G. Gnudi

Identification of the three-element windkessel model incorporating a pressure-dependent compliance

A new one-step computational procedure is presented for estimating the parameters of the nonlinear three-element windkessel model of the arterial system incorporating a pressure-dependent compliance. The data required are pulsatile aortic pressure and flow. The basic assumptions are a steadystate periodic regime and a purely elastic compliant element. By stating two conditions, zero mean flow and zero mean power in the compliant element, peripheral and characteristic resistances are determined through simple closed form formulas as functions of mean values of the square of aortic pressure, the square of aortic flow, and the product of aortic pressure with aortic flow. The pressure across as well as the flow through the compliant element can be then obtained so allowing the calculation of volume variation and compliance as functions of pressure. The feasibility of this method is studied by applying it to both simulated and experimental data relative to different circulatory conditions and comparing the results with those obtained by an iterative parameter optimization algorithm and with the actual values when available. The conclusion is that the proposed method appears to be effective in identifying the three-element windkessel even in the case of nonlinear compliance.

A dynamic morphometric model of the normal lung for studying expiratory flow limitation in mechanical ventilation

A nonlinear dynamic morphometric model of breathing mechanics during artificial ventilation is described. On the basis of the Weibel symmetrical representation of the tracheobronchial tree, the model accurately accounts for the geometrical and mechanical characteristics of the conductive zone and packs the respiratory zone into a viscoelastic Voigt body. The model also accounts for the main mechanisms limiting expiratory flow (wave speed limitation and viscous flow limitation), in order to reproduce satisfactorily, under dynamic conditions, the expiratory flow limitation phenomenon occurring in normal subjects when the difference between alveolar pressure and tracheal pressure (driving pressure) is high. Several expirations characterized by different levels of driving pressure are simulated and expiratory flow limitation is detected by plotting the isovolume pressure–flow curves. The model is used to study the time course of resistance and total cross-sectional area as well as the ratio of fluid velocity to wave speed (speed index), in conductive airway generations. The results highlight that the coupling between dissipative pressure losses and airway compliance leads to onset of expiratory flow limitation in normal lungs when driving pressure is increased significantly by applying a subatmospheric pressure to the outlet of the ventilator expiratory channel; wave speed limitation becomes predominant at still higher driving pressures.

Helium-oxygen ventilation in the presence of expiratory flow-limitation: a model study.

A comparison between air and heliox (80% helium-20% oxygen) ventilation was performed using a mathematical, non-linear dynamic, morphometric model of the respiratory system. Different obstructive conditions, all causing expiratory flow limitation (EFL), were simulated during mechanical ventilation to evaluate and interpret the effects of heliox on tidal EFL and dynamic hyperinflation. Relative to air ventilation, intrinsic positive end-expiratory pressure did not change with heliox if the obstruction was limited to the peripheral airways, i.e. beyond the seventh generation. When central airways were also involved, heliox reduced dynamic hyperinflation (DH) if the flow-limiting segment remained in the fourth to seventh airway generation during the whole expiration, but produced only minor effects if, depending on the contribution of peripheral to total apparent airway resistance, the flow-limiting segment moved eventually to the peripheral airways. In no case did heliox abolish EFL occurring with air ventilation, indicating that any increase in driving pressure would be without effect on DH. Hence, to the extent that chronic obstructive pulmonary disease (COPD) affects primarily the peripheral airways, and causes EFL through the same mechanisms operating in the model, heliox administration should not be expected to appreciably reduce DH in the majority of COPD patients who are flow-limited at rest.

Role of the mechanical properties of tracheobronchial airways in determining the respiratory resistance time course.

AbstractA physiologically based simulation model of breathing mechanics was considered in an attempt to interpret and explain the time course of input respiratory resistance during the breathing cycle, observed in recent studies on ventilated patients. The model assumes a flow-dependent Rohrer resistance for the upper extrathoracic airways and volume-dependent resistance and elastance for the intermediate airways. A volume-dependent resistance describes the dissipative pressure loss in the lower airways, and two constant elastances represent lung and chest wall elasticity. Simulated mouth flow and pressure signals obtained in a variety of well-controlled conditions were used to analyze total respiratory resistance and elastance estimated by an on-line algorithm based on a time-varying parameter model. These estimates were compared with those provided by classical estimation algorithms based on time-invariant models with two, three, and four parameters. The results show that the four-parameter model is difficult to identify, while the three-parameter one offers no substantial advantage for estimating input resistance with respect to the more simple two-parameter model. In contrast, the time-varying approach provides good on-line estimates of the simulated end-expiration and end-inspiration resistances. These values provide further information of potential clinical utility, with respect to time-invariant models. For example, the results show that the difference between the end-expiration and end-inspiration resistance increases when obstructions shift from the upper to the lower airways. The similarity of the results obtained with measured and simulated data indicates that, in spite of its simplicity, the simulation model describes important physiological mechanisms underlying changes in respiratory input resistance, specifically the mechanical properties of intermediate airways.

Variable selection for the classification of postoperative cardiac patients

A set of 13 extensively used hemodynamic, ventilatory and gas analysis variables are measured (on-line or off-line) on 200 patients in an intensive care unit (ICU) during the 6 h immediately following cardiac surgery. Since the existence of two well-separated classes of low- and high-risk patients has been previously shown the divergence criterion is then used to identify those variables which, at three equidistant observation times, possess the greatest separation power. Such variables always include the cardiac index (CI), representative of cardiac performance, and two indices related to respiratory efficiency and metabolic rate, i.e. the carbon dioxide production index (VCO2I) and the arterio-venous oxygen difference (avO2D). The Fisher linear classifier, utilizing these three features, is then tested by using the rotation method. The results show good performance of the linear classifier, which exhibits a probability of correct recognition always greater than 87%, thus suggesting the possibility of obtaining interesting improvements by means of more sophisticated classifiers.

unsupervised learning and discriminant analysis applied to identification of high risk postoperative cardiac patients

A set of 200 patients in the 6 hours immediately following cardiac surgery was analysed within a multidimensional space of 13 commonly monitored physiological variables in order to identify high risk patterns. The application of an unsupervised learning (clustering) method to these data clearly showed the existence of two well-separated classes of low and high risk patients. A stepwise discriminant analysis was then applied to patients representative of the two classes in order to find those variables which, over time, possessed the greatest separation power. The latter always included the oxygen delivery (DO2), an index related to the oxygen content in the blood (Pv(-)O2 or avO2D) and a myocardial contractility index (VF or LAP).

Automatic detection of maximal oxygen uptake and ventilatory threshold

Maximal oxygen uptake (VO(2max)) and ventilatory threshold (VT) are the most common measurements in exercise physiology laboratories for the objective characterization of the physiologic state of metabolic and respiratory systems. Several techniques for their identification were proposed in the literature: the aim of the present study was to review them and assess their performance when applied to experimental data. In the present study, the criteria to detect VO(2max) and VT from respiratory gas-exchange data were analysed and automatic procedures for the identification of these parameters were implemented. These procedures were then applied to experimental data in order to assess the verifiability, repeatability and sensitivity to measurement noise of each proposed method. The results suggest plateau- and RISE-105- as the most reliable automatic procedures for determining VO(2max), while respiratory exchange ratio-, ventilatory equivalent for O(2)- and P(ET,O2)-criteria appear to be the most reliable automatic procedures for estimating VT.

An EMG-driven model applied for predicting metabolic energy consumption during movement.

The relationship between mechanical work and metabolic energy cost during movement is not yet clear. Many studies demonstrated the utility of forward-dynamic musculoskeletal models combined with experimental data to address such question. The aim of this study was to evaluate the applicability of a muscle energy expenditure model at whole body level, using an EMG-driven approach. Four participants performed a 5-min squat exercise on unilateral leg press at two different frequencies and two load levels. Data collected were kinematics, EMG, forces and moments under the foot and gas-exchange data. This same task was simulated using a musculoskeletal model, which took EMG and kinematics as inputs and gave muscle forces and muscle energetics as outputs. Model parameters were taken from literature, but maximal isometric muscle force was optimized in order to match predicted joint moments with measured ones. Energy rates predicted by the model were compared with energy consumption measured by the gas-exchange data. Model results on metabolic energy consumption were close to the values obtained through indirect calorimetry. At the higher frequency level, the model underestimated measured energy consumption. This underestimation can be explained with an increase in energy consumption of the non-muscular mass with movement velocity. In conclusion, results obtained in comparing model predictions with experimental data were promising. More research is needed to evaluate this way of computing mechanical and metabolic work.

A simulation study of expiratory flow limitation in obstructive patients during mechanical ventilation.

Although normal lungs may be represented satisfactorily by symmetrical architecture, pathological conditions generally require accounting for asymmetrical branching of the bronchial tree, since lung heterogeneity may be significant in respiratory diseases. In the present study, a recently proposed symmetrical dynamic morphometric model of the human lung, based on Weibel’s regular dichotomy, was adapted to simulate different physiopathological scenarios of lung heterogeneity. The asymmetrical architecture was mimicked by modeling different conductive airway compartments below the main bronchi, each compartment being characterized by regular branching. The respiratory zone and chest wall were described by a Voigt body and a constant elastance, respectively.Simulation results allowed us to investigate the influence of the main mechanisms involved in expiratory flow limitation and dynamic hyperinflation in mechanically ventilated COPD patients. In brief, they showed that convective gas acceleration plays a key role in reproducing a negative relationship between driving pressure and expiratory flow. Moreover, reduced lung elastance due to emphysema resulted in a remarkable increase in dynamic hyperinflation, although it did not significantly modify expiratory flow limitation. Finally, the presence of a normal lung compartment masked pathological behaviors, preventing standard techniques from revealing expiratory flow limitation in affected compartments.

Effect of compliant intermediate airways on total respiratory resistance and elastance in mechanical ventilation

Total respiratory resistance and elastance were estimated off-line in a sample of 60 patients undergoing mechanical ventilation by means of two regression models in order to analyse and understand a possible physiological mechanism determining differences in inspiration and expiration. The first model considered a single value for resistance and elastance over a whole breathing cycle, whereas the second model considered separate values for inspiratory and expiratory resistance and a single value for elastance. Inspiratory resistance was found to be lower than expiratory resistance, and intermediate values were obtained for resistance estimated over the whole breathing cycle. Students t-test showed a highly significant difference between these resistance estimates, and principal components analysis demonstrated a significant increase in information when both inspiratory and expiratory resistances were used. Minor differences were found between values of elastance calculated with the two approaches. In an attempt to interpret these experimental results, a lung model incorporating the non-linear viscoelastic properties of the intermediate airways was considered. This model suggested that changes in intermediate airway volume play a significant role in breathing mechanics during artificial ventilation and indicated that inspiratory and expiratory resistance could be useful parameters for locating airway obstruction.