Respiratory Effort Estimator

• Respiratory effort estimator is a computational system that infers the true mechanical or neural drive required to breathe using diverse signals and sensor modalities.
• It distinguishes between direct estimation methods (e.g., audio and effort belts) and indirect or proxy approaches (e.g., ECG, PPG, and radar) that recover surrogate respiratory signals.
• These systems enhance clinical diagnostics in sleep medicine and ICU settings, although challenges with calibration and target non-equivalence persist.

A respiratory effort estimator is a computational system that infers respiratory effort or an effort-related surrogate from measured signals. In the strict physiological sense, respiratory effort refers to the mechanical or neural drive required to breathe and is often linked to pleural pressure swings, chest wall or abdominal effort belts, diaphragmatic EMG, or esophageal pressure (Addeh et al., 2024). Contemporary systems span direct estimation from nocturnal audio, effort-related motion recovery from fingertip triaxial accelerometers, downstream event inference from a single abdominal effort belt, and a broader family of indirect estimators that recover respiratory waveform, respiratory motion, respiratory pattern, or respiratory rate from ECG, PPG, video, radar, WiFi RSS, and fMRI-derived signals (Xu et al., 18 Sep 2025, Lin et al., 24 Apr 2026, Nassi et al., 2021, Rathore et al., 2021, Kite et al., 21 Aug 2025, Miao et al., 2024, Prathosh et al., 2016, Möderl et al., 2022, Abdelnasser et al., 2015, Addeh et al., 2024). A central issue across this literature is that respiratory effort, respiratory motion, respiratory waveform, respiratory variation, and respiratory rate are related but non-equivalent targets.

1. Physiological target and neighboring quantities

Respiratory effort estimation is often conflated with estimation of respiratory rate, respiratory waveform amplitude, or respiratory fluctuation. The distinction is technically decisive. Respiratory rate is a scalar temporal frequency, typically breaths per minute. Respiratory waveform estimators reconstruct a continuous signal related to breathing mechanics or airflow. Respiratory variation in the fMRI literature is a smoothed amplitude-summary target defined as the standard deviation of the respiratory waveform within a six-second sliding window, rather than a breath-by-breath effort measure (Addeh et al., 2024):

$$RV(t) = \mathrm{std}\left(r(\tau)\right), \quad \tau \in [t-3\,\text{s},\, t+3\,\text{s}].$$

Phase-derived quantities also sit adjacent to effort without being equivalent to it. In ECG-based phase estimation, fractional inspiratory time is defined by inspiratory duration over total cycle duration,

$$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$

and was framed as an obstruction-related timing measure rather than a direct effort amplitude estimate (Nyamukuru et al., 2020). Likewise, a 60-second ECG telemetry model that predicts minute-averaged respiratory rate from raw single-lead ECG estimates a scalar respiratory frequency target, not work of breathing or pressure swing (Kite et al., 21 Aug 2025).

The practical consequence is that a system may be highly accurate for respiratory rate or respiratory waveform recovery and still fail as a respiratory effort estimator. This is especially important in obstructive conditions, where effort can rise while airflow or external motion changes are attenuated or altered; the fMRI respiratory-variation study explicitly notes that a surrogate respiration-amplitude estimator may then fail to reflect true effort (Addeh et al., 2024).

2. Sensor modalities and estimator classes

The literature supports a useful division into direct effort estimation, effort-proximal motion estimation, downstream inference from effort sensors, and indirect proxy estimation. The field is heterogeneous because the target itself is heterogeneous.

Modality	Estimated target in the cited work	Relation to respiratory effort
Nocturnal audio	30-second abdominal respiratory effort waveform	Direct estimator from sound (Xu et al., 18 Sep 2025)
Fingertip triaxial accelerometer	TAA-resp surrogate and RMI	Effort-related motion surrogate (Lin et al., 24 Apr 2026)
Abdominal effort belt	Respiratory events and AHI/RDI	Downstream inference from effort waveform (Nassi et al., 2021)
ECG + accelerometer wearable	Respiration waveform and average RR	Indirect proxy estimator (Rathore et al., 2021)
fMRI BOLD + head motion	Respiratory variation waveform	Not a direct effort estimator (Addeh et al., 2024)
UWB radar	Latent respiratory chest-motion waveform	Contact-free motion surrogate (Möderl et al., 2022)

Direct or near-direct approaches use a signal already tied to respiratory mechanics. The clearest example is the audio-to-effort model trained on abdominal effort waveforms (Xu et al., 18 Sep 2025). Effort-proximal motion systems include fingertip triaxial accelerometry, radar-based chest-motion estimation, video respiratory-pattern estimation, WiFi RSS breathing-waveform recovery, and FSR-based thoracoabdominal motion sensing (Lin et al., 24 Apr 2026, Möderl et al., 2022, Prathosh et al., 2016, Abdelnasser et al., 2015, Baraeinejad et al., 2024). These measure motion consequences of breathing rather than pressure-generating effort itself. Downstream inference systems take an established effort sensor, such as an abdominal inductance plethysmography belt, and infer clinically relevant state variables such as apnea class or AHI (Nassi et al., 2021). Indirect proxy systems instead learn respiration-related dynamics from signals not acquired as respiratory channels, including ECG, PPG, rPPG, wearable audio, or fMRI nuisance variables (Rathore et al., 2021, Kite et al., 21 Aug 2025, Miao et al., 2024, Saikia et al., 19 Jun 2026, Kumar et al., 2021, Addeh et al., 2024).

3. Direct and effort-proximal estimators

The most explicit direct estimator in the supplied literature is “Estimating Respiratory Effort from Nocturnal Breathing Sounds for Obstructive Sleep Apnoea Screening” (Xu et al., 18 Sep 2025). It maps 30-second smartphone audio windows to 30-second abdominal respiratory effort segments sampled at 32 Hz, so each target has 960 samples. The input is a 64-bin log-Mel representation computed at 16 kHz with a 50 ms Hann window and 20 ms frame shift, yielding a $1500 \times 64$ time-frequency matrix per segment. The estimator uses a CNN feature extractor, an LSTM encoder, and a linear decoder that produces a 187-point scalar sequence, which is then interpolated to 960 samples. Training uses concordance correlation coefficient loss,

$\mathcal{L}_{\text{effort}} = 1 - \rho_c,$

and the reported estimator performance is $\mathrm{CCC} = 0.478 \pm 0.133$, $\mathrm{RMSE} = 1.053 \pm 0.123$, and $\mathrm{MAE} = 0.793 \pm 0.092$ on 157 nights from 103 participants under 10-fold subject-level cross-validation (Xu et al., 18 Sep 2025). This paper is unusually important because it makes respiratory effort itself the supervised target rather than a surrogate rate.

A second important effort-proximal system is the fingertip triaxial-accelerometer pipeline “Fingertip Micro-Motion as a Source of Respiratory Information During Sleep Using Triaxial Accelerometers” (Lin et al., 24 Apr 2026). Raw fingertip accelerometry is sampled at 50 Hz, integrated once along each axis, projected onto an optimal direction $\theta^*\in S^2$ chosen to maximize spectral concentration in the respiratory band $0.1$–$0.4$ Hz, and normalized to form a one-dimensional surrogate called TAA-resp. The paper then uses SST-based phase extraction and defines the respiratory motion index

$$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$0

with $$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$1 covering 0.8–1.2 Hz and 1.8–2.2 Hz in the unwrapped domain. TAA-resp correlates more strongly with thoracic and abdominal effort channels than with airflow: over high-quality segments, synchronized correlations are $$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$2 with THO, $$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$3 with ABD, and $$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$4 with airflow (Lin et al., 24 Apr 2026). The paper therefore supports an effort-related interpretation, but it also states that the magnitude of high-quality TAA-resp cannot be reliably used to infer respiratory effort.

A distinct but clinically important use of effort sensors is downstream event inference. “Automated Respiratory Event Detection Using Deep Neural Networks” (Nassi et al., 2021) uses a single abdominal respiratory effort belt as the only input to a 12-layer WaveNet-style temporal convolutional model with kernel size 2, 32 filters, and 7-minute windows. It does not estimate effort amplitude; it estimates respiratory state. On the MGH dataset, binary event detection achieves 95% accuracy, 71% sensitivity, 97% specificity, 68% precision, 70% F1-score, AUROC 0.93, AUPRC 0.74, and AHI $$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$5 (Nassi et al., 2021). Central apnea is much easier than obstructive apnea, hypopnea, or RERA from one effort channel alone, which is informative for respiratory effort estimators because it shows what one effort-belt waveform can and cannot disambiguate.

At the hardware level, “Design and Implementation of an IoT-based Respiratory Motion Sensor” (Baraeinejad et al., 2024) describes an FSR-based wearable transducer that measures thoracic or abdominal circumference changes through a voltage divider,

$$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$6

with $$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$7 and $$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$8. The device measures respiratory motion, not absolute effort, but it illustrates the sensor-design boundary between a motion transducer and a respiratory effort estimator (Baraeinejad et al., 2024).

4. Indirect estimation from secondary signals

A large part of the literature estimates respiration-related variables from signals not acquired as respiratory channels. These systems are technically relevant because they contribute architectures, fusion strategies, and quality-control mechanisms, but they should not be mistaken for direct effort estimators.

Wearable multimodal proxy learning is exemplified by “Multitask Network for Respiration Rate Estimation -- A Practical Perspective” (Rathore et al., 2021). The best configuration, CONF-E, uses three intermediate respiratory surrogates derived from ECG R-R interval modulation, ECG R-peak amplitude modulation, and accelerometer-derived respiration over 32-second windows. A shared encoder produces latent representation $$\mathrm{FIT} = \frac{T_{\mathrm{insp}}}{T_{\mathrm{tot}}},$$9, a decoder reconstructs respiration waveform $1500 \times 64$0, and an RR head predicts average respiration rate $1500 \times 64$1:

$1500 \times 64$2

Training uses Smooth $1500 \times 64$3 losses on waveform and RR targets. CONF-E reaches average RR MAE 2.35, RMSE 2.95, instantaneous RR MAE 2.95, RMSE 3.69, with 23.04 M parameters and 9.47 ms inference time (Rathore et al., 2021). The direct contribution to effort estimation is architectural: shared latent multitask learning around a reconstructed respiratory waveform.

ECG-only systems push this further toward scalable deployment. “Continuous Determination of Respiratory Rate in Hospitalized Patients using Machine Learning Applied to Electrocardiogram Telemetry” (Kite et al., 21 Aug 2025) uses 60-second, 120 Hz, single-lead ECG segments normalized per segment and processed by a 60-layer, 14.91 M-parameter 1D ConvNeXt with MSE loss. Internal MGH impedance-based validation yields MAE 0.76 bpm and $1500 \times 64$4; external MIMIC validation yields MAE 1.78 bpm and $1500 \times 64$5 (Kite et al., 21 Aug 2025). “Extracting Fractional Inspiratory Time from Electrocardiograms” (Nyamukuru et al., 2020) instead treats ECG-to-respiratory-phase inference as sample-wise binary segmentation with a multitask GRU. It estimates FIT by duty cycle,

$1500 \times 64$6

and reports MIMIC FIT RMSE 0.06 with RR RMSE 0.54 bpm, and CEBS FIT RMSE 0.11 with RR RMSE 0.66 bpm (Nyamukuru et al., 2020). Both papers show that ECG contains learnable respiratory information, but neither claims direct effort estimation.

PPG and camera-based systems take a similar route. “RespDiff” (Miao et al., 2024) formulates PPG-to-respiratory-waveform estimation as conditional diffusion. Both PPG and target respiratory waveform are downsampled to 30 Hz, low-pass filtered at 1 Hz, segmented into 5-second windows, and the model is trained with diffusion loss plus spectral loss,

$1500 \times 64$7

with $1500 \times 64$8. On BIDMC, RespDiff reports RR MAE 1.18 bpm, better than prior values ranging from 1.66 to 2.15 bpm (Miao et al., 2024). “A Skin-Tone-Aware Dual-Representation Remote Photoplethysmography Framework for Contactless Respiratory Rate Estimation” (Saikia et al., 19 Jun 2026) uses a skin-tone-aware RGB projection for the Eulerian stream,

$1500 \times 64$9

and a denoised motion-based Lagrangian stream, then fuses rate estimates. ELITE-RR reaches MAE 2.79 and RMSE 3.34 on combined COHFACE + RR-rPPG evaluation (Saikia et al., 19 Jun 2026). These works remain RR-centric, but their intermediate waveforms and motion streams are effort-relevant in principle.

Contact-free motion estimators recover a respiratory waveform or motion surrogate more directly. “Variational Message Passing-Based Respiratory Motion Estimation and Detection Using Radar Signals” (Möderl et al., 2022) models mean-subtracted UWB radar observations as

$\mathcal{L}_{\text{effort}} = 1 - \rho_c,$0

where $\mathcal{L}_{\text{effort}} = 1 - \rho_c,$1 is the latent respiratory motion waveform and $\mathcal{L}_{\text{effort}} = 1 - \rho_c,$2 the target-interacting channel. VMP jointly estimates respiratory motion and channel parameters and reaches detection probability 0.95 at $\mathcal{L}_{\text{effort}} = 1 - \rho_c,$3 dB SNR, versus 0.32 for an estimator-correlator and 0.05 for an FFT-based detector (Möderl et al., 2022). “Estimation of respiratory pattern from video using selective ensemble aggregation” (Prathosh et al., 2016) treats each pixel as a noisy LTI channel driven by a common latent respiratory pattern,

$\mathcal{L}_{\text{effort}} = 1 - \rho_c,$4

projects pixel time series into a quadratic subspace, selects a phase-consistent half-ellipse of channels, and averages them. On ventral-view recordings, RR correlation with impedance pneumography is $\mathcal{L}_{\text{effort}} = 1 - \rho_c,$5; on lateral view it is $\mathcal{L}_{\text{effort}} = 1 - \rho_c,$6 (Prathosh et al., 2016). “UbiBreathe” (Abdelnasser et al., 2015) reconstructs a breathing waveform from WiFi RSS via respiratory-band FFT selection, inverse FFT, trimmed-mean stabilization, and wavelet denoising, reporting less than 1 bpm error and apnea detection above 96% accuracy with five streams (Abdelnasser et al., 2015). These are not calibrated effort estimators, but they are direct motion- or pattern-recovery systems.

Finally, modality-specific retrospective physiological recovery can resemble effort estimation while remaining conceptually distinct. The fMRI study “Machine Learning-based Estimation of Respiratory Fluctuations in a Healthy Adult Population using BOLD fMRI and Head Motion Parameters” (Addeh et al., 2024) reconstructs respiratory variation from windows of 90 ROI-averaged BOLD signals plus six rigid-body motion traces $\mathcal{L}_{\text{effort}} = 1 - \rho_c,$7, using three 1D CNNs aligned to beginning, center, and end contexts. The strongest conclusion is not about effort; it is that motion-like nuisance channels can act as indirect respiration sensors.

5. Validation regimes and application domains

Application domain shapes both target choice and evaluation. Sleep medicine dominates the effort-specific literature. In nocturnal audio, the estimated-effort embeddings improve OSA screening relative to audio-only baselines: at AHI $\mathcal{L}_{\text{effort}} = 1 - \rho_c,$8, sensitivity rises from 0.86 to 0.88 and AUC from 0.75 to 0.86; at AHI $\mathcal{L}_{\text{effort}} = 1 - \rho_c,$9, AUC reaches 0.88 (Xu et al., 18 Sep 2025). In effort-belt-only sleep event detection, binary abnormal-vs-normal breathing is strong, but subclassification is uneven: central apnea sensitivity is 81%, obstructive apnea sensitivity 46%, RERA sensitivity 29%, and hypopnea sensitivity 16% (Nassi et al., 2021). Fingertip TAA is more intermittent: high-quality respiratory information is present over $\mathrm{CCC} = 0.478 \pm 0.133$0 of full-night recordings on average, with only 6.06% of apnea segments labeled high-quality (Lin et al., 24 Apr 2026).

Hospital telemetry emphasizes scale and generalization. The ECG telemetry study uses patient-level train/tune/validation splits and external validation, then shows respiratory-rate trajectories rising 8–10 hours before intubation-related events and reaching roughly 20% above baseline near the event (Kite et al., 21 Aug 2025). By contrast, some wearable studies are less explicit about subject independence. The ECG-plus-accelerometer multitask network states only an 80:20 train/test split, and the authors do not describe subject-wise separation (Rathore et al., 2021). The fMRI respiratory-variation paper reports 10-fold cross-validation on 900 HCP-YA resting-state scans but does not state whether folds are split by scan or by subject, which matters for leakage assessment (Addeh et al., 2024). The nocturnal audio effort paper is stronger on this point: it uses 10-fold cross-validation with subject-level 8:1:1 train/validation/test splits (Xu et al., 18 Sep 2025).

Another domain is retrospective physiological recovery rather than monitoring. The fMRI study is explicitly motivated by missing or poor-quality respiratory recordings and by the confounding role of breathing in BOLD analysis; its expected impact is lower cost and reduced participant burden because respiratory bellows are not required (Addeh et al., 2024). This application is far from clinical effort monitoring, but it highlights a recurring pattern: respiratory signals are often reconstructed because direct sensing was absent, obtrusive, or unreliable.

6. Misconceptions, limitations, and likely trajectories

A persistent misconception is that any respiration-related estimator is an effort estimator. The supplied literature repeatedly argues against that interpretation. Respiratory variation from fMRI is not effort (Addeh et al., 2024). Minute-averaged RR from ECG telemetry is not effort (Kite et al., 21 Aug 2025). FIT from ECG is an obstruction-related timing feature, not an effort amplitude (Nyamukuru et al., 2020). A reconstructed respiration waveform from ECG, PPG, or accelerometry may support downstream effort features, but amplitude fidelity is often unvalidated; the wearable multitask paper explicitly validates its reconstructed waveform mainly through downstream rate accuracy rather than waveform fidelity metrics (Rathore et al., 2021).

A second limitation is calibration. Motion transducers and motion surrogates usually measure the external consequence of breathing, not the underlying force generation. The IoT FSR device measures breathing-induced force on an FSR caused by thoracic or abdominal circumference change, and the paper is explicit that it monitors respiratory motion rather than quantitative work of breathing (Baraeinejad et al., 2024). Fingertip TAA-resp is effort-related but not amplitude-calibrated (Lin et al., 24 Apr 2026). Radar, video, and WiFi systems recover motion waveforms up to scale, geometry, or channel effects rather than absolute physiological effort (Möderl et al., 2022, Prathosh et al., 2016, Abdelnasser et al., 2015).

A third limitation is population and protocol dependence. Several studies are healthy-adult-only or healthy-exercise-only, including the fMRI respiratory-variation work and the wearable breath-audio study after exertion (Addeh et al., 2024, Kumar et al., 2021). The ECG telemetry work is ICU-heavy (Kite et al., 21 Aug 2025). Home audio effort estimation is trained in real-world conditions but still requires synchronized effort labels during development (Xu et al., 18 Sep 2025). This suggests that generalization across age, disease phenotype, sensor placement, and environmental conditions remains a primary obstacle.

A plausible implication is that future respiratory effort estimators will need direct effort-related supervision rather than rate-only or waveform-surrogate supervision. The supplied literature repeatedly points to suitable targets: esophageal pressure, chest or abdominal inductance effort belts, diaphragmatic EMG, or clinically labeled work-of-breathing measures (Addeh et al., 2024). A second plausible implication is that the most robust systems will combine waveform reconstruction with summary prediction and explicit quality gating: multitask encoders from wearable respiration estimation, latent effort embeddings from audio, motion-strength gating with RMI, and raw-waveform temporal models from radar or ECG all point in that direction (Rathore et al., 2021, Xu et al., 18 Sep 2025, Lin et al., 24 Apr 2026, Möderl et al., 2022). In that formulation, a respiratory effort estimator is less a single model than a hierarchy: signal recovery, quality assessment, effort-specific supervision, and downstream clinical inference.