High-grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases

A Network Based Model for Predicting Spatial Progression of Metastasis

Metastatic cancer is reported to have a mortality rate of 90%. Understanding the underlying principles of metastasis and quantifying them through mathematical modelling provides insights into potential treatment regimes. This work presents a partial differential equation based mathematical model embedded on a network, representing the organs and the blood vessels between them, with the aim of predicting likely secondary metastatic sites. Through this framework the relationship between metastasis and blood flow and between metastasis and the diffusive behaviour of cancer is explored. An analysis of the model predictions showed a good correlation with clinical data for some cancer types, particularly for cancers originating in the gut and liver. The model also predicts an inverse relationship between blood velocity and the concentration of cancer cells in secondary organs. Finally, for anisotropic diffusive behaviour, where the cancer experiences greater diffusivity in one direction, metastatic efficiency decreased. This is aligned with the clinical observation that gliomas of the brain, which typically show anisotropic diffusive behaviour, exhibit fewer metastases. The investigation yields some valuable results for clinical practitioners and researchers-as it clarifies some aspects of cancer that have hitherto been difficult to study, such as the impact of differing diffusive behaviours and blood flow rates on the global spread of cancer. The model provides a good framework for studying cancer progression using cancer-specific information when simulating metastasis.

Modeling of glioma growth using modified reaction-diffusion equation on brain MR images

BACKGROUND AND OBJECTIVE

Modeling of glioma growth and evolution is of key importance for cancer diagnosis, predicting clinical progression and improving treatment outcomes of neurosurgery. However, existing models are unable to characterize spatial variations of the proliferation and infiltration of tumor cells, making it difficult to achieve accurate prediction of tumor growth.

METHODS

In this paper, a new growth model of brain tumor using a reaction-diffusion equation on brain magnetic resonance images is proposed. Both the heterogeneity of brain tissue and the density of tumor cells are used to estimate the proliferation and diffusion coefficients of brain tumor cells. The diffusion coefficient that characterizes tumor diffusion and infiltration is calculated based on the ratio of tissues (white and gray matter), while the proliferation coefficient is evaluated using the spatial gradient of tumor cells. In addition, a parameter space is constructed using inverse distance weighted interpolation to describe the spatial distribution of proliferation coefficient.

RESULTS

The glioma growth predicted by the proposed model were tested by comparing with the real magnetic resonance images of the patients. Experiments and simulation results show that the proposed method achieves accurate modeling of glioma growth. The interpolation-based growth model has higher average dice score of 0.0647 and 0.0545, and higher average Jaccard index of 0.0673 and 0.0573, respectively, compared to the uniform- and gradient-based growth models.

CONCLUSIONS

The experimental results demonstrate the feasibility of calculating the proliferation and diffusion coefficients of the growth model based on patient-specific anatomy. The parameter space that characterizes spatial distribution of proliferation and diffusion coefficients is established and incorporated into the simulation of glioma growth. It enables to obtain patient-specific models about glioma growth by estimating and calibrating only a few model parameters.

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.

Overexpression of immunoproteasome low-molecular-mass polypeptide 7 and inhibiting role of next-generation proteasome inhibitor ONX 0912 on cell growth in glioma

OBJECTIVES

The aim of this study was to determine the expression level of immunoproteasome and its clinical significance in glioma preliminarily. Furthermore, we studied the function and molecular mechanism of proteasome inhibitor ONX 0912 on glioma cell.

MATERIALS AND METHODS

The expression of immunoproteasome in glioma and tumor-adjacent brain tissues was detected by western blot. Immunohistochemical technique was used to detect the expression of low-molecular-mass polypeptide 7 in 55 cases of glioma tissues and 6 cases of tumor-adjacent brain tissues. Chi-square test was used to analyze the relationship between the expression level of low-molecular-mass polypeptide 7 and clinical characteristics. Kaplan-Meier method and Cox regression analysis were applied to analyze the correlation between low-molecular-mass polypeptide 7 expression and prognosis of patients. 3-(4,5-dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4-sulfophenyl)-2Htetrazolium) (MTS) proliferation assay was introduced to detect the impact of ONX 0912 on proliferation of glioma cells. Western blot was used to detect the apoptosis- and autophagy-related protein in glioma cell treated with ONX 0912.

RESULTS

Our results showed that only low-molecular-mass polypeptide 7 expression was notably upregulated in gliomas in comparison with tumor-adjacent brain tissues and further increased in malignant gliomas compared with benign gliomas (P < 0.01). In the multivariate Cox proportional regression analyses, it was evident that low-molecular-mass polypeptide 7 was an independent unfavorable prognostic factor (P < 0.05). The results of MTS assay showed that ONX 0912 could inhibit the proliferation of glioma cell. Besides, we found that ONX 0912 could prompt apoptosis and autophagosome accumulation, which may be responsible for inhibiting glioma cell proliferation.

CONCLUSION

In conclusion, our results indicated that low-molecular-mass polypeptide 7 might be a candidate prognostic biomarker, and proteasome inhibitor ONX 0912 might act as a potential treatment agent for glioma.

Tumor ablation due to inhomogeneous anisotropic diffusion in generic three-dimensional topologies

In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.

Biomechanical modelling of spinal tumour anisotropic growth

Biomechanical abnormalities of solid tumours involve stiffening of the tissue and accumulation of mechanical stresses. Both abnormalities affect cancer cell proliferation and invasiveness and thus, play a crucial role in tumour morphology and metastasis. Even though, it has been known for more than two decades that high mechanical stresses reduce cancer cell proliferation rates driving growth towards low-stress regions, most biomechanical models of tumour growth account for isotropic growth. This cannot be valid, however, in tumours that grow within multiple host tissues of different mechanical properties, such as the spine. In these cases, structural heterogeneity would result in anisotropic growth of tumours. To this end, we present a biomechanical, biphasic model for anisotropic growth of spinal tumours. The model that accounts for both the fluid and the solid phase of the tumour was used to predict the evolution of solid stress and interstitial fluid pressure in intramedullary spinal tumours and highlight the differences between isotropic and anisotropic growth. Varying the degree of anisotropy, we found considerable differences in the shape of the tumours, leading to tumours of more realistic ellipsoidal shapes.

Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI

Previous studies to simulate brain tumor progression, often investigate either temporal changes in cancer cell density or the overall tissue-level growth of the tumor mass. Here, we developed a computational model to bridge these two approaches. The model incorporates the tumor biomechanical response at the tissue level and accounts for cellular events by modeling cancer cell proliferation, infiltration to surrounding tissues, and invasion to distant locations. Moreover, acquisition of high resolution human data from anatomical magnetic resonance imaging, diffusion tensor imaging and perfusion imaging was employed within the simulations towards a realistic and patient specific model. The model predicted the intratumoral mechanical stresses to range from 20 to 34 kPa, which caused an up to 4.5 mm displacement to the adjacent healthy tissue. Furthermore, the model predicted plausible cancer cell invasion patterns within the brain along the white matter fiber tracts. Finally, by varying the tumor vascular density and its invasive outer ring thickness, our model showed the potential of these parameters for guiding the timing (83–90 days) of cancer cell distant invasion as well as the number (0–2 sites) and location (temportal and/or parietal lobe) of the invasion sites.

Glioma growth modeling based on the effect of vital nutrients and metabolic products

Glioma brain tumors exhibit considerably aggressive behavior leading to high mortality rates. Mathematical modeling of tumor growth aims to explore the interactions between glioma cells and tissue microenvironment, which affect tumor evolution. Leveraging this concept, we present a three-dimensional model of glioma spatio-temporal evolution based on existing continuum approaches, yet incorporating novel factors of the phenomenon. The proposed model involves the interactions between different tumor cell phenotypes and their microenvironment, investigating how tumor growth is affected by complex biological exchanges. It focuses on the separate and combined effect of vital nutrients and cellular wastes on tumor expansion, leading to the formation of cell populations with different metabolic, proliferative, and diffusive profiles. Several simulations were performed on a virtual and a real glioma, using combinations of proliferation and diffusion rates for different evolution times. The model results were validated on a glioma model available in the literature and a real case of tumor progression. The experimental observations indicate that our model estimates quite satisfactorily the expansion of each region and the overall tumor growth. Based on the individual results, the proposed model may provide an important research tool for patient-specific simulation of different tumor evolution scenarios and reliable estimation of glioma evolution. Graphical Abstract Outline of the mathematical model functionality and application to glioma growth with indicative results.

Comparative study between spatio-temporal models for brain tumor growth

Modeling of brain tumor growth simulator can estimate life expectancy for individual patients, estimate future effect of brain damages toward human senses and attitude and help in evaluating the efficiency of applied treatments. Brain tumor growth can be calculated based on Spatio-Temporal mathematical models namely the isotropic reaction-diffusion model and the anisotropic reaction-diffusion model where the second model produces more realistic results. Tumor normally grows in White Matter (WM) five times faster than in Gray Matter (GM) which makes brain tissues modeled as inhomogeneous-anisotropic material to assign different parameters to each tissue. In this research a comparative study between several tumor growth models has been achieved to clarify the effect of different algorithms on modeling tumor grow.

A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects

A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double) with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient's multiscale data and experimenting in silico (ie, on the computer).

Biphasic modeling of brain tumor biomechanics and response to radiation treatment

Biomechanical forces are central in tumor progression and response to treatment. This becomes more important in brain cancers where tumors are surrounded by tissues with different mechanical properties. Existing mathematical models ignore direct mechanical interactions of the tumor with the normal brain. Here, we developed a clinically relevant model, which predicts tumor growth accounting directly for mechanical interactions. A three-dimensional model of the gray and white matter and the cerebrospinal fluid was constructed from magnetic resonance images of a normal brain. Subsequently, a biphasic tissue growth theory for an initial tumor seed was employed, incorporating the effects of radiotherapy. Additionally, three different sets of brain tissue properties taken from the literature were used to investigate their effect on tumor growth. Results show the evolution of solid stress and interstitial fluid pressure within the tumor and the normal brain. Heterogeneous distribution of the solid stress exerted on the tumor resulted in a 35% spatial variation in cancer cell proliferation. Interestingly, the model predicted that distant from the tumor, normal tissues still undergo significant deformations while it was found that intratumoral fluid pressure is elevated. Our predictions relate to clinical symptoms of brain cancers and present useful tools for therapy planning.

In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue

Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided.

A Proposed Paradigm Shift in Initializing Cancer Predictive Models with DCE-MRI Based PK Parameters: A Feasibility Study

Glioblastoma multiforme is the most aggressive type of glioma and the most common malignant primary intra-axial brain tumor. In an effort to predict the evolution of the disease and optimize therapeutical decisions, several models have been proposed for simulating the growth pattern of glioma. One of the latest models incorporates cell proliferation and invasion, angiogenic net rates, oxygen consumption, and vasculature. These factors, particularly oxygenation levels, are considered fundamental factors of tumor heterogeneity and compartmentalization. This paper focuses on the initialization of the cancer cell populations and vasculature based on imaging examinations of the patient and presents a feasibility study on vasculature prediction over time. To this end, pharmacokinetic parameters derived from dynamic contrast-enhanced magnetic resonance imaging using Toft’s model are used in order to feed the model. K^trans is used as a metric of the density of endothelial cells (vasculature); at the same time, it also helps to discriminate distinct image areas of interest, under a set of assumptions. Feasibility results of applying the model to a real clinical case are presented, including a study on the effect of certain parameters on the pattern of the simulated tumor.

Web-based workflow planning platform supporting the design and execution of complex multiscale cancer models

Significant Virtual Physiological Human efforts and projects have been concerned with cancer modeling, especially in the European Commission Seventh Framework research program, with the ambitious goal to approach personalized cancer simulation based on patient-specific data and thereby optimize therapy decisions in the clinical setting. However, building realistic in silico predictive models targeting the clinical practice requires interactive, synergetic approaches to integrate the currently fragmented efforts emanating from the systems biology and computational oncology communities all around the globe. To further this goal, we propose an intelligent graphical workflow planning system that exploits the multiscale and modular nature of cancer and allows building complex cancer models by intuitively linking/interchanging highly specialized models. The system adopts and extends current standardization efforts, key tools, and infrastructure in view of building a pool of reliable and reproducible models capable of improving current therapies and demonstrating the potential for clinical translation of these technologies.

An architecture for integrating cancer model repositories

The TUMOR project aims at developing a European clinically oriented semantic-layered cancer digital model repository from existing EU projects that will be interoperable with the US grid-enabled semantic-layered digital model repository platform at CViT.org (Center for the Development of a Virtual Tumor, Massachusetts General Hospital (MGH), Boston, USA) which is NIH/NCI-caGRID compatible. In this paper we describe the modular and federated architecture of TUMOR that effectively addresses model integration, interoperability, and security related issues.

Mathematical modelling of spatio-temporal glioma evolution

Background

Gliomas are the most common types of brain cancer, well known for their aggressive proliferation and the invasive behavior leading to a high mortality rate. Several mathematical models have been developed for identifying the interactions between glioma cells and tissue microenvironment, which play an important role in the mechanism of the tumor formation and progression.

Methods

Building and expanding on existing approaches, this paper develops a continuous three-dimensional model of avascular glioma spatio-temporal evolution. The proposed spherical model incorporates the interactions between the populations of four different glioma cell phenotypes (proliferative, hypoxic, hypoglychemic and necrotic) and their tissue microenvironment, in order to investigate how they affect tumor growth and invasion in an isotropic and homogeneous medium. The model includes two key variables involved in the proliferation and invasion processes of cancer cells; i.e. the extracellular matrix and the matrix-degradative enzymes concentrations inside the tumor and its surroundings. Additionally, the proposed model focuses on innovative features, such as the separate and independent impact of two vital nutrients, namely oxygen and glucose, in tumor growth, leading to the formation of cell populations with different metabolic profiles. The model implementation takes under consideration the variations of particular factors, such as the local cell proliferation rate, the variable conversion rates of cells from one category to another and the nutrient-dependent thresholds of conversion. All model variables (cell densities, ingredients concentrations) are continuous and described by reaction-diffusion equations.

Results

Several simulations were performed using combinations of growth and invasion rates, for different evolution times. The model results were evaluated by medical experts and validated on experimental glioma models available in the literature, revealing high agreement between simulated and experimental results.

Conclusions

Based on the experimental validation, as well as the evaluation by clinical experts, the proposed model may provide an essential tool for the patient-specific simulation of different tumor evolution scenarios and reliable prognosis of glioma spatio-temporal progression.

Simulating radiotherapy effect in high-grade glioma by using diffusive modeling and brain atlases

Applying diffusive models for simulating the spatiotemporal change of concentration of tumour cells is a modern application of predictive oncology. Diffusive models are used for modelling glioblastoma, the most aggressive type of glioma. This paper presents the results of applying a linear quadratic model for simulating the effects of radiotherapy on an advanced diffusive glioma model. This diffusive model takes into consideration the heterogeneous velocity of glioma in gray and white matter and the anisotropic migration of tumor cells, which is facilitated along white fibers. This work uses normal brain atlases for extracting the proportions of white and gray matter and the diffusion tensors used for anisotropy. The paper also presents the results of applying this glioma model on real clinical datasets.

In-depth analysis and evaluation of diffusive glioma models

Glioma is one of the most aggressive types of brain tumor. Several mathematical models have been developed during the past two decades, toward simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. Nevertheless, despite the applications presented, there has been little work on studying the details of the mathematical solution and implementation of the 3-D diffusion model and presenting a qualitative analysis of the algorithmic results. This paper presents a complete mathematical framework on the solution of the DRE using different numerical schemes. This framework takes into account all characteristics of the latest models, such as brain tissue heterogeneity, anisotropic tumor cell migration, chemotherapy, and resection modeling. The different numerical schemes presented have been evaluated based upon the degree to which the DRE exact solution is approximated. Experiments have been conducted both on real datasets and a test case for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the accuracy of the different models.

A software prototype for the assessment of tumor treatment response using diffusion and perfusion MR imaging

Advanced MRI techniques including diffusion and perfusion weighted imaging, has the potential to provide early surrogate biomarkers to detect, characterize and assess treatment response of tumors. However, the widely accepted Response Evaluation Criteria in Solid Tumors (RECIST) are still considered as the gold standard for the evaluation of treatment response in solid tumors, even if according to recent studies RECIST seem to disregard the extent of necrosis, which is the target of all effective locoregional therapies. This is partly due to the fact that measurements of tumor size aren't the best criterion for assessing actual early response. On the other hand, more sophisticated techniques such as the Apparent Diffusion Coefficient (ADC) and perfusion parameters are usually processed manually and evaluated independently using commercial CAD software, not widely available. In this paper we present an open access extensible software platform providing both diffusion and perfusion analysis in a single, user friendly environment that allows the radiologist to easily and objectively evaluate tumor response to therapy.

Integrating Imaging Data into Predictive Biomathematical and Biophysical Models of Cancer

While there is a mature literature on biomathematical and biophysical modeling in cancer, many of the existing approaches are not of clinical utility, as they require input data that are extremely difficult to obtain in an intact organism, and/or require a large number of assumptions on the free parameters included in the models. Thus, there has only been very limited application of such models to solve problems of clinical import. More recently, however, there has been increased activity at the interface of quantitative, noninvasive imaging data, and tumor mathematical modeling. In addition to reporting on bulk tumor morphology and volume, emerging imaging techniques can quantitatively report on for example tumor vascularity, glucose metabolism, cell density and proliferation, and hypoxia. In this paper, we first motivate the problem of predicting therapy response by highlighting some (acknowledged) shortcomings in existing methods. We then provide introductions to a number of representative quantitative imaging methods and describe how they are currently (and potentially can be) used to initialize and constrain patient specific mathematical and biophysical models of tumor growth and treatment response, thereby increasing the clinical utility of such approaches. We conclude by highlighting some of the exciting research directions when one integrates quantitative imaging and tumor modeling.