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

A Century of Fractionated Radiotherapy: How Mathematical Oncology Can Break the Rules

Radiotherapy is involved in 50% of all cancer treatments and 40% of cancer cures. Most of these treatments are delivered in fractions of equal doses of radiation (Fractional Equivalent Dosing (FED)) in days to weeks. This treatment paradigm has remained unchanged in the past century and does not account for the development of radioresistance during treatment. Even if under-optimized, deviating from a century of successful therapy delivered in FED can be difficult. One way of exploring the infinite space of fraction size and scheduling to identify optimal fractionation schedules is through mathematical oncology simulations that allow for in silico evaluation. This review article explores the evidence that current fractionation promotes the development of radioresistance, summarizes mathematical solutions to account for radioresistance, both in the curative and non-curative setting, and reviews current clinical data investigating non-FED fractionated radiotherapy.

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

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

Intermittent radiotherapy as alternative treatment for recurrent high grade glioma: a modeling study based on longitudinal tumor measurements

Recurrent high grade glioma patients face a poor prognosis for which no curative treatment option currently exists. In contrast to prescribing high dose hypofractionated stereotactic radiotherapy (HFSRT, [Formula: see text] Gy [Formula: see text] 5 in daily fractions) with debulking intent, we suggest a personalized treatment strategy to improve tumor control by delivering high dose intermittent radiation treatment (iRT, [Formula: see text] Gy [Formula: see text] 1 every 6 weeks). We performed a simulation analysis to compare HFSRT, iRT and iRT plus boost ([Formula: see text] Gy [Formula: see text] 3 in daily fractions at time of progression) based on a mathematical model of tumor growth, radiation response and patient-specific evolution of resistance to additional treatments (pembrolizumab and bevacizumab). Model parameters were fitted from tumor growth curves of 16 patients enrolled in the phase 1 NCT02313272 trial that combined HFSRT with bevacizumab and pembrolizumab. Then, iRT +/- boost treatments were simulated and compared to HFSRT based on time to tumor regrowth. The modeling results demonstrated that iRT + boost(- boost) treatment was equal or superior to HFSRT in 15(11) out of 16 cases and that patients that remained responsive to pembrolizumab and bevacizumab would benefit most from iRT. Time to progression could be prolonged through the application of additional, intermittently delivered fractions. iRT hence provides a promising treatment option for recurrent high grade glioma patients for prospective clinical evaluation.

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.

How heterogeneity drives tumour growth: a computational study

Although cancerous tumours usually originate from a single cell, they normally evolve into a remarkably heterogeneous agglomeration of cells. Heterogeneity is a pervasive and almost universal feature of tumours, but its origin and consequences remain poorly understood. Tumour heterogeneity has been usually associated with poor prognosis, but a better understanding of it may lead to more personalized diagnosis and therapy. Here, we study tumour heterogeneity developing a computational model in which different cell subpopulations compete for space. The model suggests that aggressive tumour subpopulations may become even more aggressive when they grow with a non-aggressive subpopulation. The model also provides a mechanistic explanation of how heterogeneity drives growth. In particular, we observed that even a mild heterogeneity in the proliferation rates of different cell subpopulations leads to a much faster overall tumour growth when compared to a homogeneous tumour. The proposed model may be a starting point to study tumour heterogeneity computationally and to suggest new hypotheses to be tested experimentally. This article is part of the theme issue 'Patterns in soft and biological matters'.

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.

Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas

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

Modeling the dynamics of oligodendrocyte precursor cells and the genesis of gliomas

Oligodendrocyte precursor cells (OPCs) have remarkable properties: they represent the most abundant cycling cell population in the adult normal brain and they manage to achieve a uniform and constant density throughout the adult brain. This equilibrium is obtained by the interplay of four processes: division, differentiation or death, migration and active self-repulsion. They are also strongly suspected to be at the origin of gliomas, when their equilibrium is disrupted. In this article, we present a model of the dynamics of OPCs, first in a normal tissue. This model is based on a cellular automaton and its rules are mimicking the ones that regulate the dynamics of real OPCs. The model is able to reproduce the homeostasis of the cell population, with the maintenance of a constant and uniform cell density and the healing of a lesion. We show that there exists a fair quantitative agreement between the simulated and experimental parameters, such as the cell velocity, the time taken to close a lesion, and the duration of the cell cycle. We present three possible scenarios of disruption of the equilibrium: the appearance of an over-proliferating cell, of a deadless/non-differentiating cell, or of a cell that lost any contact-inhibition. We show that the appearance of an over-proliferating cell is sufficient to trigger the growth of a tumor that has low-grade glioma features: an invasive behaviour, a linear radial growth of the tumor with a corresponding growth velocity of less than 2 mm per year, as well a cell density at the center which exceeds the one in normal tissue by a factor of less than two. The loss of contact inhibition leads to a more high-grade-like glioma. The results of our model contribute to the body of evidence that identify OPCs as possible cells of origin of gliomas.

Gliomas are the most common brain tumors and result in more years of life lost than any other tumor. Standard treatments only confer a limited improvement in overall survival, underscoring the need for new therapies. Finding the type of cells at the origin of these tumors could lead to the development of new drugs, specifically targeted towards these cells. The oligodendrocyte precursor cells are suspected to be these cells of origin, because they continue to proliferate through all the adult life. In this article, we present a model of the dynamics of these cells, first in the normal brain, and then we extrapolate our model to the pathological situation. We study several scenarios where, from the normal situation, a cell appears with one property different from those of the normal cells. We show that the alteration of only one of the properties of these cells in the model can lead to the formation of gliomas with different aggressiveness and very similar to real gliomas, reinforcing the suspicion that the precursor cells are at the origin of gliomas.

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.

Hypoxia in Gliomas: Opening Therapeutical Opportunities Using a Mathematical-Based Approach

This chapter explores the use of mathematical models as promising and powerful tools to understand the complexity of tumors and their, frequently, hypoxic environment. We focus on gliomas, which are primary brain tumors derived from glial cells, mainly astrocytes and/or oligodendrocytes. A variety of mathematical models, based on ordinary and/or partial differential equations, have been developed both at the micro and macroscopic levels. The aim here is to describe in a quantitative way key physiopathological mechanisms relevant in these types of malignancies and to suggest optimal therapeutical strategies. More specifically, we consider novel therapies targeting thromboembolic phenomena to decrease cell invasion in high grade glioma or to delay the malignant transformation in low grade gliomas. This study has been the basis of a multidisciplinary collaboration involving, among others, neuro-oncologists, radiation oncologists, pathologists, cancer biologists, surgeons and mathematicians.

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.