For comparison purposes, RRest toolbox [15] was used to extract respiratory waveforms from a PPG using 10 feature-based and filter-based algorithms as shown in Figure 1. The resulting respiratory waveforms were temporally aligned to correspond with the reference respiratory waveform in the test set for comparison purposes. The techniques used to derive the respiratory waveforms, as well as our LSTM method, are described in Table 1.

We propose the use of an LSTM model as an alternative to the signal processing methods described in Table 1. In this section, we discuss our training and validation procedures to determine an appropriate LSTM architecture to predict a respiratory waveform.

The core component of an LSTM architecture is a memory cell whose characteristics allow long-term data dependencies to be captured. A single LSTM cell uses gate mechanisms to forget irrelevant parts of a previous state, selectively update the current cell state, and to output the cell state [12]. Each cell contains a number of hidden units that define the dimensionality of both the current and output states. Increasing hidden units within a model may lead to overfitting. Conversely, reducing hidden units below a certain threshold will not allow a model to be trained.

The final model had around 8257 trainable parameters consisting of 300 cells, 2 layers, and 16 hidden layers. To train our final model, we used AdamOptimizer with an initial learning rate of 0.02 and batch size of 256. We conducted 5-fold cross validation with approximately 223,786 training examples per fold with early stopping.

We defined a valid window when the Pearson correlation coefficient was >0.6 between the gold standard respiratory waveform and derived tidal volume waveform (TVW) in the window. For test sets that contained valid windows, we extracted peaks and troughs in MATLAB R2016b (MathWorks Inc, Natick, MA). To find the maximum points, ‘findpeaks’ was used, and we used a linear search algorithm to find the global minimum between 2 consecutive peaks. Using the peak and trough data, we extracted the following: IBI (the period in seconds between 2 consecutive peaks within the TVW signal), inspiration time (period in seconds between a trough and peak within the TVW signal), expiration period (period in seconds between a peak and trough within the TVW signal), and I:E (ratio between consecutive inspiration time and expiration period).

We then evaluated the Bland-Altman agreement [13] between the derived respiratory metrics to reference metrics.

Additionally, the root mean square error between hypothesized RTV signal y(t) and the true RTV Y(t) was calculated for each person and respiratory rate and subsequently averaged across the 5 folds.

Data were acquired from 10 healthy subjects. One subject was excluded because of incomplete recordings due to an SD card save error on the Alice PDx. Therefore, data for 9 subjects were analyzed. The median (lower, upper quartiles) age of the analyzed subjects was 28 years (24.5 to 33.0 years). Median BMI was 23.59 kg/m² (21.28 to 30.04 kg/m²), and 3 subjects (3/9, 33%) were female. In total, we recorded 3.75 hours of data, consisting of 5 minutes * 5 breathing rates * 9 participants.

The weights and biases were saved for each epoch during training. Training was stopped when the validation error diverged to avoid overfitting. Early stopping occurred when the validation cost did not improve for 5 epochs.

In total, 225 unique test sets were created from 9 participants, at 5 respiratory rates, over 5 folds. Each test set was a window of 1000 samples (40 seconds) in length. We plotted the number of valid windows as a function of increasing Pearson correlation coefficients between derived and reference respiratory waveforms in 0.2 increments in Figure 3. For a Pearson correlation coefficient ≥0.6, our approach, X_LSTM, was valid for 191/225 (85%) windows, while the next highest performing algorithm, X_A1, was valid for 128/225 (57%) windows, followed by X_A2, which was valid for 119/225 (53%) windows. Other algorithms were excluded from further analysis due to a small percentage of valid windows: 21/225 (9%) for X_A3, 56/225 (25%) for X_B1, 38/225 (17%) for X_B2, 36/225 (16%) for X_B3, 23/225 (10%) for X_B4, 65/225 (29%) for X_B5, 52/225 (23%) for X_B6, and 11/225 (5%) for X_B10.

Breathing metrics were averaged over each 40-second test set. The mean (SD) between derived and gold standard metrics and their associated t test results are shown in Table 3. The Bland-Altman agreement between derived and gold standard metrics for all subjects and respiratory rates are reported in Table 4. In the case of X_LSTM, a Savitzky-Golay filter was used to smooth the derived respiratory waveform prior to extracting the breathing metrics.

The Bland-Altman plot for the derived breathing metrics of inspiration time, expiration period, IBI, BR, and I:E across all participants (1-9) and all respiratory rates (6, 8, 10, 12, 14) using X_LSTM is shown in Figure 4. For comparison purposes, we report the Bland-Altman plot for derived respiratory rate across all participants and all respiratory rates using the highest performing algorithm found by Charlton et al [7] in Figure 5.

Our model consistently performed comparably to the other methods, showing similar agreement (lower bias) and variability (narrower limits of agreement). The relative bias for our model was <4% for all breathing metrics examined except for I:E ratio (at 9.9%), which is within the limits of accuracy of existing standards on the estimation of breathing metrics using conventional methods [5], although the limits of variability are wide.

The differences for inspiration time are bound within the 95% CIs for average inspiration periods <4 seconds. Distinct clustering can be seen around an inspiration period of 2 seconds (Figure 4A). The differences for expiration period are bound within the 95% CIs for average expiration periods of 2-3 seconds (Figure 4B). For IBI, 4 distinct clusters occur corresponding to intervals of 4, 5, 6, and 7 seconds; however, the clustering weakens above 9 seconds (Figure 4C). For BR, 5 distinct clusters are formed corresponding to expected BRs of 6, 8, 10, 12, and 14 BPM (Figure 4D). There is noticeable clustering for I:Es of 0.8-1 (Figure 4E).

To quantify the accuracy of our model and provide a metric for future comparisons, we report the root mean square error over all participants and respiratory rates for X_LSTM for inspiration time (0.77 seconds), expiration period (0.74 seconds), IBI (0.8377 seconds), BR (0.86 BPM), and I:E (1.15).

In this work, we were interested in determining the feasibility of finding continuous measures of inspiration time, expiration period, IBI, BR, and I:E metrics from a PPG. We showed how an LSTM architecture could be used to predict these metrics for 191/225 (85%) test sets comprised of 9 participants at a respiratory rate of 6, 8, 10, 12, or 14 BPM. We conducted Bland-Altman analyses and found the LSTM was able to predict the average inspiration time of –0.16 seconds (–1.64 to 1.31 seconds) and expiration period of 0.09 seconds (–1.35 to 1.53 seconds) over a 40-second window. The LSTM was able to predict an I:E ratio of 0.09 (–0.66 to 0.84), although this was poorly correlated with reference values. However, this is the first time this metric is being reported in the literature as measured from a pulse signal.

The LSTM model was trained to minimize the error between derived and reference respiratory waveforms and was then able to generalize the breathing characteristics of 9 subjects and predict future respiratory waveforms based on PPG data. The ability to “see and learn” a reference signal presents a distinct advantage over existing methods. Through this approach, it was possible to determine the continuous average breathing metrics of inspiration time, expiration period, IBI, and BR for the majority of time (85%), exceeding a Pearson correlation threshold of 0.6. In contrast, these breathing metrics could only be derived, at best, around half the time (56% in the case of X_A1) using existing feature-based and filter-based algorithms that did not rely on any previous reference data. While we directly compared the performance of X_A1 and X_A2 to the LSTM method, other methods were excluded from this analysis due to the fact that the correlation between the derived respiratory waveform and the gold standard was <0.6 more than 80% of the time. Feature-based techniques (X_B1-X_B6, X_B10) have performed well in previous respiratory rate algorithm assessments by Charlton et al [7] and would likely have similar performance on this dataset. In the cases where breathing metrics could be extracted for X_A1and X_A2, we found that the metrics of inspiration time, expiration period, and I:E were poorly correlated with the reference metrics, as shown in Table 4.

We conducted Bland-Altman analysis on the highest performing algorithm X_B1,2,3E_T4F_M1 found by Charlton et al [7] in his comparison of classical signal processing algorithms for PPG. The bias in our dataset compared to those in the dataset used by Charlton et al [7] was higher (–1.12 vs 1). However, the 95% limits of agreement (BPM) was lower (–2.4 to 2.1 vs –5.1 to 7.2). X_LSTM compares favorably to X_B1,2,3E_T4F_M1 with similar bias (0.12 vs –1.10) and a smaller 95% limits of agreement (BPM; –2.13 to 2.37 vs –2.63 to 2.44). The bias in our model compares well against existing standards on breathing metric estimation using conventional methods, which stipulate an accuracy of at least 2% for respiratory rate. It is worth noting that the standards are formulated for infant populations who breath faster. The wide variability seen in our model could be improved, although it is lower than that obtained from other methods examined. The high degree of variability could arise from differences in accuracy with different respiratory rates. While there is insufficient data from this study to ascertain this, it justifies use of longer-term data collection for further investigation.

The hyperparameters for the LSTM model were chosen in a structured, although non-exhaustive, manner by comparing a change in the number of cells, hidden units, or layers to a fixed model. Figures 2-4 show a decreasing trend in the correlation between the LSTM-derived respiratory waveform and the reference waveform as the number of participants increased. This trend occurred irrespective of the number of cells, hidden units, or layers. This may be accounted for, in part, by the complexity for which the LSTM model must account as the participant population increases. In the specific case of 300 cells, the correlation curve decreased quasi-exponentially. However, in the case of hidden units and layers, the correlation curve decreased quasi-linearly. It remains to be seen if the minimum correlation is bound between derived and reference respiratory waveforms for a given population. The findings of this paper show that our previous network parameter was much larger than required [11].

In this work, we used the following 4 features: PPG, filtered PPG, SPO₂, and pulse rate. We did not conduct feature selection, which may have helped to improve the overall model performance. It would be useful to see the effect of removing the filtered PPG signal feature to reduce additional preprocessing time and computational power.

Due to a limited participant population, we did not conduct leave-one-out participant cross validation. The shape of each respiratory waveform varied from person to person, and it is unlikely that the LSTM model derived in this work would be able to predict respiratory metrics from an unseen participant. However, with a larger training population, the LSTM model may be exposed to enough data to enable the accurate prediction of respiratory metrics in an unseen participant. Previously, we found that participants would prefer that a wearable sensor device have a watch form factor [23]. In this paper, we did not look at the feasibility of implementing an LSTM in this type of form factor. Currently, LSTM training requires GPU-grade computational power. With current low-power Bluetooth low energy devices [11,24,25], it may be possible to acquire PPG data and stream real-time data to a cloud-based GPU server to run online training. Once the weights and biases of the LSTM architecture are found, it may also be possible for an embedded platform to perform the required processing to obtain real-time breathing metric predictions. At present, field-programmable gate arrays can be used for real-time predictions and benefit from low latency and low power consumption [26]. Additionally, the field-programmable gate array architecture is reconfigurable. This would allow any potential device to be individually tailored to a specific model.

This paper presents the feasibility of monitoring simple breathing metrics such as the IBI, BR, inspiration time, expiration period, and I:E for a person at rest. We hope this proof-of-concept paper will inspire future research to collect further data and develop more powerful machine learning algorithms. In the future, it may also be possible to derive these metrics from a wristworn device that contains a pulse oximeter and accelerometer for a person at rest and support potential longitudinal studies to determine if these metrics can provide further information on asthma type [3] and provide any clinical utility [4].