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Br J Anaesth. 2010 Jan;104(1):59-66. doi: 10.1093/bja/aep335.

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

Author information

1
Department of Anesthesiology and Cardiothoracic Surgery, Mount Sinai Medical Center, One Gustave L. Levy Place, Box 1010, New York, NY 10029, USA. gregory.fischer@mountsinai.org

Abstract

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: Sct(o(2))[t]=81.4-(11.53+0.37 x t) (1-0.88 x exp (-0.17 x t)). Higher starting Sct(o(2)) values and taller patient height were also associated with a greater decline rate of Sct(o(2)). Additionally, a predictive model was derived after the functional form of a x log (b+c x delta), where delta is the degree of Sct(o(2)) 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 degrees C as a function of time and predict the length of arrest time until a threshold value is reached.

PMID:
19933513
PMCID:
PMC2791548
DOI:
10.1093/bja/aep335
[Indexed for MEDLINE]
Free PMC Article

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