ICP-WAVES: Intracranial Pressure Waveform Analysis and Visualization for Enhanced Signal Processing

Abstract

Objective:

Intracranial pressure (ICP) waveform morphology reflects brain compliance and cerebrospinal fluid dynamics. Existing monitoring methods fail to fully capture complex temporal patterns nor enable real-time interactive analysis to improve clinical decision-making.

Methods:

We trained a transformer-based foundation model to capture temporal dynamics and generate embeddings from physiological data. The model was fine-tuned on physiological waveform data from patients with intracerebral hemorrhage (ICH) admitted to Columbia University Irving Medical Center (CUIMC) and validated on two non-overlapping datasets: a) patients with cerebral external ventricular drainage (EVD) at CUIMC and b) a synthetic ICP dataset. The embeddings generated from the foundation model were used to train a support vector machine (SVM) classifier to classify different morphologies. Model performance was evaluated using area under the receiver operating curve (AUC) and confusion matrices, by splitting the dataset into training and testing. We developed a graphical user interface to enable ad-hoc analysis, fine-tune models, and visualize ICP trends.

Results:

A total of 190 patients between March 2009 and August 2013 with ICH were included to fine-tune the foundation model with a median length of stay (LOS) of 5 [4-9.25] days, and a Glasgow Coma Scale (GCS) score of 11 [7–15]. 6s2 of these patients had ICP waveform data. A total of 23 other patients (train: 11, test 12) from January 2021 to August 2023 with EVD were used to train the SVM model to classify different ICP morphologies; with median LOS 17 [12–23] days, and GCS 7 [5–13]. Two trained experts (YL, GG) labeled 8406 ICP (train:3613, test: 4793) pulses. The model achieved AUCs of 0.90 for 3-peak compliant, 0.93 for single-peak non-compliant, and 0.78 for multi-peak non-compliant waveforms. On simulated ICP data, the AUCs were 1.00 for all the waveform classes. However, the confusion matrix analysis revealed that 1-peak compliant waveforms were classified with 77.5% accuracy while all other categories had 100% accuracy.

Conclusion:

A deep learning-based foundation model optimized for analyzing invasive ICP waveforms can extract clinically relevant information about cerebral compliance. The performance was best for distinguishing compliant from non-compliant waveforms.

I. Introduction

Elevated intracranial pressure (ICP) results in reduced cerebral perfusion pressure (CPP), which can lead to cerebral ischemia, disability, and increased rates of mortality in the pediatric and adult neurointensive care population.[1, 2] ICP monitoring is used to guide the management of patients in neurocritical care, particularly in managing conditions such as traumatic brain injury (TBI), subarachnoid hemorrhage (SAH), and intracerebral hemorrhage (ICH).[3] While commercial ICP monitoring devices are widely deployed, their predominant focus on mean ICP presents a simplified approach to analyzing complex physiological data and ignores rich temporal dynamics.

ICP waveform morphology and dynamics can enhance understanding cerebrospinal fluid (CSF) dynamics and intracranial compliance. The ICP waveform typically consists of three distinct peaks: P1 (percussive wave), P2 (tidal wave), and P3 (dicrotic wave). These peaks correspond to the arterial pulse pressure transmitted through the cerebrospinal system. The morphology of the ICP waveform can provide insights into the intracranial compliance and the compensatory mechanisms of the brain. [4, 5] Changes in ICP waveform morphology are further associated with several diseases beyond traumatic brain injury and hydrocephalus. [6] Acute brain injury, such as hemorrhage, infarct, or edema, can lead to increased ICP due to mass effect and impaired cerebrospinal fluid dynamics, which are reflected in the waveform morphology.[7] Recent studies have shown that Ventriculitis can alter ICP waveforms.[8]

Traditional methods of analyzing ICP waveforms focus on both the morphology [5, 9] and dynamics of the waveform. Approaches like Morphological Clustering and Analysis of Intracranial Pressure (MOCAIP) [9] or multi-scale peak detection method[10] identifies non-artifactual ICP pulses and their subcomponents. [4, 11] Further there are methods for classifying individual ICP pulses, ranging from normal to pathological, using either active learning[12] or deep learning techniques.[5] These advanced methods enhance the accuracy and robustness of ICP waveform analysis, providing more detailed insights into cerebrospinal compliance and patient prognosis. However, these methods rely on first segmenting ICP individual pulse, or deriving a dominant pulse, and have yet to show their ability to process ICP signals acquired using external ventricular drainage (EVD) monitoring, that requires processing to identify regions of EVD clamped data.[13]

Recent advances in machine learning, particularly in the development of foundation models, have demonstrated remarkable success in capturing complex temporal patterns across various domains.[14–19] The review articles [20, 21] (and references therein) provides a comprehensive overview of these developments. Models such as Timer [22], TimesFM [23], Chronos [24], TimesNet [17], GPT4TS [19], Moirai [25], MOMENT [18] demonstrate innovations in patch based tokenization, random masking and decoder only designs that improve computational efficiency and zero-shot generalization capabilities across varied sequence length and contexts. These models can either be utilized in zero shot fashion or fine-tuned for various downstream tasks such as forecasting, anomaly detection and representation learning. MOMENT [18] models are built on transformer architectures and pre-trained on a wide variety of time series data, including healthcare datasets making them highly suitable for analyzing complex physiological signals. In previous studies, MOMENT outperformed models such as TimesNet [17] and GPT4TS [19] in tasks like classification, anomaly detection, and imputation.[18] These models effectively capture variations in temporal resolution, sequence length, amplitude and other key aspects of physiological signals. However, these advances have not been effectively translated to ICP monitoring, where the ability to model long-term dependencies and subtle pattern changes could significantly improve patient care. Current methodologies typically analyze ICP signals in isolation, failing to leverage the vast amounts of longitudinal data available across patient populations, that could provide insights into patients’ dynamic pathological states. Furthermore, current systems provide limited capabilities for physicians to interact with and analyze data in real-time, so they must rely on basic metrics that may miss crucial patterns. The absence of comprehensive tools for real-time analysis and visualization represents another significant gap in current practice.

These methodological and practical challenges highlight the need for a shift in ICP monitoring and analysis. This paper presents a novel framework that addresses these limitations through key innovations: (1) a foundation model architecture specifically designed to capture complex temporal dynamics in ICP signals, which can be generalized to other physiological waveforms in ICU, and (2) an interactive graphical interface that enables clinicians to perform analyses and model updating. This comprehensive approach not only advances the technical capabilities of ICP monitoring but also provides a practical tool that can be integrated into clinical workflows, potentially improving patient outcomes through more sophisticated and accessible analyses of ICP dynamics.

II. Material and Methods

A. Data Acquisition and Preprocessing

1). Dataset for Model Building and fine tuning

For model building and fine-tuning, we studied consecutive subjects with intracerebral hemorrhage (ICH) who were admitted to the neurointensive care unit (NICU) between March 2009 and August 2013. This was part of an observational cohort study approved by the Columbia University Medical Center Institutional Review Board. Physiological data for the duration of the intensive care unit stay was acquired using a high-resolution acquisition system. From 2009 to 2013, BedmasterEX (Excel Medical Electronics Inc., Jupiter, FL, USA) was used to acquire physiological data from General Electric Solar 8000i monitors (Port Washington, NY, USA) at 240 samples per second.

2). Dataset for Model Evaluation

We studied consecutive subjects with EVD who were admitted to the NICU between January 2021 to August 2023. This was part of an observational cohort study approved by the Columbia University Medical Center Institutional Review Board. Physiological data were obtained from Philips Intellivue monitors (Amsterdam, the Netherlands) and were acquired at 125 samples per second using Philips Data Warehouse Connect.

3). Synthetic Dataset for Model Evaluation

We created a synthetic data set consisting of six distinct waveform categories: three compliant patterns (1-peak, 2-peaks, 3-peaks) and three non-compliant patterns (1-peak, 1.5-peaks, 3-peaks), generated with systematic variations in amplitude, phase, and noise levels (Appendix A). For each waveform class, we generated multiple segments (600 for training and 200 for testing). Each segment was normalized to unit amplitude and sampled at 512 points, producing a dataset suitable for algorithm validation and performance assessment.

B. Model Architecture

We utilized the MOMENT framework[18] to analyze Intracranial Pressure (ICP) signals from ICU patients. MOMENT processes univariate time-series data of length $T$ with a corresponding binary observation mask.[18] After applying reversible instance normalization to observed values, the series is segmented into $N$ patches of length $P$. Each patch is embedded into $D$ dimensions using either a learned linear projection (for fully observed patches) or a learnable mask embedding (for partially observed patches). An encoder only transformer processes these N patch embeddings while preserving their D-dimensional representation. A reconstruction head then maps the transformed embeddings back to the original time domain. (Fig. 1.)

Fig. 1. Architecture and workflow of the waveform data analysis pipeline.

A): The fine-tuning component consists of a Transformer Encoder architecture with multiple identical blocks, each containing a Multi-Layer Perceptron (MLP) layer, normalization layers, and multi-head attention mechanism. The model processes input data of dimension $R^{P\times N}$through reconstruction and encoding stages. B) The application workflow illustrates the sequential steps of the analysis pipeline, beginning with data loading (CSV, HDF5 formats), followed by model and region selection, data segmentation and cleaning, embedding generation from the frozen model, dimensionality reduction via PCA/t-SNE projection, and feature extraction.

(Norm: Normalization; MH: Multi-Head, MLP: Multilayer perception, PCA: Principal Component Analysis, t-SNE: t-distributed stochastic neighbor embedding)

Each signal was represented as univariate time-series data of length T, accompanied by a binary observation mask indicating the availability of data points. To standardize the input data, we applied reversible instance normalization to the observed values, ensuring consistent scaling across varying signal ranges. Subsequently, each time series was segmented into N patches, each of length P. For fully observed patches, a learned linear projection was used to embed the data into a D-dimensional latent space. For partially observed patches, a learnable embedding was applied to handle missing data effectively.

C. Training

1). Pretraining

During pretraining, random patches of the input series were masked to simulate missing data. The model was trained to minimize the masked reconstruction error, calculated as the mean squared error (MSE) between the predicted and true patches. The pretrained MOMENT model (40M parameters) served as the foundation for representation learning. The model was trained using the ‘Time Pile’ dataset, which includes five major repositories: (1) Informer datasets containing Electricity Transformer Temperature (ETT), Electricity, Traffic, Weather, Exchange, and Influenza like illness (ILI) data with varying frequencies from 15-minute to weekly measurements; (2) Monash archive featuring short-horizon forecasting datasets with different temporal granularities; (3) University of California Riverside (UCR)/University of East Anglia (UEA) archive comprising Electrocardiography (ECG), Motion Gesture, and Food Spectrograph data for classification tasks; (4) Time Series Benchmark for Unsupervised Anomaly Detection (TSB-UAD) containing Beth Israel Deaconess Medical Center (BIDMC1), and air pressure datasets for anomaly detection; and (5) UWaveGestureLibraryX datasets specialized for imputation tasks. The dataset spans diverse domains with time series lengths ranging from 24 to 720 timestamps.[18] The pretrained model was available as part of the momentfm python package.[18]

2). Fine-tuning foundation model for Physiological data

We leveraged the MOMENT framework for analyzing diverse physiological signals from ICU patients, including ICP, Arterial Blood Pressure (ABP), Respiratory Rate (RR), Blood Oxygen Saturation (SpO₂), and ECG. The MOMENT architecture, pre-trained on heterogeneous domain-agnostic time series data[18] as described above, served as our base model.

The pre-trained MOMENT framework provides three encoder configurations, Base, Small and Large, which differ in dimensions and network configurations. The Base (Small, Large) model uses a 12 (6, 24) layer Transform with hidden dimensions of size D = 768 (512, 1024), 12 (8, 16) attention heads, and feed-forward networks of size 3072 (2048, 4096), resulting in approximately 109 (35, 341) million parameters. We compared these three baseline models variants on a synthetic dataset (Appendix B) and found that they performed equally well. To reduce computational overhead, we therefore selected ‘Small’ model for our analysis.

We fine-tuned the MOMENT-1 small model (341 million parameters) using physiological timeseries data for signal reconstruction. All parameters were frozen except for those in the reconstruction head to perform representation learning leveraging and retaining baseline foundation models ability to represent temporal dynamics.

Physiological data were first filtered to remove any artifacts [13] and any missing values (NaNs) and flat-line regions. The cleaned data were segmented into contiguous, non-overlapping windows of 2-s duration, corresponding to a context length of 2xsampling frequency. Each segment was then z-scored normalized to remove amplitude bias ensuring uniform scaling across channels.

To simulate incomplete or corrupted observations, a random masking ratio of 30% was applied to each input using MOMENTs built-in masking module. The model was then trained to reconstruct the original (unmasked) signal from these partially observed inputs, promoting robust latent feature learning from physiological time series data (Fig. 1). We used the Adam optimizer with gradient clipping 1.0 and a batch size of 240. [18]

We developed both signal-specific (ECG, ABP, ICP, SPO2) models through fine-tuning on individual vital signs to capture their unique temporal characteristics, and a consolidated model trained on multiple signals to learn cross-signal relationships. This dual approach enabled both specialized analysis of individual waveforms and integrated understanding of physiological interactions across different vital signs.

D. Validation Strategy

Model validation was performed using two independent datasets: (1) a clinical dataset comprising ICP waveforms from the NICU, and (2) a synthetic dataset with controlled waveform characteristics. Both these datasets were separate from the data that was used for fine tuning the foundational model. The clinical dataset was manually annotated by two trained ICP experts (YL, GG), with disagreements resolved through consensus review by a NICU attending physician (SP). The experts labelled individual ICP pulse as either compliant (0), multi-peak non-compliant (1) or non-compliant (2) pulse and were blinded to the clinical course. The inter-rater agreement between the experts was evaluated using Cohen’s Kappa, and the results were also reported using a confusion matrix. The evaluation approach incorporated contextual information by analyzing each ICP pulse alongside its neighboring waveforms. We computed the mean of the central pulse label and its immediate neighbors on both sides. The synthetic dataset consisted of six distinct waveform categories: three compliant patterns (1-peak, 2-peaks, 3-peaks) and three non-compliant patterns (1-peak, 1.5-peaks, 3-peaks), generated with systematic variations in amplitude, phase, and noise levels (Appendix A

).

The input to the foundation model was the continuous waveform segment (n=512) without requiring prior pulse segmentation, addressing a significant limitation of existing methods that rely on precise identification of individual pulses. The output of the foundation model (embeddings) then served as input features for a support vector machine (SVM) classifier to classify different morphologies. The dataset was split into training and testing sets for evaluating the performance of the model.

Model performance was evaluated using Area Under the Curve (AUC) for classification accuracy and confusion matrices to assess class-specific performance. Models were developed using Python 3.8 with Torch and momentfm python packages.

E. Graphical User Interface: Waveform Data Analyzer

The temporal data analysis system incorporates a graphical user interface (GUI) integrated with a processing pipeline for physiological waveform analysis (Fig. 1B,2). The pipeline begins with data acquisition, supporting both CSV and HDF5 file formats (Fig. 2A). The interface provides the ability to select temporal data for further analysis for different signals, such as ECG, ABP, ICP, and SpO2 waveforms. The GUI provides three different visualizations. The long-term trend analysis window displays down-sampled waveform data, with an option to highlight regions for further processing (Fig. 2E). Once the data is selected, a high-resolution plot displays the data for detailed analysis (Fig. 2G). The next step involves selecting the model and reduction method (Fig. 2A).

Fig. 2. Waveform Data Analyzer.

(A) Data selection and model configuration panel allowing users to load temporal data (ICP) either in CSV or HDF5 format (B) Batch training interface enabling directory selection for model training across multiple datasets. (C) Model hyperparameter configuration panel for adjusting learning rate and optimizer settings. (D) Download embedding and plots for every 30 minutes interval. (E) ICP trend visualization showing temporal evolution of intracranial pressure for a sample patient. The highlighted region indicates the selected region for analysis. (F) Learned ICP representation space visualization demonstrating temporal tracking of pressure waveforms, with color-coded classification of peak patterns (1 peak: red, 2 peaks: yellow, 3 peaks: green). The grayscale contours represent the density of ICP states in the learned embedding space. Solid black lines tracks the patients embedding every half hour with ‘red’ star indicating the current point. (G) High-resolution ICP waveform display revealed when user hovers over a section of interest.

We trained models using ICP, ABP, ECG, SpO2, and a combined model trained with all the physiological data. These models are integrated into the interface, along with MOMENTs pre-trained models (small and large) (Fig. 2A). The dimensionality reduction methods include Principal Component Analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) for viewing embeddings in reduced dimensions (Fig. 2A). Once the data, model, and dimensionality reduction method are selected, the analysis begins upon clicking the ‘Analyze’ button. To ensure signal quality, especially for EVD data, we included an ICP preprocessing technique to select regions of ICP when the EVD is clamped. [13] Once the data is cleaned, the model generates embeddings for the temporal data. Dimensionality reduction, using either PCA or t-SNE, displays a two-dimensional contour in the ICP representation learning panel, with different colors indicating various compliances (green: 3 peaks; yellow: 3 peaks non-compliant; pink: 2 peaks; red: 1 peak).

The representation learning plot (Fig. 2F) displays density-based contour plots for 2D visualization of waveform embedding patterns. In this panel, each ‘black’ dot represents the state (for half an hour of data), and the transition to the next state is indicated by an arrow connecting to the subsequent dot. The current state is represented by a ‘red’ star, indicating the trajectory of the patient’s data for selected region (Fig. 2F).

The interface also provides the option to update and save existing models. Model parameters, such as learning rate and optimization algorithm can also be adjusted through the interface (Fig. 2C). Additionally, batch processing capabilities (Fig. 2B) are included to fine-tune models based for downstream tasks such as classification, anomaly detection or imputation. Furthermore, the GUI allows exporting processed features and analysis results in standardized CSV formats for use in downstream tasks (Fig. 2D).

The source code for the GUI is available on GitHub at (https://github.com/megjhani/62_ICP_Representation_learning).

III. Results

A. Patient Demographics

For model building and fine tuning, a total of 190 patients with ICH were included. The median [Q1-Q3] length of stay was 5 [4–9.25] days, the Glasgow Coma Scale score was 11 [7–15], and the ICH score was 2 [1–3]. Of these, 190 patients had ECG waveform data, 164 had ABP waveform data, 188 had SPO2 waveform data, 167 had RR waveform data, and 62 had ICP waveform data.

For ICP waveform morphology model evaluation using SVM, a total of 23 other patients (train:11, test:12) with EVD data were included. The median (Q1-Q3) length of stay was 17 [12–23] days, the GCS score was 7 [5–13.5]. In the training dataset, the experts labeled 1,574 (43.6%) compliant, 1,255 (34.7%) multi-peak non-compliant, and 784 (21.7%) non-compliant individual pulse waveforms. In the test set, the experts labeled 1,122 (23.41%) compliant, 1,126 (23.49%) multi-peak non-compliant, and 2,545 (53.10%) non-compliant individual pulse waveforms. The experts agreed 80% for compliant, 88% for multi-peak non-compliant and 84% for one peak non-compliant, with a Kappa score of 0.74 indicating substantial agreement between the raters. (Appendix B).

B. Performance on EVD ICP Data

The model achieved AUCs of 0.9 for 3 peak compliant, and 0.93 for single peak non-compliant waveforms and 0.78 for multi peak non-compliant waveform. The confusion matrix revealed 85.5% (672/785) for compliant waveforms and 54.6 (154/282) for multi-peak non-compliant waveforms and 68.5% (217/317) for single peak non-compliant waveforms. (Fig. 3)

Fig. 3. ICP waveform representation and performance of SVM models for different morphologies.

A) Projection of embeddings on t-SNE B) Project of embeddings on PCA C) Representative waveforms for each class, with class labels indicating the mean of three ICP pulses: 0 = compliant, 1 = multi-peak non-compliant, and 2 = single-peak non-compliant. D) Confusion matrix illustrating classification results for the different classes.

E) AU-ROC curves for one-vs-rest classification across the three classes (0, 1, 2).

C. Performance on simulated ICP Data

The model achieved AUCs of 1.00 for most waveform classes (2 Peaks Compliant, 3 Peaks Noncompliant, 3/2 Peaks Noncompliant, and 1 Peak Noncompliant). The confusion matrix revealed perfect classification accuracy (200/200) for all non-compliant waveforms. The 1 Peak Compliant class showed an accuracy of 77.5% (155/200), with misclassifications primarily occurring with 3 Peaks Compliant (22/200) and 2 Peaks Compliant (23/200). (Fig. 4)

Fig. 4. ICP waveform representation and performance of SVM models for simulated ICP waveform data.

A) Projection of embeddings on t-SNE B) Project of embeddings on PCA C) Simulated ICP pulse waves with added white noise and phase shift to simulate different ICP waveform morphology for different compliance. D) Confusion matrix illustrating classification results for the different classes. E) AU-ROC curves for one-vs-rest classification.

IV. Discussion

We showed the feasibility of using foundation models for deriving representations of physiological waveforms in intensive care settings, using ICP waveform analysis as our validation case. To the best of our knowledge, this represents the first application of foundation models to ICP waveform representation, offering a generalizability of the MOMENT framework to ICP and potentially other physiological signals

Our model demonstrated robust performance in discriminating between compliant and non-compliant waveforms in simulated data, achieving perfect classification (AUC = 1.00) for most waveform classes in the simulated dataset. The incorrect classification occurred between 1-peak and 3 and 2 peaks compliant variant waveforms (accuracy 77.5%), which can be attributed to similar underlying harmonic structures. However, for the ICP waveform data the SVM model was able to discriminate compliant and single peak non-compliant waveforms with an AUC of 0.9 and multi-peak noncompliant waveforms with an AUC of 0.78. The misclassification occurred between 3 peaks and multi-peak noncompliant waveforms. Additionally, we observed that accurately labelling ICP pulses might be challenging with disagreements among the ICP experts themselves (APPENDIX B). The labelling process was done solely for validation purposes.

Further our selected segment size was long enough to capture multiple ICP pulses, allowing us to integrate contextual information and improve the representation within the embedding space. This also eliminates the need to identify individual ICP pulses for morphological analysis.

The developed pipeline integrates several key innovations that address limitations in current ICU monitoring systems. First, our foundation model architecture captures complex temporal dynamics in physiological signals without the need to select individual pulses. Second, we implemented an interactive graphical interface that enables clinicians and researchers to perform real-time analysis, export results, and retrain models either for individual datasets or through batch processing. This user-centric approach bridges the gap between sophisticated machine learning models and clinical applicability and research.

Similar to previous ICP classification studies, our model’s performance showed some dependency on data quality and signal characteristics. However, unlike traditional approaches that often require multiple physiological signals for accurate classification, our model achieved high performance using only the ICP waveform. This reduces computational overhead making it more suitable for real-time clinical applications.

While our results are promising, several limitations should be noted. While our model performs well on both simulated and real data, prospective clinical studies would be valuable for validating its real-world utility. Second, further investigations into how these embeddings change across different disease etiologies are warranted. Clinical factors such as EVD blockage or partial obstruction may also alter morphology of ICP waveforms, potentially impacting the performance of downstream tasks when using these embeddings for different disease types. Although current models are trained on artifact free datasets and our pipeline explicitly includes an artifact removal step, distortion caused by patient motion and difference in data acquisition differences may still affect the performances. Our study was conducted using data from a single center, and external validation on multi-center datasets will be important to assess the generalizability. In addition, the current implementation of our GUI is model-specific, limiting its flexibility for testing and evaluating other foundation models. Our future work will focus on conducting larger-scale clinical validation studies and updating the GUI to provide user-specific access to individual (clinical vs advance researchers), offering advanced users the ability to update models and configure their analysis environment

V. Conclusion

We have demonstrated the successful application of foundation models for physiological waveform analysis in ICU settings. Our framework achieved high classification accuracy in distinguishing compliant from non-compliant waveforms while providing an intuitive interface for clinical implementation. The model’s ability to learn complex temporal patterns from single-channel data, combined with its generalizable architecture, presents a promising direction for automated physiological signal analysis in critical care. Future work will focus on expanding this framework to validate its clinical utility through large-scale prospective studies across multiple centers.

Appendix

A. Appendix A

Synthetic ICP waveforms for different compliance

We generated synthetic waveforms (to validate the embeddings generated by the foundation models) using a parametric approach based on superimposed sinusoidal functions (Fig. 4C). We created six distinct waveform classes, categorized as either compliant or non-compliant based on their temporal characteristics. Each waveform class is mathematically defined through combinations of fundamental, second, and third harmonics with varying amplitudes and phase relationships.

The primary waveform classes are described by the following equations:

$$\text{Three Peak Compliant}:{\text{f}}_1(\text{x})=\sin (\text{x})+0.5\sin (2\text{x})+0.4\sin (3x)$$

$$\text{Two}\text{Peaks}\text{Compliant}:{\text{f}}_2(\text{x})=1.3\sin (\text{x})+0.5\sin (2\text{x}+\pi /6)+0.2\sin (3x)$$

$$\text{One}\text{Peak}\text{Compliant}:{\text{f}}_3(\text{x})=1.3\sin (\text{x})+0.5\sin (2\text{x})+0.2\sin (3x)$$

$$\text{Three Peaks Non-compliant}:{\text{f}}_4(\text{x})=1.8\sin (\text{x})+0.4\sin (2(\text{x}-\pi /1.2))+0.5\sin (3(x-\pi /2))$$

$$\text{Three/Half Peaks Non-compliant}:{\text{f}}_5(\text{x})=2\sin (\text{x})+0.5\sin (2(x-\pi /1.5))+0.3\sin (3(x-\pi /3))$$

$$\text{One Peak Non-compliant}:{\text{f}}_6(\text{x})=2.4\sin (\text{x})+0.2\sin (3(\text{x}-\pi /2))$$

To simulate real-world signal variability, we added, phase shifts (φ), temporal shifts (τ), and additive noise (ε). Phase shifts were uniformly distributed within ±0.8 radians, while temporal shifts were scaled proportionally to the segment length. We incorporated both global and local Gaussian noise components (σ = 0.1) to model measurement uncertainty and background interference.

For each waveform class, we generated multiple segments (600 for training, 200 for testing) containing 2-5 pulses per segment. Each resulting segment was normalized to unit amplitude and sampled at 512 points, producing a dataset suitable for algorithm validation and performance assessment.

B. Appendix B:

Fig. Appendix B.

Inter-rater agreement between two ICP experts (GG and YL). The experts agreed 80%, 88% and 84% times when labelling Compliant, multi-peak non-compliant and one peak noncompliant waveform respectively.

Fig. Appendix C:

Performance of three pretrained models (base, small and large) on synthetic datasets. For the purposes of morphological classification, all the 3 methods performed reasonably well