KDCL_sInvResUNet for Cuffless ABP Monitoring

• The paper introduces KDCL_sInvResUNet, a model that reconstructs continuous arterial blood pressure waveforms from ECG, PPG, and its derivatives using a lightweight 1D UNet architecture.
• It employs MobileNetV2-style inverted residual blocks, squeeze-and-excitation attention, and depthwise separable convolutions to enable efficient, real-time, embedded deployment.
• The model achieves competitive performance with approximately 10 mmHg MAE and high correlation on a heterogeneous perioperative dataset comprising over 1.25 million segments.

Searching arXiv for the target paper and closely related works to ground the article. KDCL_sInvResUNet is a lightweight deep learning model for reconstructing the continuous invasive arterial blood pressure waveform from non-invasive physiological signals, specifically electrocardiogram, photoplethysmogram, the first derivative of photoplethysmogram, and the second derivative of photoplethysmogram, with a corresponding 10-second arterial blood pressure output in mmHg (Li et al., 7 Aug 2025). It is the collaboratively distilled version of sInvResUNet and was introduced for continuous, cuffless, noninvasive arterial blood pressure monitoring in perioperative and critical care settings under severe resource constraints, with explicit emphasis on real-time embedded deployment, subject-independent validation, and robustness assessment on a large-scale heterogeneous perioperative dataset.

1. Clinical scope and task formulation

KDCL_sInvResUNet is situated in perioperative and critical care monitoring, where rapid blood pressure changes and persistent hypotension or hypertension can cause organ damage. In this setting, continuous invasive arterial blood pressure via arterial lines is accurate, but it is invasive and carries risks of bleeding, thrombosis, and infection, and it is not suitable for some populations, including narrow arteries and infants. By contrast, noninvasive cuff-based devices provide discrete snapshot measurements, are uncomfortable, and are not continuous (Li et al., 7 Aug 2025).

The target problem is therefore continuous, cuffless, noninvasive arterial blood pressure waveform monitoring using standard bedside signals. Each input segment contains four channels: $ECG(t)$, $PPG(t)$, the first derivative of $PPG(t)$, and the second derivative of $PPG(t)$. The output is the corresponding 10-second arterial blood pressure waveform, represented as continuous pressure in mmHg. The intended deployment environment includes embedded and edge devices such as vital monitors and microcomputers, and the design objective is to maintain accuracy comparable to large CNN, UNet, or Transformer models while respecting low memory, low FLOPs, and low latency constraints.

A central feature of the formulation is that it targets waveform reconstruction rather than only scalar systolic or diastolic estimates. This allows downstream derivation of systolic blood pressure, diastolic blood pressure, and mean blood pressure from reconstructed pulses while preserving temporal alignment over the full 10-second window.

2. Dataset basis and preprocessing pipeline

The model was developed and evaluated on data from VitalDB via the curated PulseDB. After discarding recordings shorter than 20 minutes, the cohort comprised 2,154 patients from an original VitalDB set of 2,938. Synchronized $ECG(t)$, $PPG(t)$, and $ABP(t)$ signals were used. The original sampling rate was 125 Hz, and all signals were downsampled to 62.5 Hz for efficiency; the original PPG band was 0.5–8 Hz. Each recording was split into 10-second segments, yielding 625 samples per channel and a total of 1,257,141 segments across 2,154 individuals (Li et al., 7 Aug 2025).

Preprocessing was segment-wise. ECG and PPG were min–max normalized to $[0,1]$ within each 10-second segment, and the PPG derivatives were computed and similarly normalized. The ABP target was kept in original physical units, without normalization. Data cleaning proceeded by discarding segments with ABP outside 40–250 mmHg and removing segments with more than 50% amplitude difference between adjacent ECG peaks or abnormal RR intervals below 0.4 s or above 2.4 s.

The dataset is explicitly heterogeneous and broad-range. The systolic blood pressure range was 41–257 mmHg with mean $115.5 \pm 18.9$, and the diastolic blood pressure range was 31–234 mmHg with mean $62.8 \pm 12.0$. Intra-subject variability was also substantial: $PPG(t)$0 ranged from 20 to 180 mmHg with mean $PPG(t)$1, and $PPG(t)$2 ranged from 10 to 180 mmHg with mean $PPG(t)$3. Age ranged from 18 to 97 years with mean $PPG(t)$4, and sex distribution was balanced. This suggests that the main challenge is not merely waveform regression, but waveform regression under broad hemodynamic variation, demographic heterogeneity, and clinically relevant extremes.

3. sInvResUNet architecture and its lightweight design

KDCL_sInvResUNet preserves the sInvResUNet architecture and modifies only its training procedure. The base network is a 1D UNet-style encoder–decoder for time series. Its encoder consists of a stack of MobileNetV2-style inverted residual blocks with squeeze-and-excitation channel attention, progressive temporal downsampling, channel expansion, and residual connections with linear bottlenecks. Its decoder uses UNet-style upsampling, concatenation with corresponding encoder feature maps through skip connections, and lightweight depthwise separable convolutions instead of standard convolutions (Li et al., 7 Aug 2025).

Within an inverted residual block for a 1D feature map with $PPG(t)$5 channels, the sequence is: expansion by a pointwise $PPG(t)$6 convolution to $PPG(t)$7 channels, followed by non-linearity; depthwise 1D convolution over the temporal dimension, followed by non-linearity; projection by a pointwise $PPG(t)$8 convolution back to $PPG(t)$9 channels, typically linear; and a residual connection when stride $PPG(t)$0 and $PPG(t)$1. The stated consequences are parameter efficiency through depthwise separable convolution, representational power through high-dimensional expansion, and stable training through residual paths.

The squeeze-and-excitation block performs global average pooling over the temporal dimension, then applies two fully connected layers with channel reduction and expansion, using ReLU and H-Swish non-linearities, to produce channel-wise weights $PPG(t)$2 in $PPG(t)$3. These weights rescale the feature maps and introduce channel-wise attention, emphasizing channels most informative for arterial blood pressure reconstruction.

The decoder mirrors the encoder, using upsampling, concatenation with encoder features, and depthwise separable convolution. The temporal dimension is preserved from input to output: the input length is 625 points, and the encoder downsampling and decoder upsampling preserve the final output length at 625 points, producing a time-aligned arterial blood pressure waveform. Two variants were defined. The small sInvResUNet contains 11 inverted residual blocks, 0.89 million parameters, and 0.02 GFLOPs per 10-second segment. The large IInvResUNet contains 16 inverted residual blocks, 3.02 million parameters, and 0.05 GFLOPs. The small variant is the deployment target.

4. Collaborative learning and online distillation

KDCL_sInvResUNet denotes sInvResUNet trained within a collaborative learning and online knowledge distillation framework, abbreviated KDCL. In contrast to conventional teacher–student distillation, there is no fixed pre-trained teacher. Several models are trained jointly, and each model is simultaneously a student and a contributor to a teacher ensemble. The participating models are sInvResUNet, IInvResUNet, a classical 1D UNet baseline with 10.82 million parameters and 0.85 GFLOPs, and UTransBPNet, a UNet plus Transformer hybrid with 33.19 million parameters and 6.36 GFLOPs, described as strong at modeling both short- and long-range dependencies (Li et al., 7 Aug 2025).

Training proceeds in two phases. In Phase 1, each model is trained independently with a supervised $PPG(t)$4 waveform regression loss:

$PPG(t)$5

In Phase 2, all four models are trained jointly. For each synchronized input batch they produce four predicted waveforms, $PPG(t)$6, which are combined into a second-level teacher representation. Two teacher strategies are defined. The mean strategy is

$PPG(t)$7

with $PPG(t)$8. The minimum-error strategy selects the model with the lowest supervised loss:

$PPG(t)$9

The reported deployment configuration is the mean strategy, denoted KDCL_sInvResUNetMean.

The student loss is based on Attentive Imitation Loss:

$PPG(t)$0

Here, $PPG(t)$1 balances direct supervision against distillation, and $PPG(t)$2 dynamically modulates trust in the teacher. The teacher error vector is

$PPG(t)$3

with

$PPG(t)$4

and

$PPG(t)$5

The intended interpretation is explicit: when teacher error is small, $PPG(t)$6 is large and imitation is emphasized; when teacher error is large, $PPG(t)$7 is reduced and the student relies more heavily on the direct supervised term. This is a dynamic, error-aware form of knowledge distillation. The architecture of sInvResUNet itself is unchanged; only the training procedure is modified.

5. Training protocol, evaluation metrics, and comparative performance

Evaluation used 10-fold subject-independent cross-validation, with subjects split into 10 folds and training and testing subsets disjoint at the subject level. The same fold partition was used in both training phases to avoid leakage. Optimization used AdamW with learning rate $PPG(t)$8, weight decay $PPG(t)$9, batch size 64, and a maximum of 100 training iterations per fold. Early stopping terminated training if there was no significant improvement on sInvResUNet for 10 iterations. In the collaborative phase, this early stopping criterion was tied to the lightweight student, which ensured that the small student did not overfit while the heavy models continued indefinitely, but it also slightly limited the improvement of large models, especially UTransBPNet (Li et al., 7 Aug 2025).

Performance was reported for arterial blood pressure waveform reconstruction and for pulse-level systolic, diastolic, and mean blood pressure derived from the waveform. Mean absolute error was reported segment-wise and per individual:

$ECG(t)$0

and Pearson correlation coefficient was reported at segment level and individual level:

$ECG(t)$1

The core quantitative comparison is summarized below.

Model	Scale	Reported ABP result
sInvResUNet	0.89 M, 0.02 GFLOPs	$ECG(t)$2 mmHg; $ECG(t)$3
KDCL_sInvResUNet	0.89 M, 0.02 GFLOPs	$ECG(t)$4 mmHg; $ECG(t)$5
UNet	10.82 M, 0.85 GFLOPs	$ECG(t)$6
KDCL_UNet	10.82 M, 0.85 GFLOPs	$ECG(t)$7
UTransBPNet	33.19 M, 6.36 GFLOPs	$ECG(t)$8

Relative to plain sInvResUNet, collaborative learning produced a consistent but modest gain: approximately 0.2 mmHg reduction in $ECG(t)$9, approximately 0.23 mmHg reduction in $PPG(t)$0, and a slight improvement in correlation. KDCL_sInvResUNet was slightly worse than KDCL_UNet in $PPG(t)$1 but achieved near-UNet accuracy with an order-of-magnitude fewer parameters and substantially lower compute. The study further states that KDCL_sInvResUNet marginally but significantly outperforms others in predicting arterial blood pressure, systolic blood pressure, diastolic blood pressure, and mean blood pressure.

For KDCL_sInvResUNet specifically, the reported values were:

• ABP: $PPG(t)$2, $PPG(t)$3
• SBP: $PPG(t)$4, $PPG(t)$5
• DBP: $PPG(t)$6, $PPG(t)$7
• MBP: $PPG(t)$8, $PPG(t)$9

The corresponding individual-level correlations were $ABP(t)$0 for ABP, $ABP(t)$1 for SBP, $ABP(t)$2 for DBP, and $ABP(t)$3 for MBP. By contrast, KDCL reduced the performance of UTransBPNet, with the reported explanation that collaborative early stopping was keyed to sInvResUNet.

6. Generalization, subgroup behavior, and embedded deployment

The paper includes a detailed robustness and fairness analysis. Mean absolute error showed mild but significant correlations with age, weight, and body mass index, with $ABP(t)$4, while height showed no significant correlation. In age-stratified subgroup analysis, mean absolute error was significantly higher in the oldest group, 69–90 years, with differences of approximately 1 mmHg across age quantiles. For body mass index, the overweight group with $ABP(t)$5 had approximately 0.5 mmHg lower mean absolute error than the normal-weight group. No significant differences in mean absolute error were observed between male and female groups for any model (Li et al., 7 Aug 2025).

Cardiovascular-state analysis showed even stronger structure. Subjects were divided into quartiles for $ABP(t)$6, $ABP(t)$7, $ABP(t)$8, $ABP(t)$9, $[0,1]$0, $[0,1]$1, $[0,1]$2, $[0,1]$3, and heart-rate mean and standard deviation. The most significant influence was associated with $[0,1]$4, where the difference in mean absolute error across groups exceeded 2 mmHg and followed a center-low-and-extreme-high trend: best performance near the population-average systolic pressure and worse performance at low and high extremes. For dynamic variables such as $[0,1]$5 and $[0,1]$6, mean absolute error increased monotonically with variability. Most variables except $[0,1]$7 significantly influenced mean absolute error by ANOVA with $[0,1]$8. UNet was described as slightly more robust to cardiovascular variability, while KDCL_sInvResUNet followed similar vulnerability patterns to other population-based models.

Individual case analyses further illustrated this heterogeneity. In a subject with $[0,1]$9 mmHg, $115.5 \pm 18.9$0 mmHg, and $115.5 \pm 18.9$1 mmHg, all models performed well and KDCL_sInvResUNet was closest to the reference waveform. In a subject with $115.5 \pm 18.9$2 mmHg, $115.5 \pm 18.9$3 mmHg, and $115.5 \pm 18.9$4 mmHg, all models struggled, UTransBPNet showed more jitter, and correlations were low or negative. The interpretation given is that population-based models do not generalize uniformly across extreme ages, extreme blood pressure ranges, and high hemodynamic variability, and that data imbalance at clinically critical extremes likely exacerbates this behavior.

The same study also reports explicit embedded deployment. The hardware platforms were Raspberry Pi 4 Model B and NVIDIA Jetson TX2 NX. The runtime pipeline comprised signal acquisition from a Biopac MP160 system, transmission to the embedded board via TCP/IP, on-device downsampling to 62.5 Hz, segmentation into 10-second windows, per-segment normalization of ECG, PPG, and PPG derivatives, inference through ONNX Runtime using an ONNX version of KDCL_sInvResUNet, and streaming of the predicted arterial blood pressure waveform to a PC for real-time display. For a single 10-second segment of 625 samples, the measured inference time was 8.49 ms on Raspberry Pi 4 Model B and 6.95 ms on NVIDIA Jetson TX2 NX. The paper contrasts this with BPNet, reported at 42.53 ms on Raspberry Pi 4 for a 10-second segment, and with KD-Informer, which required 0.19 GFLOPs despite a similar parameter count. A plausible implication is that the model’s architectural efficiency, rather than parameter count alone, is central to its edge suitability.

7. Position in the literature, limitations, and future directions

The work is positioned against several classes of prior methods: feature-based machine learning and signal-processing approaches on PPG and ECG, hybrid CNN–RNN or LSTM models, encoder–decoder and UNet-style models, and Transformer-based architectures (Li et al., 7 Aug 2025). The limitations attributed to earlier deep approaches include high complexity, limited attention to embedded deployment, smaller datasets, narrower blood pressure ranges, and sample-wise validation schemes that may allow subject overlap and therefore optimistic performance estimates.

Within lightweight arterial blood pressure modeling, the study compares against BPNet, KD-Informer, DiffCNBP, and a self-attention ResUNet. BPNet was evaluated on MIMIC II with 948 subjects and 127,260 10-second segments, with restricted blood pressure range and sample-wise validation; its inference on Raspberry Pi 4 was 42.53 ms per 10-second segment. KD-Informer used Mindray and MIMIC III data with 467 patients and approximately 210k 8-second segments, 0.81 million parameters, and 0.19 GFLOPs, and reported mean absolute errors for systolic and diastolic pressure of approximately 4.18 and 3.00 mmHg in a more constrained setting. DiffCNBP was much heavier at 93 MB and 13.69 GFLOPs. The self-attention ResUNet used VitalDB but only 10% subject hold-out and incurred high computational load.

The stated contributions of KDCL_sInvResUNet are fourfold. First, it defines a 1D UNet with MobileNetV2 inverted residual blocks, squeeze-and-excitation, and depthwise separable convolution for arterial blood pressure waveform prediction, with 0.89 million parameters and 0.02 GFLOPs. Second, it applies online collaborative distillation from a multi-model ensemble comprising UNet, UTransBPNet, IInvResUNet, and sInvResUNet, using dynamic teacher representations and Attentive Imitation Loss-based reliability weighting. Third, it validates on 2,154 individuals and 1.26 million segments across a very wide blood pressure range using subject-wise 10-fold cross-validation. Fourth, it demonstrates real-time deployment on Raspberry Pi 4 and Jetson TX2 NX with sub-10 ms latency for 10-second windows. The model is described as a baseline, open-source system under the repository name KDCL_InvResUNet.

The paper also states several limitations. KDCL_sInvResUNet and all compared models do not meet IEEE 1708, which requires mean absolute error below 6 mmHg; the reported errors are approximately 10–12 mmHg for ABP, SBP, and DBP on this dataset. The dataset is intentionally difficult, with wide blood pressure range and substantial intra-subject variability, particularly in sparse extreme regions that are clinically important. Reference invasive arterial blood pressure may itself be distorted by underdamping or overdamping, contaminating the ground truth. Physiological and measurement factors such as skin temperature, contact pressure, and vascular properties are not explicitly modeled, even though they modulate the PPG–ABP relationship over time. Finally, the use of a single global model across a heterogeneous population leaves unresolved issues of personalization, fairness, and robustness at the extremes.

Suggested future directions include improved data curation through automatic identification and exclusion of underdamped and overdamped arterial blood pressure segments; demographic-aware modeling through age-specific models or inclusion of age, sex, and body mass index as inputs; fairness-aware training; subject-specific calibration or adaptation; domain adaptation across hospital populations and device setups; integration of multimodal sensing such as skin temperature, contact pressure, and arterial diameter; and self-supervised or uncertainty-aware modeling. Taken together, these proposals frame KDCL_sInvResUNet less as a clinically finished monitor than as a compact baseline and experimental platform for real-time, unobtrusive arterial blood pressure waveform estimation in resource-constrained perioperative environments.