Applying Mathematical Models to Study the Role of the Immune System in Chronic Myelogenous Leukemia

Although tyrosine kinase inhibitors (TKIs) such as imatinib have transformed chronic myelogenous leukemia (CML) into a chronic condition, these therapies are not curative in the majority of cases. Most patients must continue TKI therapy indefinitely, a requirement that is both expensive and that compromises a patient's quality of life. While TKIs are known to reduce leukemic cells' proliferative capacity and to induce apoptosis, their effects on leukemic stem cells, the immune system, and the microenvironment are not fully understood. A more complete understanding of their global therapeutic effects would help us to identify any limitations of TKI monotherapy and to address these issues through novel combination therapies. Mathematical models are a complementary tool to experimental and clinical data that can provide valuable insights into the underlying mechanisms of TKI therapy. Previous modeling efforts have focused on CML patients who show biphasic and triphasic exponential declines in BCR-ABL ratio during therapy. However, our patient data indicates that many patients treated with TKIs show fluctuations in BCR-ABL ratio yet are able to achieve durable remissions. To investigate these fluctuations, we construct a mathematical model that integrates CML with a patient's autologous immune response to the disease. In our model, we define an immune window, which is an intermediate range of leukemic concentrations that lead to an effective immune response against CML. While small leukemic concentrations provide insufficient stimulus, large leukemic concentrations actively suppress a patient's immune system, thus limiting it's ability to respond. Our patient data and modeling results suggest that at diagnosis, a patient's high leukemic concentration is able to suppress their immune system. TKI therapy drives the leukemic population into the immune window, allowing the patient's immune cells to expand and eventually mount an efficient response against the residual CML. This response drives the leukemic population below the immune window, causing the immune population to contract and allowing the leukemia to partially recover. The leukemia eventually reenters the immune window, thus stimulating a sequence of weaker immune responses as the two populations approach equilibrium. We hypothesize that a patient's autologous immune response to CML may explain the fluctuations in BCR-ABL ratio that are regularly seen during TKI therapy. These fluctuations may serve as a signature of a patient's individual immune response to CML. By applying our modeling framework to patient data, we are able to construct an immune profile that can then be used to propose patient-specific combination therapies aimed at further reducing a patient's leukemic burden. Our characterization of a patient's anti-leukemia immune response may be especially valuable in the study of drug resistance, treatment cessation, and combination therapy.

THE USE OF THE EARLY WARNING INDICATOR REPORT TO IMPACT NINTH GRADE PROMOTION RATES IN A LARGE URBAN SCHOOL DISTRICT

Abstract The purpose of this study was to examine how four high schools used an Early Warning Indicator Report (EWIR) to improve ninth grade promotion rates. Ninth grade on-time promotion is an early predictor of a student’s likelihood to graduate (Bornsheuer, Polonyi, Andrews, Fore, & Onwuegbuzie, 2011; Leckrone & Griffith, 2006; Roderick, Kelley-Kemple, Johnson, & Beechum, 2014; Zvoch, 2006). The analysis revealed both similarities and differences in the ways that the four schools used the EWIR. The research took place in a large urban school district in the Mid-Atlantic. Sixteen participants from four high schools and the district’s central office voluntarily participated in face-to-face interviews. The researcher utilized a qualitative case study method to examine the implementation of the EWIR system in Wyatt School District. The interview data was transcribed and analyzed, along with district documents, to identify categories in this cross case analysis. Three primary themes emerged from the data: (1) targeted school structures for EWIR implementation, (2) the EWIR identified necessary supports for students, and (3) the central office support for school staff. The findings revealed the various ways that the target schools implemented the EWIR in their buildings and the level of support that they received from the central office that aided them in using the EWIR to improve ninth grade promotion rates. Based on the findings of this study, the researcher provided a number of key recommendations: (1) Districts should provide professional development to schools to ensure that schools have the support they need to implement the EWIR successfully; (2) There should be increased accountability from the central office for schools using the EWIR to identify impactful interventions for ninth graders; and (3) The district needs to assign dedicated central office staff to support the implementation of the EWIR in high schools across the district. As schools continue to face the challenge of improving ninth grade promotion rates, effective use of an Early Warning Indicator Report is recommended to provide school and district staff with data needed to impact overall student performance.

Modeling the Effects of Habitat Fragmentation on the Movements of the Mongolian Gazelle in the Eastern Mongolian Steppe

The Mongolian gazelle, Procapra gutturosa, resides in the immense and dynamic ecosystem of the Eastern Mongolian Steppe. The Mongolian Steppe ecosystem dynamics, including vegetation availability, change rapidly and dramatically due to unpredictable precipitation patterns. The Mongolian gazelle has adapted to this unpredictable vegetation availability by making long range nomadic movements. However, predicting these movements is challenging and requires a complex model. An accurate model of gazelle movements is needed, as rampant habitat fragmentation due to human development projects - which inhibit gazelles from obtaining essential resources - increasingly threaten this nomadic species. We created a novel model using an Individual-based Neural Network Genetic Algorithm (ING) to predict how habitat fragmentation affects animal movement, using the Mongolian Steppe as a model ecosystem. We used Global Positioning System (GPS) collar data from real gazelles to “train” our model to emulate characteristic patterns of Mongolian gazelle movement behavior. These patterns are: preferred vegetation resources (NDVI), displacement over certain time lags, and proximity to human areas. With this trained model, we then explored how potential scenarios of habitat fragmentation may affect gazelle movement. This model can be used to predict how fragmentation of the Mongolian Steppe may affect the Mongolian gazelle. In addition, this model is novel in that it can be applied to other ecological scenarios, since we designed it in modules that are easily interchanged.