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- All Subjects: invariant region
- All Subjects: Spinal cord
- Creators: Martirosyan, Nikolay
- Creators: Preul, Mark C.
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 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.
ContributorsHarris, Duane C. (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J. (Thesis advisor) / Preul, Mark C. (Committee member) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2023
Description
The unique anatomical and functional properties of vasculature determine the susceptibility of the spinal cord to ischemia. The spinal cord vascular architecture is designed to withstand major ischemic events by compensating blood supply via important anastomotic channels. One of the important compensatory channels of the arterial basket of the conus medullaris (ABCM). ABCM consists of one or two arteries arising from the anterior spinal artery (ASA) and circumferentially connecting the ASA and the posterior spinal arteries. In addition to compensatory function, the arterial basket can be involved in arteriovenous fistulae and malformations of the conus. The morphometric anatomical analysis of the ABCM was performed with emphasis on vessel diameters and branching patterns.
A significant ischemic event that overcomes vascular compensatory capacity causes spinal cord injury (SCI). For example, SCI complicating thoracoabdominal aortic aneurysm repair is associated with ischemic injury. The rate of this devastating complication has been decreased significantly by instituting physiological methods of protection. Traumatic spinal cord injury causes complex changes in spinal cord blood flow (SCBF), which are closely related to a severity of injury. Manipulating physiological parameters such as mean arterial pressure (MAP) and intrathecal pressure (ITP) may be beneficial for patients with a spinal cord injury. It was discovered in a pig model of SCI that the combination of MAP elevation and cerebrospinal fluid drainage (CSFD) significantly and sustainably improved SCBF and spinal cord perfusion pressure.
In animal models of SCI, regeneration is usually evaluated histologically, requiring animal sacrifice. Thus, there is a need for a technique to detect changes in SCI noninvasively over time. The study was performed comparing manganese-enhanced magnetic resonance imaging (MEMRI) in hemisection and transection SCI rat models with diffusion tensor imaging (DTI) and histology. MEMERI ratio differed among transection and hemisection groups, correlating to a severity of SCI measured by fraction anisotropy and myelin load. MEMRI is a useful noninvasive tool to assess a degree of neuronal damage after SCI.
A significant ischemic event that overcomes vascular compensatory capacity causes spinal cord injury (SCI). For example, SCI complicating thoracoabdominal aortic aneurysm repair is associated with ischemic injury. The rate of this devastating complication has been decreased significantly by instituting physiological methods of protection. Traumatic spinal cord injury causes complex changes in spinal cord blood flow (SCBF), which are closely related to a severity of injury. Manipulating physiological parameters such as mean arterial pressure (MAP) and intrathecal pressure (ITP) may be beneficial for patients with a spinal cord injury. It was discovered in a pig model of SCI that the combination of MAP elevation and cerebrospinal fluid drainage (CSFD) significantly and sustainably improved SCBF and spinal cord perfusion pressure.
In animal models of SCI, regeneration is usually evaluated histologically, requiring animal sacrifice. Thus, there is a need for a technique to detect changes in SCI noninvasively over time. The study was performed comparing manganese-enhanced magnetic resonance imaging (MEMRI) in hemisection and transection SCI rat models with diffusion tensor imaging (DTI) and histology. MEMERI ratio differed among transection and hemisection groups, correlating to a severity of SCI measured by fraction anisotropy and myelin load. MEMRI is a useful noninvasive tool to assess a degree of neuronal damage after SCI.
ContributorsMartirosyan, Nikolay (Author) / Preul, Mark C (Thesis advisor) / Vernon, Brent (Thesis advisor) / Theodore, Nicholas (Committee member) / Lemole, Gerald M. (Committee member) / Vu, Eric (Committee member) / Arizona State University (Publisher)
Created2016