Relations between fractional-order model parameters and lung pathology in chronic obstructive pulmonary disease

Combined forced oscillation and fractional-order modeling in patients with work-related asthma: a case-control study analyzing respiratory biomechanics and diagnostic accuracy

BACKGROUND

Fractional-order (FrOr) models have a high potential to improve pulmonary science. These models could be useful for biomechanical studies and diagnostic purposes, offering accurate models with an improved ability to describe nature. This paper evaluates the performance of the Forced Oscillation (FO) associated with integer (InOr) and FrOr models in the analysis of respiratory alterations in work-related asthma (WRA).

METHODS

Sixty-two individuals were evaluated: 31 healthy and 31 with WRA with mild obstruction. Patients were analyzed pre- and post-bronchodilation. The diagnostic accuracy was evaluated using the area under the receiver operating characteristic curve (AUC). To evaluate how well do the studied models correspond to observed data, we analyzed the mean square root of the sum (MSEt) and the relative distance (Rd) of the estimated model values to the measured resistance and reactance measured values.

RESULTS AND DISCUSSION

Initially, the use of InOr and FrOr models increased our understanding of the WRA physiopathology, showing increased peripheral resistance, damping, and hysteresivity. The FrOr model (AUC = 0.970) outperformed standard FO (AUC = 0.929), as well as InOr modeling (AUC = 0.838) in the diagnosis of respiratory changes, achieving high accuracy. FrOr improved the curve fitting (MSEt = 0.156 ± 0.340; Rd = 3.026 ± 1.072) in comparison with the InOr model (MSEt = 0.367 ± 0.991; Rd = 3.363 ± 1.098). Finally, we demonstrated that bronchodilator use increased dynamic compliance, as well as reduced damping and peripheral resistance.

CONCLUSIONS

Taken together, these results show clear evidence of the utility of FO associated with fractional-order modeling in patients with WRA, improving our knowledge of the biomechanical abnormalities and the diagnostic accuracy in this disease.

Oscillation Mechanics, Integer and Fractional Respiratory Modeling in COPD: Effect of Obstruction Severity

Purpose

This research examines the emerging role of respiratory oscillometry associated with integer (InOr) and fractional order (FrOr) respiratory models in the context of groups of patients with increasing severity. The contributions to our understanding of the respiratory abnormalities along the course of increasing COPD severity and the diagnostic use of this method were also evaluated.

Patients and Methods

Forty-five individuals with no history of smoking or pulmonary diseases (control group) and 141 individuals with diagnoses of COPD were studied, being classified into 45 mild, 42 moderate, 36 severe and 18 very severe cases.

Results

This study has shown initially that the course of increasing COPD severity was adequately described by the model parameters. This resulted in significant and consistent correlations among these parameters and spirometric indexes. Additionally, this evaluation enhanced our understanding of the respiratory abnormalities in different COPD stages. The diagnostic accuracy analyses provided evidence that hysteresivity, obtained from FrOr modeling, allowed a highly accurate identification in patients with mild changes [area under the receiver operator characteristic curve (AUC)= 0.902]. Similar analyses in groups of moderate and severe patients showed that peripheral resistance, derived from InOr modeling, provided the most accurate parameter (AUC=0.898 and 0.998, respectively), while in very severe patients, traditional, InOr and FrOr parameters were able to reach high diagnostic accuracy (AUC>0.9).

Conclusion

InOr and FrOr modeling improved our knowledge of the respiratory abnormalities along the course of increasing COPD severity. In addition, the present study provides evidence that these models may contribute in the diagnosis of COPD. Respiratory oscillometry exams require only tidal breathing and are easy to perform. Taken together, these practical considerations and the results of the present study suggest that respiratory oscillometry associated with InOr and FrOr models may help to improve lung function tests in COPD.

A Minimal PKPD Interaction Model for Evaluating Synergy Effects of Combined NSCLC Therapies

This paper introduces a mathematical compartmental formulation of dose-effect synergy modelling for multiple therapies in non small cell lung cancer (NSCLC): antiangiogenic, immuno- and radiotherapy. The model formulates the dose-effect relationship in a unified context, with tumor proliferating rates and necrotic tissue volume progression as a function of therapy management profiles. The model accounts for inter- and intra-response variability by using surface model response terms. Slow acting peripheral compartments such as fat and muscle for drug distribution are not modelled. This minimal pharmacokinetic-pharmacodynamic (PKPD) model is evaluated with reported data in mice from literature. A systematic analysis is performed by varying only radiotherapy profiles, while antiangiogenesis and immunotherapy are fixed to their initial profiles. Three radiotherapy protocols are selected from literature: (1) a single dose 5 Gy once weekly; (2) a dose of 5 Gy × 3 days followed by a 2 Gy × 3 days after two weeks and (3) a dose of 5 Gy + 2 × 0.075 Gy followed after two weeks by a 2 Gy + 2 × 0.075 Gy dose. A reduction of 28% in tumor end-volume after 30 days was observed in Protocol 2 when compared to Protocol 1. No changes in end-volume were observed between Protocol 2 and Protocol 3, this in agreement with other literature studies. Additional analysis on drug interaction suggested that higher synergy among drugs affects up to three-fold the tumor volume (increased synergy leads to significantly lower growth ratio and lower total tumor volume). Similarly, changes in patient response indicated that increased drug resistance leads to lower reduction rates of tumor volumes, with end-volume increased up to 25–30%. In conclusion, the proposed minimal PKPD model has physiological value and can be used to study therapy management protocols and is an aiding tool in the clinical decision making process. Although developed with data from mice studies, the model is scalable to NSCLC patients.

Association of respiratory integer and fractional-order models with structural abnormalities in silicosis

BACKGROUND AND OBJECTIVE

Integer and fractional-order models have emerged as powerful methods for obtaining information regarding the anatomical or pathophysiological changes that occur during respiratory diseases. However, the precise interpretation of the model parameters in light of the lung structural changes is not known. This study analyzed the associations of the integer and fractional-order models with structural changes obtained using multidetector computed tomography densitometry (MDCT) and pulmonary function analysis.

METHODS

Integer and fractional-order models were adjusted to data obtained using the forced oscillation technique (FOT). The results obtained in controls (n = 20) were compared with those obtained in patients with silicosis (n = 32), who were submitted to spirometry, body plethysmograph, FOT, diffusing capacity of the lungs for carbon monoxide (DLCO), and MDCT. The diagnostic accuracy was also investigated using ROC analysis.

RESULTS

The observed changes in the integer and fractional-order models were consistent with the pathophysiology of silicosis. The integer-order model showed association only between inertance and the non-aerated compartment (R = -0.69). This parameter also presented the highest associations with spirometry (R = 0.81), plethysmography (-0.61) and pulmonary diffusion (R = 0.53). Considering the fractional-order model, the increase in the poorly aerated and non-aerated regions presented direct correlations with the fractional inertance (R = 0.48), respiratory damping (R = 0.37) and hysteresivity (R = 0.54) and inverse associations with its fractional exponent (R = -0.62) and elastance (-0.35). Significant associations were also observed with spirometry (R = 0.63), plethysmography (0.37) and pulmonary diffusion (R = 0.51). Receiver operator characteristic analysis showed a higher accuracy in the FrOr model (0.908) than the eRIC model (0.789).

CONCLUSIONS

Our study has shown clear associations of the integer and fractional-order parameters with anatomical changes obtained via MDCT and pulmonary function measurements. These findings help to elucidate the physiological interpretation of the integer and fractional-order parameters and provide evidence that these parameters are reflective of the abnormal changes in silicosis. We also observed that the fractional-order model showed smaller curve-fitting errors, which resulted in a higher diagnostic accuracy than that of the eRIC model. Taken together, these results provide strong motivation for further studies exploring the clinical and scientific use of these models in respiratory medicine.

Respiratory resistance and reactance in adults with sickle cell anemia: Part 2-Fractional-order modeling and a clinical decision support system for the diagnosis of respiratory disorders

BACKGROUND

A better understanding of sickle cell anemia (SCA) and improvements in drug therapy and health policy have contributed to the emergence of a large population of adults living with this disease. The mechanisms by which SCA produces adverse effects on the respiratory system of these patients are largely unknown. Fractional-order (FrOr) models have a high potential to improve pulmonary clinical science and could be useful for diagnostic purposes, offering accurate models with an improved ability to mimic nature. Part 2 of this two-part study examines the changes in respiratory mechanics in patients with SCA using the new perspective of the FrOr models. These results are compared with those obtained in traditional forced oscillation (FOT) parameters, investigated in Part 1 of the present study, complementing this first analysis.

METHODOLOGY/PRINCIPAL FINDINGS

The data consisted of three categories of subjects: controls (n = 23), patients with a normal spirometric exam (n = 21) and those presenting restriction (n = 24). The diagnostic accuracy was evaluated by investigating the area under the receiver operating characteristic curve (AUC). Initially, it was observed that biomechanical changes in SCA included increased values of fractional inertance, as well as damping and hysteresivity (p<0.001). The correlation analysis showed that FrOr parameters are associated with functional exercise capacity (R = -0.57), pulmonary diffusion (R = -0.71), respiratory muscle performance (R = 0.50), pulmonary flows (R = -0.62) and airway obstruction (R = 0.60). Fractional-order modeling showed high diagnostic accuracy in the detection of early respiratory abnormalities (AUC = 0.93), outperforming spirometry (p<0.03) and standard FOT analysis (p<0.01) used in Part 1 of this study. A combination of machine learning methods with fractional-order modeling further improved diagnostic accuracy (AUC = 0.97).

CONCLUSIONS

FrOr modeling improved our knowledge about the biomechanical abnormalities in adults with SCA. Changes in FrOr parameters are associated with functional exercise capacity decline, abnormal pulmonary mechanics and diffusion. FrOr modeling outperformed spirometric and traditional forced oscillation analyses, showing a high diagnostic accuracy in the diagnosis of early respiratory abnormalities that was further improved by an automatic clinical decision support system. This finding suggested the potential utility of this combination to help identify early respiratory changes in patients with SCA.

Acoustic Methods for Pulmonary Diagnosis

Recent developments in sensor technology and computational analysis methods enable new strategies to measure and interpret lung acoustic signals that originate internally, such as breathing or vocal sounds, or are externally introduced, such as in chest percussion or airway insonification. A better understanding of these sounds has resulted in a new instrumentation that allows for highly accurate as well as portable options for measurement in the hospital, in the clinic, and even at home. This review outlines the instrumentation for acoustic stimulation and measurement of the lungs. We first review the fundamentals of acoustic lung signals and the pathophysiology of the diseases that these signals are used to detect. Then, we focus on different methods of measuring and creating signals that have been used in recent research for pulmonary disease diagnosis. These new methods, combined with signal processing and modeling techniques, lead to a reduction in noise and allow improved feature extraction and signal classification. We conclude by presenting the results of human subject studies taking advantage of both the instrumentation and signal processing tools to accurately diagnose common lung diseases. This paper emphasizes the active areas of research within modern lung acoustics and encourages the standardization of future work in this field.

Forced oscillation technique for early detection of the effects of smoking and COPD: contribution of fractional-order modeling

Purpose

The aim of the present study was to evaluate the performance of the forced oscillation technique (FOT) for the early diagnosis of the effects of smoking and COPD. The contributions of the integer-order (InOr) and fractional-order (FrOr) models were also evaluated.

Patients and methods

In total, 120 subjects were analyzed: 40 controls, 40 smokers (20.3±9.3 pack-years) and 40 patients with mild COPD.

Results

Initially, it was observed that traditional FOT parameters and the InOr and FrOr models provided a consistent description of the COPD pathophysiology. Mild COPD introduced significant increases in the FrOr inertance, damping factor and hysteresivity (P<0.0001). These parameters were significantly correlated with the spirometric parameters of central and small airway obstruction (P<0.0001). The diagnostic accuracy analyses indicated that FOT parameters and InOr modeling may adequately identify these changes (area under the receiver operating characteristic curve – AUC >0.8). The use of FrOr modeling significantly improved this process (P<0.05), allowing the early diagnosis of smokers and patients with mild COPD with high accuracy (AUC >0.9).

Conclusion

FrOr modeling improves our knowledge of modifications that occur in the early stages of COPD. Additionally, the findings of the present study provide evidence that these models may play an important role in the early diagnosis of COPD, which is crucial for improving the clinical management of the disease.

Early Diagnosis of Respiratory Abnormalities in Asbestos-Exposed Workers by the Forced Oscillation Technique

BACKGROUND

The current reference test for the detection of respiratory abnormalities in asbestos-exposed workers is spirometry. However, spirometry has several shortcomings that greatly affect the efficacy of current asbestos control programs. The forced oscillation technique (FOT) represents the current state-of-the-art technique in the assessment of lung function. This method provides a detailed analysis of respiratory resistance and reactance at different oscillatory frequencies during tidal breathing. Here, we evaluate the FOT as an alternative method to standard spirometry for the early detection and quantification of respiratory abnormalities in asbestos-exposed workers.

METHODOLOGY/PRINCIPAL FINDINGS

Seventy-two subjects were analyzed. The control group was composed of 33 subjects with a normal spirometric exam who had no history of smoking or pulmonary disease. Thirty-nine subjects exposed to asbestos were also studied, including 32 volunteers in radiological category 0/0 and 7 volunteers with radiological categories of 0/1 or 1/1. FOT data were interpreted using classical parameters as well as integer (InOr) and fractional-order (FrOr) modeling. The diagnostic accuracy was evaluated by investigating the area under the receiver operating characteristic curve (AUC). Exposed workers presented increased obstruction (resistance p<0.001) and a reduced compliance (p<0.001), with a predominance of obstructive changes. The FOT parameter changes were correlated with the standard pulmonary function analysis methods (R = -0.52, p<0.001). Early respiratory abnormalities were identified with a high diagnostic accuracy (AUC = 0.987) using parameters obtained from the FrOr modeling. This accuracy was significantly better than those obtained with classical (p<0.001) and InOr (p<0.001) model parameters.

CONCLUSIONS

The FOT improved our knowledge about the biomechanical abnormalities in workers exposed to asbestos. Additionally, a high diagnostic accuracy in the diagnosis of early respiratory abnormalities in asbestos-exposed workers was obtained. This makes the FOT particularly useful as a screening tool in the context of asbestos control and elimination. Moreover, it can facilitate epidemiological research and the longitudinal follow-up of asbestos exposure and asbestos-related diseases.

Forced oscillation, integer and fractional-order modeling in asthma

The purpose of this study was to evaluate the use of fractional-order (FrOr) modeling in asthma. To this end, three FrOr models were compared with traditional parameters and an integer-order model (InOr). We investigated which model would best fit the data, the correlation with traditional lung function tests and the contribution to the diagnostic of airway obstruction. The data consisted of forced oscillation (FO) measurements obtained from healthy (n=22) and asthmatic volunteers with mild (n=22), moderate (n=19) and severe (n=19) obstructions. The first part of this study showed that a FrOr was the model that best fit the data (relative distance: FrOr=4.3±2.4; InOr=5.1±2.6%). The correlation analysis resulted in reasonable (R=0.36) to very good (R=0.77) associations between FrOr parameters and spirometry. The closest associations were observed between parameters related to peripheral airway obstruction, showing a clear relationship between the FrOr models and lung mechanics. Receiver-operator analysis showed that FrOr parameters presented a high potential to contribute to the detection of the mild obstruction in a clinical setting. The accuracy [area under the Receiver Operating Characteristic curve (AUC)] observed in these parameters (AUC=0.954) was higher than that observed in traditional FO parameters (AUC=0.732) and that obtained from the InOr model (AUC=0.861). Patients with moderate and severe obstruction were identified with high accuracy (AUC=0.972 and 0.977, respectively). In conclusion, the results obtained are in close agreement with asthma pathology, and provide evidence that FO measurement associated with FrOr models is a non-invasive, simple and radiation-free method for the detection of biomechanical abnormalities in asthma.

Robust stability and stabilization of fractional order linear systems with positive real uncertainty

This paper investigates the robust stability and stabilization of fractional order linear systems with positive real uncertainty. Firstly, sufficient conditions for the asymptotical stability of such uncertain fractional order systems are presented. Secondly, the existence conditions and design methods of the state feedback controller, static output feedback controller and observer-based controller for asymptotically stabilizing such uncertain fractional order systems are derived. The results are obtained in terms of linear matrix inequalities. Finally, some numerical examples are given to validate the proposed theoretical results.

Computer assessment of indirect insight during an airflow interrupter maneuver of breathing

The paper answers the questions if it is possible to conclude in objective way on more (than one -Rint - in a classical IT) number of parameters from the time domain post-interrupter signals during the occlusional measurement of respiratory mechanics and also verifies what accuracy can be achieved in such attempt. To obtain reported results, the time-domain enhanced interrupter technique (TD-EIT) was developed in this paper using computer simulations. Three-stage scheme of work was assumed in the project. First, the quality of the model identification was assessed for various combinations of pressure and flow signals recorded during the interruption. Then, the correlation between the working characteristics of the interrupter valve and the precision of the parameter estimation were assessed for the TD-EIT algorithm. Finally, a verification experiment by forward-inverse modeling was organized, in which the mechanical characteristics of a complex model were mapped with reduced analogs and with the use of neural networks for three typical modes: 'Normal state', 'Airway constriction' and 'Cheeks supported'. Obtained results show that to became effective in time-domain post-interrupter data exploration, both pressure and flow signals should be used in assessment of respiratory mechanics, taken in a range of at least 100ms and when both slopes (valve closing and opening) of quasi-step excitation are included. What is more, the faster the valve the smaller error of parameter estimation in proposed TD-EIT was observed, and this uncertainty importantly falls down for the length of time window exceeding the limit of 100ms. The pioneering use of neural network for mapping the mechanical properties of lungs with the use of interrupter experiment methodology proves that it is possible to conclude about more (than one) number of parameters characterizing the complex system and that this insight is biased with the error not exceeding of 10%; only peripheral properties are estimated worse. Such observation has a potential to change the experimental protocol, which was used in interrupter measurements up to date and to make this technique more attractive in comparison to other method, i.e. forced oscillation technique or impulse oscillometry. As regards the practical meaning of reported results for engineers and end-users (physicians and patients), proposed solution can be applied in simple portable devices with a feature of easy operation (important for e-monitoring).

Adaptive control of a pressure-controlled artificial ventilator: a simulator-based evaluation using real COPD patient data

The paper discusses the application of a direct adaptive controller to a pressure controlled artificial ventilation problem. In pressure controlled ventilators, the manipulated variable is the maximum flow applied to the patient during the active phase (inspiration), and the regulated variable is the peak pressure at end-inspiration. This simulation case study focuses on patients diagnosed with Chronic Obstructive Pulmonary Disease (COPD), which require artificial/mechanical ventilation. An adaptive PID controller ensures peak pressures below critical values, by manipulating the flow delivered by the ventilator. The simulation study is performed on fractional-order models of the respiratory impedance identified from lung function data obtained from 21 COPD patients. Additional simulation studies show the robustness of the controller in presence of varying model parameters from the respiratory impedance of the patient. Possibilities to implement the control strategy as an online adaptive algorithm are also explored. The results show that the design of the control is suitable for this kind of application and provides useful insight on realistic scenarios.

Fractional order model parameters for the respiratory input impedance in healthy and in asthmatic children

This paper provides an evaluation of a fractional order model for the respiratory input impedance, using two groups of subjects, respectively healthy and asthmatic children. The purpose is to verify if the model is able to deliver statistically meaningful parameter values in order to classify the two groups. The data are gathered with the non-invasive lung function test of forced oscillations technique, by means of a multisine signal within the 4-48Hz frequency range. Based on our previous work, a fractional order model for this range of frequencies is obtained. Additional parameters are proposed to evaluate the two groups. The results indicate that the model was unable to detect significant changes between the asthmatic children with normal spirometry results (as result of medication) and the healthy children. Due to medication intake during the hours prior to the exam, bronchial challenge did not modify substantially the respiratory parameters. Our findings correspond to similar studies reported in the specialized literature. Combined model parameters, such as the tissue damping and the tissue elastance were significantly different in the two groups (p<0.01). Two extra indexes are introduced: the quality factor and the power factor, providing significantly different results between the two groups (p≪0.01). We conclude that the model can be used in the respective frequency range to characterize the two groups efficiently.