Comparison of reduced models for blood flow using Runge-Kutta discontinuous Galerkin methods

One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ greatly in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we systematically compare several reduced models of blood flow for physiologically relevant vessel parameters, network topology, and boundary data. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods

Predictive monitoring for early detection of subacute potentially catastrophic illnesses in critical care

We wish to save lives of patients admitted to ICUs. Their mortality is high enough based simply on the severity of the original injury or illness, but is further raised by events during their stay. We target those events that are subacute but potentially catastrophic, such as infection. Sepsis, for example, is a bacterial infection of the bloodstream, that is common in ICU patients and has a \u3e 25% risk of death. Logically, early detection and treatment with antibiotics should improve outcomes. Our fundamental precepts are (1) some potentially catastrophic medical and surgical illnesses have subclinical phases during which early diagnosis and treatment might have life-saving effects, (2) these phases are characterized by changes in the normal highly complex but highly adaptive regulation and interaction of the nervous system and other organs such as the heart and lungs, (3) teams of clinicians and quantitative scientists can work together to identify clinically important abnormalities of monitoring data, to develop algorithms that match the clinicians\u27 eye in detecting abnormalities, and to undertake the clinical trials to test their impact on outcomes

Numerical method of characteristics for one-dimensional blood flow

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant

A New Algorithm for Detecting Central Apnea in Neonates

Apnea of prematurity is an important and common clinical problem, and is often the rate-limiting process in NICU discharge. Accurate detection of episodes of clinically important neonatal apnea using existing chest impedance (CI) monitoring is a clinical imperative. The technique relies on changes in impedance as the lungs fill with air, a high impedance substance. A potential confounder, however, is blood coursing through the heart. Thus, the cardiac signal during apnea might be mistaken for breathing. We report here a new filter to remove the cardiac signal from the CI that employs a novel resampling technique optimally suited to remove the heart rate signal, allowing improved apnea detection. We also develop an apnea detection method that employs the CI after cardiac filtering. The method has been applied to a large database of physiological signals, and we prove that, compared to the presently used monitors, the new method gives substantial improvement in apnea detection

Breath-by-Breath Analysis of Cardiorespiratory Interaction for Quantifying Developmental Maturity in Premature Infants

Breath-by-breath analysis of cardiorespiratory interaction for quantifying developmental maturity in premature infants. J Appl Physiol 112: 859-867, 2012. First published December 15, 2011; doi:10.1152/japplphysiol.01152.2011.-In healthy neonates, connections between the heart and lungs through brain stem chemosensory pathways and the autonomic nervous system result in cardiorespiratory synchronization. This interdependence between cardiac and respiratory dynamics can be difficult to measure because of intermittent signal quality in intensive care settings and variability of heart and breathing rates. We employed a phase-based measure suggested by Sch fer and coworkers (Sch fer C, Rosenblum MG, Kurths J, Abel HH. Nature 392: 239-240, 1998) to obtain a breath-by-breath analysis of cardiorespiratory interaction. This measure of cardiorespiratory interaction does not distinguish between cardiac control of respiration associated with cardioventilatory coupling and respiratory influences on the heart rate associated with respiratory sinus arrhythmia. We calculated, in sliding 4-min windows, the probability density of heartbeats as a function of the concurrent phase of the respiratory cycle. Probability density functions whose Shannon entropy had a \u3c 0.1% chance of occurring from random numbers were classified as exhibiting interaction. In this way, we analyzed 18 infant-years of data from 1,202 patients in the Neonatal Intensive Care Unit at University of Virginia. We found evidence of interaction in 3.3 patient-years of data (18%). Cardiorespiratory interaction increased several-fold with postnatal development, but, surprisingly, the rate of increase was not affected by gestational age at birth. We find evidence for moderate correspondence between this measure of cardiorespiratory interaction and cardioventilatory coupling and no evidence for respiratory sinus arrhythmia, leading to the need for further investigation of the underlying mechanism. Such continuous measures of physiological interaction may serve to gauge developmental maturity in neonatal intensive care patients and prove useful in decisions about incipient illness and about hospital discharge

Synchronization Engineering: Theoretical Framework and Application to Dynamical Clustering

A method for engineering the behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.Comment: To appear in CHAO

Reconstruction of two-dimensional phase dynamics from experiments on coupled oscillators

Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time

Elevated Diastolic Closing Margin Is Associated with Intraventricular Hemorrhage in Premature Infants.

OBJECTIVE: To determine whether the diastolic closing margin (DCM), defined as diastolic blood pressure minus critical closing pressure, is associated with the development of early severe intraventricular hemorrhage (IVH). STUDY DESIGN: A reanalysis of prospectively collected data was conducted. Premature infants (gestational age 23-31 weeks) receiving mechanical ventilation (n = 185) had ∼1-hour continuous recordings of umbilical arterial blood pressure, middle cerebral artery cerebral blood flow velocity, and PaCO2 during the first week of life. Models using multivariate generalized linear regression and purposeful selection were used to determine associations with severe IVH. RESULTS: Severe IVH (grades 3-4) was observed in 14.6% of the infants. Irrespective of the model used, Apgar score at 5 minutes and DCM were significantly associated with severe IVH. A clinically relevant 5-mm Hg increase in DCM was associated with a 1.83- to 1.89-fold increased odds of developing severe IVH. CONCLUSION: Elevated DCM was associated with severe IVH, consistent with previous animal data showing that IVH is associated with hyperperfusion. Measurement of DCM may be more useful than blood pressure in defining cerebral perfusion in premature infants.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Oxford University Press

Does hypothermia impair cerebrovascular autoregulation in neonates during cardiopulmonary bypass?

BACKGROUND: Autoregulation monitoring has been proposed as a means to identify optimal arterial blood pressure goals during cardiopulmonary bypass, but it has been observed that cerebral blood flow is pressure passive during hypothermic bypass. When neonates cooled during cardiopulmonary bypass are managed with vasodilators and controlled hypotension, it is not clear whether hypothermia or hypotension were the cause of impaired autoregulation. AIM: We sought to measure the effect of both arterial blood pressure and hypothermia on autoregulation in a cohort of infants cooled for bypass, hypothesizing a collinear relationship between hypothermia, hypotension, and dysautoregulation. METHODS: Cardiopulmonary bypass was performed on 72 infants at Texas Children's Hospital during 2015 and 2016 with automated physiologic data capture, including arterial blood pressure, nasopharyngeal temperature, cerebral oximetry, and a cerebral blood volume index derived from near infrared spectroscopy. Cooling to 18°C, 24°C, and 30°C was performed on 33, 12, and 22 subjects, respectively. The hemoglobin volume index was calculated as a moving correlation coefficient between mean arterial blood pressure and the cerebral blood volume index. Positive values of the hemoglobin volume index indicate impaired autoregulation. Relationships between variables were assessed utilizing a generalized estimating equation approach. RESULTS: Hypothermia was associated with hypotension, dysautoregulation, and increased cerebral oximetry. Comparing the baseline temperature of 36°C with 18°C, arterial blood pressure was 44 mm Hg (39-52) vs 25 mm Hg (21-31); the hemoglobin volume index was 0.0 (-0.02 to 0.004) vs 0.5 (0.4-0.7) and cerebral oximetry was 59% (57-61) vs 88% (80-92) (Median, 95% CI of median; P<.0001 for all three associations by linear regression with generalized estimation of equations with data from all temperatures measured). CONCLUSIONS: Arterial blood pressure, temperature, and cerebral autoregulation were collinear in this cohort. The conclusion that hypothermia causes impaired autoregulation is thus confounded. The effect of temperature on autoregulation should be delineated before clinical deployment of autoregulation monitors to prevent erroneous determination of optimal arterial blood pressure. Showing the effect of temperature on autoregulation will require a normotensive hypothermic model