Modeling Brain Cancer Progression Using Reaction-Diffusion Equations with Minimal Parameters

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Description
A description of numerical and analytical work pertaining to models that describe the growth and progression of glioblastoma multiforme (GBM), an aggressive form of primary brain cancer. Two reaction-diffusion models are used: the Fisher-Kolmogorov-Petrovsky-Piskunov equation and a 2-population model that

A description of numerical and analytical work pertaining to models that describe the growth and progression of glioblastoma multiforme (GBM), an aggressive form of primary brain cancer. Two reaction-diffusion models are used: the Fisher-Kolmogorov-Petrovsky-Piskunov equation and a 2-population model that divides the tumor into actively proliferating and quiescent (or necrotic) cells. The numerical portion of this work (chapter 2) focuses on simulating GBM expansion in patients undergoing treatment for recurrence of tumor following initial surgery. The models are simulated on 3-dimensional brain geometries derived from magnetic resonance imaging (MRI) scans provided by the Barrow Neurological Institute. The study consists of 17 clinical time intervals across 10 patients that have been followed in detail, each of whom shows significant progression of tumor over a period of 1 to 3 months on sequential follow up scans. A Taguchi sampling design is implemented to estimate the variability of the predicted tumors to using 144 different choices of model parameters. In 9 cases, model parameters can be identified such that the simulated tumor contains at least 40 percent of the volume of the observed tumor. In the analytical portion of the paper (chapters 3 and 4), a positively invariant region for our 2-population model is identified. Then, a rigorous derivation of the critical patch size associated with the model is performed. The critical patch (KISS) size is the minimum habitat size needed for a population to survive in a region. Habitats larger than the critical patch size allow a population to persist, while smaller habitats lead to extinction. The critical patch size of the 2-population model is consistent with that of the Fisher-Kolmogorov-Petrovsky-Piskunov equation, one of the first reaction-diffusion models proposed for GBM. The critical patch size may indicate that GBM tumors have a minimum size depending on the location in the brain. A theoretical relationship between the size of a GBM tumor at steady-state and its maximum cell density is also derived, which has potential applications for patient-specific parameter estimation based on magnetic resonance imaging data.
Date Created
2023
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Transorbital Skull Base Surgery; Exploratory Quantitative Assessment of the Microscopic and Endoscopic Surgical Corridor

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Description
Transorbital surgery has gained recent notoriety due to its incorporation into endoscopic skull base surgery. The body of published literature on the field is cadaveric and observation. The pre-clinical studies are focused on the use of the endoscope only. Furthermore

Transorbital surgery has gained recent notoriety due to its incorporation into endoscopic skull base surgery. The body of published literature on the field is cadaveric and observation. The pre-clinical studies are focused on the use of the endoscope only. Furthermore the methodology utilised in the published literature is inconsistent and does not embody the optimal principles of scientific experimentation. This body of work evaluates a minimally invasive novel surgical corridor - the transorbital approach - its validity in neurosurgical practice, as well as both qualitatively and quantitatively assessing available technological advances in a robust experimental fashion. While the endoscope is an established means of visualisation used in clinical transorbital surgery, the microscope has never been assessed with respect to the transorbital approach. This question is investigated here and the anatomical and surgical benefits and limitations of microscopic visualisation demonstrated. The comparative studies provide increased knowledge on specifics pertinent to neurosurgeons and other skull base specialists when planning pre-operatively, such as pathology location, involved anatomical structures, instrument maneuvrability and the advantages and disadvantages of the distinct visualisation technologies. This is all with the intention of selecting the most suitable surgical approach and technology, specific to the patient, pathology and anatomy, so as to perform the best surgical procedure. The research findings illustrated in this body of work are diverse, reproducible and applicable. The transorbital surgical corridor has substantive potential for access to the anterior cranial fossa and specific surgical target structures. The neuroquantitative metrics investigated confirm the utility and benefits specific to the respective visualisation technologies i.e. the endoscope and microscope. The most appropriate setting wherein the approach should be used is also discussed. The transorbital corridor has impressive potential, can utilise all available technological advances, promotes multi-disciplinary co-operation and learning amongst clinicians and ultimately, is a means of improving operative patient care.
Date Created
2021
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Mathematical Analysis of Glioma Growth in a Murine Model

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Description

Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of

Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm3 to 62 mm3, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.

Date Created
2017-05-31
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Intraoperative Fluorescence Imaging for Personalized Brain Tumor Resection: Current State and Future Directions

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Description

Introduction: Fluorescence-guided surgery is one of the rapidly emerging methods of surgical “theranostics.” In this review, we summarize current fluorescence techniques used in neurosurgical practice for brain tumor patients as well as future applications of recent laboratory and translational studies.

Methods:

Introduction: Fluorescence-guided surgery is one of the rapidly emerging methods of surgical “theranostics.” In this review, we summarize current fluorescence techniques used in neurosurgical practice for brain tumor patients as well as future applications of recent laboratory and translational studies.

Methods: Review of the literature.

Results: A wide spectrum of fluorophores that have been tested for brain surgery is reviewed. Beginning with a fluorescein sodium application in 1948 by Moore, fluorescence-guided brain tumor surgery is either routinely applied in some centers or is under active study in clinical trials. Besides the trinity of commonly used drugs (fluorescein sodium, 5-aminolevulinic acid, and indocyanine green), less studied fluorescent stains, such as tetracyclines, cancer-selective alkylphosphocholine analogs, cresyl violet, acridine orange, and acriflavine, can be used for rapid tumor detection and pathological tissue examination. Other emerging agents, such as activity-based probes and targeted molecular probes that can provide biomolecular specificity for surgical visualization and treatment, are reviewed. Furthermore, we review available engineering and optical solutions for fluorescent surgical visualization. Instruments for fluorescent-guided surgery are divided into wide-field imaging systems and hand-held probes. Recent advancements in quantitative fluorescence-guided surgery are discussed.

Conclusion: We are standing on the threshold of the era of marker-assisted tumor management. Innovations in the fields of surgical optics, computer image analysis, and molecular bioengineering are advancing fluorescence-guided tumor resection paradigms, leading to cell-level approaches to visualization and resection of brain tumors.

Date Created
2016-10-17
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Use of a Conformational Switching Aptamer for Rapid and Specific Ex Vivo Identification of Central Nervous System Lymphoma in a Xenograft Model

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Description

Improved tools for providing specific intraoperative diagnoses could improve patient care. In neurosurgery, intraoperatively differentiating non-operative lesions such as CNS B-cell lymphoma from operative lesions can be challenging, often necessitating immunohistochemical (IHC) procedures which require up to 24-48 hours. Here,

Improved tools for providing specific intraoperative diagnoses could improve patient care. In neurosurgery, intraoperatively differentiating non-operative lesions such as CNS B-cell lymphoma from operative lesions can be challenging, often necessitating immunohistochemical (IHC) procedures which require up to 24-48 hours. Here, we evaluate the feasibility of generating rapid ex vivo specific labeling using a novel lymphoma-specific fluorescent switchable aptamer. Our B-cell lymphoma-specific switchable aptamer produced only low-level fluorescence in its unbound conformation and generated an 8-fold increase in fluorescence once bound to its target on CD20-positive lymphoma cells. The aptamer demonstrated strong binding to B-cell lymphoma cells within 15 minutes of incubation as observed by flow cytometry. We applied the switchable aptamer to ex vivo xenograft tissue harboring B-cell lymphoma and astrocytoma, and within one hour specific visual identification of lymphoma was routinely possible. In this proof-of-concept study in human cell culture and orthotopic xenografts, we conclude that a fluorescent switchable aptamer can provide rapid and specific labeling of B-cell lymphoma, and that developing aptamer-based labeling approaches could simplify tissue staining and drastically reduce time to histopathological diagnoses compared with IHC-based methods. We propose that switchable aptamers could enhance expeditious, accurate intraoperative decision-making.

Date Created
2015-04-15
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The Ketogenic Diet Is an Effective Adjuvant to Radiation Therapy for the Treatment of Malignant Glioma

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Description

Introduction: The ketogenic diet (KD) is a high-fat, low-carbohydrate diet that alters metabolism by increasing the level of ketone bodies in the blood. KetoCal® (KC) is a nutritionally complete, commercially available 4∶1 (fat∶ carbohydrate+protein) ketogenic formula that is an effective non-pharmacologic

Introduction: The ketogenic diet (KD) is a high-fat, low-carbohydrate diet that alters metabolism by increasing the level of ketone bodies in the blood. KetoCal® (KC) is a nutritionally complete, commercially available 4∶1 (fat∶ carbohydrate+protein) ketogenic formula that is an effective non-pharmacologic treatment for the management of refractory pediatric epilepsy. Diet-induced ketosis causes changes to brain homeostasis that have potential for the treatment of other neurological diseases such as malignant gliomas.

Methods: We used an intracranial bioluminescent mouse model of malignant glioma. Following implantation animals were maintained on standard diet (SD) or KC. The mice received 2×4 Gy of whole brain radiation and tumor growth was followed by in vivo imaging.

Results: Animals fed KC had elevated levels of β-hydroxybutyrate (p = 0.0173) and an increased median survival of approximately 5 days relative to animals maintained on SD. KC plus radiation treatment were more than additive, and in 9 of 11 irradiated animals maintained on KC the bioluminescent signal from the tumor cells diminished below the level of detection (p<0.0001). Animals were switched to SD 101 days after implantation and no signs of tumor recurrence were seen for over 200 days.

Conclusions: KC significantly enhances the anti-tumor effect of radiation. This suggests that cellular metabolic alterations induced through KC may be useful as an adjuvant to the current standard of care for the treatment of human malignant gliomas.

Date Created
2012-05-01
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The Ketogenic Diet Alters the Hypoxic Response and Affects Expression of Proteins Associated With Angiogenesis, Invasive Potential, and Vascular Permeability in a Mouse Glioma Model

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Description

Background: The successful treatment of malignant gliomas remains a challenge despite the current standard of care, which consists of surgery, radiation and temozolomide. Advances in the survival of brain cancer patients require the design of new therapeutic approaches that take advantage

Background: The successful treatment of malignant gliomas remains a challenge despite the current standard of care, which consists of surgery, radiation and temozolomide. Advances in the survival of brain cancer patients require the design of new therapeutic approaches that take advantage of common phenotypes such as the altered metabolism found in cancer cells. It has therefore been postulated that the high-fat, low-carbohydrate, adequate protein ketogenic diet (KD) may be useful in the treatment of brain tumors. We have demonstrated that the KD enhances survival and potentiates standard therapy in a mouse model of malignant glioma, yet the mechanisms are not fully understood.

Methods: To explore the effects of the KD on various aspects of tumor growth and progression, we used the immunocompetent, syngeneic GL261-Luc2 mouse model of malignant glioma.

Results: Tumors from animals maintained on KD showed reduced expression of the hypoxia marker carbonic anhydrase 9, hypoxia inducible factor 1-alpha, and decreased activation of nuclear factor kappa B. Additionally, tumors from animals maintained on KD had reduced tumor microvasculature and decreased expression of vascular endothelial growth factor receptor 2, matrix metalloproteinase-2 and vimentin. Peritumoral edema was significantly reduced in animals fed the KD and protein analyses showed altered expression of zona occludens-1 and aquaporin-4.

Conclusions: The KD directly or indirectly alters the expression of several proteins involved in malignant progression and may be a useful tool for the treatment of gliomas.

Date Created
2015-06-17
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The Ketogenic Diet Reverses Gene Expression Patterns and Reduces Reactive Oxygen Species Levels When Used as an Adjuvant Therapy for Glioma

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Description

Background: Malignant brain tumors affect people of all ages and are the second leading cause of cancer deaths in children. While current treatments are effective and improve survival, there remains a substantial need for more efficacious therapeutic modalities. The ketogenic diet

Background: Malignant brain tumors affect people of all ages and are the second leading cause of cancer deaths in children. While current treatments are effective and improve survival, there remains a substantial need for more efficacious therapeutic modalities. The ketogenic diet (KD) - a high-fat, low-carbohydrate treatment for medically refractory epilepsy - has been suggested as an alternative strategy to inhibit tumor growth by altering intrinsic metabolism, especially by inducing glycopenia.

Methods: Here, we examined the effects of an experimental KD on a mouse model of glioma, and compared patterns of gene expression in tumors vs. normal brain from animals fed either a KD or a standard diet.

Results: Animals received intracranial injections of bioluminescent GL261-luc cells and tumor growth was followed in vivo. KD treatment significantly reduced the rate of tumor growth and prolonged survival. Further, the KD reduced reactive oxygen species (ROS) production in tumor cells. Gene expression profiling demonstrated that the KD induces an overall reversion to expression patterns seen in non-tumor specimens. Notably, genes involved in modulating ROS levels and oxidative stress were altered, including those encoding cyclooxygenase 2, glutathione peroxidases 3 and 7, and periredoxin 4.

Conclusions: Our data demonstrate that the KD improves survivability in our mouse model of glioma, and suggests that the mechanisms accounting for this protective effect likely involve complex alterations in cellular metabolism beyond simply a reduction in glucose.

Date Created
2010-09-10
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Accurate State Estimation From Uncertain Data and Models: An Application of Data Assimilation to Mathematical Models of Human Brain Tumors

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Description

Background:
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this

Background:
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results:
We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions:
The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.

Date Created
2011-12-21
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