Many biological tissues have layers with different extracellularmatrix components and different orientations of these components.As a result, diffusion coefficients vary from region to region(Even within a region, the diffusion coefficient depends upon thedirection of transport, a situation known as anisotropy). Considerthe steady-state, one-dimensional diffusion of a protein across atissue that consist of an acellular and a cellular phase. There areno chemical reactions. An example of such a tissue is an elasticartery that contains an elastic lamina of thickness L1 and a layerof smooth muscle cells of thickness L2 (actually, an arteryconsists of repeating layers of elastin and smooth muscle cells,but for the present discussion, consider a single layer of each).The protein diffusion coefficients of the two layers are Di1 andDi2, respectively. The concentration of the protein at the surface(x=0) is C1 = Φ1 * C0, and the concentration at x = L1 + L2 = L isC2 = Φ * CL. Determine the concentration as a function of positionx and the flux across the tissue. Show that the equation of fluxreduces to the equation of flux through a single layer when Di1 =Di2.
Many biological tissues have layers with different extracellularmatrix components and different orientations of these components.As a result, diffusion coefficients vary from region to region(Even within a region, the diffusion coefficient depends upon thedirection of transport, a situation known as anisotropy). Considerthe steady-state, one-dimensional diffusion of a protein across atissue that consist of an acellular and a cellular phase. There areno chemical reactions. An example of such a tissue is an elasticartery that contains an elastic lamina of thickness L1 and a layerof smooth muscle cells of thickness L2 (actually, an arteryconsists of repeating layers of elastin and smooth muscle cells,but for the present discussion, consider a single layer of each).The protein diffusion coefficients of the two layers are Di1 andDi2, respectively. The concentration of the protein at the surface(x=0) is C1 = Φ1 * C0, and the concentration at x = L1 + L2 = L isC2 = Φ * CL. Determine the concentration as a function of positionx and the flux across the tissue. Show that the equation of fluxreduces to the equation of flux through a single layer when Di1 =Di2.
