Mathematical modeling of tumor growth and tumor growth inhibition in oncology drug development

Advancing cancer drug development with mechanistic mathematical modeling: bridging the gap between theory and practice

Quantitative predictive modeling of cancer growth, progression, and individual response to therapy is a rapidly growing field. Researchers from mathematical modeling, systems biology, pharmaceutical industry, and regulatory bodies, are collaboratively working on predictive models that could be applied for drug development and, ultimately, the clinical management of cancer patients. A plethora of modeling paradigms and approaches have emerged, making it challenging to compile a comprehensive review across all subdisciplines. It is therefore critical to gauge fundamental design aspects against requirements, and weigh opportunities and limitations of the different model types. In this review, we discuss three fundamental types of cancer models: space-structured models, ecological models, and immune system focused models. For each type, it is our goal to illustrate which mechanisms contribute to variability and heterogeneity in cancer growth and response, so that the appropriate architecture and complexity of a new model becomes clearer. We present the main features addressed by each of the three exemplary modeling types through a subjective collection of literature and illustrative exercises to facilitate inspiration and exchange, with a focus on providing a didactic rather than exhaustive overview. We close by imagining a future multi-scale model design to impact critical decisions in oncology drug development.

Multiscale modeling of the dynamic growth of cancerous tumors under the influence of chemotherapy drugs

A comprehensive model of chemotherapy treatment of cancer can help us to optimize the drug administration/dosage and improve the treatment outcome. In the present study, a multiscale mathematical model of tumor growth during chemotherapy treatment is developed to predict its response to the medication and cancer progression. The modeling is a continuous multiscale simulation consisting of three tissue phases including cancer cells, normal cells, and extracellular matrix. In addition to the drug administration, the impacts of immune cells, programmed cell death, nutrient competition, and glucose concentration are included. The outputs of our mathematical model conform to the published experimental and clinical data, and it can be used in optimizing chemotherapy, and personalized cancer treatment.

Modeling tumor growth using fractal calculus: Insights into tumor dynamics

Important concepts like fractal calculus and fractal analysis, the sum of squared residuals, and Aikaike's information criterion must be thoroughly understood in order to correctly fit cancer-related data using the proposed models. The fractal growth models employed in this work are classified in three main categories: Sigmoidal growth models (Logistic, Gompertz, and Richards models), Power Law growth model, and Exponential growth models (Exponential and Exponential-Lineal models)". We fitted the data, computed the sum of squared residuals, and determined Aikaike's information criteria using Matlab and the web tool WebPlotDigitizer. In addition, the research investigates "double-size cancer" in the fractal temporal dimension with respect to various mathematical models.

A two-stages global sensitivity analysis by using the δ sensitivity index in presence of correlated inputs: application on a tumor growth inhibition model based on the dynamic energy budget theory

Global sensitivity analysis (GSA) evaluates the impact of variability and/or uncertainty of the model parameters on given model outputs. GSA is useful for assessing the quality of Pharmacometric model inference. Indeed, model parameters can be affected by high (estimation) uncertainty due to the sparsity of data. Independence between model parameters is a common assumption of GSA methods. However, ignoring (known) correlations between parameters may alter model predictions and, then, GSA results. To address this issue, a novel two-stages GSA technique based on the δ index, which is well-defined also in presence of correlated parameters, is here proposed. In the first step, statistical dependencies are neglected to identify parameters exerting causal effects. Correlations are introduced in the second step to consider the real distribution of the model output and investigate also the 'indirect' effects due to the correlation structure. The proposed two-stages GSA strategy was applied, as case study, to a preclinical tumor-in-host-growth inhibition model based on the Dynamic Energy Budget theory. The aim is to evaluate the impact of the model parameter estimate uncertainty (including correlations) on key model-derived metrics: the drug threshold concentration for tumor eradication, the tumor volume doubling time and a new index evaluating the drug efficacy-toxicity trade-off. This approach allowed to rank parameters according to their impact on the output, discerning whether a parameter mainly exerts a causal or 'indirect' effect. Thus, it was possible to identify uncertainties that should be necessarily reduced to obtain robust predictions for the outputs of interest.

DDX5 mRNA-targeting antisense oligonucleotide as a new promising therapeutic in combating castration-resistant prostate cancer

The heat shock protein 27 (Hsp27) has emerged as a principal factor of the castration-resistant prostate cancer (CRPC) progression. Also, an antisense oligonucleotide (ASO) against Hsp27 (OGX-427 or apatorsen) has been assessed in different clinical trials. Here, we illustrate that Hsp27 highly regulates the expression of the human DEAD-box protein 5 (DDX5), and we define DDX5 as a novel therapeutic target for CRPC treatment. DDX5 overexpression is strongly correlated with aggressive tumor features, notably with CRPC. DDX5 downregulation using a specific ASO-based inhibitor that acts on DDX5 mRNAs inhibits cell proliferation in preclinical models, and it particularly restores the treatment sensitivity of CRPC. Interestingly, through the identification and analysis of DDX5 protein interaction networks, we have identified some specific functions of DDX5 in CRPC that could contribute actively to tumor progression and therapeutic resistance. We first present the interactions of DDX5 and the Ku70/80 heterodimer and the transcription factor IIH, thereby uncovering DDX5 roles in different DNA repair pathways. Collectively, our study highlights critical functions of DDX5 contributing to CRPC progression and provides preclinical proof of concept that a combination of ASO-directed DDX5 inhibition with a DNA damage-inducing therapy can serve as a highly potential novel strategy to treat CRPC.

Hypothetical generalized framework for a new imaging endpoint of therapeutic activity in early phase clinical trials in brain tumors

Imaging response assessment is a cornerstone of patient care and drug development in oncology. Clinicians/clinical researchers rely on tumor imaging to estimate the impact of new treatments and guide decision making for patients and candidate therapies. This is important in brain cancer, where associations between tumor size/growth and emerging neurological deficits are strong. Accurately measuring the impact of a new therapy on tumor growth early in clinical development, where patient numbers are small, would be valuable for decision making regarding late-stage development activation. Current attempts to measure the impact of a new therapy have limited influence on clinical development, as determination of progression, stability or response does not currently account for individual tumor growth kinetics prior to the initiation of experimental therapies. Therefore, we posit that imaging-based response assessment, often used as a tool for estimating clinical effect, is incomplete as it does not adequately account for growth trajectories or biological characteristics of tumors prior to the introduction of an investigational agent. Here, we propose modifications to the existing framework for evaluating imaging assessment in primary brain tumors that will provide a more reliable understanding of treatment effects. Measuring tumor growth trajectories prior to a given intervention may allow us to more confidently conclude whether there is an anti-tumor effect. This updated approach to imaging-based tumor response assessment is intended to improve our ability to select candidate therapies for later-stage development, including those that may not meet currently sought thresholds for "response" and ultimately lead to identification of effective treatments.

Impact of pharmacogenetics on variability in exposure to oral vinorelbine among pediatric patients: a model-based population pharmacokinetic analysis

PURPOSE

Better understanding of pharmacokinetics of oral vinorelbine (VNR) in children would help predicting drug exposure and, beyond, clinical outcome. Here, we have characterized the population pharmacokinetics of oral VNR and studied the factors likely to explain the variability observed in VNR exposure among young patients.

DESIGN/METHODS

We collected blood samples from 36 patients (mean age 11.6 years) of the OVIMA multicentric phase II study in children with recurrent/progressive low-grade glioma. Patients received 60 mg/m² of oral VNR on days 1, 8, and 15 during the first 28-day treatment cycle and 80 mg/m², unless contraindicated, from cycle 2-12. Population pharmacokinetic analysis was performed using nonlinear mixed-effects modeling within the Monolix^® software. Fifty SNPs of pharmacokinetic-related genes were genotyped. The influence of demographic, biological, and pharmacogenetic covariates on pharmacokinetic parameters was investigated using a stepwise multivariate procedure.

RESULTS

A three-compartment model, with a delayed double zero-order absorption and a first-order elimination, best described VNR pharmacokinetics in children. Typical population estimates for the apparent central volume of distribution (V_c/F) and elimination rate constant were 803 L and 0.60 h^-1, respectively. Following covariate analysis, BSA, leukocytes count, and drug transport ABCB1-rs2032582 SNP showed a dramatic impact on V_c/F. Conversely, age and sex had no significant effect on VNR pharmacokinetics.

CONCLUSION

Beyond canonical BSA and leukocytes, ABCB1-rs2032582 polymorphism showed a meaningful impact on VNR systemic exposure. Simulations showed that the identified covariates could have an impact on both efficacy and toxicity outcomes. Thus, a personalized dosing strategy, using those covariates, could help to optimize the efficacy/toxicity balance of VNR in children.

A Quantitative Systems Pharmacology Framework for Optimal Doxorubicin Granulocyte Colony-Stimulating Factor Regimens in Triple-Negative Breast Cancer

INTRODUCTION

To mitigate the risk of neutropenia during chemotherapy treatment of triple-negative breast cancer, prophylactic and supportive therapy with granulocyte colony-stimulating factor (G-CSF) is administered concomitant to chemotherapy. The proper timing of combined chemotherapy and G-CSF is crucial for treatment outcomes.

METHODS

Leveraging our established mathematical model of neutrophil production by G-CSF, we developed quantitative systems pharmacology (QSP) framework to investigate how modulating chemotherapy dose frequency and intensity can maximize antitumour effects. To establish schedules that best control tumour size while minimizing neutropenia, we combined Gompertzian tumour growth with pharmacokinetic/pharmacodynamic models of doxorubicin and G-CSF, and our QSP model of neutrophil production.

RESULTS

We optimized a range of chemotherapeutic cycle lengths and dose sizes to establish regimens that simultaneously reduced tumour burden while minimizing neutropenia. Our results suggest that cytotoxic chemotherapy with doxorubicin 45 mg/m2 every 14 days provides effective control of tumour growth while mitigating neutropenic risks.

CONCLUSION

This work suggests future avenues for optimal regimens of chemotherapy with prophylactic G-CSF support. Importantly, the algorithmic approach that we developed can aid in balancing the anticancer and the neutropenic effects of both drugs, and therefore contributes to rational considerations in clinical decision-making in triple-negative breast cancer.

Do we really understand how drug eluted from stents modulates arterial healing?

The advent of drug-eluting stents (DES) has revolutionised the treatment of coronary artery disease. These devices, coated with anti-proliferative drugs, are deployed into stenosed or occluded vessels, compressing the plaque to restore natural blood flow, whilst simultaneously combating the evolution of restenotic tissue. Since the development of the first stent, extensive research has investigated how further advancements in stent technology can improve patient outcome. Mathematical and computational modelling has featured heavily, with models focussing on structural mechanics, computational fluid dynamics, drug elution kinetics and subsequent binding within the arterial wall; often considered separately. Smooth Muscle Cell (SMC) proliferation and neointimal growth are key features of the healing process following stent deployment. However, models which depict the action of drug on these processes are lacking. In this article, we start by reviewing current models of cell growth, which predominantly emanate from cancer research, and available published data on SMC proliferation, before presenting a series of mathematical models of varying complexity to detail the action of drug on SMC growth in vitro. Our results highlight that, at least for Sodium Salicylate and Paclitaxel, the current state-of-the-art nonlinear saturable binding model is incapable of capturing the proliferative response of SMCs across a range of drug doses and exposure times. Our findings potentially have important implications on the interpretation of current computational models and their future use to optimise and control drug release from DES and drug-coated balloons.

Novel Tumor Growth Rate Analysis in the Randomized CLARINET Study Establishes the Efficacy of Lanreotide Depot/Autogel 120 mg with Prolonged Administration in Indolent Neuroendocrine Tumors

Introduction

Tumor quantity while receiving cancer therapy is the sum of simultaneous regression of treatment‐sensitive and growth of treatment‐resistant fractions at constant rates. Exponential rate constants for tumor regression/decay (d) and growth (g) can be estimated. Previous studies established g as a biomarker for overall survival; g increases after treatment cessation, can estimate doubling times, and can assess treatment effectiveness in small cohorts by benchmarking to large reference data sets. Using this approach, we analyzed data from the clinical trial CLARINET, evaluating lanreotide depot/autogel 120 mg/4 weeks (LAN) for treatment of neuroendocrine tumors (NETs).

Methods and Materials

Computed tomography imaging data from 97 LAN‐ and 101 placebo‐treated patients from CLARINET were analyzed to estimate g and d.

Results

Data from 92% of LAN‐ and 94% of placebo‐treated patients could be fit to one of the equations to derive g and d (p < .001 in most data sets). LAN‐treated patients demonstrated significantly slower g than placebo recipients (p = .00315), a difference of 389 days in doubling times. No significant difference was observed in d. Over periods of LAN administration up to 700 days, g did not change appreciably. Simulated analysis with g as the endpoint showed a sample size of 48 sufficient to detect a difference in median g with 80% power.

Conclusion

Although treatment of NETs with LAN can affect tumor shrinkage, LAN primarily slows tumor growth rather than accelerates tumor regression. Evidence of LAN efficacy across tumors was identified. The growth‐retarding effect achieved with LAN was sustained for a prolonged period of time.

Implications for Practice

The only curative treatment for neuroendocrine tumors (NETs) is surgical resection; however, because of frequent late diagnosis, this is often impossible. Because of this, treatment of NETs is challenging and often aims to reduce tumor burden and delay progression. A novel method of analysis was used to examine data from the CLARINET trial, confirming lanreotide depot/autogel is effective at slowing tumor growth and extending progression‐free survival. By providing the expected rate and doubling time of tumor growth early in the course of treatment, this method of analysis has the potential to guide physicians in their management of patients with NETs.

Treatment of neuroendocrine tumors is challenging, mainly aiming to reduce tumor burden and delay disease progression. This article reports on the kinetics of tumor growth using a novel method of analysis and data from the CLARINET study.

Pharmacokinetic/Pharmacodynamic Modeling of the Anti-Cancer Effect of Dexamethasone in Pancreatic Cancer Xenografts and Anticipation of Human Efficacious Doses

Dexamethasone (DEX), a synthetic glucocorticoid, exhibited anti-cancer efficacy in pancreatic xenografts derived from patient tumor tissue or cancer cell lines. The aim of this study was to establish pharmacokinetic/pharmacodynamic (PK/PD) models to quantitatively characterize the inhibitory effect of DEX on tumor growth as well as its discrepancy among 3 xenograft models. Data of tumor growth profiles were collected from a patient-derived xenograft (PDX) model in NOD/SCID mice and 2 cell line-derived (PANC-1 and SW1990) xenograft models in BALB/c nude mice. Empirical PK/PD models were developed to establish mathematical relationships between plasma concentration of DEX and tumor growth dynamics after integrating PK parameters extracted from literature. Drug effect in each model was well described by a linear inhibitory function with a potency factor of 4.67, 3.14, and 2.35 L/mg for PDX, PANC-1, and SW1990 xenograft, respectively. Human efficacious doses of DEX were preliminarily predicted through model-based simulation, and 60% tumor growth inhibition at clinical exposure corresponded to a daily dose range of 26-52 mg intravenously. This modeling work quantified the preclinical anti-cancer effect of DEX and demonstrated the feasibility of its medication in pancreatic cancer, which would be conductive to future translational research.

Optimizing drug development in oncology by clinical trial simulation: Why and how?

In therapeutic research, the safety and efficacy of pharmaceutical products are necessarily tested on humans via clinical trials after an extensive and expensive preclinical development period. Methodologies such as computer modeling and clinical trial simulation (CTS) might represent a valuable option to reduce animal and human assays. The relevance of these methods is well recognized in pharmacokinetics and pharmacodynamics from the preclinical phase to postmarketing. However, they are barely used and are poorly regarded for drug approval, despite Food and Drug Administration and European Medicines Agency recommendations. The generalization of CTS could be greatly facilitated by the availability of software for modeling biological systems, by clinical trial studies and hospital databases. Data sharing and data merging raise legal, policy and technical issues that will need to be addressed. Development of future molecules will have to use CTS for faster development and thus enable better patient management. Drug activity modeling coupled with disease modeling, optimal use of medical data and increased computing speed should allow this leap forward. The realization of CTS requires not only bioinformatics tools to allow interconnection and global integration of all clinical data but also a universal legal framework to protect the privacy of every patient. While recognizing that CTS can never replace 'real-life' trials, they should be implemented in future drug development schemes to provide quantitative support for decision-making. This in silico medicine opens the way to the P4 medicine: predictive, preventive, personalized and participatory.

A Population Dynamic Energy Budget-Based Tumor Growth Inhibition Model for Etoposide Effects on Wistar Rats

PURPOSE

This work aimed to develop a population PK/PD tumor-in-host model able to describe etoposide effects on both tumor cells and host in Walker-256 tumor-bearing rats.

METHODS

Etoposide was investigated on thirty-eight Wistar rats randomized in five arms: two groups of tumor-free animals receiving either placebo or etoposide (10 mg/kg bolus for 4 days) and three groups of tumor-bearing animals receiving either placebo or etoposide (5 or 10 mg/kg bolus for 8 or 4 days, respectively). To analyze experimental data, a tumor-in-host growth inhibition (TGI) model, based on the Dynamic Energy Budget (DEB) theory, was developed. Total plasma and free-interstitial tumor etoposide concentrations were assessed as driver of tumor kinetics.

RESULTS

The model simultaneously describes tumor and host growths, etoposide antitumor effect as well as cachexia phenomena related to both the tumor and the drug treatment. The schedule-dependent inhibitory effect of etoposide is also well captured when the intratumoral drug concentration is considered as the driver of the tumor kinetics.

CONCLUSIONS

The DEB-based TGI model capabilities, up to now assessed only in mice, are fully confirmed in this study involving rats. Results suggest that well designed experiments combined with a mechanistic modeling approach could be extremely useful to understand drug effects and to describe all the dynamics characterizing in vivo tumor growth studies.

Pembrolizumab Exposure-Response Assessments Challenged by Association of Cancer Cachexia and Catabolic Clearance

PURPOSE

To investigate the relationship of pembrolizumab pharmacokinetics (PK) and overall survival (OS) in patients with advanced melanoma and non-small cell lung cancer (NSCLC).

PATIENTS AND METHODS

PK dependencies in OS were evaluated across three pembrolizumab studies of either 200 mg or 2 to 10 mg/kg every 3 weeks (Q3W). Kaplan-Meier plots of OS, stratified by dose, exposure, and baseline clearance (CL₀), were assessed per indication and study. A Cox proportional hazards model was implemented to explore imbalances of typical prognostic factors in high/low NSCLC CL₀ subgroups.

RESULTS

A total of 1,453 subjects were included: 340 with pembrolizumab-treated melanoma, 804 with pembrolizumab-treated NSCLC, and 309 with docetaxel-treated NSCLC. OS was dose independent from 2 to 10 mg/kg for pembrolizumab-treated melanoma [HR = 0.98; 95% confidence interval (CI), 0.94-1.02] and NSCLC (HR = 0.98; 95% CI, 0.95-1.01); however, a strong CL₀-OS association was identified for both cancer types (unadjusted melanoma HR = 2.56; 95% CI, 1.72-3.80 and NSCLC HR = 2.64; 95% CI, 1.94-3.57). Decreased OS in subjects with higher pembrolizumab CL₀ paralleled disease severity markers associated with end-stage cancer anorexia-cachexia syndrome. Correction for baseline prognostic factors did not fully attenuate the CL₀-OS association (multivariate-adjusted CL₀ HR = 1.64; 95% CI, 1.06-2.52 for melanoma and HR = 1.88; 95% CI, 1.22-2.89 for NSCLC).

CONCLUSIONS

These data support the lack of dose or exposure dependency in pembrolizumab OS for melanoma and NSCLC between 2 and 10 mg/kg. An association of pembrolizumab CL₀ with OS potentially reflects catabolic activity as a marker of disease severity versus a direct PK-related impact of pembrolizumab on efficacy. Similar data from other trials suggest such patterns of exposure-response confounding may be a broader phenomenon generalizable to antineoplastic mAbs.See related commentary by Coss et al., p. 5787.

Time-dependent pharmacokinetics of dexamethasone and its efficacy in human breast cancer xenograft mice: a semi-mechanism-based pharmacokinetic/pharmacodynamic model

Dexamethasone (DEX) is the substrate of CYP3A. However, the activity of CYP3A could be induced by DEX when DEX was persistently administered, resulting in auto-induction and time-dependent pharmacokinetics (pharmacokinetics with time-dependent clearance) of DEX. In this study we investigated the pharmacokinetic profiles of DEX after single or multiple doses in human breast cancer xenograft nude mice and established a semi-mechanism-based pharmacokinetic/pharmacodynamic (PK/PD) model for characterizing the time-dependent PK of DEX as well as its anti-cancer effect. The mice were orally given a single or multiple doses (8 mg/kg) of DEX, and the plasma concentrations of DEX were assessed using LC-MS/MS. Tumor volumes were recorded daily. Based on the experimental data, a two-compartment model with first order absorption and time-dependent clearance was established, and the time-dependence of clearance was modeled by a sigmoid E_max equation. Moreover, a semi-mechanism-based PK/PD model was developed, in which the auto-induction effect of DEX on its metabolizing enzyme CYP3A was integrated and drug potency was described using an E_max equation. The PK/PD model was further used to predict the drug efficacy when the auto-induction effect was or was not considered, which further revealed the necessity of adding the auto-induction effect into the final PK/PD model. This study established a semi-mechanism-based PK/PD model for characterizing the time-dependent pharmacokinetics of DEX and its anti-cancer effect in breast cancer xenograft mice. The model may serve as a reference for DEX dose adjustments or optimization in future preclinical or clinical studies.

Exploration of time points and cut-off values for early tumour shrinkage to predict survival outcomes of patients with metastatic colorectal cancer treated with first-line chemotherapy using a biexponential model for change in tumour size

Background

Several studies reported that early tumour shrinkage (ETS) was associated with overall survival in patients with metastatic colorectal cancer (mCRC) treated with first-line chemotherapy. However, appropriate time point and cut-off value for ETS remain unclear because these varied in previous studies.

Patients and methods

We investigated patients with mCRC who received FOLFOX or FOLFIRI with/without molecular-targeted agents as first-line treatment between 2005 and 2014. Using a biexponential model for change in tumour size, a relative change in the sum of the longest diameters of target lesions from baseline was estimated at a certain time point in each individual patient. Associations of survival outcomes with ETS at various time points based on various cut-off values were evaluated by Cox regression analysis with a landmark approach.

Results

Among the 67 patients reviewed, the objective response rate was 73.1% (95% CI 62.5% to 83.7%), the median progression-free survival was 10.9 months (95% CI 8.7 to 13.0 months) and the median overall survival was 25.6 months (95% CI 20.1 to 27.3 months). The model for change in tumour size agreed with the actual measured sizes well. Multivariate Cox regression analysis, including performance status, number of metastatic sites and use of targeted agents, showed that ETS at 8 weeks based on a cut-off value of 20% was most significantly associated with overall survival (HR: 0.404, 95% CI 0.231 to 0.707, P=0.0015).

Conclusion

It is suggested that a time point of 8 weeks and a cut-off value of 20% may be optimal criteria for defining ETS.

Current mathematical models for cancer drug discovery

INTRODUCTION

Pharmacometric models represent the most comprehensive approaches for extracting, summarizing and integrating information obtained in the often sparse, limited, and less-than-optimally designed experiments performed in the early phases of oncology drug discovery. Whilst empirical methodologies may be enough for screening and ranking candidate drugs, modeling approaches are needed for optimizing and making economically viable the learn-confirm cycles within an oncology research program and anticipating the dose regimens to be investigated in the subsequent clinical development. Areas covered: Papers appearing in the literature of approximately the last decade reporting modeling approaches applicable to anticancer drug discovery have been listed and commented. Papers were selected based on the interest in the proposed methodology or in its application. Expert opinion: The number of modeling approaches used in the discovery of anticancer drugs is consistently increasing and new models are developed based on the current directions of research of new candidate drugs. These approaches have contributed to a better understanding of new oncological targets and have allowed for the exploitation of the relatively sparse information generated by preclinical experiments. In addition, they are used in translational approaches for guiding and supporting the choice of dosing regimens in early clinical development.

Fractal dimension and universality in avascular tumor growth

For years, the comprehension of the tumor growth process has been intriguing scientists. New research has been constantly required to better understand the complexity of this phenomenon. In this paper, we propose a mathematical model that describes the properties, already known empirically, of avascular tumor growth. We present, from an individual-level (microscopic) framework, an explanation of some phenomenological (macroscopic) aspects of tumors, such as their spatial form and the way they develop. Our approach is based on competitive interaction between the cells. This simple rule makes the model able to reproduce evidence observed in real tumors, such as exponential growth in their early stage followed by power-law growth. The model also reproduces (i) the fractal-space distribution of tumor cells and (ii) the universal growth behavior observed in both animals and tumors. Our analyses suggest that the universal similarity between tumor and animal growth comes from the fact that both can be described by the same dynamic equation-the Bertalanffy-Richards model-even if they do not necessarily share the same biological properties.

Influence of doxorubicin inclusion into phospholipid nanoparticles on tumor accumulation and specific activity

The specific activity of drug formulation of doxorubicin embedded into phospholipid nanoparticles with diameter less than 30 nm (“Doxolip”) was studied in mice LLC carcinoma. Doxolip was prepared according to technology that was elaborated in Institute earlier. Doxorubicin tumor accumulation after intraperitoneal administration (at 4 h) was 4.5 times higher for Doxolip, than for free doxorubicin. The study of doxorubicin antitumor activity in developing tumor after single intravenous administration, 48 h after inoculation, showed, that: 1) tumor growth inhibition of Doxolip was observed at 6th day, while it was only at 11th day for free doxorubicin and revealed in less extent; 2) there was no antitumor effect of free doxorubicin at 8 days after administration of doses 2 and 4 mg/kg, but it was observed for Doxolip in dose-dependent manner, 10% and 30% correspondently. In experiment with developed tumor weekly Doxolip intraperitoneal administration (5 mg/kg, 3 weeks beginning from 7 days after inoculation) resulted in 56% decrease of tumor volume as compared with control. This parameter for free doxorubicin was 2.8 times lower. The obtained data indicate, that incorporation of doxorubicin into phospholipid nanoparticles with size up to 30 nm as delivery system increases its tumor accumulation and results to increase of specific activity both in intraperitoneal and in intravenous administration.

Translational modeling and simulation approaches for molecularly targeted small molecule anticancer agents from bench to bedside

INTRODUCTION

Recent advances in molecular biology have enabled personalized cancer therapies with molecularly targeted agents (MTAs), which offer a promising future for cancer therapy. Dynamic modeling and simulation (M&S) is a powerful mathematical approach linking drug exposures to pharmacological responses, providing a quantitative assessment of in vivo drug potency. Accordingly, a growing emphasis is being placed upon M&S to quantitatively understand therapeutic exposure-response relationships of MTAs in nonclinical models.

AREAS COVERED

An overview of M&S approaches for MTAs in nonclinical models is presented with discussion about mechanistic extrapolation of antitumor efficacy from bench to bedside. Emphasis is placed upon recent advances in M&S approaches linking drug exposures, biomarker responses (e.g. target modulation) and pharmacological outcomes (e.g. antitumor efficacy).

EXPERT OPINION

For successful personalized cancer therapies with MTAs, it is critical to mechanistically and quantitatively understand their exposure-response relationships in nonclinical models, and to logically and properly apply such knowledge to the clinic. Particularly, M&S approaches to predict pharmacologically active concentrations of MTAs in patients based upon nonclinical data would be highly valuable in guiding the design and execution of clinical trials. Proactive approaches to understand their exposure-response relationships could substantially increase probability of achieving a positive proof-of-concept in the clinic.

Optimal Design for Informative Protocols in Xenograft Tumor Growth Inhibition Experiments in Mice

Tumor growth inhibition (TGI) models are increasingly used during preclinical drug development in oncology for the in vivo evaluation of antitumor effect. Tumor sizes are measured in xenografted mice, often only during and shortly after treatment, thus preventing correct identification of some TGI model parameters. Our aims were (i) to evaluate the importance of including measurements during tumor regrowth and (ii) to investigate the proportions of mice included in each arm. For these purposes, optimal design theory based on the Fisher information matrix implemented in PFIM4.0 was applied. Published xenograft experiments, involving different drugs, schedules, and cell lines, were used to help optimize experimental settings and parameters using the Simeoni TGI model. For each experiment, a two-arm design, i.e., control versus treatment, was optimized with or without the constraint of not sampling during tumor regrowth, i.e., "short" and "long" studies, respectively. In long studies, measurements could be taken up to 6 g of tumor weight, whereas in short studies the experiment was stopped 3 days after the end of treatment. Predicted relative standard errors were smaller in long studies than in corresponding short studies. Some optimal measurement times were located in the regrowth phase, highlighting the importance of continuing the experiment after the end of treatment. In the four-arm designs, the results showed that the proportions of control and treated mice can differ. To conclude, making measurements during tumor regrowth should become a general rule for informative preclinical studies in oncology, especially when a delayed drug effect is suspected.

Pharmacokinetic-pharmacodynamic modeling of the antitumor effect of TM208 and EGFR-TKI resistance in human breast cancer xenograft mice

AIM

The novel anticancer compound TM208 is an EGFR tyrosine kinase inhibitor (EGFR-TKI). Since the development of resistance to EGFR-TKIs is a major challenge in their clinical usage, we investigated the profiles of resistance following continuous treatment with TM208 in human breast cancer xenograft mice, and identified the relationship between the tumor pEGFR levels and tumor growth inhibition.

METHODS

Female BALB/c nude mice were implanted with human breast cancer MCF-7 cells, and the xenograft mice received TM208 (50 or 150 mg·kg(-1)·d(-1), ig) or vehicle for 18 d. The pharmacokinetics (PK) and pharmacodynamics (PD) of TM208 were evaluated.

RESULTS

The PK properties of TM208 were described by a one-compartment model with first-order absorption kinetics. Our study showed the inhibitory effects of TM208 on tumor pEGFR levels gradually reached a maximum effect, after which it became weaker over time, which was characterized by a combined tolerance/indirect response PD model with an estimated EC50 (55.9 μg/L), as well as three parameters ('a' of 27.2%, 'b' of 2730%, 'c' of 0.58 h(-1)) denoting the maximum, extent and rate of resistance, respectively. The relationship between the tumor pEGFR levels and tumor growth inhibition was characterized by a combined logistic tumor growth/transit compartment model with estimated parameters associated with tumor growth characteristics kng (0.282 day(-1)), drug potency kTM208 (0.0499 cm(3)/day) and the kinetics of tumor cell death k1 (0.141 day(-1)), which provided insight into drug mechanisms and behaviors.

CONCLUSION

The proposed PK/PD model provides a better understanding of the pharmacological properties of TM208 in the treatment of breast cancer. Furthermore, simulation based on a tolerance model allows prediction of the occurrence of resistance.

Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

Xenografts -as simplified animal models of cancer- differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic.

To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen -as a surrogate for endocrine delivery- is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate (kR′) represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. kR′ gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (k_p) deals with cell line specific factors to promote growth. The K_H,K_N describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models.

Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of kR′ and lower k_p, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate (kR′) and vary greatly in k_p, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth.

However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.

Tumour-bearing animal models of cancer are needed to discover new drugs to treat cancer. We aim in this article to capture—through mathematics- some underlying phenomena of tumour growth in animals. We propose a set of equations that, despite being very simple, describe tumour growth, hypoxia and necrosis. Cells under low oxygen levels change into a stress state called “hypoxia”, which will ultimately lead to tissue death, also known as “necrosis” and “apoptosis”. Hypoxic cells undergo a variety of changes which impact tumour growth, development, metastasis and -most importantly- response to therapy. Hence, oxygen distribution is important. We simulate oxygen profiles to locate hypoxic and necrotic tumour regions. Finally, this mathematical model allows us to compare and classify animal models from a grounded and physiological perspective, rather than a more convenient and empirical one. This will help us understand how well (or poorly) animal tumours mimic tumours in patients. The simplicity of our mathematical model allows us to obtain more information out of the same animal sets without any further experiments, hopefully saving time, money and animal usage.

Optimizing oncology therapeutics through quantitative translational and clinical pharmacology: challenges and opportunities

Despite advances in biomedical research that have deepened our understanding of cancer hallmarks, resulting in the discovery and development of targeted therapies, the success rates of oncology drug development remain low. Opportunities remain for objective dose selection informed by exposure-response understanding to optimize the benefit-risk balance of novel therapies for cancer patients. This review article discusses the principles and applications of modeling and simulation approaches across the lifecycle of development of oncology therapeutics. Illustrative examples are used to convey the value gained from integration of quantitative clinical pharmacology strategies from the preclinical-translational phase through confirmatory clinical evaluation of efficacy and safety.

Classical mathematical models for description and prediction of experimental tumor growth

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Translational pharmacokinetic-pharmacodynamic modeling for an orally available novel inhibitor of anaplastic lymphoma kinase and c-Ros oncogene 1

An orally available macrocyclic small molecule, PF06463922 [(10R)-7-amino-12-fluoro-2,10,16-trimethyl-15-oxo-10,15,16,17-tetrahydro-2H-8,4-(metheno)pyrazolo[4,3-h][2,5,11]benzoxadiazacyclotetradecine-3-carbonitrile], is a selective inhibitor of anaplastic lymphoma kinase (ALK) and c-Ros oncogene 1 (ROS1). The objectives of the present study were to characterize the pharmacokinetic-pharmacodynamic relationships of PF06463922 between its systemic exposures, pharmacodynamic biomarker (target modulation), and pharmacologic response (antitumor efficacy) in athymic mice implanted with H3122 non-small cell lung carcinomas expressing echinoderm microtubule-associated protein-like 4 (EML4)-ALK mutation (EML4-ALK(L1196M)) and with NIH3T3 cells expressing CD74-ROS1. In these nonclinical tumor models, PF06463922 was orally administered to animals with EML4-ALK(L1196M) and CD74-ROS1 at twice daily doses of 0.3-20 and 0.01-3 mg/kg per dose, respectively. Plasma concentration-time profiles of PF06463922 were adequately described by a one-compartment pharmacokinetic model. Using the model-simulated plasma concentrations, a pharmacodynamic indirect response model with a modulator sufficiently fit the time courses of target modulation (i.e., ALK phosphorylation) in tumors of EML4-ALK(L1196M)-driven models with EC50,in vivo of 36 nM free. A drug-disease model based on an indirect response model reasonably fit individual tumor growth curves in both EML4-ALK(L1196M)- and CD74-ROS1-driven models with the estimated tumor stasis concentrations of 51 and 6.2 nM free, respectively. Thus, the EC60,in vivo (52 nM free) for ALK inhibition roughly corresponded to the tumor stasis concentration in an EML4-ALK(L1196M)-driven model, suggesting that 60% ALK inhibition would be required for tumor stasis. Accordingly, we proposed that the EC60,in vivo for ALK inhibition corresponding to the tumor stasis could be considered a minimum target efficacious concentration of PF06463922 for cancer patients in a phase I trial.

Implementation of pharmacokinetic and pharmacodynamic strategies in early research phases of drug discovery and development at Novartis Institute of Biomedical Research

Characterizing the relationship between the pharmacokinetics (PK, concentration vs. time) and pharmacodynamics (PD, effect vs. time) is an important tool in the discovery and development of new drugs in the pharmaceutical industry. The purpose of this publication is to serve as a guide for drug discovery scientists toward optimal design and conduct of PK/PD studies in the research phase. This review is a result of the collaborative efforts of DMPK scientists from various Metabolism and Pharmacokinetic (MAP) departments of the global organization Novartis Institute of Biomedical Research (NIBR). We recommend that PK/PD strategies be implemented in early research phases of drug discovery projects to enable successful transition to drug development. Effective PK/PD study design, analysis, and interpretation can help scientists elucidate the relationship between PK and PD, understand the mechanism of drug action, and identify PK properties for further improvement and optimal compound design. Additionally, PK/PD modeling can help increase the translation of in vitro compound potency to the in vivo setting, reduce the number of in vivo animal studies, and improve translation of findings from preclinical species into the clinical setting. This review focuses on three important elements of successful PK/PD studies, namely partnership among key scientists involved in the study execution; parameters that influence study designs; and data analysis and interpretation. Specific examples and case studies are highlighted to help demonstrate key points for consideration. The intent is to provide a broad PK/PD foundation for colleagues in the pharmaceutical industry and serve as a tool to promote appropriate discussions on early research project teams with key scientists involved in PK/PD studies.

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.

Modeling NSCLC progression: recent advances and opportunities available

Non-small cell lung cancer (NSCLC) is one of the leading causes of death around the world with an estimated 5-year relative survival rate of 16% at diagnosis. Development of drugs treating NSCLC is not easy, and the success rate for an anticancer treatment to pass through the whole clinical development process is as low as 5%. Modeling and simulation lend themselves as tools which can potentially streamline drug development. A critical component of the models developed is a description of how the disease progresses over time and how a treatment would affect its trajectory. Our aim was to review the literature to present the models and growth functions which have been used for describing NSCLC dynamics, and how anticancer treatments can affect such dynamics, both in animals and in humans. Only a limited set of models were identified for such a purpose. Most of the models which have been used were descriptive of tumor growth, yet there were attempts to account for the underlying processes, especially in animals where it is more feasible to collect data needed for developing such models. Moreover, we discuss how modeling and simulation can aid in decision making across the different stages of drug development. Based on some encouraging results from trials of other cancer types where modeling tumor dynamics has played an important role, we propose further exploration of NSCLC using model-based techniques and further use of these techniques in designing and evaluating NSCLC trials.

Preclinical pharmacokinetic/pharmacodynamic models to predict schedule-dependent interaction between erlotinib and gemcitabine

PURPOSE

To investigate the pharmacological effects of different erlotinib (ER) and gemcitabine (GM) combination schedules by in vitro and in vivo experiments and PK/PD models in non-small cell lung cancer cells.

METHODS

H1299 cells were exposed to different ER combined with GM schedules. Cell growth inhibition was analyzed to evaluate these schedules. A preclinical in vivo study was then conducted to compare tumor suppression effects of different schedules in H1299 xenografts. PK/PD models were developed to quantify the anti-tumor interaction of ER and GM.

RESULTS

Synergism was observed when ER preceded GM, but other sequences showed antagonism. The optimal in vitro schedule, or interval schedule, was applied to the animal study, which showed greater anti-tumor effect than simultaneous group. PK/PD models implied that interaction of the two drugs was additive in simultaneous treatment but synergistic in interval schedule. The simulation results showed that interval schedule can delay tumor growth for a longer time, and demonstrated more evident anti-tumor effect compared with simultaneous group if the treatment duration was longer.

CONCLUSIONS

Interval schedule of the two drugs can achieve synergistic anti-tumor effect, and is superior to simultaneous treatment.