Making mathematical models to study fentanyl and morphine pharmacokinetics

Pain is an unpleasant feeling that includes emotional and physical aspects. It may be connected to an injury or the risk of becoming hurt. On the other hand, analgesia is the relief of pain by a variety of pharmaceutical and non-pharmacological techniques, depending on the kind and degree of the pain. Pharmacokinetics is the study of how a drug moves through the body when it is administered and ends with excretion. Pharmacokinetics often uses compartmental modelling to describe how medications travel through the body and are eliminated. Recently published research examined many mathematical model types to comprehend medication pharmacokinetics. On the drug kinetics, the impact of starting concentration and rate constants was examined. The effectiveness and long-term effects of morphine and fentanyl on the human body were investigated using models specifically designed for these drugs.

Drug distribution, transition, and concentration in the bodily compartments were theoretically analysed using non-linear ordinary differential equations and numerical analytic approaches. A computer application called MATLAB, version 2023a from Math Works, Inc. was used to characterise how the drug's kinetics were affected by beginning concentration and rate constants. Pharmacokinetic parameters were plotted to determine a specific therapeutic concentration of fentanyl and morphine in blood.

The study's findings demonstrated how long it takes for morphine and fentanyl to accumulate to a point in the bloodstream where they may provide the desired therapeutic effects. The pharmacokinetics of fentanyl and morphine were compared mathematically, and the results indicated that fentanyl was metabolised and excreted from the body more quickly (44 minutes sooner than morphine) and reached the target therapeutic concentration 125 minutes earlier.

Several mathematical models were used in this work to describe the behaviour of drugs within the human body. The pharmacokinetics of morphine and fentanyl were plotted with the use of compartment modelling; it was discovered that fentanyl took less time to reach the goal therapeutic threshold established in the blood. Fentanyl exited the body sooner than morphine. In order to define medication interactions inside the human body, optimise dosage schedules, forecast drug effects, and plan clinical trials, pharmacokinetic models are essential. These mathematical models improve our knowledge of how medications affect various targets and pathways by predicting and quantifying drug-drug interactions caused by one drug changing the effects of another. Nevertheless, by dividing the human body into two compartments, these models are limited to the bolus administration of the medication.

Reference –

Shenoy, Prathvi; Rao, Mahadev1; Chokkadi, Shreesha2; Bhatnagar, Sushma3; Salins, Naveen4. Developing mathematical models to compare and analyse the pharmacokinetics of morphine and fentanyl. Indian Journal of Anaesthesia 68(1):p 111-117, January 2024. | DOI: 10.4103/ija.ija_1036_23