Diffusion out of capillary Part 1: Concentration profile using finite difference approximation Equation 4 shows a changing concentration with respect to radial position as well as to time, making it a partial differential equation. Finite difference approximation is one way to numerically solve a partial differential equation. To solve the diffusion term of this equation using this method we can express the O2 diffusion for each slice or annulus around the tube. Writing the equation for the jth annulus we find that for j>1 20-1) This equation is valid for all annuli. To construct a concentration profile for the system, you will need to create a MATLAB code that solves equation 6 for each radial annuli using a loop Solving the loop over a certain number of radial annli will give you a diffusion profile along a radial slice for one point in time. You must then construct another loop to solve for the change in radial diffusion profile over time. You can assume the diffusion coefficient of O2 into the tissue (D) is 3.3310-5 cm 2/s [2], and that you have an initial concentration of 0 just outside the capillary and a uniform internal concentration of 53mM [3]. Use a capillary radius of 7 um. You may neglect all source and sink terms in the equations above and model only the diffusion of O2 through the srrounding tissue. The program should generate two plots: a) A 3-dimensional surface plot describing the concentration profile of O2 as a function of time and distance (from the center of the capillary). Using the 3-dimensional plot, determine the distance at which the tissue has 10% of the capillary O2 concentration after 30 seconds. b) A linear plot describing the concentration profile of O2 from the edge of the capillary to the distance you found at point a at 15 seconds. Diffusion out of capillary Part 1: Concentration profile using finite difference approximation Equation 4 shows a changing concentration with respect to radial position as well as to time, making it a partial differential equation. Finite difference approximation is one way to numerically solve a partial differential equation. To solve the diffusion term of this equation using this method we can express the O2 diffusion for each slice or annulus around the tube. Writing the equation for the jth annulus we find that for j>1 20-1) This equation is valid for all annuli. To construct a concentration profile for the system, you will need to create a MATLAB code that solves equation 6 for each radial annuli using a loop Solving the loop over a certain number of radial annli will give you a diffusion profile along a radial slice for one point in time. You must then construct another loop to solve for the change in radial diffusion profile over time. You can assume the diffusion coefficient of O2 into the tissue (D) is 3.3310-5 cm 2/s [2], and that you have an initial concentration of 0 just outside the capillary and a uniform internal concentration of 53mM [3]. Use a capillary radius of 7 um. You may neglect all source and sink terms in the equations above and model only the diffusion of O2 through the srrounding tissue. The program should generate two plots: a) A 3-dimensional surface plot describing the concentration profile of O2 as a function of time and distance (from the center of the capillary). Using the 3-dimensional plot, determine the distance at which the tissue has 10% of the capillary O2 concentration after 30 seconds. b) A linear plot describing the concentration profile of O2 from the edge of the capillary to the distance you found at point a at 15 seconds