A mathematical model of brain tumour response to radiotherapy and chemotherapy considering radiobiological aspects

Evaluation of in vitro intrinsic radiosensitivity and characterization of five canine high-grade glioma cell lines

Glioma is the most common primary brain tumor in dogs and predominantly affects brachycephalic breeds. Diagnosis relies on CT or MRI imaging, and the proposed treatments include surgical resection, chemotherapy, and radiotherapy depending on the tumor's location. Canine glioma from domestic dogs could be used as a more powerful model to study radiotherapy for human glioma than the murine model. Indeed, (i) contrary to mice, immunocompetent dogs develop spontaneous glioma, (ii) the canine brain structure is closer to human than mice, and (iii) domestic dogs are exposed to the same environmental factors than humans. Moreover, imaging techniques and radiation therapy used in human medicine can be applied to dogs, facilitating the direct transposition of results. The objective of this study is to fully characterize 5 canine glioma cell lines and to evaluate their intrinsic radiosensitivity. Canine cell lines present numerous analogies between the data obtained during this study on different glioma cell lines in dogs. Cell morphology is identical, such as doubling time, clonality test and karyotype. Immunohistochemical study of surface proteins, directly on cell lines and after stereotaxic injection in mice also reveals close similarity. Radiosensitivity profile of canine glial cells present high profile of radioresistance.

Interactions between ploidy and resource availability shape clonal interference at initiation and recurrence of glioblastoma

Glioblastoma (GBM) is the most aggressive form of primary brain tumor. Complete surgical resection of GBM is almost impossible due to the infiltrative nature of the cancer. While no evidence for recent selection events have been found after diagnosis, the selective forces that govern gliomagenesis are strong, shaping the tumor's cell composition during the initial progression to malignancy with late consequences for invasiveness and therapy response. We present a mathematical model that simulates the growth and invasion of a glioma, given its ploidy level and the nature of its brain tissue micro-environment (TME), and use it to make inferences about GBM initiation and response to standard-of-care treatment. We approximate the spatial distribution of resource access in the TME through integration of in-silico modelling, multi-omics data and image analysis of primary and recurrent GBM. In the pre-malignant setting, our in-silico results suggest that low ploidy cancer cells are more resistant to starvation-induced cell death. In the malignant setting, between first and second surgery, simulated tumors with different ploidy compositions progressed at different rates. Whether higher ploidy predicted fast recurrence, however, depended on the TME. Historical data supports this dependence on TME resources, as shown by a significant correlation between the median glucose uptake rates in human tissues and the median ploidy of cancer types that arise in the respective tissues (Spearman r = -0.70; P = 0.026). Taken together our findings suggest that availability of metabolic substrates in the TME drives different cell fate decisions for cancer cells with different ploidy and shapes GBM disease initiation and relapse characteristics.

Agent-Based Modelling Reveals the Role of the Tumor Microenvironment on the Short-Term Success of Combination Temozolomide/Immune Checkpoint Blockade to Treat Glioblastoma

Glioblastoma is the most common and deadly primary brain tumor in adults. All glioblastoma patients receiving standard-of-care surgery-radiotherapy-chemotherapy (i.e., temozolomide (TMZ)) recur, with an average survival time of only 15 months. New approaches to the treatment of glioblastoma, including immune checkpoint blockade and oncolytic viruses, offer the possibility of improving glioblastoma outcomes and have as such been under intense study. Unfortunately, these treatment modalities have thus far failed to achieve approval. Recently, in an attempt to bolster efficacy and improve patient outcomes, regimens combining chemotherapy and immune checkpoint inhibitors have been tested in trials. Unfortunately, these efforts have not resulted in significant increases to patient survival. To better understand the various factors impacting treatment outcomes of combined TMZ and immune checkpoint blockade, we developed a systems-level, computational model that describes the interplay between glioblastoma, immune, and stromal cells with this combination treatment. Initializing our model to spatial resection patient samples labeled using imaging mass cytometry, our model's predictions show how the localization of glioblastoma cells, influence therapeutic success. We further validated these predictions in samples of brain metastases from patients given they generally respond better to checkpoint blockade compared with primary glioblastoma. Ultimately, our model provides novel insights into the mechanisms of therapeutic success of immune checkpoint inhibitors in brain tumors and delineates strategies to translate combination immunotherapy regimens more effectively into the clinic. SIGNIFICANCE STATEMENT: Extending survival times for glioblastoma patients remains a critical challenge. Although immunotherapies in combination with chemotherapy hold promise, clinical trials have not shown much success. Here, systems models calibrated to and validated against patient samples can improve preclinical and clinical studies by shedding light on the factors distinguishing responses/failures. By initializing our model with imaging mass cytometry visualization of patient samples, we elucidate how factors such as localization of glioblastoma cells and CD8+ T cell infiltration impact treatment outcomes.

Optimal managements of elderly patients with glioblastoma

Optimizing the management of elderly patients with glioblastoma is an ongoing task in neuro-oncology. The number of patients with this tumor type is gradually increasing with the aging of the population. Although available data and practice recommendations remain limited, the current strategy is maximal safe surgical resection followed by radiotherapy in combination with temozolomide. However, survival is significantly worse than that in the younger population. Surgical resection provides survival benefit in patients with good performance status. Hypofractionated radiotherapy decreases toxicities while maintaining therapeutic efficacy, thus improving treatment adherence and subsequently leading to better quality of life. The intensity of these treatments should be balanced with patient-specific factors and consideration of quality of life. This review discusses the current optimal management in terms of efficacy and safety, as well as future perspectives.

A randomized phase III study of short-course radiotherapy combined with Temozolomide in elderly patients with newly diagnosed glioblastoma; Japan clinical oncology group study JCOG1910 (AgedGlio-PIII)

Background

The current standard treatment for elderly patients with newly diagnosed glioblastoma is surgery followed by short-course radiotherapy with temozolomide. In recent studies, 40 Gy in 15 fractions vs. 60 Gy in 30 fractions, 34 Gy in 10 fractions vs. 60 Gy in 30 fractions, and 40 Gy in 15 fractions vs. 25 Gy in 5 fractions have been reported as non-inferior. The addition of temozolomide increased the survival benefit of radiotherapy with 40 Gy in 15 fractions. However, the optimal regimen for radiotherapy plus concomitant temozolomide remains unresolved.

Methods

This multi-institutional randomized phase III trial was commenced to confirm the non-inferiority of radiotherapy comprising 25 Gy in 5 fractions with concomitant (150 mg/m²/day, 5 days) and adjuvant temozolomide over 40 Gy in 15 fractions with concomitant (75 mg/m²/day, every day from first to last day of radiation) and adjuvant temozolomide in terms of overall survival (OS) in elderly patients with newly diagnosed glioblastoma. A total of 270 patients will be accrued from 51 Japanese institutions in 4 years and follow-up will last 2 years. Patients 71 years of age or older, or 71–75 years old with resection of less than 90% of the contrast-enhanced region, will be registered and randomly assigned to each group with 1:1 allocation. The primary endpoint is OS, and the secondary endpoints are progression-free survival, frequency of adverse events, proportion of Karnofsky performance status preservation, and proportion of health-related quality of life preservation. The Japan Clinical Oncology Group Protocol Review Committee approved this study protocol in April 2020. Ethics approval was granted by the National Cancer Center Hospital Certified Review Board. Patient enrollment began in August 2020.

Discussion

If the primary endpoint is met, short-course radiotherapy comprising 25 Gy in 5 fractions with concomitant and adjuvant temozolomide will be a standard of care for elderly patients with newly diagnosed glioblastoma.

Trial registration

Registry number: jRCTs031200099.

Date of Registration: 27/Aug/2020. Date of First Participant Enrollment: 4/Sep/2020.

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.

A neuro evolutionary algorithm for patient calibrated prediction of survival in Glioblastoma patients

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is the most common and malignant type of primary brain tumors. Radiation therapy (RT) plus concomitant and adjuvant Temozolomide (TMZ) constitute standard treatment of GBM. Existing models for GBM growth do not consider the effect of different schedules on tumor growth and patient survival. However, clinical trials show that treatment schedule and drug dosage significantly affect patient survival. The goal is to provide a patient calibrated model for predicting survival according to the treatment schedule.

METHODS

We propose a top-down method based on artificial neural networks (ANN) and genetic algorithm (GA) to predict survival of GBM patients. A feed forward undercomplete Autoencoder network is integrated with the neuro-evolutionary (NE) algorithm in order to extract a compressed representation of input clinical data. The proposed NE algorithm uses GA to obtain optimal architecture of a multi-layer perceptron (MLP). Taguchi L₁₆ orthogonal design of experiments is used to tune parameters of the proposed NE algorithm. Finally, the optimal MLP is used to predict survival of GBM patients.

RESULTS

Data from 8 related clinical trials have been collected and integrated to train the model. From 847 evaluable cases, 719 were used for train and validation and the remaining 128 cases were used to test the model. Mean absolute error of the predictions on the test data is 0.087 months which shows excellent performance of the proposed model in predicting survival of the patients. Also, the results show that the proposed NE algorithm is superior to other existing models in both the mean and variability of the prediction error.

A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma

Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic model of GBM, the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model, we explore the phenotypic drivers of this observed behavior. We have extended the PIHNA model to include a new nutrient-based vascular efficiency term that encodes the ability of local vasculature to provide nutrients to the simulated tumor. The extended model suggests sensitivity to a hypoxic microenvironment and the inherent migration and proliferation rates of the tumor cells are key factors that drive distal recurrence.

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.

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.

Proton Therapy and Src Family Kinase Inhibitor Combined Treatments on U87 Human Glioblastoma Multiforme Cell Line

Glioblastoma Multiforme (GBM) is the most common of malignant gliomas in adults with an exiguous life expectancy. Standard treatments are not curative and the resistance to both chemotherapy and conventional radiotherapy (RT) plans is the main cause of GBM care failures. Proton therapy (PT) shows a ballistic precision and a higher dose conformity than conventional RT. In this study we investigated the radiosensitive effects of a new targeted compound, SRC inhibitor, named Si306, in combination with PT on the U87 glioblastoma cell line. Clonogenic survival assay, dose modifying factor calculation and linear-quadratic model were performed to evaluate radiosensitizing effects mediated by combination of the Si306 with PT. Gene expression profiling by microarray was also conducted after PT treatments alone or combined, to identify gene signatures as biomarkers of response to treatments. Our results indicate that the Si306 compound exhibits a radiosensitizing action on the U87 cells causing a synergic cytotoxic effect with PT. In addition, microarray data confirm the SRC role as the main Si306 target and highlights new genes modulated by the combined action of Si306 and PT. We suggest, the Si306 as a new candidate to treat GBM in combination with PT, overcoming resistance to conventional treatments.

The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies

BACKGROUND

Prediction of radiobiological response is a major challenge in radiotherapy. Of several radiobiological models, the linear-quadratic (LQ) model has been best validated by experimental and clinical data. Clinically, the LQ model is mainly used to estimate equivalent radiotherapy schedules (e.g. calculate the equivalent dose in 2 Gy fractions, EQD₂), but increasingly also to predict tumour control probability (TCP) and normal tissue complication probability (NTCP) using logistic models. The selection of accurate LQ parameters α, β and α/β is pivotal for a reliable estimate of radiation response. The aim of this review is to provide an overview of published values for the LQ parameters of human tumours as a guideline for radiation oncologists and radiation researchers to select appropriate radiobiological parameter values for LQ modelling in clinical radiotherapy.

METHODS AND MATERIALS

We performed a systematic literature search and found sixty-four clinical studies reporting α, β and α/β for tumours. Tumour site, histology, stage, number of patients, type of LQ model, radiation type, TCP model, clinical endpoint and radiobiological parameter estimates were extracted. Next, we stratified by tumour site and by tumour histology. Study heterogeneity was expressed by the I² statistic, i.e. the percentage of variance in reported values not explained by chance.

RESULTS

A large heterogeneity in LQ parameters was found within and between studies (I² > 75%). For the same tumour site, differences in histology partially explain differences in the LQ parameters: epithelial tumours have higher α/β values than adenocarcinomas. For tumour sites with different histologies, such as in oesophageal cancer, the α/β estimates correlate well with histology. However, many other factors contribute to the study heterogeneity of LQ parameters, e.g. tumour stage, type of LQ model, TCP model and clinical endpoint (i.e. survival, tumour control and biochemical control).

CONCLUSIONS

The value of LQ parameters for tumours as published in clinical radiotherapy studies depends on many clinical and methodological factors. Therefore, for clinical use of the LQ model, LQ parameters for tumour should be selected carefully, based on tumour site, histology and the applied LQ model. To account for uncertainties in LQ parameter estimates, exploring a range of values is recommended.

The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies

Background

Prediction of radiobiological response is a major challenge in radiotherapy. Of several radiobiological models, the linear-quadratic (LQ) model has been best validated by experimental and clinical data. Clinically, the LQ model is mainly used to estimate equivalent radiotherapy schedules (e.g. calculate the equivalent dose in 2 Gy fractions, EQD₂), but increasingly also to predict tumour control probability (TCP) and normal tissue complication probability (NTCP) using logistic models. The selection of accurate LQ parameters α, β and α/β is pivotal for a reliable estimate of radiation response. The aim of this review is to provide an overview of published values for the LQ parameters of human tumours as a guideline for radiation oncologists and radiation researchers to select appropriate radiobiological parameter values for LQ modelling in clinical radiotherapy.

Methods and materials

We performed a systematic literature search and found sixty-four clinical studies reporting α, β and α/β for tumours. Tumour site, histology, stage, number of patients, type of LQ model, radiation type, TCP model, clinical endpoint and radiobiological parameter estimates were extracted. Next, we stratified by tumour site and by tumour histology. Study heterogeneity was expressed by the I² statistic, i.e. the percentage of variance in reported values not explained by chance.

Results

A large heterogeneity in LQ parameters was found within and between studies (I² > 75%). For the same tumour site, differences in histology partially explain differences in the LQ parameters: epithelial tumours have higher α/β values than adenocarcinomas. For tumour sites with different histologies, such as in oesophageal cancer, the α/β estimates correlate well with histology. However, many other factors contribute to the study heterogeneity of LQ parameters, e.g. tumour stage, type of LQ model, TCP model and clinical endpoint (i.e. survival, tumour control and biochemical control).

Conclusions

The value of LQ parameters for tumours as published in clinical radiotherapy studies depends on many clinical and methodological factors. Therefore, for clinical use of the LQ model, LQ parameters for tumour should be selected carefully, based on tumour site, histology and the applied LQ model. To account for uncertainties in LQ parameter estimates, exploring a range of values is recommended.

Electronic supplementary material

The online version of this article (10.1186/s13014-018-1040-z) contains supplementary material, which is available to authorized users.

Mathematical Modelling for Patient Selection in Proton Therapy

Proton beam therapy (PBT) is still relatively new in cancer treatment and the clinical evidence base is relatively sparse. Mathematical modelling offers assistance when selecting patients for PBT and predicting the demand for service. Discrete event simulation, normal tissue complication probability, quality-adjusted life-years and Markov Chain models are all mathematical and statistical modelling techniques currently used but none is dominant. As new evidence and outcome data become available from PBT, comprehensive models will emerge that are less dependent on the specific technologies of radiotherapy planning and delivery.

Additive Damage Models for Cellular Pharmacodynamics of Radiation-Chemotherapy Combinations

Many cancer patients receive combination treatments with radiation and chemotherapy. Available mathematical models for cellular pharmacodynamics have limited ability to represent observed in vitro responses to radiochemotherapy. Here, a family of additive damage models is proposed to describe cell kill resulting from radiochemotherapy with fixed schedule and variable doses. The pathways by which the agents produce cellular damage are assumed to converge in a single cell death process, so that survival depends on total damage, which can be represented as a sum of contributions from the various damage pathways. Heterogeneity in response across the cell population is ascribed to variations in the damage threshold for cell kill. The family of proposed models includes effects of one or two pathways of damage for each agent, saturation in drug responses, and cooperative or antagonistic interactions between agents. Models from this family with 4-7 unknown parameters are tested for their ability to fit 218 in vitro literature data sets for a range of drugs and cell lines. Overall, the additive damage models are found to outperform models based on the existing concept of independent cell kill, according to the corrected Akaike Information Criterion. The results are used to assess the importance of the various effects included in the models. These additive damage models have potential applications to the optimization of treatment and to the analysis and interpretation of in vitro screening data for new drug-radiation combinations.

A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications

Gliomas are the most frequent type of primary brain tumours. Low grade gliomas (LGGs, WHO grade II gliomas) may grow very slowly for the long periods of time, however they inevitably cause death due to the phenomenon known as the malignant transformation. This refers to the transition of LGGs to more aggressive forms of high grade gliomas (HGGs, WHO grade III and IV gliomas). In this paper we propose a mathematical model describing the spatio-temporal transition of LGGs into HGGs. Our modelling approach is based on two cellular populations with transitions between them being driven by the tumour microenvironment transformation occurring when the tumour cell density grows beyond a critical level. We show that the proposed model describes real patient data well. We discuss the relationship between patient prognosis and model parameters. We approximate tumour radius and velocity before malignant transformation as well as estimate the onset of this process.

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.

Post-Surgery Glioma Growth Modeling from Magnetic Resonance Images for Patients with Treatment

Reaction diffusion is the most common growth modelling methodology due to its simplicity and consistency with the biological tumor growth process. However, current extensions of the reaction diffusion model lack one or more of the following: efficient inclusion of treatments' effects, taking into account the viscoelasticity of brain tissues, and guaranteed stability of the numerical solution. We propose a new model to overcome the aforementioned drawbacks. Guided by directional information derived from diffusion tensor imaging, our model relates tissue heterogeneity with the absorption of the chemotherapy, adopts the linear-quadratic term to simulate the radiotherapy effect, employs Maxwell-Weichert model to incorporate brain viscoelasticity, and ensures the stability of the numerical solution. The performance is verified through experiments on synthetic and real MR images. Experiments on 9 MR datasets of patients with low grade gliomas undergoing surgery with different treatment regimens are carried out and validated using Jaccard score and Dice coefficient. The growth simulation accuracies of the proposed model are in ranges of [0.673 0.822] and [0.805 0.902] for Jaccard scores and Dice coefficients, respectively. The accuracies decrease up to 4% and 2.4% when ignoring treatment effects and the tensor information, while brain viscoelasticity has no significant impact on the accuracies.

Modelling and Bayesian adaptive prediction of individual patients' tumour volume change during radiotherapy

The aim of this study is to develop a mathematical modelling method that can predict individual patients’ response to radiotherapy, in terms of tumour volume change during the treatment. The main concept is to start from a population-average model, which is subsequently updated from an individual’s tumour volume measurement. The model becomes increasingly personalized and so too does the prediction it produces. This idea of adaptive prediction was realised by using a Bayesian approach for updating the model parameters. The feasibility of the developed method was demonstrated on the data from 25 non-small cell lung cancer patients treated with helical tomotherapy, during which tumour volume was measured from daily imaging as part of the image-guided radiotherapy. The method could provide useful information for adaptive treatment planning and dose scheduling based on the patient’s personalised response.

Modeling the efficacy of the extent of surgical resection in the setting of radiation therapy for glioblastoma

Standard therapy for glioblastoma (GBM) includes maximal surgical resection and radiation therapy. While it is established that radiation therapy provides the greatest survival benefit of standard treatment modalities, the impact of the extent of surgical resection (EOR) on patient outcome remains highly controversial. While some studies describe no correlation between EOR and patient survival even up to total resection, others propose either qualitative (partial versus subtotal versus complete resection) or quantitative EOR thresholds, below which there is no correlation with survival. This work uses a mathematical model in the form of a reaction–diffusion partial differential equation to simulate tumor growth and treatment with radiation therapy and surgical resection based on tumor‐specific rates of diffusion and proliferation. Simulation of 36 tumors across a wide spectrum of diffusion and proliferation rates suggests that while partial or subtotal resections generally do not provide a survival advantage, complete resection significantly improves patient outcomes. Furthermore, our model predicts a tumor‐specific quantitative threshold below which EOR has no effect on patient survival and demonstrates that this threshold increases with tumor aggressiveness, particularly with the rate of proliferation. Thus, this model may serve as an aid for determining both when surgical resection is indicated as well as the surgical margins necessary to provide clinically significant improvements in patient survival. In addition, by assigning relative benefits to radiation and surgical resection based on tumor invasiveness and proliferation, this model confirms that (with the exception of the least aggressive tumors) the survival benefit of radiation therapy exceeds that of surgical resection.

Impact of Timing of Concurrent Chemoradiation for Newly Diagnosed Glioblastoma: A Critical Review of Current Evidence

ABBREVIATIONS

EORTC/NCIC, European Organisation for Research and Treatment of Cancer/National Cancer Institute of CanadaGBM, glioblastomaOS, overall survivalPFS, progression-free survivalSEER, Surveillance, Epidemiology, and End ResultsTMZ, temozolomide.

The Effect of Timing of Concurrent Chemoradiation in Patients With Newly Diagnosed Glioblastoma

BACKGROUND

The effect of timing of initiation of concurrent radiation and chemotherapy after surgery on outcome of patients with glioblastoma (GBM) remains unclear.

OBJECTIVE

To further explore this issue, we analyzed 4 clinical trials for patients newly diagnosed with GBM receiving concurrent and adjuvant temozolomide.

METHODS

The cohort study included 198 adult patients with newly diagnosed supratentorial GBM who were enrolled from 2004 to 2010 in 4 clinical trials consisting of radiation plus temozolomide and an experimental agent. The interval to initiation of therapy was determined from the time of surgical resection. The partitioning deletion/substitution/addition algorithm was used to determine the cutoff points for timing of chemoradiation at which there was a significant difference in overall survival (OS) and progression-free survival (PFS).

RESULTS

The median wait time between surgery and initiation of concurrent chemoradiation was 29.5 days (range, 7-56 days). A short delay in chemoradiation administration (at 30-34 days) was predictive of prolonged OS (hazard ratio [HR]: 0.63, P = .03) and prolonged PFS (HR: 0.68, P = .06) compared with early initiation of concurrent chemoradiation (<30 days), after adjusting for protocol and baseline prognostic variables including extent of resection by multivariate analysis. A longer delay to chemoradiation beyond 34 days was not associated with improved OS or PFS compared with early initiation (HR: 0.94, P = .77 and HR: 0.91, P = .63, respectively).

CONCLUSION

A short delay in the start of concurrent chemoradiation is beyond the classic paradigm of 4 weeks post-resection and may be associated with prolonged OS and PFS.

Towards the Personalized Treatment of Glioblastoma: Integrating Patient-Specific Clinical Data in a Continuous Mechanical Model

Glioblastoma multiforme (GBM) is the most aggressive and malignant among brain tumors. In addition to uncontrolled proliferation and genetic instability, GBM is characterized by a diffuse infiltration, developing long protrusions that penetrate deeply along the fibers of the white matter. These features, combined with the underestimation of the invading GBM area by available imaging techniques, make a definitive treatment of GBM particularly difficult. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of GBM evolution in every single patient throughout his/her oncological history, in order to target therapeutic weapons in a patient-specific manner. In this work, we propose a continuous mechanical model and we perform numerical simulations of GBM invasion combining the main mechano-biological characteristics of GBM with the micro-structural information extracted from radiological images, i.e. by elaborating patient-specific Diffusion Tensor Imaging (DTI) data. The numerical simulations highlight the influence of the different biological parameters on tumor progression and they demonstrate the fundamental importance of including anisotropic and heterogeneous patient-specific DTI data in order to obtain a more accurate prediction of GBM evolution. The results of the proposed mathematical model have the potential to provide a relevant benefit for clinicians involved in the treatment of this particularly aggressive disease and, more importantly, they might drive progress towards improving tumor control and patient’s prognosis.

Optimal radiation fractionation for low-grade gliomas: Insights from a mathematical model

We study optimal radiotherapy fractionations for low-grade glioma using mathematical models. Both space-independent and space-dependent models are studied. Two different optimization criteria have been developed, the first one accounting for the global effect of the tumor mass on the disease symptoms and the second one related to the delay of the malignant transformation of the tumor. The models are studied theoretically and numerically using the method of feasible directions. We have searched for optimal distributions of the daily doses dj in the standard protocol of 30 fractions using both models and the two different optimization criteria. The optimal results found in all cases are minor deviations from the standard protocol and provide only marginal potential gains. Thus, our results support the optimality of current radiation fractionations over the standard 6 week treatment period. This is also in agreement with the observation that minor variations of the fractionation have failed to provide measurable gains in survival or progression free survival, pointing out to a certain optimality of the current approach.

Extreme protraction for low-grade gliomas: theoretical proof of concept of a novel therapeutical strategy

Grade II gliomas are slowly growing primary brain tumours that affect mostly young patients and become fatal after a variable time period. Current clinical handling includes surgery as first-line treatment. Cytotoxic therapies (radiotherapy RT or chemotherapy QT) are used initially only for patients having a bad prognosis. Therapies are administered following the 'maximum dose in minimum time' principle, which is the same schedule used for high-grade brain tumours. Using mathematical models describing the growth of these tumours in response to radiotherapy, we find that an extreme protraction therapeutical strategy, i.e. enlarging substantially the time interval between RT fractions, may lead to better tumour control. Explicit formulas are found providing the optimal spacing between doses in a very good agreement with the simulations of the full 3D mathematical model approximating the tumour spatiotemporal dynamics. This idea, although breaking the well-established paradigm, has biological meaning since, in these slowly growing tumours, it may be more favourable to treat the tumour as the tumour cells leave the quiescent compartment and move into the cell cycle.

Mathematical modelling of tumour volume dynamics in response to stereotactic ablative radiotherapy for non-small cell lung cancer

This paper reports a modelling study of tumour volume dynamics in response to stereotactic ablative radiotherapy (SABR). The main objective was to develop a model that is adequate to describe tumour volume change measured during SABR, and at the same time is not excessively complex as lacking support from clinical data. To this end, various modelling options were explored, and a rigorous statistical method, the Akaike information criterion, was used to help determine a trade-off between model accuracy and complexity. The models were calibrated to the data from 11 non-small cell lung cancer patients treated with SABR. The results showed that it is feasible to model the tumour volume dynamics during SABR, opening up the potential for using such models in a clinical environment in the future.

Computer implementation of a new therapeutic model for GBM tumor

Modeling the tumor behavior in the host organ as function of time and radiation dose has been a major study in the previous decades. Here the effort in estimation of cancerous and normal cell proliferation and growth in glioblastoma multiform (GBM) tumor is presented. This paper introduces a new mathematical model in the form of differential equation of tumor growth. The model contains dose delivery amount in the treatment scheme as an input term. It also can be utilized to optimize the treatment process in order to increase the patient survival period. Gene expression programming (GEP) as a new concept is used for estimating this model. The LQ model has also been applied to GEP as an initial value, causing acceleration and improvement of the algorithm estimation. The model shows the number of the tumor and normal brain cells during the treatment process using the status of normal and cancerous cells in the initiation of treatment, the timing and amount of dose delivery to the patient, and a coefficient that describes the brain condition. A critical level is defined for normal cell when the patient's death occurs. In the end the model has been verified by clinical data obtained from previous accepted formulae and some of our experimental resources. The proposed model helps to predict tumor growth during treatment process in which further treatment processes can be controlled.

Basic ingredients for mathematical modeling of tumor growth in vitro: cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space.

A Monte Carlo based formalism to identify potential locations at high risk of tumor recurrence with a numerical model for glioblastoma multiforme

PURPOSE

The strategy currently used to treat glioblastoma multiforme (GBM) patients, which mostly relies on population-based failure patterns, does not consider the important variability in such patterns reported in the literature. As part of the multidisciplinary efforts being made to develop personalized therapeutic approaches, numerical models of tumor growth and treatment are increasingly being used by different groups around the world. In this study, a new formalism relying on the proliferation-invasion model is developed to identify potential locations of GBM recurrences. The authors assess the sensitivity of the location of potential tumor recurrences to the input parameter values predicted for a given patient by varying those values using a Monte-Carlo based approach. Our approach is designed to be prospective in the sense that it relies on patient-specific imaging data that can be gathered in one single preradiotherapy imaging session.

METHODS

The authors modeled the infiltration paths of glial cells using patient-specific diffusion tensor imaging (DTI) data. Nine GBM patients with preradiotherapy DTI data are considered in this study. The possible locations of tumor recurrences are determined by randomly selecting many ensembles of values for each of the growth and radiobiological parameters in the GBM growth model. A novel concept, the occurrence probability (OP), is introduced to assess the sensitivity of potential tumor recurrence locations to the input parameter values. For a given patient, the OP map is derived from a superposition of all potential tumor recurrence locations obtained with all sets of parameter values.

RESULTS

For eight out of nine of patients, the authors have identified a statistically significant region where the OP is above 50%. For two patients, these high risk regions are found to be located at a distance greater than 3.9 cm from the border of the gross tumor volume highlighting the inaccuracy of current margins for some patients. The exact location and size of these volumes with OP > 50 % are, however, sensitive to the number N of ensembles of parameter values for N ≲ 400. On the other hand, the authors have identified for each patient a threshold OP, the OP(T), which defines a volume that converges more rapidly with increasing N. The OP(T) for each patient varies between 20% and 40%. The volume defined by OP > OP(T) may be an adequate candidate to define a personalized margin for radiotherapy treatment planning of GBM patients.

CONCLUSIONS

A new Monte-Carlo based formalism was described and used to assess the variability of sites of potential recurrence predicted by the proliferation-invasion model to input parameter values. The authors have shown that high risk areas could be consistently identified with a limited number of sets (N ≲ 400) of randomly chosen parameter values. A major strength of this formalism is its potential prospective nature. Although a validation of the accuracy of the model-predicted tumor recurrence location still remains to be done, our method is potentially applicable to orient patient-specific definition of margins.

Dilemmas concerning dose distribution and the influence of relative biological effect in proton beam therapy of medulloblastoma

OBJECTIVE

To improve medulloblastoma proton therapy. Although considered ideal for proton therapy, there are potential disadvantages. Expected benefits include reduced radiation-induced cancer and circulatory complications, while avoiding small brain volumes of dose in-homogeneity when compared with conventional X-rays. Several aspects of proton therapy might contribute to reduced tumour control due to (a) the use of more homogenous dose levels which can result in under-dosage, (b) differences in relative biological effectiveness (RBE) between that prescription RBE of 1.1 and the RBE of brain and spinal cord (likely to exceed 1.1) and in medulloblastoma cells (where RBE is likely to be below 1.1). Such changes, although speculative for RBE, might result in potential underdosage of tumour cells and a higher bio-effect in brain tissue.

METHODS

Dose distributions for X-ray and proton treatment are compared, with allocation of likely RBE values for fast growing medullolastoma cells and stable central nervous system tissue.

RESULTS

These physical and radiobiological factors are shown to combine to give a higher risk of tumour recurrence with further risks on tumour control when dose reduction schedules used for X-ray therapy are replicated for proton therapy for "low-risk" patients.

CONCLUSION

The dose distributions and prescribed doses of proton therapy, taking into account RBE, in children and adults with medulloblastoma, need to be reconsidered.

Boron neutron capture therapy for newly diagnosed glioblastoma multiforme: an assessment of clinical potential

The purpose of this analysis was to assess the potential of BNCT, with L-boronophenylalanine (L-BPA), as first line radiotherapy for glioblastoma multiforme (GBM). The survival of patients with newly diagnosed GBM from a phase II BNCT study was compared with those from the two arms of a phase III study with conventional radiotherapy (RT) vs. RT plus concomitant and adjuvant medication with temozolomide (TMZ). A small subgroup, for which the methylation status of the O(6)-methylguanine-DNA methyltransferase (MGMT) DNA-repair gene was known, was also considered. The results indicated that the use of BNCT with BPA should be explored in a stratified randomized phase II trial in which patients with the unmethylated MGMT DNA-repair gene are offered BNCT vs. RT plus TMZ.