The role of porous media in biomedical engineering as related to magnetic resonance imaging and drug delivery

Pertinent works associated with magnetic resonance imaging (MRI) and drug delivery are reviewed in this work to demonstrate the role of transport theory in porous media in advancing the progress in biomedical applications. Diffusion process is considered significant in many therapies such as delivering drugs to the brain. Progress in development of the diffusion equation using local volume-averaging technique and evaluation of the applications associated with the diffusion equation are analyzed. Tortuosity and porosity have a significant effect on the diffusion transport. Different relevant models of tortuosity are presented and mathematical modeling of drug release from biodegradable delivery systems are analyzed in this investigation. New models for the kinetics of drug release from porous biodegradable polymeric microspheres under bulk erosion and surface erosion of the polymer matrix are presented in this study. Diffusion of the dissolved drug, dissolution of the drug from the solid phase, and erosion of the polymer matrix are found to play a central role in controlling the overall drug release process. This study paves the road for the researchers in the area of MRI and drug delivery to develop comprehensive models based on porous media theory utilizing fewer assumptions as compared to other approaches. List of symbols a Empirical constant aE Einestein radius ADC Apparent diffusion coefficient b Empirical constant BSat Saturation concentration of the drug in the polymer phase Bs Undissolved drug concentration in the polymer ÆCæ Volume average of concentration CL Drug concentration in the liquid phase Co Initial drug concentration Csat Saturation concentration of the drug CSe Drug concentration in the effective solid phase Cs Undissolved drug concentration in the pores dp Pore diameter D Effective diffusion coefficient DB Polymer diffusion coefficient ECS Extracellular space fn Viscosity function F Geometric function F1, F2 Correction factors F(C) Uptake term hm Mass transfer coefficient k Permeability kdis Dissolution rate constant kero Surface erosion constant KB Forward rate constant KC Backward rate constant KDB Dissolution rate constant in polymer KDC Dissolution rate constant in pore KHero Hyperbolic erosion rate constant for bulk erosion KLero Linear erosion rate constant for bulk erosion K. Khanafer Vascular Mechanics Lab, Biomedical Engineering Department, University of Michigan, Ann Arbor, MI 48109, USA K. Vafai (&) Mechanical Engineering Department, University of California, Riverside, CA 92505, USA e-mail: [email protected] Heat Mass Transfer (2006) 42:939–953 DOI 10.1007/s00231-006-0142-6