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Many biological tissues have layers with extracellular matrix components and different orientations of these components. As a result, diffusion coefficients vary from region to region.

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Many biological tissues have layers with extracellular matrix components and different orientations of these components. As a result, diffusion coefficients vary from region to region. Consider the steady-state, one-dimensional diffusion of a protein across a tissue that consists of a cellular phase and an acellular phase (like an artery wall consisting of a layer of smooth muscle cells and a layer of elastic lamina. Assume no reactions occur in either layer. The protein diffusion coefficients in the layers (1 and 2 ) are Di,1 and Di,2. The concentration at one edge is (x=0)Ci=C0; on the other edge (x=L1+L2=L)Ci=CL. Assume that all partition coefficients in both layers are equal to 1 . Use the figure below to help. Determine (A) the concentration as a function of position x,(B) the flux of the protein solute across the tissue, and (C) the effective diffusion coefficient if the system is modeled as a single layer. (Hint: at the interface (x=L1), the concentrations will be equal and the flux will be equal.)

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