Question

You are working on a new drug to treat overactive bladder. You need to find the diffusion coefficient of your new drug through the bladder wall. You take a thin section of fresh pig bladder and place it between two large chambers each loaded with 100mM of your drug (see figure below). The chambers are very large compared to the bladder tissue, and therefore, the concentration of drug in the chambers does not change and can be treated as constant. The chambers are well mixed (e.g. hm à infinity). After 8 hours, you remove the bladder tissue and find that the drug concentration in the center of the 5mm thick tissue is 80mM. What is the effective diffusion coefficient of your drug in bladder tissue in cm2/s? You can assume the partition coefficient is exactly 1.

Answer 1

The effective diffusion coefficient of a drug in bladder tissue can be calculated using a formula derived from Fick's law, given the steady-state concentration data and the time over which diffusion occurs. By using the given parameters, including the distance, time, and concentration at the center and edges of the tissue, the diffusion coefficient can be determined in cm2/s.

Step-by-step explanation:

To find the effective diffusion coefficient of a drug in bladder tissue, we utilize the fact that diffusion is governed by Fick's law, which states that the diffusion flux is proportional to the concentration gradient. Given the experimental setup, we can assume steady-state diffusion, as the concentration in the chambers remains constant due to their size relative to the tissue, and the partition coefficient is given as 1. We also have the time (8 hours), the distance (center of the tissue, which is 2.5 mm from either side), and the concentration at the center (80 mM).

The formula to calculate the diffusion coefficient D in such a case, considering a steady-state one-dimensional diffusion, is:

D = (x^2) / (6*t*ln((C0-Cx)/(C0-Ct)))

Where:

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• x is the distance from one side to the center of the tissue (2.5 mm = 0.25 cm)
• 
  
• t is the time in seconds (8 hours = 28800 seconds)
• 
  
• C0 is the initial concentration (100 mM)
• 
  
• Cx is the concentration at the center of the tissue (80 mM)
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• Ct is the concentration at the edge of the tissue, assumed to be equal to C0 because the partition coefficient is 1 and the chambers are very large

Using these values, we can perform the calculations to determine the diffusion coefficient of the drug in cm2/s.