Radiotherapy planning for glioblastoma based on a tumor growth model: implications for spatial dose redistribution

An Integrated Monte Carlo Model for Heterogeneous Glioblastoma Treated with Boron Neutron Capture Therapy

BACKGROUND

Glioblastomas (GBMs) are notorious for their aggressive features, e.g., intrinsic radioresistance, extensive heterogeneity, hypoxia, and highly infiltrative behaviours. The prognosis has remained poor despite recent advances in systemic and modern X-ray radiotherapy. Boron neutron capture therapy (BNCT) represents an alternative radiotherapy technique for GBM. Previously, a Geant4 BNCT modelling framework was developed for a simplified model of GBM.

PURPOSE

The current work expands on the previous model by applying a more realistic in silico GBM model with heterogeneous radiosensitivity and anisotropic microscopic extensions (ME).

METHODS

Each cell within the GBM model was assigned an α/β value associated with different GBM cell lines and a 10B concentration. Dosimetry matrices corresponding to various MEs were calculated and combined to evaluate cell survival fractions (SF) using clinical target volume (CTV) margins of 2.0 & 2.5 cm. SFs for the BNCT simulation were compared with external X-ray radiotherapy (EBRT) SFs.

RESULTS

The SFs within the beam region decreased by more than two times compared to EBRT. It was demonstrated that BNCT results in markedly reduced SFs for both CTV margins compared to EBRT. However, the SF reduction as a result of the CTV margin extension using BNCT was significantly lower than using X-ray EBRT for one MEP distribution, while it remained similar for the other two MEP models.

CONCLUSIONS

Although the efficiency of BNCT in terms of cell kill is superior to EBRT, the extension of the CTV margin by 0.5 cm may not increase the BNCT treatment outcome significantly.

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.

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.

Analyzing magnetic resonance imaging data from glioma patients using deep learning

The quantitative analysis of images acquired in the diagnosis and treatment of patients with brain tumors has seen a significant rise in the clinical use of computational tools. The underlying technology to the vast majority of these tools are machine learning methods and, in particular, deep learning algorithms. This review offers clinical background information of key diagnostic biomarkers in the diagnosis of glioma, the most common primary brain tumor. It offers an overview of publicly available resources and datasets for developing new computational tools and image biomarkers, with emphasis on those related to the Multimodal Brain Tumor Segmentation (BraTS) Challenge. We further offer an overview of the state-of-the-art methods in glioma image segmentation, again with an emphasis on publicly available tools and deep learning algorithms that emerged in the context of the BraTS challenge.

Probabilistic definition of the clinical target volume-implications for tumor control probability modeling and optimization

Evidence has been presented that moving beyond the binary definition of clinical target volume (CTV) towards a probabilistic CTV can result in better treatment plans. The probabilistic CTV takes the likelihood of disease spread outside of the gross tumor into account. An open question is: how to optimize tumor control probability (TCP) based on the probabilistic CTV. We derive expressions for TCP under the assumptions of voxel independence and dependence. For the dependent case, we make the assumption that tumors grow outward from the gross tumor volume. We maximize the (non-convex) TCP under convex dose constraints for all models. For small numbers of voxels, and when a dose-influence matrix is not used, we use exhaustive search or Lagrange multiplier theory to compute optimal dose distributions. For larger cases we present (1) a multi-start strategy using linear programming with a random cost vector to provide random feasible starting solutions, followed by a local search, and (2) a heuristic strategy that greedily selects which subvolumes to dose, and then for each subvolume assignment runs a convex approximation of the optimization problem. The optimal dose distributions are in general different for the independent and dependent models even though the probabilities of each voxel being tumorous are set to the same in both cases. We observe phase transitions, where a subvolume is either dosed to a high level, or it gets 'sacrificed' by not dosing it at all. The greedy strategy often yields solutions indistinguishable from the multi-start solutions, but for the 2D case involving organs-at-risk and the dependent TCP model, discrepancies of around 5% (absolute) for TCP are observed. For realistic geometries, although correlated voxels is a more reasonable assumption, the correlation function is in general unknown. We demonstrate a tractable heuristic that works very well for the independent models and reasonably well for the dependent models. All data are provided.

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.

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.

Spatial optimization for radiation therapy of brain tumours

Glioblastomas are the most common primary brain tumours. They are known for their highly aggressive growth and invasion, leading to short survival times. Treatments for glioblastomas commonly involve a combination of surgical intervention, chemotherapy, and external beam radiation therapy (XRT). Previous works have not only successfully modelled the natural growth of glioblastomas in vivo, but also show potential for the prediction of response to radiation prior to treatment. This suggests that the efficacy of XRT can be optimized before treatment in order to yield longer survival times. However, while current efforts focus on optimal scheduling of radiotherapy treatment, they do not include a similarly sophisticated spatial optimization. In an effort to improve XRT, we present a method for the spatial optimization of radiation profiles. We expand upon previous results in the general problem and examine the more physically reasonable cases of 1-step and 2-step radiation profiles during the first and second XRT fractions. The results show that by including spatial optimization in XRT, while retaining a constant prescribed total dose amount, we are able to increase the total cell kill from the clinically-applied uniform case.

Distinct Tumor Microenvironment at Tumor Edge as a Result of Astrocyte Activation Is Associated With Therapeutic Resistance for Brain Tumor

Tumor vasculatures and hypoxia are critical tumor micro-environmental factors associated with tumor response to the therapy and heterogeneous in both time- and location-dependent manner. Using a murine orthotopic anaplastic astrocytoma model, ALTS1C1, this study showed that brain tumor edge had a very unique microenvironment, having higher microvascular density (MVD) and better vessel function than the tumor core, but on the other hand was also positive for hypoxia markers, such as pimonidazole (PIMO), hypoxia inducible factor-1α (HIF-1α), and carbonic anhydrase IV (CAIX). The hypoxia at tumor edge was transient, named as peripheral hypoxia, and caused by different mechanisms from the chronic hypoxia in tumor core. The correlation of CAIX staining with astrocyte activation marker, glial fibrillary acid protein (GFAP), at the tumor edge indicated the involvement of astrocyte activation on the development of peripheral hypoxia. Peripheral hypoxia was a specific trait of orthotopic brain tumors at tumor edge, regardless of tumor origin. The hypoxic cells were resistant to the therapy, regardless of their location. Surviving cells, particularly those at the hypoxic region of tumor edge, are likely the cause of tumor recurrence after the therapy. New therapeutic platform that targets cells in tumor edge is likely to achieve better treatment outcomes.

Diffusion tensor magnetic resonance imaging driven growth modeling for radiotherapy target definition in glioblastoma

BACKGROUND

The clinical target volume (CTV) in radiotherapy is routinely based on gadolinium contrast enhanced T1 weighted (T1w + Gd) and T2 weighted fluid attenuated inversion recovery (T2w FLAIR) magnetic resonance imaging (MRI) sequences which have been shown to over- or underestimate the microscopic tumor cell spread. Gliomas favor spread along the white matter fiber tracts. Tumor growth models incorporating the MRI diffusion tensors (DTI) allow to account more consistently for the glioma growth. The aim of the study was to investigate the potential of a DTI driven growth model to improve target definition in glioblastoma (GBM).

MATERIAL AND METHODS

Eleven GBM patients were scanned using T1w, T2w FLAIR, T1w + Gd and DTI. The brain was segmented into white matter, gray matter and cerebrospinal fluid. The Fisher-Kolmogorov growth model was used assuming uniform proliferation and a difference in white and gray matter diffusion of a ratio of 10. The tensor directionality was tested using an anisotropy weighting parameter set to zero (γ0) and twenty (γ20). The volumetric comparison was performed using Hausdorff distance, Dice similarity coefficient (DSC) and surface area.

RESULTS

The median of the standard CTV (CTVstandard) was 180 cm³. The median surface area of CTVstandard was 211 cm². The median surface area of respective CTV_γ0 and CTV_γ20 significantly increased to 338 and 376 cm², respectively. The Hausdorff distance was greater than zero and significantly increased for both CTV_γ0 and CTV_γ20 with respective median of 18.7 and 25.2 mm. The DSC for both CTV_γ0 and CTV_γ20 were significantly below one with respective median of 0.74 and 0.72, which means that 74 and 72% of CTVstandard were included in CTV_γ0 and CTV_γ20, respectively.

CONCLUSIONS

DTI driven growth models result in CTVs with a significantly increased surface area, a significantly increased Hausdorff distance and decreased overlap between the standard and model derived volume.

Clinical implications of in silico mathematical modeling for glioblastoma: a critical review

Glioblastoma remains a clinical challenge in spite of years of extensive research. Novel approaches are needed in order to integrate the existing knowledge. This is the potential role of mathematical oncology. This paper reviews mathematical models on glioblastoma from the clinical doctor's point of view, with focus on 3D modeling approaches of radiation response of in vivo glioblastomas based on contemporary imaging techniques. As these models aim to provide a clinically useful tool in the era of personalized medicine, the integration of the latest advances in molecular and imaging science and in clinical practice by the in silico models is crucial for their clinical relevance. Our aim is to indicate areas of GBM research that have not yet been addressed by in silico models and to point out evidence that has come up from in silico experiments, which may be worth considering in the clinic. This review examines how close these models have come in predicting the outcome of treatment protocols and in shaping the future of radiotherapy treatments.

Development of an integrated Monte Carlo model for glioblastoma multiforme treated with boron neutron capture therapy

Glioblastomas (GBM) are notorious for their high fatality rate. Boron Neutron Capture Therapy (BNCT) being a biochemically targeted type of radiotherapy is a potent modality for GBM. In the current work, a BNCT treatment modelling framework for GBM was developed. Optimal Clinical Target Volume (CTV) margins for GBM-BNCT and the BNCT efficacy have been investigated. The model integrated a cell-based dosimetry model, an in-house-developed epithermal neutron beam model and previously-developed Microscopic Extension Probability (MEP) model. The system was defined as a cubic ICRP-brain phantom divided into 20 μm side voxels. The corresponding ¹⁰B concentrations in GBM and normal brain cells were applied. The in-silico model was irradiated with the epithermal neutron beam using 2 and 2.5 cm CTV margins. Results from the cell-based dosimetry and the MEP models were combined to calculate GBM cell survival fractions (SF) post BNCT and compared to x-ray radiotherapy (XRT) SFs. Compared to XRT, the SF within the beam decreased by five orders of magnitudes and the total SF was reduced three times following BNCT. CTV extension by 0.5 cm reduced the SF by additional (53.8 ± 0.3)%. In conclusion, BNCT results in a more efficient cell kill. The extension of the CTV margin, however, may not increase the treatment outcome significantly.

The clinical target volume in lung, head-and-neck, and esophageal cancer: Lessons from pathological measurement and recurrence analysis

Radiotherapy research has achieved remarkable progress in target volume definition. Advances in medical imaging facilitate more precise localization of the gross tumor volume, alongside a more detailed understanding of the geometric uncertainties associated with treatment delivery that has enabled robust safety margins to be customized to the specific treatment scenario at hand. By contrast, the clinical target volume, meant to encompass gross tumor, as well as, adjacent sub-clinical disease, has evolved very little. It is more often defined by clinician experience and institutional convention than on a patient-specific basis. This disparity arises from the inherent invisibility of sub-clinical disease in current medical imaging. Its incidence and expanse can only be ascertained via indirect means. This article reviews two such strategies: histopathological measurements on resection specimen and analyses of locoregional recurrences after radiotherapy.

Personalized Radiotherapy Planning Based on a Computational Tumor Growth Model

In this article, we propose a proof of concept for the automatic planning of personalized radiotherapy for brain tumors. A computational model of glioblastoma growth is combined with an exponential cell survival model to describe the effect of radiotherapy. The model is personalized to the magnetic resonance images (MRIs) of a given patient. It takes into account the uncertainty in the model parameters, together with the uncertainty in the MRI segmentations. The computed probability distribution over tumor cell densities, together with the cell survival model, is used to define the prescription dose distribution, which is the basis for subsequent Intensity Modulated Radiation Therapy (IMRT) planning. Depending on the clinical data available, we compare three different scenarios to personalize the model. First, we consider a single MRI acquisition before therapy, as it would usually be the case in clinical routine. Second, we use two MRI acquisitions at two distinct time points in order to personalize the model and plan radiotherapy. Third, we include the uncertainty in the segmentation process. We present the application of our approach on two patients diagnosed with high grade glioma. We introduce two methods to derive the radiotherapy prescription dose distribution, which are based on minimizing integral tumor cell survival using the maximum a posteriori or the expected tumor cell density. We show how our method allows the user to compute a patient specific radiotherapy planning conformal to the tumor infiltration. We further present extensions of the method in order to spare adjacent organs at risk by re-distributing the dose. The presented approach and its proof of concept may help in the future to better target the tumor and spare organs at risk.

Diffusion Kurtosis Imaging of Gliomas Grades II and III - A Study of Perilesional Tumor Infiltration, Tumor Grades and Subtypes at Clinical Presentation

BACKGROUND

Diffusion kurtosis imaging (DKI) allows for assessment of diffusion influenced by microcellular structures. We analyzed DKI in suspected low-grade gliomas prior to histopathological diagnosis. The aim was to investigate if diffusion parameters in the perilesional normal-appearing white matter (NAWM) differed from contralesional white matter, and to investigate differences between glioma malignancy grades II and III and glioma subtypes (astrocytomas and oligodendrogliomas).

PATIENTS AND METHODS

Forty-eight patients with suspected low-grade glioma were prospectively recruited to this institutional review board-approved study and investigated with preoperative DKI at 3T after written informed consent. Patients with histologically proven glioma grades II or III were further analyzed (n=35). Regions of interest (ROIs) were delineated on T2FLAIR images and co-registered to diffusion MRI parameter maps. Mean DKI data were compared between perilesional and contralesional NAWM (student's t-test for dependent samples, Wilcoxon matched pairs test). Histogram DKI data were compared between glioma types and glioma grades (multiple comparisons of mean ranks for all groups). The discriminating potential for DKI in assessing glioma type and grade was assessed with receiver operating characteristics (ROC) curves.

RESULTS

There were significant differences in all mean DKI variables between perilesional and contralesional NAWM (p=<0.000), except for axial kurtosis (p=0.099). Forty-four histogram variables differed significantly between glioma grades II (n=23) and III (n=12) (p=0.003-0.048) and 10 variables differed significantly between ACs (n=18) and ODs (n=17) (p=0.011-0.050). ROC curves of the best discriminating variables had an area under the curve (AUC) of 0.657-0.815.

CONCLUSIONS

Mean DKI variables in perilesional NAWM differ significantly from contralesional NAWM, suggesting altered microstructure by tumor infiltration not depicted on morphological MRI. Histogram analysis of DKI data identifies differences between glioma grades and subtypes.

MRI Based Bayesian Personalization of a Tumor Growth Model

The mathematical modeling of brain tumor growth has been the topic of numerous research studies. Most of this work focuses on the reaction-diffusion model, which suggests that the diffusion coefficient and the proliferation rate can be related to clinically relevant information. However, estimating the parameters of the reaction-diffusion model is difficult because of the lack of identifiability of the parameters, the uncertainty in the tumor segmentations, and the model approximation, which cannot perfectly capture the complex dynamics of the tumor evolution. Our approach aims at analyzing the uncertainty in the patient specific parameters of a tumor growth model, by sampling from the posterior probability of the parameters knowing the magnetic resonance images of a given patient. The estimation of the posterior probability is based on: 1) a highly parallelized implementation of the reaction-diffusion equation using the Lattice Boltzmann Method (LBM), and 2) a high acceptance rate Monte Carlo technique called Gaussian Process Hamiltonian Monte Carlo (GPHMC). We compare this personalization approach with two commonly used methods based on the spherical asymptotic analysis of the reaction-diffusion model, and on a derivative-free optimization algorithm. We demonstrate the performance of the method on synthetic data, and on seven patients with a glioblastoma, the most aggressive primary brain tumor. This Bayesian personalization produces more informative results. In particular, it provides samples from the regions of interest and highlights the presence of several modes for some patients. In contrast, previous approaches based on optimization strategies fail to reveal the presence of different modes, and correlation between parameters.

Image based modeling of tumor growth

Tumors are a main cause of morbidity and mortality worldwide. Despite the efforts of the clinical and research communities, little has been achieved in the past decades in terms of improving the treatment of aggressive tumors. Understanding the underlying mechanism of tumor growth and evaluating the effects of different therapies are valuable steps in predicting the survival time and improving the patients' quality of life. Several studies have been devoted to tumor growth modeling at different levels to improve the clinical outcome by predicting the results of specific treatments. Recent studies have proposed patient-specific models using clinical data usually obtained from clinical images and evaluating the effects of various therapies. The aim of this review is to highlight the imaging role in tumor growth modeling and provide a worthwhile reference for biomedical and mathematical researchers with respect to tumor modeling using the clinical data to develop personalized models of tumor growth and evaluating the effect of different therapies.

Volumetric relationship between 2-hydroxyglutarate and FLAIR hyperintensity has potential implications for radiotherapy planning of mutant IDH glioma patients

BACKGROUND

Gliomas with mutant isocitrate dehydrogenase (IDH) produce high levels of 2-hydroxyglutarate (2HG) that can be quantitatively measured by 3D magnetic resonance spectroscopic imaging (MRSI). Current glioma MRI primarily relies upon fluid-attenuated inversion recovery (FLAIR) hyperintensity for treatment planning, although this lacks specificity for tumor cells. Here, we investigated the relationship between 2HG and FLAIR in mutant IDH glioma patients to determine whether 2HG mapping is valuable for radiotherapy planning.

METHODS

Seventeen patients with mutant IDH1 gliomas were imaged by 3 T MRI. A 3D MRSI sequence was employed to specifically image 2HG. FLAIR imaging was performed using standard clinical protocol. Regions of interest (ROIs) were determined for FLAIR and optimally thresholded 2HG hyperintensities. The overlap, displacement, and volumes of 2HG and FLAIR ROIs were calculated.

RESULTS

In 8 of 17 (47%) patients, the 2HG volume was larger than FLAIR volume. Across the entire cohort, the mean volume of 2HG was 35.3 cc (range, 5.3-92.7 cc), while the mean volume of FLAIR was 35.8 cc (range, 6.3-140.8 cc). FLAIR and 2HG ROIs had mean overlap of 0.28 (Dice coefficients range, 0.03-0.57) and mean displacement of 12.2 mm (range, 3.2-23.5 mm) between their centers of mass.

CONCLUSIONS

Our results indicate that for a substantial number of patients, the 2HG volumetric assessment of tumor burden is more extensive than FLAIR volume. In addition, there is only partial overlap and asymmetric displacement between the centers of FLAIR and 2HG ROIs. These results may have important implications for radiotherapy planning of IDH mutant glioma.

Radiation oncology in the era of precision medicine

Technological advances and clinical research over the past few decades have given radiation oncologists the capability to personalize treatments for accurate delivery of radiation dose based on clinical parameters and anatomical information. Eradication of gross and microscopic tumours with preservation of health-related quality of life can be achieved in many patients. Two major strategies, acting synergistically, will enable further widening of the therapeutic window of radiation oncology in the era of precision medicine: technology-driven improvement of treatment conformity, including advanced image guidance and particle therapy, and novel biological concepts for personalized treatment, including biomarker-guided prescription, combined treatment modalities and adaptation of treatment during its course.

The universal growth rate behavior and regime transition in adherent cell colonies

In this work, we used five cell lineages, cultivated in vitro, to show they follow a common functional form to the growth rate: a sigmoidal curve, suggesting that competition and cooperation (usual mechanisms for systems with this behavior) might be present. Both theoretical and experimental investigations, on the causes of this behavior, are challenging for the research field; since the sigmoidal form to the growth rate seems to absorb important properties of such systems, e.g., cell deformation and statistical interactions. We shed some light on this subject by showing how cell spreading affects the radius behavior of the growing colonies. Doing numerical time derivatives of the experimental data, we obtained the growth rates. Using reduced variables for the time and rates, we obtained the collapse of all colonies growth rates onto one curve with sigmoidal shape. This suggests a universal-type behavior, with regime transition related to a morphological transition of adherent cell colonies.

Radiotherapy planning for glioblastoma based on a tumor growth model: improving target volume delineation

Glioblastoma differ from many other tumors in the sense that they grow infiltratively into the brain tissue instead of forming a solid tumor mass with a defined boundary. Only the part of the tumor with high tumor cell density can be localized through imaging directly. In contrast, brain tissue infiltrated by tumor cells at low density appears normal on current imaging modalities. In current clinical practice, a uniform margin, typically two centimeters, is applied to account for microscopic spread of disease that is not directly assessable through imaging. The current treatment planning procedure can potentially be improved by accounting for the anisotropy of tumor growth, which arises from different factors: anatomical barriers such as the falx cerebri represent boundaries for migrating tumor cells. In addition, tumor cells primarily spread in white matter and infiltrate gray matter at lower rate. We investigate the use of a phenomenological tumor growth model for treatment planning. The model is based on the Fisher-Kolmogorov equation, which formalizes these growth characteristics and estimates the spatial distribution of tumor cells in normal appearing regions of the brain. The target volume for radiotherapy planning can be defined as an isoline of the simulated tumor cell density. This paper analyzes the model with respect to implications for target volume definition and identifies its most critical components. A retrospective study involving ten glioblastoma patients treated at our institution has been performed. To illustrate the main findings of the study, a detailed case study is presented for a glioblastoma located close to the falx. In this situation, the falx represents a boundary for migrating tumor cells, whereas the corpus callosum provides a route for the tumor to spread to the contralateral hemisphere. We further discuss the sensitivity of the model with respect to the input parameters. Correct segmentation of the brain appears to be the most crucial model input. We conclude that the tumor growth model provides a method to account for anisotropic growth patterns of glioma, and may therefore provide a tool to make target delineation more objective and automated.