Synthesis of Flow and Thermal Transport in Porous Media as Applied to Biological Applications

Abstract

The biological systems are tied to the molecular transport across the living tissues which in turn highly depend on kinetic and thermal energy exchanges. For various applications ranging from artery modeling to very sensitive tissue modeling such as the brain, porous media modeling accurately predicts the biological behavior. This article elaborately addresses the fundamentals of porous media and provides a comprehensive synthesis of the theory development from the primary methods available in the literature to the modern mathematical formulations. Specifically, this manuscript concentrates on two remarkable biological applications including (1) blood flow interactions with the porous tissue and (2) hydrodynamic impacts of particle-particle interactions in the microscale modeling that requires Lagrangian frame.

Computational Modeling of Microwave Tumor Ablation

“…Cowin [ 64 ] concluded that most studies related to the mixture theory have an unusually large number of equations. As the structure of biological tissues is porous and consists of different cells and a microvascular bed, the theory of porous media for heat transfer in tissues is more appropriate than that of a homogenous model [ 65 , 66 ]. Most previous models of heat transport have focused on single-layer porous media biomaterials [ 67 , 68 , 69 ].…”

Multifractal approach for a biological porous media: Human dentin case

“…It has been shown that real systems exhibit nonlinear behaviors (Garcia‐Ruiz et al, 2012; Meakin, 1998), examples of fields where these behaviors can be observed are: pluvimetry (García‐Marín, 2007), texture food (Serrano et al, 2019), medical signal and image analysis (Baish & Jain, 2000; dos Santos Menezes et al, 2021; Hua et al, 2009; Jud et al, 2016; Lopes & Betrouni, 2009; N'Diaye et al, 2013; Reishofer et al, 2018; Silvetti & Delrieux, 2010), and porous media (Ehlers & Wagner, 2019; Jiang & Tchelepi, 2019; Shen et al, 2018) the latest one is of our interest. Actually, scientific communications on porous systems cover multiple disciplines of science and engineering, some examples are: materials science and fluid dynamics (Calvo‐Guirado et al, 2019; Ehlers & Wagner, 2019; Hosseinikhah et al, 2020) thermodynamics (Alizadeh et al, 2021; Sheikholeslami et al, 2019) and biological systems (Khazayinejad et al, 2021; Kosari & Vafai, 2021), for instance; bones (Alves et al, 2017; Borowska et al, 2015; Camargo et al, 2016; Harrar et al, 2011; Hua et al, 2009; Koh et al, 2012; Sanchez‐Molina et al, 2013; Xiao et al, 2020; Zehani et al, 2016) and teeth (Nezafat et al, 2019; Solaymani et al, 2018, 2020)—on which we focus on. Teeth and bones share some similarities like mineral composition (calcium phosphate) and both contain internally living porous tissue, but the main difference between them is that bones can regenerate by their own, unlike teeth (Okazaki, 2021).…”