Applications of mathematical modelling in demand analgesia
This thesis describes applications of mathematical modelling to systems of demand analgesia for the relief of acute postoperative pain. It builds upon work described in the D.Phil. thesis of M.P. Reasbeck. Following major surgery, patients are given a hand-held button which they press when in need of pain relief. The relief is afforded by automatic intravenous infusion of opiates. New clinical demand analgesia hardware, PRODAC, has been developed and data have been collected with it in two major trials involving a total of 80 patients. Patients' drug requirements have been found not to be correlated with body weight, contrary to conventional teaching. The type of operation was also found to have no significant influence upon drug requirements. The performance of transcutaneous nerve stimulation (TNS) as a method of analgesia for acute postoperative pain has been studied and found to be poor. Reasbeck's mathematical model of patients in pain has been corrected and extended. The representation of pharmacokinetics has been enhanced by modelling the transfer of drug between blood plasma and analgesic receptor sites as a first-order process. The time constant of this process has been calculated for morphine using a novel method and found to be 12 minutes. On line estimation of 2nd order pharmacokinetic time constants has been found in simulation not to be feasible. New software has been used to tune the revised model to the clinical data collected with PRODAC. Model behaviour is now demonstrably life-like, which was not previously the case. Blood samples taken during demand analgesia have permitted a comparison between measured and estimated drug concentrations, with good results.