Biocomputing: numerical simulation of glioblastoma growth using diffusion tensor imaging

Atomic Force Microscope Nanoindentation Analysis of Diffuse Astrocytic Tumor Elasticity: Relation with Tumor Histopathology

This study aims to investigate the influence of isocitrate dehydrogenase gene family (IDH) mutations, World Health Organization (WHO) grade, and mechanical preconditioning on glioma and adjacent brain elasticity through standard monotonic and repetitive atomic force microscope (AFM) nanoindentation. The elastic modulus was measured ex vivo on fresh tissue specimens acquired during craniotomy from the tumor and the peritumoral white matter of 16 diffuse glioma patients. Linear mixed-effects models examined the impact of tumor traits and preconditioning on tissue elasticity. Tissues from IDH-mutant cases were stiffer than those from IDH-wildtype ones among anaplastic astrocytoma patients (p = 0.0496) but of similar elasticity to IDH-wildtype cases for diffuse astrocytoma patients (p = 0.480). The tumor was found to be non-significantly softer than white matter in anaplastic astrocytomas (p = 0.070), but of similar elasticity to adjacent brain in diffuse astrocytomas (p = 0.492) and glioblastomas (p = 0.593). During repetitive indentation, both tumor (p = 0.002) and white matter (p = 0.003) showed initial stiffening followed by softening. Stiffening was fully reversed in white matter (p = 0.942) and partially reversed in tumor (p = 0.015). Tissue elasticity comprises a phenotypic characteristic closely related to glioma histopathology. Heterogeneity between patients should be further explored.

Mechanical properties of human glioma

Brain gliomas represent some of the most aggressive tumors encountered by modern medicine and, despite major efforts to optimize early diagnosis and treatment, the prognosis remains poor. Due to the complex structure of the brain and the unique mechanical properties of the extracellular matrix, gliomas invade and expand into the brain parenchyma, along white matter tracts and within perivascular spaces, usually sparing normal vessels. Different methods have been developed to study the mechanical properties of gliomas in a wide range of scales, from cells and the microscale to tissues and the macroscale. In this review, the current view on glioma mechanics is presented and the methods used to determine glioma mechanical properties are outlined. Their principles and current state of affairs are discussed.

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

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

Computational modeling in glioblastoma: from the prediction of blood-brain barrier permeability to the simulation of tumor behavior

The integrated in silico-in vitro-in vivo approaches have fostered the development of new treatment strategies for glioblastoma patients and improved diagnosis, establishing the bridge between biochemical research and clinical practice. These approaches have provided new insights on the identification of bioactive compounds and on the complex mechanisms underlying the interactions among glioblastoma cells, and the tumor microenvironment. This review focuses on the key advances pertaining to computational modeling in glioblastoma, including predictive data on drug permeability across the blood-brain barrier, tumor growth and treatment responses. Structure- and ligand-based methods have been widely adopted, enabling the study of dynamic and evolutionary aspects of glioblastoma. Their potential applications as predictive tools and the advantages over other well-known methodologies are outlined. Challenges regarding in silico approaches for predicting tumor properties are also discussed.

Predicting brain tumor regrowth in relation to motor areas by functional brain mapping

Background

Due to frequent recurrences, high-grade gliomas still confer a poor prognosis. Several regrowth prediction models have been developed, but most of these models are based on cellular models or dynamic mathematical calculations, thus limiting direct clinical use. The present study aims to evaluate whether navigated transcranial magnetic stimulation (nTMS) or functional magnetic resonance imaging (fMRI) may be used to predict the direction of tumor regrowth.

Methods

Sixty consecutive patients with high-grade gliomas were enrolled prospectively and analyzed in a case-control design after tumor recurrence. All patients underwent serial MRI after surgery and suffered from recurrent tumors during a mean follow-up of 13.2 ± 14.9 months. Tumor regrowth speed and direction were measured in relation to motor areas defined by nTMS, nTMS-based tractography, and fMRI. Depending on initial resection, patients were separated into three groups (group 1: without residual tumor, group 2: residual tumor away from motor areas, and group 3: residual tumor facing motor areas).

Results

Sixty-nine percent of patients in group 1, 64.3% in group 2, and 66.7% in group 3 showed tumor recurrence towards motor eloquence on contrast-enhanced T1-weighted sequences (P = .9527). Average growth towards motor areas on contrast-enhanced T1-weighted sequences was 0.6 ± 1.5 (group 1), 0.6 ± 2.4 (group 2), and 2.3 ± 5.5 (group 3) mm/month (P = .0492).

Conclusion

This study suggests a new strategy to predict tumor regrowth patterns in high-grade glioma patients. Our approach could be directly applied in the clinical setting, thus having clinical impact on both surgical treatment and radiotherapy planning.

Ethics Committee Registration Number

2793/10.

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.

Mathematical Analysis of Glioma Growth in a Murine Model

Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm³ to 62 mm³, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.

A data-motivated density-dependent diffusion model of in vitro glioblastoma growth

Glioblastoma multiforme is an aggressive brain cancer that is extremely fatal. It is characterized by both proliferation and large amounts of migration, which contributes to the difficulty of treatment. Previous models of this type of cancer growth often include two separate equations to model proliferation or migration. We propose a single equation which uses density-dependent diffusion to capture the behavior of both proliferation and migration. We analyze the model to determine the existence of traveling wave solutions. To prove the viability of the density-dependent diffusion function chosen, we compare our model with well-known in vitro experimental data.

Mathematically modeling the biological properties of gliomas: A review

Although mathematical modeling is a mainstay for industrial and many scientific studies, such approaches have found little application in neurosurgery. However, the fusion of biological studies and applied mathematics is rapidly changing this environment, especially for cancer research. This review focuses on the exciting potential for mathematical models to provide new avenues for studying the growth of gliomas to practical use. In vitro studies are often used to simulate the effects of specific model parameters that would be difficult in a larger-scale model. With regard to glioma invasive properties, metabolic and vascular attributes can be modeled to gain insight into the infiltrative mechanisms that are attributable to the tumor's aggressive behavior. Morphologically, gliomas show different characteristics that may allow their growth stage and invasive properties to be predicted, and models continue to offer insight about how these attributes are manifested visually. Recent studies have attempted to predict the efficacy of certain treatment modalities and exactly how they should be administered relative to each other. Imaging is also a crucial component in simulating clinically relevant tumors and their influence on the surrounding anatomical structures in the brain.

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.

An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas

We present a numerical scheme for solving a parameter estimation problem for a model of low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor concentration, as well as the magnitude of anisotropic tumor diffusion. We use a constrained optimization formulation with a reaction-diffusion model that results in a system of nonlinear partial differential equations. In our formulation, we estimate the parameters using partially observed, noisy tumor concentration data at two different time instances, along with white matter fiber directions derived from diffusion tensor imaging. The optimization problem is solved with a Gauss-Newton reduced space algorithm. We present the formulation and outline the numerical algorithms for solving the resulting equations. We test the method using a synthetic dataset and compute the reconstruction error for different noise levels and detection thresholds for monofocal and multifocal test cases.

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.

Glioma follow white matter tracts: a multiscale DTI-based model

Gliomas are a class of rarely curable tumors arising from abnormal glia cells in the human brain. The understanding of glioma spreading patterns is essential for both radiological therapy as well as surgical treatment. Diffusion tensor imaging (DTI) allows to infer the white matter fibre structure of the brain in a noninvasive way. Painter and Hillen (J Theor Biol 323:25-39, 2013) used a kinetic partial differential equation to include DTI data into a class of anisotropic diffusion models for glioma spread. Here we extend this model to explicitly include adhesion mechanisms between glioma cells and the extracellular matrix components which are associated to white matter tracts. The mathematical modelling follows the multiscale approach proposed by Kelkel and Surulescu (Math Models Methods Appl Sci 23(3), 2012). We use scaling arguments to deduce a macroscopic advection-diffusion model for this process. The tumor diffusion tensor and the tumor drift velocity depend on both, the directions of the white matter tracts as well as the binding dynamics of the adhesion molecules. The advanced computational platform DUNE enables us to accurately solve our macroscopic model. It turns out that the inclusion of cell binding dynamics on the microlevel is an important factor to explain finger-like spread of glioma.

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications

Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hyperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.

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.

Improving the time-machine: estimating date of birth of grade II gliomas

OBJECTIVES

Here we present a model aiming to provide an estimate of time from tumour genesis, for grade II gliomas. The model is based on a differential equation describing the diffusion-proliferation process. We have applied our model to situations where tumour diameter was shown to increase linearly with time, with characteristic diametric velocity.

MATERIALS AND METHODS

We have performed numerical simulations to analyse data, on patients with grade II gliomas and to extract information concerning time of tumour biological onset, as well as radiology and distribution of model parameters.

RESULTS AND CONCLUSIONS

We show that the estimate of tumour onset obtained from extrapolation using a constant velocity assumption, always underestimates biological tumour age, and that the correction one should add to this estimate is given roughly by 20/v (year), where v is the diametric velocity of expansion of the tumour (expressed in mm/year). Within the assumptions of the model, we have identified two types of tumour: the first corresponds to very slowly growing tumours that appear during adolescence, and the second type corresponds to slowly growing tumours that appear later, during early adulthood. That all these tumours become detectable around a mean patient age of 30 years could be interesting for formulation of strategies for early detection of tumours.

Bright solitary waves in malignant gliomas

We put forward a nonlinear wave model describing the fundamental dynamical features of an aggressive type of brain tumors. Our model accounts for the invasion of normal tissue by a proliferating and propagating rim of active glioma cancer cells in the tumor boundary and the subsequent formation of a necrotic core. By resorting to numerical simulations, phase space analysis, and exact solutions we prove that bright solitary tumor waves develop in such systems. Possible implications of our model as a tool to extract relevant patient specific tumor parameters in combination with standard preoperative clinical imaging are also discussed.

[Radiotherapy in adult glioblastomas]

Radiation therapy is a treatment of malignant gliomas in adults. It improves survival rates, whether used alone, in addition to surgery, or in combination with chemotherapy. Three-dimensional imaging techniques, image fusion, and conformational radiotherapy are optimizing treatment plans for the treatment of these tumors and are sparing healthy tissue. After a review of the physical and biological bases of ionizing radiation, we present the techniques, results, side effects, and results of irradiation of glioblastomas.

In-silico oncology: an approximate model of brain tumor mass effect based on directly manipulated free form deformation

PURPOSE

The present work introduces a novel method for approximating mass effect of primary brain tumors.

METHODS

The spatio-temporal dynamics of cancerous cells are modeled by means of a deterministic reaction-diffusion equation. Diffusion tensor information obtained from a probabilistic diffusion tensor imaging atlas is incorporated into the model to simulate anisotropic diffusion of cancerous cells. To account for the expansive nature of the tumor, the computed net cell density of malignant cells is linked to a parametric deformation model. This mass effect model is based on the so-called directly manipulated free form deformation. Spatial correspondence between two successive simulation steps is established by tracking landmarks, which are attached to the boundary of the gross tumor volume. The movement of these landmarks is used to compute the new configuration of the control points and, hence, determines the resulting deformation. To prevent a deformation of rigid structures (i.e. the skull), fixed shielding landmarks are introduced. In a refinement step, an adaptive landmark scheme ensures a dense sampling of the tumor isosurface, which in turn allows for an appropriate representation of the tumor shape.

RESULTS

The influence of different parameters on the model is demonstrated by a set of simulations. Additionally, simulation results are qualitatively compared to an exemplary set of clinical magnetic resonance images of patients diagnosed with high-grade glioma.

CONCLUSIONS

Careful visual inspection of the results demonstrates the potential of the implemented model and provides first evidence that the computed approximation of tumor mass effect is sensible. The shape of diffusive brain tumors (glioblastoma multiforme) can be recovered and approximately matches the observations in real clinical data.

Modeling tumor growth and treatment response based on quantitative imaging data

We review current approaches to predicting tumor growth and treatment response that combine non-invasive imaging data with mathematical models of cancer progression, and propose some new directions for integrating quantitative imaging measurements with such numerical analyses. Historically, tumor modeling has been described by parameters that are measurable by invasive methods only or in isolated in vitro or ex vivo systems. This limits the practical usefulness of such models because it is not possible to test their predictions experimentally. Recent advances in three-dimensional magnetic resonance imaging, single photon emission computed tomography, and positron emission tomography techniques provide new opportunities to acquire measurements of relevant molecular and cellular features of tumors non-invasively and with high spatial resolution. Such data can be incorporated into mathematical models of tumors. We highlight some recent examples of this approach and identify several simple examples that allow for conventional mathematical models of tumor growth to be recast in terms of parameters that can be measured by imaging, thus raising the possibility of designing and constraining models that can be tested in clinical practice. It is our hope that this Perspective will stimulate further work in this evolving and exciting field.

The integration of quantitative multi-modality imaging data into mathematical models of tumors

Quantitative imaging data obtained from multiple modalities may be integrated into mathematical models of tumor growth and treatment response to achieve additional insights of practical predictive value. We show how this approach can describe the development of tumors that appear realistic in terms of producing proliferating tumor rims and necrotic cores. Two established models (the logistic model with and without the effects of treatment) and one novel model built a priori from available imaging data have been studied. We modify the logistic model to predict the spatial expansion of a tumor driven by tumor cell migration after a voxel's carrying capacity has been reached. Depending on the efficacy of a simulated cytotoxic treatment, we show that the tumor may either continue to expand, or contract. The novel model includes hypoxia as a driver of tumor cell movement. The starting conditions for these models are based on imaging data related to the tumor cell number (as estimated from diffusion-weighted MRI), apoptosis (from 99mTc-Annexin-V SPECT), cell proliferation and hypoxia (from PET). We conclude that integrating multi-modality imaging data into mathematical models of tumor growth is a promising combination that can capture the salient features of tumor growth and treatment response and this indicates the direction for additional research.

An agent-based model identifies MRI regions of probable tumor invasion in a patient with glioblastoma

We present an application of a previously developed agent-based glioma model (Chen et al 2009 Biosystems 95 234-42) for predicting spatio-temporal tumor progression using a patient-specific MRI lattice derived from apparent diffusion coefficient (ADC) data. Agents representing collections of migrating glioma cells are initialized based upon voxels at the outer border of the tumor identified on T1-weighted (Gd+) MRI at an initial time point. These simulated migratory cells exhibit a specific biologically inspired spatial search paradigm, representing a weighting of the differential contribution from haptotactic permission and biomechanical resistance on the migration decision process. ADC data from 9 months after the initial tumor resection were used to select the best search paradigm for the simulation, which was initiated using data from 6 months after the initial operation. Using this search paradigm, 100 simulations were performed to derive a probabilistic map of tumor invasion locations. The simulation was able to successfully predict a recurrence in the dorsal/posterior aspect long before it was depicted on T1-weighted MRI, 18 months after the initial operation.

Non-diffeomorphic registration of brain tumor images by simulating tissue loss and tumor growth

Although a variety of diffeomorphic deformable registration methods exist in the literature, application of these methods in the presence of space-occupying lesions is not straightforward. The motivation of this work is spatial normalization of MR images from patients with brain tumors in a common stereotaxic space, aiming to pool data from different patients into a common space in order to perform group analyses. Additionally, transfer of structural and functional information from neuroanatomical brain atlases into the individual patient's space can be achieved via the inverse mapping, for the purpose of segmenting brains and facilitating surgical or radiotherapy treatment planning. A method that estimates the brain tissue loss and replacement by tumor is applied for achieving equivalent image content between an atlas and a patient's scan, based on a biomechanical model of tumor growth. Automated estimation of the parameters modeling brain tissue loss and displacement is performed via optimization of an objective function reflecting feature-based similarity and elastic stretching energy, which is optimized in parallel via APPSPACK (Asynchronous Parallel Pattern Search). The results of the method, applied to 21 brain tumor patients, indicate that the registration accuracy is relatively high in areas around the tumor, as well as in the healthy portion of the brain. Also, the calculated deformation in the vicinity of the tumor is shown to correlate highly with expert-defined visual scores indicating the tumor mass effect, thereby potentially leading to an objective approach to quantification of mass effect, which is commonly used in diagnosis.

An imaging-based tumour growth and treatment response model: investigating the effect of tumour oxygenation on radiation therapy response

A multiscale tumour simulation model employing cell-line-specific biological parameters and functional information derived from pre-therapy PET/CT imaging data was developed to investigate effects of different oxygenation levels on the response to radiation therapy. For each tumour voxel, stochastic simulations were performed to model cellular growth and therapeutic response. Model parameters were fitted to published preclinical experiments of head and neck squamous cell carcinoma (HNSCC). Using the obtained parameters, the model was applied to a human HNSCC case to investigate effects of different uniform and non-uniform oxygenation levels and results were compared for treatment efficacy. Simulations of the preclinical studies showed excellent agreement with published data and underlined the model's ability to quantitatively reproduce tumour behaviour within experimental uncertainties. When using a simplified transformation to derive non-uniform oxygenation levels from molecular imaging data, simulations of the clinical case showed heterogeneous tumour response and variability in radioresistance with decreasing oxygen levels. Once clinically validated, this model could be used to transform patient-specific data into voxel-based biological objectives for treatment planning and to investigate biologically optimized dose prescriptions.