Physiological interpretations based on lumped element models fit torespiratory impedance data: use of forward-inverse modeling

Respiratory impedance (Zrs) data at lower (less than 4 Hz) and higher (greater than 32 Hz) frequencies require more complicated inverse models than the standard series combination of a respiratory resistance, inertance, and compliance. In this paper, a forward-inverse modeling approach was used to provide insight on how the parameters in these more complicated inverse models reflect the true physiological system. Forward models are set up to incorporate explicit physiological and anatomical detail. Simulated forward data are then fit with identifiable inverse models and the parameter estimates related to the known detail in the forward model. It is shown that inverse fitting of low frequency data alone will not allow a distinction between frequency dependence due to airway inhomogeneities and frequency dependence due to tissue viscoelasticity. With higher frequency data, a forward model based on an asymmetric branching airways network was used to simulate Zrs from 0.1-128 Hz with increasing amounts of nonuniform peripheral airway obstruction. Here, inverse modeling is more amenable to sensibly separating estimates of airway and tissue properties. A key result, however, is that changes in the tissue parameters of an inverse model (which provides an excellent fit to Zrs data) will appropriately occur in response to inhomogeneous alterations in airway diameters only. The apparent altered tissue properties reflect the decreased communication of some tissue segments with the airway opening and not an explicit change at the tissue level. These phenomena present a substantial problem for the inverse modeler. Finally, inverse model fitting of low and high frequency Zrs data simultaneously with a single model is not helpful for extracting additional physiological detail. Instead, separate models should be applied to each frequency range.     

Simulation of lung function evolution after heart-lung transplantation using a numerical model

A morphometry-based computational model for expiratory flow in humans was used to study the unusual configuration of the maximum expiratory flow-volume (MEFV) curve associated with alterations in lung function after heart-lung transplantation (HLT). The postoperative MEFV curve showed a peak, followed by a gently sloping plateau over the midvolume range, ending in a knee where the flow suddenly fell, instead of the usual observed uniform decrease in expiratory flow. We have tested several hypotheses about the relationship between the pattern of changes in the configuration of the MEFV curve and pathological changes in the airway mechanics through computer simulations. Principally, effects of lung denervation and airway obstruction, associated with the development of bronchiolitis obliterans in the lung periphery, have been investigated. The calculated curves are similar in appearance to the measured postoperative flow-volume curves and confirm reliability of the earlier hypotheses. We conclude that the plateau-knee configuration of the MEFV curve can result from flow limitation in one of the first airway generations, that this flow limitation coupled with an increase in peripheral airway resistance results in plateau shortening, and that flows exceeding predicted values during the second part of expiration may be produced by lung denervation. Additionally our results demonstrate that airways larger than the transitional and respiratory bronchioles can be involved in pulmonary function deterioration observed in patients affected with obliterative bronchiolitis. Our findings indicate that the computational model, based on a symmetrical dichotomous branching structure of the bronchial tree, along with pathological data, can be employed to evaluate the effects of heterogeneous changes in the lung periphery. Index Terms-Airway mechanics, forced expiration, lung transplantation, mathematical modeling, maximal expiratory flow-volume curve.     

Parameter Estipiates in a Five-Element Respiratory Mechanical Model

Using four sets of forced random noise impedance data from each of five normal subjects and five patients with obstructuve lung disease, we computed parameter estimates for a three-element series model and a five-element parallel compartment model. For normal subjects, the five-element model provided no better fit to the impedance data than did the simple series model. Estimates obtained from normal subjects using this three-element model were reasonable and reproducible within 25 percent. For all subjects with lung disease, the five-element model provided a significantly (p 0.05) better fit than the three-element model. Estimates for parameters representing central inertance and resistance, airway compliance, and peripheral resistance were reasonable and reproducible-within 18 percent. However, estimates for the compliance of the lung and chest wall were more variable since measured impedance appeared to be insensitive to this parameter in the frequency range used.     

Analog Computer Simulation of Maximum Expiratory Flow Limitation

This paper extends previous modeling work in our laboratory on the simulation of the panting maneuver executed in a body plethysmograph [8] to the simulation of a wider range of pulmonary function tests and, in particular, the maximum expiratory flow-volume (MEFV) curve. The simulation is implemented on an analog computer for ease of parameter manipulation; the effects of changes in several model parameters (such as large and small airway resistance, and airway and lung compliance) on the MEFV curve are discussed. The model structure presented here is much simpler than the ventilatory system models of Fry [6] and Pardaens et al. [18], and yet yields the same information in a diagnostic sense.     

Mathematical Modeling of Pulmonary Airway Dynamics

A mathematical model has been derived that describes the pressure-flow relationship in the ventilatory system under conditions of constant lung volume. The parameters of the model include small airway resistance, large airway resistance, and lung elastic recoil. A collapsible airway segment is included to model compression of the airways during expiration.     

Estimation of Mechanical Parameters in Multicompartment Models Applied to Normal and Obstructed Lungs During Tidal Breathing

A technique is presented which allows quantitative assessment of the use of parallel compartment models for characterizing pulmonary mechanical function during tidal breathing. A model consisting of a conducting airway leading to two parallel parenchymal regions is used. Numerical simulation and sensitivity analysis indicated that a) the compliance of the conducting airway was not significant under the experimental conditions of interest and that b) estimates of the distribution of central and peripheral resistances would not be precise. The techniques were demonstrated using measurements of transpulmonary pressure, flow, and volume changes during tidal breathing obtained from a human subject with normal lungs and a human subject with obstructed lungs. Optimal estimates of the parameters were obtained by minimizing the difference between the model output and experimental data combined from two breathing frequencies. In the estimation procedure, the sum of the peripheral compliances was constrained to equal the independently measured static lung compliance. This constraint was critical for correct evaluation of nonuniform mechanical lung function. From the parameter estimates, the ratio of parenchymal time constants was about five in the subject with normal lungs and 60 in the subject with obstructed lungs. These results suggest that a full study with several normal and obstructed lung subjects is warranted.     

Assessment of Changes in Upper Airway Obstruction by Automatic Identification of Inspiratory Flow Limitation During Sleep

New techniques for automatic invasive and noninvasive identification of inspiratory flow limitation (IFL) are presented. Data were collected from 11 patients with full nocturnal polysomnography and gold-standard esophageal pressure (Pes) measurement. A total of 38,782 breaths were extracted and automatically analyzed. An exponential model is proposed to reproduce the relationship between Pes and airflow of an inspiration and achieve an objective assessment of changes in upper airway obstruction. The characterization performance of the model is appraised with three evaluation parameters: mean-squared error when estimating resistance at peak pressure, coefficient of determination, and assessment of IFL episodes. The model's results are compared to the two best-performing models in the literature. The obtained gold-standard IFL annotations were then employed to train, test, and validate a new noninvasive automatic IFL classification system. Discriminant analysis, support vector machines, and Adaboost algorithms were employed to objectively classify breaths noninvasively with features extracted from the time and frequency domains of the breathspsila flow patterns. The results indicated that the exponential model characterizes IFL and subtle relative changes in upper airway obstruction with the highest accuracy and objectivity. The new noninvasive automatic classification system also succeeded in identifying IFL episodes, achieving a sensitivity of 0.87 and a specificity of 0.85.     

Measurement of fractional order model parameters of respiratory mechanical impedance in total liquid ventilation

This study presents a methodology for applying the forced-oscillation technique in total liquid ventilation. It mainly consists of applying sinusoidal volumetric excitation to the respiratory system, and determining the transfer function between the delivered flow rate and resulting airway pressure. The investigated frequency range was f ∈ [0.05, 4] Hz at a constant flow amplitude of 7.5 mL/s. The five parameters of a fractional order lung model, the existing "5-parameter constant-phase model," were identified based on measured impedance spectra. The identification method was validated in silico on computer-generated datasets and the overall process was validated in vitro on a simplified single-compartment mechanical lung model. In vivo data on ten newborn lambs suggested the appropriateness of a fractional-order compliance term to the mechanical impedance to describe the low-frequency behavior of the lung, but did not demonstrate the relevance of a fractional-order inertance term. Typical respiratory system frequency response is presented together with statistical data of the measured in vivo impedance model parameters. This information will be useful for both the design of a robust pressure controller for total liquid ventilators and the monitoring of the patient's respiratory parameters during total liquid ventilation treatment.     

Contribution à la modélisation de lignes hyperfréquences supraconductrices à haute température critique par la méthode FDTD

The purpose of this study is to determine the electrical behaviour of high-Tc superconductor microstrip lines. TheFdtd method is used to put into discrete terms Maxwell’s equations. The two-fluid model has been chosen to describe the behaviour of the superconductor. The variation of electrical parameters such as surface resistance as a function of frequency up to 60 GHz is presented.     

Estimating lung mechanics of dogs with unilateral lung injury

Extended least-squares algorithms using transpulmonary pressure and airway flow data from ventilatory waveforms were studied for their ability to track parameters of one- and two-compartment models of lung mechanics. A recursive extended least-squares algorithm with discounted measures estimated parameters of discrete-time models during synchronized intermittent mandatory ventilation. In tests on seven dogs developing oleic acid-induced unilateral hemorrhagic pulmonary edema, the one-compartment estimator responded rapidly and appropriately to changes in mechanics: compliance fell to 0.55 +/- 0.15 of its initial value and resistance rose by a factor of 1.8 +/- 0.5 in 3 h following injection of oleic acid. One-compartment parameter estimates revealed a difference between the airway resistance of inspiration and expiration. Two-compartment estimates were seldom physiologically plausible. The difference between inspiratory and expiratory resistance may have caused the two-compartment estimator to fail when applied to data from the entire respiratory cycle; when only expiratory data were used for estimation, the two-compartment estimates were meaningful. These estimates demonstrated increasing lung inhomogeneity after oleic acid was injected; at the end of 3 h, the ratio of the time constants of the two compartments ranged from 5 to 20 in six of the seven dogs. We conclude that the one- and two-compartment estimates may be combined to provide a meaningful assessment of lung mechanics.     

A rapidly converging algorithm for estimating respiratory mechanical parameters in a five-element model

A rapidly converging algorithm for computing values for respiratory mechanical parameters from forced random noise independance data was developed and verified. The algorithm, which was based on a five-element Mead-type model, minimized the sum of squared differences between the model's response and experimental data, while imposing a nonnegativity constraint on the parameter values. It yielded parameter values that showed excellent agreement with values obtained previously using standard nonlinear regression analysis, but required much less computer time, 10 s versus 1 h. When this algorithm is coupled with the forced random impedance data collection techniques, it provides a rapid noninvasive method for estimating respiratory inertance, central resistance, peripheral resistance, and airway compliance. The problem of estimating peripheral compliance was not solved by this algorithm.     

CAD-oriented cavity model for rectangular patches

A cavity model well suited for computed-aided design is presented. The patch antenna is described by geometrical and electrical parameters. Using a cavity model, input impedance as a function of frequency is then calculated with a fast computer program implemented on a PC. Resonant resistance and resonant frequency are deduced.<>     

The characteristics of electrically short, umbrella top-loaded antennas

Experimental measurements of the electrical characteristics of umbrella top-loaded, electrically short antennas have been performed. Electrically short antennas can be represented by a series RLC circuit with good accuracy up to and including their first series resonant frequency. Electrically short antennas generally have very high Q's and, consequently, narrow bandwidths. Top-loading, such as umbrella top-loading of electrically short monopole antennas, leads to antennas which have lower Q's and larger bandwidths. The experimental measurements were made using a scale model facility. The antennas measured on the scale model facility were one-hundredth scale models of the anticipated full scale antennas. The equivalent inductance, capacitance, resistance, and effective height of these scale model antennas were determined and compared with values of static capacitance, static effective height, and static resistance obtained from a computer calculation [1], [2] and good correlation was obtained. Additionally, the dynamic characteristics of the antennas were determined from the model studies. The dynamic parameters determined were the antenna inductance, the dynamic radiation resistance, and the dynamic effective height. The measured data obtained from the model study are summarized in graphs and tables and compared with other reported experimental results as well as with computer calculations. Nomograms summarizing the computed data have been constructed and are presented.     

激光陀螺信号检测系统的理论与实验研究

本文研制了一种新型的、低噪声、大动态范围的激光陀螺信号检测系统。通过引入数学机械化的方法,我们采用近些年提出的旨在统一求解一大类非线性问题的理论方法-分解法对系统模型进行了分析,并给予实验验证。理论分析和实验结果表明:该检测系统完全能满足陀螺的应用要求。     

An analytic method to determine GaAs FET parasitic inductances anddrain resistance under active bias conditions

An analytic technique to determine the parasitic inductances, source resistance, and drain resistance of the FET equivalent circuit is presented in this paper. The method exploits the frequency dependence of the extracted circuit parameters to determine the parasitic inductances and drain resistance from S-parameters measured over frequency for one active bias condition. Given a value for the parasitic gate resistance R _g, all of the other equivalent-circuit parameters are uniquely extracted. The method is fast and robust, making it suitable for in-line statistical process tracking, as well as device modeling. A process tracking example for a 12-wafer 1864-device sample and FET modeling results up to 40 GHz are also presented     

An improved model for noise characterization of microwave GaAs FETs

A broadband noise model for microwave FETs has been described. The model consists of small-signal lumped elements together with two noise sources. A measurement of broadband S parameters plus a single-frequency measurement of optimum source susceptance can yield enough information to determine the model, although greater accuracy is obtained using additional noise data to determine the precise value of the gate resistance. The model's predictions match well with measured noise parameter data for a high-performance GaAs FET over a wide frequency range     

Resonant frequency of a tunable rectangular patch antenna

The uniform transmission-line model is applied to determine the resonant frequency of a coaxial probe fed rectangular patch antenna tuned by a number of passive metallic posts suitably placed within the antenna's boundary. An approximate expression is given for the resonant frequency as a function of the post location and number, and of the other characteristic parameters of the antenna. Theoretical results are compared with available measured values.     

Frequency domain identification of transfer function model of a disk drive actuator

In this paper, we present a method of identifying the transfer function model of a linear time-invariant (LTI) dynamic system from its frequency response data. The presented algorithm is based on the principle of least-square fit on the complex plane. It fits the frequency response data to the response of a transfer function model, minimizing the sum of square of residual errors. Thus a transfer function model is extracted from the measurement of the frequency response at a discrete set of frequencies. We select the order of the transfer function model through the interpretation of the cost functions obtained from least-square estimation (LSE) for different orders of the transfer function.The effectiveness of the proposed technique is verified by estimating the transfer function model of a hard disk drive actuator.     

The Edge-Guided Mode Nonreciprocal Phase Shifter

Results of a theoretical study are presented for a four-region model of a nonreciprocal dielectric-ferrite loaded stripline phase shifter employing the edge-guided dynamic mode. The behavior of our model in terms of the differential phase shift, the insertion loss, and the effective bandwidth is explored as a function of the various parameters involved.     

Statistical Measures of Parameter Estimates from Models Fit to Respiratory Impedance Data: Emphasis on Joint Vanabilities

To describe respiratory mechanical impedance data, many investigators have proposed electromechanical models and then fit them to data using formal parameter estimation techniques. This approach has resulted in confusion as to how to interpret the resulting estimated values, and hence as to which model is most appropriate. A key cause of this confusion is that most studies rely on the quality of fit between the model and the data as the only measure of model validity rather than performing adequate statistical analysis of the parameter estimates themselves. This paper describes several statistical measures that should be applied to parameter estimates obtained from forced oscillation data. Specifically, we describe standard errors of the parameter estimates, confidence intervals for each parameter estimate, and the joint confidence region for the parameters. Much emphasis is placed on the joint confidence region which, unlike the interval, allows for simultaneous variations in parameters. The measures are applied to an often used six-element model for respiratory impedance data of dogs from 4 to 64 Hz. This application indicated that even when fitting data over this frequency range, parameter estimates are not well defined and the parameter estimated with least accuracy is airway resistance.