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Mathematical Modeling of Ischemia–Reperfusion Injury and Postconditioning Therapy

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Abstract

Reperfusion (restoration of blood flow) after a period of ischemia (interruption of blood flow) can paradoxically place tissues at risk of further injury: so-called ischemia–reperfusion injury or IR injury. Recent studies have shown that postconditioning (intermittent periods of further ischemia applied during reperfusion) can reduce IR injury. We develop a mathematical model to describe the reperfusion and postconditioning process following an ischemic insult, treating the blood vessel as a two-dimensional channel, lined with a monolayer of endothelial cells that interact (respiration and mechanotransduction) with the blood flow. We investigate how postconditioning affects the total cell density within the endothelial layer, by varying the frequency of the pulsatile flow and the oxygen concentration at the inflow boundary. We find that, in the scenarios we consider, the pulsatile flow should be of high frequency to minimize cellular damage, while oxygen concentration at the inflow boundary should be held constant, or subject to only low-frequency variations, to maximize cell proliferation.

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Notes

  1. Limiting the mPTP aperture can therefore limit cellular injury considerably, which has made mPTP an attractive target for pharmacological treatment of IR injury (Argaud et al. 2005; Mockford et al. 2009; Yellon and Hausenloy 2007).

  2. In this paper, asterisks * distinguish dimensional quantities from their dimensionless equivalents.

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Acknowledgements

We gratefully acknowledge many useful discussions with Raquel Perez-Castillejos, who introduced us to this problem and who suggested the experimental setup that could be used to test model predictions in vitro.

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Authors and Affiliations

  1. Department of Mathematics and Science, U.S. Merchant Marine Academy, 300 Steamboat Road, Kings Point, NY, 11024, USA

    D. Fong

  2. Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102, USA

    L. J. Cummings

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  1. D. Fong
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Correspondence to D. Fong.

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The views expressed in this article are the author’s own and not those of the US Merchant Marine Academy, the Maritime Administration, the Department of Transportation, or the US government.

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Fong, D., Cummings, L.J. Mathematical Modeling of Ischemia–Reperfusion Injury and Postconditioning Therapy. Bull Math Biol 79, 2474–2511 (2017). https://doi.org/10.1007/s11538-017-0337-7

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  • DOI: https://doi.org/10.1007/s11538-017-0337-7

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