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J. Cook

Bio: J. Cook is an academic researcher from University of California, Los Angeles. The author has contributed to research in topics: Anaplastic astrocytoma. The author has an hindex of 2, co-authored 2 publications receiving 178 citations.

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TL;DR: The model quantitatively supports the ideas that gliomas infiltrate so diffusely that they cannot be cured by resection alone, surgical or radiological, and the more extensive the resection, regardless of the degree of malignancy of the glioma, the greater the life expectancy.
Abstract: We have developed a mathematical model based on proliferation and infiltration of neoplastic cells that allows predictions to be made concerning the life expectancies following various extents of surgical resection of gliomas of all grades of malignancy. The key model parameters are the growth rate and the diffusion rate. These rates were initially derived from analysis of a case of recurrent anaplastic astrocytoma treated by chemotherapies. Numerical simulations allow us to estimate what would have happened to that patient if various extents of surgical resection, rather than chemotherapies, had been used. In each case, the shell of the infiltrating tumour that remains after 'gross total removal' or even a maximal excision continues to grow and regenerates the tumour mass remarkably rapidly. By developing a model that allows the growth and diffusion rates to define the distribution of cells at the time of diagnosis, and then varying these rates by about 50%, we created a hypothetical tumour patient population whose survival times show good agreement with the results recently reported by Kreth for treatments of glioblastomas. Tenfold decreases in the rates of growth and diffusion mimic the results reported by many other investigators with more slowly growing gliomas. Thus, the model quantitatively supports the ideas that (i) gliomas infiltrate so diffusely that they cannot be cured by resection alone, surgical or radiological, no matter how extensive that may be; (ii) the more extensive the resection, regardless of the degree of malignancy of the glioma, the greater the life expectancy; and (iii) measurements of the two rates, growth and diffusion, may be able to predict survival rates better than the current histological estimates of the type and grade of gliomas.

165 citations

Journal ArticleDOI
TL;DR: A model is described for the complex patterns formed by bacterial colonies, specifically Escherichia coli, and derive and analyse a model firmly based on experimental data, and the results from the model compare well with experiment.
Abstract: Although the development of spatial pattern and form is a central issue in biology the mechanisms which generate them are generally unknown. The interdisciplinary modelling challenge is to construct realistic mechanisms which capture the key biological processes and show how they are orchestrated to create the observed pattern. We discuss two specific patterning problems of current widespread interest in biomedicine. In the first, possible mechanisms of dermal wound healing are reviewed with a discussion of what is needed of realistic models for studying wound healing. We then list a series of open problems. In the second problem we describe a model for the complex patterns formed by bacterial colonies, specifically Escherichia coli, and derive and analyse a model firmly based on experimental data. The results from the model compare well with experiment. Mathematically, the class of models discussed gives rise to novel systems of partial differential equations which pose challenging problems, both analytical and numerical. The models have provided the experimentalist with insight as to how such patterns might be formed and have suggested possible experiments to elucidate the underlying biological processes.

20 citations


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Journal ArticleDOI
TL;DR: In this paper, the authors discuss mechanisms of glioma invasion, characteristics of the invasive cell, and consequences of this cellular phenotype for surgical resection, oncologic treatments, and future perspectives for anti-invasive strategies.
Abstract: Tumors of glial origin consist of a core mass and a penumbra of invasive, single cells, decreasing in numbers towards the periphery and still detectable several centimeters away from the core lesion. Several decades ago, the diffuse nature of malignant gliomas was recognized by neurosurgeons when super-radical resections using hemispherectomies failed to eradicate these tumors. Local invasiveness eventually leads to regrowth of a recurrent tumor predominantly adjacent to the resection cavity, which is not significantly altered by radiation or chemotherapy. This raises the question of whether invasive glioma cells activate cellular programs that render these cells resistant to conventional treatments. Clinical and experimental data demonstrate that glioma invasion is determined by several independent mechanisms that facilitate the spread of these tumors along different anatomic and molecular structures. A common denominator of this cellular behavior may be cell motility. Gene-expression profiling showed upregulation of genes related to motility, and functional studies demonstrated that cell motility contributes to the invasive phenotype of malignant gliomas. There is accumulating evidence that invasive glioma cells show a decreased proliferation rate and a relative resistance to apoptosis, which may contribute to chemotherapy and radiation resistance. Interestingly, interference with cell motility by different strategies results in increased susceptibility to apoptosis, indicating that this dynamic relationship can potentially be exploited as an anti-invasive treatment paradigm. In this review, we discuss mechanisms of glioma invasion, characteristics of the invasive cell, and consequences of this cellular phenotype for surgical resection, oncologic treatments, and future perspectives for anti-invasive strategies.

1,135 citations

Journal ArticleDOI
TL;DR: A review of the recent developments in mathematical modeling of gliomas can be found in this article, where the authors conclude that the velocity of expansion is linear with time and varies about 10-fold, from about 4 mm/year for low-grade glioma to about 3 mm/month for high-grade ones.

563 citations

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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

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TL;DR: 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, according to a mixed model.
Abstract: 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.

455 citations

Journal ArticleDOI
TL;DR: Using a detailed mapping of the white and grey matter in the brain developed for a MRI simulator, a mathematical model of gliomas is extended to incorporate the effects of augmented cell motility in white matter as compared to grey matter to give insight into microscopic and submicroscopic invasion of the human brain by glioma cells.
Abstract: We have extended a mathematical model of gliomas based on proliferation and diffusion rates to incorporate the effects of augmented cell motility in white matter as compared to grey matter. Using a detailed mapping of the white and grey matter in the brain developed for a MRI simulator, we have been able to simulate model tumours on an anatomically accurate brain domain. Our simulations show good agreement with clinically observed tumour geometries and suggest paths of submicroscopic tumour invasion not detectable on CT or MRI images. We expect this model to give insight into microscopic and submicroscopic invasion of the human brain by glioma cells. This method gives insight in microscopic and submicroscopic invasion of the human brain by glioma cells. Additionally, the model can be useful in defining expected pathways of invasion by glioma cells and thereby identify regions of the brain on which to focus treatments.

432 citations