Mathematical Modeling in Tissue Engineering Applications

Mathematical modelling has become integral to the design and optimisation of engineered tissues and bioreactor systems, enabling quantitative prediction of cell behaviour, nutrient transport and mechanical stimuli within complex constructs. Continuum formulations coupling fluid dynamics, mass transport and cellular kinetics allow simulation of oxygen and metabolite distributions in perfused scaffolds, while reaction–diffusion and advection–reaction–diffusion equations capture the interplay between nutrient supply, waste removal and cell proliferation. Reduced and multiscale models exploit geometric slenderness or hierarchical organisation to simplify computations without sacrificing essential physics, thereby guiding scaffold architecture, pore morphology and operating parameters in hollow-fibre and perfusion bioreactors. Discrete and hybrid frameworks further resolve cell–cell interactions and local substrate uptake, informing optimal seeding densities and spatial cell distributions. By integrating mechanotransductive effects, such as shear-stress-dependent growth laws, these models bridge experimental and clinical objectives, accelerating translation of regenerative therapies and enabling rational design of tissue implants with tailored mechanical, biochemical and mass-transport properties.

Research from Nature Portfolio

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Research from all publishers

Recent work has underscored the value of embedding mathematical and computational methods across all stages of regenerative medicine development. One study presents a comprehensive framework for integrating quantitative data analysis and predictive models into the pipeline, demonstrating how coupling experimental measurements with continuum bioprocess models can accelerate the translation of tissue-engineered products. A separate investigation develops a systematically reduced continuum model for organoid expansion, exploiting the thin geometry of a bioreactor to simplify glucose and lactate transport equations, thereby enabling rapid assessment of how inlet flow rate and cell seeding density shape metabolite distributions and culture outcomes. Further research combines experimental characterisation of scaffold pore morphology with non-dimensional analysis, using dimensionless groups such as Péclet and Damköhler numbers to predict glucose concentration profiles within hollow-fibre membrane bioreactors, guiding scaffold design and operating regimes for bone tissue engineering applications.

Mathematical Modeling in Tissue Engineering Applications publication trend

The graph below shows the total number of articles in mathematical modeling in tissue engineering applications across all publications each year (not limited to Nature Index journals).

Technical terms

Continuum model: A mathematical representation treating tissue constructs and fluids as continuous media governed by differential equations for transport and mechanics.

Reaction–diffusion equation: A partial differential equation describing how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions and diffusion.

Péclet number: A dimensionless parameter quantifying the relative importance of advective transport to diffusive transport in fluid flow.

Damköhler number: A dimensionless ratio comparing the timescale of chemical reaction to the timescale of transport processes.

Scaffold porosity: The proportion of void space within a biomaterial scaffold that determines fluid permeability and cell infiltration.

Mechanotransduction: The cellular process by which mechanical forces, such as shear stress, are converted into biochemical signals affecting growth and differentiation.

References

1. Regenerative medicine meets mathematical modelling: developing symbiotic relationships. npj Regenerative Medicine (2021).
2. Curvature- and fluid-stress-driven tissue growth in a tissue-engineering scaffold pore. Biomechanics and Modeling in Mechanobiology (2018).
3. Multiphase modelling of the influence of fluid flow and chemical concentration on tissue growth in a hollow fibre membrane bioreactor. Mathematical Medicine and Biology A Journal of the IMA (2013).
4. A strategy to determine operating parameters in tissue engineering hollow fiber bioreactors. Biotechnology and Bioengineering (2011).
5. Effects of Scaffold Pore Morphologies on Glucose Transport Limitations in Hollow Fibre Membrane Bioreactor for Bone Tissue Engineering: Experiments and Numerical Modelling. Membranes (2021).
6. A Systematically Reduced Mathematical Model for Organoid Expansion. Frontiers in Bioengineering and Biotechnology (2021).
7. Evaluation of Diffusive Transport and Cellular Uptake of Nutrients in Tissue Engineered Constructs Using a Hybrid Discrete Mathematical Model. Processes (2014).