Six methods to determine expiratory time constants in mechanically ventilated patients: a prospective observational physiology study.

BACKGROUND: Expiratory time constant (τ) objectively assesses the speed of exhalation and can guide adjustments of the respiratory rate and the I:E ratio with the goal of achieving complete exhalation. Multiple methods of obtaining τ are available, but they have not been compared. The purpose of this study was to compare six different methods to obtain τ and to test if the exponentially decaying flow corresponds to the measured time constants. METHODS: In this prospective study, pressure, flow, and volume waveforms of 30 postoperative patients undergoing volume (VCV) and pressure-controlled ventilation (PCV) were obtained using a data acquisition device and analyzed. τ was measured as the first 63% of the exhaled tidal volume (VT) and compared to the calculated τ as the product of expiratory resistance (RE) and respiratory system compliance (CRS), or τ derived from passive flow/volume waveforms using previously published equations as proposed by Aerts, Brunner, Guttmann, and Lourens. We tested if the duration of exponentially decaying flow during exhalation corresponded to the duration of the predicted second and third τ, based on multiples of the first measured τ. RESULTS: Mean (95% CI) measured τ was 0.59 (0.57-0.62) s and 0.60 (0.58-0.63) s for PCV and VCV (p = 0.45), respectively. Aerts method showed the shortest values of all methods for both modes: 0.57 (0.54-0.59) s for PCV and 0.58 (0.55-0.61) s for VCV. Calculated (CRS * RE) and Brunner's τ were identical with mean τ of 0.64 (0.61-0.67) s for PCV and 0.66 (0.63-069) s for VCV. Mean Guttmann's τ was 0.64 (0.61-0.68) in PCV and 0.65 (0.62-0.69) in VCV. Comparison of each τ method between PCV and VCV was not significant. Predicted time to exhale 95% of the VT (i.e., 3*τ) was 1.77 (1.70-1.84) s for PCV and 1.80 (1.73-1.88) s for VCV, which was significantly longer than measured values: 1.27 (1.22-1.32) for PCV and 1.30 (1.25-1.35) s for VCV (p < 0.0001). The first, the second and the third measured τ were progressively shorter: 0.6, 0.4 and 0.3 s, in both ventilation modes (p < 0.0001). CONCLUSION: All six methods to determine τ show similar values and are feasible in postoperative mechanically ventilated patients in both PCV and VCV modes.

Modeling the Steady-State Effects of Mean Arterial Pressure on the Kidneys.

Goal: We describe the relationship between mean arterial pressure (MAP) and glomerular filtration rate (GFR) since therapies affecting MAP can have large effects on kidney function. Methods: We developed a closed-loop, steady-state mechanistic model of the human kidney with a reduced parameter set estimated from measurements. Results: The model was first validated against literature models. Further, GFR was validated against intensive care patient data (root mean squared error (RMSE) 13.5 mL/min) and against hypertensive patients receiving sodium nitroprusside (SNP) (RMSE less than 5 mL/min). A sensitivity analysis of the model reinforced the fact that vascular resistance is inversely related to GFR and showed that changes to either vascular resistance or renal autoregulation cause a significant change in sodium concentration in the descending limb of Henle. Conclusions: This model can be used to determine the impact of MAP on GFR and overall kidney health. The modeling framework lends itself to personalization of the model to a specific human.

Alveolar Tissue Fiber and Surfactant Effects on Lung Mechanics-Model Development and Validation on ARDS and IPF Patients.

Goal: Alveolar compliance is a main determinant of lung airflow. The compliance of the alveoli is a function of their tissue fiber elasticity, fiber volume, and surface tension. The compliance varies during respiration because of the nonlinear nature of fiber elasticity and the time-varying surface tension coating the alveoli. Respiratory conditions, like acute respiratory distress syndrome (ARDS) and idiopathic pulmonary fibrosis (IPF) affect fiber elasticity, fiber volume and surface tension. In this paper, we study the alveolar tissue fibers and surface tension effects on lung mechanics. Methods: To better understand the lungs, we developed a physiology-based mathematical model to 1) describe the effect of tissue fiber elasticity, fiber volume and surface tension on alveolar compliance, and 2) the effect of time-varying alveolar compliance on lung mechanics for healthy, ARDS and IPF conditions. Results: We first present the model sensitivity analysis to show the effects of model parameters on the lung mechanics variables. Then, we perform model simulation and validate on healthy non-ventilated subjects and ventilated ARDS or IPF patients. Finally, we assess the robustness and stability of this dynamic system. Conclusions: We developed a mathematical model of the lung mechanics comprising alveolar tissue and surfactant properties that generates reasonable lung pressures and volumes compared to healthy, ARDS, and IPF patient data.

Heart-Lung Interactions During Mechanical Ventilation: Analysis via a Cardiopulmonary Simulation Model.

Heart-lung interaction mechanisms are generally not well understood. Mechanical ventilation, for example, accentuates such interactions and could compromise cardiac activity. Thereby, assessment of ventilation-induced changes in cardiac function is considered an unmet clinical need. We believe that mathematical models of the human cardiopulmonary system can provide invaluable insights into such cardiorespiratory interactions. In this article, we aim to use a mathematical model to explain heart-lung interaction phenomena and provide physiologic hypotheses to certain contradictory experimental observations during mechanical ventilation. To accomplish this task, we highlight three model components that play a crucial role in heart-lung interactions: 1) pericardial membrane, 2) interventricular septum, and 3) pulmonary circulation that enables pulmonary capillary compression due to lung inflation. Evaluation of the model's response under simulated ventilation scenarios shows good agreement with experimental data from the literature. A sensitivity analysis is also presented to evaluate the relative impact of the model's highlighted components on the cyclic ventilation-induced changes in cardiac function.

Modeling of Transport Mechanisms in the Respiratory System: Validation via Congestive Heart Failure Patients.

The heart and lungs are intricately related. For congestive heart failure patients, fluid (plasma) backs up into the pulmonary system. As a result, pulmonary capillary pressure increases, causing fluid to seep into the lungs (pulmonary edema) within minutes. This excess fluid induces extra stress during breathing that affects respiratory health. In this paper, we focus on the effect that high pulmonary capillary pressure has on the development of this extravascular lung water (EVLW). A mathematical model of pulmonary fluid and mass transport mechanisms is developed in order to quantitatively analyze the transport phenomena in the pulmonary system. The model is then validated on 15 male heart failure patients from published literature [1]. The model shows reasonable estimation of EVLW in heart failure patients, which is useful in assessing the severity of pulmonary edema.

Effects of septum and pericardium on heart-lung interactions in a cardiopulmonary simulation model.

Mechanical heart-lung interactions are often overlooked in clinical settings. However, their impact on cardiac function can be quite significant. Mechanistic physiology-based models can provide invaluable insights into such cardiorespiratory interactions, which occur not only under external mechanical ventilatory support but in normal physiology as well. In this work, we focus on the cardiac component of a previously developed mathematical model of the human cardiopulmonary system, aiming to improve the model's response to the intrathoracic pressure variations that are associated with the respiratory cycle. Interventricular septum and pericardial membrane are integrated into the existing model. Their effect on the overall cardiac response is explained by means of comparison against simulation results from the original model as well as experimental data from literature.

An integrated mathematical model of the human cardiopulmonary system: model validation under hypercapnia and hypoxia.

A novel integrated physiological model of the interactions between the cardiovascular and respiratory systems has been in development for the past few years. The model has hundreds of parameters and variables representing the physical and physiological properties of the human cardiopulmonary system. It can simulate many dynamic states and scenarios. The description of the model and the results in normal resting conditions were presented in a companion paper (Albanese A, Cheng L, Ursino M, Chbat NW.Am J Physiol Heart Circ Physiol 310: 2016; doi:10.1152/ajpheart.00230.2014), where model predictions were compared against average population data from literature. However, it is also essential to test the model in abnormal or pathological conditions to prove its consistency. Hence, in this paper, we concentrate on testing the cardiopulmonary model under hypercapnic and hypoxic conditions, by comparing model's outputs to population-averaged cardiorespiratory data reported in the literature. The utility of this comprehensive model is demonstrated by testing the internal consistency of the simulated responses of a significant number of cardiovascular variables (heart rate, arterial pressure, and cardiac output) and respiratory variables (tidal volume, respiratory rate, minute ventilation, alveolar O2 and CO2 partial pressures) over a wide range of perturbations and conditions; namely, hypercapnia at 3-7% CO2 levels and hypoxia at 7-9% O2 levels with controlled CO2(isocapnic hypoxia) and without controlled CO2(hypocapnic hypoxia). Finally, a sensitivity analysis is performed to analyze the role of the main cardiorespiratory control mechanisms triggered by hypercapnia and hypoxia.

Patient emulator: a tool for testing mechanical ventilation therapies.

Several modes of mechanical ventilation are clinically available. The differences among them in terms of efficacy and patient outcomes are not clear yet. Testing and comparison of mechanical ventilation modes via human or animal trials is a very challenging and costly process. In this paper, we present the patient emulator (PE), a novel system that can be used as a platform for in-silico testing of mechanical ventilation therapies. The system is based on a large-scale integrated mathematical model of the human cardiopulmonary system interfaced with a physical ventilator via a controlled piston-cylinder actuator. The performance of the proposed PE is demonstrated by simulating a realistic pressure support ventilation step protocol. The PE-simulated patient's response is then compared against averaged data from 33 human subjects. The agreement between the simulated data and their experimental counterparts shows the potential of the proposed PE to be used as a substitute for or in addition to conventional animal and human trials.

Noninvasive estimation of alveolar pressure.

This paper presents an algorithm for noninvasive estimation of alveolar pressure in mechanically ventilated patients who are spontaneously breathing. Continual monitoring of alveolar pressure is desirable to prevent ventilator-induced lung injury and to assess the intrinsic positive end-expiratory pressure (PEEPi), which is a parameter of clinical relevance in respiratory care and difficult to measure noninvasively. The algorithm is based on a physiological model of the respiratory system and, as such, it also provides insight into the respiratory mechanics of the patient under mechanical ventilation. In particular, the algorithm allows one to correctly estimate other clinical parameters of interest such as the patient's respiratory resistance and elastance, even in the presence of PEEPi.

Noninvasive Estimation of Respiratory Mechanics in Spontaneously Breathing Ventilated Patients: A Constrained Optimization Approach.

This paper presents a method for breath-by-breath noninvasive estimation of respiratory resistance and elastance in mechanically ventilated patients. For passive patients, well-established approaches exist. However, when patients are breathing spontaneously, taking into account the diaphragmatic effort in the estimation process is still an open challenge. Mechanical ventilators require maneuvers to obtain reliable estimates for respiratory mechanics parameters. Such maneuvers interfere with the desired ventilation pattern to be delivered to the patient. Alternatively, invasive procedures are needed. The method presented in this paper is a noninvasive way requiring only measurements of airway pressure and flow that are routinely available for ventilated patients. It is based on a first-order single-compartment model of the respiratory system, from which a cost function is constructed as the sum of squared errors between model-based airway pressure predictions and actual measurements. Physiological considerations are translated into mathematical constraints that restrict the space of feasible solutions and make the resulting optimization problem strictly convex. Existing quadratic programming techniques are used to efficiently find the minimizing solution, which yields an estimate of the respiratory system resistance and elastance. The method is illustrated via numerical examples and experimental data from animal tests. Results show that taking into account the patient effort consistently improves the estimation of respiratory mechanics. The method is suitable for real-time patient monitoring, providing clinicians with noninvasive measurements that could be used for diagnosis and therapy optimization.

An integrated mathematical model of the human cardiopulmonary system: model development.

Several cardiovascular and pulmonary models have been proposed in the last few decades. However, very few have addressed the interactions between these two systems. Our group has developed an integrated cardiopulmonary model (CP Model) that mathematically describes the interactions between the cardiovascular and respiratory systems, along with their main short-term control mechanisms. The model has been compared with human and animal data taken from published literature. Due to the volume of the work, the paper is divided in two parts. The present paper is on model development and normophysiology, whereas the second is on the model's validation on hypoxic and hypercapnic conditions. The CP Model incorporates cardiovascular circulation, respiratory mechanics, tissue and alveolar gas exchange, as well as short-term neural control mechanisms acting on both the cardiovascular and the respiratory functions. The model is able to simulate physiological variables typically observed in adult humans under normal and pathological conditions and to explain the underlying mechanisms and dynamics.

Cardiovascular system identification: Simulation study using arterial and central venous pressures.

The paper presents a study of the identifiability of a lumped model of the cardiovascular system. The significance of this work from the existing literature is in the potential advantage of using both arterial and central venous (CVP) pressures, two signals that are frequently monitored in the critical care unit. The analysis is done on the system's state-space representation via control theory and system identification techniques. Non-parametric state-space identification is preferred over other identification techniques as it optimally assesses the order of a model, which best describes the input-output data, without any prior knowledge about the system. In particular, a recent system identification algorithm, namely Observer Kalman Filter Identification with Deterministic Projection, is used to identify a simplified version of an existing cardiopulmonary model. The outcome of the study highlights the following two facts. In the deterministic (noiseless) case, the theoretical indicators report that the model is fully identifiable, whereas the stochastic case reveals the difficulty in determining the complete system's dynamics. This suggests that even with the use of CVP as an additional pressure signal, the identification of a more detailed (high order) model of the circulatory system remains a challenging task.

Constrained optimization for noninvasive estimation of work of breathing.

This paper presents a technique for noninvasive estimation of respiratory muscle effort (also known as work of breathing, WOB) in mechanically ventilated patients. Continual and real-time assessment of the patient WOB is desirable, as it helps the clinician make decisions about increasing or decreasing mechanical respiratory support. The technique presented is based on a physiological model of the respiratory system, from which a cost function is constructed as the sum of squared errors between model-based airway pressure predictions and actual measurements. Quadratic programming methods are used to minimize this cost function. An experimental example on animal data shows the effectiveness of the technique.

Cardiorespiratory adaptation to breath-holding in air: Analysis via a cardiopulmonary simulation model.

Apnea via breath-holding (BH) in air induces cardiorespiratory adaptation that involves the activation of several reflex mechanisms and their complex interactions. Hence, the effects of BH in air on cardiorespiratory function can become hardly predictable and difficult to be interpreted. Particularly, the effect on heart rate is not yet completely understood because of the contradicting results of different physiological studies. In this paper we apply our previously developed cardiopulmonary model (CP Model) to a scenario of BH with a twofold intent: (1) further validating the CP Model via comparison against experimental data; (2) gaining insights into the physiological reasoning for such contradicting experimental results. Model predictions agreed with published experimental animal and human data and indicated that heart rate increases during BH in air. Changes in the balance between sympathetic and vagal effects on heart rate within the model proved to be effective in inverting directions of the heart rate changes during BH. Hence, the model suggests that intra-subject differences in such sympatho-vagal balance may be one of the reasons for the contradicting experimental results.

Real-time noninvasive estimation of intrapleural pressure in mechanically ventilated patients: a feasibility study.

A method for real-time noninvasive estimation of intrapleural pressure in mechanically ventilated patients is proposed. The method employs a simple first-order lung mechanics model that is fitted in real-time to flow and pressure signals acquired non-invasively at the opening of the patient airways, in order to estimate lung resistance (RL), lung compliance (CL) and intrapleural pressure (Ppl) continuously in time. Estimation is achieved by minimizing the sum of squared residuals between measured and model predicted airway pressure using a modified Recursive Least Squares (RLS) approach. Particularly, two different RLS algorithms, namely the conventional RLS with Exponential Forgetting (EF-RLS) and the RLS with Vector-type Forgetting Factor (VFF-RLS), are considered in this study and their performances are first evaluated using simulated data. Simulations suggest that the conventional EF-RLS algorithm is not suitable for our purposes, whereas the VFF-RLS method provides satisfactory results. The potential of the VFF-RLS based method is then proved on experimental data collected from a mechanically ventilated pig. Results show that the method provides continuous estimated lung resistance and compliance in normal physiological ranges and pleural pressure in good agreement with invasive esophageal pressure measurements.

Systems modeling and simulation applications for critical care medicine.

Critical care delivery is a complex, expensive, error prone, medical specialty and remains the focal point of major improvement efforts in healthcare delivery. Various modeling and simulation techniques offer unique opportunities to better understand the interactions between clinical physiology and care delivery. The novel insights gained from the systems perspective can then be used to develop and test new treatment strategies and make critical care delivery more efficient and effective. However, modeling and simulation applications in critical care remain underutilized. This article provides an overview of major computer-based simulation techniques as applied to critical care medicine. We provide three application examples of different simulation techniques, including a) pathophysiological model of acute lung injury, b) process modeling of critical care delivery, and c) an agent-based model to study interaction between pathophysiology and healthcare delivery. Finally, we identify certain challenges to, and opportunities for, future research in the area.

Clinical knowledge-based inference model for early detection of acute lung injury.

Acute lung injury (ALI) is a devastating complication of acute illness and one of the leading causes of multiple organ failure and mortality in the intensive care unit (ICU). The detection of this syndrome is limited due to the complexity of the disease, insufficient understanding of its development and progression, and the large amount of risk factors and modifiers. In this preliminary study, we present a novel mathematical model for ALI detection. It is constructed based on clinical and research knowledge using three complementary techniques: rule-based fuzzy inference systems, Bayesian networks, and finite state machines. The model is developed in Matlab(®)'s Simulink environment and takes as input pre-ICU and ICU data feeds of critically ill patients. Results of the simulation model were validated against actual patient data from an epidemiologic study. By appropriately combining all three techniques the performance attained is in the range of 71.7-92.6% sensitivity and 60.3-78.4% specificity.

A comprehensive cardiopulmonary simulation model for the analysis of hypercapnic respiratory failure.

We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions.

Bayesian tracking of a nonlinear model of the capnogram.

Capnography, the monitoring of expired carbon dioxide (CO2) has been employed clinically as a non-invasive measure for the adequacy of ventilation of the alveoli of the lung. In combination with air flow measurements, the capnogram can be used to estimate the partial pressure of CO2 in the alveolar sacs. In addition, physiologically relevant parameters, such as the extent of CO2 rebreathing, the airway dead space, and the metabolic CO2 production can be predicted. To calculate these parameters, mathematical models have been previously formulated and applied to experimental data using off-line optimization procedures. Unfortunately, this does not permit online identification of the capnogram to detect changes in the physiological model parameters. In the present study, a Bayesian method for breath-by-breath identification of the volumetric capnogram is presented. The method integrates a model of CO2 exchange in the lungs, which is nonlinear due to the nature of human tidal breathing, with a particle filtering algorithm for estimation of the model parameters and changes therein. In addition, this allowed for a dynamic prediction of the unmeasured alveolar CO2 tension. The method is demonstrated using simulations of the capnogram. The proposed method could aid the clinician in the interpretation of the capnogram.