# Solution-How to control the cell differentiation

There are many hydrogels used to control the stem cell differentiation, such as Hydrolytically degradable PEG hydrogels, Photodegradable PEG hydrogels, Enzymatically Degradable PEG hydrogels, etc. Please use some mathematical equations to derivative the hydrogel properties, like diffusion rate, oxygen transfer, etc. You can write any properties you want, but show it how to control the cell differentiation. And then write a discussion for the comparison, shows that which hydrogel provide a good control in the same condition.

4~5 pages with 1.5 space, time new roman 12 size, 2cm margin all around. No figure or picture include. Don’t need introduction for hydrogel or cell differentiation. Just the mathematical equation and discussion.

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Mathematical Methods

Design of hydrogel system for the tissue engineering and cell differentiation study include consideration of physical and chemical properties of such biomaterials. In particular, it is important to identify the effect of solute that interacts with the molecules of gel, which is reflective with the mathematical explanation for the partition between gel phase and surrounding liquid phase. The said term is linked with the swelling property of the molecules.

Swelling property

In general for the hydrogels, the ideal characteristics can be determined with the overall permeation of the nutrient (inside direction) and outward movement of the cellular content of the gel. Thus, during the initial phase, the water molecules will be absorbed that will enter into the matrix and will form the primarily bound water. This will also cause the hydration of polar group first, then covering of the hydrophilic patch, and later it will cause swelling of the gels. Once the hydrophobic patch is covered with water molecules, the subsequent entry of water and its interaction with the hydrogel molecules is usually termed as secondary water. Thus, the estimate of total bound water (TBW) in the calculation of the wetting of the hydrogels can be calculated with the below mentioned equation (Billiet, 2012).

TBW = Primary water + Secondary water

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