Mette Olufsen - US grants

The purpose of this investigation is to determine mechanisms of cerebrovascular autoregulation during orthostatic stress and their alterations due to aging and hypertension using a mathematical model based on principles of fluid dynamics. The specific aim is to develop a lumped parameter model that can reproduce a dynamic changes of pulsatile blood flow velocity (BFV) and pressure (BP) in the middle cerebral artery (MCA) during posture change from sitting to standing, and use this model to unravel differences in regulatory mechanisms governing cerebral blood flow (CBF) in two groups of subjects: (i) normotensive elderly subjects and (ii) elderly subjects with untreated hypertension. Extensive data on pulsatile BFV in the MCA and BP have already been gathered in Dr. Lipsitz's laboratory. We will analyze these data using the mathematical model and extract parameters, such as systemic and peripheral cerebrovascular resistance and compliance. Once differences among the groups of normotensive and untreated hypertensive subjects and between males and females have been established, we will (in a full RO1 proposal) investigate side effects related to vasodilator treatment of hypertension and effects related to vasovagal syncope. This study builds upon previous modeling work by Drs. Olufsen, Nadim, and Lipsitz, showing a biphasic cerebrovascular response to acute posture change in healthy young subjects, characterized by initial (baroreflex-mediated) vasoconstriction (and increased pulsatility), followed by autoregulatory cerebral vasodilation that restores blood flow to normal. Based on these results and preliminary observations of MCA blood flow in hypertensive subjects lack initial increase in cerebral pulsatility during posture change due to impairments in initial (baroreflex-mediated) peripheral cerebral vasoconstriction and cardioacceleration, (ii) this defect is exaggerated in untreated hypertensive elders. This work represents a unique collaboration between a clinical investigator in cardiovascular aging, Dr. Lipsitz and mathematicians specialized in modeling circulatory dynamics in branched arterial systems, Drs. Olufsen and Nadim. The proposed study responds to the goal of the RFA and helps Dr. Olufsen continue to build a successful independent research career in the important areas of cardiovascular physiology and aging.

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Olufsen
This award supports the development of a mathematical model predicting short-term cardiovascular regulation during orthostatic stress and hypovolemia. The model to be derived will contain three sub-models: A cardiovascular model predicting blood pressure and flow in the cardiovascular system, a model predicting sympathetic and parasympathetic activity of the autonomic nervous system, and a model predicting concentrations of carbon dioxide and oxygen. These models will be combined through models for autonomic regulation and autoregulation. In addition, formal statistical and computational methods will be used to estimate parameters in the models with emphasis on accounting for and exploring variability underlying mechanisms across different individuals. In particular, the mathematical model will be validated against already existing data from hypovolemia and orthostatic stress tests, obtained during postural change from sitting to standing, head up tilt, and lower body negative pressure.

This research project is a collaborative effort between the PIs, J. Ottesen of Denmark, and J. Batzel and F. Kappel of Austria. In the past, each group has conducted successful research projects in related areas. With the attention and expertise of the US and foreign groups focused on this project, the collaboration will make significant progress in this area of research.

In order to enhance antihypertensive therapy, further knowledge of the effects of aging and hypertension on the cerebral circulation is essential. Since recent studies show a relationship between hypertension and development of cognitive dysfunction, it is crucial to understand the effect of hypertension on cerebral perfusion. Despite the importance of these clinical questions, progress towards answering them has been impeded by inadequate non-invasive methods to measure cerebral autoregulation, and inadequately tested assumptions about cerebral vasomotion. This award will support research designed to aid in the detection and remediation of these and other potentially life threatening injuries or conditions.

Cerebral autoregulation is one of the most critical control systems in the body, as a constant tissue perfusion is necessary for proper functioning of the brain. As a response to changes in blood pressure, this control system modulates cardiovascular parameters to maintain a constant cerebral blood flow. Transcranial Doppler ultrasound measurements are routinely used to measure blood flow velocity in the middle cerebral arteries, one of the largest suppliers of blood to the brain. These measurements are then used to estimate blood flow and assess efficacy of cerebral autoregulation. However, these measurements do not currently provide reliable indicators for early diagnosis of potential impairments in the cerebral arteries, as they lack the necessary accuracy. One problem from basing the estimates derived from measurements is the questionable assumption that regulation only influences the diameter of microvasculature, while the diameter of larger vessels, such as the middle cerebral artery, remains constant. It is now clear that the large arteries are compliant suggesting that the diameter of the middle cerebral artery can indeed change in response to variations in pulsatility. In addition, estimates derived from measurements do not account for topological variations in network of cerebral arteries, such as the main distribution system, the circle of Willis. These questions will be studied using a new one-dimensional fluid dynamic model of the circle of Willis. Geometric data for this model will be obtained from magnetic resonance angiographs. To solve these equations, new numerical methods will be used. Viscoelastic equations describing the compliance of the vascular wall will be introduced and the effects of including non-Newtonian flow will be studied. Additionally, the effects of curvature of the vessel topology will be estimated. In particular, the internal carotid artery, curves about 180 degrees from when it enters the scull to it is attached to the circle of Willis. To validate this model, computed results will be compared with measurements of cerebral blood flow and network topology. The model will be used to predict effects of changes in the topology as well as changes in outflow boundary conditions. For example, plan to study the effects on distribution of blood flow in response to changes in boundary conditions and compare this with changes in diameters of the proximal vessels. Furthermore, we plan to study changes between healthy subjects and in elderly DM patients. Mathematical models have long been used to study fluid dynamic properties of arteries, however no studies have used this approach to design patient specific models to predict CBF and cerebral autoregulation.

Cerebral autoregulation is a critical control system in the body, as constant tissue perfusion is necessary for proper functioning of the brain. In response to changes in blood pressure, this control system modulates cardiovascular parameters to maintain a constant cerebral blood flow. Impairments in cerebral autoregulation have been observed in patients with type II diabetes and are associated with an increased risk of stroke. Ultrasound measurements are routinely used to measure blood flow velocity in the cerebral arteries, the largest suppliers of blood to the brain. These measurements are then used to estimate cerebral blood flow and assess efficacy of cerebral autoregulation. One problem is the questionable assumption that regulation only influences the diameter of the microvasculature, while the diameter of larger vessels, such as the middle cerebral artery, remains constant. It is now clear that the large arteries are compliant suggesting that the diameter of middle cerebral artery can indeed change in response to variations in pulsatility. In addition, estimates derived from measurements do not account for topological variations in network of cerebral arteries, such as the main distribution system, the circle of Willis. These facts suggest that there is a need for development of more advanced methods to estimate cerebral blood flow. In this study we propose to combine physiological data analysis with mathematical fluid dynamic modeling to predict cerebral blood in healthy and diabetic patients. Mathematical models have long been used to study fluid dynamic properties of arteries, however no studies have used this approach to design patient specific models to predict cerebral blood flow. Modeling detailed hemodynamics allows us to develop hypotheses that can predict mechanisms that underlie regulatory failure. The proposed model and new numerical methods for fluid dynamics models with time dependent boundary conditions will be a considerable contribution to applied mathematics and biological sciences applications. Students, who will be doing research in this area, will have skills and knowledge in applied and computational mathematics, and physiology. Such professionals are in great demand.

The autonomic nervous system is complex with many interacting components. This is why analysis of separate elements does not give a satisfactory view of the syncope mechanisms. In this study, the aim is to achieve a better understanding of the control mechanisms and their dynamics via patient specific mathematical modeling where knowledge of the individual elements and their dynamics is integrated. To this end, a dynamic cardiovascular system model coupled with a control model is developed that allows the investigators to predict the autonomic nervous system's ability to adjust the heart and vessel properties to maintain blood pressure and pumping function of the heart at reference levels. Several control models are considered including a detailed cellular model allowing prediction of the afferent baroreflex firing-rate based on analysis of ionic currents, a lumped model predicting efferent responses (changes in heart and vascular properties) as a function of sympathetic and parasympathetic outflow, and a coarse model directly predicting efferent responses. For the latter model, the applicability of receding horizon control theory is investigated. These models are composed of nonlinear dynamical systems whose solution poses considerable computational challenges. Their application to clinical data involves computational and conceptual complications due to the inherent noise in the model and data. To ensure high fidelity of our model, the investigators employ methodologies allowing computation of parameter sensitivity, identifiability, and estimation. Sensitivity and identifiability analyses are used to formulate guidelines for model calibration including the selection of parameters best suited for estimation. In particular, the nonlinear Kalman filter based approach is considered for the parameter estimation problem. This method possesses several desirable properties, among them: it takes explicitly into account noise in the model and data, it is an efficient and simple to implement computational tool, and it can take into account a priori information.

A simple change of the body from supine to sitting or standing position requires activation of a series of control mechanisms to maintain homeostasis. Upon postural change, the baroreceptors register a fall in arterial blood pressure and reduced filling of the heart. Activation of the autonomic nervous system then adjusts the heart and vessel properties to increase pressure and pump function of the heart back toward their reference level. This regulation can be disrupted in patients with peripheral and central nervous system diseases. Such patients usually experience dizziness and syncope due to altered function of the autonomic nervous system. These defects are often observed in patients with diabetes, hypertension, and other neurological diseases of which Parkinson?s disease is the most dominating. This project brings to bear tools from mathematical modeling, analysis, and computation on questions related to this phenomenon, with the goal of gaining insights into the dynamics involved and a better understanding of how this regulatory system functions. Additionally, the project involves interdisciplinary collaborations with experimentalists and includes the participation of students, providing considerable opportunities for broader impacts.

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.

This Research Training Group (RTG) grant will train undergraduate students, graduate students and postdoctoral researchers, in statistical and inverse problem methodologies applied to mathematical models for biological systems. The research component of the RTG will revolve around a number of projects that represent different disciplinary applications of modeling and development of parameter estimation methodologies in the biological sciences. Each project will involve at least four RTG participants, including faculty, students and/or postdoctoral researchers. Some projects will focus more on development of new methodologies, while others aim more at utilizing these methodologies in a particular biological setting. Important cross-cutting themes will include parameter estimation and parameter identifiability, model selection, model robustness, uncertainty quantification and model-based experimental design. Students will receive preparation for research activities in this area through a number of supporting courses, the majority of which will be offered at the graduate level, but will be accessible to advanced undergraduates. Interdisciplinarity and team-working skills will be emphasized and developed through careful mentoring and using a number of activities, such as regular research presentations, both within and between the project groups, and journal clubs. Professional development sessions will help prepare participants for current and future careers in interdisciplinary environments both inside and outside of academia. These will be offered at various levels, designed to cater for the needs of the different participants, in some cases focusing on issues unique to scientists working in the biological realm. An annual RTG workshop, including external speakers, will showcase participants' accomplishments and give opportunity to reflect on the successful (and less successful) aspects of the year's research and training activities. In alternate years, the workshop will be expanded to include a week-long lecture, tutorial and laboratory course, providing a condensed presentation of chosen aspects of the RTG curriculum to external participants, primarily advanced undergraduates and early-stage graduate students.

Ever increasing amounts of biological data are being collected, at a range of scales from the molecular and cellular through to the population and ecosystem. Mechanistic mathematical models are increasingly being used as a way of making sense of this data, providing important insights into the workings of biological systems. The success of this enterprise not only requires development and analysis of biologically appropriate models but confrontation of these models with biological data. This, in turn requires development of methodologies that allow this confrontation to occur, including practical methods that allow researchers to analyze biological data using mechanistic models. The main objective of this RTG is to develop training and research activities that will train cohorts of mathematical scientists with strengths in both applied mathematics and statistics who will have the interdisciplinary skills to work effectively with biologists, preparing them for the challenges and opportunities of the scientific workplace of the 21st century.

Syncope or, more colloquially, fainting, is a surprisingly common and little understood condition. The long term goal of the proposed line of work is the identification of the root causes of syncope. Fainting can result from the failure of one or more internal control mechanisms. There are currently no clear causal links between these controls and the observed symptoms. In order to understand the involved mechanisms, this project will start by analyzing clinical data to determine the number and characterization of the different types of syncope. A better understanding hinges on the analysis of clinical data, here time series, and the ability to infer from these, patient classification. Various scenarios will be tested through mathematical modeling to confirm both the soundness of the obtained classification and the nature and source of the pathology for each identified class. The ability to identify subjects as members of a class or group also 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". This approach will also be applicable to the study of other diseases where similar clinical data are being collected such as epilepsy.

Time series data are ubiquitous. In fact, the development of an ever increasing number of applications depends on their analysis, from stock market and economics to weather predictions. Practical issues include signal matching, classification, pattern detection and early prediction. Signals of interest are often high dimensional and noisy and the underlying dynamics are generally unknown. This award supports initiation of a collaborative research project that addresses all the above issues in the context of medical times series data and, more specifically, for syncope. To do so, a novel paradigm combining non-parametric statistics, machine learning, and applied mathematics is proposed. The first objective is to design and compute features in multivariate time series that are well adapted to classification and clustering. The proposed approach relies on recent advances in the evaluation of variable importance for scattered data. The second objective is to facilitate calibration of mathematical models by extending machine-learning concepts to this new realm. The goal is to determine how much data is necessary to "learn" biomathematics models and increasing their predictive power. This award is supported by the National Institutes of Health Big Data to Knowledge (BD2K) Initiative in partnership with the National Science Foundation Division of Mathematical Sciences.

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.