The evolution of mathematical modeling of glioma proliferation and invasion.
01 Jan 2007-Journal of Neuropathology and Experimental Neurology (Lippincott Williams and Wilkins)-Vol. 66, Iss: 1, pp 1-9
TL;DR: A history of the use of mathematical modeling in the study of the proliferative-invasive growth of gliomas is presented, illustrating the progress made in understanding the in vivo dynamics of invasion and proliferation of tumor cells.
Abstract: 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.
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TL;DR: To fulfill the future goal of developing novel therapies to collapse CSC dynamics, drawing parallels to other normal and pathological states that are highly interactive with their microenvironments and that use developmental signaling pathways will be beneficial.
Abstract: Tissues with defined cellular hierarchies in development and homeostasis give rise to tumors with cellular hierarchies, suggesting that tumors recapitulate specific tissues and mimic their origins. Glioblastoma (GBM) is the most prevalent and malignant primary brain tumor and contains self-renewing, tumorigenic cancer stem cells (CSCs) that contribute to tumor initiation and therapeutic resistance. As normal stem and progenitor cells participate in tissue development and repair, these developmental programs re-emerge in CSCs to support the development and progressive growth of tumors. Elucidation of the molecular mechanisms that govern CSCs has informed the development of novel targeted therapeutics for GBM and other brain cancers. CSCs are not self-autonomous units; rather, they function within an ecological system, both actively remodeling the microenvironment and receiving critical maintenance cues from their niches. To fulfill the future goal of developing novel therapies to collapse CSC dynamics, drawing parallels to other normal and pathological states that are highly interactive with their microenvironments and that use developmental signaling pathways will be beneficial.
1,193 citations
Cites background from "The evolution of mathematical model..."
...Proliferation and invasion are phenotypes that have been modeled (Harpold et al. 2007)....
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TL;DR: The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance.
Abstract: Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.
563 citations
TL;DR: In this paper, the authors provide an overview of multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis, and limit the scope further by considering models of tumor progression that do not distinguish tumour cells by their age and do not consider immune system interactions nor do they describe models of therapy.
Abstract: Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.
541 citations
TL;DR: In contrast to almost all other brain tumors, diffuse gliomas infiltrate extensively in the neuropil, and this growth pattern is a major factor in therapeutic failure, so a more targeted (“search & destroy”) tactic may be needed for these tumors.
Abstract: In contrast to almost all other brain tumors, diffuse gliomas infiltrate extensively in the neuropil. This growth pattern is a major factor in therapeutic failure. Diffuse infiltrative glioma cells show some similarities with guerilla warriors. Histopathologically, the tumor cells tend to invade individually or in small groups in between the dense network of neuronal and glial cell processes. Meanwhile, in large areas of diffuse gliomas the tumor cells abuse pre-existent "supply lines" for oxygen and nutrients rather than constructing their own. Radiological visualization of the invasive front of diffuse gliomas is difficult. Although the knowledge about migration of (tumor)cells is rapidly increasing, the exact molecular mechanisms underlying infiltration of glioma cells in the neuropil have not yet been elucidated. As the efficacy of conventional methods to fight diffuse infiltrative glioma cells is limited, a more targeted ("search & destroy") tactic may be needed for these tumors. Hopefully, the study of original human glioma tissue and of genotypically and phenotypically relevant glioma models will soon provide information about the Achilles heel of diffuse infiltrative glioma cells that can be used for more effective therapeutic strategies.
533 citations
Cites background from "The evolution of mathematical model..."
...excellent recent reviews on (some of) these aspects we refer the reader to [40, 57, 69, 70, 99, 137, 148, 172]....
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TL;DR: Examining mathematical models of tumorigenesis as a complex process and validating their findings by experimental and clinical observations seems to be one way to reconcile molecular reductionist with quantitative holistic approaches and produce an integrative mathematical oncology view of cancer progression.
Abstract: Cancer research attracts broad resources and scientists from many disciplines, and has produced some impressive advances in the treatment and understanding of this disease. However, a comprehensive mechanistic view of the cancer process remains elusive. To achieve this it seems clear that one must assemble a physically integrated team of interdisciplinary scientists that includes mathematicians, to develop mathematical models of tumorigenesis as a complex process. Examining these models and validating their findings by experimental and clinical observations seems to be one way to reconcile molecular reductionist with quantitative holistic approaches and produce an integrative mathematical oncology view of cancer progression.
407 citations
Cites background from "The evolution of mathematical model..."
...It is perhaps worth noting that, in this arena, alternative modelling approaches that might only consider a single scale might be appropriate, such as models for growth at the tissue scal...
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References
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TL;DR: Gross-total tumor resection is associated with longer survival in patients with GBM, especially when other predictive variables are favorable.
Abstract: Object. The extent of tumor resection that should be undertaken in patients with glioblastoma multiforme (GBM) remains controversial. The purpose of this study was to identify significant independent predictors of survival in these patients and to determine whether the extent of resection was associated with increased survival time. Methods. The authors retrospectively analyzed 416 consecutive patients with histologically proven GBM who underwent tumor resection at the authors' institution between June 1993 and June 1999. Volumetric data and other tumor characteristics identified on magnetic resonance (MR) imaging were collected prospectively. Conclusions. Five independent predictors of survival were identified: age, Karnofsky Performance Scale (KPS) score, extent of resection, and the degree of necrosis and enhancement on preoperative MR imaging studies. A significant survival advantage was associated with resection of 98% or more of the tumor volume (median survival 13 months, 95% confidence interval [C...
2,641 citations
TL;DR: The authors present a realistic, high-resolution, digital, volumetric phantom of the human brain, which can be used to simulate tomographic images of the head and is the ideal tool to test intermodality registration algorithms.
Abstract: After conception and implementation of any new medical image processing algorithm, validation is an important step to ensure that the procedure fulfils all requirements set forth at the initial design stage. Although the algorithm must be evaluated on real data, a comprehensive validation requires the additional use of simulated data since it is impossible to establish ground truth with in vivo data. Experiments with simulated data permit controlled evaluation over a wide range of conditions (e.g., different levels of noise, contrast, intensity artefacts, or geometric distortion). Such considerations have become increasingly important with the rapid growth of neuroimaging, i.e., computational analysis of brain structure and function using brain scanning methods such as positron emission tomography and magnetic resonance imaging. Since simple objects such as ellipsoids or parallelepipedes do not reflect the complexity of natural brain anatomy, the authors present the design and creation of a realistic, high-resolution, digital, volumetric phantom of the human brain. This three-dimensional digital brain phantom is made up of ten volumetric data sets that define the spatial distribution for different tissues (e.g., grey matter, white matter, muscle, skin, etc.), where voxel intensity is proportional to the fraction of tissue within the voxel. The digital brain phantom can be used to simulate tomographic images of the head. Since the contribution of each tissue type to each voxel in the brain phantom is known, it can be used as the gold standard to test analysis algorithms such as classification procedures which seek to identify the tissue "type" of each image voxel. Furthermore, since the same anatomical phantom may be used to drive simulators for different modalities, it is the ideal tool to test intermodality registration algorithms. The brain phantom and simulated MR images have been made publicly available on the Internet (http://www.bic.mni.mcgill.ca/brainweb).
1,811 citations
"The evolution of mathematical model..." refers methods in this paper
...Fortunately, the neuro-anatomical atlas from the BrainWeb database was available, providing a spatial distribution of grey and white matter for the entire brain at a resolution of 1 mm(3) voxels (34, 35)....
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TL;DR: It is argued that gliomas arise from neural stem cells and the clinical implications of this concept are discussed.
Abstract: Little progress has been made in the treatment of gliomas during the past 25 years. One reason is our poor understanding of the cell of origin in these tumors and of the mechanisms that bring that cell into a malignant state. This review argues that gliomas arise from neural stem cells and discusses the clinical implications of this concept.
1,011 citations
"The evolution of mathematical model..." refers background in this paper
...Gliomas, the most common primary brain tumors, are thought to arise from the supporting glial cells of the brain or their precursors (1)....
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Journal Article•
740 citations
"The evolution of mathematical model..." refers background or methods in this paper
...The progress of mathematical modeling in the field of human oncology has greatly expanded from the major contributions of Collins et al in 1956 (2) and Steel in 1977 (12)....
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...Among the pioneers in the study of human cancers were Collins et al, who observed that metastases in the lungs visualized by plain x-rays of the chest grew at constant volume-doubling rates according to a simple exponential ‘‘law’’ (2)....
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TL;DR: Histological analysis of 195 biopsy specimens obtained from various locations within the volumes defined by CT and MRI revealed that contrast enhancement most often corresponded to tumor tissue without intervening parenchyma, and isolated tumor cell infiltration extended at least as far as T2 prolongation on magnetic resonance images.
Abstract: ✓ Forty patients with previously untreated intracranial glial neoplasms underwent stereotaxic serial biopsies assisted by computerized tomography (CT) and magnetic resonance imaging (MRI). Tumor volumes defined by computer reconstruction of contrast enhancement and low-attenuation boundaries on CT and T1 and T2 prolongation on MRI revealed that tumor volumes defined by T2-weighted MRI scans were larger than those defined by low-attenuation or contrast enhancement on CT scans. Histological analysis of 195 biopsy specimens obtained from various locations within the volumes defined by CT and MRI revealed that: 1) contrast enhancement most often corresponded to tumor tissue without intervening parenchyma; 2) hypodensity corresponded to parenchyma infiltrated by isolated tumor cells or in some instances to tumor tissue in low-grade gliomas or to simple edema; and 3) isolated tumor cell infiltration extended at least as far as T2 prolongation on magnetic resonance images. This information may be useful in plann...
736 citations
"The evolution of mathematical model..." refers methods in this paper
...In addition to the CT observations of Lewander et al (39) and Greene et al (40), Kelly et al (21, 41) and Dalrymple et al (20) reported that the histologic ‘‘edge’’ of the ‘‘solid tumor’’ coincided approximately with the circumference of the tumor visualized by enhanced CT or MRI (T1-Gd) and that ‘‘isolated tumor cells’’ could be seen microscopically inside and less commonly outside of the circumference of the tumor visualized in the T2 image....
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