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Biological Systems: Multiscale Modeling Based on Mixture Theory

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Multiscale Modeling in Biomechanics and Mechanobiology

Abstract

Scientific understanding of complex biological systems has recently benefited from mathematical and computational modeling. Classical biological studies are focused on observation and experimentation. However, mathematical modeling and computer simulation can provide useful guidance and insightful interpretations for experimental studies. Mathematical modeling can also be used to characterize complex biological phenomena, such as cell migration, cancer metastasis, tumor growth, bone remodeling, and wound healing. Since these phenomena occur over varying spatial and temporal scales, it is necessary to use multiscale modeling approaches. This book chapter provides an overview of multiscale mathematical methods for developing models for aforementioned biological phenomena based on so-called mixture theory. In Sect. 11.1, we cover the background about multiscale modeling in general applications as well as biology specific applications, Sect. 11.2 presents the multiscale computational methods and the challenges associated with modeling complex biological systems and processes, Sect. 11.3 presents theories and their applications of four example model problems, and Sect. 11.4 concludes with open questions in multiscale mathematical modeling, especially in biomedical areas.

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Acknowledgments

The authors would like to express our sincere gratitude to J. Cliff Zhou for his early involvement in this work, and Dr. M.N. Rylander and her group for providing information regarding the 3D in vitro cell culture system. The funding from NSF/CREST program \(\sharp {0932339}\) is highly appreciated and acknowledged.

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Authors and Affiliations

  1. The University of Texas at San Antonio, One UTSA Circle San Antonio, TX, 78249, USA

    Yusheng Feng, Sarah J. Boukhris, Rakesh Ranjan & Raul A. Valencia

Authors
  1. Yusheng Feng
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  2. Sarah J. Boukhris
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  3. Rakesh Ranjan
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  4. Raul A. Valencia
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Corresponding author

Correspondence to Yusheng Feng .

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Editors and Affiliations

  1. Dept. of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York, USA

    Suvranu De

  2. Dept. of Biomedical Engineering, Texas A&M University, College Station, Texas, USA

    Wonmuk Hwang

  3. Dept.of Mechanical Engineering Bioengineering & Cardiothoracic Surgery, Stanford University, Stanford, California, USA

    Ellen Kuhl

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Feng, Y., Boukhris, S.J., Ranjan, R., Valencia, R.A. (2015). Biological Systems: Multiscale Modeling Based on Mixture Theory. In: De, S., Hwang, W., Kuhl, E. (eds) Multiscale Modeling in Biomechanics and Mechanobiology. Springer, London. https://doi.org/10.1007/978-1-4471-6599-6_11

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  • DOI: https://doi.org/10.1007/978-1-4471-6599-6_11

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-6598-9

  • Online ISBN: 978-1-4471-6599-6

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