Original article was published by Manu Raghavan P V on Artificial Intelligence on Medium
The way we perceive and treat tumors has significantly changed over the last century. But what is the next big leap of advancement in the field of oncology? Well, according to a team of 5 French scientists, one of the possible answers is introducing mathematical modelling into the equation and propelling the timeline for inclusion of computational oncology into the routine treatment regimens. The basic idea of computational oncology is to use mathematical models to come up with more effective means of cancer treatment in humans than the ones existing at the moment. The relatively recent advances in computational efficiency and mathematical modelling has helped us understand how a tumor behaves inside the human body and hence aided in the development of better medication for the same. Another application of this concept is to come up with efficient personalized diagnosis, dosage and treatment schedules for cancer patients. Hence, we explore some of the major models used for these bio-medical (oncological) purposes.
PK/PD-model based dosing optimization
Pharmacokinetic/Pharmacodynamic(PK/PD)-based modelling is a method where we express the efficacy after administering a drug dose as a set of mathematical equations and then use that for computing mathematical models. The first step towards this is called Therapeutic Drug Monitoring. TDM is basically the measure of appropriate drug dosage & exposure for a patient and thus provides us with the knowledge base from which we will be able to design appropriate computational models. After that we use software packages(like Monolix, NONMEM etc.) to obtain the mean parameters for a reference population. Now, we go ahead and collect rich data sets from individual patients(around 20) and go on to do a Bayesian estimation of our individual parameters using various standard mathematical estimation techniques(Maximum Likelihood Estimation(MLE). Weighted Least Squares(WLSQ) regression etc.). The final step is to use these individual parameters to compute the parameters for a newly treated patient using standard mathematical modelling techniques( Non-linear mixed effect modelling, Non-parametric expectation maximization). We can improve the accuracy of this method by identifying variables that can impact our model. The advantage of this technique over the standard medical dosage model we use at the moment is the ability to adapt the parameters in accordance with the patient’s response to the cancer treatment. Some variables that have thus been identified so far include overexposure, age, sex, weight, body surface area(BSA), and time-dependent oncological variables(like tumor burden during treatment).
Apart from these standard modelling techniques, there are a few other methods of greater sophistication that can be developed for greater efficiency and optimization for specific purposes(like specific tumor reduction) but these require equally sophisticated and complex computing power along with a highly skilled workforce and hence has never been routinely applied to clinical situations yet.
Along with making mathematical models for drug dosage, we also have to take care of the toxic effects the drugs may have on the patients. Hence we use similar modelling techniques as before to model the toxicities of the administered drugs. One of the most frequent toxicities encountered during treatment is blood-related(Haematological) toxicities and hence predicting these would help us minimize the same while drug administration. There are however, other(non-haematological) toxicities too (like the ones that cause hand–foot syndrome or hypertension as a side effect of the therapy) which could be a potential roadblock in cancer treatment. Thus modelling these in combination with haematological toxicities help us come up with combination therapies to limit the toxicity levels to acceptable ranges. In addition, we also consider cases where several milder toxicities in combination exceed the acceptable toxicity limits in our mathematical models. The toxicity models also help us identify when to intensify or de-intensify a patient’s treatment and to what degree.
Along with toxicity models, the efficacy is the other main factor in deciding the drug dosage. We measure the efficacy of a dosage by measuring the mass of the tumor that gets reduced per cycle of therapy. Hence modelling of tumor growth can help us in this calculation. There are a variety of proposed models that help us understand the behavior of tumors in the natural environment and also when it comes up against an anti-cancer agents(mainly two categories: 1)phenomenological models where biological process are minimally considered), 2) mechanistic models where complex biological phenomenon are also taken in consideration while modelling).
While the traditional systems for cancer treatment and drug dosage have proven to be extremely useful, introducing computational modelling is turning to be the next leap in the right direction and coming up with more sophisticated Bayesian models with higher levels of precision is potentially the next frontier in the integration of biology, medicine, mathematics and computing. While rigorous, these methods are far from impossible and with the fast paced improvement in both computing power and cancer therapy, these adaptive treatment methods could, in fact prove better than the traditional routine for drug dosage and therapy. So hopefully in the coming years, these adaptive drug administration methods aided by mathematical modelling techniques can become the rule and not the exception.