1 EBIO 216 Problem Set#8 – Due April 20, 2021 Post your work to D2L by 5:00pm 1. The pharmacokinetics of nicotine can be approximated with the material balance: ?? ???? ???? = ??1?? − ??2?? − ??3??...

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1 EBIO 216 Problem Set#8 – Due April 20, 2021 Post your work to D2L by 5:00pm 1. The pharmacokinetics of nicotine can be approximated with the material balance: ?? ???? ???? = ??1?? − ??2?? − ??3?? when smoking; IC C = Co at t = 0 ?? ???? ???? = − ??2?? − ??3?? when done smoking; with IC C = Co at t = 0 where V 40 l volume of distribution of nicotine in the body C ng ml-1 plasma concentration of nicotine n number of cigarettes smoked per hour k1 800,000 ng amount of nicotine absorbed per cigarette k2 25 l h-1 rate coefficient for hepatic metabolism k3 11 l h-1 rate coefficient for renal clearance t h time (a) Label each term in the first balance with the letter(s) corresponding to its significance. Some terms may have more than one correct answer; in that case give both appropriate answers. A. Accumulation B. Flow in C. Flow out D. Generation E. Consumption F. Growth G. Metabolism H. Recycle I. Mass transfer J. Excretion 2 (b) Circle each of the following that are true about this model A. Assumes the volume V is well-mixed (instantaneous distribution) B. Assumes zero-order kinetics of nicotine metabolism in the liver C. Assumes steady-state D. Assumes no loss of nicotine through exhaled breath E. Assumes gas-liquid equilibrium partitioning of nicotine in the lung F. Assumes first-order kinetics of nicotine elimination via the urine G. Assumes no generation of nicotine in the body (c) What is the half-life of nicotine in the body after smoking stops? (d) Suppose it is desired to design a transdermal anti-smoking aid patch that will deliver nicotine continuously to the body through the skin. The target blood concentration of nicotine is 12 ng ml-1. What is the required nicotine delivery rate (in ng h-1) to achieve this steady concentration? TIP: replace the term in the material balance that is associated with delivery of nicotine from cigarettes with a term for delivery from the patch. (e) The solution to the first differential equation given above is: ?? = ??1?? ??2 + ??3 �1 − ?? −(??2+ ??3)?? ?? � + ??0?? −−(??2+ ??3)???? How long does it take after putting the patch on to reach 10 ng ml-1? Assume there is no nicotine in the blood initially. 2. A two-layered controlled drug release device is to be designed to deliver a burst of drug immediately upon implantation and then a sustained release of drug for an additional two days. The initial burst should release 200 mg (Mbo) and then an additional 600 mg (Mso) should be released over the next two days. The device is layered as diagrammed here: 3 These parameter definitions apply: A cm2 area of device a mm day-1 erosion rate of sustained release layer Cbo mg cm-3 concentration of drug in burst layer Cso mg cm-3 concentration of drug in sustained release layer db mm thickness of burst layer ds mm thickness of sustained release layer Mb mg mass of drug in burst layer Mbo mg mass of drug in burst layer initially Ms mg mass of drug in sustained release layer Mso mg mass of drug in sustained release layer initially t day time after device implantation The area of the two layers must be the same. (a) The available options for the burst layer and the sustained release layer are detailed in the tables below. Suggest a design (pick one option for the burst layer and one option for the sustained released layer) that meets the requirements specified above. Table 1. Options - burst layer design. Table 2. Options - sustained release layer design. Option (mm) db (mg/cm3) Cbo (cm2) A Option (mm) ds (mg/cm3) Cso (cm2) A (mm/day) a B 0.6 333 10 F 1.2 833 0.6 C 0.8 417 G 2.0 600 0.6 D 0.8 500 H 2.0 500 0.6 E 1.2 333 I 2.0 417 1.0 (b) Formulate a differential equation to describe the change in drug mass in the sustained release layer as a function of time. State the initial condition. 4 3. A controlled drug release device is made in a cylinder shape as sketched below. The outer shell of the device consists of a drug-loaded polymer that bulk erodes quickly after implantation releasing a burst of drug. This rapidly raises the blood concentration to the target steady state value, CSS. The inner core erodes slowly from just one of the flat ends (not from the curved sides or second end). The purpose of the sustained release from the rod in the core is to maintain the blood concentration at CSS. b 0.1 d-1 rate coefficient of drug metabolism C mg l-1 concentration of drug in the body CSS 30 mg l-1 target steady-state concentration of drug L cm length of drug release device dL/dt 0.1 cm d-1 rate of erosion of device �̇�? mg d-1 rate of drug release from inner cylinder core R1 cm radius of inner cylinder core R2 cm radius of entire cylinder ρ1 620 mg cm-3 drug loading density in inner cylinder core ρ2 870 mg cm-3 drug loading density in outer shell t h time V 50 l volume of distribution 5 (a) A material balance on the drug in the body after implantation of the device and dissolution of the burst layer can be written: ??(????) ???? = �̇�? − ?????? Circle all of the following that are assumed in writing this balance (there may be more than one correct answer.) A. No metabolism B. Excretion by zero-order kinetics (constant rate) C. Steady state D. Linear dose-response E. Consumption according to first-order kinetics F. Constant rate of drug delivery (b) Once the target concentration is attained after the burst release of drug, what should the rate of drug release from the inner cylinder (�̇�?) be to maintain a steady-state concentration equal to CSS? (c) Circle the expression below that accurately calculates the drug release rate. A. �̇�? = ??12????1 ???? ???? B. �̇�? = ??1????12 ???? ???? C. �̇�? = ??12???? ????1 ???? D. �̇�? = ??1 ?? 2 ??1?? ????1 ???? E. �̇�? = ??12????1 ????1 ???? (d) What should the radius of the inner core (R1) be to achieve the desired drug release rate? (e) What should the length (L) of the device be to have a lifetime of 30 days? (f) What should the outer radius of the device be (R2) to provide the correct burst drug release? (g) How long does it take after the drug release core part of the device is completely dissolved for the drug concentration in the body to fall to one-quarter of its steady state value?