Mathematical evaluation of responses to surgical stimuli under general anesthesia

Abstract

Surgical invasion activates nociception, while anesthesia suppresses it. Under general anesthesia, stimulation, which is the balance between nociception and anti-nociception, induces responses, including activation of the autonomic nervous system. To evaluate the associations between stimulation (S) and the resultant responses (R), we examined R values, which were calculated using mathematical models of Stevens’ power law, Gompertz function and logistic function. The previously developed Nociceptive Response (NR) formula was applied as a modified logistic model. S values were calculated using a linear function in the NR formula. In a retrospective study, we developed an exponential model of Stevens’ power law and a sigmoidal model of Gompertz function using differential equations, by adjusting R values to correspond to NR values, in consecutive patients undergoing surgery under general anesthesia (n = 4,395). In a subsequent prospective study, we validated the superiority of R values of Gompertz function and the NR formula in an exponential model in adult patients undergoing tympanoplasty (n = 141) and laparoscopic cholecystectomy (n = 86). In conclusion, both modified logistic function and Gompertz function are likely appropriate mathematical models for representing responses to stimulation resulting from the balance between nociception/anti-nociception during surgical procedures under general anesthesia.

Association between thoracic epidural block and major complications after pleurectomy/decortication for malignant pleural mesothelioma under general anesthesia

“…To assess the primary outcome of the association between epidural block and major complications in this study, we obtained perioperative data of age, sex, body mass index (BMI), American Society of Anesthesiologists-physical status (ASA-PS), emergency status, surgical procedure, anesthetic management, and complications occurring within 30 days after surgery from our institutional medical records. To evaluate intraoperative nociception and perioperative inflammatory status, both the value on the nociceptive response (NR) index during surgery14 15 and serum concentrations of C-reactive protein (CRP) before surgery and on postoperative day (POD) 1 were also obtained. We retrospectively reviewed these data, which were obtained from the patients’ medical records.…”

“…The NR index, as a dimensionless number between 0 and 1, is a quantitative value for assessing physiologic responses to the balance between nociception secondary to surgical stimuli and antinociception due to anesthesia during surgery under general anesthesia14 15 The NR index was calculated every 1 min during surgery using the NR formula, which includes the intraoperative hemodynamic variables of heart rate, systolic blood pressure (SBP), and perfusion index (PI) 14 15. Increase in nociception or decrease in antinociception increases the NR value.…”

Association between averaged intraoperative nociceptive response index and postoperative complications after lung resection surgery

“…VATS was performed through the single-port or two-port approach with a small incision around 4 cm in the lateral decubitus position. NR index, which represents an objective value of the balance between nociception and anti-nociception under general anaesthesia, was calculated every 1 min during surgery from an equation that includes HR, SBP and PI, as follows [ 7 , 8 ]: …”

“…The nociceptive response (NR) index, which is a dimensionless number between 0 and 1, was developed to quantitatively evaluate physiological responses caused by the balance between nociception induced by surgical stimuli and anti-nociception due to anaesthetic management in patients under general anaesthesia [ 7 , 8 ]. NR values are calculated using 3 haemodynamic variables of heart rate (HR), systolic blood pressure (SBP) and perfusion index (PI).…”

Developing a robust model to predict depth of anesthesia from single channel EEG signal

“…Currently Bispectral Index (BIS) is considered the standard device for prediction the DoA [22][23][24][25]. Although the BIS has been proven to be effective in practice, it has limitations in many aspects [18][19][20][21]. For example, it does not work effectively with all anaesthetic drugs, is not accurate across patients, and is being delayed [26,27].…”