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

G. W. Fischer, P. B. Benni, H. M. Lin, A. Satyapriya, A. Afonso, G. Di Luozzo, R. B. Griepp, D. L. Reich

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


BackgroundSurgical 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.MethodsCerebral 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.ResultsThe average rate of cerebral desaturation during DHCA can be described as: Scto2[t]=81.4-(11.53+0.37×t) (1-0.88×exp (-0.17×t)). 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 a×log (b+c×δ), where δ 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.ConclusionsWe 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.

Original languageEnglish
Pages (from-to)59-66
Number of pages8
JournalBritish Journal of Anaesthesia
Issue number1
StatePublished - Jan 2010


  • Brain, ischaemia
  • Brain, oxygen consumption
  • Hypothermia


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