Evaluation of Diffusive Transport and Cellular Uptake of Nutrients in Tissue Engineered Constructs Using a Hybrid Discrete Mathematical Model

Andreas C Aristotelous ,Mansoor A Haider

doi:10.3390/pr2020333

Andreas C Aristotelous , Mansoor A Haider

Open Access

https://doi.org/10.3390/pr2020333

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Journal: Processes	Publication Date: Mar 28, 2014
Citations: 21	License type: CC BY 4.0

Affiliation: Duke University, North Carolina State University

Abstract

Tissue engineering systems for orthopedic tissues, such as articular cartilage, are often based on the use of biomaterial scaffolds that are seeded with cells and supplied with nutrients or growth factors. In such systems, relationships between the functional outcomes of the engineered tissue construct and aspects of the initial system design are not well known, suggesting the use of mathematical models as an additional tool for optimal system design. This study develops a reaction-diffusion model that quantitatively describes the competing effects of nutrient diffusion and the cellular uptake of nutrients in a closed bioreactor system consisting of a cell-seeded scaffold adjacent to a nutrient-rich bath. An off-lattice hybrid discrete modeling framework is employed in which the diffusion equation incorporates a loss term that accounts for absorption due to nutrient uptake by cells that are modeled individually. Numerical solutions are developed based on a discontinuous Galerkin finite element method with high order quadrature to accurately resolve fine-scale cellular effects. The resulting model is applied to demonstrate that the ability of cells to absorb nutrients over time is highly dependent on both the normal distance to the nutrient bath, as well as the nutrient uptake rate for individual cells.

Highlights

In tissue engineering applications for orthopedic tissues, such as articular cartilage or bone, a common bioreactor system consists of cells seeded in a biomaterial scaffold that is supplemented with nutrients or growth factors
A reaction-diffusion model was developed to study the competing effects of diffusive nutrient transport and cellular uptake of nutrients in a closed bioreactor system comprised of a cell-seeded scaffold adjacent to a nutrient-rich bath
The model was formulated within the framework of off-lattice hybrid discrete models [14,15,16] that couple cellular effects to partial differential equations (PDEs) models for nutrient diffusion via a loss term that accounts for nutrient absorption by each individual cell

Summary

Introduction

In tissue engineering applications for orthopedic tissues, such as articular cartilage or bone, a common bioreactor system consists of cells seeded in a biomaterial scaffold that is supplemented with nutrients or growth factors In such systems, a diverse set of biophysical and physiological mechanisms interact to govern the formation of extracellular matrix that gives rise to the tissue’s structure and resilient load bearing properties. In theory, it may be possible to systematically quantify ensemble effects based on multiscale modeling techniques, such as numerical homogenization [2,3], this approach typically requires a priori specification of the constitutive forms of relations among dependent variables in the system These constitutive relations may not be identified and, overall, such techniques have seen little application in modeling orthopedic tissue engineering in cell-scaffold systems. It should be noted that these studies involve the representation and solution of a forward model, and the design of tissue engineered constructs necessitates the integration of such models into with optimality criteria; see e.g., [12]

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