Esra Saatci

Lung Model Parameter Estimation by Unscented Kalman Filter

Dynamic nonlinear models are the best choice to analyze respiratory systems and to describe system mechanics. In this work, unscented Kalman filtering (UKF) was used to estimate the dynamic nonlinear model parameters of the lung model by using the measured airway flow, mask pressure and integrated lung volume. Artificially generated data and the data from chronic obstructive pulmonary diseased (COPD) patients were analyzed by the proposed model and the proposed UKF algorithm. Simulation results for both cases demonstrated that UKF is a promising estimation method for the respiratory system analysis.

Respiratory parameter estimation in non-invasive ventilation based on generalized Gaussian noise models

Modeling of respiratory system under non-invasive ventilation by using measured respiratory signals is of great interest in respiratory mechanics research area. Statistical processing techniques in the time-domain may be utilized as an alternative to the commonly used frequency-domain analysis to estimate model parameters. In this work, we propose using a generalized Gaussian distribution (GGD) to model the measurement noise in the respiratory system identification problem. The parameters of the GGD (i.e. the mean, the variance and the shape) are estimated by maximum likelihood (ML) and moment based estimators. However, the estimation error should also be taken into account which is in fact investigated as measurement innovations together with the measurement noise. Thus the Kalman iterations are applied with the help of the score function to compute the measurement innovations. Finally, the complete picture of the measurement noise and innovation analysis of the respiratory models is obtained which helped us to evaluate the non-Gaussian noise extension in the respiratory system analysis.

Respiratory parameter estimation in linear lung models

If the respiratory system is represented as a one compartment model composed of linear electrical elements, the Minimum Variance Unbiased Estimation (MVUE) is the optimum statistical method to estimate the model parameters. Two well known linear models, RIC and Viscoelastic models were chosen and their parameters were estimated by MVUE. Synthetic data simulations showed that minimum 100Hz sampling rate is required in order to have minimum variance. Estimation of lung inertance and viscoelastic tissue compliance parameters resulted in very large estimation variance, whereas the rest of the parameters were estimated successfully. Both parameter values and estimator variances have their own characterization in terms of patient discrimination for diagnostic purposes.

Inverse modeling of respiratory system during noninvasive ventilation by maximum likelihood estimation

We propose a procedure to estimate the model parameters of presented nonlinear Resistance-Capacitance (RC) and the widely used linear Resistance-Inductance-Capacitance (RIC) models of the respiratory system by Maximum Likelihood Estimator (MLE). The measurement noise is assumed to be Generalized Gaussian Distributed (GGD), and the variance and the shape factor of the measurement noise are estimated by MLE and Kurtosis method, respectively. The performance of the MLE algorithm is also demonstrated by the Cramer-Rao Lower Bound (CRLB) with artificially produced respiratory signals. Airway flow, mask pressure, and lung volume are measured from patients with Chronic Obstructive Pulmonary Disease (COPD) under the noninvasive ventilation and from healthy subjects. Simulations show that respiratory signals from healthy subjects are better represented by the RIC model compared to the nonlinear RC model. On the other hand, the Patient group respiratory signals are fitted to the nonlinear RC model with lower measurement noise variance, better converged measurement noise shape factor, and model parameter tracks. Also, it is observed that for the Patient group the shape factor of the measurement noise converges to values between 1 and 2 whereas for the Control group shape factor values are estimated in the super-Gaussian area.

Posterior Cramer-Rao Lower Bounds for dual Kalman estimation

We present the Posterior Cramer-Rao Lower Bounds (PCRLB) for the dual Kalman filter estimation where the parameters are assumed to be time-invariant and stationary random variables. Relations between the PCRLB, the states, and the parameters are established and recursions are obtained for finite observation time. As a case study, the closed-form expressions of the PCRLB for a linear lung model, called the Mead respiratory model, are derived. Distribution of the parameters is assumed to be Generalized Gaussian Distribution (GGD) which enabled an investigation of different shape factors. Simulations performed on the signals collected from the human respiratory system yielded encouraging results. It is concluded that the parameter distribution should be chosen as Gaussian to super-Gaussian in order for the PCRLB algorithm to converge.

Dual Unscented Kalman Filter and Its Applications to Respiratory System Modelling

Unscented Kalman Filter (UKF) (Julier & Uhlmann, 1997) was developed as an improvement of Extended Kalman Filter (EKF) (Grewal & Andrews, 2001) for discrete-time filtering of the nonlinear dynamic systems. Comparison between different statistical approaches on the state and parameter estimation of the dynamic systems revealed that the performance of UKF is superior to EKF in many Kalman Filter (KF) applications (Chow et al., 2007); (Xiong et al., 2006); (Wan & Merwe, 2001); (Kandepu et al., 2008). Nonlinear dynamic systems with uncertain observations were often appeared in, for instance, communication systems (Wan & Merwe, 2001), medical systems (Polak & Mroczka, 2006) and machine learning (Chen, 2003). Medical systems, described by stochastic difference equations with measurement models including nonlinear and non-Gaussian components, are good candidates for the UKF analysis. Although there are many medical signal applications of Kalman Filters (KF); (Vauhkonen et al., 1998) and EKF (Avendano et al., 2006), some medical diagnostic and therapeutic measures are processed by UKF from indirect sensor measurements including statistical brain signal analysis to study cognitive brain functions by Electroencephalography (EEG) and functional Magnetic Resonance Imaging (fMRI) (Brochwell et al., 2007), ECG model-based denoising (Sameni et al., 2007), medical image processing (Ijaz et al., 2008), and evoke potential analysis in the neuroscience. These works demonstrated that UKF can be considered as an effective framework for medical signal analysing, modelling and filtering. Also, it was shown that UKF is a promising alternative in a variety of applications’ domains including state and parameter estimation simultaneously which is dual estimation. Respiratory mechanics is the dynamic relationship between appropriate pressures and flows in the respiratory system and assessment of it is an important problem in the diagnosis and monitoring of respiratory disorders, especially of Chronic Obstructive Pulmonary Disease (COPD). The primarily goal on the determination of the respiratory mechanics is the computation, or estimation, of the respiratory parameters non-invasively, continuously, effectively and without any patient cooperation. Direct approach to this problem is the measurement of the mechanics by the lung catheter or the alveolar capsule (Bates & Lutchen, 2005). However, these direct measurement methods are invasive and not suitable for continuous monitoring. On the other hand, the studies revealed that analysis of pressure O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

Generalized Gauss Distribution noise model for respiratory parameter estimation

In this study, measurement noise is modelled as a Generalized Gauss Distribution and a new method is presented to estimate the model parameters. The estimator algorithm consists of the Kurtosis method, Kalman iterarions and the Maximum likelihood method. The proposed method is successfully applied to linear lung model parameter estimation problem.

Dual Kalman Filter based State-Parameter Estimation in Linear Lung Models

Time-domain approach to inverse modeling of respiratory system requires estimation of the parameters from the noisy observation. In this work, states and parameters of the linear lung models are estimated simultaneously by dual Kalman filter where the algorithm use two-observation forms. We also employ Kalman smoother for fine tuning the parameters. It is found that the state estimates are more robust to initial filter parameters than the model parameter convergences. Both viscoelastic and the Mead models yielded encouraging results and compatible estimator variances.

Cyclostationary Analysis of Respiratory Signals with Application of Rate Determination

Respiratory signals are periodic-like signals where the noisy periodic pattern repeats itself. Therefore, based on a stationarity assumption, autocorrelation function contains noisy cycles in time-lag with the same rate as the respiration rate. In this work, cyclostationarity test is performed on the respiratory signals in order to determine cyclic characteristics of the time varying autocorrelation function. Our specific aim is to check whether the cycle period in time corresponds to the respiration rate. Lung simulator was used to generate the respiratory signals. Time varying autocorrelation variance was computed by using both the modified windowed, and the blocked signal methods. Our simulations resulted that the cycle period was the same as the respiration period. Moreover, we observed that cyclic frequencies corresponded to the respiratory rate and its harmonics.

Determination of the minimum sampling frequency in bandpass sampling by geometric approach and geometric programming

This paper presents a simple and fast approach to find a minimum sampling frequency for multi-band signals. Instead of neighbor and boundary conditions, constraints on the sampling frequency were derived by using the geometric approach to the bandpass sampling theorem. Reformulation of the constraints on the minimum sampling frequency enabled to represent the problem as an optimization problem which was structured by the geometric programming and mixed-integer nonlinear programming methods. The convex optimization problem was then solved by the proposed algorithm applying interior point approach in the line search framework. It was demonstrated that this unified structure directly linked the geometric approach of the bandpass sampling theorem to the optimization problem. The proposed method was verified through numerical simulations in terms of the minimum sampling frequency and the computational efficiency. Results illustrated the feasibility of the geometric approach and the proposed algorithm in the determination of the minimum sampling frequency by providing the savings in the number of iterations and the decrease in the valid minimum sampling frequency.