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Biomed Microdevices. 2019 Apr 4;21(2):40. doi: 10.1007/s10544-019-0380-2.

Mathematical modeling in cancer nanomedicine: a review.

Author information

1
Mathematics in Medicine Program, The Houston Methodist Research Institute, HMRI R8-122, 6670 Bertner Ave, Houston, TX, 77030, USA.
2
Department of Mathematics, California State University, Northridge, CA, 91330, USA.
3
Department of Chemical Materials and Industrial Production Engineering, University of Naples Federico II, 80125, Naples, Italy.
4
Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX, 77030, USA.
5
Center for Micro-Engineered Materials, University of New Mexico, Albuquerque, NM, 87131, USA.
6
Chemical and Biological Engineering, University of New Mexico, Albuquerque, NM, 87131, USA.
7
Cancer Research and Treatment Center, Molecular Genetics and Microbiology, University of New Mexico, Albuquerque, NM, 87131, USA.
8
Self-Assembled Materials Department, Sandia National Laboratories, Albuquerque, NM, 87185, USA.
9
Department of Imaging Physics, University of Texas MD Anderson Cancer Center, Houston, TX, 78701, USA.
10
Mathematics in Medicine Program, The Houston Methodist Research Institute, HMRI R8-122, 6670 Bertner Ave, Houston, TX, 77030, USA. zwang@houstonmethodist.org.
11
Department of Imaging Physics, University of Texas MD Anderson Cancer Center, Houston, TX, 78701, USA. zwang@houstonmethodist.org.

Abstract

Cancer continues to be among the leading healthcare problems worldwide, and efforts continue not just to find better drugs, but also better drug delivery methods. The need for delivering cytotoxic agents selectively to cancerous cells, for improved safety and efficacy, has triggered the application of nanotechnology in medicine. This effort has provided drug delivery systems that can potentially revolutionize cancer treatment. Nanocarriers, due to their capacity for targeted drug delivery, can shift the balance of cytotoxicity from healthy to cancerous cells. The field of cancer nanomedicine has made significant progress, but challenges remain that impede its clinical translation. Several biophysical barriers to the transport of nanocarriers to the tumor exist, and a much deeper understanding of nano-bio interactions is necessary to change the status quo. Mathematical modeling has been instrumental in improving our understanding of the physicochemical and physiological underpinnings of nanomaterial behavior in biological systems. Here, we present a comprehensive review of literature on mathematical modeling works that have been and are being employed towards a better understanding of nano-bio interactions for improved tumor delivery efficacy.

KEYWORDS:

Agent-based modeling; Cancer treatment; Drug transport; Mechanistic modeling; Multiscale; Pharmacokinetics and pharmacodynamics

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