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 con-centration profile in the body through a controlled release ofthe drug over time. Drugs are often administered as pills. Inorder to derive a simple dynamic model of pill dissolution,assume that the rate of dissolution rd of the pill in a patientis 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 theaqueous medium,csis the saturation value,Ais 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 rd=k Acs.(a)Derive a dynamic model that can be used to calculate pill mass M as a function of time. You can make the following sim-plifying assumptions:(i)The rate of dissolution of the pill is given by rd=k Acs.(ii)The pill can be approximated as a cylinder with radius r and height h. It can be assumed that h /r≫1. Thus the pill surface area can be approximated as A=2πrh.(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? ρ=1.2g∕ml r0=0.4cm h=1.8cm cs=500 g∕L k=0.016 cm∕min
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 con-centration profile in the body through a controlled release ofthe drug over time. Drugs are often administered as pills. Inorder to derive a simple dynamic model of pill dissolution,assume that the rate of dissolution rd of the pill in a patientis 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 theaqueous medium,csis the saturation value,Ais the surface area of the pill, and k is the
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