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Mass Transport in Biological Systems. OBJECTIVES To discuss how to model mass transport processes within the body. OUTLINE review Fick’s first and second laws consider diffusion + (reaction + convection)

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mass transport in biological systems
Mass Transport in Biological Systems
  • OBJECTIVES
  • To discuss how to model mass transport processes within the body.
  • OUTLINE
    • review Fick’s first and second laws
    • consider diffusion + (reaction + convection)
    • apply these concepts to solute movement across cell membranes/capillary walls, protein adsorption

CHEE 340

mass transport
Mass Transport
  • Can be achieved by both convection and diffusion. Mass transport is measured in terms of flux (= amount of material crossing a unit area normal to the direction of transport per unit time).
  • Most biological systems are dilute, so v is assumed to be the solvent velocity, and the transport of each component through the solvent can be studied as if the mixture was binary.

CHEE 340

fick s laws of diffusion
Fick’s Laws of diffusion
  • strictly valid only for dilute solutions

Fick’s 1st law :

slab

cylinder

Fick’s 2nd law :

sphere

CHEE 340

diffusion across a membrane steady state
Diffusion across a membrane: Steady-state
  • skin, buccal mucosa, cell membrane…

Co

C

CL

L

distance, x

CHEE 340

example
Example
  • Scopolamine is available in a transdermal patch for the treatment of motion sickness. You are involved in the design of a new patch for this drug and need to first determine the diffusion coefficient of the drug in the outer layer of the skin. To do this, you set up a diffusion cell using excised human skin (thickness = 100 m). The donor solution has a constant scopolamine concentration of 4.6 mg/ml. The concentration in the receptor solution is maintained at a concentration very much smaller than 4.6 mg/ml. The skin section you use is circular with a radius of 0.5 cm. The amount of the drug that has passed through the skin versus time is given in the following Table. Using this data and the fact that scopolamine has a partition coefficient (skin/water) of 17.4, calculate the diffusion coefficient of scopolamine in the skin.
  • Total mass of scopolamine transported versus time

CHEE 340

diffusion reaction the krogh capillary
Diffusion + Reaction: The Krogh Capillary
  • Consider oxygen delivery to tissue at steady-state. The oxygen is also being consumed in the tissue. This consumption is modeled using Michaelis-Menten kinetics.

r

z

2Ro

2Rc

CHEE 340

example8
Example
  • Given that the reaction rate of oxygen in skeletal muscle is 10-7 mol/(cm3 s), the capillary radius is 1.5 to 4 m, the diffusion coefficient of oxygen in muscle is 2(10-5) cm2/s, and the concentration of oxygen in plasma is 4.05(10-8) mol/cm3, determine the maximum intercapillary radius. If the total oxygen content in the blood entering the capillary is 2 (10-3)M and during exercise the average flow rate in the blood is 0.2 cm/s, determine the capillary distance at which the concentration of oxygen in the blood is zero.

CHEE 340

unsteady state diffusion
Unsteady-State Diffusion
  • Examples include injection of a drug into the muscle or sub-cutaneously followed by absorption into the blood stream, and the initial stages of protein adsorption to a biomaterial.
  • Consider protein adsorption:

C

at t= 0, C = Co

x = 0

CHEE 340