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Mathematical Medicine and Biology Advance Access originally published online on November 5, 2008
Mathematical Medicine and Biology 2008 25(4):323-335; doi:10.1093/imammb/dqn022
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Understanding post-operative temperature drop in cardiac surgery: a mathematical model

M. J. Tindall{dagger}

Centre for Mathematical Biology, Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, UK

M. A. Peletier

Faculteit Wiskunde & Informatica, Technische Universiteit Eindhoven, Den Dolech 2, Postbus 513, 5600 MB, Eindhoven, The Netherlands

N. M. W. Severens

Faculteit Werktuigbouwkunde, Technische Universiteit Eindhoven, Den Dolech 2, Postbus 513, 5600 MB, Eindhoven, The Netherlands and Academisch Medisch Centrum, Universiteit van Amsterdam, Meibergdreef 9, 1105 AZ, Amsterdam, The Netherlands

D. J. Veldman and B. A. J. M. de Mol

Academisch Medisch Centrum, Universiteit van Amsterdam, Meibergdreef 9, 1105 AZ, Amsterdam, The Netherlands

{dagger} Email: m.tinall{at}reading.ac.uk

Received on January 28, 2008. Revised on July 21, 2008. Accepted on September 15, 2008.

A mathematical model is presented to understand heat transfer processes during the cooling and re-warming of patients during cardiac surgery. Our compartmental model is able to account for many of the qualitative features observed in the cooling of various regions of the body including the central core containing the majority of organs, the rectal region containing the intestines and the outer peripheral region of skin and muscle. In particular, we focus on the issue of afterdrop: a drop in core temperature following patient re-warming, which can lead to serious post-operative complications. Model results for a typical cooling and re-warming procedure during surgery are in qualitative agreement with experimental data in producing the afterdrop effect and the observed dynamical variation in temperature between the core, rectal and peripheral regions. The influence of heat transfer processes and the volume of each compartmental region on the afterdrop effect is discussed. We find that excess fat on the peripheral and rectal regions leads to an increase in the afterdrop effect. Our model predicts that, by allowing constant re-warming after the core temperature has been raised, the afterdrop effect will be reduced.

Keywords: afterdrop; cardiac surgery; mathematical model


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