Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach

Tumor growth for remodeling process: A 2D approach

This paper aims to present a comprehensive framework for coupling tumor-bone remodeling processes in a 2-dimensional geometry. This is achieved by introducing a bio-inspired damage that represents the growing tumor, which subsequently affects the main populations involved in the remodeling process, namely, osteoclasts, osteoblasts, and bone tissue. The model is constructed using a set of differential equations based on the Komarova's and Ayati's models, modified to incorporate the bio-inspired damage that may result in tumor mass formation. Three distinct models were developed. The first two models are based on the Komarova's governing equations, with one demonstrating an osteolytic behavior and the second one an osteoblastic model. The third model is a variation of Ayati's model, where the bio-inspired damage is induced through the paracrine and autocrine parameters, exhibiting an osteolytic behavior. The obtained results are consistent with existing literature, leading us to believe that our in-silico experiments will serve as a cornerstone for paving the way towards targeted interventions and personalized treatment strategies, ultimately improving the quality of life for those affected by these conditions.

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.

Simulating tumor volume dynamics in response to radiotherapy: Implications of model selection

From the beginning of the usage of radiotherapy (RT) for cancer treatment, mathematical modeling has been integral to understanding radiobiology and for designing treatment approaches and schedules. There has been extensive modeling of response to RT with the inclusion of various degrees of biological complexity. In this study, we compare three models of tumor volume dynamics: (1) exponential growth with RT directly reducing tumor volume, (2) logistic growth with direct tumor volume reduction, and (3) logistic growth with RT reducing the tumor carrying capacity with the objective of understanding the implications of model selection and informing the process of model calibration and parameterization. For all three models, we: examined the rates of change in tumor volume during and RT treatment course; performed parameter sensitivity and identifiability analyses; and investigated the impact of the parameter sensitivity on the tumor volume trajectories. In examining the tumor volume dynamics trends, we coined a new metric - the point of maximum reduction of tumor volume (MRV) - to quantify the magnitude and timing of the expected largest impact of RT during a treatment course. We found distinct timing differences in MRV, dependent on model selection. The parameter identifiability and sensitivity analyses revealed the interdependence of the different model parameters and that it is only possible to independently identify tumor growth and radiation response parameters if the underlying tumor growth rate is sufficiently large. Ultimately, the results of these analyses help us to better understand the implications of model selection while simultaneously generating falsifiable hypotheses about MRV timing that can be tested on longitudinal measurements of tumor volume from pre-clinical or clinical data with high acquisition frequency. Although, our study only compares three particular models, the results demonstrate that caution is necessary in selecting models of response to RT, given the artifacts imposed by each model.

Predicting the spatio-temporal response of recurrent glioblastoma treated with rhenium-186 labelled nanoliposomes

Rhenium-186 (186Re) labeled nanoliposome (RNL) therapy for recurrent glioblastoma patients has shown promise to improve outcomes by locally delivering radiation to affected areas. To optimize the delivery of RNL, we have developed a framework to predict patient-specific response to RNL using image-guided mathematical models.

Methods

We calibrated a family of reaction-diffusion type models with multi-modality imaging data from ten patients (NCR01906385) to predict the spatio-temporal dynamics of each patient's tumor. The data consisted of longitudinal magnetic resonance imaging (MRI) and single photon emission computed tomography (SPECT) to estimate tumor burden and local RNL activity, respectively. The optimal model from the family was selected and used to predict future growth. A simplified version of the model was used in a leave-one-out analysis to predict the development of an individual patient's tumor, based on cohort parameters.

Results

Across the cohort, predictions using patient-specific parameters with the selected model were able to achieve Spearman correlation coefficients (SCC) of 0.98 and 0.93 for tumor volume and total cell number, respectively, when compared to the measured data. Predictions utilizing the leave-one-out method achieved SCCs of 0.89 and 0.88 for volume and total cell number across the population, respectively.

Conclusion

We have shown that patient-specific calibrations of a biology-based mathematical model can be used to make early predictions of response to RNL therapy. Furthermore, the leave-one-out framework indicates that radiation doses determined by SPECT can be used to assign model parameters to make predictions directly following the conclusion of RNL treatment.

Statement of Significance

This manuscript explores the application of computational models to predict response to radionuclide therapy in glioblastoma. There are few, to our knowledge, examples of mathematical models used in clinical radionuclide therapy. We have tested a family of models to determine the applicability of different radiation coupling terms for response to the localized radiation delivery. We show that with patient-specific parameter estimation, we can make accurate predictions of future glioblastoma response to the treatment. As a comparison, we have shown that population trends in response can be used to forecast growth from the moment the treatment has been delivered.In addition to the high simulation and prediction accuracy our modeling methods have achieved, the evaluation of a family of models has given insight into the response dynamics of radionuclide therapy. These dynamics, while different than we had initially hypothesized, should encourage future imaging studies involving high dosage radiation treatments, with specific emphasis on the local immune and vascular response.

Modelling microtube driven invasion of glioma

Malignant gliomas are notoriously invasive, a major impediment against their successful treatment. This invasive growth has motivated the use of predictive partial differential equation models, formulated at varying levels of detail, and including (i) "proliferation-infiltration" models, (ii) "go-or-grow" models, and (iii) anisotropic diffusion models. Often, these models use macroscopic observations of a diffuse tumour interface to motivate a phenomenological description of invasion, rather than performing a detailed and mechanistic modelling of glioma cell invasion processes. Here we close this gap. Based on experiments that support an important role played by long cellular protrusions, termed tumour microtubes, we formulate a new model for microtube-driven glioma invasion. In particular, we model a population of tumour cells that extend tissue-infiltrating microtubes. Mitosis leads to new nuclei that migrate along the microtubes and settle elsewhere. A combination of steady state analysis and numerical simulation is employed to show that the model can predict an expanding tumour, with travelling wave solutions led by microtube dynamics. A sequence of scaling arguments allows us reduce the detailed model into simpler formulations, including models falling into each of the general classes (i), (ii), and (iii) above. This analysis allows us to clearly identify the assumptions under which these various models can be a posteriori justified in the context of microtube-driven glioma invasion. Numerical simulations are used to compare the various model classes and we discuss their advantages and disadvantages.

A systematic review and meta-analysis of stereotactic radiosurgery as a primary treatment in fast-growing vestibular schwannomas

BACKGROUND

Stereotactic radiosurgery has been shown to be an effective method of managing vestibular schwannomas. The primary aim here is to establish the impact of pre-treatment fast-growing vestibular schwannomas on the efficacy of stereotactic radiosurgery.

METHODS

PubMed, Medline and Embase databases were used. The ROBINS-I ('Risk Of Bias In Non-randomised Studies - of Interventions') tool was utilised to assess for risk of bias. Proportionate meta-analysis and sub-analysis for fast-growing tumours were performed to explore the success rate of stereotactic radiosurgery in stabilising or decreasing the tumour burden in vestibular schwannomas.

RESULTS

Four moderate risk studies were included in the analysis. Overall, 91 per cent (95 per cent confidence interval = 0.83-0.97, p < 0.01, I2 = 80 per cent) of the tumours demonstrated successful size reduction or stabilisation following stereotactic radiosurgery. Nevertheless, the efficacy of stereotactic radiosurgery in reducing or stabilising fast-growing vestibular schwannomas decreased by 79 per cent (95 per cent confidence interval = 0.64-0.91, p = 0.11, I2 = 62 per cent).

CONCLUSION

Stereotactic radiosurgery has a statistically significant success rate in stabilising or decreasing the vestibular schwannoma size. This success rate is diminished in fast-growing vestibular schwannomas.

Quantifying the Growth of Glioblastoma Tumors Using Multimodal MRI Brain Images

Predicting the eventual volume of tumor cells, that might proliferate from a given tumor, can help in cancer early detection and medical procedure planning to prevent their migration to other organs. In this work, a new statistical framework is proposed using Bayesian techniques for detecting the eventual volume of cells expected to proliferate from a glioblastoma (GBM) tumor. Specifically, the tumor region was first extracted using a parallel image segmentation algorithm. Once the tumor region was determined, we were interested in the number of cells that could proliferate from this tumor until its survival time. For this, we constructed the posterior distribution of the tumor cell numbers based on the proposed likelihood function and a certain prior volume. Furthermore, we extended the detection model and conducted a Bayesian regression analysis by incorporating radiomic features to discover those non-tumor cells that remained undetected. The main focus of the study was to develop a time-independent prediction model that could reliably predict the ultimate volume a malignant tumor of the fourth-grade severity could attain and which could also determine if the incorporation of the radiomic properties of the tumor enhanced the chances of no malignant cells remaining undetected.

Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations

Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but its use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here, we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials.

Predicting regrowth of low-grade gliomas after radiotherapy

Diffuse low grade gliomas are invasive and incurable brain tumors that inevitably transform into higher grade ones. A classical treatment to delay this transition is radiotherapy (RT). Following RT, the tumor gradually shrinks during a period of typically 6 months to 4 years before regrowing. To improve the patient’s health-related quality of life and help clinicians build personalized follow-ups, one would benefit from predictions of the time during which the tumor is expected to decrease. The challenge is to provide a reliable estimate of this regrowth time shortly after RT (i.e. with few data), although patients react differently to the treatment. To this end, we analyze the tumor size dynamics from a batch of 20 high-quality longitudinal data, and propose a simple and robust analytical model, with just 4 parameters. From the study of their correlations, we build a statistical constraint that helps determine the regrowth time even for patients for which we have only a few measurements of the tumor size. We validate the procedure on the data and predict the regrowth time at the moment of the first MRI after RT, with precision of, typically, 6 months. Using virtual patients, we study whether some forecast is still possible just three months after RT. We obtain some reliable estimates of the regrowth time in 75% of the cases, in particular for all “fast-responders”. The remaining 25% represent cases where the actual regrowth time is large and can be safely estimated with another measurement a year later. These results show the feasibility of making personalized predictions of the tumor regrowth time shortly after RT.

Deep learning characterization of brain tumours with diffusion weighted imaging

Glioblastoma multiforme (GBM) is one of the most deadly forms of cancer. Methods of characterizing these tumours are valuable for improving predictions of their progression and response to treatment. A mathematical model called the proliferation-invasion (PI) model has been used extensively in the literature to model the growth of these tumours, though it relies on known values of two key parameters: the tumour cell diffusivity and proliferation rate. Unfortunately, these parameters are difficult to estimate in a patient-specific manner, making personalized tumour forecasting challenging. In this paper, we develop and apply a deep learning model capable of making accurate estimates of these key GBM-characterizing parameters while simultaneously producing a full prediction of the tumour progression curve. Our method uses two sets of multi sequence MRI in order to produce estimations and relies on a preprocessing pipeline which includes brain tumour segmentation and conversion to tumour cellularity. We first apply our deep learning model to synthetic tumours to showcase the model's capabilities and identify situations where prediction errors are likely to occur. We then apply our model to a clinical dataset consisting of five patients diagnosed with GBM. For all patients, we derive evidence-based estimates for each of the PI model parameters and predictions for the future progression of the tumour, along with estimates of the parameter uncertainties. Our work provides a new, easily generalizable method for the estimation of patient-specific tumour parameters, which can be built upon to aid physicians in designing personalized treatments.

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.

Deep Learning for Reaction-Diffusion Glioma Growth Modeling: Towards a Fully Personalized Model?

Simple Summary

Mathematical tumor growth models have been proposed for decades to capture the growth of gliomas, an aggressive form of brain tumor. However, the estimation of the tumor cell-density distribution at diagnosis and model parameters from partial observations provided by magnetic resonance imaging are ill-posed problems. In this work, we propose a deep learning-based approach to address these problems. 1200 synthetic tumors are first generated using the mathematical model over brain geometries of 6 volunteers. Two deep convolutional neural networks are then trained to (i) reconstruct a whole tumor cell-density distribution and (ii) evaluate the model parameters from partial observations provided in the form of threshold-like imaging contours, with state-of-the-art results. From the estimated cell-density distribution and parameter values, the spatio-temporal evolution of the tumor can ultimately be accurately captured by the mathematical model. Such an approach could be of great interest for glioma characterization and therapy planning.

Abstract

Reaction-diffusion models have been proposed for decades to capture the growth of gliomas, the most common primary brain tumors. However, ill-posedness of the initialization at diagnosis time and parameter estimation of such models have restrained their clinical use as a personalized predictive tool. In this work, we investigate the ability of deep convolutional neural networks (DCNNs) to address commonly encountered pitfalls in the field. Based on 1200 synthetic tumors grown over real brain geometries derived from magnetic resonance (MR) data of six healthy subjects, we demonstrate the ability of DCNNs to reconstruct a whole tumor cell-density distribution from only two imaging contours at a single time point. With an additional imaging contour extracted at a prior time point, we also demonstrate the ability of DCNNs to accurately estimate the individual diffusivity and proliferation parameters of the model. From this knowledge, the spatio-temporal evolution of the tumor cell-density distribution at later time points can ultimately be precisely captured using the model. We finally show the applicability of our approach to MR data of a real glioblastoma patient. This approach may open the perspective of a clinical application of reaction-diffusion growth models for tumor prognosis and treatment planning.

Inducing Biomechanical Heterogeneity in Brain Tumor Modeling by MR Elastography: Effects on Tumor Growth, Vascular Density and Delivery of Therapeutics

Simple Summary

Biomechanical forces aggravate brain tumor progression. In this study, magnetic resonance elastography (MRE) is employed to extract tissue biomechanical properties from five glioblastoma patients and a healthy subject, and data are incorporated in a mathematical model that simulates tumor growth. Mathematical modeling enables further understanding of glioblastoma development and allows patient-specific predictions for tumor vascularity and delivery of drugs. Incorporating MRE data results in a more realistic intratumoral distribution of mechanical stress and anisotropic tumor growth and a better description of subsequent events that are closely related to the development of stresses, including heterogeneity of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Abstract

The purpose of this study is to develop a methodology that incorporates a more accurate assessment of tissue mechanical properties compared to current mathematical modeling by use of biomechanical data from magnetic resonance elastography. The elastography data were derived from five glioblastoma patients and a healthy subject and used in a model that simulates tumor growth, vascular changes due to mechanical stresses and delivery of therapeutic agents. The model investigates the effect of tumor-specific biomechanical properties on tumor anisotropic growth, vascular density heterogeneity and chemotherapy delivery. The results showed that including elastography data provides a more realistic distribution of the mechanical stresses in the tumor and induces anisotropic tumor growth. Solid stress distribution differs among patients, which, in turn, induces a distinct functional vascular density distribution—owing to the compression of tumor vessels—and intratumoral drug distribution for each patient. In conclusion, incorporating elastography data results in a more accurate calculation of intratumoral mechanical stresses and enables a better mathematical description of subsequent events, such as the heterogeneous development of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Effect of energy requirements in the growth of brain tumor: a theoretical approach

A malignant tumor is an uncontrolled growth of tissues receiving energy in form of the nutrients provided by the microvascular networks. It is proposed that the supplied energy to a tumor is used for three purposes: the creation of new cells, maintenance of tumor cells, and tumor volume expansion by overcoming external pressure. A mathematical model studying the effects of energy required for maintenance and overcoming external pressure, the energy required creating a single cell, death rate, and tumor cell density on tumor development has been formulated. Including a term, residual energy for tumor growth in the tumor growth equation, the well-known logistic equation has been re-derived for tumors. Analytical solutions have been developed, and numerical analysis for the growth in brain tumors with the variation of parameters related to energy supply, the energy required for maintenance, and expansion of tumor has been performed. Expressions for the tumor growth rate(r) and carrying capacity(C) of the tumor are formulated in terms of the parameters used in the model. The range of 'r', estimated using our model is found within the ranges of tumor growth rates in gliomas reported by the other researchers. Selecting the model parameters precisely for a particular individual, the tumor growth rate and carrying capacity could be estimated accurately. Our study indicates that the actual growth rate and carrying capacity of a tumor reduce and tumor saturation time increases with the increase of death rate, the energy required for a single cell division, and energy requirement for the tumor cell maintenance.

Quantitative magnetic resonance imaging and tumor forecasting of breast cancer patients in the community setting

This protocol describes a complete data acquisition, analysis and computational forecasting pipeline for employing quantitative MRI data to predict the response of locally advanced breast cancer to neoadjuvant therapy in a community-based care setting. The methodology has previously been successfully applied to a heterogeneous patient population. The protocol details how to acquire the necessary images followed by registration, segmentation, quantitative perfusion and diffusion analysis, model calibration, and prediction. The data collection portion of the protocol requires ~25 min of scanning, postprocessing requires 2-3 h, and the model calibration and prediction components require ~10 h per patient depending on tumor size. The response of individual breast cancer patients to neoadjuvant therapy is forecast by application of a biophysical, reaction-diffusion mathematical model to these data. Successful application of the protocol results in coregistered MRI data from at least two scan visits that quantifies an individual tumor's size, cellularity and vascular properties. This enables a spatially resolved prediction of how a particular patient's tumor will respond to therapy. Expertise in image acquisition and analysis, as well as the numerical solution of partial differential equations, is required to carry out this protocol.

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.

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.

Kinetic modeling and numerical simulations to predict patient-specific responses to radiotherapy

Recent research indicates that quiescent tumor cells are significantly less radiosensitive with a greater repair capacity than proliferative cells. In order to better predict patient-specific responses to radiotherapy, we develop a mathematical model with treatment terms to describe dynamical behaviors of tumor growth. The global stabilities of the tumor-free equilibrium, the tumor-present equilibrium and the corresponding sufficient criteria are obtained. In addition, we simulate volumetric imaging data from 12 head-and-neck cancer patients and estimate the patient-specific responses to radiotherapy. Results indicate that radiosensitivity of proliferative cells is a critical factor that determines a successful radiotherapy. By comparison with previous simulation results, we find that the model presented in this paper is more suitable to describe the radiotherapy procedure of head-and-neck cancer. Finally, we discuss the influences of different radiotherapy strategies on therapeutic effect. The results show that treatment strategies with large dose or short treatment cycle can obtain better treatment effect.

A perspective on the radiopharmaceutical requirements for imaging and therapy of glioblastoma

Despite numerous clinical trials and pre-clinical developments, the treatment of glioblastoma (GB) remains a challenge. The current survival rate of GB averages one year, even with an optimal standard of care. However, the future promises efficient patient-tailored treatments, including targeted radionuclide therapy (TRT). Advances in radiopharmaceutical development have unlocked the possibility to assess disease at the molecular level allowing individual diagnosis. This leads to the possibility of choosing a tailored, targeted approach for therapeutic modalities. Therapeutic modalities based on radiopharmaceuticals are an exciting development with great potential to promote a personalised approach to medicine. However, an effective targeted radionuclide therapy (TRT) for the treatment of GB entails caveats and requisites. This review provides an overview of existing nuclear imaging and TRT strategies for GB. A critical discussion of the optimal characteristics for new GB targeting therapeutic radiopharmaceuticals and clinical indications are provided. Considerations for target selection are discussed, i.e. specific presence of the target, expression level and pharmacological access to the target, with particular attention to blood-brain barrier crossing. An overview of the most promising radionuclides is given along with a validation of the relevant radiopharmaceuticals and theranostic agents (based on small molecules, peptides and monoclonal antibodies). Moreover, toxicity issues and safety pharmacology aspects will be presented, both in general and for the brain in particular.

In Silico Mathematical Modelling for Glioblastoma: A Critical Review and a Patient-Specific Case

Glioblastoma extensively infiltrates the brain; despite surgery and aggressive therapies, the prognosis is poor. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of glioblastoma evolution in every single patient, with the aim of tailoring therapeutic weapons. In particular, the ultimate goal of biomathematics for cancer is the identification of the most suitable theoretical models and simulation tools, both to describe the biological complexity of carcinogenesis and to predict tumor evolution. In this report, we describe the results of a critical review about different mathematical models in neuro-oncology with their clinical implications. A comprehensive literature search and review for English-language articles concerning mathematical modelling in glioblastoma has been conducted. The review explored the different proposed models, classifying them and indicating the significative advances of each one. Furthermore, we present a specific case of a glioblastoma patient in which our recently proposed innovative mechanical model has been applied. The results of the mathematical models have the potential to provide a relevant benefit for clinicians and, more importantly, they might drive progress towards improving tumor control and patient's prognosis. Further prospective comparative trials, however, are still necessary to prove the impact of mathematical neuro-oncology in clinical practice.

Image-based personalization of computational models for predicting response of high-grade glioma to chemoradiation

High-grade gliomas are an aggressive and invasive malignancy which are susceptible to treatment resistance due to heterogeneity in intratumoral properties such as cell proliferation and density and perfusion. Non-invasive imaging approaches can measure these properties, which can then be used to calibrate patient-specific mathematical models of tumor growth and response. We employed multiparametric magnetic resonance imaging (MRI) to identify tumor extent (via contrast-enhanced T1-weighted, and T2-FLAIR) and capture intratumoral heterogeneity in cell density (via diffusion-weighted imaging) to calibrate a family of mathematical models of chemoradiation response in nine patients with unresected or partially resected disease. The calibrated model parameters were used to forecast spatially-mapped individual tumor response at future imaging visits. We then employed the Akaike information criteria to select the most parsimonious member from the family, a novel two-species model describing the enhancing and non-enhancing components of the tumor. Using this model, we achieved low error in predictions of the enhancing volume (median: - 2.5%, interquartile range: 10.0%) and a strong correlation in total cell count (Kendall correlation coefficient 0.79) at 3-months post-treatment. These preliminary results demonstrate the plausibility of using multiparametric MRI data to inform spatially-informative, biologically-based predictive models of tumor response in the setting of clinical high-grade gliomas.

Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment

Gliomas are primary brain tumors with a high invasive potential and infiltrative spread. Among them, glioblastoma multiforme (GBM) exhibits microvascular hyperplasia and pronounced necrosis triggered by hypoxia. Histological samples showing garland-like hypercellular structures (so-called pseudopalisades) centered around the occlusion site of a capillary are typical for GBM and hint on poor prognosis of patient survival. We propose a multiscale modeling approach in the kinetic theory of active particles framework and deduce by an upscaling process a reaction-diffusion model with repellent pH-taxis. We prove existence of a unique global bounded classical solution for a version of the obtained macroscopic system and investigate the asymptotic behavior of the solution. Moreover, we study two different types of scaling and compare the behavior of the obtained macroscopic PDEs by way of simulations. These show that patterns (not necessarily of Turing type), including pseudopalisades, can be formed for some parameter ranges, in accordance with the tumor grade. This is true when the PDEs are obtained via parabolic scaling (undirected tissue), while no such patterns are observed for the PDEs arising by a hyperbolic limit (directed tissue). This suggests that brain tissue might be undirected - at least as far as glioma migration is concerned. We also investigate two different ways of including cell level descriptions of response to hypoxia and the way they are related .

Towards an Image-Informed Mathematical Model of In Vivo Response to Fractionated Radiation Therapy

Simple Summary

Using medical imaging data and computational models, we develop a modeling framework to provide personalized treatment response forecasts to fractionated radiation therapy for individual tumors. We evaluate this approach in an animal model of brain cancer and forecast changes in tumor cellularity and vasculature.

Abstract

Fractionated radiation therapy is central to the treatment of numerous malignancies, including high-grade gliomas where complete surgical resection is often impractical due to its highly invasive nature. Development of approaches to forecast response to fractionated radiation therapy may provide the ability to optimize or adapt treatment plans for radiotherapy. Towards this end, we have developed a family of 18 biologically-based mathematical models describing the response of both tumor and vasculature to fractionated radiation therapy. Importantly, these models can be personalized for individual tumors via quantitative imaging measurements. To evaluate this family of models, rats (n = 7) with U-87 glioblastomas were imaged with magnetic resonance imaging (MRI) before, during, and after treatment with fractionated radiotherapy (with doses of either 2 Gy/day or 4 Gy/day for up to 10 days). Estimates of tumor and blood volume fractions, provided by diffusion-weighted MRI and dynamic contrast-enhanced MRI, respectively, were used to calibrate tumor-specific model parameters. The Akaike Information Criterion was employed to select the most parsimonious model and determine an ensemble averaged model, and the resulting forecasts were evaluated at the global and local level. At the global level, the selected model’s forecast resulted in less than 16.2% error in tumor volume estimates. At the local (voxel) level, the median Pearson correlation coefficient across all prediction time points ranged from 0.57 to 0.87 for all animals. While the ensemble average forecast resulted in increased error (ranging from 4.0% to 1063%) in tumor volume predictions over the selected model, it increased the voxel wise correlation (by greater than 12.3%) for three of the animals. This study demonstrates the feasibility of calibrating a model of response by serial quantitative MRI data collected during fractionated radiotherapy to predict response at the conclusion of treatment.

Towards a Reduced In Silico Model Predicting Biochemical Recurrence After Radiotherapy in Prostate Cancer

OBJECTIVE

Purposes of this work were i) to develop an in silico model of tumor response to radiotherapy, ii) to perform an exhaustive sensitivity analysis in order to iii) propose a simplified version and iv) to predict biochemical recurrence with both the comprehensive and the reduced model.

METHODS

A multiscale computational model of tumor response to radiotherapy was developed. It integrated the following radiobiological mechanisms: oxygenation, including hypoxic death; division of tumor cells; VEGF diffusion driving angiogenesis; division of healthy cells and oxygen-dependent response to irradiation, considering, cycle arrest and mitotic catastrophe. A thorough sensitivity analysis using the Morris screening method was performed on 21 prostate computational tissues. Tumor control probability (TCP) curves of the comprehensive model and 15 reduced versions were compared. Logistic regression was performed to predict biochemical recurrence after radiotherapy on 76 localized prostate cancer patients using an output of the comprehensive and the reduced models.

RESULTS

No significant difference was found between the TCP curves of the comprehensive and a simplified version which only considered oxygenation, division of tumor cells and their response to irradiation. Biochemical recurrence predictions using the comprehensive and the reduced models improved those made from pre-treatment imaging parameters (AUC = 0.81 ± 0.02 and 0.82 ± 0.02 vs. 0.75 ± 0.03, respectively).

CONCLUSION

A reduced model of tumor response to radiotherapy able to predict biochemical recurrence in prostate cancer was obtained.

SIGNIFICANCE

This reduced model may be used in the future to optimize personalized fractionation schedules.

WAM to SeeSaw model for cancer therapy - overcoming LQM difficulties

PURPOSE

The assessment of biological effects caused by radiation exposure has been currently carried out with the linear-quadratic (LQ) model as an extension of the linear non-threshold (LNT) model. In this study, we suggest a new mathematical model named as SeaSaw (SS) model, which describes proliferation and cell death effects by taking account of Bergonie-Tribondeau's law in terms of a differential equation in time. We show how this model overcomes the long-standing difficulties of the LQ model.

MATERIALS AND METHODS

We construct the SS model as an extended Wack-A-Mole (WAM) model by using a differential equation with respect to time in order to express the dynamics of the proliferation effect. A large number of accumulated data of such parameters as α and β in the LQ based models provide us with valuable pieces of information on the corresponding parameter b 1 and the maximum volume V m of the SS model. The dose rate b 1 and the notion of active cell can explain the present data without introduction of β, which is obtained by comparing the SS model with not only the cancer therapy data but also with in vitro experimental data. Numerical calculations are presented to grasp the global features of the SS model.

RESULTS

The SS model predicts the time dependence of the number of active- and inactive-cells. The SS model clarifies how the effect of radiation depends on the cancer stage at the starting time in the treatment. Further, the time dependence of the tumor volume is calculated by changing individual dose strength, which results in the change of the irradiation duration for the same effect. We can consider continuous irradiation in the SS model with interesting outcome on the time dependence of the tumor volume for various dose rates. Especially by choosing the value of the dose rate to be balanced with the total growth rate, the tumor volume is kept constant.

CONCLUSIONS

The SS model gives a simple equation to study the situation of clinical radiation therapy and risk estimation of radiation. The radiation parameter extracted from the cancer therapy is close to the value obtained from animal experiment in vitro and in vivo. We expect the SS model leads us to a unified description of radiation therapy and protection and provides a great development in cancer-therapy clinical-planning.

Mathematical formulation and parametric analysis of in vitro cell models in microfluidic devices: application to different stages of glioblastoma evolution

In silico models and computer simulation are invaluable tools to better understand complex biological processes such as cancer evolution. However, the complexity of the biological environment, with many cell mechanisms in response to changing physical and chemical external stimuli, makes the associated mathematical models highly non-linear and multiparametric. One of the main problems of these models is the determination of the parameters’ values, which are usually fitted for specific conditions, making the conclusions drawn difficult to generalise. We analyse here an important biological problem: the evolution of hypoxia-driven migratory structures in Glioblastoma Multiforme (GBM), the most aggressive and lethal primary brain tumour. We establish a mathematical model considering the interaction of the tumour cells with oxygen concentration in what is called the go or grow paradigm. We reproduce in this work three different experiments, showing the main GBM structures (pseudopalisade and necrotic core formation), only changing the initial and boundary conditions. We prove that it is possible to obtain versatile mathematical tools which, together with a sound parametric analysis, allow to explain complex biological phenomena. We show the utility of this hybrid “biomimetic in vitro-in silico” platform to help to elucidate the mechanisms involved in cancer processes, to better understand the role of the different phenomena, to test new scientific hypotheses and to design new data-driven experiments.

Evaluating patient-specific neoadjuvant regimens for breast cancer via a mathematical model constrained by quantitative magnetic resonance imaging data

The ability to accurately predict response and then rigorously optimize a therapeutic regimen on a patient-specific basis, would transform oncology. Toward this end, we have developed an experimental-mathematical framework that integrates quantitative magnetic resonance imaging (MRI) data into a biophysical model to predict patient-specific treatment response of locally advanced breast cancer to neoadjuvant therapy. Diffusion-weighted and dynamic contrast-enhanced MRI data is collected prior to therapy, after 1 cycle of therapy, and at the completion of the first therapeutic regimen. The model is initialized and calibrated with the first 2 patient-specific MRI data sets to predict response at the third, which is then compared to patient outcomes (N = 18). The model's predictions for total cellularity, total volume, and the longest axis at the completion of the regimen are significant within expected measurement precision (P< 0.05) and strongly correlated with measured response (P < 0.01). Further, we use the model to investigate, in silico, a range of (practical) alternative treatment plans to achieve the greatest possible tumor control for each individual in a subgroup of patients (N = 13). The model identifies alternative dosing strategies predicted to achieve greater tumor control compared to the standard of care for 12 of 13 patients (P < 0.01). In summary, a predictive, mechanism-based mathematical model has demonstrated the ability to identify alternative treatment regimens that are forecasted to outperform the therapeutic regimens the patients clinically. This has important implications for clinical trial design with the opportunity to alter oncology care in the future.

Towards integration of 64Cu-DOTA-trastuzumab PET-CT and MRI with mathematical modeling to predict response to neoadjuvant therapy in HER2 + breast cancer

While targeted therapies exist for human epidermal growth factor receptor 2 positive (HER2 +) breast cancer, HER2 + patients do not always respond to therapy. We present the results of utilizing a biophysical mathematical model to predict tumor response for two HER2 + breast cancer patients treated with the same therapeutic regimen but who achieved different treatment outcomes. Quantitative data from magnetic resonance imaging (MRI) and 64Cu-DOTA-trastuzumab positron emission tomography (PET) are used to estimate tumor density, perfusion, and distribution of HER2-targeted antibodies for each individual patient. MRI and PET data are collected prior to therapy, and follow-up MRI scans are acquired at a midpoint in therapy. Given these data types, we align the data sets to a common image space to enable model calibration. Once the model is parameterized with these data, we forecast treatment response with and without HER2-targeted therapy. By incorporating targeted therapy into the model, the resulting predictions are able to distinguish between the two different patient responses, increasing the difference in tumor volume change between the two patients by > 40%. This work provides a proof-of-concept strategy for processing and integrating PET and MRI modalities into a predictive, clinical-mathematical framework to provide patient-specific predictions of HER2 + treatment response.

Prediction of Cranial Radiotherapy Treatment in Pediatric Acute Lymphoblastic Leukemia Patients Using Machine Learning: A Case Study at MAHAK Hospital

Background:

Acute Lymphoblastic Leukemia (ALL) is the most common blood disease in children and is responsible for the most deaths amongst children. Due to major improvements in the treatment protocols in the 50-years period, the survivability of this disease has witnessed dramatic rise until this date which is about 90 percent. There are many investigations tending to indicate the efficiency of cranial radiotherapy found out that without that, outcome of the patients did not change and even it improved at some cases.

Methods:

the main aim of this study is predicting cranial radiotherapy treatment in pediatric acute lymphoblastic leukemia patients using machine learning. Scope of this paper is intertwined with predicting the necessity of one of the treatment modalities that has been used for many years for this group of patients named Cranial Radiotherapy (CRT). For this purpose, a case study is considered at Mahak charity hospital. In this paper, our focus is on ALL patients aged 0 to 17 treated at Mahak hospital, one of the best centers for treatment of childhood malignancies in Iran. Dataset analyzed in this study is gathered by the research team from patient’s paper-based files. Our dataset consists of 241 observations on patients with 31 attributes after the data cleaning process. Our designed machine learning model for predicting cranial radiotherapy treatment in pediatric acute lymphoblastic leukemia patients is a stacked ensemble classifier of independently strong models with a meta-learner to tune the weights and parameters of the base classifiers.

Results:

The stacked ensemble classifier show highly reasonable performance with AUC of 87.52%. Moreover, the attributes are ranked based on their predictive power and the most important variable for CRT necessity prediction is the disease relapse.

Conclusion:

In order to conclude, derived from previous studies regarding CRT it is not only cost-effective but also more healthy to eradicate the use of CRT for the treatment of childhood ALL. Furthermore, it is valuable to increase the clinical databases by creating more synthetic health databases not only for research purposes but also for physicians to keep track of their patient’s status.

Bayesian Information-Theoretic Calibration of Radiotherapy Sensitivity Parameters for Informing Effective Scanning Protocols in Cancer

With new advancements in technology, it is now possible to collect data for a variety of different metrics describing tumor growth, including tumor volume, composition, and vascularity, among others. For any proposed model of tumor growth and treatment, we observe large variability among individual patients’ parameter values, particularly those relating to treatment response; thus, exploiting the use of these various metrics for model calibration can be helpful to infer such patient-specific parameters both accurately and early, so that treatment protocols can be adjusted mid-course for maximum efficacy. However, taking measurements can be costly and invasive, limiting clinicians to a sparse collection schedule. As such, the determination of optimal times and metrics for which to collect data in order to best inform proper treatment protocols could be of great assistance to clinicians. In this investigation, we employ a Bayesian information-theoretic calibration protocol for experimental design in order to identify the optimal times at which to collect data for informing treatment parameters. Within this procedure, data collection times are chosen sequentially to maximize the reduction in parameter uncertainty with each added measurement, ensuring that a budget of n high-fidelity experimental measurements results in maximum information gain about the low-fidelity model parameter values. In addition to investigating the optimal temporal pattern for data collection, we also develop a framework for deciding which metrics should be utilized at each data collection point. We illustrate this framework with a variety of toy examples, each utilizing a radiotherapy treatment regimen. For each scenario, we analyze the dependence of the predictive power of the low-fidelity model upon the measurement budget.

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.

Reinforcement learning for optimal scheduling of Glioblastoma treatment with Temozolomide

BACKGROUND

Glioblastoma multiforme (GBM) is the most frequent primary brain tumor in adults and Temozolomide (TMZ) is an effective chemotherapeutic agent for its treatment. In Silico models of GBM growth provide an appropriate foundation for analysis and comparison of different regimens. We propose a mathematical frame for patient specific design of optimal chemotherapy regimens for GBM patients.

METHODS

The proposed frame includes online interaction of a virtual GBM with an optimizing agent. Spatiotemporal dynamics of GBM growth and its response to TMZ are simulated with a three dimensional hybrid cellular automaton. Q learning is tailored to the virtual GBM for treatment optimization aimed at minimizing tumor size at the end of treatment course. Q learning consists of a learning agent that interacts with the virtual GBM. System state is affected by the agent decisions and the obtained rewards guide Q learning to the optimal schedule.

RESULTS

Computational results confirm that the optimal chemotherapy schedule depends on some patient specific parameters including body weight, tumor size and its position in the brain. Furthermore, the algorithm is used for scheduling 2100 mg of TMZ on a virtual GBM and the obtained schedule is to administer150 mg of TMZ every other day. The obtained schedule is compared to the standard 7/14 regimen and the results show that it is superior to the 7/14 regimen in minimizing tumor size.

CONCLUSION

The proposed frame is an appropriate decision support system for patient specific design of TMZ administration regimens on GBM patients. Also, since the obtained optimal schedule outperforms the standard 7/14 regimen, it is worthy of further clinical testing.

Optimization of Dose Fractionation for Radiotherapy of a Solid Tumor with Account of Oxygen Effect and Proliferative Heterogeneity

A spatially-distributed continuous mathematical model of solid tumor growth and treatment by fractionated radiotherapy is presented. The model explicitly accounts for three time and space-dependent factors that influence the efficiency of radiotherapy fractionation schemes—tumor cell repopulation, reoxygenation and redistribution of proliferative states. A special algorithm is developed, aimed at finding the fractionation schemes that provide increased tumor cure probability under the constraints of maximum normal tissue damage and maximum fractional dose. The optimization procedure is performed for varied radiosensitivity of tumor cells under the values of model parameters, corresponding to different degrees of tumor malignancy. The resulting optimized schemes consist of two stages. The first stages are aimed to increase the radiosensitivity of the tumor cells, remaining after their end, sparing the caused normal tissue damage. This allows to increase the doses during the second stages and thus take advantage of the obtained increased radiosensitivity. Such method leads to significant expansions in the curative ranges of the values of tumor radiosensitivity parameters. Overall, the results of this study represent the theoretical proof of concept that non-uniform radiotherapy fractionation schemes may be considerably more effective that uniform ones, due to the time and space-dependent effects.

Tumor Volume Dynamics as an Early Biomarker for Patient-Specific Evolution of Resistance and Progression in Recurrent High-Grade Glioma

Recurrent high-grade glioma (HGG) remains incurable with inevitable evolution of resistance and high inter-patient heterogeneity in time to progression (TTP). Here, we evaluate if early tumor volume response dynamics can calibrate a mathematical model to predict patient-specific resistance to develop opportunities for treatment adaptation for patients with a high risk of progression. A total of 95 T1-weighted contrast-enhanced (T1post) MRIs from 14 patients treated in a phase I clinical trial with hypo-fractionated stereotactic radiation (HFSRT; 6 Gy × 5) plus pembrolizumab (100 or 200 mg, every 3 weeks) and bevacizumab (10 mg/kg, every 2 weeks; NCT02313272) were delineated to derive longitudinal tumor volumes. We developed, calibrated, and validated a mathematical model that simulates and forecasts tumor volume dynamics with rate of resistance evolution as the single patient-specific parameter. Model prediction performance is evaluated based on how early progression is predicted and the number of false-negative predictions. The model with one patient-specific parameter describing the rate of evolution of resistance to therapy fits untrained data ( R 2 = 0.70 ). In a leave-one-out study, for the nine patients that had T1post tumor volumes ≥1 cm3, the model was able to predict progression on average two imaging cycles early, with a median of 9.3 (range: 3-39.3) weeks early (median progression-free survival was 27.4 weeks). Our results demonstrate that early tumor volume dynamics measured on T1post MRI has the potential to predict progression following the protocol therapy in select patients with recurrent HGG. Future work will include testing on an independent patient dataset and evaluation of the developed framework on T2/FLAIR-derived data.

Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response. In this review, we identify and discuss approaches that use multiparametric imaging data, including diffusion-weighted magnetic resonance imaging, dynamic contrast-enhanced magnetic resonance imaging, diffusion tensor imaging, contrast-enhanced computed tomography, [¹⁸F]fluorodeoxyglucose positron emission tomography, and [¹⁸F]fluoromisonidazole positron emission tomography to initialize and calibrate mechanistic models of tumor growth and response. We focus the discussion on brain and breast cancers; however, we also identify three emerging areas of application in kidney, pancreatic, and lung cancers. We conclude with a discussion of the future directions for incorporating multiparametric imaging data and mechanistic modeling into clinical decision making for patients with cancer.

Quantifying Uncertainty and Robustness in a Biomathematical Model-Based Patient-Specific Response Metric for Glioblastoma

Purpose

Glioblastomas, lethal primary brain tumors, are known for their heterogeneity and invasiveness. A growing body of literature has been developed demonstrating the clinical relevance of a biomathematical model, the proliferation-invasion model, of glioblastoma growth. Of interest here is the development of a treatment response metric, days gained (DG). This metric is based on individual tumor kinetics estimated through segmented volumes of hyperintense regions on T1-weighted gadolinium-enhanced and T2-weighted magnetic resonance images. This metric was shown to be prognostic of time to progression. Furthermore, it was shown to be more prognostic of outcome than standard response metrics. Although promising, the original article did not account for uncertainty in the calculation of the DG metric, leaving the robustness of this cutoff in question.

Methods

We harnessed the Bayesian framework to consider the impact of two sources of uncertainty: (1) image acquisition and (2) interobserver error in image segmentation. We first used synthetic data to characterize what nonerror variants are influencing the final uncertainty in the DG metric. We then considered the original patient cohort to investigate clinical patterns of uncertainty and to determine how robust this metric is for predicting time to progression and overall survival.

Results

Our results indicate that the key clinical variants are the time between pretreatment images and the underlying tumor growth kinetics, matching our observations in the clinical cohort. Finally, we demonstrated that for this cohort, there was a continuous range of cutoffs between 94 and 105 for which the prediction of the time to progression was over 80% reliable.

Conclusion

Although additional validation must be performed, this work represents a key step in ascertaining the clinical utility of this metric.

Glioblastoma Recurrence and the Role of O6-Methylguanine-DNA Methyltransferase Promoter Methylation

Tumor recurrence in glioblastoma multiforme (GBM) is often attributed to acquired resistance to the standard chemotherapeutic agent, temozolomide (TMZ). Promoter methylation of the DNA repair gene MGMT (O⁶-methylguanine-DNA methyltransferase) has been associated with sensitivity to TMZ, whereas increased expression of MGMT has been associated with TMZ resistance. Clinical studies have observed a downward shift in MGMT methylation percentage from primary to recurrent stage tumors; however, the evolutionary processes that drive this shift and more generally the emergence and growth of TMZ-resistant tumor subpopulations are still poorly understood. Here, we develop a mathematical model, parameterized using clinical and experimental data, to investigate the role of MGMT methylation in TMZ resistance during the standard treatment regimen for GBM-surgery, chemotherapy, and radiation. We first found that the observed downward shift in MGMT promoter methylation status between detection and recurrence cannot be explained solely by evolutionary selection. Next, our model suggests that TMZ has an inhibitory effect on maintenance methylation of MGMT after cell division. Finally, incorporating this inhibitory effect, we study the optimal number of TMZ doses per adjuvant cycle for patients with GBM with high and low levels of MGMT methylation at diagnosis.

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (a) detection/segmentation of tumor subregions and (b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of (a) biophysical growth modeling and simulation,(b) inverse problems for model calibration, (c) these models' integration with imaging workflows, and (d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.

Simulating glioblastoma growth consisting both visible and invisible parts of the tumor using a diffusion-reaction model followed by resection and radiotherapy

Glioblastoma is known to be among one of the deadliest brain tumors in the world today. There have been major improvements in the detection of cancerous cells in the twenty-first century. However, the threshold of detection of these cancerous cells varies in different scanning techniques such as magnetic resonance imaging (MRI) and computed tomography (CT). The growth of these tumors and different treatments have been modeled to assist medical experts in better predictions of the related tumor growth and in the selection of more accurate treatments. In clinical terms the tumor consisted of two parts known as the visible part, which is the part of the tumor that is above the threshold of the detecting device and the invisible part, which is below the detecting threshold. In this study, the common reaction-diffusion model of tumor growth is used to simulate the growth of the glioblastoma tumor. Also resection and radiotherapy have been modeled as methods to prevent the growth of the tumor. The results demonstrate that although the selected treatments were effective in reducing the number of cancerous cells to under the threshold of detection, they did not eliminate all cancerous cells and if no further treatments were applied, the cancerous cells would spread and become malignant again. Although previous studies have suggested that the ratio of proliferation to diffusion could describe the malignancy of the tumor, this study in addition shows the importance of each of the coefficients regarding the malignancy of the tumor.

Sex-specific impact of patterns of imageable tumor growth on survival of primary glioblastoma patients

Background

Sex is recognized as a significant determinant of outcome among glioblastoma patients, but the relative prognostic importance of glioblastoma features has not been thoroughly explored for sex differences.

Methods

Combining multi-modal MR images, biomathematical models, and patient clinical information, this investigation assesses which pretreatment variables have a sex-specific impact on the survival of glioblastoma patients (299 males and 195 females).

Results

Among males, tumor (T1Gd) radius was a predictor of overall survival (HR = 1.027, p = 0.044). Among females, higher tumor cell net invasion rate was a significant detriment to overall survival (HR = 1.011, p < 0.001). Female extreme survivors had significantly smaller tumors (T1Gd) (p = 0.010 t-test), but tumor size was not correlated with female overall survival (p = 0.955 CPH). Both male and female extreme survivors had significantly lower tumor cell net proliferation rates than other patients (M p = 0.004, F p = 0.001, t-test).

Conclusion

Despite similar distributions of the MR imaging parameters between males and females, there was a sex-specific difference in how these parameters related to outcomes.

Mathematical oncology and it's application in non melanoma skin cancer - A primer for radiation oncology professionals

Cancers of the skin (the majority of which are basal and squamous cell skin carcinomas, but also include the rarer Merkel cell carcinoma) are overwhelmingly the most common of all types of cancer. Most of these are treated surgically, with radiation reserved for those patients with high risk features or anatomical locations less suitable for surgery. Given the high incidence of both basal and squamous cell carcinomas, as well as the relatively poor outcome for Merkel cell carcinoma, it is useful to investigate the role of other disciplines regarding their diagnosis, staging and treatment. Mathematical modelling is one such area of investigation. The use of mathematical modelling is a relatively recent addition to the armamentarium of cancer treatment. It has long been recognised that tumour growth and treatment response is a complex, non-linear biological phenomenon with many mechanisms yet to be understood. Despite decades of research, including clinical, population and basic science approaches, we continue to be challenged by the complexity, heterogeneity and adaptability of tumours, both in individual patients in the oncology clinic and across wider patient populations. Prospective clinical trials predominantly focus on average outcome, with little understanding as to why individual patients may or may not respond. The use of mathematical models may lead to a greater understanding of tumour initiation, growth dynamics and treatment response.

Sex differences in GBM revealed by analysis of patient imaging, transcriptome, and survival data

Sex differences in the incidence and outcome of human disease are broadly recognized but, in most cases, not sufficiently understood to enable sex-specific approaches to treatment. Glioblastoma (GBM), the most common malignant brain tumor, provides a case in point. Despite well-established differences in incidence and emerging indications of differences in outcome, there are few insights that distinguish male and female GBM at the molecular level or allow specific targeting of these biological differences. Here, using a quantitative imaging-based measure of response, we found that standard therapy is more effective in female compared with male patients with GBM. We then applied a computational algorithm to linked GBM transcriptome and outcome data and identified sex-specific molecular subtypes of GBM in which cell cycle and integrin signaling are the critical determinants of survival for male and female patients, respectively. The clinical relevance of cell cycle and integrin signaling pathway signatures was further established through correlations between gene expression and in vitro chemotherapy sensitivity in a panel of male and female patient-derived GBM cell lines. Together, these results suggest that greater precision in GBM molecular subtyping can be achieved through sex-specific analyses and that improved outcomes for all patients might be accomplished by tailoring treatment to sex differences in molecular mechanisms.

A minimal modeling framework of radiation and immune system synergy to assist radiotherapy planning

Recent evidence indicates the ability of radiotherapy to induce local and systemic tumor-specific immune responses as a result of immunogenic cell death. However, fractionation regimes routinely used in clinical practice typically ignore the synergy between radiation and the immune system, and instead attempt to completely eradicate tumors by the direct lethal effect of radiation on cancer cells. This paradigm is expected to change in the near future due to the potential benefits of considering radiation-induced antitumor immunity during treatment planning. Towards this goal, we propose a minimal modeling framework based on key aspects of the tumor-immune system interplay to simulate the effects of radiation on tumors and the immunological consequences of radiotherapy. The impacts of tumor-associated vasculature and intratumoral oxygen-mediated heterogeneity on treatment outcomes are ininvestigated. The model provides estimates of the minimum radiation doses required for tumor eradication given a certain number of treatment fractions. Moreover, estimates of treatment duration for disease control given predetermined fractional radiation doses can be also obtained. Although theoretical in nature, this study motivates the development and establishment of immune-based decision-support tools in radiotherapy planning.

Personalized image-based tumor growth prediction in a convection-diffusion-reaction model

Inter-individual heterogeneity of tumors leads to non-effectiveness of unique therapy plans. This issue has caused a growing interest in the field of personalized medicine and its application in tumor growth evaluation. Accordingly, in this paper, a framework of personalized medicine is presented for growth prediction of brain glioma tumors. A convection-diffusion-reaction model is used as the patient-specific tumor growth model which is associated with multimodal magnetic resonance images (MRIs). Two parameters of intracellular area fraction (ICAF) and metabolic rate have been used to incorporate the physiological data obtained from medical images into the model. The framework is tested on the data of two cases of glioma tumors to document the approach; parameter estimation is made using particle swarm optimization (PSO) and genetic algorithm (GA) and the model is evaluated by comparing the predicted tumors with the observed tumors in terms of root mean square error of the ICAF maps (IRMSE), relative area difference (RAD) and Dice's coefficient (DC). Results show the differences of IRMSE, RAD and DC in 4.1 ∓ 1.15%, 0.099 ∓ 0.041 and 85.5 ∓ 7.5%, respectively. Survival times are estimated by assuming the tumor radius of 35 mm as the fatal burden. Results confirm that less-diffusive tumors lead to higher survival times. The represented framework makes it possible to personally predict the growth behavior of glioma tumors only based on patients' routine MRIs and provides a basis for modeling the personalized therapy and walking in the path of personalized medicine.

Mathematical deconvolution of CAR T-cell proliferation and exhaustion from real-time killing assay data

Chimeric antigen receptor (CAR) T-cell therapy has shown promise in the treatment of haematological cancers and is currently being investigated for solid tumours, including high-grade glioma brain tumours. There is a desperate need to quantitatively study the factors that contribute to the efficacy of CAR T-cell therapy in solid tumours. In this work, we use a mathematical model of predator–prey dynamics to explore the kinetics of CAR T-cell killing in glioma: the Chimeric Antigen Receptor T-cell treatment Response in GliOma (CARRGO) model. The model includes rates of cancer cell proliferation, CAR T-cell killing, proliferation, exhaustion, and persistence. We use patient-derived and engineered cancer cell lines with an in vitro real-time cell analyser to parametrize the CARRGO model. We observe that CAR T-cell dose correlates inversely with the killing rate and correlates directly with the net rate of proliferation and exhaustion. This suggests that at a lower dose of CAR T-cells, individual T-cells kill more cancer cells but become more exhausted when compared with higher doses. Furthermore, the exhaustion rate was observed to increase significantly with tumour growth rate and was dependent on level of antigen expression. The CARRGO model highlights nonlinear dynamics involved in CAR T-cell therapy and provides novel insights into the kinetics of CAR T-cell killing. The model suggests that CAR T-cell treatment may be tailored to individual tumour characteristics including tumour growth rate and antigen level to maximize therapeutic benefit.

Days gained response discriminates treatment response in patients with recurrent glioblastoma receiving bevacizumab-based therapies

Background

Accurate assessments of patient response to therapy are a critical component of personalized medicine. In glioblastoma (GBM), the most aggressive form of brain cancer, tumor growth dynamics are heterogenous across patients, complicating assessment of treatment response. This study aimed to analyze days gained (DG), a burgeoning model-based dynamic metric, for response assessment in patients with recurrent GBM who received bevacizumab-based therapies.

Methods

DG response scores were calculated using volumetric tumor segmentations for patients receiving bevacizumab with and without concurrent cytotoxic therapy (N = 62). Kaplan–Meier and Cox proportional hazards analyses were implemented to examine DG prognostic relationship to overall (OS) and progression-free survival (PFS) from the onset of treatment for recurrent GBM.

Results

In patients receiving concurrent bevacizumab and cytotoxic therapy, Kaplan–Meier analysis showed significant differences in OS and PFS at DG cutoffs consistent with previously identified values from newly diagnosed GBM using T1-weighted gadolinium-enhanced magnetic resonance imaging (T1Gd). DG scores for bevacizumab monotherapy patients only approached significance for PFS. Cox regression showed that increases of 25 DG on T1Gd imaging were significantly associated with a 12.5% reduction in OS hazard for concurrent therapy patients and a 4.4% reduction in PFS hazard for bevacizumab monotherapy patients.

Conclusion

DG has significant meaning in recurrent therapy as a metric of treatment response, even in the context of anti-angiogenic therapies. This provides further evidence supporting the use of DG as an adjunct response metric that quantitatively connects treatment response and clinical outcomes.