Heat and Mass Transfer

, 42:939 | Cite as

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

  • K. Khanafer
  • K. VafaiEmail author
Special Issue


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.


Porous Medium Drug Release Apparent Diffusion Coefficient Diffusion Equation External Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Empirical constant


Einestein radius


Apparent diffusion coefficient


Empirical constant


Saturation concentration of the drug in the polymer phase


Undissolved drug concentration in the polymer


Volume average of concentration


Drug concentration in the liquid phase


Initial drug concentration


Saturation concentration of the drug


Drug concentration in the effective solid phase


Undissolved drug concentration in the pores


Pore diameter


Effective diffusion coefficient


Polymer diffusion coefficient


Extracellular space


Viscosity function


Geometric function

F1, F2

Correction factors


Uptake term


Mass transfer coefficient




Dissolution rate constant


Surface erosion constant


Forward rate constant


Backward rate constant


Dissolution rate constant in polymer


Dissolution rate constant in pore


Hyperbolic erosion rate constant for bulk erosion


Linear erosion rate constant for bulk erosion


Michele-menten constant


‘S’ erosion rate constant for bulk erosion


Cumulative amount of drug released at time infinity


Cumulative amount of drug released at time t


Magnetic resonance imaging


Fluid pressure


Pore radius


Radius of microparticles


Mass source density


Sherwood number




Velocity vector


Representative elementary volume


Effective volume of the microsphere


Rate constant


Pore volume

Greek symbols


Fluid density




Geometrical tortuosity

λx, λ y, λ z

Tortuosity components


Dynamic viscosity of the pure fluid


Surface area


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Vascular Mechanics Lab, Biomedical Engineering DepartmentUniversity of MichiganAnn ArborUSA
  2. 2.Mechanical Engineering DepartmentUniversity of CaliforniaRiversideUSA

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