Identification of causal relations between haemodynamic variables, auditory evoked potentials and isoflurane by means of fuzzy logic

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Abstract
The aim of this study was to identify a possible relationship between haemodynamic variables, auditory evoked potentials (AEP) and inspired fraction of isoflurane (ISOFl). Two different models (isoflurane and mean arterial pressure) were identified using the fuzzy inductive reasoning (FIR) methodology. A fuzzy model is able to identify non-linear and linear components of a causal relationship by means of optimization of information content of available data. Nine young female patients undergoing hysterectomy under general anaesthesia were included. Mean arterial pressure (MAP), heart rate (HR), end-tidal expired carbon dioxide (CO2ET), AEP and ISOFl were monitored with a sampling time of 10 s. The AEP was extracted using an autoregressive model with exogenous input (ARX model) which decreased the processing time compared with a moving time average. The AEP was mapped into a scalar, termed the depth of anaesthesia index (DAI) normalized to 100 when the patient was awake and descending to an average of 25 during loss of consciousness. The FIR methodology identified those variables among the input variables (MAP, HR, CO2ET, DAI or ISOFl) that had the highest causal relation with the output variables (ISOFl and MAP). The variables with highest causal relation constitute the ISOFl and MAP models. The isoflurane model predicted the given anaesthetic dose with a mean error of 12.1 (SD 10.0)% and the mean arterial pressure model predicted MAP with a mean error of 8.5 (7.8)%.

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