2017
DOI: 10.1007/s11012-017-0638-9
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A poroelastic mixture model of mechanobiological processes in biomass growth: theory and application to tissue engineering

Abstract: In this article we propose a novel mathematical description of biomass growth that combines poroelastic theory of mixtures and cellular population models. The formulation, potentially applicable to general mechanobiological processes, is here used to study the engineered cultivation in bioreactors of articular chondrocytes, a process of Regenerative Medicine characterized by a complex interaction among spatial scales (from nanometers to centimeters), temporal scales (from seconds to weeks) and biophysical phen… Show more

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Cited by 24 publications
(22 citation statements)
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“…Many mathematical models of passive transport into a poroelastic medium do not take into account exchanges between phases (Basser 1992;Støverud et al 2011;Chapelle and Moireau 2014). In (Fusi et al 2006;Lemon et al 2006;Sacco et al 2017), models including exchanges between phases are presented on closed poroelastic mixtures (no external sources or sinks). However, the changes are not mediated by external species.…”
Section: Resultsmentioning
confidence: 99%
“…Many mathematical models of passive transport into a poroelastic medium do not take into account exchanges between phases (Basser 1992;Støverud et al 2011;Chapelle and Moireau 2014). In (Fusi et al 2006;Lemon et al 2006;Sacco et al 2017), models including exchanges between phases are presented on closed poroelastic mixtures (no external sources or sinks). However, the changes are not mediated by external species.…”
Section: Resultsmentioning
confidence: 99%
“…If we need to track the variations of the nutrient concentration, we may use effective continuity equations for chemical concentration in tissues [30,31]. For the limiting concentration c n :…”
Section: Final Equationsmentioning
confidence: 99%
“…We update the cellular fields solving (30) with the stationary concentration values for (31). The time derivatives in (31) are small, so that time evolution is driven by the source terms reflecting cell activity and changes in the biofilm boundaries.…”
mentioning
confidence: 99%
“…The topic of fluid flow in biological tissues is analyzed in the papers [1][2][3][4]. The paper by Sacco, Causin, Lelli, and Raimondi applies concepts from mixture theory to the processes of biomass growth for applications in tissue engineering [1].…”
mentioning
confidence: 99%
“…The paper by Sacco, Causin, Lelli, and Raimondi applies concepts from mixture theory to the processes of biomass growth for applications in tissue engineering [1]. Grillo, Carfagna, and Federico examine non-Darcian effects in solvent transport in fiber-reinforced biological tissues [2].…”
mentioning
confidence: 99%