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      Patient-Specific Mathematical Neuro-Oncology: Using a Simple Proliferation and Invasion Tumor Model to Inform Clinical Practice


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          Glioblastoma multiforme (GBM) is the most common malignant primary brain tumor associated with a poor median survival of 15–18 months, yet there is wide heterogeneity across and within patients. This heterogeneity has been the source of significant clinical challenges facing patients with GBM and has hampered the drive toward more precision or personalized medicine approaches to treating these challenging tumors. Over the last two decades, the field of Mathematical Neuro-oncology has grown out of desire to use (often patient-specific) mathematical modeling to better treat GBMs. Here, we will focus on a series of clinically relevant results using patient-specific mathematical modeling. The core model at the center of these results incorporates two hallmark features of GBM, proliferation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\rho )$$\end{document} and invasion ( D), as key parameters. Based on routinely obtained magnetic resonance images, each patient’s tumor can be characterized using these two parameters. The Proliferation-Invasion (PI) model uses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document} and D to create patient-specific growth predictions. The PI model, its predictions, and parameters have been used in a number of ways to derive biological insight. Beyond predicting growth, the PI model has been utilized to identify patients who benefit from different surgery strategies, to prognosticate response to radiation therapy, to develop a treatment response metric, and to connect clinical imaging features and genetic information. Demonstration of the PI model’s clinical relevance supports the growing role for it and other mathematical models in routine clinical practice.

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          Independent association of extent of resection with survival in patients with malignant brain astrocytoma.

          With recent advances in the adjuvant treatment of malignant brain astrocytomas, it is increasingly debated whether extent of resection affects survival. In this study, the authors investigate this issue after primary and revision resection of these lesions. The authors retrospectively reviewed the cases of 1215 patients who underwent surgery for malignant brain astrocytomas (World Health Organization [WHO] Grade III or IV) at a single institution from 1996 to 2006. Patients with deep-seated or unresectable lesions were excluded. Based on MR imaging results obtained < 48 hours after surgery, gross-total resection (GTR) was defined as no residual enhancement, near-total resection (NTR) as having thin rim enhancement of the resection cavity only, and subtotal resection (STR) as having residual nodular enhancement. The independent association of extent of resection and subsequent survival was assessed via a multivariate proportional hazards regression analysis. Magnetic resonance imaging studies were available for review in 949 cases. The mean age and mean Karnofsky Performance Scale (KPS) score at time of surgery were 51 +/- 16 years and 80 +/- 10, respectively. Surgery consisted of primary resection in 549 patients (58%) and revision resection for tumor recurrence in 400 patients (42%). The lesion was WHO Grade IV in 700 patients (74%) and Grade III in 249 (26%); there were 167 astrocytomas and 82 mixed oligoastrocytoma. Among patients who underwent resection, GTR, NTR, and STR were achieved in 330 (35%), 388 (41%), and 231 cases (24%), respectively. Adjusting for factors associated with survival (for example, age, KPS score, Gliadel and/or temozolomide use, and subsequent resection), GTR versus NTR (p < 0.05) and NTR versus STR (p < 0.05) were independently associated with improved survival after both primary and revision resection of glioblastoma multiforme (GBM). For primary GBM resection, the median survival after GTR, NTR, and STR was 13, 11, and 8 months, respectively. After revision resection, the median survival after GTR, NTR, and STR was 11, 9, and 5 months, respectively. Adjusting for factors associated with survival for WHO Grade III astrocytoma (age, KPS score, and revision resection), GTR versus STR (p < 0.05) was associated with improved survival. Gross-total resection versus NTR was not associated with an independent survival benefit in patients with WHO Grade III astrocytomas. The median survival after primary resection of WHO Grade III (mixed oligoastrocytomas excluded) for GTR, NTR, and STR was 58, 46, and 34 months, respectively. In the authors' experience with both primary and secondary resection of malignant brain astrocytomas, increasing extent of resection was associated with improved survival independent of age, degree of disability, WHO grade, or subsequent treatment modalities used. The maximum extent of resection should be safely attempted while minimizing the risk of surgically induced neurological injury.
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            Chemoradiotherapy in malignant glioma: standard of care and future directions.

            Glioma has been considered resistant to chemotherapy and radiation. Recently, concomitant and adjuvant chemoradiotherapy with temozolomide has become the standard treatment for newly diagnosed glioblastoma. Conversely (neo-)adjuvant PCV (procarbazine, lomustine, vincristine) failed to improve survival in the more chemoresponsive tumor entities of anaplastic oligoastrocytoma and oligodendroglioma. Preclinical investigations suggest synergism or additivity of radiotherapy and temozolomide in glioma cell lines. Although the relative contribution of the concomitant and the adjuvant chemotherapy, respectively, cannot be assessed, the early introduction of chemotherapy and the simultaneous administration with radiotherapy appear to be key for the improvement of outcome. Epigenetic inactivation of the DNA repair enzyme methylguanine methyltransferase (MGMT) seems to be the strongest predictive marker for outcome in patients treated with alkylating agent chemotherapy. Patients whose tumors do not have MGMT promoter methylation are less likely to benefit from the addition of temozolomide chemotherapy and require alternative treatment strategies. The predictive value of MGMT gene promoter methylation is being validated in ongoing trials aiming at overcoming this resistance by a dose-dense continuous temozolomide administration or in combination with MGMT inhibitors. Understanding of molecular mechanisms allows for rational targeting of specific pathways of repair, signaling, and angiogenesis. The addition of tyrosine kinase inhibitors vatalanib (PTK787) and vandetinib (ZD6474), the integrin inhibitor cilengitide, the monoclonal antibodies bevacizumab and cetuximab, the mammalian target of rapamycin inhibitors temsirolimus and everolimus, and the protein kinase C inhibitor enzastaurin, among other agents, are in clinical investigation, building on the established chemoradiotherapy regimen for newly diagnosed glioblastoma.
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              Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach.

              Glioblastoma multiforme (GBM) is the most malignant form of primary brain tumors known as gliomas. They proliferate and invade extensively and yield short life expectancies despite aggressive treatment. Response to treatment is usually measured in terms of the survival of groups of patients treated similarly, but this statistical approach misses the subgroups that may have responded to or may have been injured by treatment. Such statistics offer scant reassurance to individual patients who have suffered through these treatments. Furthermore, current imaging-based treatment response metrics in individual patients ignore patient-specific differences in tumor growth kinetics, which have been shown to vary widely across patients even within the same histological diagnosis and, unfortunately, these metrics have shown only minimal success in predicting patient outcome. We consider nine newly diagnosed GBM patients receiving diagnostic biopsy followed by standard-of-care external beam radiation therapy (XRT). We present and apply a patient-specific, biologically based mathematical model for glioma growth that quantifies response to XRT in individual patients in vivo. The mathematical model uses net rates of proliferation and migration of malignant tumor cells to characterize the tumor's growth and invasion along with the linear-quadratic model for the response to radiation therapy. Using only routinely available pre-treatment MRIs to inform the patient-specific bio-mathematical model simulations, we find that radiation response in these patients, quantified by both clinical and model-generated measures, could have been predicted prior to treatment with high accuracy. Specifically, we find that the net proliferation rate is correlated with the radiation response parameter (r = 0.89, p = 0.0007), resulting in a predictive relationship that is tested with a leave-one-out cross-validation technique. This relationship predicts the tumor size post-therapy to within inter-observer tumor volume uncertainty. The results of this study suggest that a mathematical model can create a virtual in silico tumor with the same growth kinetics as a particular patient and can not only predict treatment response in individual patients in vivo but also provide a basis for evaluation of response in each patient to any given therapy.

                Author and article information

                312.695.9441 , kraeswanson@gmail.com
                Bull Math Biol
                Bull. Math. Biol
                Bulletin of Mathematical Biology
                Springer US (New York )
                21 March 2015
                21 March 2015
                : 77
                : 5
                : 846-856
                [ ]Mathematical NeuroOncology Lab, Department of Neurological Surgery, Northwestern University Feinberg School of Medicine, 676 N St Clair Street, Suite 1300, Chicago, IL 60611 USA
                [ ]Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL USA
                © The Author(s) 2015

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

                : 7 August 2014
                : 10 February 2015
                Review Paper
                Custom metadata
                © Society for Mathematical Biology 2015

                Quantitative & Systems biology
                glioblastoma,mathematical model,patient-specific
                Quantitative & Systems biology
                glioblastoma, mathematical model, patient-specific


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