1. In medical applications the chief objectives for drug delivery are to deliver the drug to the correct location in the patient's body, and to obtain a specified drug concentration profile in the body through a controlled release of the drug over time. Drugs are often administered as pills. To derive a simple dynamic model of pill dissolution, assume that the rate of dissolution ra of the pill in a patient is proportional to the product of the pill surface area and the concentration driving force: Id = KA(Cs - Caq) where Caq is the concentration of the dissolved drug in the aqueous medium, C, is the saturation value, A is the surface area of the pill, and k is the mass transfer coefficient. a. where Caq is the concentration of the dissolved drug in the aqueous medium, C, is the saturation value, A is the surface area of the pill, and k is the mass transfer coefficient. Derive a dynamic model that can be used to calculate pill mass M as a function of time. The pill can be approximated as a cylinder with radius r and height h. It can be assumed that h/r > 1 and that the pill surface area can be approximated as A= 2лrh. (10 points) b. For the conditions given below, how much time is required for the pill radius r to be reduced by 90% from its initial value of ro? p = 1.2 g/ml ro = 0.4 cm h = 1.8 cm Cs=500 g/L k = 0.016 cm/min (10 points)