Processing Photoplethysmograms Recorded by Smartwatches to Improve the Quality of Derived Pulse Rate Variability.

Cardiac monitoring based on wearable photoplethysmography (PPG) is widespread because of its usability and low cost. Unfortunately, PPG is negatively affected by various types of disruptions, which could introduce errors to the algorithm that extracts pulse rate variability (PRV). This study aims to identify the nature of such artifacts caused by various types of factors under the conditions of precisely planned experiments. We also propose methods for their reduction based solely on the PPG signal while preserving the frequency content of PRV. The accuracy of PRV derived from PPG was compared to heart rate variability (HRV) derived from the accompanying ECG. The results indicate that filtering PPG signals using the discrete wavelet transform and its inverse (DWT/IDWT) is suitable for removing slow components and high-frequency noise. Moreover, the main benefit of amplitude demodulation is better preparation of the PPG to determine the duration of pulse cycles and reduce the impact of some other artifacts. Post-processing applied to HRV and PRV indicates that the correction of outliers based on local statistical measures of signals and the autoregressive (AR) model is only important when the PPG is of low quality and has no effect under good signal quality. The main conclusion is that the DWT/IDWT, followed by amplitude demodulation, enables the proper preparation of the PPG signal for the subsequent use of PRV extraction algorithms, particularly at rest. However, post-processing in the proposed form should be applied more in the situations of observed strong artifacts than in motionless laboratory experiments.

Algebraic approximation of the distributed model for the pressure drop in the respiratory airways.

The complexity of the human respiratory system causes that one of the main methods of analyzing the dynamic pulmonary phenomena and interpreting experimental results are simulations of its computational models. Among the most compound elements of these models, apart from the bronchial tree structure, is the phenomenon of flow limitation in flexible bronchi, which causes them to collapse with increasing flow, thus their properties, such as resistance, compliance and inertance, are highly nonlinear and time-varying. Commonly, this phenomenon is ignored, or a distributed model for the airway pressure drop is applied, simulated with a modified numerical solver of this differential equation (ODE). The disadvantages of this solution are the problems with taking into account the inherent singularity of the model and the long computation time due to iterative nature of the ODE procedure. The aim of the work was to derive an algebraic approximation of this distributed model, suitable for implementation in continuous dynamic models, to validate it by comparing the results of simulations with the respiratory system model including approximate and original (ODE solver) numerical procedures, as well as to evaluate possible acceleration of calculations. All simulations, including spontaneous breathing, mechanical ventilation with the optimal ventilatory waveform and forced expiration, proved that algebraic approximation yielded results negligibly differing from the ODE solution, and shortened the computation time by an order. The proposed approach is an attractive alternative in the case of computer implementations of pulmonary models, where simulations of flows and pressures in the complex respiratory system are of primary importance.

Derivation of Frequency Components from Overnight Heart Rate Variability Using an Adaptive Variational Mode Decomposition.

Heart rate variability (HRV) is a non-stationary, irregularly sampled signal that represents changes in heart rate over time. The HRV spectrum can be divided into four main ranges covering high, low, very low and ultra-low frequencies. The components lying in these bands, both amplitude and frequency modulated, provide valuable information about various physiological processes. The aim of this study was to verify the usefulness of adaptive variational mode decomposition (AVMD) in the extraction of these components from overnight HRV. The effectiveness of this new approach was compared to multiband filtering (MBF) using a synthetically generated signal, as well as real data from three patients. AVMD turned out to be more robust and effective than MBF, particularly in the high and low frequency ranges, making it a reliable method for deriving the HRV frequency components.Clinical Relevance-The extracted frequency components of heart rate variability provide insight into the regulation of basic physiological processes by the autonomic nervous system.

Quantitative Assessment of the Airway Response to Bronchial Tests Based on a Spirometric Curve Shift.

OBJECTIVE: Although spirometry is the most common pulmonary function test, there is no method to quantitatively infer about airway resistance or other properties from the flow-volume curves. Recently, an identifiable inverse model for forced expiration was proposed, as well as the idea to deduce changes in airway resistances and compliances from spirometric curve evolution. The aim of this work was to combine the above advances in a method for assessing the airway response to bronchial tests from a spirometric curve shift. METHODS: The approach is based on the differential measurement of the degree, site of maximal effect and width of changes, further recalculated into relative changes in the distribution of airway resistances (δRg) and compliances (δCg) along the bronchial tree. To this end, appropriate models were identified using the pre- and post-test spirometry data. The accuracy was validated using sets of data simulated by the anatomy and physiology based models. Finally, the method was used to analyze the bronchodilation tests of three asthmatic subjects. RESULTS: The expected errors in assessing the degree, site and width of changes in the zone of conducting airways were 6.3%, 2.4 generations and 22%, respectively, and for δRg and δCg were 5-10% and 13-16%, respectively. The analyses of clinical data indicated a significant reduction in resistances and an increase in compliances of airway generations 8-12, consistent with clinical knowledge. CONCLUSION: An unprecedented method to plausibly transforming the spirometry data into the site and degree of changes in airway properties has been proposed. SIGNIFICANCE: The method can be used to deduce about the effects of bronchial tests, as well as to monitor changes in the airways between visits or to investigate how inhaled pharmaceuticals affect the bronchi.

Effects of homogeneous and heterogeneous changes in the lung periphery on spirometry results.

BACKGROUND AND OBJECTIVES: The most widespread chronic pulmonary disorders are associated with heterogeneous changes in the lung periphery and spirometry is the most commonly used test to monitor these diseases. So far only a few attempts have been undertaken to investigate the effects of lung inhomogeneity on spirometry results. The aim of this work was to evaluate whether the spirometric curve and indexes are sensitive to parallel peripheral inhomogeneities, and if the level of heterogeneity can be deduced from this test. METHODS: To this end, an enhanced computational model for forced expiration, taking into account a heterogeneous structure and properties of the respiratory system, was used. Two main phenomena were mimicked: small airways narrowing and the loss of tissue elastic recoil. Numerical simulations were performed with the model having 76 separate peripheral compartments. For a given degree of mean change, three heterogeneity levels were investigated and compared to the effects of homogeneous alterations. RESULTS: All spirometric curves representing different patterns of inhomogeneous constriction, computed for each of the investigated cases, almost coincided with the curve originating from homogeneous changes, regardless of the heterogeneity level. Also the differences between the spirometric indexes obtained for heterogeneous and homogeneous alterations were negligible in comparison to their values. CONCLUSION: The main finding is that the spirometry results are insensitive to the level of heterogeneity in the lung periphery and that it is practically impossible to distinguish between the homogeneous or heterogeneous nature of pathological processes occurring in this lung region.

Effectiveness of Sleep Apnea Detection Based on One vs. Two Symmetrical EEG Channels.

Typically, two symmetrical EEG channels are recorded during polysomnography (PSG). As a rule, only the recommended channel is used for sleep stage scoring or sleep apnea detection, and the other for backup. Concurrently, there are many works demonstrating the asymmetry in brain activity. The aim of this work was to compare the accuracy of sleep apnea detection with the use of features obtained from one (C3-A2 or C4-A1) versus these two symmetrical EEG channels. To this end, the relevant data from the PhysioBank database (25 whole-night PSGs) were used. The same methodology of feature extraction and selection was applied for one and combined EEG channels. Automated classification was performed using the k-nearest neighbors algorithm (kNN) with k = 12 and cityblock metric for the three classes of EEG epochs, representing normal breathing, obstructive apnea and hypopnea, and central apnea and hypopnea. The accuracy of kNN-based classification was 63.8 %, 64.3 % and 70.3 % for C3-A2, C4-A1 and both EEG channels, respectively. The statistical tests have indicated that the accuracy of classification based on two combined symmetrical EEG channels is significantly higher compared to the single-channel cases.

Analysis of Features Extracted from EEG Epochs by Discrete Wavelet Decomposition and Hilbert Transform for Sleep Apnea Detection.

Sleep apnea (SA) is one of the most common disorders manifesting during sleep and the electroencephalo-gram (EEG) belongs to these biomedical signals that change during apnea and hypopnea episodes. In recent years, a few publications reported approaches to the automatic classification of sleep apnea episodes based only on the EEG. The purpose of this work was to analyze statistical features extracted from the EEG epochs by combined discrete wavelet transform (DWT) and Hilbert transform (HT). Additionally, the selected most discriminative 30 features were then used in the automatic classification of normal breathing and obstructive (OSA) and central (CSA) apnea by a feedforward neural network with 17+7 neurons in two hidden layers. This classifier returned the accuracy of 73.9% for the training and 77.3% for the testing set. The analysis of features extracted from EEG epochs revealed the importance of theta, beta and gamma brain waves.

Tomographic image reconstruction via estimation of sparse unidirectional gradients.

Since computed tomography (CT) was developed over 35 years ago, new mathematical ideas and computational algorithms have been continuingly elaborated to improve the quality of reconstructed images. In recent years, a considerable effort can be noticed to apply the sparse solution of underdetermined system theory to the reconstruction of CT images from undersampled data. Its significance stems from the possibility of obtaining good quality CT images from low dose projections. Among diverse approaches, total variation (TV) minimizing 2D gradients of an image, seems to be the most popular method. In this paper, a new method for CT image reconstruction via sparse gradients estimation (SGE), is proposed. It consists in estimating 1D gradients specified in four directions using the iterative reweighting algorithm. To investigate its properties and to compare it with TV and other related methods, numerical simulations were performed according to the Monte Carlo scheme, using the Shepp-Logan and more realistic brain phantoms scanned at 9-60 directions in the range from 0 to 179°, with measurement data disturbed by additive Gaussians noise characterized by the relative level of 0.1%, 0.2%, 0.5%, 1%, 2% and 5%. The accuracy of image reconstruction was assessed in terms of the relative root-mean-square (RMS) error. The results show that the proposed SGE algorithm has returned more accurate images than TV for the cases fulfilling the sparsity conditions. Particularly, it preserves sharp edges of regions representing different tissues or organs and yields images of much better quality reconstructed from a small number of projections disturbed by relatively low measurement noise.

Analysis of the method for ventilation heterogeneity assessment using the Otis model and forced oscillations.

Increased heterogeneity of the lung disturbs pulmonary gas exchange. During bronchoconstriction, inflammation of lung parenchyma or acute respiratory distress syndrome, inhomogeneous lung ventilation can become bimodal and increase the risk of ventilator-induced lung injury during mechanical ventilation. A simple index sensitive to ventilation heterogeneity would be very useful in clinical practice. In the case of bimodal ventilation, the index (H) can be defined as the ratio between the longer and shorter time constant characterising regions of contrary mechanical properties. These time constants can be derived from the Otis model fitted to input impedance (Zin) measured using forced oscillations. In this paper we systematically investigated properties of the aforementioned approach. The research included both numerical simulations and real experiments with a dual-lung simulator. Firstly, a computational model mimicking the physical simulator was derived and then used as a forward model to generate synthetic flow and pressure signals. These data were used to calculate the input impedance and then the Otis inverse model was fitted to Zin by means of the Levenberg-Marquardt (LM) algorithm. Finally, the obtained estimates of model parameters were used to compute H. The analysis of the above procedure was performed in the frame of Monte Carlo simulations. For each selected value of H, forward simulations with randomly chosen lung parameters were repeated 1000 times. Resulting signals were superimposed by additive Gaussian noise. The estimated values of H properly indicated the increasing level of simulated inhomogeneity, however with underestimation and variation increasing with H. The main factor responsible for the growing estimation bias was the fixed starting vector required by the LM algorithm. Introduction of a correction formula perfectly reduced this systematic error. The experimental results with the dual-lung simulator confirmed potential of the proposed procedure to properly deduce the lung heterogeneity level. We conclude that the heterogeneity index H can be used to assess bimodal ventilation imbalances in cases when this phenomenon dominates lung properties, however future analyses, including the impact of lung tissue viscoelasticity and distributed airway or tissue inhomogeneity on H estimates, as well as studies in the time domain, are advisable.

Analysis of multiple linear regression algorithms used for respiratory mechanics monitoring during artificial ventilation.

Many patients undergo long-term artificial ventilation and their respiratory system mechanics should be monitored to detect changes in the patient's state and to optimize ventilator settings. In this work the most popular algorithms for tracking variations of respiratory resistance (R(rs)) and elastance (E(rs)) over a ventilatory cycle were analysed in terms of systematic and random errors. Additionally, a new approach was proposed and compared to the previous ones. It takes into account an exact description of flow integration by volume-dependent lung compliance. The results of analyses showed advantages of this new approach and enabled to form several suggestions. Algorithms including R(rs) and E(rs) dependencies on airflow and lung volume can be effectively applied only at low levels of noise present in measurement data, otherwise the use of the simplest model with constant parameters is preferable. Additionally, one should avoid including the resistance dependence on airflow alone, since this considerably destroys the retrieved trace of R(rs). Finally, the estimated cyclic trajectories of R(rs) and E(rs) are more sensitive to noise present in pressure than in the flow signal, and the elastance traces are estimated more accurately than the resistance ones.

Preliminary study on the accuracy of respiratory input impedance measurement using the interrupter technique.

Respiratory input impedance contains information about the state of pulmonary mechanics in the frequency domain. In this paper the possibility of respiratory impedance measurement by interrupter technique as well as the accuracy of this approach are assessed. Transient states of flow and pressure recorded during expiratory flow interruption are simulated with a complex, linear model for the respiratory system and then used to calculate the impedance, including three states of respiratory mechanics and the influence of the measurement noise. The results of computations are compared to the known, theoretical impedance of the model. At 1 kHz sampling rate, the optimal time window lays between 100 and 200 ms and is centred around the pressure jump caused by the flow interruption. The proposed algorithm yields satisfactory accuracy in the range from 10 to 400 Hz, particularly to 150 Hz. Depending on the simulated respiratory system state, the error of calculated impedance (relative Euclidean distance between the vectors of computed and theoretical values), for the window of 190 ms, varies between 5.0% and 7.1%.

A model-based method for flow limitation analysis in the heterogeneous human lung.

Flow limitation in the airways is a fundamental process constituting the maximal expiratory flow-volume curve. Its location is referred to as the choke point. In this work, expressions enabling the calculation of critical flows in the case of wave-speed, turbulent or viscous limitation were derived. Then a computational model for the forced expiration from the heterogeneous lung was used to analyse the regime and degree of flow limitation as well as movement and arrangement of the choke points. The conclusion is that flow limitation begins at similar time in every branch of the bronchial tree developing a parallel arrangement of the choke points. A serial configuration of flow-limiting sites is possible for short time periods in the case of increased airway heterogeneity. The most probable locations of choke points are the regions of airway junctions. The wave-speed mechanism is responsible for flow choking over most of vital capacity and viscous dissipation of pressure for the last part of the test. Turbulent dissipation, however, may play a significant role as a supporting factor in transition between wave-speed and viscous flow limitation.

Nonlinear model for mechanical ventilation of human lungs.

A complex nonlinear model for mechanical ventilation, its computer implementation and validation are presented. The model includes the morphometry-based symmetrical structure of the 23 airway generations, dynamic properties of the respiratory system, as well as the description of a ventilator. Distributed character of airway mechanical properties is taken into account when determining airway inertance, resistance and compliance, including turbulence of flow, airway collapsing and the wave speed theory. In effect, the airway parameters vary within the ventilatory cycle and their values are nonlinear functions of control signals. Results of simulations corresponding to normal conditions and airway narrowing are consistent with the published experimental data. The model enables investigations on how specific pathological changes influence the signals and physiological variables during mechanical ventilation, as well as testing known and developing new algorithms tracking time-variability of the respiratory parameters.

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.

Computational model for forced expiration from asymmetric normal lungs.

We present a computational model to predict maximal expiration through a morphometry-based asymmetrical bronchial tree. A computational model with the Horsfield-like geometry of the airway structure, including wave-speed flow limitation and taking into consideration separate airflows from several independent alveolar compartments has been derived. The airflow values are calculated for quasistatic conditions by solving a system of nonlinear differential equations describing static pressure losses along the airway branches. Calculations done for succeeding lung volumes result in the semidynamic maximal expiratory flow-volume (MEFV) curve. Simulations performed show that the model captures the main phenomena observed in vivo during forced expiration: effort independence of the flow-volume curve for the most of vital capacity, independence of limited flow on the properties of airways downstream to the choke points, characteristic differences of lung regional pressures and volumes, and a shape of their variability during exhalation. Some new insights into the flow limitation mechanism were achieved. First, flow limitation begins at slightly different time instants in individual branches of the bronchial tree, however after a short period of time, all regional flows are limited in a parallel fashion. Hence, total flow at the mouth is limited for most of the expired lung volume. Second, each of the airway branches contribute their own flow-volume shape and just these individual flows constitute the measured MEFV curve. Third, central airway heterogeneity can play a crucial role in modification of the entire flow. Fourth, the bronchial tree asymmetry is responsible for a nongravitational component of regional volume variability. Finally, increased inhomogeneity yields results that cannot be explained nor re-created with the use of a symmetrical structure of the bronchial tree.