Image-driven modeling of the proliferation and necrosis of glioblastoma multiforme.

BACKGROUND: The heterogeneity of response to treatment in patients with glioblastoma multiforme suggests that the optimal therapeutic approach incorporates an individualized assessment of expected lesion progression. In this work, we develop a novel computational model for the proliferation and necrosis of glioblastoma multiforme. METHODS: The model parameters are selected based on the magnetic resonance imaging features of each tumor, and the proposed technique accounts for intrinsic cell division, tumor cell migration along white matter tracts, as well as central tumor necrosis. As a validation of this approach, tumor growth is simulated in the brain of a healthy adult volunteer using parameters derived from the imaging of a patient with glioblastoma multiforme. A mutual information metric is calculated between the simulated tumor profile and observed tumor. RESULTS: The tumor progression profile generated by the proposed model is compared with those produced by existing models and with the actual observed tumor progression. Both qualitative and quantitative analyses show that the model introduced in this work replicates the observed progression of glioblastoma more accurately relative to prior techniques. CONCLUSIONS: This image-driven model generates improved tumor progression profiles and may contribute to the development of more reliable prognostic estimates in patients with glioblastoma multiforme.

A 3-dimensional DTI MRI-based model of GBM growth and response to radiation therapy.

Glioblastoma (GBM) is both the most common and the most aggressive intra-axial brain tumor, with a notoriously poor prognosis. To improve this prognosis, it is necessary to understand the dynamics of GBM growth, response to treatment and recurrence. The present study presents a mathematical diffusion-proliferation model of GBM growth and response to radiation therapy based on diffusion tensor (DTI) MRI imaging. This represents an important advance because it allows 3-dimensional tumor modeling in the anatomical context of the brain. Specifically, tumor infiltration is guided by the direction of the white matter tracts along which glioma cells infiltrate. This provides the potential to model different tumor growth patterns based on location within the brain, and to simulate the tumor's response to different radiation therapy regimens. Tumor infiltration across the corpus callosum is simulated in biologically accurate time frames. The response to radiation therapy, including changes in cell density gradients and how these compare across different radiation fractionation protocols, can be rendered. Also, the model can estimate the amount of subthreshold tumor which has extended beyond the visible MR imaging margins. When combined with the ability of being able to estimate the biological parameters of invasiveness and proliferation of a particular GBM from serial MRI scans, it is shown that the model has potential to simulate realistic tumor growth, response and recurrence patterns in individual patients. To the best of our knowledge, this is the first presentation of a DTI-based GBM growth and radiation therapy treatment model.

Estimating subthreshold tumor on MRI using a 3D-DTI growth model for GBM: An adjunct to radiation therapy planning.

Mathematical modeling and serial magnetic resonance imaging (MRI) used to calculate patient-specific rates of tumor diffusion, D, and proliferation, ρ, can be combined to simulate glioblastoma multiforme (GBM) growth. We showed that the proportion and distribution of tumor cells below the MRI threshold are determined by the D/ρ ratio of the tumor. As most radiation fields incorporate a 1­3 cm margin to account for subthreshold tumor, accurate characterization of subthreshold tumor aids the design of optimal radiation fields. This study compared two models: a standard one­dimensional (1D) isotropic model and a three­dimensional (3D) anisotropic model using the advanced imaging method of diffusion tensor imaging (DTI) ­ with regards to the D/ρ ratio's effect on the proportion and spatial extent of the subthreshold tumor. A validated reaction­diffusion equation accounting for tumor diffusion and proliferation modeled tumor concentration in time and space. For the isotropic and anisotropic models, nine tumors with different D/ρ ratios were grown to a T1 radius of 1.5 cm. For each tumor, the percent and extent of tumor cells beyond the T2 radius were calculated. For both models, higher D/ρ ratios were correlated with a greater proportion and extent of subthreshold tumor. Anisotropic modeling demonstrated a higher proportion and extent of subthreshold tumor than predicted by the isotropic modeling. Because the quantity and distribution of subthreshold tumor depended on the D/ρ ratio, this ratio should influence radiation field demarcation. Furthermore, the use of DTI data to account for anisotropic tumor growth allows for more refined characterization of the subthreshold tumor based on the patient-specific D/ρ ratio.

Modeling the efficacy of the extent of surgical resection in the setting of radiation therapy for glioblastoma.

Standard therapy for glioblastoma (GBM) includes maximal surgical resection and radiation therapy. While it is established that radiation therapy provides the greatest survival benefit of standard treatment modalities, the impact of the extent of surgical resection (EOR) on patient outcome remains highly controversial. While some studies describe no correlation between EOR and patient survival even up to total resection, others propose either qualitative (partial versus subtotal versus complete resection) or quantitative EOR thresholds, below which there is no correlation with survival. This work uses a mathematical model in the form of a reaction-diffusion partial differential equation to simulate tumor growth and treatment with radiation therapy and surgical resection based on tumor-specific rates of diffusion and proliferation. Simulation of 36 tumors across a wide spectrum of diffusion and proliferation rates suggests that while partial or subtotal resections generally do not provide a survival advantage, complete resection significantly improves patient outcomes. Furthermore, our model predicts a tumor-specific quantitative threshold below which EOR has no effect on patient survival and demonstrates that this threshold increases with tumor aggressiveness, particularly with the rate of proliferation. Thus, this model may serve as an aid for determining both when surgical resection is indicated as well as the surgical margins necessary to provide clinically significant improvements in patient survival. In addition, by assigning relative benefits to radiation and surgical resection based on tumor invasiveness and proliferation, this model confirms that (with the exception of the least aggressive tumors) the survival benefit of radiation therapy exceeds that of surgical resection.

White matter changes in chronic alcoholic liver disease: Hypothesized association and putative biochemical mechanisms.

Advanced liver disease has long been associated with cerebral abnormalities. These abnormalities, termed acquired hepatocerebral degeneration, are typically visualized as T1 weighted hyperintensity on MRI in the deep gray matter of the basal ganglia. Recent reports, however, have demonstrated that a subset of patients with chronic alcoholic liver disease may also develop white matter abnormalities. Thus far, the morphology of these changes is not well characterized. Previous studies have described these changes as patchy, sporadic white matter abnormalities but have not posited localization of these changes to any particular white matter tracts. This paper hypothesizes that the white matter findings associated with advanced alcoholic liver disease localize to the corticocerebellar tracts. As an initial investigation of this hypothesis, 78 patients with a diagnosis of liver cirrhosis and an MRI showing clearly abnormal T1 weighted hyperintensity in the bilateral globus pallidus, characteristic of chronic liver disease, were examined for white matter signal abnormalities in the corticocerebellar tracts using FLAIR and T2 weighted images. The corticocerebellar tracts were subdivided into two regions: periventricular white matter (consisting of the sum of the centrum-semiovale and corona radiata), and lower white matter (consisting of the corona radiata, internal capsules, middle cerebral peduncles, middle cerebellar peduncles and cerebellum). As compared to matched controls, significantly greater signal abnormalities in both the periventricular white matter and lower white matter regions of the corticocerebellar tracts were observed in patients with known liver cirrhosis and abnormal T1 W hyperintensity in the globi pallidi. This difference was most pronounced in the lower white matter region of the corticocerebellar tract, with statistical significance of p<0.0005. Furthermore, the pathophysiologic mechanism underlying these changes remains unknown. This paper hypothesizes that the etiology of white matter changes associated with advanced liver disease may resemble that of white matter findings in subacute combined degeneration secondary to vitamin B12 deficiency. Specifically, significant evidence suggests that dysfunctional methionine metabolism as well as dysregulated cytokine production secondary to B12 deficiency play a major role in the development of subacute combined degeneration. Similar dysfunction of methionine metabolism and cytokine regulation is seen in alcoholic liver disease and is hypothesized in this paper to, at least in part, lead to white matter findings associated with alcoholic liver disease.

Radial expansion rates and tumor growth kinetics predict malignant transformation in contrast-enhancing low-grade diffuse astrocytoma.

BACKGROUND: Contrast-enhancing low-grade diffuse astrocytomas are an understudied, aggressive subtype at increased risk because of few radiographic indications of malignant transformation. In the current study, we tested whether tumor growth kinetics could identify tumors that undergo malignant transformation to higher grades. METHODS: Thirty patients with untreated diffuse astrocytomas (WHO II) that underwent tumor progression were enrolled. Contrast-enhancing and T2 hyperintense tumor regions were segmented and the radius of tumor at two time points leading to progression was estimated. Radial expansion rates were used to estimate proliferation and invasion rates using a biomathematical model. RESULTS: Radial expansion rates for both contrast-enhancing (p = 0.0040) and T2 hyperintense regions (p = 0.0016) were significantly higher in WHO II-IV tumors compared with nontransformers. Similarly, model estimates showed a significantly higher proliferation (p = 0.0324) and invasion rate (p = 0.0050) in WHO II-IV tumors compared with nontransformers. CONCLUSION: Tumor growth kinetics can identify contrast-enhancing diffuse astrocytomas undergoing malignant transformation.

Patient-specific characterization of the invasiveness and proliferation of low-grade gliomas using serial MR imaging and a mathematical model of tumor growth.

Low-grade gliomas (LGGs) represent a significant proportion of hemispheric gliomas in adults. Although less aggressive than glioblastomas (GBMs), they have a broad range of biologic behavior, and often a limited prognosis. The aim of the present study was to explore LGG growth kinetics through a combination of routine MRI imaging and a novel adaptation of a mathematical tumor model. MRI imaging in 14 retrospectively identified grade II LGGs that showed some tumor enhancement was used to assess tumor radii at two separate time-points. This information was combined with a reaction-diffusion partial-differential equation model of tumor growth to calculate diffusion (D) and proliferation (ρ) coefficients for each tumor, representing measures of tumor invasiveness and cellular multiplication, respectively. The results were compared to previously published data on GBMs. The average value of D was 0.034 mm(2)/day and ρ was 0.0056/day. Grade II LGGs had a broad range of D and ρ. On average, the proliferation coefficient ρ was significantly lower than previously published values for GBM, by about an order of magnitude. The diffusion coefficient, modeling invasiveness, however, was only slightly lower but without statistical significance. It was possible to calculate detailed growth kinetic parameters for some LGGs, potentially providing a new way to assess tumor aggressiveness and possibly gauge prognosis. Even within a single-grade (WHO II), LGGs were found to have broad range of D and ρ, possibly correlating to their variable biologic behavior. Overall, the model parameters suggest that LGG is less aggressive than GBM based primarily on a lower index of tumor proliferation rather than on lesser invasiveness.

A novel bicompartmental mathematical model of glioblastoma multiforme.

Glioblastoma multiforme (GBM) is the most common primary CNS neoplasm, and continues to have a dismal prognosis. A widely-used approach to the mathematical modeling of GBM involves utilizing a reaction-diffusion model of cell density as a function of space and time, which accounts for both the infiltrative nature of the tumor using a diffusion term, and the proliferation of tumor cells using a proliferation term. The current paper extends the standard models by incorporating an advection term to account for the so-called 'cell streaming' which is often seen with GBM, where some of the tumor cells seem to stream widely along the white matter pathways. The current paper introduces a bicompartmental GBM model in the form of coupled partial differential equations with a component of dispersive cells. The parameters needed for this model are explored. It is shown that this model can account for the rapid distant dispersal of GBM cells in the CNS, as well as such phenomena as multifocal gliomas with tumor foci distant from the core tumor site. The model suggests a higher percentage of tumor cells below the threshold of MRI images in comparison to the standard model. By incorporating an advection component, the proposed model is able to account for phenomena such as multicentric gliomas and rapid distant dispersion of a small fraction of tumor cells throughout the CNS, features important to the prognosis of GBM, but not easily accounted for by current models.

The right to practice medicine without repercussions: ethical issues in times of political strife.

This commentary examines the incursion on the neutrality of medical personnel now taking place as part of the human rights crises in Bahrain and Syria, and the ethical dilemmas which these incursions place not only in front of physicians practicing in those nations, but in front of the international community as a whole.In Bahrain, physicians have recently received harsh prison terms, apparently for treating demonstrators who clashed with government forces. In Syria, physicians are under the same political pressure to avoid treating political demonstrators or to act as informants against their own patients, turning them in to government authorities. This pressure has been severe, to the point that some physicians have become complicit in the abuse of patients who were also political demonstrators.This paper posits that physicians in certain countries in the Middle East during the "Arab Spring," specifically Syria and Bahrain, are being used as both political pawns and political weapons in clear violation of Geneva Convention and World Medical Association guidelines, and that this puts them into the most extreme sort of "dual loyalty" dilemma. They are being forced to choose between their own safety and well-being and that of their patients - a negative sum scenario wherein there is no optimal choice. As such, an international call for a United Nations inquiry must be made in order to protect the neutrality of medical care and personnel during times of armed conflict.

Vascular tortuosity: a mathematical modeling perspective.

Although vascular tortuosity is a ubiquitous phenomenon, almost no mathematical models exist to describe its shape. Given that the shape of tortuous vessel curves seems fairly uniform across orders of magnitude of vessel size and across vast differences in anatomic substrata, it is hypothesized that the shape of tortuosity is not purely random but rather is governed by physical principles. We present a mathematical model of tortuosity based on optimality principles, and show how this model can potentially be used to distinguish physiologic tortuosity from abnormal tortuosity which may exist in disease states. Using the calculus of variations, a model of tortuosity has been developed which minimizes average curvature per unit length. The model is tested against curves in normal vessels and in diseased vessels in a case of Fabry's disease. It is found that the theoretical model provides a good fit for normal vessel tortuosity. This suggests that blood vessels obey optimality principles, and curve in such a way as to minimize average curvature. The model may also be able to distinguish physiologic tortuosity from abnormal tortuosity found in disease states.

Nitrous oxide-induced B12 deficiency myelopathy: Perspectives on the clinical biochemistry of vitamin B12.

Beginning with a case report of nitrous oxide (N2O)-induced B12 deficiency myelopathy, this article reviews the clinical biochemistry of vitamin B12, and examines the pathogenetic mechanisms by which B12 deficiency leads to neurologic damage, and how this damage is potentiated by N2O exposure. The article systematically examines the available experimental data relating to the two main coenzyme mechanisms that are usually suggested in clinical articles, particularly the deficient methylation hypothesis. The article demonstrates that neither of these mechanisms is fully consistent with the available data. The article then presents a novel mechanism based on new data from the neuroimmunology basic science literature which suggests that the pathogenesis of B12 deficiency myelopathy may not be related to its role as a coenzyme, but rather to newly discovered functions of B12 in regulating cytokines and growth factors.