范围的影响。进行分叉分析以确定加载参数的阈值。结果是，提供了有关如何调整相关参数以在不发生分叉的情况下生成理想的大刚度范围的指南。提供了两个示例，在这些示例中选择了适当的参数，从而得出适合皮肤和甲状腺组织干细胞分化的硬度范围。