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21 Pages

### BMED+3300+Lecture+2+Slides+082411

Course: BME 3300, Spring 2011
School: Georgia Tech
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Word Count: 1233

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3300 BMED Biotransport BMED 3300 Biotransport Lecture 2 August 24, 2011. Professor Julie Babensee Ficks First Law of Diffusion v J A = D ABC A z z=0 Diffusion J A, z = D AB dC A dz (For diffusion in the z-direction only) For dilute biological solutions, NA,z = JA,z JA = molar flux in the z-direction relative to the molar average velocity, [mol/cm2s] dC A = the concentration gradient in the z direction...

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3300 BMED Biotransport BMED 3300 Biotransport Lecture 2 August 24, 2011. Professor Julie Babensee Ficks First Law of Diffusion v J A = D ABC A z z=0 Diffusion J A, z = D AB dC A dz (For diffusion in the z-direction only) For dilute biological solutions, NA,z = JA,z JA = molar flux in the z-direction relative to the molar average velocity, [mol/cm2s] dC A = the concentration gradient in the z direction [mol/cm3/cm] dz DAB = mass diffusivity or diffusion coefficient for component A diffusing through component [cm diffusing through component B [cm2/s] Diffusivity Diffusivity Units for diffusivity J A, z M L2 1 = = D AB = 2 3 1/ L t dC A / dz L t M / L D = f (P, T, composition) (P For gases, D = 5x10-6 1 x 10-5 m2/s For liquids, D = 10-10 10-9 m2/s For solids, D = 10-14 10-10 m2/s solids 10 Liquid Liquid-Mass Diffusivity Diffusivity D AB B 7.4 108 ( B M B )1 / 2 = 0 T V A.6 For nonelectrolytes in an dilute solutions Where, DAB is the mass diffusivity of A diffusing through liquid solvent B in cm2/s B is the viscosity of the solution in centipoises T is the absolute temperature in Kelvin is the absolute temperature in Kelvin MB is the molecular weight of the solvent VA is the molal (or molecular) volume of solute at normal boiling point in cm3/g mol (See Table 24.4, 24.5, WWWR p. 439-440) B is the association parameter for solvent B (see WWWR p. 440) th WWWR 440) (Wilke and Chang, 1955) Other empirical relationships for diffusivity as a function of molecular weight for biological systems exist Vast Differences in Extracellular and Intracellular Fluid Composition D. O. Cooney, Biomedical Engineering Principles An Introduction to Fluid, Heat Fl and Mass Transport Processes, Marcel Dekker, Inc., 1976. Transport of Species Through the Cell Membrane Occur by: Ordinary passive diffusion Facilitated diffusion (species aided by a carrier) Active transport (carrier-aided transfer against a concentration gradient, requiring biochemical energy) Cell membranes are 80 100 thick Postulated structure is a lipid bilayer with 8 pores Permeability Permeability is used to describe solute transport (Ns, for example in gmoles/sec) across a membrane such as a capillary membrane or a hemodialysis membrane. Permeability is defined by the following expression using the total membrane surface area S. N S = Pm S (Chigh Clow ) (Chigh Clow) is the difference in the surface concentration on either side of the membrane. ith th Permeability is also equal to the effective diffusivity of the solute in the membrane, Dm, times the oil/water partition coefficient of the species, K, (a measure of the relative solubility of a solute within a membrane; K = C membrane / C interstital fluid), divided di by the thickness of the membrane, tm. Pm = KDm tm Permeability: Effects of Molecular/Pore Diameter D. O. Cooney, Biomedical Engineering Principles An Introduction to Fluid, Heat Fl and Mass Transport Processes, Marcel Dekker, Inc., 1976. Diffusion in Porous Membrane A A Solvent B Dm = f(DAB, pore morphology) Dm << 1 D AB Dm 1 = D AB F F = shape factor = tortuosity; 1 < < 3 A Permeability: Effects of Partition Coefficient W.M. Saltzman, Drug Delivery Engineering Principles for Drug Therapy, Oxford University Press, 2001. Permeability: Effects of Solute Molecular Weight W.M. Saltzman, Drug Delivery Engineering Principles for Drug Therapy, Oxford University Press, 2001. Membrane Permeability CA1 J A, x = D AB C1 C C2 J ss = Dm 1 l CA2 C2 x=0 x=l dC A = J ss dx Partition coefficient, K. between CA,ambient and CA,membrane Depends on relative solubility of species in ambient phase versus polymer phase If ideal solution, K f(C) C C K= 1 = 2 C A1 C A2 K= C1 C A1 J ss = Dm K C A1 C A2 DK J ss = m C l l Two different in ways which polymer membrane permeability is represented KDm = Pm Is one way of defining permeability [Dm] = cm2/s [K] = dimensionless [Pm] = cm2/s I prefer this definition of permeability which is that Pm = Here permeability has units of cm/s KDm tm Example: Permeability of Polymer Membrane to Insulin A novel membrane for the encapsulation of islets as an insulin delivery system is being developed in the lab that you are doing research project in. Your task is being developed in the lab that you are doing a research project in. Your task is to determine the permeability of this membrane to insulin. You decide to use a diffusion cell as depicted in the figure below to determine the permeability of the membrane to insulin. A 100 m thick sample of your polymer membrane is placed between reservoir 1 and reservoir 2. At the start of your experiment (t=0) you place th (t an insulin solution in saline into reservoir 1 with a saline solution with no insulin in reservoir 2. You allow enough time for steady state to be set up and you make the following measurements. You determine that the insulin concentration in reservoir 1 is 1 g/mL, the insulin concentration in reservoir 2 is 1 mg/mL, and the steady state flux of insulin across the membrane is 3.6 x 10-5 g/cm2.s. What is the permeability of the membrane to insulin? Reservoir 2 Reservoir Reservoir 1 CA1 CA2 X= l X= 0 Polymer membrane Solution Solution J SS = KDm C l 3 5 = KD (1 0.001 g/cm ) 3.6 10 m 0.01 cm KDm = 3.6 107 cm2 /s KDm 3.6 107 cm2 /s Pm = = = 3.6 105 cm/s tm 0.01 cm Example: Drug Delivery Device Safety Example: Drug Delivery Device Safety A simple drug delivery device uses a synthetic simple drug delivery device uses synthetic membrane to control the release of a drug from a reservoir into the target tissue, typically inside the body. Consider device with Consider a device with a 3 cm2 of membrane, separating cm membrane separating a drug in solution at a concentration of 1 mg/mL from the body (total volume 50L), where the drug is essentially at zero concentration The membrane diffusion coefficient zero concentration. The membrane diffusion coefficient is 2x10-6 cm2/s, the partition coefficient is 0.85 and its thickness is 10 m. The rate of drug delivery should never exceed never exceed .0075 mg/s due to safety issues mg/s due to safety issues concerning drug toxicity. Is this drug delivery device safe? Solution Solution The rate of drug delivery is just the concentration difference between both sides multiplied by the diffusion coefficient given information: membrane thickness (10 m), l = 10 x 10-6 m = 0.001 cm surface area = 3 cm2 diffusion coefficient, Dm = 2 x 10-6 cm2 / s J A, x = D AB dC A = J ss dx J ss = KDm C l = (0.85)(2 x106 ) (1 0) 0.001 = 0.0017 mg/cm2s rate of drug delivery = Flux x surface area = 0.0017 x 3 = 0.0051 mg/s 0.0051 < 0.0075 mg/s therefore safe Convective Mass Transfer Convective mass transfer occurs between a moving fluid and fl a surface or between two relatively immiscible moving fluids Fluid Flow Fluid Flow y y CA=CA =(y) x CA CAs-CA=[CAs-CA](y) CAs > CA Concentration and velocity profiles for a fluid and velocity profiles for fluid flowing past a solid surface Convective Mass Transfer Convective mass transfer described by: N A = kc C A Where, NA [e.g., moles/cm2s] is the molar mass transfer of species A measured relative to fixed spatial coordinates measured relative to fixed spatial coordinates CA [e.g., moles/cm3] is the concentration difference between the boundary surface concentration (CA,s) and the average concentration of the fluid stream of the diffusing species (CA) (C kC [cm/s] is the convective mass transfer coefficient Convective mass transfer occurs in the direction of decreasing concentration
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