The Olufsen group will contribute to Aim 2 using and further developing our existing 1D arterial and venous network model that can predict blood flow and pressure in the pulmonary circulation. Using this model, we will predict shear stress in both the large and small vessels and develop a novel sheet model to predict alveolar perfusion as specified in detail in the project description. One of the advantages of our modeling approach is our unique ability to combine modeling with subject specific data allowing us to verify the model and use it for subject-specific predictions. Our model uses a unique approach to couple large and small arterial and venous vessels giving us the opportunity to generate predictions in both large and small vessels, enabling us to study how disease affects different parts of the system, an essential feature to generate better treatment strategies.

The overarching goals of the Directed Research for Undergraduates in Mathematics and Statistics (DRUMS) REU program at North Carolina State University (NCSU) are i) to get more undergraduate (UG) students with diverse backgrounds interested in graduate degrees in mathematical and statistical sciences and ii) to provide research opportunities that can generate high-quality outputs. DRUMS is a collaborative effort built on the world-class research being conducted by the Mathematics and Statistics Departments at NCSU. Paired with an ambitious professional development plan, DRUMS will produce a diverse cadre of UG researchers with technical and soft skills eager to pursue graduate pro-grams in STEM fields.

The Olufsen group will contribute to Aim 2 using and further developing our existing 1D arterial and venous network model that can predict blood flow and pressure in the pulmonary circulation. Using this model, we will predict shear stress in both the large and small vessels and develop a novel sheet model to predict alveolar perfusion as specified in detail in the project description. One of the advantages of our modeling approach is our unique ability to combine modeling with subject specific data allowing us to verify the model and use it for subject-specific predictions. Our model uses a unique approach to couple large and small arterial and venous vessels giving us the opportunity to generate predictions in both large and small vessels, enabling us to study how disease affects different parts of the system, an essential feature to generate better treatment strategies.

The overarching goals of the Directed Research for Undergraduates in Mathematics and Statistics (DRUMS) REU program at North Carolina State University (NCSU) are i) to get more undergraduate (UG) students with diverse backgrounds interested in graduate degrees in mathematical and statisti-cal sciences and ii) to provide research opportunities that can generate high-quality outputs. DRUMS is a collaborative effort built on the world-class research being conducted by the Mathematics and Statistics Departments at NCSU. Paired with an ambitious professional development plan, DRUMS will produce a diverse cadre of UG researchers with technical and soft skills eager to pursue gradu-ate programs in STEM fields.module; and c) online group meetings in the fall semester to help to increase the number of publications generated during the program. Targeted students will be rising juniors and seniors, from research-intensive universities, smaller colleges, and primarily minority-serving institutions. Research teams will consist of 4 undergraduate students, a graduate student mentor, and a faculty mentor, providing a vertically integrated research experience. Students will receive training in key professional development activities including seminars on how to apply for graduate school, the NSF graduate research fellowship, and professional ethics. The program will continue attracting diverse participants: Since its inception in 2006, the program has had great success attracting more than 50% women, about 25% from underrepresented groups, and about two-thirds from institutions with limited STEM research opportunities.

The overarching goals of the Directed Research for Undergraduates in Mathematics and Statistics (DRUMS) REU program at North Carolina State University (NCSU) are i) to get more undergraduate (UG) students with diverse backgrounds interested in graduate degrees in mathematical and statisti-cal sciences and ii) to provide research opportunities that can generate high-quality outputs. DRUMS is a collaborative effort built on the world-class research being conducted by the Mathematics and Statistics Departments at NCSU. Paired with an ambitious professional development plan, DRUMS will produce a diverse cadre of UG researchers with technical and soft skills eager to pursue gradu-ate programs in STEM fields.module; and c) online group meetings in the fall semester to help to increase the number of publications generated during the program. Targeted students will be rising juniors and seniors, from research-intensive universities, smaller colleges, and primarily minority-serving institutions. Research teams will consist of 4 undergraduate students, a graduate student mentor, and a faculty mentor, providing a vertically integrated research experience. Students will receive training in key professional development activities including seminars on how to apply for graduate school, the NSF graduate research fellowship, and professional ethics. The program will continue attracting diverse participants: Since its inception in 2006, the program has had great success attracting more than 50% women, about 25% from underrepresented groups, and about two-thirds from institutions with limited STEM research opportunities.

This new REU site proposal at NC State University extends the previous successful REU Site that has been running since 2006. The objectives for the NCSU Math REU site are to: a) recruit outstanding undergraduate students with diverse backgrounds from high achieving universities and from STEM underrepresented groups; b) generate a program with projects integrating pure and applied mathematics to provide students a substantive research experience in mathematical sciences; c) increase a pool of future faculty/scientists through the vertical REU-mentoring. Novel components include introduction of a three- module format with a) online training modules to prepare students before the beginning of the summer program; b) a traditional 10-week summer face-to-face research module; and c) online group meetings in the fall semester to help to increase the number of publications generated during the program. Targeted students will be rising juniors and seniors, from research-intensive universities, smaller colleges, and primarily minority-serving institutions. Research teams will consist of 4 undergraduate students, a graduate student mentor, and a faculty mentor, providing a vertically integrated research experience. Students will receive training in key professional development activities including seminars on how to apply for graduate school, the NSF graduate research fellowship, and professional ethics. The program will continue attracting diverse participants: Since its inception in 2006, the program has had great success attracting more than 50% women, about 25% from underrepresented groups, and about two-thirds from institutions with limited STEM research opportunities.

Overview: Patients with pulmonary arterial blood pressure higher than 25 mmHg are diagnosed with pulmonary hypertension (PH). This disease encompasses five etiologies including pulmonary arterial hypertension (PAH) and PH due to hypoxia. While PH is a relatively rare disorder, the disease has no cure, and despite new therapies, the median survival of PAH patients are 6-7 years. Diagnosis of PH is difficult requiring invasive measurements of blood pressure, associated with a significant cost and risk to the patient. Moreover, patients diagnosed with PH are examined repeatedly to assess disease progression. The primary objective of this proposal is to develop and integrate cardiovascular models to predict hemodynamic quantities including blood pressure and flow, and to use the integrated model to understand how these quantities change with disease progression for patients with PAH and hypoxia. The model will be validated against mouse and human data obtained from our collaborators at the University of Wisconsin-Madison and the Scottish Pulmonary Vascular Unit. Our second objective is to test if the validated model can be used to predict pulmonary arterial pressure during follow-up visits from non-invasive MRI-based measurements; such a capability would have significant impact in enabling physicians to reduce the total number of invasive pressure measurements. Intellectual Merit: The proposed study involves development of a system-level 1D fluid dynamics model of the pulmonary circulation. This model will include the right ventricle, left atrium, the large and small pulmonary arteries and veins. To our knowledge no other studies have developed a comprehensive model of this sort for the pulmonary vasculature. Major model development activities include: 1) Design of a physiologically based arterial and venous wall model accounting for collagen and elastin content that can also capture wall remodeling in response to PH. This model will be rooted in nonlinear elasticity theory resulting in a more robust pressure-area relation that can be integrated with the 1D fluid dynamics model. The wall model will be linearized to facilitate transition from large to small vessels. 2) Design of a physiologically based right ventricle model combining ideas from simple elastance functions and single-fiber models enabling us to predict the elastance as a function of the thickness of the right ventricle. Results developed here will focus on the pulmonary circulation, but the methodology can easily be applied to the study of systemic circulation and could be used for development of a comprehensive closed loop 1D model. 3a) Conduct simulations predicting features associated with disease progression. 3b) Sensitivity analysis and parameter estimation will be employed to render the model patient-specific, and to test if the model can be used to predict pulmonary arterial blood pressure from non-invasive MRI measurements of flow and area. This will be the first attempt to use a 1D system level model to assess disease progression associated with PH. Broader Impacts: PH may be rare, but the disease progresses rapidly with a high mortality rate, and treatment possibilities are limited. To monitor disease progression, after initial diagnosis patients are brought back for follow-up visits every 3-6 months. The proposed pulmonary cardiovascular model has potential to be used as part of a diagnostic protocol by predicting pressure using non-invasive measurements, thereby eliminating some of the invasive follow-up procedures. Moreover, the pulmonary cardiovascular model also serves as a vital component for identifying signatures associated with each type of PH and its level of progression. The proposed work provides an excellent opportunity for vertically integrated training among a postdoc, graduate students, and undergraduates. All participants are expected to participate in activities with members of the EPSRC center SofTMech, Glasgow. The PIs will use this collaboration to establish formal exchange programs for students between NCSU and University of Glasgow. The interdisciplinary nature of this project, including collaboration with both animal experimentalists and physicians, will provide students and postdocs a unique opportunity to learn how mathematical modeling can directly impact the life sciences. Results from the proposed study will be submitted to leading peer-reviewed journals and presented at both mathematical and biological conferences. Software developed during the proposed research will be shared on the PIs websites and uploaded to publicly available databases.

This project will train undergraduate and graduate students, together with postdoctoral fellows, in creating mathematical models of biological systems and confronting them with biological data. Combining approaches from applied mathematics and statistics, trainees will learn a wide range of modeling and parameter estimation methodologies, producing cohorts of mathematical scientists that have received an interdisciplinary training and who are versed in cutting-edge modeling and statistical techniques.

Pulmonary hypertension (PH) affects roughly 80% of patients with heart failure and is the third most common cardiovascular ailment behind coronary heart disease and systemic hypertension. The disease is characterized by a mean pulmonary arterial blood pressure 25 mmHg at rest measured by invasive right heart catheterization. Although tests can be performed to address disease severity, diagnosis of PH does not occur until years after initial onset, thus decreasing survival rates. Screening tools such as Doppler echocardiogram are subject to large amounts of uncertainty, thus introducing a need for more accurate, non-invasive diagnostic tools. Characteristic features of PH include increased blood vessel stiffening, decreased compliance, and increased resistance in small arteries, yet quantification of these changes are hard to identify in vivo. Our preliminary studies have identified changes in hemodynamic parameters using parameter estimation and computational fluid dynamics (CFD) in control and PH induced mice. Of major significance, our results indicated that hypertensive mice have increased stiffness in the large arteries and that the vascular beds had higher resistance and lower compliance values when compared to the control animals. This matches physiological understanding of PH progression and indicates that model properties align with physiological mechanisms. We have also developed novel algorithms for reconstructing the pulmonary trees, which allows us to model the pulmonary circulation as an expansive network of blood vessels. However, these techniques have not yet been applied to human data, and must be verified using human imaging data. There is also a level of uncertainty in measurements obtained from medical imaging modalities, which must be quantified and understood. Hence the central focus of this grant is to quantify PH progression and sources of medical instrument uncertainty using a patient-specific CFD model and uncertainty quantification techniques. Aim 1 will focus on constructing and quantifying pulmonary networks from PH patients and implementing their geometry in to the CFD model. Aim 2 will concurrently quantify the uncertainties in both patient data and predicted hemodynamic parameters and test the robustness of model predictions under the influence of these uncertainties.

Overview: Progress in our understanding of several diseases such as syncope or epilepsy resides in part in our ability to analyze large quantity of data--usually time series--collected for that very purpose. The long term goal of the proposed line of work is the identification of the root causes of syncope. The tools to be developed rely on a novel interplay between hypotheses, models, data, and learning algorithms; they are relevant to a large class of medical and non medical applications sharing the same type of data (multivariate, high-dimensional, non-stationary time series) and needs (classification and clustering). More generally, the ability to identify subjects as members of a class or group makes it possible to leverage information about the other members of that group for individual diagnosis purposes. The methodology developed here will contribute to the implementation of this approach, sometimes referred to as "bringing cohort studies to the bedside". Intellectual Merit: There is a profound divide in quantitative sciences between model based approaches and data based approaches. Machine learning and "standard" applied mathematics live at opposite ends of this spectrum. The study of syncope provides an example where these two worlds have to come together in order to solve a specific scientific challenge: better understanding and, eventually, improved medical treatment of syncope and its several types of pathologies. Do current medical hypotheses regarding these types correspond to reality? Are there too many types or too few? Nobody knows for sure. These questions pertain to classification and clustering. The methods from this project combine supervised and unsupervised learning to facilitate the identification of critical features in patient specific data and signals. This leaves, however, an important question unanswered: the identification of distinct types does not yield root causes for the various observed pathologies. This is the contribution of mathematical modeling which provides possible scenarios to be tested. A key weakness of this approach is its over-reliance on the calibration of large numbers of parameters. A novel calibration process is proposed whereby surrogates from statistical learning inform the mathematical models. This approach significantly reduces the amount data necessary for calibration. Broader Impacts: Progress in our understanding of several diseases such as syncope, epilepsy or the human papilloma virus (HPV) resides in part in our ability to analyze large quantity of data--usually time series--collected for that very purpose. The long term goal of the proposed line of work is the identification of the root causes of syncope. The tools to be developed rely on a novel interplay between hypotheses, models, data, and learning algorithms; they are relevant to a large class of medical and non medical applications sharing the same type of data (multivariate, high-dimensional, non-stationary time series) and needs (classification and clustering). The ability to identify subjects as members of a class or group makes it possible to leverage information about the other members of that group for individual diagnosis purposes. The methodology developed here will contribute to the implementation of this approach, sometimes referred to as "bringing cohort studies to the bedside".