2002 — 2005 |
Haider, Mansoor |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Modeling Mechanical Cell-Matrix Interactions in Articular Cartilage @ North Carolina State University
Haider 0211154 The investigator is developing multiphasic models for mechanical interactions between the cells and extracellular matrix in articular cartilage. A combination of analytical and numerical methods are used to solve: (1) contact problems that model experiments used to determine mechanical properties of isolated cell (chondrocyte) and cell-matrix (chondron) units, (2) interface problems that model local cell-matrix mechanics of the chondron in vivo, and (3) fast boundary integral models for transmission of mechanical signals in a tissue layer populated with many cells. Through collaboration with an orthopaedic research lab, the models developed by the investigator are being applied to: (a) the determination of material properties of cell and tissue explants using in-vitro micropipette testing and video microscopy, and (b) the simulation of local cell-matrix mechanics and comparison to confocal microscopy of dynamic loading in a tissue layer. A fundamental goal of this project is to quantify the dependence of local cell mechanics on external loading. By correlating experimental measurements of cell metabolic activity to mechanical components of the local cell environment, the complex relationship between tissue metabolism and cell mechanics is analyzed. Variations in chondron material and geometric properties, within and across a variety of tissue populations, are also incorporated into the models. This project contributes to understanding of the role of mechanics in maintenance of the extracellular matrix, and associated matrix degeneration with aging due to osteoarthritis. Articular cartilage is the primary load-bearing tissue in joints such as the knee, shoulder and hip. Degeneration of cartilage leads to osteoarthritis, a painful condition that affects millions of Americans and is predominantly associated with aging. Under repeated loading, the structural matrix of cartilage is in a continual state of turnover that is regulated by specialized cells called chondrocytes. These cells synthesize matrix components yet, remarkably, have no neural connection to the brain. As a result, cell metabolic activities directed at repairing the structural matrix are highly dependent on the local cell environment. In this project, a mathematical modeler collaborates with an orthopaedic research lab to understand the role of mechanical forces in the maintenance of cartilage. At the cellular level, forces in cartilage result from a complex coupling of solid and fluid mechanics with energy dissipation. Results of this work predict the dependence of local forces at the cellular scale on external loading. Local force predictions facilitate a quantitative description of the complex relationship between cell metabolic activity and cell mechanics. In conjunction with associated experiments for a variety of tissue populations, the models lead to an understanding of how these remarkable cells can maintain cartilage over the course of a lifetime, and how structural degeneration of cartilage is initiated in osteoarthritis.
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0.915 |
2007 — 2013 |
Gremaud, Pierre (co-PI) [⬀] Medhin, Negash (co-PI) [⬀] Haider, Mansoor Smith, Ralph [⬀] Shearer, Michael (co-PI) [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Emsw21-Rtg Mathematics of Materials: Model Development, Analysis, Simulation and Control @ North Carolina State University
The program "Mathematics of Materials" provides a wide range of interdisciplinary research and training opportunities for undergraduates, graduate students, and postdocs in the mathematical sciences. The research activities are organized around five topics that play a fundamental role in emerging technologies: multifunctional materials, polymers and composites including carbon nanotubes, orthopaedic biomaterials, dynamics of thin material layers, and material behavior of laser welding. Within each topic, investigations focus on fundamental model development, mathematical solution, numerical simulation, and control design. Each project involves substantial collaboration with experimental colleagues that provides interdisciplinary training opportunities to mathematics students and postdocs. The training component is designed to prepare students and postdocs for the varied roles of interdisciplinary research mathematicians. This includes training modules that introduce participants to research and career topics not typically covered in coursework, targeted courses on topics pertaining to research areas and national research agendas, and participation in summer internships and national conferences.
"Mathematics of Materials" is an interdisciplinary research training group program designed for undergraduates, graduate students and postdocs in the mathematical sciences. The research activities are organized around five topics that play a fundamental role in emerging technologies: multifunctional materials, polymers and composites including carbon nanotubes, orthopaedic biomaterials, dynamics of thin material layers, and material behavior of laser welding. The training component involves a coordinated set of activities designed to prepare students and postdocs for the varied roles of interdisciplinary research mathematicians. This includes training modules that introduce participants to research and career topics not covered in traditional coursework, new courses pertaining to the five research topics and areas of national need, and participation in summer internships and national conferences spanning multiple disciplines. The objective of the program is to attract and train highly qualified students and postdocs for academic and nonacademic careers at the interface between applied mathematics, materials science, engineering, physics, and advanced technology.
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0.915 |
2011 — 2016 |
Olufsen, Mette [⬀] Haider, Mansoor |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Arterial Wall Viscoelasticity and Cardiovascular Networks @ North Carolina State University
This project develops mathematical and computational models of the cardiovascular system that couple dynamics of blood flow to vessel wall viscoelasticity at the scale of individual vessel segments and vessel networks. The project design integrates novel mathematical modeling, new numerical techniques for soft tissue viscoelasticity, and extensive data analysis via collaboration with experimentalists at the Republic University, Montevideo, Uruguay. Models of both individual vessel segments and networks of multiple vessels will be developed in coordination with a systematic analysis of experimental data that employs parameter estimation and sensitivity analysis techniques. The highly integrative and interdisciplinary nature of this study will yield outcomes that can lead to new standards for modeling cardiovascular dynamics in vessel networks. In particular, the importance of arterial wall viscoelasticity will be analyzed according to vessel location and type, species (sheep, humans) and experimental conditions (in-vivo, ex-vivo). In addition, effects of disease will be simulated with an emphasis on variables of clinical relevance. The models developed in this project will facilitate accurate prediction of waveforms for blood flow, blood pressure, and vessel cross-sectional area in cardiovascular networks.
This project develops a novel, integrative approach to analyzing cardiovascular dynamics both in single vessels as well as vessel networks by coordinating mathematical and computational modeling with a systematic and comprehensive approach to analysis of experimental data. Present approaches rely on models that neglect energy loss (viscoelasticity) in the deformation of individual vessel walls, or models that do not consider downstream effects on blood pressure, blood flow, and vessel cross-sectional area in cardiovascular networks of blood vessels. The models developed in this project will be assessed, calibrated and refined in coordination with experimental collaborators allowing analysis of data from varying experimental conditions, different species (sheep, human), and in different states of health (healthy vs. hypertensives). The techniques and outcomes of this project have the potential for setting a new standard in modeling cardiovascular blood flow and can also be applied to study effects of other diseases (e.g., diabetes) that significantly affect cardiovascular health. The models of vessel networks developed in this project have the potential to provide clinicians with a reference library of blood pressure waveforms that can be incorporated into medical simulators and databases for diagnostic applications in cardiovascular medicine.
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0.915 |
2012 — 2015 |
Hauenstein, Jonathan Haider, Mansoor |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Computational Methods in Numerical Algebraic Geometry @ North Carolina State University
This project aims to contribute to numerical algebraic geometry by developing and implementing new algorithms used to solve polynomial systems arising in many applications. One goal is the development of an algorithm for solving large-scale structured polynomial systems which naturally arise in computing overconstrained mechanisms as well as computing real and singular points on algebraic sets. This algorithm will utilize the regeneration method, developed by Hauenstein, Sommese, and Wampler, which computes the solutions of a polynomial system by building from the solutions of smaller polynomial systems. Regeneration together with the exploitation of structure will allow one to solve many naturally occurring polynomial systems which are beyond the reach of current methods. Another goal is the training of one or more undergraduate students in this area. The students will also help with the development of some of the algorithms and testing of the software developed by this proposal. Additionally, as a group, we will apply the newly developed algorithms to new problems arising from applications.
Polynomial systems naturally arise in many areas of science, engineering, economics, and biology with their solutions, for example, describing the design of specialized robots, equilibria of chemical reactions and economic models, and describing the stability of tumors. The real solutions to these polynomial systems are often of particular interest to researchers as they often describe the physically meaningful solutions, e.g., a constructible robot. The new algorithms and software developed will allow a broad range of scientists, engineers, and economists who encounter polynomial systems to compute physically meaningful solutions to systems which are beyond the reach of current solving techniques. Additionally, the students involved in this project will gain knowledge and research experience in the mathematical sciences.
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0.915 |
2016 — 2019 |
Haider, Mansoor Olufsen, Mette [⬀] Qureshi, Muhammad Umar |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Remodeling of Pulmonary Cardiovascular Networks in the Presence of Hypertension @ North Carolina State University
The research team will develop mathematical and computational models for the study of pulmonary hypertension. This is a rare but rapidly progressing cardiovascular disease with a high mortality rate. Pulmonary hypertension involves both elevated blood pressure and changes in vessel wall stiffness, and thickness within the pulmonary circulation. These issues worsen with the severity of the disease. Diagnostic disease categories are associated with different parts of the pulmonary circulation network, yet pinpointing locations where the disease initiates is challenging. Models will be developed in conjunction with the use of experimental data provided by collaborators. This data will be obtained from non-invasive imaging of vascular blood flow and vessel network structure, and from invasive measurements of blood pressure in pulmonary vessels in mice and humans obtained via catheterization. Effects of the heart chambers, large vessels, small vessel networks and their interactions will be captured based on modeling and methodological approaches from fluid mechanics, solid mechanics, network analysis, inverse problems and parameter estimation. The proposed pulmonary cardiovascular model has potential to be incorporated into diagnostic protocols predicting pressure using non-invasive measurements to reduce the number of the invasive follow-up procedures, and to serve as a vital component for identifying signatures associated with disease diagnostic categories and the degree of disease progression. The overall project also provides a variety of opportunities for integrated training of a postdoc, and graduate and undergraduate students, in data-driven biomedical research.
System-level, one-dimensional mathematical and computational fluid dynamics models of the pulmonary circulation will be developed. These models will include the right ventricle, left atrium, the large and small pulmonary arteries and veins, and account for alterations in the system components due to pulmonary hypertension. A physiologically based arterial and venous wall model that accounts for collagen and elastin content and that can also capture remodeling of wall constituents in response to pulmonary hypertension will be designed. This model will be rooted in nonlinear elasticity theory and will yield a more robust pressure-area relation that can be integrated within the fluid dynamics model, and linearized to facilitate the transition from large to small vessels. A second physiologically based right ventricle model combining ideas from simple elastance functions and single-fiber models will also be provided. This model will enable prediction of elastance as a function of right ventricle thickness. The analysis will focus on the pulmonary circulation, but impacts on modeling systemic circulation in a comprehensive closed loop model will also be considered. The models developed in these two aims will be used to simulate and identify flow and pressure waveforms that predict features associated with disease progression and, via sensitivity analysis and parameter estimation, to render the model patient-specific. With these innovations it will be possible to use the one dimensional system level model combined with pulmonary arterial blood pressure from non-invasive measurements of flow to assess disease progression associated with pulmonary hypertension while also reducing the number of invasive measurements.
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0.915 |