BME 314 Lecture 6 2010

# BME 314 Lecture 6 2010 - Drug Delivery I Krish Roy, Ph.D....

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Unformatted text preview: Drug Delivery I Krish Roy, Ph.D. Associate Professor Dept. of Biomedical Engineering Learning Objectives At the end of this lecture students should be able to Write the diffusion equations (Fick’s Laws of Diffusion) Derive the kinetic diffusion equation from first principles Explain why they need to understand diffusion and transport in order to study drug delivery, tissue engineering etc. Define and explain what is meant by controlled release of drugs Outline the advantages of controlled release concepts Define and mathematically express the release kinetics from controlled release drug delivery devices Understand how the diffusion constant varies with different parameters Explain and discuss in the various methods of controlled drug delivery First law of diffusion: Fick’s Law Diffusion is defined as the movement of solute molecules from a higher to a lower concentration gradient. This molecular movement occurs by a “random walk” mechanism in which molecules are continually colliding with each other while moving “on average” towards a particular direction The diffusive flux, i.e. the mass per unit time of solute movement is mathematically expressed as : Where δ C/ δ x is the concentration gradient in the direction of solute movement And D is the constant of proportionality and is defined as the Diffusion constant or Diffusion coefficient From a “random walk” derivation D is related to the root mean square displacement and time interval (t) by If a particle takes time T to diffuse L mm. how long will it take to diffuse 2L mm? x C D J ∂ ∂- = Dt x rms 2 = Mass conservation: Second law of diffusion Δx Δy Δz x z y J x (x) J x (x + Δx) J y (y) J y (y + Δy) J z (z) J z (z + Δz) General Balance Equation = (in – out) + generation = Accumulation Mass conservation: Second law of diffusion From the law of conservation of mass: Dividing by ∆ x ∆ y ∆ z and taking the limit of the differential volume 0, we get Combining equation (1) and (2) we get: z y x t C a y x J J z x J J z y J J z z z y y y x x x ∆ ∆ ∆ ∂ ∂ = + ∆ ∆-- ∆ ∆-- ∆ ∆-- ∆ + ∆ + ∆ + ) ( ]...
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## This note was uploaded on 11/29/2010 for the course BME 314 taught by Professor Frey during the Fall '08 term at University of Texas.

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BME 314 Lecture 6 2010 - Drug Delivery I Krish Roy, Ph.D....

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