In medical applications the chief objectives for drug

Chapter 2, Problem 2.16

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In medical applications the chief objectives for drug delivery are: (i) to deliver the drug to the correct location in the patient's body, and (ii) 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. In order to derive a simple dynamic model of pill dissolution, assume that the rate of dissolution r d of the pill in a patient is proportional to the product of the pill surface area and the concentration driving force: rd = kA(cs - Caq) where Caq is the concentration of the dissolved drug in the aqueous medium, Cs is the saturation value, A is the surface area of the pill, and k is the mass transfer coefficient. Because Cs .. Caq, even if the pill dissolves completely, the rate of dissolution reduces to r d = kAcs. (a) Derive a dynamic model that can be used to calculate pill mass M as a function of time. You can make the following simplifying assumptions: (i) The rate of dissolution of the pill is given by r d = kAcs. (ii) The pill can be approximated as a cylinder with radius r and height h. It can be assumed that hlr .. 1. Thus the pill surface area can be approximated as A= 2-rrrh. (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 r0? p = 1.2 g/ml ro = 0.4 em h = 1.8 em Cs = 500 g/L k = 0.016 em/min