Integrated Solution Combining Low-Frequency Forced Oscillation Technique and Continuous Equivital Sensor Monitoring for Assessment of Non-Invasive Ambulatory Respiratory Mechanics

Abstract

Early assessment of respiratory mechanics is crucial for early-stage diagnosing and managing lung diseases, leading to greater patient outcomes. Traditional methods like spirometry are limited in continuous monitoring and patient compliance as they require forced maneuvers with significant patient cooperation, which may not be available in fragile individuals. The Forced Oscillation Technique (FOT) is a non-invasive measurement method, only based on the tidal breathing at rest from the patient for a limited time period. The proposed solution integrates low-frequency FOT with continuous monitoring using Equivital (EQV) sensors to enhance respiratory mechanics information with heart rate variability. Data were collected over a two-hour period from six healthy volunteers, measuring respiratory impedance every 7 min and continuously recording physiological parameters. The best-fitting fractional-order models for impedance data were identified using genetic algorithms. This study also explores the correlation between impedance model parameters and EQV data, discussing the potential of AI tools for forecasting respiratory properties. Our findings indicate that combined monitoring techniques and AI analysis provides additional complementary information, subsequently aiding the improved evaluation of respiratory function and tissue mechanics. The proposed protocol allows for ambulatory assessment and can be easily performed in normal breathing conditions.

1. Introduction

The accurate assessment of respiratory mechanics is fundamental for diagnosing and managing various lung diseases. Traditional methods, such as spirometry, provide valuable information but are limited in their ability to provide continuous monitoring since they require continuous patient cooperation in forced maneuvers, which can be challenging for some individuals [1,2,3,4]. The Forced Oscillation Technique (FOT) has emerged as a valuable alternative, providing non-invasive measurements of respiratory impedance by applying oscillatory pressure waves during normal breathing conditions to the respiratory system and measuring the resultant airflow and pressure responses.

Extensive research has been conducted on respiratory impedance and its clinical implications, leading to the development of advanced monitoring systems. Low-frequency FOT (0.1–2 Hz) has proven to be effective in reflecting disease stages and predicting deterioration in conditions such as idiopathic pulmonary fibrosis [5]. Comparative studies of forced oscillometry and other measurement techniques have highlighted the strengths and limitations of these methods, guiding their optimization [6,7,8,9,10,11,12].

Recent advancements have focused on low-frequency FOT to enhance understanding of the mechanical behavior of lung tissues and peripheral airways [5,13,14]. This frequency range is sensitive to changes in compliance and resistance, making it particularly useful for detecting early alterations in lung function [3,4,15]. Innovations such as adaptive excitation signals have further improved the precision and reliability of low-frequency FOT measurements in various clinical settings [2].

In addition, high-frequency FOT (20–200 Hz) provides complementary insights by assessing different mechanical properties of the respiratory system. At these frequencies, impedance is more influenced by central airway properties and inertial effects, offering a broader perspective [10,13,16]. Despite its potential, the continuous use of FOT in clinical practice is hindered by challenges such as patient discomfort and the impracticality of long-term measurements.

To address these challenges, this study integrates low-frequency FOT with continuous monitoring using Equivital (EQV) sensors in smart textiles. Sensors, integrated within these textiles, can continuously track key physiological indicators, such as heart rate, respiratory rate, and skin temperature, providing a comprehensive overview of a patient’s condition without the need for invasive procedures [17,18]. This integration aims to enhance respiratory mechanics assessment by leveraging the strengths of both FOT and EQV technologies, ultimately improving patient outcomes and advancing respiratory monitoring [19]. By measuring respiratory impedance every 7 min over a 2 h period and continuously recording physiological data with EQV sensors, we aim to identify the best-fitting fractional-order models for impedance data using genetic algorithms. Additionally, we explore the correlation between impedance model parameters and EQV data, and discuss the potential of using AI tools for forecasting respiratory mechanics based on these integrated datasets.

This paper is organized as follows: In Section 2, we detail the methodology used for the experiments, including the design of the FOT and continuous monitoring setup with the EQV sensor. Section 3 presents the experimental results, focusing on the comparison between different models of respiratory mechanics and the correlation between impedance data and physiological parameters. In Section 4, we discuss the implications of these results, including the potential for integrating AI tools to enhance respiratory assessment. Finally, Section 5 concludes this paper, summarizing the key findings and proposing directions for future research.

2. Material and Methods

2.1. Forced Oscillation Technique

At rest, normal breathing, such as that used during the Forced Oscillation Technique (FOT) lung function test, involves the contraction of the diaphragm, parasternal muscles, and scaleni. During inhalation, the diaphragm moves downward, pulling the lower surfaces of the lungs with it. Exhalation occurs when these muscles relax. Variations in the elastic recoil of the lungs, which can make them more or less stiff, impact their normal functioning, particularly affecting total lung volume and the pressure–volume relationship. The shape and area under the pressure–volume loop provide information upon the mechanical workload of the respiratory system and is used for diagnosis [13].

Lung function mechanics are evaluated by the FOT lung function test with a superimposed multisine of multiple frequencies, assessing the frequency response of the lung tissue and airways [13,20]. This evaluation provides information known as respiratory impedance, a complex variable. The real part of respiratory impedance characterizes total resistance, while the imaginary part reflects the balance between inertive and compliant (reactance) mechanical properties [21]. Resistance and reactance, which are mathematically distinct contributions to respiratory system impedance, correlate with morphological changes in the lungs. These changes are represented by mechanical properties in the 4–50 Hz frequency interval [5,22]. At frequencies below 5 Hz, impedance is predominantly influenced by the mechanical properties of the small peripheral airways and alveolar tissues. The FOT at low-frequency measurement involves superimposing a customized amplitude—frequency multisine signal onto the patient’s natural breathing. The main advantages of FOT measurements include it being effortless, requiring minimal patient cooperation, which is especially beneficial for pediatric or critically ill patients; the frequency-dependent characteristics of impedance allow for the differentiation of obstructions within various lung structures; and impedance data offer insights into the pathophysiological changes in lung structure and function, which can be interpreted using specific mathematical models calibrated with real data.

In this study, both low-frequency and high-frequency respiratory devices are employed to comprehensively evaluate respiratory function. The low-frequency prototype device (4P-FOT). This device was developed by the Dynamical Systems and Control (DySC) Research Group at Ghent University, located in Ghent, Belgium, depicted in Figure 1A, measuring in the frequency range of 0.05–5 Hz, provides detailed insights into the viscoelastic properties of the lungs and airway remodeling [10]. In contrast, the high-frequency commercial device (Resmon Pro Full) is depicted in Figure 1B. This device was manufactured by ResTech in Milano, Italy, and distributed by MGC Diagnostics, based in Minnesota, USA. It measures in the frequency range 5–37 Hz, and gives a broader analysis of airway resistance and reactance, capturing dynamic changes in respiratory mechanics under various physiological conditions [10]. Both devices offer complementary insights into respiratory mechanics. Therefore, it is ideal to combine the information provided from both.

2.2. Equivital Physiological Signals Monitoring

The Equivital (EQV) LifeMonitor (Cambridge, UK) is an advanced wearable sensor system designed for the continuous monitoring of physiological parameters, making it particularly useful for long time intervals of respiratory function evaluation. The device integrated in a smart textile environment is employed in both clinical and research settings to provide real-time data of vital signs such as heart rate (HR), respiratory rate (RR), skin temperature (ST), and electrocardiogram (ECG). The EQV integrates multiple sensors to capture detailed physiological data—a tri-axis accelerometer for movement and position tracking, ECG electrodes for HR monitoring, and respiratory inductive plethysmography (RIP) bands to measure RR and effort—providing a comprehensive picture of an individual’s tidal breathing patterns. EQV is a user-friendly and comfortable device for long-term monitoring, making it a suitable candidate for continuous patient monitoring, including remote monitoring.

This device is mainly used in monitoring vital signal during exercises; its potential for clinical application is yet to be explored. From a clinical point of view, the EQV could be a valuable tool in monitoring of respiratory diseases, e.g., Chronic Obstructive Pulmonary Disease (COPD). A recent study has employed the EQV device to monitor changes in vital signals in patients with COPD [23]. The study highlighted the device’s ability to detect significant variations in respiratory rate and heart rate, which are critical indicators and would enable healthcare providers to intervene early potentially improving patient outcomes.

In this study, the EQV sensor monitor depicted in Figure 2 continuously collects data, including ECG heart rate, respiratory rate, and skin temperature, over a two-hour measurement period for each patient. Simultaneously, the FOT and RESMON devices measure data alternately. Therefore, a synchronization step is essential to align EQV data with FOT measurements for a detailed analysis.

2.3. Impedance Model Selection

It has been already proven that fractional-order impedance models are natural solutions for characterizing frequency response of the anatomical and structural composition of the respiratory system [13]. The fractional-order model for human respiratory system provides an expression for the input impedance (measured at the mouth of the patient) by considering a series arrangement of a resistance in series with two fractance elements, as follows:

$$Z_r\left(s\right)=R_r+L_r{s}^{{\alpha }_r}+{\displaystyle \frac{1}{C_r{s}^{{\beta }_r}}}$$

(1)

where $Z_r\left(s\right)$ is the respiratory impedance; $R_r$ is airway resistance in kPa/(l/s); $L_r$ is inductance kPa/(l/$s^2$); $C_r$ is capacitance in L/kPa; ${\beta }_r$ is the fractional order; s is the Laplace operator; and the subscript r denotes respiratory model. The basic concept of a fractional order in the frequency domain is given in Appendix A.

From the identified model parameters, one can derive the tissue damping $G_r$ and elastance $H_r$, defined as [13]:

$$\begin{array}{c}{G}_r={\displaystyle \frac{1}{C_r{\omega }^{{\beta }_r}}}\cos ({\beta }_r{\displaystyle \frac{\pi }{2}})\\ H_r={\displaystyle \frac{1}{C_r{\omega }^{{\beta }_r}}}\sin ({\beta }_r{\displaystyle \frac{\pi }{2}})\end{array}$$

(2)

The hysteresivity coefficient ${\eta }_r$ (dimensionless) is defined as [24]

$${\eta }_r={\displaystyle \frac{G_r}{H_r}}$$

(3)

This parameter characterizes the heterogeneity of the lung tissue and has been shown to vary and correlate significantly with pathology [13].

In this study, two other fractional-order models, i.e., a Cole model and a Warburg model, were used to fit the measured data. A fractional-order Cole model has shown to be successful in characterizing biological tissues [25]:

$$Z_c\left(s\right)=R_c+{\displaystyle \frac{K_c}{1+{\left(\frac{1}{p}\right)}^{{\beta }_c}}}$$

(4)

where $R_c$ denotes the gain at infinite frequencies, $K_c$ denotes the relative gain difference between low and high frequencies, ${\left({\displaystyle \frac{1}{p}}\right)}^{{\beta }_c}$ denotes pseudo-capacitance of the constant phase element, and the subscript c denotes the Cole model. It follows that $\tau ={\displaystyle \frac{1}{p}}$ is the relaxation time constant as per analogy to Debye material characteristics. Lastly, the Warburg diffusion element that models the diffusion process in dielectric spectroscopy is considered as

$$Z_w\left(s\right)={\displaystyle \frac{K_w}{\sqrt{s}}}$$

(5)

where $K_w$ is the Warburg coefficient (or the Warburg constant).

The best-fitting fractional-order impedance model is selected using the total error between the real impedance and the model estimated impedance, which is calculated as

$$E_T=\sqrt{E_R^2+E_I^2}$$

(6)

where $E_R$ and $E_I$ denote the errors on the real and imaginary parts, respectively. They are found using following formulas:

$$E_R={\displaystyle \frac{1}{N_s}}\sqrt{\sum _{k=1}^{N_s}{({Z_R}_k-{\widehat{Z_R}}_k)}^2}{E}_I={\displaystyle \frac{1}{N_s}}\sqrt{\sum _{k=1}^{N_s}{({Z_I}_k-{\widehat{Z_I}}_k)}^2}$$

(7)

where ${Z_R}_k$ and ${Z_I}_k$ represent the real and imaginary parts of the real impedance, respectively, while ${\widehat{Z}}_{R,k}$ and ${\widehat{Z}}_{I,k}$ are their model estimated impedance values. $N_s$ is the total number of measured points in the frequency interval of interest.

2.4. Identification and Optimum Solution Using Genetic Algorithms

The genetic algorithm (GA) was selected, using the Matlab (2023b) function ga, to choose the optimal parameters for each fractional-order model. The parameters were selected based on the the optimization of the cost function, as detailed in [26,27]. The GA is a heuristic optimization technique inspired by the process of natural selection, which mimics biological evolution to iteratively improve solutions to optimization problems. The algorithm tackles stochastic global optimization problems by modifying a population of potential solutions.

The genetic algorithm was used to find the parameters of each model. Initially, it generates a random population of parameters for each of the FO models. Each set of parameters is evaluated using a fitness function, which measures the difference between the predicted impedances and the measured impedances. Through processes of selection, crossover, and mutation, a new generation of potential solutions is produced, with individuals that better fit the data being more likely to be selected as parents. The optimization process continues until the population converges towards an optimal or near-optimal solution, resulting in optimal parameter $(R_r^{*},L_r^{*},{\alpha }_r^{*},C_r^{*},{\beta }_r^{*})$ for the respiratory system, $(R_c^{*},K_c^{*},{\beta }_c^{*},p^{*})$ for the fatigue-induced changes and skeletal muscle damage model, and $\left(K_w^{*}\right)$ for the Warburg model. The optimal parameters are chosen so that they best fit the experimental impedance data with minimal error [28,29].

To ensure the best solution for each patient, the Normalized Root Mean Square Error (NRMSE) is calculated for each optimal parameter vector generated after each GA iteration. An NRMSE of less than 0.1 indicates a good fit, with a fit value of 0 representing a perfect fit. Parameter sets that meet this condition and occur most frequently are used to initialize the model for the online procedure of the same patient. The fitting percentage is given by $fit=100\ast (1-NRMSE)$. The optimization results are shown in

Table 1. Fractional-order impedance model (1) parameter values (mean ± standard deviation).

	R	${\mathit{L}}_{\mathit{r}}$	${\mathit{\alpha }}_{\mathit{r}}$	$\mathit{D}=1/\mathit{C}$	${\mathit{\beta }}_{\mathit{r}}$
FOT	$0.01$	$0.0066$	$0.7537$	$0.0135$	$0.2499$
	$\pm 0.01$	$\pm 0.0017$	$\pm 0.1014$	$\pm 0.0011$	$\pm 0.0506$
Resmon	$0.2344$	$0.0004$	$0.2854$	$0.0009$	$1.1540$
	$\pm 0.028$	$\pm 0.0003$	$\pm 0.064$	$\pm 0.0003$	$\pm 0.111$

for the fractional-order model using (1),

Table 2. Cole model parameter values (mean ± standard deviation).

	R	K	p	$\mathit{\alpha }$
FOT	$0.0174$	$1.3839$	$0.4979$	$1.7629$
	$\pm 0.0024$	$\pm 1.7558$	$\pm 0.2292$	$\pm 0.1494$
Resmon	$0.2142$	$0.0030$	$31.6556$	$1.9727$
	$\pm 0.034$	$\pm 0.001$	$\pm 0.1627$	$\pm 0.009$

for the Cole model using (4), and

Table 3. Warburg model parameter values (mean ± standard deviation).

	#1	#2	#3	#4	#5	#6
FOT	0.0412	1.4833	1.6037	0.0215	1.9717	1.9261
Resmon	1.151	1.211	1.030	0.965	1.161	0.915

for the Warburg model using (5). An illustrative example of the GA algorithm is given in Figure 3.

The MRSE and NMRSE are calculated using Equations (8) and (9):

$$\mathrm{RMSE}(y,\widehat{y})=\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=0}^{N-1}{(y_i-{\widehat{y}}_i)}^2}$$

(8)

$$\mathrm{NRMSE}(y,\widehat{y})={\displaystyle \frac{\mathrm{RMSE}(y,\widehat{y})}{y_{\max }-y_{\min }}}$$

(9)

Over successive generations, the population of parameter sets converges towards an optimal or near-optimal solution until stopping conditions are met. The final parameter set is chosen based on the global best-fitting solution per patient. The fitness function (6) used in our study minimizes the error between the actual impedance measurements and those predicted by the fractional-order models (1). This approach ensures that the fractional-order models’ parameters obtained provide the best fit for the experimental data with the lowest error.

2.5. Data Analysis Using Spectrograms

An important step in the pre-processing of signals such as ECG, HR, and BR is the generation of spectrograms. Spectrograms provide a time–frequency analysis that reveals the energy distribution of the waveform across both time and frequency domains. This is achieved by segmenting the signal into shorter intervals and calculating the amplitudes of harmonic components within each segment. This method streamlines subsequent signal processing stages, eliminating many preliminary steps typically involved.

Linear interpolation is necessary because the recording of a single heartbeat consists of discrete points. The spectrogram, created using a moving window sample interval-based Fourier transform, displays changes in frequency over time, providing a comprehensive way to analyze biomedical signals by highlighting their frequency content and temporal variations.

For the BR signal, the spectrogram reveals regular breathing patterns and their frequency components. In the ECG signal, the spectrogram displays the periodic nature of heartbeats and their spectral characteristics. Similarly, HR spectrograms depict the dynamic changes in heart rate over time. An illustrative example of information gathered usign spectrograms is given in Figure 4, which shows the spectrograms for the measured signals with the EQV sensor, including HR, BR, and ECG. These spectrograms illustrate the spectral content changes of these signals over time, providing insights into their temporal and frequency characteristics. The time plot shows the time domain signals for BR, HR, and ECG over a period of 120 min.

The 2D spectrograms offer a different perspective, with the x-axis representing time (s) and the y-axis representing frequency (Hz). The color intensity indicates the amplitude of the frequencies. For the BR signal, the spectrogram highlights the dominant frequencies in the BR signal and their variations over time. In the case of the HR signal, a spectrogram shows the dynamic changes in heart rate, with higher frequencies corresponding to faster heart rates. For ECG signals, it provides a clearer view of the frequency components over time. This representation is useful for identifying specific frequency bands that correspond to different phases of the cardiac cycle.

In the 3D spectrogram representation, a detailed view on how the frequency components of the signals evolve over time is shown. The x-axis represents frequency (Hz), the y-axis represents time (s), and the z-axis (color intensity) represents the amplitude of the frequency components. For the BR, the spectrogram reveals periodic changes in frequency, indicative of the regular breathing pattern. In the case of the HR, the spectrogram reveals the dynamic changes in heart rate, with higher frequencies corresponding to faster heart rates. For the ECG, the spectrogram indicates the periodic nature of the heartbeats and the frequency variations between them.

2.6. Measurement Protocol

A protocol has been designed to facilitate integration of incoming data recorded at various sample time intervals and non-equally distributed in time and frequency domains. The protocol enables the synchronization of both respiratory lung function test data and the EQV data. The measurement protocol begins with a 2 min measurement using FOT, followed by a 5 min rest. Next, we measure for 1 min with RESMON and then the rest for another 5 min. This cycle continues with another 2 min the FOT measurement. Figure 5 illustrates the measurement protocol timeline over a two-hour duration, structured into ten measurements (Meas). Each measurement combines FOT and Resmon measurements interposed with rest periods to ensure tidal breathing conditions (diaphragm muscle relaxation between measurements).

Figure 6 illustrates the real-time clinical setup used for the measurement protocol, showcasing the two FOT devices and their associated components, alongside the EQV real-time physiological monitoring sensor. The setup includes the standalone Resmon PRO FULL device (highlighted with parts such as the device itself, an arm holder, and a touchscreen display for user interaction). Additionally, the lower-frequency 4P-FOT device is mounted on an adjustable table and connected to a laptop equipped with built-in programs for recording data and interacting with the system.

This figure also highlights the EQV sensor used for continuous physiological monitoring, displaying the real-time heart rate, respiratory rate, and other vital signals. The combination of these systems is fundamental for the comprehensive assessment of ambulatory respiratory mechanics performed in this study.

From the initialization of the patient’s measurement, we extract data over 2 min intervals and then discard them 11 min before extracting another 2 min interval, repeating this pattern until the end of the measurement. This way, we ensure that the EQV data are accurately synchronized with FOT measurements for a thorough analysis. The protocol timeline begins at 0 min and extends to 125 min (2 h and 5 min), with each measurement window being 13 min. For Meas 10, the measurement will not end with the final rest period as it reaches the end of the measurement protocol. Therefore, Meas 10 takes 8 min instead of the typical 13 min. The measurement protocol is defined as follows:

• Two min FOT Measurement: Represented in blue, this phase marks the beginning of each measurement session. Participants were instructed to breathe normally while seated for 120 s.
• Five min Rest: Indicated in gray, this phase is a rest period.
• One min Resmon Measurement: Depicted in pink, this phase involves using the Resmon device. Participants were asked to breathe normally while seated for 60 s.
• Five min Rest: Another rest period, shown in gray.

2.7. Subjects

In this study, a cohort of six healthy volunteers was evaluated in our laboratory during the two-hour measurement protocol. The biometric data are given in

Table 4. Biometric parameters of the volunteers.

ID	Age (Years)	Weight (kg)	Height (cm)	BMI (kg/${\mathbf{m}}^2$)
1	37	53	165	19
2	40	85	180	26
3	28	62	160	24
4	35	78	172	26
5	29	90	179	28
6	28	51	163	19

. All subjects were informed about the measurement protocol and provided their consent to participate.

3. Results

In Figure 7, the results obtained for the models introduced in Section 2.3 for the data recorded with the 4P-FOT device are depicted. The results presented in Figure 7 provide a comparative analysis of three investigated models, optimized using genetic algorithms. Figure 7a highlights the convergence of the genetic algorithm, demonstrating its efficacy in parameter optimization. The good fit between the measured data and the fractional-order model (1) indicates that the model accurately captures the properties of the respiratory system, suggesting that it has high fidelity in representing physiological phenomena (Figure 7b for one subject and Figure 7c for all subjects). The results obtained for the fractional-order impedance models in (4) and (5) are depicted in Figure 7d,e, respectively. These results also indicate a relatively good performance. The boxplot comparison of the error metrics shown in Figure 7f reveals that while all three models exhibit strong performance, the fractional-order impedance model given by (1) globally achieves the lowest error. The additional advantage of this particular type of fractional-order impedance model is that its parameters and its structure were extensively linked to anatomical and structural properties of the human lung [13].

In Figure 8, the results obtained for the identified models using the data measured with the RESMON are shown. The results presented in Figure 8 provide a comparative analysis of three investigated models, optimized using genetic algorithms. Figure 8a highlights the convergence of the genetic algorithm. The model fitting for the fractional-order impedance models from (1) for one subject is shown in Figure 8b and for all subjects in Figure 8c. The results obtained for the models from (4) and (5) are depicted in Figure 8d,e, respectively. Figure 8f illustrates the comparison of the error metrics between the models by means of a boxplot representation. Again, also in the case of high frequencies, it can be concluded that the fractional-order impedance model from (1)) delivers the best performance.

Identified model parameter values for the fractional-order, Cole, and Warburg models, respectively, for both the FOT and RESMON devices, are displayed in Table 1, Table 2 and Table 3. The results indicate that the fractional-order impedance model from (1) provides a good fit for both low-frequency and high-frequency measurements, with lower standard deviations suggesting consistent parameter estimation across subjects. The parameter values reflect the viscoelastic properties of lung tissues, with differences between the FOT and Resmon measurements highlighting the sensitivity of each method to different aspects of respiratory mechanics. The Cole model’s parameters exhibit higher variability compared to the fractional-order model, particularly in the high-frequency Resmon measurements. This variability may be due to the model’s sensitivity to high-frequency components and individual differences in respiratory impedance responses. The Warburg model’s parameters show notable differences between subjects, particularly in high-frequency Resmon measurements.

Overall, the parameter estimates from the three models provide valuable insights into the mechanical properties of the respiratory system. The fractional-order impedance model demonstrates superior performance in capturing the complex viscoelastic behavior of lung tissues, as evidenced by its lower error metrics and consistent parameter estimates. The Cole and Warburg models, while useful in specific contexts, exhibit higher variability and may be more sensitive to individual differences and measurement conditions. These findings suggest the importance of selecting appropriate models, which are based on the specific characteristics of the respiratory system being studied.

In Figure 9, the tissue damping ($G_r$), tissue elastance ($H_r$), and tissue hysteresivity ($\eta$) for both the 4P-FOT (Figure 9A) and RESMON (Figure 9B) devices are given. The damping factor is a material characteristic that indicates its ability to absorb energy. In materials such as polymers, which exhibit properties similar to lung tissue, damping primarily results from viscous tissue properties, i.e., the strain response lagging behind the applied stresses [13]. Significant changes in $G_r$ or $H_r$ parameters indicate enhanced or altered secretions that cause dysfunction in small airways. Changes in $H_r$ will induce changes in tissue elastance.

The tissue damping parameter ($G_r$) reflects the energy dissipation within the lung tissues, with the 4P-FOT measurements showing relatively consistent Gr values across subjects, indicating similar viscoelastic properties at low frequencies. In contrast, Resmon measurements exhibit greater variability in $G_r$, suggesting that high-frequency measurements are more sensitive to individual differences in tissue damping properties.

The tissue elastance parameter ($H_r$) represents the stiffness of the lung tissues, with the 4P-FOT measurements revealing moderate variability in $H_r$ among subjects, which may be attributed to differences in lung compliance and airway resistance. Resmon measurements show higher $H_r$ values with greater variability, indicating that high-frequency oscillations capture a broader range of elastance-related characteristics, potentially influenced by central airway properties and inertial effects.

The tissue hysteresivity parameter (${\eta }_r$), the ratio of tissue damping to tissue elastance, characterizes the heterogeneity of the lung tissue. 4P-FOT measurements show relatively low and consistent (${\eta }_r$) values across subjects, reflecting uniform viscoelastic behavior at low frequencies. The Resmon measurements display higher ${\eta }_r$ values with significant variability, suggesting that high-frequency measurements are more sensitive to heterogeneous tissue properties and regional differences within the lungs.

Changes in $G_r$ and $H_r$ indicate alterations in tissue composition and mechanics, relevant for conditions such as fibrosis and emphysema, while variations in (${\eta }_r$) can provide insights into the degree of tissue heterogeneity, crucial for diagnosing and managing obstructive lung diseases.

Figure 10, Figure 11 and Figure 12 present the spectrograms of HR data for intervals 1 to 24, measured using the EQV sensor. The spectrograms offer a comprehensive view of the temporal and frequency characteristics of the HR signals over the two-hour monitoring period. The HR signal exhibits significant frequency variations over time, indicative of natural fluctuations in heart rate due to physiological processes such as respiration, physical activity, etc. Dominant frequency components, corresponding to the fundamental heart rate and its harmonics, suggest periodicity in the HR signal, characteristic of regular cardiac cycles. Changes in the color intensity of the spectrograms reflect amplitude modulations in the HR signal, attributable to variations in cardiac output influenced by factors such as stress (which could have been the case for some of the subjects).

The HR spectrograms in Figure 10, Figure 11 and Figure 12 demonstrate the utility of continuous EQV sensor monitoring combined with spectrogram analysis for the comprehensive assessment of heart rate dynamics, enabling real-time tracking of cardiovascular function and potentially improving clinical decision making and patient outcomes. This integration offers a robust framework for understanding the complex interactions between physiological processes and heart rate variability, with future studies having the potential to investigate the correlation between spectrogram features and specific clinical conditions to enhance the diagnostic and prognostic capabilities of this technique.

To generate these spectrograms, the HR signal was first segmented into shorter intervals, each representing a five-minute segment of data. For each segment, a moving window Fourier transform was applied to compute the spectrogram. The window size and overlap were carefully chosen to balance time and frequency resolution, ensuring that both rapid and slow variations in the HR signal could be accurately captured.

The parameters for the spectrograms were determined with a window size of 20 samples to balance frequency resolution and time localization, an overlap appropriate to ensure continuity and reduce spectral leakage, a frequency range of 0 to 0.5 Hz to capture typical HR variability components, and an FFT length of 20 to match the window size for an efficient computation. These parameters were optimized based on preliminary analyses using a grid search with the meshgrid and ndgrid functions, along with cross-validation by employing the crossval function in MATLAB—Mathworks, which are techniques commonly used in Artificial Intelligence (AI) tools—to ensure that the spectrograms accurately reflected the temporal and frequency dynamics of the HR signals. The HR spectrograms for all patients can be found in the Supplementary Materials.

Figure 13 presents the correlation matrices between the impedance model parameters and the physiological parameters measured by the EQV sensor for six different subjects.

Across all matrices, certain correlations consistently stand out. For instance, the parameter ${\eta }_r$ shows a strong correlation with ECG Lead 1 in three subjects (subjects 1, 2, and 6), with values reaching up to 0.94. The heart rate (HR) also exhibits notable correlations with Hr and ${\eta }_r$ in multiple subjects, e.g., patient 1 and patient 6.

Some correlations remain strong across different subjects, and others vary. For example, the correlation between the R and ECG Lead 1 is high for patient 3 but not consistently strong across others. Likewise, the parameter $G_r$ shows moderate to high correlations with the HR in several subjects, indicating a less consistent but still significant relationship.

The strong correlation of ${\eta }_r$ with ECG Lead 1 across multiple subjects suggests that ${\eta }_r$, representing the ratio of tissue damping $G_r$ to tissue elastance $H_r$, is closely related to the electrical properties of cardiac activity. This relationship indicates that variations in cardiac cycles significantly influence impedance, reflecting changes in heart function, and could serve as an additional estimator for lung disease.

The notable correlations between HR and impedance parameters, such as $H_r$ and ${\eta }_r$, further suggest that heart activity can be an additional indicator of a lung condition. Since $H_r$ represents tissue elastance, its correlation with HR suggests that the mechanical properties of the lung tissue, such as stiffness, are interconnected with heart function. Additionally, the variability in correlations across different subjects, such as between R and ECG Lead 1 or $G_r$ and HR, highlights the individual differences in impedance responses. This variability highlights the importance of personalized assessments in clinical settings, as individual physiological differences can significantly impact impedance measurements.

Recent advancements in physical neural networks, such as programmable surface plasmonic neural networks for microwave detection and processing [30] and planar diffractive neural networks for direct electromagnetic information processing [31], offer promising avenues for improving the real-time processing and analysis of physiological signals. These systems provide opportunities for integrating more sophisticated machine learning models directly into the hardware used for monitoring, reducing the computational complexity and enhancing data processing speed. In the context of our study, incorporating such techniques could enable a faster and more accurate analysis of respiratory impedance data, particularly in continuous monitoring environments. Future research could explore how these novel physical neural networks can be adapted to enhance respiratory diagnostics and monitoring through real-time signal processing in wearable devices.

4. Discussion

This study integrates FOT with continuous EQV sensor monitoring to enable complementary information into the assessment of respiratory mechanics. The primary objective was to develop a comprehensive framework that integrates into a feasible ambulatory protocol the strengths of FOT and EQV technologies to improve respiratory monitoring.

The findings of this study offer a promising framework for advancing non-invasive respiratory mechanics assessments using a combination of low-frequency FOT and continuous monitoring with wearable sensors. Future research could explore the application of this integrated approach in clinical settings, particularly for the early diagnosis and management of chronic respiratory conditions such as COPD and idiopathic pulmonary fibrosis. Additionally, the potential to incorporate artificial AI tools for real-time data analysis and forecasting opens new avenues for predictive diagnostics. This study has laid the groundwork for further exploration into the role of smart textiles and continuous physiological monitoring in personalized healthcare for wearable health technology, which continues to evolve. Expanding this work to include diverse patient populations and different respiratory conditions will be essential for validating its clinical utility and enhancing its effectiveness in long-term monitoring and disease management.

In this study, we compared different models for respiratory mechanics assessments, including the fractional-order impedance model and the Cole–Cole model, to determine which model best fits the data collected through both FOT and EQV continuous monitoring. While previous studies have utilized FOT for respiratory mechanics, our integration of the EQV wearable sensor system for continuous monitoring introduces a novel approach that has not been previously explored. The EQV system enables continuous tracking of physiological signals in real-life, ambulatory conditions, offering an advantage over traditional methods that rely on short-term, isolated measurements. Although there are no directly comparable studies using this combination of technologies, our results indicate that the EQV-FOT integration holds significant potential for enhancing respiratory assessments, particularly for long-term monitoring. Additionally, the incorporation of AI tools for real-time analysis further strengthens the utility of this approach by enabling predictive modeling and more personalized assessments [32]. The findings suggest that EQV, combined with FOT calibration, could serve as a robust tool for ambulatory respiratory monitoring and open new research directions in the field.

One of the limitations of FOT is the potential discomfort and impracticality of long-term use. While FOT provides detailed measurements of respiratory impedance, its application in continuous monitoring is limited due to the need for frequent and often intrusive measurements. This study addresses these limitations by integrating EQV sensors, which offer continuous, non-invasive monitoring of vital signals such as heart rate, respiratory rate, and skin temperature. Utilizing EQV for continuous monitoring reduces the need for repeated FOT measurements, thereby enhancing patient comfort and compliance. The ability to continuously monitor vital signals using EQV sensors and correlate them with impedance model parameters, providing a robust framework for the real-time assessments of lung function.

Moreover, the use of AI tools to analyze the obtained datasets from FOT and EQV highlights the potential to significantly enhance predictive capabilities, seeming to be a good candidate to continuously monitor patients for long time periods. AI algorithms based on time signals and correlations, as well as time–frequency image-based data such as spectrograms, can identify patterns and correlations that may not be apparent through traditional analyses. For instance, combining respiratory mechanic parameters with continuous monitoring data from EQV sensors could provide additional information to clinicians with respect to changes in lung function, potentially indicating the onset or progression of respiratory conditions. Based on this information, clinicians can decide if a FOT measurement is also needed to further investigate and confirm the observed changes in lung mechanics or to adjust treatment plans accordingly.

The results of this study suggest the advantages of using a multi-faceted approach to assess respiratory mechanics. By integrating FOT measurements with continuous EQV monitoring, a more comprehensive picture of lung function can be obtained. This approach not only improves the accuracy of respiratory assessments but also provides valuable insights into the dynamic behavior of the respiratory system under various conditions.

Hence, the integration of low-frequency FOT with continuous EQV sensor monitoring, coupled with the application of AI tools, offers a promising framework for enhancing respiratory mechanic assessment. Future research should focus on validating these findings in larger and more diverse populations, exploring the potential of AI-driven predictive models, and refining the integration of these technologies for broader clinical applications. This comprehensive approach has the potential to significantly improve the diagnosis, monitoring, and management of lung diseases, ultimately leading to better patient outcomes.

The protocol outlined in this paper involves rigorous and repetitive measurements. However, taking measurements over a two-hour period could be physically demanding and potentially exhausting for subjects with lung disease. AI analysis presents a promising solution to meet these challenges and can enhance the efficiency and accuracy of data collection, processing, and analysis, potentially reducing the need for prolonged measurement sessions. For instance, AI algorithms can predict respiratory mechanics by analyzing smaller sets of data and extrapolating results with high accuracy, which minimizes the physical strain on subjects.

Recent studies have demonstrated the application of AI in predicting and forecasting respiratory conditions. For example, a study used AI algorithms to predict the optimal timing for weaning subjects from mechanical ventilation in respiratory care. This study employed various AI algorithms, including random forests, support vector machines (SVMs), and neural networks, to analyze 26 feature variables from 670 intubated subjects. The models achieved high accuracy, with the area under the receiver operating characteristic curve (AUC) ranging from 0.792 to 0.868. The AI intervention reduced the mean number of ventilator days by 0.5 [33]. Another study applied AI methods, specifically long short-term memory (LSTM) networks, to predict emergency room visits for respiratory diseases based on environmental and physiological data. The inputs included air quality indices, weather data, and patient historical health records. The LSTM model effectively forecasted respiratory health crises, demonstrating AI’s ability to handle temporal data and provide early warnings for health interventions [34]. Furthermore, the use of deep learning techniques, such as convolutional neural networks (CNNs), to predict respiratory rates from biosignals has shown high accuracy. One study used CNNs to analyze photoplethysmography (PPG) signals, achieving an accuracy of over 90% in predicting respiratory rates. This approach underscores AI’s potential in continuous respiratory monitoring, providing real-time insights into respiratory mechanics and enabling timely responses to any abnormalities [35].

The spectrograms herein produced offer image-based time-varying information for AI analysis at various time intervals of evaluations. A small time period of variability in the breathing frequency will indicate the need for an increased effort in maintaining respiratory perfusion during measurement, indicating a rather low threshold of pressure–volume workload and a more viscous tissue. In contrast, a lack of variability will suggest a more elastic property of the lung tissue, with a longer maintenance period of constant effort. It is visible from Figure 13 that the model parameters are strongly correlated with the ECG and HR, as higher effort in breathing function is paired with a higher cardiac effort with an increased frequency. Spectrograms are ideal for detecting and capturing these variability patterns, with AI analysis being able to be used for diagnosis.

Several limitations are present in this work. One limitation of this study is the exclusion of measurements taken in different body postures and during simulated apnea. The position of the heart within the chest can vary with changes in posture, potentially impacting respiratory impedance measurements. Testing participants in positions such as lying on their side with the arm bent under the head, as is often carried out in clinical procedures like ultrasounds, could provide further insights into how body positioning affects respiratory mechanics. Additionally, the absence of simulated apnea tests during peak inhalation and exhalation may have limited our ability to observe impedance changes, especially in conditions where fluid accumulation or respiratory issues are present, such as during severe colds or in patients with lung diseases. While these experiments were outside the scope of the current study, future research should consider incorporating these factors to provide a more comprehensive understanding of respiratory mechanics in varying physiological conditions. Another limitation of this study is its small sample size of only six volunteers. The primary objective of this work was to demonstrate a proof of concept by integrating the Forced Oscillation Technique (FOT) with continuous Equivital sensor monitoring for an assessment of non-invasive respiratory mechanics. While the data collected from this limited sample provided valuable initial insights and supported the feasibility of the approach, we recognize that a larger cohort would be necessary to draw more statistically robust and generalizable conclusions. Future studies should involve a greater number of participants, including individuals with diverse demographic characteristics and various respiratory conditions, to further validate the findings and to better assess the variability and reliability of the proposed methods.

5. Conclusions and Future Perspectives

This study demonstrates the feasibility and advantages of integrating low-frequency FOT with continuous monitoring using Equivital (EQV) sensors for enhanced respiratory mechanics assessments. The integration allows for continuous, non-invasive monitoring, addressing the limitations of traditional FOT methods. Our findings suggest that fractional-order models, optimized via genetic algorithms, accurately capture the mechanical properties of the respiratory system. The correlation analysis between impedance model parameters and EQV data highlights the potential of using physiological signals to help in predicting respiratory mechanics. Additionally, the application of AI tools could further enhance the efficiency and accuracy of respiratory monitoring, reducing the need for prolonged measurement sessions. This approach leverages the strengths of both FOT and EQV technologies, providing a robust framework for continuous respiratory monitoring and early detection of lung function changes, which could significantly improve patient outcomes and advance respiratory monitoring and diagnosis. Recent studies have demonstrated the utility of these techniques in various settings, highlighting their potential for broader clinical applications and integration into everyday respiratory care. Future research should explore the clinical applications of this methodology in patients with respiratory diseases to validate its efficacy and broaden its applicability. While there have been previous studies that investigated the Forced Oscillation Technique (FOT) for the assessment of respiratory mechanics, the integration of continuous monitoring using wearable Equivital sensors in this study offers a novel approach. Traditional methods have largely focused on snapshot measurements using FOT, whereas our approach enables continuous monitoring of physiological signals, such as heart rate and respiratory rate, over extended periods. This continuous monitoring provides additional insights into the dynamic nature of respiratory function in real-life conditions. Furthermore, the use of fractional-order impedance models to analyze respiratory mechanics is another distinguishing feature of our study, as this method allows for a more detailed and accurate representation of tissue properties. Compared to other techniques, our proposed method offers the potential for non-invasive, ambulatory monitoring of patients, which could lead to improved diagnosis and management of chronic respiratory conditions. These advancements, coupled with the potential application of AI tools for real-time data analysis, set this study apart from existing research and provide a foundation for future exploration in the field.