Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion

Swanson, Kristin R.; Bridge, Carly; Murray, J. D.; Alvord, Ellsworth C.

doi:10.1016/j.jns.2003.06.001

Cited by 537 publications

(488 citation statements)

References 34 publications

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“…This model, studied by Swanson et al (2008) (Harpold et al, 2007), has proven to be an accurate predictor of anatomical changes that can be imaged by MRI in individual patients Szeto et al, 2009;Swanson et al, 2003Swanson et al, , 2008Rockne et al, 2009). Further, patient-specific PI model parameters for biological aggressiveness (D and ρ) can be estimated from routinely available pre-treatment MRIs (Harpold et al, 2007).…”

Section: Patient-specific Mathematical Modelling Of Gbm: Proliferatiomentioning

confidence: 99%

“…Further, patient-specific PI model parameters for biological aggressiveness (D and ρ) can be estimated from routinely available pre-treatment MRIs (Harpold et al, 2007). These patient-specific proliferation and invasion kinetic rates are prognostic of survival ) and response to therapy (Swanson et al, 2003(Swanson et al, , 2008Rockne et al, 2009) in individual patients. Although the PI model has been validated on both the population and patient-specific levels, it provides limited insight with regard to tumour activity at the molecular level.…”

Section: Patient-specific Mathematical Modelling Of Gbm: Proliferatiomentioning

confidence: 99%

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Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images

Gu¹,

Chakraborty²,

Champley³

et al. 2011

Mathematical Medicine and Biology

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Glioblastoma multiforme (GBM) is a class of primary brain tumours characterized by their ability to rapidly proliferate and diffusely infiltrate surrounding brain tissue. The aggressive growth of GBM leads to the development of regions of low oxygenation (hypoxia), which can be clinically assessed through [18F]-fluoromisonidazole (FMISO) positron emission tomography (PET) imaging. Building upon the success of our previous mathematical modelling efforts, we have expanded our model to include the tumour microenvironment, specifically incorporating hypoxia, necrosis and angiogenesis. A pharmacokinetic model for the FMISO-PET tracer is applied at each spatial location throughout the brain and an analytical simulator for the image acquisition and reconstruction methods is applied to the resultant tracer activity map. The combination of our anatomical model with one for FMISO tracer dynamics and PET image reconstruction is able to produce a patient-specific virtual PET image that reproduces the image characteristics of the clinical PET scan as well as shows no statistical difference in the distribution of hypoxia within the tumour. This work establishes proof of principle for a link between anatomical (magnetic resonance image [MRI]) and molecular (PET) imaging on a patient-specific basis as well as address otherwise untenable questions in molecular imaging, such as determining the effect on tracer activity from cellular density. Although further investigation is necessary to establish the predictive value of this technique, this unique tool provides a better dynamic understanding of the biological connection between anatomical changes seen on MRI and biochemical activity seen on PET of GBM in vivo.

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Section: Patient-specific Mathematical Modelling Of Gbm: Proliferatiomentioning

confidence: 99%

Section: Patient-specific Mathematical Modelling Of Gbm: Proliferatiomentioning

confidence: 99%

Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images

Gu¹,

Chakraborty²,

Champley³

et al. 2011

Mathematical Medicine and Biology

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“…In the case of infiltrative tumors such as low-grade gliomas, it is usual to model the evolution of cell concentration. Generally, tumor growth due to net cell division can be represented by a differential equation in time, ‫ץ‬c ‫ץ‬t ϭ f͑c͒, [1] where c is the glioma cell concentration and f is a function representing the temporal evolution pattern of the growth. For example, some functions f that have been used in other works are (14) f͑c͒ ϭ c (exponential proliferation)…”

Section: Modelmentioning

confidence: 99%

“…Recently, a biomathematical model (1) has been proposed to quantitatively describe the growth rates of gliomas visualized radiologically. This model takes into account the two major biological phenomena underlying the growth of gliomas at the cellular scale: proliferation and diffusion.…”

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confidence: 99%

Simulation of anisotropic growth of low‐grade gliomas using diffusion tensor imaging

Jbabdi

Mandonnet

Duffau

et al. 2005

Magnetic Resonance in Med

259

274

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A recent computational model of brain tumor growth, developed to better describe how gliomas invade through the adjacent brain parenchyma, is based on two major elements: cell proliferation and isotropic cell diffusion. On the basis of this model, glioma growth has been simulated in a virtual brain, provided by a 3D segmented MRI atlas. However, it is commonly accepted that glial cells preferentially migrate along the direction of fiber tracts. Therefore, in this paper, the model has been improved by including anisotropic extension of gliomas. The method is based on a cell diffusion tensor derived from water diffusion tensor (as given by MRI diffusion tensor imaging). Results of simulations have been compared with two clinical examples demonstrating typical growth patterns of lowgrade gliomas centered around the insula. The shape and the kinetic evolution are better simulated with anisotropic rather than isotropic diffusion. The best fit is obtained when the anisotropy of the cell diffusion tensor is increased to greater anisotropy than the observed water diffusion tensor. The shape of the tumor is also influenced by the initial location of the tumor. Anisotropic brain tumor growth simulations provide a means to determine the initial location of a low-grade glioma as well as its cell diffusion tensor, both of which might reflect the biological characteristics of invasion. Key words: computational modeling; glioma; anisotropic growth; diffusion tensor; cell migration Low-grade (WHO grade II) gliomas are initially slowly evolving tumors, but can become rapidly fatal after anaplastic transformation. Because of their infiltrative characteristics, surgery alone fails to cure these tumors, even in their premalignant stage. Indeed, these tumors may not form a solid mass but may invade diffusely throughout the brain parenchyma as "gliomatosis cerebri."Recently, a biomathematical model (1) has been proposed to quantitatively describe the growth rates of gliomas visualized radiologically. This model takes into account the two major biological phenomena underlying the growth of gliomas at the cellular scale: proliferation and diffusion. The simplest choice for the proliferation term is a constant growth rate , leading to an exponentially growing total number of glioma cells. For the invasive properties of gliomas, cell migration is assumed to be a random walk, corresponding to a passive (Fickian) diffusion characterized by a single coefficient D. Simulations of this proliferation-diffusion equation are performed on a 3D T 1 MR structural image of the brain, with segmentation of CSF (which corresponds to the boundaries of the parenchyma), white matter, and gray matter images.In previous publications (2), the diffusion of cells in white matter is assumed to be 5 (to 100) times higher than in gray matter, consistent with observations that glioma cells migrate more quickly in white matter than in gray. Within white (or gray) matter, cell diffusion was considered an isotropic phenomenon. However, it is commonly accepted that gl...

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“…Some tissue shift is inevitable, but in this study, we did not perceive this tissue shift to be a significant problem. Other studies have specifically modeled the growth and infiltration of brain tumors in a mathematical sense [36]. These models have more recently been combined with prior knowledge available from diffusion tensor imaging studies [37].…”

Section: Discussionmentioning

confidence: 99%

Supervised pattern recognition for the prediction of contrast-enhancement appearance in brain tumors from multivariate magnetic resonance imaging and spectroscopy

Lee¹,

Nelson²

2008

Artificial Intelligence in Medicine

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Objective: The purpose of this study was to develop a pattern classification algorithm for use in predicting the location of new contrast-enhancement in brain tumor patients using data obtained via multivariate magnetic resonance imaging from a prior scan. We also explore the use of feature selection or weighting in improving the accuracy of the pattern classifier. Methods and materials:Contrast-enhanced MR images, perfusion images, diffusion images, and proton spectroscopic imaging data were obtained from 26 patients with glioblastoma multiforme brain tumors, divided into a design set and an unseen test set for verification of results. A k-NN algorithm was implemented to classify unknown data based on a set of training data with ground truth derived from post-treatment contrast enhanced images; the quality of the k-NN results was evaluated using a leave-one-out cross-validation method. A genetic algorithm was implemented to select optimal features and feature weights for the k-NN algorithm. The binary representation of the weights was varied from 1 to 4 bits. Each individual parameter was thresholded as a simple classification technique, and the results compared with the k-NN. Results:The feature selection k-NN was able to achieve a sensitivity of 0.78 ± 0.18 and specificity of 0.79 ± 0.06 on the holdout test data using only 7 of the 38 original features. Similar results were obtained with non-binary weights, but using a larger number of features. Overfitting was also observed in the higher bit representations. The best single-variable classifier, based on a choline-to-NAA abnormality index computed from spectroscopic data, achieved a sensitivity of 0.79 ± 0.20 and specificity of 0.71 ± 0.11. The k-NN results had lower variation across patients than the single-variable classifiers. Conclusions:We have demonstrated that the an optimized k-NN rule could be used for quantitative analysis of multivariate images, and be applied to a specific clinical research question. Selecting features was found to be useful in improving the accuracy of feature weighting algorithms and improving the comprehensibility of the results. We believe that in addition to

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Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion

Cited by 537 publications

References 34 publications

Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images

Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images

Simulation of anisotropic growth of low‐grade gliomas using diffusion tensor imaging

Supervised pattern recognition for the prediction of contrast-enhancement appearance in brain tumors from multivariate magnetic resonance imaging and spectroscopy

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