Krogh Tissue Cylinder

Harvir Humpal

BMED 425-02

hhumpal@calpoly.edu

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

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

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)

Mesh Description

• Type: Free Tetrahedral Mesh

• Fineness : Extra Fine

• Triangular Elements: 54298

• Quadrilateral Elements: 0

• Edge Elements: 1920

• Vertex Elements: 6

Surface Plot; Velocity in Capillary

3D Oxygen Conc. Profile (Tissue 1)

3D Oxygen Conc. Profile (Tissue 2)

3D Oxygen Conc. Profile (Tissue 3)

Concentration Line Plot (Tissue 1)

• blue:inlet

• green:mid

• red:outlet

Concentration Line Plot (Tissue 2)

Concentration Line Plot (Tissue 3)

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

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

3D Oxygen Conc. Profile (Tissue 2) with 50% increase in flow rate

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.