A tumor growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy

Probabilistic analysis of tumor growth inhibition models to Support trial design

A large enough sample size of patients is required to statistically show that one treatment is better than another. However, too large a sample size is expensive and can also result in findings that are statistically significant, but not clinically relevant. How sample sizes should be chosen is a well-studied problem in classical statistics and analytical expressions can be derived from the appropriate test statistic. However, these expressions require information regarding the efficacy of the treatment, which may not be available, particularly for newly developed drugs. Tumor growth inhibition (TGI) models are frequently used to quantify the efficacy of newly developed anticancer drugs. In these models, the tumor growth dynamics are commonly described by a set of ordinary differential equations containing parameters that must be estimated using experimental data. One widely used endpoint in clinical trials is the proportion of patients in different response categories determined using the Response Evaluation Criteria In Solid Tumors (RECIST) framework. From the TGI model, we derive analytical expressions for the probability of patient response to combination therapy. The probabilistic expressions are used together with classical statistics to derive a parametric model for the sample size required to achieve a certain significance level and test power when comparing two treatments. Furthermore, the probabilistic expressions are used to generalize the Tumor Static Exposure concept to be more suitable for predicting clinical response. The derivatives of the probabilistic expressions are used to derive two additional expressions characterizing the exposure and its sensitivity. Finally, our results are illustrated using parameters obtained from calibrating the model to preclinical data.

Machine Learning Methods for Precision Dosing in Anticancer Drug Therapy: A Scoping Review

INTRODUCTION

In the last decade, various Machine Learning techniques have been proposed aiming to individualise the dose of anticancer drugs mostly based on a presumed drug effect or measured effect biomarkers. The aim of this scoping review was to comprehensively summarise the research status on the use of Machine Learning for precision dosing in anticancer drug therapy.

METHODS

This scoping review was conducted in accordance with the interim guidance by Cochrane and the Joanna Briggs Institute. We systematically searched the databases Medline (via PubMed), Embase and the Cochrane Library for research articles and reviews including results published after 2016. Results were reported according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews (PRISMA-ScR) checklist.

RESULTS

A total of 17 relevant studies was identified. In 12 of the included studies, Reinforcement Learning methods were used, including Classical, Deep, Double Deep and Conservative Q-Learning and Fuzzy Reinforcement Learning. Furthermore, classical Machine Learning methods were compared in terms of their performance and an artificial intelligence platform based on parabolic equations was used to guide dosing prospectively and retrospectively, albeit only in a limited number of patients. Due to the significantly different algorithm structures, a meaningful comparison between the various Machine Learning approaches was not possible.

CONCLUSION

Overall, this review emphasises the clinical relevance of Machine Learning methods for anticancer drug dose optimisation, as many algorithms have shown promising results enabling model-free predictions with the potential to maximise efficacy and minimise toxicity when compared to standard protocols.

Model-Informed Reinforcement Learning for Enabling Precision Dosing Via Adaptive Dosing

Precision dosing, the tailoring of drug doses to optimize therapeutic benefits and minimize risks in each patient, is essential for drugs with a narrow therapeutic window and severe adverse effects. Adaptive dosing strategies extend the precision dosing concept to time-varying treatments which require sequential dose adjustments based on evolving patient conditions. Reinforcement learning (RL) naturally fits this paradigm: it perfectly mimics the sequential decision-making process where clinicians adapt dose administration based on patient response and evolution monitoring. This paper aims to investigate the potentiality of coupling RL with population PK/PD models to develop precision dosing algorithms, reviewing the most relevant works in the field. Case studies in which PK/PD models were integrated within RL algorithms as simulation engine to predict consequences of any dosing action have been considered and discussed. They mainly concern propofol-induced anesthesia, anticoagulant therapy with warfarin and a variety of anticancer treatments differing for administered agents and/or monitored biomarkers. The resulted picture highlights a certain heterogeneity in terms of precision dosing approaches, applied methodologies, and degree of adherence to the clinical domain. In addition, a tutorial on how a precision dosing problem should be formulated in terms of the key elements composing the RL framework (i.e., system state, agent actions and reward function), and on how PK/PD models could enhance RL approaches is proposed for readers interested in delving in this field. Overall, the integration of PK/PD models into a RL-framework holds great promise for precision dosing, but further investigations and advancements are still needed to address current limitations and extend the applicability of this methodology to drugs requiring adaptive dosing strategies.

A Mathematical Model of Stroma-Supported Allometric Tumor Growth

Mounting empirical research suggests that the stroma, or interface between healthy and cancerous tissue, is a critical determinate of cancer invasion. At the same time, a cancer cell's location and potential to proliferate can influence its sensitivity to cancer treatments. In this paper, we use ordinary differential equations to develop spatially structured models for solid tumors wherein the growth of tumor components is coordinated. The model tumors feature two components, a proliferating peripheral growth region, which potentially includes a mix of cancerous and noncancerous stroma cells, and a solid tumor core. Mathematical and numerical analysis are used to investigate how coordinated expansion of the tumor growth region and core can influence overall growth dynamics in a variety of tumor types. Model assumptions, which are motivated by empirical and in silico solid tumor research, are evaluated through comparison to tumor volume data and existing models of tumor growth.

Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling

Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often proposed to predict treatment outcome in this context, and have the potential to guide clinical decision-making and inform personalised fractionation protocols. Hindering effective use of models in this context is the sparsity of clinical measurements juxtaposed with the model complexity required to produce the full range of possible patient responses. In this work, we present a compartment model of tumour volume and tumour composition, which, despite relative simplicity, is capable of producing a wide range of patient responses. We then develop novel statistical methodology and leverage a cohort of existing clinical data to produce a predictive model of both tumour volume progression and the associated level of uncertainty that evolves throughout a patient's course of treatment. To capture inter-patient variability, all model parameters are patient specific, with a bootstrap particle filter-like Bayesian approach developed to model a set of training data as prior knowledge. We validate our approach against a subset of unseen data, and demonstrate both the predictive ability of our trained model and its limitations.

Focused ultrasound ablation of melanoma with boiling histotripsy yields abscopal tumor control and antigen-dependent dendritic cell activation

Background

Boiling histotripsy (BH), a mechanical focused ultrasound ablation strategy, can elicit intriguing signatures of anti-tumor immunity. However, the influence of BH on dendritic cell function is unknown, compromising our ability to optimally combine BH with immunotherapies to control metastatic disease.

Methods

BH was applied using a sparse scan (1 mm spacing between sonications) protocol to B16F10-ZsGreen melanoma in bilateral and unilateral settings. Ipsilateral and contralateral tumor growth was measured. Flow cytometry was used to track ZsGreen antigen and assess how BH drives dendritic cell behavior.

Results

BH monotherapy elicited ipsilateral and abscopal tumor control in this highly aggressive model. Tumor antigen presence in immune cells in the tumor-draining lymph nodes (TDLNs) was ~3-fold greater at 24h after BH, but this abated by 96h. B cells, macrophages, monocytes, granulocytes, and both conventional dendritic cell subsets (i.e. cDC1s and cDC2s) acquired markedly more antigen with BH. BH drove activation of both cDC subsets, with activation being dependent upon tumor antigen acquisition. Our data also suggest that BH-liberated tumor antigen is complexed with damage-associated molecular patterns (DAMPs) and that cDCs do not traffic to the TDLN with antigen. Rather, they acquire antigen as it flows through afferent lymph vessels into the TDLN.

Conclusion

When applied with a sparse scan protocol, BH monotherapy elicits abscopal melanoma control and shapes dendritic cell function through several previously unappreciated mechanisms. These results offer new insight into how to best combine BH with immunotherapies for the treatment of metastatic melanoma.

Overcoming chemotherapy resistance in low-grade gliomas: A computational approach

Low-grade gliomas are primary brain tumors that arise from glial cells and are usually treated with temozolomide (TMZ) as a chemotherapeutic option. They are often incurable, but patients have a prolonged survival. One of the shortcomings of the treatment is that patients eventually develop drug resistance. Recent findings show that persisters, cells that enter a dormancy state to resist treatment, play an important role in the development of resistance to TMZ. In this study we constructed a mathematical model of low-grade glioma response to TMZ incorporating a persister population. The model was able to describe the volumetric longitudinal dynamics, observed in routine FLAIR 3D sequences, of low-grade glioma patients acquiring TMZ resistance. We used the model to explore different TMZ administration protocols, first on virtual clones of real patients and afterwards on virtual patients preserving the relationships between parameters of real patients. In silico clinical trials showed that resistance development was deferred by protocols in which individual doses are administered after rest periods, rather than the 28-days cycle standard protocol. This led to median survival gains in virtual patients of more than 15 months when using resting periods between two and three weeks and agreed with recent experimental observations in animal models. Additionally, we tested adaptive variations of these new protocols, what showed a potential reduction in toxicity, but no survival gain. Our computational results highlight the need of further clinical trials that could obtain better results from treatment with TMZ in low grade gliomas.

Mechanistic characterization of oscillatory patterns in unperturbed tumor growth dynamics: The interplay between cancer cells and components of tumor microenvironment

Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks. The most commonly used unperturbed tumor growth models (i.e. linear, exponential, Gompertz and Simeoni) describe a monotonic increase and although they capture the mean trend of the data reasonably well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics through a mathematical framework. The overall goal of this work is to develop a data-driven semi-mechanistic model describing non-monotonic tumor growth in untreated mice. For this purpose, longitudinal tumor volume profiles from different tumor types and cell lines were pooled together and analyzed using the population approach. After characterizing the oscillatory patterns (oscillator half-periods between 8-11 days) and confirming that they were systematically observed across the different preclinical experiments available (p<10-9), a tumor growth model was built including the interplay between resources (i.e. oxygen or nutrients), angiogenesis and cancer cells. The new structure, in addition to improving the model diagnostic compared to the previously used tumor growth models (i.e. AIC reduction of 71.48 and absence of autocorrelation in the residuals (p>0.05)), allows the evaluation of the different oncologic treatments in a mechanistic way. Drug effects can potentially, be included in relevant processes taking place during tumor growth. In brief, the new model, in addition to describing non-monotonic tumor growth and the interaction between biological factors of the tumor microenvironment, can be used to explore different drug scenarios in monotherapy or combination during preclinical drug development.

Model-based assessment of combination therapies - ranking of radiosensitizing agents in oncology

BACKGROUND

To increase the chances of finding efficacious anticancer drugs, improve development times and reduce costs, it is of interest to rank test compounds based on their potential for human use as early as possible in the drug development process. In this paper, we present a method for ranking radiosensitizers using preclinical data.

METHODS

We used data from three xenograft mice studies to calibrate a model that accounts for radiation treatment combined with radiosensitizers. A nonlinear mixed effects approach was utilized where between-subject variability and inter-study variability were considered. Using the calibrated model, we ranked three different Ataxia telangiectasia-mutated inhibitors in terms of anticancer activity. The ranking was based on the Tumor Static Exposure (TSE) concept and primarily illustrated through TSE-curves.

RESULTS

The model described data well and the predicted number of eradicated tumors was in good agreement with experimental data. The efficacy of the radiosensitizers was evaluated for the median individual and the 95% population percentile. Simulations predicted that a total dose of 220 Gy (5 radiation sessions a week for 6 weeks) was required for 95% of tumors to be eradicated when radiation was given alone. When radiation was combined with doses that achieved at least 8 [Formula: see text] of each radiosensitizer in mouse blood, it was predicted that the radiation dose could be decreased to 50, 65, and 100 Gy, respectively, while maintaining 95% eradication.

CONCLUSIONS

A simulation-based method for calculating TSE-curves was developed, which provides more accurate predictions of tumor eradication than earlier, analytically derived, TSE-curves. The tool we present can potentially be used for radiosensitizer selection before proceeding to subsequent phases of the drug discovery and development process.

On tumoural growth and treatment under cellular dedifferentiation

Differentiated cancer cells may regain stem cell characteristics; however, the effects of such a cellular dedifferentiation on tumoural growth and treatment are currently understudied. Thus, we here extend a mathematical model of cancer stem cell (CSC) driven tumour growth to also include dedifferentiation. We show that dedifferentiation increases the likelihood of tumorigenesis and the speed of tumoural growth, both modulated by the proliferative potential of the non-stem cancer cells (NSCCs). We demonstrate that dedifferentiation also may lead to treatment evasion, especially when a treatment solely targets CSCs. Conversely, targeting both CSCs and NSCCs in parallel is shown to be more robust to dedifferentiation. Despite dedifferentiation, perturbing CSC-related parameters continues to exert the largest relative effect on tumoural growth; however, we show the existence of synergies between specific CSC- and NSCC-directed treatments which cause superadditive reductions of tumoural growth. Overall, our study demonstrates various effects of dedifferentiation on growth and treatment of tumoural lesions, and we anticipate our results to be helpful in guiding future molecular and clinical research on limiting tumoural growth in vivo.

Virtual clinical trials of anti-PD-1 and anti-CTLA-4 immunotherapy in advanced hepatocellular carcinoma using a quantitative systems pharmacology model

BACKGROUND

Hepatocellular carcinoma (HCC) is the most common form of primary liver cancer and is the third-leading cause of cancer-related death worldwide. Most patients with HCC are diagnosed at an advanced stage, and the median survival for patients with advanced HCC treated with modern systemic therapy is less than 2 years. This leaves the advanced stage patients with limited treatment options. Immune checkpoint inhibitors (ICIs) targeting programmed cell death protein 1 (PD-1) or its ligand, are widely used in the treatment of HCC and are associated with durable responses in a subset of patients. ICIs targeting cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) also have clinical activity in HCC. Combination therapy of nivolumab (anti-PD-1) and ipilimumab (anti-CTLA-4) is the first treatment option for HCC to be approved by Food and Drug Administration that targets more than one immune checkpoints.

METHODS

In this study, we used the framework of quantitative systems pharmacology (QSP) to perform a virtual clinical trial for nivolumab and ipilimumab in HCC patients. Our model incorporates detailed biological mechanisms of interactions of immune cells and cancer cells leading to antitumor response. To conduct virtual clinical trial, we generate virtual patient from a cohort of 5,000 proposed patients by extending recent algorithms from literature. The model was calibrated using the data of the clinical trial CheckMate 040 (ClinicalTrials.gov number, NCT01658878).

RESULTS

Retrospective analyses were performed for different immune checkpoint therapies as performed in CheckMate 040. Using machine learning approach, we predict the importance of potential biomarkers for immune blockade therapies.

CONCLUSIONS

This is the first QSP model for HCC with ICIs and the predictions are consistent with clinically observed outcomes. This study demonstrates that using a mechanistic understanding of the underlying pathophysiology, QSP models can facilitate patient selection and design clinical trials with improved success.

Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer

The promise of precision medicine has been limited by the pervasive resistance to many targeted therapies for cancer. Inferring the timing (i.e., pre-existing or acquired) and mechanism (i.e., drug-induced) of such resistance is crucial for designing effective new therapeutics. This paper studies cetuximab resistance in head and neck squamous cell carcinoma (HNSCC) using tumor volume data obtained from patient-derived tumor xenografts. We ask if resistance mechanisms can be determined from this data alone, and if not, what data would be needed to deduce the underlying mode(s) of resistance. To answer these questions, we propose a family of mathematical models, with each member of the family assuming a different timing and mechanism of resistance. We present a method for fitting these models to individual volumetric data, and utilize model selection and parameter sensitivity analyses to ask: which member(s) of the family of models best describes HNSCC response to cetuximab, and what does that tell us about the timing and mechanisms driving resistance? We find that along with time-course volumetric data to a single dose of cetuximab, the initial resistance fraction and, in some instances, dose escalation volumetric data are required to distinguish among the family of models and thereby infer the mechanisms of resistance. These findings can inform future experimental design so that we can best leverage the synergy of wet laboratory experimentation and mathematical modeling in the study of novel targeted cancer therapeutics.

Aiding early clinical drug development by elucidation of the relationship between tumor growth inhibition and survival in relapsed/refractory multiple myeloma patients

Early prognosis of clinical efficacy is an urgent need for oncology drug development. Herein, we systemically examined the quantitative approach of tumor growth inhibition (TGI) and survival modeling in the space of relapsed and refractory multiple myeloma (MM), aiming to provide insights into clinical drug development. Longitudinal serum M-protein and progression-free survival (PFS) data from three phase III studies (N = 1367) across six treatment regimens and different patient populations were leveraged. The TGI model successfully described the longitudinal M-protein data in patients with MM. The tumor inhibition and growth parameters were found to vary as per each study, likely due to the patient population and treatment regimen difference. Based on a parametric time-to-event model for PFS, M-protein reduction at week 4 was identified as a significant prognostic factor for PFS across the three studies. Other factors, including Eastern Cooperative Oncology Group performance status, prior anti-myeloma therapeutics, and baseline serum ß2-microglobulin level, were correlated with PFS as well. In conclusion, patient disease characteristics (i.e., baseline tumor burden and treatment lines) were important determinants of tumor inhibition and PFS in MM patients. M-protein change at week 4 was an early prognostic biomarker for PFS.

Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modeling of the delivery of radiotherapy and immunotherapy

Immunotherapy has become a fourth pillar in the treatment of brain tumors and, when combined with radiation therapy, may improve patient outcomes and reduce the neurotoxicity. As with other combination therapies, the identification of a treatment schedule that maximizes the synergistic effect of radiation- and immune-therapy is a fundamental challenge. Mechanism-based mathematical modeling is one promising approach to systematically investigate therapeutic combinations to maximize positive outcomes within a rigorous framework. However, successful clinical translation of model-generated combinations of treatment requires patient-specific data to allow the models to be meaningfully initialized and parameterized. Quantitative imaging techniques have emerged as a promising source of high quality, spatially and temporally resolved data for the development and validation of mathematical models. In this review, we will present approaches to personalize mechanism-based modeling frameworks with patient data, and then discuss how these techniques could be leveraged to improve brain cancer outcomes through patient-specific modeling and optimization of treatment strategies.

Simulating the behaviour of glioblastoma multiforme based on patient MRI during treatments

Glioblastoma multiforme is a brain cancer that still shows poor prognosis for patients despite the active research for new treatments. In this work, the goal is to model and simulate the evolution of tumour associated angiogenesis and the therapeutic response to glioblastoma multiforme. Multiple phenomena are modelled in order to fit different biological pathways, such as the cellular cycle, apoptosis, hypoxia or angiogenesis. This leads to a nonlinear system with 4 equations and 4 unknowns: the density of tumour cells, the [Formula: see text] concentration, the density of endothelial cells and the vascular endothelial growth factor concentration. This system is solved numerically on a mesh fitting the geometry of the brain and the tumour of a patient based on a 2D slice of MRI. We show that our numerical scheme is positive, and we give the energy estimates on the discrete solution to ensure its existence. The numerical scheme uses nonlinear control volume finite elements in space and is implicit in time. Numerical simulations have been done using the different standard treatments: surgery, chemotherapy and radiotherapy, in order to conform to the behaviour of a tumour in response to treatments according to empirical clinical knowledge. We find that our theoretical model exhibits realistic behaviours.

Reinforcement learning as an innovative model-based approach: Examples from precision dosing, digital health and computational psychiatry

Model-based approaches are instrumental for successful drug development and use. Anchored within pharmacological principles, through mathematical modeling they contribute to the quantification of drug response variability and enables precision dosing. Reinforcement learning (RL)-a set of computational methods addressing optimization problems as a continuous learning process-shows relevance for precision dosing with high flexibility for dosing rule adaptation and for coping with high dimensional efficacy and/or safety markers, constituting a relevant approach to take advantage of data from digital health technologies. RL can also support contributions to the successful development of digital health applications, recognized as key players of the future healthcare systems, in particular for reducing the burden of non-communicable diseases to society. RL is also pivotal in computational psychiatry-a way to characterize mental dysfunctions in terms of aberrant brain computations-and represents an innovative modeling approach forpsychiatric indications such as depression or substance abuse disorders for which digital therapeutics are foreseen as promising modalities.

Optimal Combinations of Chemotherapy and Radiotherapy in Low-Grade Gliomas: A Mathematical Approach

Low-grade gliomas (LGGs) are brain tumors characterized by their slow growth and infiltrative nature. Treatment options for these tumors are surgery, radiation therapy and chemotherapy. The optimal use of radiation therapy and chemotherapy is still under study. In this paper, we construct a mathematical model of LGG response to combinations of chemotherapy, specifically to the alkylating agent temozolomide and radiation therapy. Patient-specific parameters were obtained from longitudinal imaging data of the response of real LGG patients. Computer simulations showed that concurrent cycles of radiation therapy and temozolomide could provide the best therapeutic efficacy in-silico for the patients included in the study. The patient cohort was extended computationally to a set of 3000 virtual patients. This virtual cohort was subject to an in-silico trial in which matching the doses of radiotherapy to those of temozolomide in the first five days of each cycle improved overall survival over concomitant radio-chemotherapy according to RTOG 0424. Thus, the proposed treatment schedule could be investigated in a clinical setting to improve combination treatments in LGGs with substantial survival benefits.

Supermodeling in predictive diagnostics of cancer under treatment

Classical data assimilation (DA) techniques, synchronizing a computer model with observations, are highly demanding computationally, particularly, for complex over-parametrized cancer models. Consequently, current models are not sufficiently flexible to interactively explore various therapy strategies, and to become a key tool of predictive oncology. We show that, by using supermodeling, it is possible to develop a prediction/correction scheme that could attain the required time regimes and be directly used to support decision-making in anticancer therapies. A supermodel is an interconnected ensemble of individual models (sub-models); in this case, the variously parametrized baseline tumor models. The sub-model connection weights are trained from data, thereby incorporating the advantages of the individual models. Simultaneously, by optimizing the strengths of the connections, the sub-models tend to partially synchronize with one another. As a result, during the evolution of the supermodel, the systematic errors of the individual models partially cancel each other. We find that supermodeling allows for a radical increase in the accuracy and efficiency of data assimilation. We demonstrate that it can be considered as a meta-procedure for any classical parameter fitting algorithm, thus it represents the next - latent - level of abstraction of data assimilation. We conclude that supermodeling is a very promising paradigm that can considerably increase the quality of prognosis in predictive oncology.

The Effect of Radiotherapy on Diffuse Low-Grade Gliomas Evolution: Confronting Theory with Clinical Data

Diffuse low-grade gliomas are slowly growing tumors that always recur after treatment. In this paper, we revisit the modeling of the evolution of the tumor radius before and after the radiotherapy process and propose a novel model that is simple yet biologically motivated and that remedies some shortcomings of previously proposed ones. We confront this with clinical data consisting of time series of tumor radii from 43 patient records by using a stochastic optimization technique and obtain very good fits in all cases. Since our model describes the evolution of a tumor from the very first glioma cell, it gives access to the possible age of the tumor. Using the technique of profile likelihood to extract all of the information from the data, we build confidence intervals for the tumor birth age and confirm the fact that low-grade gliomas seem to appear in the late teenage years. Moreover, an approximate analytical expression of the temporal evolution of the tumor radius allows us to explain the correlations observed in the data.

Characterization and quantification of necrotic tissues and morphology in multicellular ovarian cancer tumor spheroids using optical coherence tomography

The three-dimensional (3D) tumor spheroid model is a critical tool for high-throughput ovarian cancer research and anticancer drug development in vitro. However, the 3D structure prevents high-resolution imaging of the inner side of the spheroids. We aim to visualize and characterize 3D morphological and physiological information of the contact multicellular ovarian tumor spheroids growing over time. We intend to further evaluate the distinctive evolutions of the tumor spheroid and necrotic tissue volumes in different cell numbers and determine the most appropriate mathematical model for fitting the growth of tumor spheroids and necrotic tissues. A label-free and noninvasive swept-source optical coherence tomography (SS-OCT) imaging platform was applied to obtain two-dimensional (2D) and 3D morphologies of ovarian tumor spheroids over 18 days. Ovarian tumor spheroids of two different initial cell numbers (5,000- and 50,000- cells) were cultured and imaged (each day) over the time of growth in 18 days. Four mathematical models (Exponential-Linear, Gompertz, logistic, and Boltzmann) were employed to describe the growth kinetics of the tumor spheroids volume and necrotic tissues. Ovarian tumor spheroids have different growth curves with different initial cell numbers and their growths contain different stages with various growth rates over 18 days. The volumes of 50,000-cells spheroids and the corresponding necrotic tissues are larger than that of the 5,000-cells spheroids. The formation of necrotic tissue in 5,000-cells numbers is slower than that in the 50,000-cells ones. Moreover, the Boltzmann model exhibits the best fitting performance for the growth of tumor spheroids and necrotic tissues. Optical coherence tomography (OCT) can serve as a promising imaging modality to visualize and characterize morphological and physiological features of multicellular ovarian tumor spheroids. The Boltzmann model integrating with 3D OCT data of ovarian tumor spheroids provides great potential for high-throughput cancer research in vitro and aiding in drug development.

Model-based evaluation of image-guided fractionated whole-brain radiation therapy in pediatric diffuse intrinsic pontine glioma xenografts

Radiation therapy (RT) is currently the standard treatment for diffuse intrinsic pontine glioma (DIPG), the most common cause of death in children with brain cancer. A pharmacodynamic model was developed to describe the radiation-induced tumor shrinkage and overall survival in mice bearing DIPG. CD1-nude mice were implanted in the brain cortex with luciferase-labeled patient-derived orthotopic xenografts of DIPG (SJDIPGx7 H3F3AWT / K27 M and SJDIPGx37 H3F3AK27M / K27M ). Mice were treated with image-guided whole-brain RT at 1 or 2 Gy/fraction 5-days-on 2-days-off for a cumulative dose of 20 or 54 Gy. Tumor progression was monitored with bioluminescent imaging (BLI). A mathematical model describing BLI and overall survival was developed with data from mice receiving 2 Gy/fraction and validated using data from mice receiving 1 Gy/fraction. BLI data were adequately fitted with a logistic tumor growth function and a signal distribution model with linear radiation-induced killing effect. A higher tumor growth rate in SJDIPGx37 versus SJDIPGx7 xenografts and a killing effect decreasing with higher tumor baseline (p < 0.0001) were identified. Cumulative radiation dose was suggested to inhibit the tumor growth rate according to a Hill function. Survival distribution was best described with a Weibull hazard function in which the hazard baseline was a continuous function of tumor BLI. Significant differences were further identified between DIPG cell lines and untreated versus treated mice. The model was adequately validated with mice receiving 1 Gy/fraction and will be useful in guiding future preclinical trials incorporating radiation and to support systemic combination therapies with RT.

Drug Exposure to Establish Pharmacokinetic-Response Relationships in Oncology

In the oncology field, understanding the relationship between the dose administered and the exerted effect is particularly important because of the narrow therapeutic index associated with anti-cancer drugs and the high interpatient variability. Therefore, in this review, we provide a critical perspective of the different methods of characterising treatment exposure in the oncology setting. The increasing number of modelling applications in oncology reflects the applicability and the impact of pharmacometrics on all phases of the drug development process and patient management as well. Pharmacometric modelling is a worthy component within the current paradigm of model-based drug development, but pharmacometric modelling techniques are also accessible for the clinician in the optimisation of current oncology therapies. Consequently, the application of population models in a hospital setting by generating close collaborations between physicians and pharmacometricians is highly recommended, providing a systematic means of developing and assessing model-based metrics as 'drivers' for various responses to treatments, which can then be evaluated as predictors for treatment success. Characterising the key determinants of variability in exposure is of particular importance for anticancer agents, as efficacy and toxicity are associated with exposure. We present the different strategies to describe and predict drug exposure that can be applied depending on the data available, with the objective of obtaining the most useful information in the patients' favour throughout the full drug cycle. Therefore, the objective of the present article is to review the different approaches used to characterise a patient's exposure to oncology drugs, which will result in a better understanding of the time course of the response and the magnitude of interpatient variability.

Tumor growth inhibition modeling of individual lesion dynamics and interorgan variability in HER2-negative breast cancer patients treated with docetaxel

Information on individual lesion dynamics and organ location are often ignored in pharmacometric modeling analyses of tumor response. Typically, the sum of their longest diameters is utilized. Herein, a tumor growth inhibition model was developed for describing the individual lesion time-course data from 183 patients with metastatic HER2-negative breast cancer receiving docetaxel. The interindividual variability (IIV), interlesion variability (ILV), and interorgan variability of parameters describing the lesion time-courses were evaluated. Additionally, a model describing the probability of new lesion appearance and a time-to-event model for overall survival (OS), were developed. Before treatment initiation, the lesions were largest in the soft tissues and smallest in the lungs, and associated with a significant IIV and ILV. The tumor growth rate was 2.6 times higher in the breasts and liver, compared with other metastatic sites. The docetaxel drug effect in the liver, breasts, and soft tissues was greater than or equal to 1.2 times higher compared with other organs. The time-course of the largest lesion, the presence of at least 3 liver lesions, and the time since study enrollment, increased the probability of new lesion appearance. New lesion appearance, along with the time to growth and time-course of the largest lesion at baseline, were identified as the best predictors of OS. This tumor modeling approach, incorporating individual lesion dynamics, provided a more complete understanding of heterogeneity in tumor growth and drug effect in different organs. Thus, there may be potential to tailor treatments based on lesion location, lesion size, and early lesion response to provide better clinical outcomes.

Volumetric analysis of IDH-mutant lower-grade glioma: a natural history study of tumor growth rates before and after treatment

BACKGROUND

Lower-grade gliomas (LGGs) with isocitrate dehydrogenase 1 and/or 2 (IDH1/2) mutations have long survival times, making evaluation of treatment efficacy difficult. We investigated the volumetric growth rate of IDH mutant gliomas before and after treatment with established glioma therapies to determine whether a significant change in growth rate could be documented and perhaps be used in the future to evaluate treatment response to investigational agents in LGG trials.

METHODS

In this multicenter retrospective study, 230 adult patients with IDH1/2 mutated LGGs (World Health Organization grade II or III) undergoing surgery, radiation, or chemotherapy for progressive non-enhancing tumor were identified. Subjects were required to have 3 MRI scans containing T2/fluid attenuated inversion recovery imaging spanning a minimum of 6 months prior to treatment. A mixed-effect model was used to estimate tumor growth prior to treatment. A subset of 95 patients who received chemotherapy, radiotherapy, or chemoradiotherapy and had 2 posttreatment imaging time points available were evaluated for change in pre- and posttreatment volumetric growth rates using a piecewise mixed model.

RESULTS

The pretreatment volumetric growth rate across all 230 patients was 27.37%/180 days (95% CI: [23.36%, 31.51%]). In the 95 patients with both pre- and posttreatment scans available, there was a significant difference in volumetric growth rates before (26.63%/180 days, 95% CI: [19.31%, 34.40%]) and after treatment (-15.24% /180 days, 95% CI: [-21.37%, -8.62%]) (P < 0.0001). The growth rates for patient subgroup with 1p/19q codeletion (N = 118) was significantly slower than the rate of the 1p/19q non-codeleted group (N = 68) (22.84% vs 35.49%, P = 0.0108).

CONCLUSION

In this study, we evaluated the growth rates of IDH mutant gliomas before and after standard therapy. Further study is needed to establish whether a change in growth rate is associated with patient survival and its use as a surrogate endpoint in clinical trials for IDH mutant LGGs.

Modeling CAR T-Cell Therapy with Patient Preconditioning

The Federal Drug Administration approved the first Chimeric Antigen Receptor T-cell (CAR T-cell) therapies for the treatment of several blood cancers in 2017, and efforts are underway to broaden CAR T technology to address other cancer types. Standard treatment protocols incorporate a preconditioning regimen of lymphodepleting chemotherapy prior to CAR T-cell infusion. However, the connection between preconditioning regimens and patient outcomes is still not fully understood. Optimizing patient preconditioning plans and reducing the CAR T-cell dose necessary for achieving remission could make therapy safer. In this paper, we test treatment regimens consisting of sequential administration of chemotherapy and CAR T-cell therapy on a system of differential equations that models the tumor-immune interaction. We use numerical simulations of treatment plans from within the scope of current medical practice to assess the effect of preconditioning plans on the success of CAR T-cell therapy. Model results affirm clinical observations that preconditioning can be crucial for most patients, not just to reduce side effects, but to even achieve remission at all. We demonstrate that preconditioning plans using the same CAR T-cell dose and the same total concentration of chemotherapy can lead to different patient outcomes due to different delivery schedules. Results from sensitivity analysis of the model parameters suggest that making small improvements in the effectiveness of CAR T-cells in attacking cancer cells will significantly reduce the minimum dose required for successful treatment. Our modeling framework represents a starting point for evaluating the efficacy of patient preconditioning in the context of CAR T-cell therapy.

Spatial mechanistic modeling for prediction of the growth of asymptomatic meningiomas

BACKGROUND AND OBJECTIVE

Mathematical modeling of tumor growth draws interest from the medical community as they have the potential to improve patients' care and the use of public health resources. The main objectives of this work are to model the growth of meningiomas - slow-growing benign tumors requiring extended imaging follow-up - and to predict tumor volume and shape at a later desired time using only two times examinations.

METHODS

We develop two variants of a 3D partial differential system of equations (PDE) which yield after a spatial integration systems of ordinary differential equations (ODE) that relate tumor volume with time. Estimation of models parameters is a crucial step to obtain a personalized model for a patient that can be used for descriptive or predictive purposes. As PDE and ODE systems share the same parameters, they are both estimated by fitting the ODE systems to the tumor volumes obtained from MRI examinations acquired at different times. A population approach allows to compensate for sparse sampling times and measurement uncertainties by constraining the variability of the parameters in the population.

RESULTS

Description capabilities of the models are investigated in 39 patients with benign asymptomatic meningiomas who had had at least three surveillance MRI examinations. The two models can fit to the data accurately and more realistically than a naive linear regression. Prediction performances are validated for 33 patients using a population approach. Mean relative errors in volume predictions are less than 10% with ODE systems versus 12.5% with the naive linear model using only two times examinations. Concerning the shape, the mean Sørensen-Dice coefficients are 85% with the PDE systems in a subset of 10 representative patients.

CONCLUSIONS

Our strategy - based on personalization of mathematical model - provides a good insight on meningioma growth and may help decide whether to extend the follow-up or to treat the tumor.

Radial basis function-generated finite difference scheme for simulating the brain cancer growth model under radiotherapy in various types of computational domains

BACKGROUND AND OBJECTIVES

We extend the original mathematical model, i.e., Swanson's reaction-diffusion equation to the surfaces with no boundary, and we find a new numerical method based on a meshless approach for solving numerically Swanson's reaction-diffusion model in the square and on the sphere.

METHODS

To solve numerically the Swanson's reaction-diffusion model and its extension version, a collocation meshless technique, namely radial basis function-generated finite difference (RBF-FD) scheme is employed for approximating the spatial variables in the square domain and on the sphere, respectively. Also, to approximate the time variable of the studied models, a first-order semi-implicit backward Euler scheme is used. The resulting fully discrete scheme is a linear system of algebraic equations per time step that is solved via the biconjugate gradient stabilized (BiCGSTAB) iterative algorithm with a zero-fill incomplete lower-upper (ILU) preconditioner.

RESULTS

The numerical simulations show the growth of untreated and treated brain tumors with radiotherapy using estimated and clinical data (given from magnetic resonance imaging (MRI) scans of patients). Moreover, the results reported here can be used for improving the treatment strategies of the invasive brain tumor.

CONCLUSIONS

Using the developed numerical scheme in this paper, we can simulate the behavior of the invasive form of brain tumor response to radiotherapy. Also, we can see the effects of radiation response on the brain tumor cell concentration of individual patients. The proposed meshless technique, which is applied for solving numerically the studied model, does not depend on any background mesh or triangulation for approximation in comparison with mesh-dependent methods. Moreover, we apply this technique to the sphere via any set of distributed points easily.

Artificial Intelligence and Mechanistic Modeling for Clinical Decision Making in Oncology

The amount of "big" data generated in clinical oncology, whether from molecular, imaging, pharmacological, or biological origin, brings novel challenges. To mine efficiently this source of information, mathematical models able to produce predictive algorithms and simulations are required, with applications for diagnosis, prognosis, drug development, or prediction of the response to therapy. Such mathematical and computational constructs can be subdivided into two broad classes: biologically agnostic, statistical models using artificial intelligence techniques, and physiologically based, mechanistic models. In this review, recent advances in the applications of such methods in clinical oncology are outlined. These include machine learning applied to big data (omics, imaging, or electronic health records), pharmacometrics and quantitative systems pharmacology, as well as tumor kinetics and metastasis modeling. Focus is set on studies with high potential of clinical translation, and particular attention is given to cancer immunotherapy. Perspectives are given in terms of combinations of the two approaches: "mechanistic learning."

Different ODE models of tumor growth can deliver similar results

BACKGROUND

Simeoni and colleagues introduced a compartmental model for tumor growth that has proved quite successful in modeling experimental therapeutic regimens in oncology. The model is based on a system of ordinary differential equations (ODEs), and accommodates a lag in therapeutic action through delay compartments. There is some ambiguity in the appropriate number of delay compartments, which we examine in this note.

METHODS

We devised an explicit delay differential equation model that reflects the main features of the Simeoni ODE model. We evaluated the original Simeoni model and this adaptation with a sample data set of mammary tumor growth in the FVB/N-Tg(MMTVneu)202Mul/J mouse model.

RESULTS

The experimental data evinced tumor growth heterogeneity and inter-individual diversity in response, which could be accommodated statistically through mixed models. We found little difference in goodness of fit between the original Simeoni model and the delay differential equation model relative to the sample data set.

CONCLUSIONS

One should exercise caution if asserting a particular mathematical model uniquely characterizes tumor growth curve data. The Simeoni ODE model of tumor growth is not unique in that alternative models can provide equivalent representations of tumor growth.

Model-Informed Artificial Intelligence: Reinforcement Learning for Precision Dosing

The availability of multidimensional data together with the development of modern techniques for data analysis represent an exceptional opportunity for clinical pharmacology. Data science-defined in this special issue as the novel approaches to the collection, aggregation, and analysis of data-can significantly contribute to characterize drug-response variability at the individual level, thus enabling clinical pharmacology to become a critical contributor to personalized healthcare through precision dosing. We propose a minireview of methodologies for achieving precision dosing with a focus on an artificial intelligence technique called reinforcement learning, which is currently used for individualizing dosing regimen in patients with life-threatening diseases. We highlight the interplay of such techniques with conventional pharmacokinetic/pharmacodynamic approaches and discuss applicability in drug research and early development.

From cells to tissue: How cell scale heterogeneity impacts glioblastoma growth and treatment response

Glioblastomas are aggressive primary brain tumors known for their inter- and intratumor heterogeneity. This disease is uniformly fatal, with intratumor heterogeneity the major reason for treatment failure and recurrence. Just like the nature vs nurture debate, heterogeneity can arise from intrinsic or environmental influences. Whilst it is impossible to clinically separate observed behavior of cells from their environmental context, using a mathematical framework combined with multiscale data gives us insight into the relative roles of variation from different sources. To better understand the implications of intratumor heterogeneity on therapeutic outcomes, we created a hybrid agent-based mathematical model that captures both the overall tumor kinetics and the individual cellular behavior. We track single cells as agents, cell density on a coarser scale, and growth factor diffusion and dynamics on a finer scale over time and space. Our model parameters were fit utilizing serial MRI imaging and cell tracking data from ex vivo tissue slices acquired from a growth-factor driven glioblastoma murine model. When fitting our model to serial imaging only, there was a spectrum of equally-good parameter fits corresponding to a wide range of phenotypic behaviors. When fitting our model using imaging and cell scale data, we determined that environmental heterogeneity alone is insufficient to match the single cell data, and intrinsic heterogeneity is required to fully capture the migration behavior. The wide spectrum of in silico tumors also had a wide variety of responses to an application of an anti-proliferative treatment. Recurrent tumors were generally less proliferative than pre-treatment tumors as measured via the model simulations and validated from human GBM patient histology. Further, we found that all tumors continued to grow with an anti-migratory treatment alone, but the anti-proliferative/anti-migratory combination generally showed improvement over an anti-proliferative treatment alone. Together our results emphasize the need to better understand the underlying phenotypes and tumor heterogeneity present in a tumor when designing therapeutic regimens.

Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors

Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported population-level correlation between the Gompertz parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a reduced Gompertz function consisting of a single individual parameter (and one population parameter). Leveraging the population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.

Progress and Opportunities to Advance Clinical Cancer Therapeutics Using Tumor Dynamic Models

There is a need for new approaches and endpoints in oncology drug development, particularly with the advent of immunotherapies and the multiple drug combinations under investigation. Tumor dynamics modeling, a key component to oncology "model-informed drug development," has shown a growing number of applications and a broader adoption by drug developers and regulatory agencies in the past years to support drug development and approval in a variety of ways. Tumor dynamics modeling is also being investigated in personalized cancer therapy approaches. These models and applications are reviewed and discussed, as well as the limitations and issues open for further investigations. A close collaboration between stakeholders like clinical investigators, statisticians, and pharmacometricians is warranted to advance clinical cancer therapeutics.

Radiation protraction schedules for low-grade gliomas: a comparison between different mathematical models

We optimize radiotherapy (RT) administration strategies for treating low-grade gliomas. Specifically, we consider different tumour growth laws, both with and without spatial effects. In each scenario, we find the optimal treatment in the sense of maximizing the overall survival time of a virtual low-grade glioma patient, whose tumour progresses according to the examined growth laws. We discover that an extreme protraction therapeutic strategy, which amounts to substantially extending the time interval between RT sessions, may lead to better tumour control. The clinical implications of our results are also presented.

Towards quantitative imaging biomarkers of tumor dissemination: A multi-scale parametric modeling of multiple myeloma

The advent of medical imaging and automatic image analysis is bringing the full quantitative assessment of lesions and tumor burden at every clinical examination within reach. This opens avenues for the development and testing of functional disease models, as well as their use in the clinical practice for personalized medicine. In this paper, we introduce a Bayesian statistical framework, based on mixed-effects models, to quantitatively test and learn functional disease models at different scales, on population longitudinal data. We also derive an effective mathematical model for the crossover between initially detected lesions and tumor dissemination, based on the Iwata-Kawasaki-Shigesada model. We finally propose to leverage this descriptive disease progression model into model-aware biomarkers for personalized risk-assessment, taking all available examinations and relevant covariates into account. As a use case, we study Multiple Myeloma, a disseminated plasma cell cancer, in which proper diagnostics is essential, to differentiate frequent precursor state without end-organ damage from the rapidly developing disease requiring therapy. After learning the best biological models for local lesion growth and global tumor burden evolution on clinical data, and computing corresponding population priors, we use individual model parameters as biomarkers, and can study them systematically for correlation with external covariates, such as sex or location of the lesion. On our cohort of 63 patients with smoldering Multiple Myeloma, we show that they perform substantially better than other radiological criteria, to predict progression into symptomatic Multiple Myeloma. Our study paves the way for modeling disease progression patterns for Multiple Myeloma, but also for other metastatic and disseminated tumor growth processes, and for analyzing large longitudinal image data sets acquired in oncological imaging. It shows the unprecedented potential of model-based biomarkers for better and more personalized treatment decisions and deserves being validated on larger cohorts to establish its role in clinical decision making.

A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model‐based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model‐based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.

Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas

Here we put forward a mathematical model describing the response of low-grade (WHO grade II) oligodendrogliomas (LGO) to temozolomide (TMZ). The model describes the longitudinal volumetric dynamics of tumor response to TMZ of a cohort of 11 LGO patients treated with TMZ. After finding patient-specific parameters, different therapeutic strategies were tried computationally on the 'in-silico twins' of those patients. Chemotherapy schedules with larger-than-standard rest periods between consecutive cycles had either the same or better long-term efficacy than the standard 28-day cycles. The results were confirmed in a large trial of 2000 virtual patients. These long-cycle schemes would also have reduced toxicity and defer the appearance of resistances. On the basis of those results, a combination scheme consisting of five induction TMZ cycles given monthly plus 12 maintenance cycles given every three months was found to provide substantial survival benefits for the in-silico twins of the 11 LGO patients (median 5.69 years, range: 0.67 to 68.45 years) and in a large virtual trial including 2000 patients. We used 220 sets of experiments in-silico to show that a clinical trial incorporating 100 patients per arm (standard intensive treatment versus 5 + 12 scheme) could demonstrate the superiority of the novel scheme after a follow-up period of 10 years. Thus, the proposed treatment plan could be the basis for a standardized TMZ treatment for LGO patients with survival benefits.

Understanding the relationship between cell death and tissue shrinkage via a stochastic agent-based model

Cell death, a process which can occur both naturally and in response to insult, is both a complex and diverse phenomenon. Under some circumstances, dying cells actively contract and cause their neighbors to rearrange and maintain tissue integrity. Under other circumstances, dying cells leave behind gaps, which results in tissue separation. A better understanding of how the cellular scale features of cell death manifest on the population scale has implications ranging from morphogenesis to tumor response to treatment. However, the mechanistic relationship between cell death and population scale shrinkage is not well understood, and computational methods for studying these relationships are not well established. Here we propose a mechanically robust agent-based cell model designed to capture the implications of cell death on the population scale. In our agent-based model, algorithmic rules applied on the cellular level emerge on the population scale where their effects are quantified. To better quantify model uncertainty and parameter interactions, we implement a recently developed technique for conducting a variance-based sensitivity analysis on the stochastic model. From this analysis and subsequent investigation, we find that cellular scale shrinkage has the largest influence of all model parameters tested, and that by adjusting cellular scale shrinkage population shrinkage varies widely even across simulations which contain the same fraction of dying cells. We anticipate that the methods and results presented here are a starting point for significant future investigation toward quantifying the implications of different mechanisms of cell death on population and tissue scale behavior.

Data-Driven Predictive Models of Diffuse Low-Grade Gliomas Under Chemotherapy

Diffuse low-grade gliomas (DLGG) are brain tumors of young adults. They affect the quality of life of the inflicted patients and, if untreated, they evolve into higher grade tumors where the patient's life is at risk. Therapeutic management of DLGGs includes chemotherapy, and tumor diameter is particularly important for the follow-up of DLGG evolution. In fact, the main clinical basis for deciding whether to continue chemotherapy is tumor diameter growth rate. In order to reliably assist the doctors in selecting the most appropriate time to stop treatment, we propose a novel clinical decision support system. Based on two mathematical models, one linear and one exponential, we are able to predict the evolution of tumor diameter under Temozolomide chemotherapy as a first treatment and thus offer a prognosis on when to end it. We present the results of an implementation of these models on a database of 42 patients from Nancy and Montpellier University Hospitals. In this database, 38 patients followed the linear model and four patients followed the exponential model. From a training data set of a minimal size of five, we are able to predict the next tumor diameter with high accuracy. Thanks to the corresponding prediction interval, it is possible to check if the new observation corresponds to the predicted diameter. If the observed diameter is within the prediction interval, the clinician is notified that the trend is within a normal range. Otherwise, the practitioner is alerted of a significant change in tumor diameter.

Model-Based Evaluation of Radiation and Radiosensitizing Agents in Oncology

Radiotherapy is one of the major therapy forms in oncology, and combination therapies involving radiation and chemical compounds can yield highly effective tumor eradication. In this paper, we develop a tumor growth inhibition model for combination therapy with radiation and radiosensitizing agents. Moreover, we extend previous analyses of drug combinations by introducing the tumor static exposure (TSE) curve. The TSE curve for radiation and radiosensitizer visualizes exposure combinations sufficient for tumor regression. The model and TSE analysis are then tested on xenograft data. The calibrated model indicates that the highest dose of combination therapy increases the time until tumor regrowth 10-fold. The TSE curve shows that with an average radiosensitizer concentration of 1.0 μg/mL the radiation dose can be decreased from 2.2 Gy to 0.7 Gy. Finally, we successfully predict the effect of a clinically relevant treatment schedule, which contributes to validating both the model and the TSE concept.

Non-standard radiotherapy fractionations delay the time to malignant transformation of low-grade gliomas

Grade II gliomas are slowly growing primary brain tumors that affect mostly young patients. Cytotoxic therapies (radiotherapy and/or chemotherapy) are used initially only for patients having a bad prognosis. These therapies are planned following the “maximum dose in minimum time” principle, i. e. the same schedule used for high-grade brain tumors in spite of their very different behavior. These tumors transform after a variable time into high-grade gliomas, which significantly decreases the patient’s life expectancy. In this paper we study mathematical models describing the growth of grade II gliomas in response to radiotherapy. We find that protracted metronomic fractionations, i.e. therapeutical schedules enlarging the time interval between low-dose radiotherapy fractions, may lead to a better tumor control without an increase in toxicity. Other non-standard fractionations such as protracted or hypoprotracted schemes may also be beneficial. The potential survival improvement depends on the tumor’s proliferation rate and can be even of the order of years. A conservative metronomic scheme, still being a suboptimal treatment, delays the time to malignant progression by at least one year when compared to the standard scheme.

Drug-disease modeling in the pharmaceutical industry - where mechanistic systems pharmacology and statistical pharmacometrics meet

Modeling & simulation (M&S) methodologies are established quantitative tools, which have proven to be useful in supporting the research, development (R&D), regulatory approval, and marketing of novel therapeutics. Applications of M&S help design efficient studies and interpret their results in context of all available data and knowledge to enable effective decision-making during the R&D process. In this mini-review, we focus on two sets of modeling approaches: population-based models, which are well-established within the pharmaceutical industry today, and fall under the discipline of clinical pharmacometrics (PMX); and systems dynamics models, which encompass a range of models of (patho-)physiology amenable to pharmacological intervention, of signaling pathways in biology, and of substance distribution in the body (today known as physiologically-based pharmacokinetic models) - which today may be collectively referred to as quantitative systems pharmacology models (QSP). We next describe the convergence - or rather selected integration - of PMX and QSP approaches into 'middle-out' drug-disease models, which retain selected mechanistic aspects, while remaining parsimonious, fit-for-purpose, and able to address variability and the testing of covariates. We further propose development opportunities for drug-disease systems models, to increase their utility and applicability throughout the preclinical and clinical spectrum of pharmaceutical R&D.

In Vitro Radiosensitizing Effects of Temozolomide on U87MG Cell Lines of Human Glioblastoma Multiforme

BACKGROUND

Glioma is the most common primary brain tumor with poor prognosis. Temozolomide (TMZ) has been used with irradiation (IR) to treat gliomas. The aim of the present study was to evaluate the cytotoxic and radiosensitizing effect of TMZ when combined with high-dose and high-dose rate of gamma irradiation in vitro.

METHODS

Two 'U87MG' cell lines and skin fibroblast were cultured and assigned to five groups for 24, 48, and 72 hours. The groups were namely, TMZ group (2000 μM/L), IR group (5 Gy), TMZ plus IR group, control group, and control solvent group. MTT assay was applied to evaluate cell viability. Data were analyzed with SPSS 21.0 software using one-way ANOVA and Kruskal-Wallis test. P<0.05 were considered statistically significant.

RESULTS

The slope of growth curve U87MG cells in semi-logarithmic scale was equal to 27.36±0.89 hours. The viability of cells was determined for different TMZ and IR treatment groups. In terms of cell viability, there were no significant differences between the control and control solvent groups (P=0.35) and between treated group by IR (5 Gy) alone and TMZ (2000 µM/ml) alone (P=0.15). Data obtained for the cell viability of combined TMZ plus IR in both cell lines compared to TMZ or IR treated group alone showed a significant difference (P=0.002).

CONCLUSION

The evaluation of cells viability showed that TMZ in combination with IR on glioma cells led to a significant radiosensitivity compared to IR alone.

Predictive models for diffuse low-grade glioma patients under chemotherapy

Diffuse low-grade gliomas are rare primitive cerebral tumours of adults. These tumors progress continuously over time and then turn to a higher grade of malignancy associated with neurological disability, leading ultimately to death. Tumour size is one of the most important prognostic factors. Thus, it is of great importance to be able to assess the volume of the tumor during the patients' monitoring. MRI is nowadays the recommended modality to achieve this. Furthermore, if surgery remains the first option for diffuse low-grade gliomas, chemotherapy is increasingly used (before or after a possible surgery). However, crucial and difficult questions remain to be answered: identifying subgroups of patients who could benefit from chemotherapy, determining the best time to initiate chemotherapy, defining the duration of chemotherapy and evaluating the optimal time to perform surgery, or otherwise radiotherapy. In this study, we propose to help clinicians in decision-making, by designing new predictive models dedicated to the evolution of the diameter of the tumor. Two proposed statistical models (linear and exponential) have been validated on a database of 16 patients whose temozolomide-based chemotherapy lasted between 14 and 32 months, with an average duration of 22.8 months. The selection of the most appropriate model has been achieved with the corrected Akaike's Information Criterion. The results are very promising, with coefficients of determination varying from 0.79 to 0.97 with an average value of 0.90 for the linear model. This shows it is possible to alert the clinician to a change in the tumor diameter's dynamics.

Analysis of temozolomide resistance in low-grade gliomas using a mechanistic mathematical model

Understanding how tumors develop resistance to chemotherapy is a major issue in oncology. When treated with temozolomide (TMZ), an oral alkylating chemotherapy drug, most low-grade gliomas (LGG) show an initial volume decrease but this effect is rarely long lasting. In addition, it has been suggested that TMZ may drive tumor progression in a subset of patients as a result of acquired resistance. Using longitudinal tumor size measurements from 121 patients, the aim of this study was to develop a semi-mechanistic mathematical model to determine whether resistance of LGG to TMZ was more likely to result from primary and/or from chemotherapy-induced acquired resistance that may contribute to tumor progression. We applied the model to a series of patients treated upfront with TMZ (n = 109) or PCV (procarbazine, CCNU, vincristine) chemotherapy (n = 12) and used a population mixture approach to classify patients according to the mechanism of resistance most likely to explain individual tumor growth dynamics. Our modeling results predicted acquired resistance in 51% of LGG treated with TMZ. In agreement with the different biological effects of nitrosoureas, none of the patients treated with PCV were classified in the acquired resistance group. Consistent with the mutational analysis of recurrent LGG, analysis of growth dynamics using mathematical modeling suggested that in a subset of patients, TMZ might paradoxically contribute to tumor progression as a result of chemotherapy-induced resistance. Identification of patients at risk of developing acquired resistance is warranted to better define the role of TMZ in LGG.