title: Mathematical model for describing cerebral oxygen desaturation in patients undergoing deep hypothermic circulatory arrest.
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.
authors.affiliation: 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
authors.forename: G W
authors.initials: GW
authors.lastname: Fischer
authors.forename: P B
authors.initials: PB
authors.lastname: Benni
authors.forename: H-M
authors.initials: HM
authors.lastname: Lin
authors.forename: A
authors.initials: A
authors.lastname: Satyapriya
authors.forename: A
authors.initials: A
authors.lastname: Afonso
authors.forename: G
authors.initials: G
authors.lastname: Di Luozzo
authors.forename: R B
authors.initials: RB
authors.lastname: Griepp
authors.forename: D L
authors.initials: DL
authors.lastname: Reich
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000768:Anesthesia, General / Q000379:methods; D001013:Aorta, Thoracic / Q000601:surgery*; D002545:Brain Ischemia / Q000175:diagnosis / Q000209:etiology*; D002245:Carbon Dioxide / Q000097:blood; D050792:Circulatory Arrest, Deep Hypothermia Induced / Q000009:adverse effects*; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D016343:Monitoring, Intraoperative / Q000379:methods; D010100:Oxygen / Q000097:blood; D010101:Oxygen Consumption; D010313:Partial Pressure
chemical_list: D002245:Carbon Dioxide; D010100:Oxygen