Nobile. Added-mass effect in the design of partitioned algorithms for fluid-structure problems.

In vitro tissue engineering is investigated as a potential source of functional tissue constructs for cartilage repair, as well as a model system for controlled studies of cartilage development and function. Among the different kinds of devices for the cultivation of 3D cartilage cell colonies, we consider here polymeric scaffold-based perfusion bioreactors, where an interstitial fluid supplies nutrients and oxygen to the growing biomass. At the same time, the fluid-induced shear acts as a physiologically relevant stimulus for the metabolic activity of cells, provided that the shear stress level is appropriately tuned. In this complex environment, mathematical and computational modeling can help in the optimal design of the bioreactor configuration. In this perspective, we propose a computational model for the simulation of the biomass growth, under given inlet and geometrical conditions, where nutrient concentration, fluid dynamic field and cell growth are consistently coupled. The biomass growth model is calibrated with respect to the shear stress dependence on experimental data using a simplified short-time analysis in which the nutrient concentration and the fluid-induced shear stress are assumed constant in time and uniform in space. Volume averaging techniques are used to derive effective parameters that allow to upscale the microscopic structural properties to the macroscopic level. The biomass growth predictions obtained in this way are significant for long times of culture.

In this work we present a mathematical model for the coupling between biomechanics and hemodynamics in the lamina cribrosa, a thin porous tissue at the base of the optic nerve head which is thought to be the site of injury in ocular neurodegenerative diseases such as glaucoma. In this exploratory two-dimensional investigation, the lamina cribrosa is modeled as a poroelastic material where blood vessels are viewed as pores in a solid elastic matrix. The model is used to investigate the influence on the distributions of stress, blood volume fraction (or vascular porosity) and blood velocity within the lamina cribrosa due to the application of different levels of the intraocular pressure (IOP) and the enforcement of different mechanical constraints at the lamina's boundary. The model simulations suggest that the degree of fixity of the boundary constraint strongly influences the lamina's response to IOP elevation. Specifically, when the boundary is mechanically clamped, IOP elevation leads to an increase in stress close to the lamina's boundary, making it more susceptible to tissue damage. On the other hand, when rotations are allowed at the boundary, the most vulnerable region appears to be located at the lamina's central axis, in proximity of the eye globe, where increased stress and reduced vascular porosity and blood velocity are predicted for increased levels of IOP.

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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 phenomena (fluid-controlled nutrient transport, delivery and consumption; mechanical deformation of a multiphase porous medium). The principal contribution of this research is the inclusion of the concept of cellular ''force isotropy'' as one of the main factors influencing cellular activity. In this description, the induced cytoskeletal tensional states trigger signalling transduction cascades regulating functional cell behavior. This mechanims is modeled by a parameter which estimates the influence of local force isotropy by the norm of the deviatoric part of the total stress tensor. According to the value of the estimator, isotropic mechanical conditions are assumed to be the promoting factor of extracellular matrix production whereas anisotropic conditions are assumed to promote cell proliferation. The resulting mathematical formulation is a coupled system of nonlinear partial differential equations comprising: conservation laws for mass and linear momentum of the growing biomass; advection-diffusion-reaction laws for nutrient (oxygen) transport, delivery and consumption; and kinetic laws for cellular population dynamics. To develop a reliable computational tool for the simulation of the engineered tissue growth process the nonlinear differential problem is numerically solved by: (1) temporal semidiscretization; (2) linearization via a fixed-point map; and (3) finite element spatial approximation. The biophysical accuracy of the mechanobiological model is assessed in the analysis of a simplified 1D geometrical setting. Simulation results show that: (1) isotropic/anisotropic conditions are strongly influenced by both maximum cell specific growth rate and mechanical boundary 123Meccanica (2017) 52: 3273-3297 DOI 10.1007/s11012-017-0638-9 conditions enforced at the interface between the biomass construct and the interstitial fluid; (2) experimentally measured features of cultivated articular chondrocytes, such as the early proliferation phase and the delayed extracellular matrix production, are well described by the computed spatial and temporal evolutions of cellular populations.

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.