Multi-time scale perspective in analyzing cardiovascular data

Cardiovascular dynamic and variability data are commonly used in experimental protocols involving cognitive challenge. Usually, the analysis is based on a sometimes more and sometimes less well motivated single specific time resolution ranging from a few seconds to several minutes. The present paper aimed at investigating in detail the impact of different time resolutions of the cardiovascular data on the interpretation of effects. We compared three template tasks involving varying types of challenge, in order to provide a case study of specific effects and combinations of effects over different time frames and using different time resolutions. Averaged values of hemodynamic variables across an entire protocol confirmed typical findings regarding the effects of mental challenge and social observation. However, the hemodynamic response also incorporates transient variations in variables reflecting important features of the control system response. The fine-grained analysis of the transient behavior of hemodynamic variables demonstrates that information that is important for interpreting effects may be lost when only average values over the entire protocol are used as a representative of the system response. The study provides useful indications of how cardiovascular measures may be fruitfully used in experiments involving cognitive demands, allowing inferences on the physiological processes underlying the responses.

Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia

This study develops a lumped cardiovascular-respiratory system-level model that incorporates patient-specific data to predict cardiorespiratory response to hypercapnia (increased CO(2) partial pressure) for a patient with congestive heart failure (CHF). In particular, the study focuses on predicting cerebral CO(2) reactivity, which can be defined as the ability of vessels in the cerebral vasculature to expand or contract in response CO(2) induced challenges. It is difficult to characterize cerebral CO(2) reactivity directly from measurements, since no methods exist to dynamically measure vasomotion of vessels in the cerebral vasculature. In this study we show how mathematical modeling can be combined with available data to predict cerebral CO(2) reactivity via dynamic predictions of cerebral vascular resistance, which can be directly related to vasomotion of vessels in the cerebral vasculature. To this end we have developed a coupled cardiovascular and respiratory model that predicts blood pressure, flow, and concentration of gasses (CO(2) and O(2)) in the systemic, cerebral, and pulmonary arteries and veins. Cerebral vascular resistance is incorporated via a model parameter separating cerebral arteries and veins. The model was adapted to a specific patient using parameter estimation combined with sensitivity analysis and subset selection. These techniques allowed estimation of cerebral vascular resistance along with other cardiovascular and respiratory parameters. Parameter estimation was carried out during eucapnia (breathing room air), first for the cardiovascular model and then for the respiratory model. Then, hypercapnia was introduced by increasing inspired CO(2) partial pressure. During eucapnia, seven cardiovascular parameters and four respiratory parameters was be identified and estimated, including cerebral and systemic resistance. During the transition from eucapnia to hypercapnia, the model predicted a drop in cerebral vascular resistance consistent with cerebral vasodilation.

Maximizing information from space data resources: a case for expanding integration across research disciplines

Regulatory systems are affected in space by exposure to weightlessness, high-energy radiation or other spaceflight-induced changes. The impact of spaceflight occurs across multiple scales and systems. Exploring such interactions and interdependencies via an integrative approach provides new opportunities for elucidating these complex responses. This paper argues the case for increased emphasis on integration, systematically archiving, and the coordination of past, present and future space and ground-based analogue experiments. We also discuss possible mechanisms for such integration across disciplines and missions. This article then introduces several discipline-specific reviews that show how such integration can be implemented. Areas explored include: adaptation of the central nervous system to space; cerebral autoregulation and weightlessness; modelling of the cardiovascular system in space exploration; human metabolic response to spaceflight; and exercise, artificial gravity, and physiologic countermeasures for spaceflight. In summary, spaceflight physiology research needs a conceptual framework that extends problem solving beyond disciplinary barriers. Administrative commitment and a high degree of cooperation among investigators are needed to further such a process. Well-designed interdisciplinary research can expand opportunities for broad interpretation of results across multiple physiological systems, which may have applications on Earth.

Teaching fluid shifts during orthostasis using a classic paper by Foux et al

Hypovolemic and orthostatic challenge can be simulated in humans by the application of lower body negative pressure (LBNP), because this perturbation leads to peripheral blood pooling and, consequently, central hypovolemia. The classic paper by Foux and colleagues clearly shows the effects of orthostasis simulated by LBNP on fluid shifts and homeostatic mechanisms. The carefully carried out experiments reported in this paper show the interplay between different physiological control systems to ensure blood pressure regulation, failure of which could lead to critical decreases in cerebral blood flow and syncope. Here, a teaching seminar for graduate students is described that is designed in the context of this paper and aimed at allowing students to learn how Foux and colleagues have advanced this field by addressing important aspects of blood regulation. This seminar is also designed to put their research into perspective by including important components of LBNP testing and protocols developed in subsequent research in the field. Learning about comprehensive protocols and carefully controlled studies can reduce confounding variables and allow for an optimal analysis and elucidation of the physiological responses that are being investigated. Finally, in collaboration with researchers in mathematical modeling, in the future, we will incorporate the concepts of applicable mathematical models into our curriculum.

Time delay in physiological systems: analyzing and modeling its impact

This article examines the functional and clinical impact of time delays that arise in human physiological systems, especially control systems. An overview of the mathematical and physiological contexts for considering time delays will be illustrated, from the system level to cell level, by examining models that incorporate time delays. This examination will highlight how such delays in combination with other system structures and parameters influence system dynamics. Model analysis that reveals the influence of delays can also reveal related physiological effects which may have medical consequences and clinical applications.

Modeling cardio-respiratory system response to inhaled CO2 in patients with congestive heart failure

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.

Modeling the cardiovascular-respiratory control system: data, model analysis, and parameter estimation

Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.

Aspects of control of the cardiovascular-respiratory system during orthostatic stress induced by lower body negative pressure

This paper considers a model developed to study the cardiovascular control system response to orthostatic stress as induced by two variations of lower body negative pressure (LBNP) experiments. This modeling approach has been previously applied to study control responses to transition from rest to aerobic exercise, to transition to non-REM sleep and to orthostatic stress as produced by the head up tilt (HUT) experiment. LBNP induces a blood volume shift because negative pressure changes the volume loading characteristics of the compartment which is subject to the negative pressure. This volume shift induces a fall in blood pressure which must be counteracted by a complicated control response involving a variety of mechanisms of the cardiovascular control system. There are a number of medical issues connected to these questions such as orthostatic intolerance in the elderly resulting in dizziness or fainting during the transition from sitting to standing. The model presented here is used to study the interaction of changes in systemic resistance, unstressed venous volume, venous compliance, heart rate, and contractility in the control of orthostatic stress. The overall short term response depends on a combination of these physiological reactions which may vary from individual to individual. There remain open questions about which factors have greater importance. The model simulations are compared to experimental data collected for LBNP exerted from the hips to feet and from ribs to feet.

A cardiovascular-respiratory control system model including state delay with application to congestive heart failure in humans

This paper considers a model of the human cardiovascular-respiratory control system with one and two transport delays in the state equations describing the respiratory system. The effectiveness of the control of the ventilation rate is influenced by such transport delays because blood gases must be transported a physical distance from the lungs to the sensory sites where these gases are measured. The short term cardiovascular control system does not involve such transport delays although delays do arise in other contexts such as the baroreflex loop (see [46]) for example. This baroreflex delay is not considered here. The interaction between heart rate, blood pressure, cardiac output, and blood vessel resistance is quite complex and given the limited knowledge available of this interaction, we will model the cardiovascular control mechanism via an optimal control derived from control theory. This control will be stabilizing and is a reasonable approach based on mathematical considerations as well as being further motivated by the observation that many physiologists cite optimization as a potential influence in the evolution of biological systems (see, e.g., Kenner [29] or Swan [62]). In this paper we adapt a model, previously considered (Timischl [63] and Timischl et al. [64]), to include the effects of one and two transport delays. We will first implement an optimal control for the combined cardiovascular-respiratory model with one state space delay. We will then consider the effects of a second delay in the state space by modeling the respiratory control via an empirical formula with delay while the the complex relationships in the cardiovascular control will still be modeled by optimal control. This second transport delay associated with the sensory system of the respiratory control plays an important role in respiratory stability. As an application of this model we will consider congestive heart failure where this transport delay is larger than normal and the transition from the quiet awake state to stage 4 (NREM) sleep. The model can be used to study the interaction between cardiovascular and respiratory function in various situations as well as to consider the influence of optimal function in physiological control system performance.

Stability of the human respiratory control system. I. Analysis of a two-dimensional delay state-space model

A number of mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system. Among them, periodic breathing (including Cheyne-Stokes respiration and apneustic breathing) is a collection of regular but involuntary breathing patterns that have important medical implications. The hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of Grodins et al. in the early 1950's [12]. The purpose of this paper is to study the stability characteristics of a feedback control system of five differential equations with delays in both the state and control variables presented by Khoo et al. [17] in 1991 for modeling human respiration. The paper is divided in two parts. Part I studies a simplified mathematical model of two nonlinear state equations modeling arterial partial pressures of O2 and CO2 and a peripheral controller. Analysis was done on this model to illuminate the effect of delay on the stability. It shows that delay dependent stability is affected by the controller gain, compartmental volumes and the manner in which changes in the ventilation rate is produced (i.e., by deeper breathing or faster breathing). In addition, numerical simulations were performed to validate analytical results. Part II extends the model in Part I to include both peripheral and central controllers. This, however, necessitates the introduction of a third state equation modeling CO2 levels in the brain. In addition to analytical studies on delay dependent stability, it shows that the decreased cardiac output (and hence increased delay) resulting from the congestive heart condition can induce instability at certain control gain levels. These analytical results were also confirmed by numerical simulations.

Stability of the human respiratory control system. II. Analysis of a three-dimensional delay state-space model

A number of mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system. Among them, periodic breathing (including Cheyne-Stokes respiration and apneustic breathing) is a collection of regular but involuntary breathing patterns that have important medical implications. The hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of Grodins et al. in the early 1950's [1]. The purpose of this paper is to study the stability characteristics of a feedback control system of five differential equations with delays in both the state and control variables presented by Khoo et al. [4] in 1991 for modeling human respiration. The paper is divided in two parts. Part I studies a simplified mathematical model of two nonlinear state equations modeling arterial partial pressures of O2 and CO2 and a peripheral controller. Analysis was done on this model to illuminate the effect of delay on the stability. It shows that delay dependent stability is affected by the controller gain, compartmental volumes and the manner in which changes in the ventilation rate is produced (i.e., by deeper breathing or faster breathing). In addition, numerical simulations were performed to validate analytical results. Part II extends the model in Part I to include both peripheral and central controllers. This, however, necessitates the introduction of a third state equation modeling CO2 levels in the brain. In addition to analytical studies on delay dependent stability, it shows that the decreased cardiac output (and hence increased delay) resulting from the congestive heart condition can induce instability at certain control gain levels. These analytical results were also confirmed by numerical simulations.