Question

1. Quantitative: Fick’s first law helps us understand the relationship between a molecule’s concentration gradient (the difference in its concentration at two locations) and its flux.  This can be super important for the delivery of drugs to help cure human illnesses. As one example, we’ll think about a transdermal patch that provides medicine to the body. Scopolamine patches are used to treat motion sickness. Scopolamine comes from the nightshade family and is similar to acetylcholine. It antagonizes acetylcholine activity, preventing acetylcholine from stimulating your motion sensing nerves. The goal of the patch is to get a relatively constant supply of scopolamine into your bloodstream. Here we are going to model some things using numbers that are mostly based on real data for the patch.

1. Draw a picture of a patch from the side showing 1) the patch, 2) the layer of skin the medicine diffuses through and 3) a blood vessel so you can see the geometry of how the medicine is moving from the patch into the blood stream.

2. Write Fick’s equation for the flux of scopolamine. Label your drawing above with the key variables in the equation.

3. Typically you put the scopolamine patch behind your ear where the blood vessels are pretty close (~0.5 mm) to the surface. If you put the patch on your arm where the blood vessels were 2mm beneath the skin, what would happen to the scopolamine flux as compared to placing the patch behind your ear?

4. The initial patch concentration is 13.6 mg / cm³of scopolamine.  The concentration in the blood is initially 0, but once the patch starts working, the equilibrium blood concentration rises to 354 pg / cm³.  How does the flux from the patch change from the initial to equilibrium conditions?

5. If the diffusion coefficient of scopolamine is 2 x 10^-7cm²/ s, how long does it take a scopolamine molecule to diffuse from the patch to the blood vessel?

6. Based on (e), why do they tell you to put the patch on 3 hrs before taking a trip?

7. We’d like to know how long the patch is able to provide relief from motion sickness. This boils down to figuring out how long the delivery rate stays high enough to be effective. We already showed the delivery rate does not depend on the level in the blood so it will just depend on the concentration in the patch. The patch is pretty small and as the scopolamine is delivered, its concentration in the patch decreases. Let’s say once the delivery rate drops below 35% of the initial rate, the patch is no longer providing enough medicine to treat symptoms.  What is the concentration in the patch at this end point?

8. If the initial patch has 1.5 mg of scopolamine, how much scopolamine remains when the delivery rate drops to 35%?

1. How much scopolamine has been delivered to the body when the delivery rate reaches 35%?

10. Big finish: Let’s assume that during the time the patch is effective, the average delivery rate is 14 ug/hr. We can also assume the amount of scopolamine delivered to the body during this efficacy time (see 2i) is equal to the efficacy time times the average delivery rate. So, how long can the patch provide an effective delivery rate of scopolamine, i.e what is the efficacy time?

Answer 1

1. Image:

b. We can assume this through this image:

The above image refers to the description flux across the skin from a transdermal patch where J is the molecular flux, C2 is the active molecule concentration in the patch, C1 is the active molecule concentration in the body, D is the diffusion coefficient, L is the cross sectional diffusion thickness and t is the time of diffusion.The equation shows the Law of Diffusion of Fick:
J = -D(dc/dt)
Here D is the diffusion coefficient and dc/dt is concentration gradient.