Drug diffusion through the skin is usually modelled using the diffusion equation

Question

Drug diffusion through the skin is usually modelled using the diffusion equation c(x,t)/ t = D 2c(x,t)/ x2 where c(x,t) is the concentration of drug at depth x and time t. The skin is modelled as a homogenous membrane of thickness h, with the following boundary conditions: At the upper skin surface (x = 0), the concentration is constant, equal to the concentration C applied to the skin (this is because such a small fraction of drug enters the skin) At the lower skin surface (x = h), the concentration is zero (because any drug that makes it through the skin membrane is cleared away by the blood stream almost immediately Initially (t = 0), there is no drug in the skin Show from the diffusion equation that the Laplace transform of c(x, t) in the skin must take the form Show that the upper and lower surface boundary conditions lead to the following expression for (x,s): From this expression, the Laplace transform of the flux of drug through area A of skin can be shown to be for constants K and td. Using complex integration, invert the Laplace transform to derive a series expansion for Q(t)

Explanation / Answer

c the best condition for this

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