An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers

Implications of IL-21 in solid tumor therapy

Cancer, the most deadly disease, is known as a recent dilemma worldwide. Presently different treatments are used for curing cancers, especially solid cancers. Because of the immune-enhancing functions of cytokine, IL-21 as a cytokine may have new possibilities to manipulate the immune system in disease conditions, as it stimulates NK and CTL functions and drives IgG antibody production. Indeed, IL-21 has been revealed to elicit antitumor-immune responses in several tumor models. Combining IL-21 with other agents, which target tumor cells, immune-regulatory circuits, or other immune-enhancing molecules enhances this activity. The exciting breakthrough in the results obtained in pre-clinical situations has led to the early outset of present developing clinical trials in cancer patients. In the paper, we have reviewed the function of IL-21 in solid tumor immunotherapy.

Accelerating the Development of Personalized Cancer Immunotherapy by Integrating Molecular Patients' Profiles with Dynamic Mathematical Models

We review the evolution, achievements, and limitations of the current paradigm shift in medicine, from the "one-size-fits-all" model to "Precision Medicine." Precision, or personalized, medicine-tailoring the medical treatment to the personal characteristics of each patient-engages advanced statistical methods to evaluate the relationships between static patient profiling (e.g., genomic and proteomic), and a simple clinically motivated output (e.g., yes/no responder). Today, precision medicine technologies that have facilitated groundbreaking advances in oncology, notably in cancer immunotherapy, are approaching the limits of their potential, mainly due to the scarcity of methods for integrating genomic, proteomic and clinical patient information. A different approach to treatment personalization involves methodologies focusing on the dynamic interactions in the patient-disease-drug system, as portrayed in mathematical modeling. Achievements of this scientific approach, in the form of algorithms for predicting personal disease dynamics in individual patients under immunotherapeutic drugs, are reviewed as well. The contribution of the dynamic approaches to precision medicine is limited, at present, due to insufficient applicability and validation. Yet, the time is ripe for amalgamating together these two approaches, for maximizing their joint potential to personalize and improve cancer immunotherapy. We suggest the roadmap toward achieving this goal, technologically, and urge clinicians, pharmacologists, and computational biologists to join forces along the pharmaco-clinical track of this development.

Mathematical Models of Cancer: When to Predict Novel Therapies, and When Not to

The number of publications on mathematical modeling of cancer is growing at an exponential rate, according to PubMed records, provided by the US National Library of Medicine and the National Institutes of Health. Seminal papers have initiated and promoted mathematical modeling of cancer and have helped define the field of mathematical oncology (Norton and Simon in J Natl Cancer Inst 58:1735-1741, 1977; Norton in Can Res 48:7067-7071, 1988; Hahnfeldt et al. in Can Res 59:4770-4775, 1999; Anderson et al. in Comput Math Methods Med 2:129-154, 2000. https://doi.org/10.1080/10273660008833042 ; Michor et al. in Nature 435:1267-1270, 2005. https://doi.org/10.1038/nature03669 ; Anderson et al. in Cell 127:905-915, 2006. https://doi.org/10.1016/j.cell.2006.09.042 ; Benzekry et al. in PLoS Comput Biol 10:e1003800, 2014. https://doi.org/10.1371/journal.pcbi.1003800 ). Following the introduction of undergraduate and graduate programs in mathematical biology, we have begun to see curricula developing with specific and exclusive focus on mathematical oncology. In 2018, 218 articles on mathematical modeling of cancer were published in various journals, including not only traditional modeling journals like the Bulletin of Mathematical Biology and the Journal of Theoretical Biology, but also publications in renowned science, biology, and cancer journals with tremendous impact in the cancer field (Cell, Cancer Research, Clinical Cancer Research, Cancer Discovery, Scientific Reports, PNAS, PLoS Biology, Nature Communications, eLife, etc). This shows the breadth of cancer models that are being developed for multiple purposes. While some models are phenomenological in nature following a bottom-up approach, other models are more top-down data-driven. Here, we discuss the emerging trend in mathematical oncology publications to predict novel, optimal, sometimes even patient-specific treatments, and propose a convention when to use a model to predict novel treatments and, probably more importantly, when not to.

Computational Approaches in Theranostics: Mining and Predicting Cancer Data

The ability to understand the complexity of cancer-related data has been prompted by the applications of (1) computer and data sciences, including data mining, predictive analytics, machine learning, and artificial intelligence, and (2) advances in imaging technology and probe development. Computational modelling and simulation are systematic and cost-effective tools able to identify important temporal/spatial patterns (and relationships), characterize distinct molecular features of cancer states, and address other relevant aspects, including tumor detection and heterogeneity, progression and metastasis, and drug resistance. These approaches have provided invaluable insights for improving the experimental design of therapeutic delivery systems and for increasing the translational value of the results obtained from early and preclinical studies. The big question is: Could cancer theranostics be determined and controlled in silico? This review describes the recent progress in the development of computational models and methods used to facilitate research on the molecular basis of cancer and on the respective diagnosis and optimized treatment, with particular emphasis on the design and optimization of theranostic systems. The current role of computational approaches is providing innovative, incremental, and complementary data-driven solutions for the prediction, simplification, and characterization of cancer and intrinsic mechanisms, and to promote new data-intensive, accurate diagnostics and therapeutics.

Mathematical modeling of tumor-immune cell interactions

The anti-tumor activity of the immune system is increasingly recognized as critical for the mounting of a prolonged and effective response to cancer growth and invasion, and for preventing recurrence following resection or treatment. As the knowledge of tumor-immune cell interactions has advanced, experimental investigation has been complemented by mathematical modeling with the goal to quantify and predict these interactions. This succinct review offers an overview of recent tumor-immune continuum modeling approaches, highlighting spatial models. The focus is on work published in the past decade, incorporating one or more immune cell types and evaluating immune cell effects on tumor progression. Due to their relevance to cancer, the following immune cells and their combinations are described: macrophages, Cytotoxic T Lymphocytes, Natural Killer cells, dendritic cells, T regulatory cells, and CD4+ T helper cells. Although important insight has been gained from a mathematical modeling perspective, the development of models incorporating patient-specific data remains an important goal yet to be realized for potential clinical benefit.

Population pharmacokinetics of oxaliplatin after intraperitoneal administration with hyperthermia in Wistar rats

BACKGROUND

The evaluation of the efficacy and toxicity of hyperthermic intraoperative peritoneal chemotherapy presents some difficulties, due in part to the lack of information about the pharmacokinetic behavior of the drugs administered in this procedure. The aim of this study was to characterize the population pharmacokinetics of hyperthermic intraoperative peritoneal oxaliplatin in Wistar rats and to evaluate the effect of treatment-related covariates dose, instillation time and temperature on the pharmacokinetic parameters.

METHODS

Oxaliplatin peritoneal and plasma concentrations from 37 rats treated by either intravenous or intraperitoneal oxaliplatin administrations under different instillation times, temperatures and doses were analyzed according to a population pharmacokinetic approach using the software NONMEM V7.3®.

RESULTS

Intraperitoneal (n = 115) and plasma (n = 263) concentrations were successfully described according to a two-compartment model with first order absorption. No significant effect of dose, temperature and instillation time on pharmacokinetic parameters was found. However, an abrupt decrease in the elimination process was observed, reflected in the structural pharmacokinetic model through a modification in clearance. The typical parameters values and the interindividual variability (CV %) in clearance, central and peripheral volume of distribution were 3.25 mL/min (39.1%), 53.6 mL (37.8%) and 54.1 mL (77.3%), respectively. Clearance decreased to 0.151 mL/min (39.1%) when the instillation was still ongoing, at 31.4 min. One of the possible reasons behind the clearance decrease would be an alteration of renal function due to surgery and/or hyperthermia.

CONCLUSIONS

This study described the deterioration of the drug elimination process due to the procedure, and estimated the time at which this deterioration is most likely to occur. In addition, dose, instillation time and temperature had no influence in the PK parameters.

Optimal dynamic regimens with artificial intelligence: The case of temozolomide

We determine an optimal protocol for temozolomide using population variability and dynamic optimization techniques inspired by artificial intelligence. We use a Pharmacokinetics/Pharmacodynamics (PK/PD) model based on Faivre and coauthors (Faivre, et al., 2013) for the pharmacokinetics of temozolomide, as well as the pharmacodynamics of its efficacy. For toxicity, which is measured by the nadir of the normalized absolute neutrophil count, we formalize the myelosuppression effect of temozolomide with the physiological model of Panetta and coauthors (Panetta, et al., 2003). We apply the model to a population with variability as given in Panetta and coauthors (Panetta, et al., 2003). Our optimization algorithm is a variant in the class of Monte-Carlo tree search algorithms. We do not impose periodicity constraint on our solution. We set the objective of tumor size minimization while not allowing more severe toxicity levels than the standard Maximum Tolerated Dose (MTD) regimen. The protocol we propose achieves higher efficacy in the sense that –compared to the usual MTD regimen– it divides the tumor size by approximately 7.66 after 336 days –the 95% confidence interval being [7.36–7.97]. The toxicity is similar to MTD. Overall, our protocol, obtained with a very flexible method, gives significant results for the present case of temozolomide and calls for further research mixing operational research or artificial intelligence and clinical research in oncology.

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development.

Prediction of the Optimal Dosing Regimen Using a Mathematical Model of Tumor Uptake for Immunocytokine-Based Cancer Immunotherapy

Purpose: Optimal dosing is critical for immunocytokine-based cancer immunotherapy to maximize efficacy and minimize toxicity. Cergutuzumab amunaleukin (CEA-IL2v) is a novel CEA-targeted immunocytokine. We set out to develop a mathematical model to predict intratumoral CEA-IL2v concentrations following various systemic dosing intensities.Experimental Design: Sequential measurements of CEA-IL2v plasma concentrations in 74 patients with solid tumors were applied in a series of differential equations to devise a model that also incorporates the peripheral concentrations of IL2 receptor-positive cell populations (i.e., CD8⁺, CD4⁺, NK, and B cells), which affect tumor bioavailability of CEA-IL2v. Imaging data from a subset of 14 patients were subsequently utilized to additionally predict antibody uptake in tumor tissues.Results: We created a pharmacokinetic/pharmacodynamic mathematical model that incorporates the expansion of IL2R-positive target cells at multiple dose levels and different schedules of CEA-IL2v. Model-based prediction of drug levels correlated with the concentration of IL2R-positive cells in the peripheral blood of patients. The pharmacokinetic model was further refined and extended by adding a model of antibody uptake, which is based on drug dose and the biological properties of the tumor. In silico predictions of our model correlated with imaging data and demonstrated that a dose-dense schedule comprising escalating doses and shortened intervals of drug administration can improve intratumoral drug uptake and overcome consumption of CEA-IL2v by the expanding population of IL2R-positive cells.Conclusions: The model presented here allows simulation of individualized treatment plans for optimal dosing and scheduling of immunocytokines for anticancer immunotherapy. Clin Cancer Res; 24(14); 3325-33. ©2018 AACRSee related commentary by Ruiz-Cerdá et al., p. 3236.

Demystifying the cytokine network: Mathematical models point the way

Cytokines provide the means by which immune cells communicate with each other and with parenchymal cells. There are over one hundred cytokines and many exist in families that share receptor components and signal transduction pathways, creating complex networks. Reductionist approaches to understanding the role of specific cytokines, through the use of gene-targeted mice, have revealed further complexity in the form of redundancy and pleiotropy in cytokine function. Creating an understanding of the complex interactions between cytokines and their target cells is challenging experimentally. Mathematical and computational modeling provides a robust set of tools by which complex interactions between cytokines can be studied and analyzed, in the process creating novel insights that can be further tested experimentally. This review will discuss and provide examples of the different modeling approaches that have been used to increase our understanding of cytokine networks. This includes discussion of knowledge-based and data-driven modeling approaches and the recent advance in single-cell analysis. The use of modeling to optimize cytokine-based therapies will also be discussed.

Pharmacological considerations for predicting PK/PD at the site of action for therapeutic proteins

For therapeutic proteins whose sites of action are distal to the systemic circulation, both drug and target concentrations at the tissue sites are not necessarily proportional to those in systemic circulation, highlighting the importance of understanding pharmacokinetic/pharmacodynamic (PK/PD) relationship at the sites of action. This review summarizes the pharmacological considerations for predicting local PK/PD and the importance of measuring PK and PD at site of action. Three case examples are presented to show how mechanistic and physiologically based PK/PD (PBPK/PD) models which incorporated the PK and PD at the tissue site can be used to facilitate understanding the exposure-response relationship for therapeutic proteins.

Personalizing immunotherapy: Balancing predictability and precision

Despite great expectations and research efforts, anticancer immunotherapy has not yet become a definitive cure. Perhaps, this is because past reductionist approaches were too simplistic for the patient-specific complex system of co-evolving tumor cells and host immunity. Recent efforts based on a systems-based approach promise improved clinical outcomes engendered by a dynamic modification of personalized therapeutic regimens.

A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis

Population modeling of tumor size dynamics has recently emerged as an important tool in pharmacometric research. A series of new mixed-effects models have been reported recently, and we present herein a synthetic view of models with published mathematical equations aimed at describing the dynamics of tumor size in cancer patients following anticancer drug treatment. This selection of models will constitute the basis for the Drug Disease Model Resources (DDMoRe) repository for models on oncology.

Mathematical model approach to describe tumour response in mice after vaccine administration and its applicability to immune-stimulatory cytokine-based strategies

Immunotherapy is a growing therapeutic strategy in oncology based on the stimulation of innate and adaptive immune systems to induce the death of tumour cells. In this paper, we have developed a population semi-mechanistic model able to characterize the mechanisms implied in tumour growth dynamic after the administration of CyaA-E7, a vaccine able to target antigen to dendritic cells, thus triggering a potent immune response. The mathematical model developed presented the following main components: (1) tumour progression in the animals without treatment was described with a linear model, (2) vaccine effects were modelled assuming that vaccine triggers a non-instantaneous immune response inducing cell death. Delayed response was described with a series of two transit compartments, (3) a resistance effect decreasing vaccine efficiency was also incorporated through a regulator compartment dependent upon tumour size, and (4) a mixture model at the level of the elimination of the induced signal vaccine (k 2) to model tumour relapse after treatment, observed in a small percentage of animals (15.6%). The proposed model structure was successfully applied to describe antitumor effect of IL-12, suggesting its applicability to different immune-stimulatory therapies. In addition, a simulation exercise to evaluate in silico the impact on tumour size of possible combination therapies has been shown. This type of mathematical approaches may be helpful to maximize the information obtained from experiments in mice, reducing the number of animals and the cost of developing new antitumor immunotherapies.