About this note
A plain-language summary of the 1 publication listed under this topic on Academic Publications (Topic-wise). Full citations are under References.
Why this matters
Biothermofluids, or biothermology, is the study of fluid flow, heat transfer and mass transfer in living systems: how the body regulates its temperature, how blood carries oxygen, how drugs diffuse through tissue, how a laser heats the retina. Organs are complex and hard to reach for measurement, so computer models have become essential. The challenge is to simplify the biology enough to compute it without losing the physics (Narasimhan, 2011).
The porous medium approach offers such a simplification. Tissues are classic three-dimensional porous media: cells and fibres separated by spaces through which interstitial fluid and blood move. The idea applies at many scales, from organs down to cells. This invited review sets out the concepts and surveys research since about 2002 that has used them.
What we did
The review begins with a working definition: a porous medium is a region with at least two constituents, at least one of them fixed or only slightly deformable, characterised by its porosity (the fraction of volume that is open) and permeability (a measure of how easily fluid passes through). The central idea is volume averaging. Viewed from far enough away, the boundaries between solid and fluid blur, and each point stands for a small averaging volume, the representative elemental volume, over which properties are smoothed. This works when the pores are much smaller, usually by about three orders of magnitude, than the region being studied (Narasimhan, 2011).
It then traces the history of the momentum equation for porous media, from Henry Darcy’s 1856 filtration experiments in Dijon, which first identified permeability, through the Hazen, Dupuit and Forchheimer additions for fluid properties and inertia, to a general equation with Brinkman’s viscous term and a form drag term. It explains the energy equation under local thermal equilibrium, where solid and fluid share one temperature at each point, and local thermal non-equilibrium, where tissue and blood are allowed different temperatures and exchange heat across their interface.
With these tools the review surveys two broad areas:
- Bio-mass transport: LDL (cholesterol) transport into artery walls, nutrient and medium flow in scaffolds for growing tissue, drug delivery (including our porous medium model of drug transport through the sclera and choroid of the eye), drug-eluting stents, organs modelled as porous media (the lungs, heart muscle, kidneys and artificial kidneys, the brain, and peristaltic flows), and the transport of microbes through soil and groundwater.
- Bio-heat transport: bio-heat equations derived from porous medium theory as alternatives to the classical Pennes equation, and non-Fourier heat conduction, in which heat travels at a finite speed with a time lag between temperature gradient and heat flux.
What we found
The review concludes that porous medium modelling will play a growing part as biology, health and medicine call for simpler, cost-effective engineering understanding of living processes. For it to contribute further, several things are needed: detailed mapping of the internal geometry of tissues (for example by tomography) to obtain their porous medium properties; models for porous media that react chemically and deform, as living tissue does; and wider use of the general porous medium momentum equation and of two-energy-equation models based on local thermal non-equilibrium, whose potential in biology has yet to be fully realised (Narasimhan, 2011).
Related
- Drug Delivery in Human Organs, Non-Fourier Bio-heat Transfer and Bio-Fluid Dynamics and Mass Transfer in Human Lungs: our own studies that apply these ideas.
- Hydrodynamics in Porous Media: the fluid mechanics of porous media in engineering.
References
- Narasimhan, A., (2011), “The Role of Porous Medium Modeling in Biothermofluids,” J. Indian Institute of Science, 91 (3), 243-266.