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Jacobs J, Rockne RC, Hawkins-Daarud AJ, Jackson PR, Johnston SK, Kinahan P, Swanson KR. Improved model prediction of glioma growth utilizing tissue-specific boundary effects. Math Biosci 2019; 312:59-66. [PMID: 31009624 DOI: 10.1016/j.mbs.2019.04.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2017] [Revised: 05/04/2018] [Accepted: 04/19/2019] [Indexed: 10/27/2022]
Abstract
Kinetic parameter estimates for mathematical models of glioblastoma multiforme (GBM), derived from clinical scans, have been used to predict the occurrence of hypoxia, necrosis, response to radiation therapy, and overall survival. Modeling GBM growth in a cerebral model encounters anatomical boundaries that interfere with model calibration from clinical measurements. METHODS The effect of boundaries is examined on both spherically symmetric and anatomical models of tumor growth. This effect is incorporated into a method that updates kinetic parameters. The efficacy of this method in reproducing clinical image-derived subject data is evaluated. RESULTS Spherically symmetric simulations of tumor growth with simple boundaries behave predictably when in a linear phase of growth. Anatomic simulations of eleven out of twenty subjects demonstrated improved fit to subject data with the new method. When only subjects exhibiting linear growth are considered, eight out of nine subject demonstrate improved fit to the data. CONCLUSION Anatomical boundaries to tumor growth measurably deflect progression and affect estimates of kinetic parameters. The presented method reliably updates kinetic parameters to fit anatomic computational models to clinically derived subject data when those data are in a linear regime.
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Affiliation(s)
- Joshua Jacobs
- Department of Neurosurgery, Mayo Clinic, Rochester, MN, USA.
| | - Russell C Rockne
- Division of Mathematical Oncology, City of Hope, Duarte, CA, USA
| | | | | | | | - Paul Kinahan
- Department of Radiology, University of Washington, Seattle, WA, USA
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Jacobs JJ, Capek S, Spinner RJ, Swanson KR. Mathematical model of perineural tumor spread: a pilot study. Acta Neurochir (Wien) 2018; 160:655-661. [PMID: 29264779 DOI: 10.1007/s00701-017-3423-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Accepted: 12/03/2017] [Indexed: 10/18/2022]
Abstract
BACKGROUND Perineural spread (PNS) of pelvic cancer along the lumbosacral plexus is an emerging explanation for neoplastic lumbosacral plexopathy (nLSP) and an underestimated source of patient morbidity and mortality. Despite the increased incidence of PNS, these patients are often times a clinical conundrum-to diagnose and to treat. Building on previous results in modeling glioblastoma multiforme (GBM), we present a mathematical model for predicting the course and extent of the PNS of recurrent tumors. METHODS We created three-dimensional models of perineurally spreading tumor along the lumbosacral plexus from consecutive magnetic resonance imaging scans of two patients (one each with prostate cancer and cervical cancer). We adapted and applied a previously reported mathematical model of GBM to progression of tumor growth along the nerves on an anatomical model obtained from a healthy subject. RESULTS We were able to successfully model and visualize perineurally spreading pelvic cancer in two patients; average growth rates were 60.7 mm/year for subject 1 and 129 mm/year for subject 2. The model correlated well with extent of PNS on MRI scans at given time points. CONCLUSIONS This is the first attempt to model perineural tumor spread and we believe that it provides a glimpse into the future of disease progression monitoring. Every tumor and every patient are different, and the possibility to report treatment response using a unified scale-as "days gained"-will be a necessity in the era of individualized medicine. We hope our work will serve as a springboard for future connections between mathematics and medicine.
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Neal ML, Trister AD, Cloke T, Sodt R, Ahn S, Baldock AL, Bridge CA, Lai A, Cloughesy TF, Mrugala MM, Rockhill JK, Rockne RC, Swanson KR. Discriminating survival outcomes in patients with glioblastoma using a simulation-based, patient-specific response metric. PLoS One 2013; 8:e51951. [PMID: 23372647 PMCID: PMC3553125 DOI: 10.1371/journal.pone.0051951] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2012] [Accepted: 11/06/2012] [Indexed: 11/23/2022] Open
Abstract
Accurate clinical assessment of a patient's response to treatment for glioblastoma multiforme (GBM), the most malignant type of primary brain tumor, is undermined by the wide patient-to-patient variability in GBM dynamics and responsiveness to therapy. Using computational models that account for the unique geometry and kinetics of individual patients' tumors, we developed a method for assessing treatment response that discriminates progression-free and overall survival following therapy for GBM. Applying these models as untreated virtual controls, we generate a patient-specific “Days Gained” response metric that estimates the number of days a therapy delayed imageable tumor progression. We assessed treatment response in terms of Days Gained scores for 33 patients at the time of their first MRI scan following first-line radiation therapy. Based on Kaplan-Meier analyses, patients with Days Gained scores of 100 or more had improved progression-free survival, and patients with scores of 117 or more had improved overall survival. Our results demonstrate that the Days Gained response metric calculated at the routinely acquired first post-radiation treatment time point provides prognostic information regarding progression and survival outcomes. Applied prospectively, our model-based approach has the potential to improve GBM treatment by accounting for patient-to-patient heterogeneity in GBM dynamics and responses to therapy.
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Affiliation(s)
- Maxwell Lewis Neal
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
- * E-mail: (MLN); (KRS)
| | - Andrew D. Trister
- Department of Radiation Oncology, University of Washington, Seattle, Washington, United States of America
| | - Tyler Cloke
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
| | - Rita Sodt
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
| | - Sunyoung Ahn
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
| | - Anne L. Baldock
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
- Department of Neurological Surgery, Northwestern University, Chicago, Illinois, United States of America
- Northwestern Brain Tumor Institute, Chicago, Illinois, United States of America
| | - Carly A. Bridge
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
- Department of Neurological Surgery, Northwestern University, Chicago, Illinois, United States of America
- Northwestern Brain Tumor Institute, Chicago, Illinois, United States of America
| | - Albert Lai
- Department of Neurology, University of California Los Angeles, Los Angeles, California, United States of America
| | - Timothy F. Cloughesy
- Department of Neurology, University of California Los Angeles, Los Angeles, California, United States of America
| | - Maciej M. Mrugala
- Department of Neurology, University of Washington, Seattle, Washington, United States of America
| | - Jason K. Rockhill
- Department of Radiation Oncology, University of Washington, Seattle, Washington, United States of America
| | - Russell C. Rockne
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
- Department of Neurological Surgery, Northwestern University, Chicago, Illinois, United States of America
- Northwestern Brain Tumor Institute, Chicago, Illinois, United States of America
| | - Kristin R. Swanson
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
- Department of Neurological Surgery, Northwestern University, Chicago, Illinois, United States of America
- Northwestern Brain Tumor Institute, Chicago, Illinois, United States of America
- Department of Applied Mathematics, University of Washington, Seattle, Washington, United States of America
- Nancy and Buster Alvord Brain Tumor Center, University of Washington, Seattle, Washington, United States of America
- * E-mail: (MLN); (KRS)
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