Acute cardiac syndrome (ACS) due to arterial thrombosis is a leading cause of death in the US. There is a clear need to develop methods for quantitative risk assessment and analysis of ACS. However, due to inadequate, imperfect and uncertain knowledge regarding the various parameters that control arterial thrombosis, such methods do not exist. Given current incomplete knowledge, the proposed approach seeks to develop efficient simulation techniques to gain insight into thrombogenesis and to make probabilistic predictions of outcomes such as the probability of clot formation over specific time intervals. Coupling continuum mechanics to ideas from estimation theory and statistical signal processing the PIs will develop models whose parameters are random variables that allows for the incorporation of variability of parameters in the modeling stage itself. By ensuring that the continuum models have the structure of Hidden Markov Models (HMMs) it is possible to use the powerful tools of estimation theory to find probability distributions for the hidden variables from experimental measurements. In order to simulate the biochemistry of clotting and its complex interaction with blood flow and artery deformation, and to carry out risk analysis, the PIs will use parallelizable computational algorithms for the simulations. The PIs plan to replace the usual discrete approximation of the traditional balance laws of mechanics with highly parallelizable stochastic or ?probability flow? based simulation techniques.
Disorders of coagulation and bleeding are of substantial clinical importance. Such conditions including ACS, myocardial infarction, pulmonary embolus, deep vein thrombosis and hemorrhagic disorders, amongst others are major contributors to mortality in the western world. The proposed research will provide an understanding of the processes of coagulation and bleeding and has the potential to have a tremendous impact on a variety of blood disorders. The proposed work is transformative in that it will meld together ideas from various scientific communities from biomedicine and biomechanics, mathematics, statistics and probability theory, estimation theory and signal processing, and has the potential to have significant impact on numerous scientific communities. As the researchers have a substantial track record in educational innovations the proposed research will also have salutary effect on educational aspects.
The objective of this collaborative project is to integrate statistical and deterministic approaches to the modeling of complex biochemical systems. In particular, with the recent availability of high powered computers, one can depart from standard approaches consisting of making model simplifications or analytic approximations, and move towards numerical simulation-based approaches to address the full complexity of real problems. An attractive approach consists of Monte Carlo algorithms. These algorithms are remarkably flexible and extremely powerful. In particular, the sequential Monte Carlo (SMC) techniques recently emerged in the fields of statistics and engineering shows a great promise in solving a large class of inference problems that are nonlinear, non-Gaussian, and nonstationary. SMC can be loosely defined as a family of techniques that use Monte Carlo simulations to solve online estimation and prediction problems in stochastic dynamic systems. By recursively generating Monte Carlo samples of the state variables or some other latent variables, these methods can adapt flexibly to the dynamics of the underlying stochastic systems. Intellectual merit: In this project, we first simplified the biochemical reactions that are instrumental in coagulation and lysis so that we can get it to a manageable system of equations wherein one can carry out statistical inference and prediction of the phenomena. We then developed a number of SMC-based inference algorithms and applied them to analyze biological data. During the course of this project, we have addressed four key issues related to the inherent challenges associated with network inference in most natural biological systems: (1) Structural inference of biological networks subject to connectivity and/or such other design constraints; (2) Development of better trade off strategies between theoretical optimality and computational expediency for biological network identification, including through the use of underlying biomolecular interaction constraints; (3) Use of statistical network inference results in combination with biochemical kinetics to identify and infer the behavior of missing or unobserved species, and (4) Elucidation of approaches able to generalize network inference results obtained under the steady-state assumption to those describing non-equilibrium system kinetics as well. Broader impact: Students from both the Electrical Engineering field and biological science field have benefited tremendously from this interdisciplinary by learning from the collaborators in the other field and applying its own tools to solve problems in other filed. The Columbia Undergraduate Research Involvement Program (URIP) provided funding for undergraduates interested in summer research experience. The Center for Technology, Innovation & Community Engagement (CTICE) that recruits students from Harlem (in which the student population is > 85% composed of underrepresented groups) and prepares them for challenging careers in math, science, and engineering. CTICE enrolls a broad range of ages (starting in the first grade) and prepares innovative hands-on classroom and field programs to excite and engage students in various science and technology projects. As students progress, the high school students help teach the lower grades and develop new modules for delivery. We have engaged students in the program in projects, taught classes, and also provided lab modules and materials for the classroom learning experiences.
