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

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 predicitve 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.

Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology.

Gliomas are uniformly fatal forms of primary brain neoplasms that vary from low- to high-grade (glioblastoma). Whereas low-grade gliomas are weakly angiogenic, glioblastomas are among the most angiogenic tumors. Thus, interactions between glioma cells and their tissue microenvironment may play an important role in aggressive tumor formation and progression. To quantitatively explore how tumor cells interact with their tissue microenvironment, we incorporated the interactions of normoxic glioma cells, hypoxic glioma cells, vascular endothelial cells, diffusible angiogenic factors, and necrosis formation into a first-generation, biologically based mathematical model for glioma growth and invasion. Model simulations quantitatively described the spectrum of in vivo dynamics of gliomas visualized with medical imaging. Furthermore, we investigated how proliferation and dispersal of glioma cells combine to induce increasing degrees of cellularity, mitoses, hypoxia-induced neoangiogenesis and necrosis, features that characterize increasing degrees of "malignancy," and we found that changes in the net rates of proliferation (ρ) and invasion (D) are not always necessary for malignant progression. Thus, although other factors, including the accumulation of genetic mutations, can change cellular phenotype (e.g., proliferation and invasion rates), this study suggests that these are not required for malignant progression. Simulated results are placed in the context of the current clinical World Health Organization grading scheme for studying specific patient examples. This study suggests that through the application of the proposed model for tumor-microenvironment interactions, predictable patterns of dynamic changes in glioma histology distinct from changes in cellular phenotype (e.g., proliferation and invasion rates) may be identified, thus providing a powerful clinical tool.

Quantitative proteomic analysis of oligodendrogliomas with and without 1p/19q deletion.

Approximately 50-80% of oligodendrogliomas demonstrate a combined loss of chromosome 1p and 19q. Chromosome 1p/19q deletion, appearing early in tumorigenesis, is associated with improved clinical outcomes, including response to chemotherapy and radiation. Although many hypotheses have been proposed, the molecular mechanisms underlying improved clinical outcomes with 1p/19q deletion in oligodendrogliomas have not been characterized fully. To investigate the molecular differences between oligodendrogliomas, we employed an unbiased proteomic approach using microcapillary liquid chromatography mass spectrometry, along with a quantitative technique called isotope-coded affinity tags, on patient samples of grade II oligodendrogliomas. Following conventional biochemical separation of pooled tumor tissue from five samples of undeleted and 1p/19q deleted grade II oligodendrogliomas into nuclei-, mitochondria-, and cytosol-enriched fractions, relative changes in protein abundance were quantified. Among the 442 total proteins identified, 163 nonredundant proteins displayed significant changes in relative abundance in at least one of the three fractions between oligodendroglioma with and without 1p/19q deletion. Bioinformatic analyses of differentially regulated proteins supported the potential importance of metabolism and invasion/migration to the codeleted phenotype. A subset of altered proteins, including the pro-invasive extracellular matrix protein BCAN, was further validated by Western blotting as candidate markers for the more aggressive undeleted phenotype. These studies demonstrate the utility of proteomic analysis to identify candidate biological motifs and molecular mechanisms that drive differential malignancy related to 1p19q phenotypes. Future analysis of larger patient samples are warranted to further refine biomarker panels to predict biological behavior and assist in the identification of deleted gene products that define the 1p/19q phenotype.

Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model.

Glioblastomas are the most aggressive primary brain tumors, characterized by their rapid proliferation and diffuse infiltration of the brain tissue. Survival patterns in patients with glioblastoma have been associated with a number of clinicopathologic factors including age and neurologic status, yet a significant quantitative link to in vivo growth kinetics of each glioma has remained elusive. Exploiting a recently developed tool for quantifying glioma net proliferation and invasion rates in individual patients using routinely available magnetic resonance images (MRI), we propose to link these patient-specific kinetic rates of biological aggressiveness to prognostic significance. Using our biologically based mathematical model for glioma growth and invasion, examination of serial pretreatment MRIs of 32 glioblastoma patients allowed quantification of these rates for each patient's tumor. Survival analyses revealed that even when controlling for standard clinical parameters (e.g., age and Karnofsky performance status), these model-defined parameters quantifying biological aggressiveness (net proliferation and invasion rates) were significantly associated with prognosis. One hypothesis generated was that the ratio of the actual survival time after whatever therapies were used to the duration of survival predicted (by the model) without any therapy would provide a therapeutic response index (TRI) of the overall effectiveness of the therapies. The TRI may provide important information, not otherwise available, about the effectiveness of the treatments in individual patients. To our knowledge, this is the first report indicating that dynamic insight from routinely obtained pretreatment imaging may be quantitatively useful in characterizing the survival of individual patients with glioblastoma. Such a hybrid tool bridging mathematical modeling and clinical imaging may allow for stratifying patients for clinical studies relative to their pretreatment biological aggressiveness.

Quantitative metrics of net proliferation and invasion link biological aggressiveness assessed by MRI with hypoxia assessed by FMISO-PET in newly diagnosed glioblastomas.

Glioblastoma multiforme (GBM) are aggressive and uniformly fatal primary brain tumors characterized by their diffuse invasion of the normal-appearing parenchyma peripheral to the clinical imaging abnormality. Hypoxia, a hallmark of aggressive tumor behavior often noted in GBMs, has been associated with resistance to therapy, poorer survival, and more malignant tumor phenotypes. Based on the existence of a set of novel imaging techniques and modeling tools, our objective was to assess a hypothesized quantitative link between tumor growth kinetics [assessed via mathematical models and routine magnetic resonance imaging (MRI)] and the hypoxic burden of the tumor [assessed via positron emission tomography (PET) imaging]. Our biomathematical model for glioma kinetics describes the spatial and temporal evolution of a glioma in terms of concentration of malignant tumor cells. This model has already been proven useful as a novel tool to dynamically quantify the net rates of proliferation (rho) and invasion (D) of the glioma cells in individual patients. Estimates of these kinetic rates can be calculated from routinely available pretreatment MRI in vivo. Eleven adults with GBM were imaged preoperatively with (18)F-fluoromisonidazole (FMISO)-PET and serial gadolinium-enhanced T1- and T2-weighted MRIs to allow the estimation of patient-specific net rates of proliferation (rho) and invasion (D). Hypoxic volumes were quantified from each FMISO-PET scan following standard techniques. To control for tumor size variability, two measures of hypoxic burden were considered: relative hypoxia (RH), defined as the ratio of the hypoxic volume to the T2-defined tumor volume, and the mean intensity on FMISO-PET scaled to the blood activity of the tracer (mean T/B). Pearson correlations between RH and the net rate of cell proliferation (rho) reached significance (P < 0.04). Moreover, highly significant positive correlations were found between biological aggressiveness ratio (rho/D) and both RH (P < 0.00003) and the mean T/B (P < 0.0007).

The evolution of mathematical modeling of glioma proliferation and invasion.

Gliomas are well known for their potential for aggressive proliferation as well as their diffuse invasion of the normal-appearing parenchyma peripheral to the bulk lesion. This review presents a history of the use of mathematical modeling in the study of the proliferative-invasive growth of gliomas, illustrating the progress made in understanding the in vivo dynamics of invasion and proliferation of tumor cells. Mathematical modeling is based on a sequence of observation, speculation, development of hypotheses to be tested, and comparisons between theory and reality. These mathematical investigations, iteratively compared with experimental and clinical work, demonstrate the essential relationship between experimental and theoretical approaches. Together, these efforts have extended our knowledge and insight into in vivo brain tumor growth dynamics that should enhance current diagnoses and treatments.

"Just look," he said.

Five personal examples are given illustrating the general principle that one can see if one looks or, conversely, that one cannot see anything that one believes not to exist.

March 2004: a 24-year-old woman with bifrontal headaches.

A 24-year-old woman with bifrontal headaches was found to have a well-circumscribed lesion in the frontal lobe subcortical white matter. Microscopic examination showed clusters of small round cells separated by hypocellular neuropil-like areas, and a distinct border between tumor and surrounding white matter. Synaptophysin was diffusely positive in neuropil-like areas, and many tumor cells expressed NeuN. Based on these findings, a diagnosis of "extraventricular neurocytoma" was made. A double-label immunofluorescence stain was performed with NeuN and Ki-67 antibodies to determine if NeuN+ cells remained in the mitotic cycle. No colocalization of these markers was found, thus supporting the hypothesis that neuronal differentiation (as marked by NeuN expression) is incompatible with continued proliferation of tumor cells, as well as normal neurons.

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

Over the last 10 years increasingly complex mathematical models of cancerous growths have been developed, especially on solid tumors, in which growth primarily comes from cellular proliferation. The invasiveness of gliomas, however, requires a change in the concept to include cellular motility in addition to proliferative growth. In this article we review some of the recent developments in mathematical modeling of gliomas. We begin with a model of untreated gliomas and continue with models of polyclonal gliomas following chemotherapy or surgical resection. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have recently been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter on a geometrically complex brain domain, including sulcal boundaries, with a resolution of 1 mm(3) voxels. We conclude that the velocity of expansion is linear with time and varies about 10-fold, from about 4 mm/year for low-grade gliomas to about 3 mm/month for high-grade ones.

Continuous growth of mean tumor diameter in a subset of grade II gliomas.

Serial magnetic resonance images of 27 patients with untreated World Health Organization grade II oligodendrogliomas or mixed gliomas were reviewed retrospectively to study the kinetics of tumor growth before anaplastic transformation. Analysis of the mean tumor diameters over time showed constant growth. Linear regression, using a mixed model, found an average slope of 4.1mm per year (95% confidence interval, 3.8-4.4mm/year). Untreated low-grade oligodendrogliomas or mixed gliomas grow continuously during their premalignant phase, and their pattern of growth can be predicted within a relatively narrow range. These findings could be of interest to optimize patients management and follow-up.

Quantifying efficacy of chemotherapy of brain tumors with homogeneous and heterogeneous drug delivery.

Gliomas are diffuse and invasive brain tumors with the nefarious ability to evade even seemingly draconian treatment measures. Here we introduce a simple mathematical model for drug delivery of chemotherapeutic agents to treat such a tumor. The model predicts that heterogeneity in drug delivery related to variability in vascular density throughout the brain results in an apparent tumor reduction based on imaging studies despite continual spread beyond the resolution of the imaging modality. We discuss a clinical example for which the model-predicted scenario is relevant. The analysis and results suggest an explanation for the clinical problem of the long-standing confounding observation of shrinkage of the lesion in certain areas of the brain with continued growth in other areas.