A multiscale approach in the computational modeling of the biophysical environment in artificial cartilage tissue regeneration

Abstract

Tissue Engineering is a strongly interdisciplinary scientific area aimed at understanding the principles of tissue growth to produce biologically functional replacements for clinical use. To achieve such an ambitious goal, complex biophysical phenomena must be understood in order to provide the appropriate environment to cells (nutrient delivery, fluid-mechanical loading and structural support) in the bioengineered device. Such a problem has an inherent multiphysics/multiscale nature, as it is characterized by material heterogeneities and interplaying processes occurring within a wide range of temporal and spatial scales. In this context, computational models are useful to gain a quantitative and comprehensive understanding of phenomena often difficult to be accessed experimentally. In this paper, we propose a mathematical and computational model that represents, to our knowledge, the first example of a self-consistent multiscale description of coupled nutrient mass transport, fluid-dynamics and biomass production in bioengineered constructs. We specifically focus on articular cartilage regeneration based on dynamically perfused bioreactors, and we investigate by numerical simulations three issues critical in this application. First, we study oxygen distribution in the construct, since achieving an optimal level throughout the construct is a main control variable to improve tissue quality. Second, we provide a quantitative evaluation of how interstitial perfusion can enhance nutrient delivery and, ultimately, biomass production, compared with static culture. Third, we perform a sensitivity analysis with respect to biophysical parameters related to matrix production, assessing their role in tissue regeneration.

A poroelastic mixture model of mechanobiological processes in biomass growth: theory and application to tissue engineering

“…In the above relation, V cell is the volume of a single cell, the constant of proportionality E [ 1 accounts for the heterogeneous composition of cartilagineous ECM (water for 70-80% of its wet weight, collagen fibrils for 10-15% and GAG for 5%) [14], c is oxygen concentration and k GAG a growth factor. The last term model the fact that ECM synthesis attains its maximum value when no extracellular matrix is present because more space is available for matrix production.…”

“…A phenomenological indicator of the stress/strain state of the continuum construct is proposed, based on the on the norm of the deviatoric part of the total stress tensor computed via the poroelastic theory. Similarly to other models in tissue engineering applications (see, e.g., [14,47], we also include the effect of nutrient (oxygen) availability by solving for it a transport-diffusion-reaction equations. Nutrient levels are supposed to be as well driving mechanisms in the cellular pool exchange.…”

“…as in [14]. These values are characteristic of a culture in a perfusion bioreactor where an external hydrodynamic shear stress is applied [55,58,63].…”

A sensitivity analysis for tissue development by varying model parameters and input variables

“…In this sense, also due to the complexity of the models used in tissue engineering, sensitivity analysis is an interesting tool for use in this field, since it may provide a computational evaluation of the predictive capacity and robustness of computational models and identification of the critical parameters of a model . Sensitivity analysis can be used to study the role of each parameter variation in tissue development, to clarify the mechanisms that most affect the studied phenomenon, to optimize the computational mesh, to analyze the effect of different culture conditions, and to evaluate the influence of additional factors and processes to the model . In addition, it can be used for the simplification of a model through the identification of input variables whose variation does not result in a significant change on the outputs of the model.…”

Multiple approaches to predicting oxygen and glucose consumptions by HepG2 cells on porous scaffolds in an axial‐flow bioreactor

“…A number of modeling studies have been performed using computational fluid dynamics (CFD) to better understand fluid dynamics and nutrient distribution in bioreactors (Cioffi et al, 2006;Patrachari et al, 2012;Wendt et al, 2011). To better understand the dynamic process of tissue regeneration, some have used a multi-scale continuum modeling approach, which describe cell growth to ECM deposition and degradation (Causin et al, 2013;O'Dea et al, 2013). Some have utilized the Boltzmann-Lattice model to incorporate pore heterogeneity using small size scaffolds to avoid computational overload (Spencer et al, 2013).…”