Matching Items (43)

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Mathematical Models of Androgen Resistance in Prostate Cancer Patients under Intermittent Androgen Suppression Therapy

Description

Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and

Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). We accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). While these models are simplifications of a previously published model, they fit data with similar accuracy and improve forecasting results. Both models describe the progression of androgen resistance. Although Model 1 is simpler than the more realistic Model 2, it can fit clinical data to a greater precision. However, we found that Model 2 can forecast future PSA levels more accurately. These findings suggest that including more realistic mechanisms of androgen dynamics in a two population model may help androgen resistance timing prediction.

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Created

Date Created
  • 2016-11-16

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Multi-Parametric MRI and Texture Analysis to Visualize Spatial Histologic Heterogeneity and Tumor Extent in Glioblastoma

Description

Background
Genetic profiling represents the future of neuro-oncology but suffers from inadequate biopsies in heterogeneous tumors like Glioblastoma (GBM). Contrast-enhanced MRI (CE-MRI) targets enhancing core (ENH) but yields adequate tumor

Background
Genetic profiling represents the future of neuro-oncology but suffers from inadequate biopsies in heterogeneous tumors like Glioblastoma (GBM). Contrast-enhanced MRI (CE-MRI) targets enhancing core (ENH) but yields adequate tumor in only ~60% of cases. Further, CE-MRI poorly localizes infiltrative tumor within surrounding non-enhancing parenchyma, or brain-around-tumor (BAT), despite the importance of characterizing this tumor segment, which universally recurs. In this study, we use multiple texture analysis and machine learning (ML) algorithms to analyze multi-parametric MRI, and produce new images indicating tumor-rich targets in GBM.
Methods
We recruited primary GBM patients undergoing image-guided biopsies and acquired pre-operative MRI: CE-MRI, Dynamic-Susceptibility-weighted-Contrast-enhanced-MRI, and Diffusion Tensor Imaging. Following image coregistration and region of interest placement at biopsy locations, we compared MRI metrics and regional texture with histologic diagnoses of high- vs low-tumor content (≥80% vs <80% tumor nuclei) for corresponding samples. In a training set, we used three texture analysis algorithms and three ML methods to identify MRI-texture features that optimized model accuracy to distinguish tumor content. We confirmed model accuracy in a separate validation set.
Results
We collected 82 biopsies from 18 GBMs throughout ENH and BAT. The MRI-based model achieved 85% cross-validated accuracy to diagnose high- vs low-tumor in the training set (60 biopsies, 11 patients). The model achieved 81.8% accuracy in the validation set (22 biopsies, 7 patients).
Conclusion
Multi-parametric MRI and texture analysis can help characterize and visualize GBM’s spatial histologic heterogeneity to identify regional tumor-rich biopsy targets.

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Created

Date Created
  • 2015-11-24

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Prevention and Control of Zika as a Mosquito-Borne and Sexually Transmitted Disease: A Mathematical Modeling Analysis

Description

The ongoing Zika virus (ZIKV) epidemic in the Americas poses a major global public health emergency. While ZIKV is transmitted from human to human by bites of Aedes mosquitoes, recent

The ongoing Zika virus (ZIKV) epidemic in the Americas poses a major global public health emergency. While ZIKV is transmitted from human to human by bites of Aedes mosquitoes, recent evidence indicates that ZIKV can also be transmitted via sexual contact with cases of sexually transmitted ZIKV reported in Argentina, Canada, Chile, France, Italy, New Zealand, Peru, Portugal, and the USA. Yet, the role of sexual transmission on the spread and control of ZIKV infection is not well-understood. We introduce a mathematical model to investigate the impact of mosquito-borne and sexual transmission on the spread and control of ZIKV and calibrate the model to ZIKV epidemic data from Brazil, Colombia, and El Salvador. Parameter estimates yielded a basic reproduction number R[subscript 0] = 2.055 (95% CI: 0.523–6.300), in which the percentage contribution of sexual transmission is 3.044% (95% CI: 0.123–45.73). Our sensitivity analyses indicate that R[subscript 0] is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. Prevention and control efforts against ZIKV should target both the mosquito-borne and sexual transmission routes.

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Date Created
  • 2016-06-17

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Structural alterations of the brainstem in migraine

Description

Atypical brainstem modulation of pain might contribute to changes in sensory processing typical of migraine. The study objective was to investigate whether migraine is associated with brainstem structural alterations that

Atypical brainstem modulation of pain might contribute to changes in sensory processing typical of migraine. The study objective was to investigate whether migraine is associated with brainstem structural alterations that correlate with this altered pain processing.
MRI T1-weighted images of 55 migraine patients and 58 healthy controls were used to: (1) create deformable mesh models of the brainstem that allow for shape analyses; (2) calculate volumes of the midbrain, pons, medulla and the superior cerebellar peduncles; (3) interrogate correlations between regional brainstem volumes, cutaneous heat pain thresholds, and allodynia symptoms.
Migraineurs had smaller midbrain volumes (healthy controls = 61.28 mm[superscript 3], SD = 5.89; migraineurs = 58.80 mm[superscript 3], SD = 6.64; p = 0.038), and significant (p < 0.05) inward deformations in the ventral midbrain and pons, and outward deformations in the lateral medulla and dorsolateral pons relative to healthy controls. Migraineurs had a negative correlation between ASC-12 allodynia symptom severity with midbrain volume (r = − 0.32; p = 0.019) and a positive correlation between cutaneous heat pain thresholds with medulla (r = 0.337; p = 0.012) and cerebellar peduncle volumes (r = 0.435; p = 0.001).
Migraineurs with greater symptoms of allodynia have smaller midbrain volumes and migraineurs with lower heat pain thresholds have smaller medulla and cerebellar peduncles. The brainstem likely plays a role in altered sensory processing in migraine and brainstem structure might reflect severity of allodynia and hypersensitivity to pain in migraine.

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Created

Date Created
  • 2016-11-02

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Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase

Description

A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model

A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R[subscript 0] and the CTL immune response reproduction number R[subscript CTL]. Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection.

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Date Created
  • 2017-08-21

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Mathematical Analysis of Glioma Growth in a Murine Model

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 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 mm[superscript 3] to 62 mm[superscript 3], 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.

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Date Created
  • 2017-05-31

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Stochastic parameterization of the proliferation-diffusion model of brain cancer in a Murine model

Description

Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made

Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.

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Created

Date Created
  • 2016-05

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Volume Distributions of Metastatic Brain Tumors

Description

Magnetic resonance imaging (MRI) data of metastatic brain cancer patients at the Barrow Neurological Institute sparked interest in the radiology department due to the possibility that tumor size distributions might

Magnetic resonance imaging (MRI) data of metastatic brain cancer patients at the Barrow Neurological Institute sparked interest in the radiology department due to the possibility that tumor size distributions might mimic a power law or an exponential distribution. In order to consider the question regarding the growth trends of metastatic brain tumors, this thesis analyzes the volume measurements of the tumor sizes from the BNI data and attempts to explain such size distributions through mathematical models. More specifically, a basic stochastic cellular automaton model is used and has three-dimensional results that show similar size distributions of those of the BNI data. Results of the models are investigated using the likelihood ratio test suggesting that, when the tumor volumes are measured based on assuming tumor sphericity, the tumor size distributions significantly mimic the power law over an exponential distribution.

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Date Created
  • 2018-12

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Modeling Brain Tumors: Simulating individual Patient Cases of Glioblastoma Multiforme

Description

Glioblastoma multiforme (GBMs) is the most prevalent brain tumor type and causes approximately 40% of all non-metastic primary tumors in adult patients [1]. GBMs are malignant, grade-4 brain tumors, the

Glioblastoma multiforme (GBMs) is the most prevalent brain tumor type and causes approximately 40% of all non-metastic primary tumors in adult patients [1]. GBMs are malignant, grade-4 brain tumors, the most aggressive classication as established by the World Health Organization and are marked by their low survival rate; the median survival time is only twelve months from initial diagnosis: Patients who live more than three years are considered long-term survivors [2]. GBMs are highly invasive and their diffusive growth pattern makes it impossible to remove the tumors by surgery alone [3]. The purpose of this paper is to use individual patient data to parameterize a model of GBMs that allows for data on tumor growth and development to be captured on a clinically relevant time scale. Such an endeavor is the rst step to a clinically applicable predictions of GBMs. Previous research has yielded models that adequately represent the development of GBMs, but they have not attempted to follow specic patient cases through the entire tumor process. Using the model utilized by Kostelich et al. [4], I will attempt to redress this deciency. In doing so, I will improve upon a family of models that can be used to approximate the time of development and/or structure evolution in GBMs. The eventual goal is to incorporate Magnetic Resonance Imaging (MRI) data into a parameterized model of GBMs in such a way that it can be used clinically to predict tumor growth and behavior. Furthermore, I hope to come to a denitive conclusion as to the accuracy of the Koteslich et al. model throughout the development of GBMs tumors.

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Date Created
  • 2012-12

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Fetal Growth Models of Cardiac Size and Function, and Prediction of Congenital Cardiomyopathy in Fetuses with Diabetic Mothers

Description

2D fetal echocardiography (ECHO) can be used for monitoring heart development in utero. This study’s purpose is to empirically model normal fetal heart growth and function changes during development by

2D fetal echocardiography (ECHO) can be used for monitoring heart development in utero. This study’s purpose is to empirically model normal fetal heart growth and function changes during development by ECHO and compare these to fetuses diagnosed with and without cardiomyopathy with diabetic mothers. There are existing mathematical models describing fetal heart development but they warrant revalidation and adjustment. 377 normal fetuses with healthy mothers, 98 normal fetuses with diabetic mothers, and 37 fetuses with cardiomyopathy and diabetic mothers had their cardiac structural dimensions, cardiothoracic ratio, valve flow velocities, and heart rates measured by fetal ECHO in a retrospective chart review. Cardiac features were fitted to linear functions, with respect to gestational age, femur length, head circumference, and biparietal diameter and z-scores were created to model normal fetal growth for all parameters. These z-scores were used to assess what metrics had no difference in means between the normal fetuses of both healthy and diabetic mothers but differed from those diagnosed with cardiomyopathy. It was found that functional metrics like mitral and tricuspid E wave and pulmonary velocity could be important predictors for cardiomyopathy when fitted by gestational age, femur length, head circumference, and biparietal diameter. Additionally, aortic and tricuspid annulus diameters when fitted to estimated gestational age showed potential to be predictors for fetal cardiomyopathy. While the metrics overlapped over their full range, combining them together may have the potential for predicting cardiomyopathy in utero. Future directions of this study will explore creating a classifier model that can predict cardiomyopathy using the metrics assessed in this study.

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Created

Date Created
  • 2021-05