- Apex, North Carolina, United States
Mette Olufsen
North Carolina State University, Mathematics, Faculty Member
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The Valsalva maneuver (VM) is a diagnostic protocol examining sympathetic and parasympathetic activity in patients with autonomic dysfunction (AD) impacting cardiovascular control. Because direct measurement of these signals is costly and... more
The Valsalva maneuver (VM) is a diagnostic protocol examining sympathetic and parasympathetic activity in patients with autonomic dysfunction (AD) impacting cardiovascular control. Because direct measurement of these signals is costly and invasive, AD is typically assessed indirectly by analyzing heart rate and blood pressure response patterns. This study introduces a mathematical model that can predict sympathetic and parasympathetic dynamics. Our model-based analysis includes two control mechanisms: respiratory sinus arrhythmia (RSA) and the baroreceptor reflex (baroreflex). The RSA submodel integrates an electrocardiogram-derived respiratory signal with intrathoracic pressure, and the baroreflex submodel differentiates aortic and carotid baroreceptor regions. Patient-specific afferent and efferent signals are determined for 34 control subjects and 5 AD patients, estimating parameters fitting the model output to heart rate data. Results show that inclusion of RSA and distinguishing aortic/carotid regions are necessary to model the heart rate response to the VM. Comparing control subjects to patients shows that RSA and baroreflex responses are significantly diminished. This study compares estimated parameter values from the model-based predictions to indices used in clinical practice. Three indices are computed to determine adrenergic function from the slope of the systolic blood pressure in phase II [ α (a new index)], the baroreceptor sensitivity ( β), and the Valsalva ratio ( γ). Results show that these indices can distinguish between normal and abnormal states, but model-based analysis is needed to differentiate pathological signals. In summary, the model simulates various VM responses and, by combining indices and model predictions, we study the pathologies for 5 AD patients. NEW & NOTEWORTHY We introduce a patient-specific model analyzing heart rate and blood pressure during a Valsalva maneuver (VM). The model predicts autonomic function incorporating the baroreflex and respiratory sinus arrhythmia (RSA) control mechanisms. We introduce a novel index ( α) characterizing sympathetic activity, which can distinguish control and abnormal patients. However, we assert that modeling and parameter estimation are necessary to explain pathologies. Finally, we show that aortic baroreceptors contribute significantly to the VM and RSA affects early VM.
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Background: Sensitivity analysis is the assessment of the effect on a model output from changing model parameters. Quantitatively, local sensitivity analysis can be performed by computing the derivative of the model output with respect to... more
Background: Sensitivity analysis is the assessment of the effect on a model output from changing model parameters. Quantitatively, local sensitivity analysis can be performed by computing the derivative of the model output with respect to the model parameters. Measures obtained are called local sensitivities as the derivatives are evaluated at some nominal parameter values. Hence, if the uncertainty in the parameter values is high or the model is highly nonlinear, local sensitivity analysis may be inadequate. Results: This study shows how global sensitivities can be computed using simple integration of local sensitivities over the allowed parameter space utilizing quasi-Monte Carlo integration with low-discrepancy sequences. In addition we show that analysis of parameter sets displaying specific behaviors can lead to a better understanding of the role of certain parameters and be used to set bounds for the parameter space. We illustrate the approach for global sensitivity computation using a baroreceptor reflex model, which describes heart rate regulation during head-up tilt. Conclusions: Global sensitivities were calculated for an improved baroreceptor reflex model, by averaging local sensitivities. Parameter sets causing rapid fluctuations in local sensitivities, as well as parameter sets causing infeasible model behavior or solver errors, were recorded. Analysis revealed nontransparent model dynamics and
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The cardiovascular control system is continuously engaged to maintain homeostasis, but it is known to fail in a large cohort of patients suffering from orthostatic intolerance. Numerous clinical studies have been put forward to understand... more
The cardiovascular control system is continuously engaged to maintain homeostasis, but it is known to fail in a large cohort of patients suffering from orthostatic intolerance. Numerous clinical studies have been put forward to understand how the system fails, yet non-invasive clinical data are sparse, typical studies only include measurements of heart rate and blood pressure, as a result it is difficult to determine what mechanisms that are impaired. It is known, that blood pressure regulation is mediated by changes in heart rate, vascular resistance, cardiac contractility and a number of other factors. Given that numerous factors contribute to changing these quantities it is difficult to devise a physiological model describing how they change in time. One way is to build a model that allows these controlled quantities to change and to compare dynamics between subject groups. To do so, requires more knowledge of how these quantities change for healthy subjects. This study compares two methods predicting time-varying changes in cardiac contractility and vascular resistance during headup tilt. Similar to the study by Williams et al. [57], the first method uses piecewise linear splines, while the second uses the ensemble transform Kalman filter (ETKF) [1], [12], [13], [35]. In addition, we show that the delayed rejection adaptive Metropolis (DRAM) algorithm can be used for predicting parameter uncertainties within the spline methodology, which is compared with the variability obtained with the ETKF. While the spline method is easier to set up, this study shows that the ETKF has a significantly shorter computational time. Moreover, while uncertainty of predictions can be augmented to spline predictions using DRAM, these are readily available with the ETKF.
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Research Interests: Computer Science, Algorithms, Materials Science, Biomedical Engineering, Data Analysis, and 15 moreBiomedical, Elasticity, Blood Pressure, Animals, Male, Inverse Problem, Mathematical Model, Elastic Modulus, Elastic Properties, Experimental Measurement, Equipment Design, Electrical And Electronic Engineering, Confidence Interval, Biomechanical Phenomena, and Arteries
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In this paper we examine a cardiovascular-respiratory model of mid-level complexity designed to predict the dynamics of end-tidal carbon dioxide (CO(2)) and cerebral blood flow velocity in response to a CO(2) challenge. Respiratory... more
In this paper we examine a cardiovascular-respiratory model of mid-level complexity designed to predict the dynamics of end-tidal carbon dioxide (CO(2)) and cerebral blood flow velocity in response to a CO(2) challenge. Respiratory problems often emerge as heart function diminishes in congestive heart failure patients. To assess system function, various tests can be performed including inhalation of a higher than normal CO(2) level. CO(2) is a key quantity firstly because any perturbation in system CO(2) quickly influences ventilation (oxygen perturbations need to be more severe). Secondly, the CO(2) response gain has been associated with respiratory system control instability. Thirdly, CO(2) in a short time impacts the degree of cerebral vascular constriction, allowing for the assessment of cerebral vasculature function. The presented model can be used to study key system characteristics including cerebral vessel CO(2) reactivity and ventilatory feedback factors influencing ventilatory stability in patients with congestive heart failure. Accurate modeling of the dynamics of system response to CO(2) challenge, in conjunction with robust parameter identification of key system parameters, can help in assessing patient system status.
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ABSTRACT This paper combines a generalized viscoelastic model with a one-dimensional (1D) fluid dynamics model for the prediction of blood flow, pressure, and vessel area in systemic arteries. The 1D fluid dynamics model is derived from... more
ABSTRACT This paper combines a generalized viscoelastic model with a one-dimensional (1D) fluid dynamics model for the prediction of blood flow, pressure, and vessel area in systemic arteries. The 1D fluid dynamics model is derived from the Navier—Stokes equations for an incompressible Newtonian flow through a network of cylindrical vessels. This model predicts pressure and flow and is combined with a viscoelastic constitutive equation derived using the quasilinear viscoelasticity theory that relates pressure and vessel area. This formulation allows for inclusion of an elastic response as well as an appropriate creep function allowing for the description of the viscoelastic deformation of the arterial wall. Three constitutive models were investigated: a linear elastic model and two viscoelastic models. The Kelvin and sigmoidal viscoelastic models provide linear and nonlinear elastic responses, respectively. For the fluid domain, the model assumes that a given flow profile is prescribed at the inlet, that flow is conserved and pressure is continuous across vessel junctions, and that it incorporates a multiscale boundary condition (a three element Windkessel model) at each outlet. This outlet boundary condition allows prediction of the overall impact on the flow and pressure generated by the downstream vasculature. The coupled fluid structure interaction model is solved using a finite element method that is adapted to account for time history of the viscoelastic model. Results of this study demonstrate that incorporation of a viscoelastic wall model allows more physiologic prediction of arterial blood pressure and vessel deformation, which often is overestimated with the simple elastic wall models, while blood flow does not differ significantly between models.
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Cerebral autoregulation is a homeostatic mechanism which maintains blood flow despite changes in blood pressure in order to meet local metabolic demands. Several mechanisms play a role in cerebral autoregulation in order to adjust... more
Cerebral autoregulation is a homeostatic mechanism which maintains blood flow despite changes in blood pressure in order to meet local metabolic demands. Several mechanisms play a role in cerebral autoregulation in order to adjust vascular tone and caliber of the cerebral vessels, but the exact etiology of the dynamics of these mechanism is not well understood. In this study, we discuss two patient specific models predicting cerebral blood flow velocity during postural change from sitting to standing. One model characterises cerebral autoregulation, the other describes the beat-to-beat distribution of blood flow to the major regions of the brain. Both models have been validated against experimental data from a healthy young subject.
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Dynamic changes in cerebral blood flow and the associated vascular responses accompanying posture change that enable the brain to maintain perfusion during hypotensive stress are not fully understood. The aim of this work is to use a... more
Dynamic changes in cerebral blood flow and the associated vascular responses accompanying posture change that enable the brain to maintain perfusion during hypotensive stress are not fully understood. The aim of this work is to use a lumped parameter model of cerebral blood flow to analyze changes in key parameters (systemic and cerebrovascular resistances) during posture change from sitting to standing. Such a model sheds light on vascular adaptation to hypotensive stress, and could ultimately help determine the changes in cerebral autoregulation that occur in aging, hypertension, and other clinical conditions.
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Research Interests: Mathematics, Compliance, Fluid Dynamics, Medicine, Library and Information Studies, and 15 moreHumans, Blood Pressure, Magnetic Resonance, Standard Model, Wave Equation, Outflow, Wave propagation, Blood Flow, Tapering, Boundary Condition, Boundary Value Problem, Blood Flow Velocity, Vascular Resistance, Arteries, and Springer Ebooks
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ABSTRACT The work presented in this paper shows how the multipulse method from digital signal processing can be used to accurately model signals obtained from blood pressure and flow velocity sensors. This model produces very good... more
ABSTRACT The work presented in this paper shows how the multipulse method from digital signal processing can be used to accurately model signals obtained from blood pressure and flow velocity sensors. This model produces very good modelling of the signals on a resolution that allows analysis between heartbeats. The AR coefficients can be transformed to reflection coefficients and tube radii associated with digital wave guides, as well as pole-zero representations. These parameters permit additional insight and interpretation that will produce deeper insight into the biological control mechanisms.
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Research Interests: Chemical Engineering, Applied Mathematics, Physics, Acoustics, Biomedical Engineering, and 13 moreSignal Processing, Digital Signal Processing, Medicine, Blood Pressure, Mathematical Model, High Resolution, Blood Flow, Blood Flow Velocity, Blood Vessel, Amplitude, Representation Politics, Autoregressive model, and Digital filter
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Research Interests: Chemical Engineering, Mathematics, Applied Mathematics, Cardiology, Biomedical Engineering, and 15 moreMedicine, Brain, Humans, Computer Simulation, Blood Pressure, Female, Male, Arterial Blood Pressure, Mathematical, Aged, Adult, Experimental Measurement, Cerebral Blood Flow, Blood Flow Velocity, and cerebral arteries
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