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Mathematical Modeling for Nerve Repair Research

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Peripheral Nerve Tissue Engineering and Regeneration

Part of the book series: Reference Series in Biomedical Engineering ((TIENRE))

Abstract

Peripheral nerve tissue engineering has great promise for growing replacement tissues to treat peripheral nerve injuries. To date, the design of replacement tissues has focused on in vitro and in vivo experiments to characterize and test the impact of a vast range of materials, cells, and other factors, with limited translation to human trials. Here we propose and discuss the use of in silico modeling as a complementary approach to inform and accelerate the design of engineered replacement tissues.

Mathematical modeling in nerve regeneration is a small research field; however, there is a rich literature in using mathematical modeling to describe a host of highly relevant underpinning mechanisms (such as neurite growth, chemical diffusion, and angiogenesis) in different contexts. These models broadly fall into three categories: continuum (or averaged), discrete (or individual), and hybrid approaches, which combine the two. The key features and potential of these modeling categories are presented alongside a decision tree for matching a specific biological problem to the appropriate modeling approach. To be predictive, it is essential that mathematical models are benchmarked against experimental data. We present tools to efficiently fit models to such data (optimization) and investigate the reliability of model predictions (sensitivity analysis). Finally, this work concludes with two demonstrative case studies on the use of mathematical modeling (one continuum, one discrete) to tackle biological and design questions in peripheral nerve injury repair.

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Authors and Affiliations

  1. UCL Mechanical Engineering, London, UK

    Simão Laranjeira, Rachel Coy & Rebecca J. Shipley

  2. UCL Centre for Nerve Engineering, London, UK

    Simão Laranjeira, Rachel Coy & Rebecca J. Shipley

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  1. Simão Laranjeira
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  2. Rachel Coy
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Correspondence to Simão Laranjeira .

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Editors and Affiliations

  1. Pharmacology, UCL School of Pharmacy, University College London Pharmacology, UCL School of Pharmacy, London, UK

    James Phillips

  2. Experimentelle u Klinische Traumatologie, Ludwig Boltzmann Institut für, Wien, Wien, Austria

    David Hercher

  3. Trauma Surgery, AUVA Unfallkrankenhaus Lorenz Böhler, Wien, Wien, Austria

    Thomas Hausner

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Laranjeira, S., Coy, R., Shipley, R.J. (2021). Mathematical Modeling for Nerve Repair Research. In: Phillips, J., Hercher, D., Hausner, T. (eds) Peripheral Nerve Tissue Engineering and Regeneration. Reference Series in Biomedical Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-030-06217-0_10-1

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