biological tissues have layers with different extracellular matrix 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 on the direction of transport, a situation know as anisotropy. Consider the steady-state, one-dimensional diffusion of a molecule across an artery wall consist of an acellular phase and a cellular phase. There are no chemical reactions. An example of such a tissue is an elastic artery that contains a layer of smooth muscle cells of thickness L1 and an elastic lamina of thickness L2. (Actually, an artery consists of repeating layers of elastin and smooth muscle cells, but for the present discussion, consider a single layer of each.) The molecule diffusion coefficients of the two layers are Di, 1 and Di, 2 respectively. The concentration of the molecule at the lumen surface (x = 0) is C0, and the concentration at x = L1 + L2 = L is CL. L1 = 600 μm, L2 = 400 μm, Di, 1 = 850 μm2/s and partition coefficient=1.1. The concentration of the molecule in plasma is C0 = 70 μM. Assume Di,2=1000 μm2/s and partition coefficient = 0.9 and concentration of the molecule in the interstitial space is CL = 1 μM. (a) Determine the concentration as a fu
Many biological tissues have layers with different extracellular matrix 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 on the direction of transport, a situation know as anisotropy. Consider the steady-state, one-dimensional diffusion of a molecule across an artery wall consist of an acellular phase and a cellular phase. There are no chemical reactions. An example of such a tissue is an elastic artery that contains a layer of smooth muscle cells of thickness L1 and an elastic lamina of thickness L2. (Actually, an artery consists of repeating layers of elastin and smooth muscle cells, but for the present discussion, consider a single layer of each.) The molecule diffusion coefficients of the two layers are Di, 1 and Di, 2 respectively. The concentration of the molecule at the lumen surface (x = 0) is C0, and the concentration at x = L1 + L2 = L is CL.
L1 = 600 μm, L2 = 400 μm, Di, 1 = 850 μm2/s and partition coefficient=1.1. The concentration of the molecule in plasma is C0 = 70 μM. Assume Di,2=1000 μm2/s and partition coefficient = 0.9 and concentration of the molecule in the interstitial space is CL = 1 μM.
(a) Determine the concentration as a function of position x. Calculate the concentration at the interface of L1 and L2, and on the elastic lamina side. *Give answer in μM*
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
