(688f) A General Strategy for Optimal, Individualized Drug Dosing, Based on Hybrid Models and Dynamic Optimization Under Uncertainty

Optimal, individualized drug administration is an unresolved problem with important repercussions on the chance of recovery of critically ill patients and quality of life of both critically and chronically ill patients, and with important, indirect implications for the healthcare system (average healthcare costs, average hospital bed turnover, minimum hospital capacity needed per geographical area, etc.) and for drug supply chain operations (optimal trade-off between efficiency and resiliency in drug production, storage and distribution). The most important challenges that must be overcome to solve this complex problem include: (I) the development of accurate pharmacokinetic/pharmacodynamic models, despite the incomplete understanding of the mechanisms of action of most drugs, the significant inter-patient and intra-patient variabilities, and the difficulties in collecting reliable and comprehensive pharmacokinetic data; (II) the development of a systematic approach to assess the benefits, offered by individualized drug dosing over one-size-fits-all treatment options; and (III) the challenges to the adoption of model-based decision support tools into the routine clinical practice.

Over the last 15 years, the process systems engineering community has addressed and partially solved some of the aforementioned challenges. For example, Doyle et al. (2014) developed a closed-loop approach to insulin administration (the “artificial pancreas”), which relies on physiologically based pharmacokinetic (PB-PK) models. Nașcu et al. (2017) devised a closed-loop systems for inducing and maintaining anesthesia, based on PB-PK models, and analyzed the impact of inter-patient variability on the results of their calculations. Savoca at al. (2018) studied the transdermal administration of melatonin, using dedicated PB-PK models, which include special compartments that model the diffusion of melatonin through the skin. Laínez et al. (2011) proposed general strategies for modeling inter-patient variability, based on Bayesian statistics. And, finally, Hartmanshenn et al. (2018) proposed to improve existing physiologically based pharmacokinetic and pharmacodynamic (PB-PK/PD) models, by combining omics approaches with the conventional PB-PK/PD modeling paradigm. However, despite the substantial progress, made over the last decade, individualized medicine is a research area that still offers significant challenges and opportunities.

In this contribution, we propose a general approach to optimal, individualized drug administration (Fig. 1), which encompasses: (I) development of hybrid, physiologically based pharmacokinetic/pharmacodynamic models, able to predict the patient’s response to treatment with the drug product of interest, complemented with predictions of its degree of uncertainty; (II) estimation of optimal drug dosage regimes by dynamic optimization under uncertainty; and (III) extensive, rigorous analysis of the benefits of individualized drug dosing over one-size-first-all approaches. More specifically, we first gather pharmacokinetic data from clinical trials and/or post marketing surveillance studies of the drug product of interest for as many different types of patients as possible and organize it by key patient covariates (for example, sex, ethnicity, age and pre-existing conditions). Then, we build, train and validate (Fig. 1 – A , B ,C) a preliminary, hybrid PB-PK/PD model (a first-principles-inspired pharmacokinetic/pharmacodynamic model, including as much information as possible on the actual mechanism of action of the drug of interest, augmented with Bayesian hierarchical model components), which can predict the drug concentration in plasma, urine, stool and other organs/tissues/fluids of interest, together with its degree of uncertainty, for each patient group, as a function of the drug dosage regimen. Next, we individualize this preliminary, hybrid PB-PK/PD model to the specific new patient being treated, using a small number of specific pharmacokinetic measurements, obtained for that patient. Then, we estimate optimal, individualized drug dosage regimens (for example, the number of dosage forms per day, the strength of each of these dosage forms, and the time elapsed between consecutive ingestion) for the new patient by dynamic optimization under uncertainty (Rossi et al., 2016), combined with appropriate therapeutic information, as shown in Fig. 1 – D (the objective of this dynamic optimization problem is to maximize the therapeutic effect and minimize the risk for adverse effects, under appropriate dosing restrictions and periodicity constraints). Finally, we assess the benefits, offered by the aforementioned, optimal, individualized drug dosage regimens, over conventional, one-size-fits-all approaches, using appropriate statistical indicators (for example, the average fraction of the day in which the drug concentration lies outside of the therapeutic limits and the maximum daily violation of such therapeutic limits).

Note that the major innovation, introduced by this approach to optimal, individualized drug administration, is the systematic use of hybrid, first-principles-inspired and Bayesian pharmacokinetic/pharmacodynamic models, which retain the most important benefits of both first-principles and machine learning models while also mitigating the most significant disadvantages of either modeling technique, at the cost of a higher computational complexity. These new types of models are physics-aware as conventional first-principles models but keep learning from new experimental data, as it becomes available, like machine learning models (the latter feature is particularly useful in individualized drug dosing problems because the patient outcomes from any administered dose can be used to improve the prediction of the next dose). In addition, they require smaller training datasets than conventional machine learning models, offer a certain degree of robustness to the presence of gross errors in the training data, and can be “safely” extrapolated beyond the range of the training set (all these features are very useful in individualized drug dosing problems because of the lack of reliable and comprehensive pharmacokinetic data). All these features allow mitigation of most of the challenges which we need to overcome to realize the goal of optimal, individualized drug administration.

As a proof of this, the results of the application of this general strategy for individualized drug administration to Lisinopril (an angiotensin-converting enzyme inhibitor, utilized to treat high blood pressure) are very encouraging, in that optimal, individualized Lisinopril dosing appears to outperform conventional dosing strategies, in terms of both efficacy and safety.

References

Doyle III, F. J., Huyett, L. M., Lee, J. B., Zisser, H. C., & Dassau, E. (2014). Closed-loop artificial pancreas systems: engineering the algorithms. Diabetes care, 37, 1191-1197.

Hartmanshenn, C., Rao, R. T., Bae, S. A., Scherholz, M. L., Acevedo, A., Pierre, K. K., & Androulakis, I. P. (2018). Quantitative systems pharmacology: Extending the envelope through systems engineering. Computer Aided Chemical Engineering, 42, 3-34.

Laínez, J. M., Blau, G., Mockus, L., Orçun, S., & Reklaitis, G. V. (2011). Pharmacokinetic based design of individualized dosage regimens using a Bayesian approach. Industrial & Engineering Chemistry Research, 50, 5114-5130.

Nașcu, I., Oberdieck, R., & Pistikopoulos, E. N. (2017). Explicit hybrid model predictive control strategies for intravenous anaesthesia. Computers & Chemical Engineering, 106, 814-825.

Savoca, A., Mistraletti, G., & Manca, D. (2018). A physiologically-based diffusion-compartment model for transdermal administration–The melatonin case study. Computers & Chemical Engineering, 113, 115-124.

Rossi, F., Reklaitis, G., Manenti, F., & Buzzi-Ferraris, G. (2016). Multi-scenario robust online optimization and control of fed-batch systems via dynamic model-based scenario selection. AIChE Journal, 62, 3264-3284.