harvir humpal_krogh tissue cylinder (1)
TRANSCRIPT
![Page 2: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/2.jpg)
Problem Statement
• The purpose of this lab is to To illustrate and predict Oxygen transport from the blood in a capillary with coupled fluid flow and diffusion.
• COMSOL will be used to determine the velocity profile in the capillary, 3D oxygen concentration profiles for each radius, and an Oxygen Concentration Point Evaluation
![Page 3: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/3.jpg)
Given Assumptions
• Assumptions: • The arterial below the skin is 2 mm below the Epidermis/Stratus Corneum layer
• The diffusivity of the drug in the tissue between the skin layer and the arterial is approximately equal to the thickness of the dermis multiplied by the Pm of the dermis.
• The diffusivity in Blood is ~ 1e-5 m^2/s
• An average Arteriole blood velocity is 10 cm/s
![Page 4: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/4.jpg)
Given Data
Object Value
Capillary Radius 4 microns
Capillary Length 500 microns
Tissue 1 Radius 25 microns
Tissue 2 Radius 45 microns
Tissue 3 Radius 65 microns
Object Value
Plasma Viscosity 1.5e-3 Pa*s
Plasma Density 1050 Kg/m^3
Average Velocity 0.096 cm/s
Diffusivity in
Plasma
1.0e-6 m^2/s
Diffusivity in
Tissue
1.0e-9 m^2/s
O2 Conc. in
Plasma
0.1216
moles/m^3
O2 Consumption
Rate
-45e-4
moles
/(s*m^3)
![Page 5: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/5.jpg)
Mesh Description
• Type: Free Tetrahedral Mesh
• Fineness : Extra Fine
• Triangular Elements: 54298
• Quadrilateral Elements: 0
• Edge Elements: 1920
• Vertex Elements: 6
![Page 6: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/6.jpg)
Surface Plot; Velocity in Capillary
![Page 7: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/7.jpg)
3D Oxygen Conc. Profile (Tissue 1)
![Page 8: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/8.jpg)
3D Oxygen Conc. Profile (Tissue 2)
![Page 9: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/9.jpg)
3D Oxygen Conc. Profile (Tissue 3)
![Page 10: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/10.jpg)
Concentration Line Plot (Tissue 1)
• blue:inlet
• green:mid
• red:outlet
![Page 11: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/11.jpg)
Concentration Line Plot (Tissue 2)
![Page 12: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/12.jpg)
Concentration Line Plot (Tissue 3)
![Page 13: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/13.jpg)
Oxygen Concentration Point Evaluation at point of lowest concentration
Tissue Radius O2 Concentration (mol/m^3)
25 microns 0.094883
45 microns 0.046370
65 microns -0.021066
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Optimal radius for the tissue cylinder with the minimum concentration of oxygen in the
tissue (1mmHg)
• The radius of 59 microns is the closest value to the minimum concentration which is 0.001149 mole/m^3
• The minimum concentration value is 0.001282 mole/m^3
![Page 15: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/15.jpg)
3D Oxygen Conc. Profile (Tissue 2) with 50% increase in flow rate
![Page 16: Harvir Humpal_Krogh Tissue Cylinder (1)](https://reader034.vdocument.in/reader034/viewer/2022051213/55cebbf3bb61eba32f8b462e/html5/thumbnails/16.jpg)
Conclusions, Future Directions
• It becomes clear that minimum oxygen concentration decreases with increasing tissue size
• There are no real errors on this lab. However, the assumptions that were used simplified this lab and aren’t an exact indication of what the true values of concentration are.
• The calculated values of concentration can be used to calculated to analyze other aspects of these vessels such as volumetric flow rate or the stress that a medical device will need to account for.