# Name 8 5 elution of drug from a stent duration of

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Name: _______________________________________8
5. Elution of drug from a stent - duration of release (25 points).In Problem Set 3, you determined how a polymer-coated stent can release drug into theblood. Now we will determine how long it will take to deplete the drug from the polymer layer.Consider the same diagram as before, but now a new set of assumptions:i.The drug is embedded in a polymer layer at concentration (CD,P) thatWILLchangeover time. The initial drug concentration is given by C’D,P.ii.The transport of drug from the polymer layer into the blood is exclusively bydiffusion, and can be characterized by the rate constant G.iii.The constant G can be treated with a diffusing capacity (DD) approach, just like gastransport between the lung and capillary. The polymer layer is fully wetted by theblood, so assume that drug is already soluble in water inside the polymer layer.iv.The concentration of drug in the blood entering the region of the stent is zero.v.Assume that the blood is well-mixed. While this assumption is not accurate, it willgreatly simplify the problem. The concentration of drug inside and outside the stentwill now be CD,b.Find the drug release half-life by answering the following.A.(5 points) Draw a diagram of the vessel, stent, polymer layer, and blood. Use a close-upview of a single section of blood vessel. Include all variables that may be relevant withinthe polymer layer and blood. Use Assumption III to characterize G.B.(5 points) Perform a mass balance on drug within the polymer layer to obtain adifferential equation describing the change in concentration with time.C.(2 points) State the reason why we cannot solve the differential equation at this point.D.(6 points) Perform a mass balance on drug within the blood and find a relationship thatdescribes how CD,band CD,Pare related. *Hint: will drug accumulate in the blood?E.(4 points) Use the result of part D to solve the differential equation in part B and find anequation for CD,P(t).F.(3 points) Rearrange this equation to find the drug half-life (CD,P= C’D,P/2) given a bloodflow rate, drug diffusing capacity, and polymer volumes of 5 L/min, 1x10-5mL/min, and50 mL, respectively.Name: _______________________________________11

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