Role of Porous Medium Modelling in Biothermofluids


Recently, I was invited to write a review article on the role of porous medium modelling in biothermofluids for the IISc Journal, a quarterly with exclusive invited reviews on special topics chosen by guest editors. The journal website is here: and the issue content can be accessed as pdf files.

Six reviews have appeared in the current special issue (vol. 91) on Biofluid Dynamics, guest edited by Prof. Jayawant Arakeri, ME, IISc. The Fluid Dynamics of Swimming Microorganisms and Cells by Ganesh Subramanian and Prabhu R. Nott (pages 283-314) is an interesting read.

My review presents an overview of the post-2002 research on the modelling aspects of several biothermofluid processes based primarily on the porous medium approach.

Here is some teaser content from the review:

The porous medium modelling approach, now an established methodology in other engineering disciplines, has made forays into biomechanical modelling over the past two decades. Many biological systems involving multi constituents can readily be approached as porous media for simplified analysis. An obvious example of mass transport in biological systems that can be modelled as porous medium is the diffusion of nutrients and other macromolecules (drugs etc.) across and within biological tissues. An earlier review by Khaled and Vafai [1] describes studies carried out prior to 2002 on porous medium models used in specific biological and biomedical applications such as tissue generation in scaffolds, transport in brain tissues, MRI applications, liquid chromatography, transport of macromolecules in aortic media, blood flow through muscles, and interstitial fluid flow in axi-symmetric soft connective tissue.

The review begins with a definition for porous medium suited for analysing transport phenomena, concepts of volume averaging, momentum and energy conservation statements are briefly discussed to motivate the ensuing review discussions. Porous medium modelling of several biomedical processes pertaining to human physiology is then discussed under two broad categories of bio-mass and bio-heat transport. The bio-mass transport section discusses LDL transport in arteries, drug delivery, drug eluting stents, functions of organs modelled as porous medium, porous medium modelling of microbial transport. Under the bio-heat transport section, porous medium approach based bio-heat equations are described accompanied by a literature review. A final subsection discusses non-Fourier type bio-heat conduction phenomena. Requirement of analysis and computational efforts in the future using the generalized porous medium momentum equation and the local thermal non-equilibrium based two energy equations are highlighted.

While seeking simplifications for biological processes through porous medium models is an exciting and useful multidisciplinary pursuit, a note of caution is also in order. As Francis Crick, one of the giants of biology having moved to it from physics, learned (to quote from [2]), “you have to adjust from the elegance and deep simplicity of physics to the elaborate chemical mechanisms that natural selection has evolved over billions of years.” A related point recently [3] made by Walter Gratzer is worth mentioning: “physicists, along with chemists and engineers, are surging into biology. This has rejuvenated both the biological and the physical sciences, even if the leading physics journals now publish a profusion of poorly refereed papers whose authors have not followed the excellent precept not to think what one wants to think until one knows what one ought to know.”

Biology is primarily governed not by fundamental physical laws — few and rigid — but by an evolutionary process of adaptation (as implied by Bio, which means life). Seeking modelling simplifications from physical principles for such complex and myriad processes could often result in incremental progress – with particular solutions of limited range of utility or general solutions to approximations that has oversimplified biological reality.

The reference list (about 90 references) compiled on the topic with BibTeX and DOI links in place is provided as a keyword-searchable, standalone HTML file:

View or download this HTML file (click to open the html file in your browser and save it).

Write to me if you need a pdf of any of these reviews.

Arunn Narasimhan (2011). The Role of Porous Medium Modeling in Biothermofluids, Journal of the Indian Institute of Science, 91 (3), 243-266 | Article PDF download


[1] A.-R. Khaled, K. Vafai, The role of porous media in modeling flow and heat transfer in biological tissues, International Journal of Heat and Mass Transfer 46 (26) (2003) 4989 – 5003. doi:10.1016/S0017-9310(03)00301-6.

[2] H.-X. Zhou, Q&a: What is biophysics?, BMC Biology 9 (1) (2011) 13. doi:10.1186/1741-7007-9-13.

[3] W. Gratzer, Biophysics – whence, whither, wherefore – or hold that hyphen, BMC Biology 9 (1) (2011) 12. doi:10.1186/1741-7007-9-12.