Aaron Lee Fogelson - US grants

This research will improve mathematical models and numerical methods for studying platelet aggregation during blood clotting and the flow of fluid-particle suspensions. These are large- scale problems of considerable complexity. Consequently, the research will involve a high degree of computation, much of which will require use of a supercomputer. A new particle-based algorithm for solving a multidimensional convection-dominated convection-diffusion equation will be developed. The use of localized forces to represent platelets and suspended particles will be extended to the representation of blood vessel walls. This work should shed light on a central question in aggregation: how the blood's local fluid dynamics and the geometry of the blood vessel interact to influence the location, rate, and extent of aggregate formation. It will aid in the design of nonthrombogenic artificial internal organs.

Platelet aggregates form on blood vessel walls in response to vascular injury; they are also major constituents of the life-threatening blood clots associated with vascular disease and with the use of cardiovascular prostheses. Microscopic-scale models of aggregation, which involve interactions among the blood's fluid dynamics and the mechanics and chemistry of the platelets, are appropriate for studying aggregation in the small vessels of the microcirculation. The project will explore changes in the models to attain more realistic aggregate growth rates, and improvements in the associated numerical methods to extend simulations to three dimensions and to substantially longer time periods. These changes will complement recent advances in experimental technique to allow the first detailed comparison of simulations with experiments. To facilitate these comparisons, the investigator has established collaborations with leading experimental scientists. The investigator will also continue computational and analytical exploration of a new class of continuum models he has formulated for studying aggregation in larger vessels such as the coronary arteries. Of particular interest is the chemically-induced liquid-to-solid phase transition exhibited by these models. The project will characterize its dependence on flow and chemical parameters. The mathematical analysis and simulations to be carried out in this project complement traditional laboratory experimentation. They provide detailed information, of a type which is generally not attainable in the laboratory, about the dynamic interactions among the components of the aggregation response. This additional information will increase insight into the physical and chemical controls on the aggregation process. These studies will also lay the foundations for further development of models of aggregation and for their application to clinically interesting questions such as how flow and vessel geometry interact to influence aggregation within natural vessels, such as the coronary arteries, or prosthetic devices, such as vascular grafts or artificial hearts.

9307643 Fogelson The investigator extends earlier analytical and computational work on a microscopic-scale model of aggregation of blood platelets in small diameter blood vessels, and on a continuum model of aggregation in large diameter vessels. Both models involve interactions between the blood's fluid dynamics and the mechanics and chemistry of developing aggregates. For the microscopic-scale model, the project involves: 1) completing the development of the numerical tools needed to extend simulations to three dimensions; 2) exploring and implementing strategies for performing computationally intensive three-dimensional calculations on high-performance parallel computers; 3) constructing a computational analogue of the experimental flow chamber of his collaborator J. Hubbell (Chemical Engineering, University of Texas) and comparing simulations with it to Hubbell's data on the dynamics of aggregate growth; 4) modifying aspects of the model that concern a platelet's response to pro-aggregating agents and the efficiency of platelet-platelet cohesion; and 5) exploring the range of behavior of the model and its sensitivity to parameter variations. For the continuum model, the project requires: 1) developing numerical methods to study forms of the model that allow strain-dependent aggregate breakup; 2) developing techniques for incorporating into this model platelet interactions with the blood vessel's wall or the reactive surface of a prosthetic cardiac valve; and 3) studying the behavior of the model when aggregation is initiated by exogenous stimuli in bulk flow, or by contact with a reactive wall of a coronary-artery-sized vessel. In the latter context, it is of particular interest to study how the interaction between flow and vessel geometry affects aggregate formation. Platelet aggregates form on blood vessel walls in response to vascular injury; they are also major constituents of the life-threatening blood clots associated with vascular diseas e and with the use of cardiovascular prostheses. The modeling and simulations carried out in this project complement traditional laboratory experimentation. They provide detailed information, of a type that is generally not attainable in the laboratory, about the dynamic interactions among the components of the aggregation response. This additional information will increase our insight into the physical and chemical controls on the aggregation process. These studies also lay the foundations for further development of aggregation models and for their application to clinically interesting questions, including how flow and vessel geometry interact to influence aggregation within natural vessels, such as the coronary arteries, or prosthetic devices, such as vascular grafts or artificial hearts. The numerical tools developed in this project should also be valuable in solving a broad range of biofluid dynamics and engineering problems. ***

Othmer The investigator and his colleagues conduct a special year in mathematical biology in the Department of Mathematics at the University of Utah. Cooperating departments include the Departments of Biology, Bioengineering and Human Genetics and the Nora Eccles Harrison Cardiovascular Research and Training Institute. The primary objective of the special year is to train graduate students and post-docs in the art and science of modeling applied to biological problems. Each quarter focuses on a specific area of biology in which mathematics has had a significant impact and in which there are significant new opportunities: Ecology and Evolution (Fall 1995), Physiology and Cell Biology (Winter 1996), and Cardiovascular Physiology and Biological Fluid Dynamics (Spring 1996). The educational program includes (i) a full year course entitled `Mathematical Modeling in Biology' given by visiting principal lecturers, who present a case study of applying mathematical modeling to a biological problem in their area of expertise, (ii) a weekly seminar series given by principal lecturers, other visitors, and scientists from the University of Utah, (iii) a quarterly minisymposium in an active research area within the purview of that quarter, and (iv) a student/post-doc seminar aimed at informal presentation of ideas, new results, and open problems. The notes from the course will be published. The goal of the Special Year in Mathematical Biology at the University of Utah is to train young scientists in mathematical modeling of biological problems. Graduate students and post-docs are immersed in an interdisciplinary educational and collaborative environment that brings them together with leading mathematicians and scientists. Although mathematics has long provided important insights into biological processes, developments in biology and mathematics have made the link more important. Basic biological research has increasing relevance to national priorities such as health care and environmental protection, and powerful new experimental techniques have made it possible to observe previously inaccessible mechanisms in physiology, genetics, and ecology. Expanded access to powerful computers has enabled researchers to simulate complex and realistic models of ecological and physiological systems, establishing modeling and computation as a new mode of experimentation in the life sciences. Unfortunately, the training of most biologists and mathematicians fails to prepare them for this type of research. The Special Year in Mathematical Biology prepares young researchers at the pre- and junior post-doctoral level for these new demands. The speakers and researchers invited to this Special Year have established records of successfully collaborating with both mathematicians and life scientists. The program focuses on three active areas of research in the life sciences: ecology and evolution, physiology and cell biology, and cardiovascular physiology and biological fluid dynamics. These areas have been fertile ground for successful collaboration and modeling in the past. The Special Year introduces young researchers to these successes, involves them in current research, and illustrates the conceptual connections between the different fields. These students, and those benefiting from the book developed from the Special Year, will be the catalysts for further development of this vital connection.

Fogelson
9805518
The investigator undertakes modeling and computational
simulation of platelet aggregation and coagulation. These are
the components of normal blood clotting and of the
life-threatening blood clots associated with vascular disease and
with the use of cardiovascular prostheses. The investigator and
coworkers continue to explore and refine their models of platelet
aggregation in small and large diameter vessels; continue
development of models of coagulation including the effects of
flow, transport, and surface reactions; and integrate the
platelet aggregation and coagulation models to form a more
comprehensive model of the hemostatic and thrombotic processes.
These models use coupled systems of nonlinear partial and
ordinary differential equations to describe interactions between
the blood's fluid dynamics, the transport of platelets and
chemicals in the blood plasma, the mechanics and chemistry of
developing aggregates, and the solution-phase and surface-bound
biochemistry of the coagulation process. The models present
substantial computational challenges that require development and
use of state-of-the-art numerical methods for their solution.
These include immersed boundary methods for fluid-material
interactions, high-resolution finite-difference methods combined
with Fourier-collocation spectral methods, immersed-interface
methods for handling transport in regions of complex geometry,
and parallel computation. This work involves extensive
comparisons between computational results and laboratory
experiments and is aided by collaboration with leading experts on
flow and thrombosis. The proposal is also concerned with
developing state-of-the-art parallel computational methods for
simulating biofluid dynamic flows like those involved in
aggregation and coagulation, and with including these
computational tools in a powerful and easy-to-use problem solving
environment that facilitates solving a wide range of complex
biofluid dynamic problems.
Thrombosis, which is the formation of blood clots within
vessels of the circulatory system, is the proximal cause of most
heart attacks and of other severe cardiovascular problems such as
ischemia and angina. It is also a major problem associated with
the use of blood-contacting prostheses such as mechanical heart
valves. The process by which these blood clots form is very
complex and involves many dynamic, sometimes competing, sometimes
mutually-reinforcing, biophysical and biochemical processes. A
major part of this project involves developing powerful
mathematical and computational tools for studying this complex
process, and using these tools to probe the factors that effect
the location, extent, and speed of formation of thrombi.
Computational modeling complements traditional experimental
approaches and provides a way to simulate complex dynamic events,
like the dynamic interactions among fluid, blood cells, clotting
factors, and blood vessel or prosthesis surface that lead to
thrombosis, that are beyond the reach of current laboratory
techniques. Such simulations can give new insights into the
basic mechanisms that control this important biological process,
and can ultimately help in the more rational design of
therapeutic interventions and prosthetic devices. Many other
challenging biological and biomedical flow problems have features
in common with that of simulating thrombosis, and so the
state-of-the-art parallel computational methods developed for
this project potentially have wide-spread application to problems
important to basic science, health care, and biotechnology. To
help realize this potential the investigators develop and
disseminate an easy-to-use software package that facilitates
using these computational methods to set up and carry out
simulations of important biofluid dynamics problems.

The importance of biogels in the function of biological
systems is increasingly recognized, yet little theoretical work
has been done to understand their behavior. Mathematics is
well-suited to sorting out the interplay among the many forces
(mechanical, electrochemical, and biochemical) that determine
biogel structure and function. The investigators use
mathematical tools to explore four closely related problems of
biogel growth and dynamics, with an emphasis on pattern-forming
mechanisms and the relationship between pattern and function.
The four problems are biofilm and blood clot formation and
function, gastric protection of the stomach, and the behavior of
biogels in contact with a moving fluid. Models are developed to
understand how physical properties such as the viscoelastic
constitutive properties and the gel morphology are determined and
controlled, and how these properties affect the biological
function of the biogel. The investigators use analytical and
computational tools to examine gel growth and dynamics on
different scales using various models (continuum, discrete,
isotropic, anisotropic), while attempting to incorporate what is
known experimentally, and to expand the experimental database
about specific biogel systems.
Biogels are composites of water, filamentous protein
networks, and other chemicals, and are increasingly recognized as
having profound influence on the function of many biological
systems. Important biological settings in which these biogels
play a major role include blood clot formation,
difficult-to-treat bacterial infections, and the proper
protective functioning of the stomach lining. Improved
understanding of how biogels are formed and how their properties
are regulated is critical to understanding these important
processes and how they can be manipulated to improve human
health. Because the formation and regulation of biogels is
governed by physical and chemical properties and because these
properties can be expressed mathematically, mathematical tools
can be brought to bear on these problems. Through mathematical
analysis and computational simulations of biogels, a wealth of
detailed data can be obtained that complements the data
obtainable from traditional laboratory experiments. Hence the
combination of mathematical and experimental investigators
brought together in this project is expected to lead to important
new insights about biogel behavior. The project includes
mathematicians, a bioengineer, and a biologist, and provides
interdisciplinary research and training opportunities for
students and postdocs.

This IGERT project will develop a graduate program of cross-disciplinary research and training in Mathematical Biology. The goal of the program is to give students a solid training in core mathematics and genuine expertise in an area of contemporary biology. Such training will bring to bear the power of mathematics on the exciting and challenging problems of modern biology. Students will be recruited from a broad spectrum of mathematical, scientific and cultural backgrounds. It is expected that the graduates of this program will receive Ph.D.'s in mathematics, but by virtue of their broad-based training will be able to contribute to collaborative research efforts in numerous academic and industrial settings. In the process, the program seeks to build many new bridges between mathematics and biology potentially reshaping research for a new generation of mathematical biologists. The research and training program will be organized around the four research themes of biofluids, ecology and evolutionary biology, neuroscience, and physiology. A unique feature of this research and training program will be the establishment of Special Interest Groups (SIG's). Each SIG will be led by one or more faculty members with activities that include discussion of research problems, discussion of recent seminars, formal and informal talks about recent papers, student presented talks on background literature, etc. The training of students will also include formal coursework in both Mathematics and Biology, laboratory rotations or field work in an area of the life sciences, mentoring by both mathematics and life science faculty, and journal clubs, laboratory group meetings, and workshops. In these ways, the training of students will put great emphasis on collaboration and interaction across traditional academic disciplines.

IGERT is an NSF-wide program intended to meet the challenges of educating U.S. Ph.D. scientists and engineers with the multidisciplinary backgrounds and the technical, professional, and personal skills needed for the career demands of the future. The program is intended to catalyze a cultural change in graduate education by establishing innovative new models for graduate education and training in a fertile environment for collaborative research that transcends traditional disciplinary boundaries. In the fifth year of the program, awards are being made to twenty-one institutions for programs that collectively span the areas of science and engineering supported by NSF.

0354259 Keener

Research Training in Mathematical and Computational Biology
Abstract:

The investigator and his colleagues will continue development of a comprehensive program of cross-disciplinary research and training in Mathematical and Computational Biology. The goal of this program is to bring to bear the power of mathematics on the challenging problems of modern biology by initiating collaborative research projects with a wide variety of laboratory life scientists and by training young mathematicians and computational scientists in the art of cross-disciplinary research. The research program will develop and use mathematical and computational models to study complex biological processes, organized around four major research themes of biofluids, ecology and evolutionary biology, neuroscience and physiology.

This program will begin to address the critical need for more people with high-level mathematical skills who have the ability to contribute in a significant way to the many challenging problems of biological and medical significance. The program will impact young mathematical scientists at the undergraduate, graduate, and postdoctoral levels, and will provide an environment in which collaboration across levels and across disciplines is the norm rather than the exception. Research projects will involve investigators from several fields with the result that all participants will receive mentoring from several individuals. Educational and training activities supporting this research will include coursework, journal clubs, laboratory group meetings (SIG's or Special Interest Groups), seminars and workshops, laboratory experience and internships. Together, these vehicles of training will help to develop young researchers with a broad knowledge of mathematical and computational biology coupled with expertise in specific biological problems. The long-term effect of this program will be to produce a new generation of applied mathematical scientists who will work effectively to build bridges between traditional disciplines and academia, industry and the public sector.

The investigators will use mathematical analysis and computations to explore the mechanical and chemical dynamics of physiological gels. The fact that there are many polymer networks with gel-like properties in biological systems has been largely overlooked by experimentalists and theorists. Indeed, quantitative studies of biogels are scant in comparison with those of other physiological structures and processes. One aim of this project, therefore, is to bring to bear the tools of applied mathematics to several closely related problems of biogel growth and dynamic behavior. More specifically, the goal of this proposal is to study the processes of gel formation, secretion, and degradation; their regulation; and the relationship between these and function in dynamic physiological biogels. The investigators will study these issues by examining three specific problems: i) The growth of fibrin gel networks during blood clotting. ii) Vesicular exocytosis of mucin gel. iii) The growth and regulation of the mucin layer in the stomach and its role in gastric protection. The studies will involve multiple spatial and temporal scales, and will examine how microscopic properties and events affect macroscopic function. Mathematical models will be developed to understand how physical properties such as the viscoelastic constitutive properties and the gel morphology are determined and controlled, and how these properties affect the physiological function of the biogel. At the same time, the investigators will look for general principles of biogel dynamics that have consequences in other systems.

Polymer networks with gel-like properties arise in a wide range of physiological settings and processes. Better insight into how such gels are formed and how their properties are regulated is critical to understanding these important processes and how they can be manipulated to improve human health. Because the formation and regulation of biogels is governed by physical and chemical properties and because these properties can be expressed mathematically, mathematical tools can be brought to bear on these problems. Through mathematical analysis and computational simulations of biogels, a wealth of detailed data can be obtained that complements the data obtainable from traditional laboratory experiments. Hence the combination of mathematical and experimental investigators brought together in this project is expected to lead to important new insights about biogel behavior in important physiological and pathological situations including blood clotting, mucin secretion, and protection of the stomach lining.

The long term goal of this project is to develop state of the art computational models of thrombosis in order to explore how physical and chemical factors interact to determine its progression. An integral component of the developmental work will be the experimental validation of the models using well-established perfusion systems and confocal microscopy for determining the characteristics of thrombus deposition. Specifically, 3D computational models of i) platelet mural thrombosis in small diameter blood vessels (arterioles), and ii) combined platelet thrombosis and coagulation in small vessels (arterioles and venules) will be developed. The models will be designed to take full advantage of high performance parallel computing capabilities as well as innovative mathematical and computational methods and will permit exploration of the complex, dynamic, and multiscale interplay between flow, chemistry and vascular biology in thrombosis. Through a Consortium arrangement with Dr. Vincent Turitto and his thrombosis group at the Illinois Institute of Technology, experiments will be conducted to provide the necessary experimental data. Modification of the models will occur through close interaction between the computational and experimental groups, and with the assistance of an Advisory Group of thrombosis experts. The project thus brings together a unique cross-disciplinary team of mathematicians, computational scientists, biomedical engineers and life scientists in a well integrated computational and experimental effort to understand intravascular thrombosis and to develop reliable models for predicting the course of thrombotic events that can help in designing improved medical devices and therapies to prevent and treat thrombosis.

This RTG program will continue the development of a comprehensive program of cross-disciplinary research and training in Mathematical and Computational Biology, housed within the Department of Mathematics at the University of Utah. The training component will give students a high level of mathematical training, substantial exposure to biological problems and techniques, and extensive experience in communication and collaboration with experimental life scientists. The research component will develop and use mathematical and computational methods to study complex biological processes, organized around four major research themes of biofluids, ecology and evolutionary biology, neuroscience and physiology. The training of students in this program will include traditional and non-traditional coursework, journal clubs, seminars, laboratory rotations, extramural research experiences, research group meetings, mentoring, consulting and teaching experiences, as well as a variety of professional development experiences. Students will receive research mentoring by mathematicians and experimentalists in a highly interactive setting in which they learn the necessary biology and develop the ability to do non-traditional, cross-disciplinary, cutting edge research.

This program will train fully integrated, collaborative researchers, scholars and educators in mathematical and computational biology, thus bringing to bear the power of mathematics on the challenging problems of modern biology. Many collaborative research projects will be initiated as a result of our research training paradigm, as students become engaged with other students and faculty in other departments and institutions. By placing quantitatively trained individuals in an environment where medical and biological problems are at the forefront, the possibilities for new insights and discoveries are truly outstanding. The long term effect of this program will be a new generation of applied mathematical scientists who can work effectively to build bridges between traditional disciplines and among academia, industry and the public sector.

This project concerns development and analysis of mathematical models of several complex biological processes, each with major importance to the fundamental and health sciences: cellular blebbing and its role in cellular locomotion through extracellular matrix, platelet deposition and fibrin gelation in arterial blood clotting, mucin secretion and its role in acid transport in the stomach, protein sorting and trafficking by the Golgi apparatus. Although the details of the biology of these processes are vastly different, a common theme is that each involves a complex viscoelastic material mixture whose behavior is determined by the dynamic interplay of mechanics, flow, physical structure, and chemistry. The mathematical description of these processes requires equations describing multiphase flow, the evolution of composition, structure and chemistry, and the relationship between stresses and composition/structure. The solution and analysis of sophisticated models that combine these elements will pose substantial mathematical and computational challenges. To meet these challenges, the investigators will develop and apply advanced numerical algorithms to gain fundamental insights into the mechanisms of function of these important physiological processes. This work will lead to novel and important advances in understanding the essential role of the mechanics and dynamics of complex materials in the function of biological systems. This, in turn, will support improved diagnosis and treatment of a range of serious medical disorders including coronary artery disease, cancer, and metabolic disease. The work will also lead to better understanding of complex materials in general and contribute to the design of novel new materials for meeting pressing technological challenges. Furthermore, the design of new computational algorithms will lead to new capabilities in the use of high-performance computing in science and engineering. The highly interdisciplinary nature of the project will provide many opportunities for training young scientists in the new multi-disciplinary approach to science.

Many important physiological processes involve interactions between materials of different types (for example, water and cells or water and polymer gels) and which move relative to one another. The physical interactions between the materials can be strongly influenced by chemical reactions, and the chemical reactions in turn are influenced by the materials' motion and other interactions. Better insight into how such complex systems work and are regulated is critical to understanding these important processes and how they can be manipulated to improve human health. Because these processes are governed by physical and chemical principles and properties, and because these principles and properties can be expressed mathematically, mathematical tools can be brought to bear on these problems. Through mathematical analysis and computational simulations, new insights into the materials' behavior can be developed and a wealth of data can be obtained that complements the data obtainable from traditional laboratory experiments. Hence the combination of mathematical and experimental investigators brought together in this project is expected to lead to significant new insights in important physiological and pathological situations including blood clotting, metabolism, and cancer metastasis. Further the mathematics and computational tools developed in the project will impact the development of non-biological complex materials to meet pressing technological challenges.

This project brings together computational scientists and mathematical modelers to solve a fundamental multifaceted multiscale problem in human physiology, namely understanding the platelet aggregation and coagulation (PAC) processes that comprise blood clotting. Over the past two decades, mathematical biology experts, including the current investigators, have worked to apply sound mathematical modeling principles and computational methods to attempt to dissect the complex interactions that occur within the platelet aggregation and coagulation process - fluid-structure interactions, mechanical-chemical interactions, and structure-structure interactions, to name a few. The complexity of this problem is due to its multiscale nature in both space and time, the complex disparate physical and chemical processes involved, as well as the challenge of attempting to model processes for which experimental validation is difficult. Over recent years, the experimental world has made significant advances in accumulating data that might both help us model the PAC cascade more faithfully, and allow us to predict its pathological deviations. The challenge is in connecting these two worlds and this project has as its goal employed modern computing concepts (numerical and algorithmic) to meet this challenge. While this project focuses on the PAC cascade, it will also have impact in a wide range of multiscale, multidiscipline applications such as chemical engineering and material science.

The physiological time scale for PAC is on the order of minutes. To date, the only model able to simulate the entire PAC process over such time scales is a meso-scale (continuum) model developed by co-PI Fogelson and collaborators. This capability comes at the cost of coarse-graining the geometry and mechanics of the PAC process. The co-PI has also developed a fine-grained model of platelet aggregation that is at the forefront of platelet modeling. However, while conceptually faithful to the mechanics of the PAC process and the geometric intricacies of the developing aggregates, the fine-grained model does not yet contain treatment of the chemical processes of coagulation. Further, this model is computationally expensive and can, in a reasonable amount of time, only simulate a small fraction of the physical time that the meso-scale model can. Consequently, the goals of this project are two-fold: first, to extend the simulation capabilities of the fine-grained model both in terms of conceptual fidelity to the PAC cascade, and also in terms of computational efficiency by implementation on hybrid (CPU/GPU) architectures; and second, to cross-validate in the multiscale context current meso-scale and the extended fine-scale PAC models. Accomplishing these goals is critical to our longer-term research objective of developing hybrid multiscale models - enabled by current and future experimental data - that combine the best features of both these models.

? DESCRIPTION: The goals of the proposed research are to investigate how upstream platelet-agonist interactions affect the downstream platelet interactions with blood-contacting biomaterials. Almost all past research efforts in the field of biomaterial hem compatibility have focused on the local biomaterial surface properties. While these observations are essential for predicting a material's behavior in circulation, they do not reflect the whole story. For example, upstream suturing of a vascular graft creates an anastomosis (a surgical connection between biomaterial and native blood vessel) that has the potential to transiently expose different agonists to circulating platelets. Our preliminary experiments and mathematical modeling suggest that this upstream history of platelet-agonist interaction significantly influences plateet behavior downstream of an anastomotic site. The upstream priming effects are compounded by the fact that no blood-contacting biomaterials are perfectly hem compatible. It is hypothesized here that the magnitude of the downstream biomaterial-platelet interactions is strongly influenced by the transient platelet exposure to upstream platelet agonists that can prime platelets for adhesion and activation. Platelets exposed to agonists are thus more likely to adhere to and become activated by a downstream biomaterial than in the absence of such agonists. It is not known how far downstream these priming effects persist, how much time is required for the primed platelets to become quiescent again, and by which mechanism this phenomenon takes place. From a biomaterials point of view, this problem translates into determining the acceptable tolerance for the extent of upstream priming. In other words, even biomaterials that have very little tendency to activate platelets may do so simply because of the upstream priming of platelets. The proposed study of upstream platelet-agonist effects is expected to result in a new paradigm in the field of biomaterial-derived platelet aggregation and thrombus growth; one that is not exclusively dependent on the local biomaterial surface properties but includes upstream anastomoses and perturbed blood flow. The combination of experiments and modeling in the proposed study will provide new insight into the roles of different upstream agonists and thus has the potential for establishing predictive parameters that could be used to improve the design of blood contacting devices such as catheters, grafts, and other vascular implants.

This project brings together mathematical and computational scientists and bioengineers to study the fundamental biophysical and biochemical mechanisms underlying the formation of blood clots within stenosed (constricted) arteries. These are the blood clots responsible for most heart attacks and many strokes, and understanding how they can form under the extreme physical conditions in a stenotic artery may lead to new ideas for how to prevent them. The very fast blood flow in severely stenosed arteries means that many of the well-studied processes responsible for blood clotting in more physiologically typical situations can play at most a minor role in these arteries. Recent experiments, including ones from the laboratory of one of the current investigators, suggest the importance of a specific flow-sensitive protein in the blood in allowing blood platelets to clump together to form a clot in stenotic arteries. This project involves incorporating the hypothesized role of this protein into a novel and sophisticated computational model of arterial blood clot formation, developed by this project's other investigators, and to use the expanded model to characterize the conditions under which that protein's known properties could explain clot formation in stenotic arteries. Through comparisons of the new model's predictions with further laboratory experiments, the model will be refined and its predictive capabilities improved, and our understanding of how blood clots form under the extreme physical conditions in stenotic arteries will be increased. Because the challenges of forming a blood clot under the conditions in a stenotic artery are similar to those of stanching hemorrhage from a major artery, understanding of how such clots form may also aid in development of interventions to limit bleeding following trauma.

Most arterial blood clots are formed by the adhesion of blood cells known as platelets to an injured blood vessel wall and by platelets? cohesion to one another. Platelet adhesion and cohesion are both accomplished through the formation of molecular bonds that involve specific proteins on the platelets? surfaces binding to other specific proteins on the vascular wall or in the blood plasma. To hold the platelets together, the bonds must collectively be able to withstand the forces imposed on the platelet clump by the blood flow. For many types of platelet-platelet bonds, a platelet can form that type of bond only if the platelet has already become activated in response to appropriate chemical or physical stimuli. The platelet activation process takes time. For a platelet moving through a highly constricted artery, there is not enough time to respond to activation stimuli and the forces that the fluid exerts on it if it tries to attach to the vessel wall are enormous. How clots form in this situation is poorly understood, but recent experiments lead to the hypothesis that bonds mediated by a uniquely flow-sensitive protein (von Willebrand factor) in the blood are critical. This project will explore that hypothesis through a combination of mathematical modeling, computer simulation, and laboratory experimentation. A novel multiphase model will be developed of the mechanical interactions between a viscous fluid representing the blood and a permeable, viscoelastic, fracturable material representing a growing platelet clot. Development of robust and efficient numerical methods will allow exploration of the model?s behavior. Model results will be compared with results from an in vitro physical model of a stenotic artery. The comparison will lead to model refinements and to the design and interpretation of the physical experiments. Such interplay between modeling and experiments provides a powerful engine for driving scientific discovery.

This proposal brings together a team of applied mathematicians and experimental physicists, engineers, and biologists, with expertise in biogels, mucus physics, microbiology and bacterial motility, and gastroenterology to tackle an important problem in physiology and pathology: how the gastric mucus layer is maintained and how it responds to infecting bacteria and to changes in topology and size in gastric organoids (GOs). Cells in the stomach epithelium secrete the mucin that forms a mucus layer to protect the epithelium from the harsh environment of the stomach lumen, which is acidic and contains digestive enzymes such as pepsin. Epithelial cells also secrete acid, neutralizing bicarbonate, and pepsinogen, the inactive precursor to pepsin. These secretions form a complex coupled system since the rheology of mucin depends on pH and ionic strength, acid can be bound by negatively charged mucin, ions and mucin electrostatically interact, pepsinogen activation is pH dependent, and pepsin catalyzes mucin degradation. Goal #1 of this proposal is to understand how this coupled system maintains homeostasis. Goal #2 is to understand infection by Helicobacter pylori, which must swim across the mucus layer to colonize the epithelium. It locally modifies the gel rheology as it swims by secreting neutralizing ammonia. Goal #3 is to understand whether gastric organoids (GOs), spherical 3D cultures of a monolayer of differentiated epithelial cells, can accurately model gastric mucus layer physiology and pathology. The approach is to A: Build a mathematical model that fully couples mucin, ion, and enzyme transport and interactions. Validate it through in vitro experiments on acid transport through mucin. B: Investigate mechanisms of mucus layer homeostasis and acid transport using the mathematical model, flat 2D layers of cultured epithelium, and physical models of mucus, by exploring volumetric, spatial, and temporal variations of secretion rates. C: Mathematically model interaction of swimming H. pylori with mucus and experimentally image and track single bacteria together with local ion concentrations and micro-rheology. Model and experimentally observe collective effects of infection by dense populations of bacteria. D: Model and experimentally test how variations in size and spatial localization of secretion affect mucus layer formation in GOs to learn how and when they may be used as accurate models of physiology/pathology.

This proposal brings together a team of applied mathematicians and experimental physicists, engineers, and biologists, with expertise in biogels, mucus physics, microbiology and bacterial motility, and gastroenterology to tackle an important problem in physiology and pathology: how the gastric mucus layer is maintained and how it responds to infecting bacteria and to changes in topology and size in gastric organoids (GOs). Cells in the stomach epithelium secrete the mucin that forms a mucus layer to protect the epithelium from the harsh environment of the stomach lumen, which is acidic and contains digestive enzymes such as pepsin. Epithelial cells also secrete acid, neutralizing bicarbonate, and pepsinogen, the inactive precursor to pepsin. These secretions form a complex coupled system since the rheology of mucin depends on pH and ionic strength, acid can be bound by negatively charged mucin, ions and mucin electrostatically interact, pepsinogen activation is pH dependent, and pepsin catalyzes mucin degradation. Goal #1 of this proposal is to understand how this coupled system maintains homeostasis. Goal #2 is to understand infection by Helicobacter pylori, which must swim across the mucus layer to colonize the epithelium. It locally modifies the gel rheology as it swims by secreting neutralizing ammonia. Goal #3 is to understand whether gastric organoids (GOs), spherical 3D cultures of a monolayer of differentiated epithelial cells, can accurately model gastric mucus layer physiology and pathology. The approach is to A: Build a mathematical model that fully couples mucin, ion, and enzyme transport and interactions. Validate it through in vitro experiments on acid transport through mucin. B: Investigate mechanisms of mucus layer homeostasis and acid transport using the mathematical model, flat 2D layers of cultured epithelium, and physical models of mucus, by exploring volumetric, spatial, and temporal variations of secretion rates. C: Mathematically model interaction of swimming H. pylori with mucus and experimentally image and track single bacteria together with local ion concentrations and micro-rheology. Model and experimentally observe collective effects of infection by dense populations of bacteria. D: Model and experimentally test how variations in size and spatial localization of secretion affect mucus layer formation in GOs to learn how and when they may be used as accurate models of physiology/pathology.