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1.  Mathematical model for describing cerebral oxygen desaturation in patients undergoing deep hypothermic circulatory arrest 
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+0.37×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.
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.
doi:10.1093/bja/aep335
PMCID: PMC2791548  PMID: 19933513
brain, ischaemia; brain, oxygen consumption; hypothermia
2.  Real-time expert system for advising anesthesiologists in the cardiac operating room. 
This paper describes the initial work towards building a distributed real-time expert system for advising anesthesiologists in the cardiac operating room. The goal of this project is to build a vigilant system that contains knowledge relevant to the practice of cardiac anesthesiology. The system is being designed to use this knowledge in conjunction with continuous automated patient data acquisition in order to provide clinically useful differential diagnoses and treatment recommendations in real time.
PMCID: PMC2247823  PMID: 7949847
3.  Estimation of pharmacokinetic model parameters. 
This paper addresses the problem of estimating the depth of anesthesia in clinical practice where many drugs are used in combination. The aim of the project is to use pharmacokinetically-derived data to predict episodes of light anesthesia. The weighted linear combination of anesthetic drug concentrations was computed using a stochastic pharmacokinetic model. The clinical definition of light anesthesia was based on the hemodynamic consequences of autonomic nervous system responses to surgical stimuli. A rule-based expert system was used to review anesthesia records to determine instances of light anesthesia using hemodynamic criteria. It was assumed that light anesthesia was a direct consequence of the weighted linear combination of drug concentrations in the patient's body that decreased below a certain threshold. We augmented traditional two-compartment models with a stochastic component of anesthetics' concentrations to compensate for interpatient pharmacokinetic and pharmacodynamic variability. A cohort of 532 clinical anesthesia cases was examined and parameters of two compartment pharmacokinetic models for 6 intravenously administered anesthetic drugs (fentanyl, thiopenthal, morphine, propofol, midazolam, ketamine) were estimated, as well as the parameters for 2 inhalational anesthetics (N2O and isoflurane). These parameters were then prospectively applied to 22 cases that were not used for parameter estimation, and the predictive ability of the pharmacokinetic model was determined. The goal of the study is the development of a pharmacokinetic model that will be useful in predicting light anesthesia in the clinically relevant circumstance where many drugs are used concurrently.
PMCID: PMC2579053  PMID: 8563327

Results 1-3 (3)