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BJA Advance Access published online on November 20, 2009
British Journal of Anaesthesia, doi:10.1093/bja/aep335
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© The Author [2009]. Published by Oxford University Press on behalf of the British Journal of Anaesthesia. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournal.org

Mathematical model for describing cerebral oxygen desaturation in patients undergoing deep hypothermic circulatory arrest

G. W. Fischer*, P. B. Benni{dagger}, H.-M. Lin, A. Satyapriya, A. Afonso, G. Di Luozzo, R. B. Griepp and D. L. Reich

Department of Anesthesiology and Cardiothoracic Surgery, Mount Sinai Medical Center, One Gustave L. Levy Place, Box 1010, New York, NY 10029, USA

* Corresponding author. E-mail: gregory.fischer{at}mountsinai.org

Background: Surgical treatment for aortic arch disease requiring periods of circulatory arrest is associated with a spectrum of neurological sequelae. Cerebral oximetry can non-invasively monitor patients for cerebral ischaemia even during periods of circulatory arrest. We hypothesized that cerebral desaturation during circulatory arrest could be described by a mathematical relationship that is time-dependent.

Methods: Cerebral desaturation curves obtained from 36 patients undergoing aortic surgery with deep hypothermic circulatory arrest (DHCA) were used to create a non-linear mixed model. The model assumes that the rate of oxygen decline is greatest at the beginning before steadily transitioning to a constant. Leave-one-out cross-validation and jackknife methods were used to evaluate the validity of the predictive model.

Results: The average rate of cerebral desaturation during DHCA can be described as: SctO2[t]=81.4–(11.53+0.37xt) (1–0.88xexp (–0.17xt)). Higher starting SctO2 values and taller patient height were also associated with a greater decline rate of SctO2. Additionally, a predictive model was derived after the functional form of axlog (b+cx{delta}), where {delta} is the degree of SctO2 decline after 15 min of DHCA. The model enables the estimation of a maximal acceptable arrest time before reaching an ischaemic threshold. Validation tests showed that, for the majority, the prediction error is no more than ±3 min.

Conclusions: We were able to create two mathematical models, which can accurately describe the rate of cerebral desaturation during circulatory arrest at 12–15°C as a function of time and predict the length of arrest time until a threshold value is reached.

Keywords: brain, ischaemia; brain, oxygen consumption; hypothermia

{dagger} Declaration of interest. P.B.B. is the chief scientific officer at CASMED, the company that manufactures the FORE-SIGHT®.


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