Machine learning-enabled estimation of cardiac output from peripheral waveforms is independent of blood pressure measurement locations in the in-silico population.

Arterial Sites of Interest

According to the hierarchical branching structure of the vascular tree, each peripheral location reaches from the heart via a unique arterial pathway. The sum of branches encountered along the passageway reflects the unique topology complexity of arterial locations in variants of Weibel generation numbers.¹⁸.

Select the left common carotid artery, i.e. the left common carotid artery, the left common carotid artery, the left surface temporal and left radial bone artery, due to ease and accessibility of local quasi-surface measurements. Applanation Tonometry is a non-invasive method for obtaining arterial pressure waveforms widely used in vascular research (see¹⁹ (For a detailed explanation). A clear topology of each location is shown in Table 1 in terms of distance from the branching junction and the heart.

Silico population

A large silico population of n = 3818 has been previously generated and used in various hypothesis-driven and proof-of-concept studies for non-invasive hemodynamic monitoring.^{17, 21, 22}. Virtual databases were entered by a validated 1D model of systemic circulation^20,23via sampling of demographics and anthropometric parameters within physiological value ranges. The original publication includes detailed descriptions of the virtual cohort generation and cardiovascular metrics^{twenty four}. Below are the metrics related to your current work:

The In Silico dataset consists of two different subpopulations identified afterwards based on cardiac output values. The normal dynamic group with normal CO (5.5 ± 1.0 L/min, n = 2620) and the hyperdynamic group (6.9 ± 1.0 L/min, n = 1198) that significantly increased CO (6.9 ± 1.0 L/min, n = 1198) as shown in Figures 1a,b, but this data-driven group was not predefined, but emerged from analysis of CO distribution (Figure 1A). The morphology of the radial pressure waves differs between the two groups (Fig. 1C), and the additional individual examples shown in the supplementary material are in Fig. S1. The mean aortic pressure was significantly lower in the high dynamic group (85.8 ± 11.8 mmHg) than in the standard mechanics group (108.1 ± 20.2 mmHg; Fig. 1D). Heart rates do not differ substantially between groups. The hyperdynamic group shows an average HR of 83.9 ± 7.7 bpm (range of minimum max range) [62.5, 101.6]), the average HR for the normal dynamic group is 81.9 ± 8.3 bpm (min – MAX range range [61.1, 101.6]). Overall, the high DYNAMIC group has higher CO, lower systemic vascular resistance, lower mean aortic pressure, and similar HR as the standard mechanical group. This is a pattern that suggests a vasodilated, high power state.

A summary of blood pressure data for the ascending aorta and the three peripheral sites under investigation (left superficial temporal, left common carotid artery, and left radial bone artery) is shown in Table 2.

Pressure waveform pre-processing

In the current work, deep learning models are used to predict cardiac output based on full-cycle blood pressure waveforms. In the virtual population, heart rates differ (mean ± SD 83 ± 8 bpm) and result in pressure waveforms of different lengths. Set a fixed single waveform vector size of 150 data points to standardize the model input while preserving the waveform morphology. Therefore, all pressure waveforms are sampled below or excessively to make the array length even and even. Resampling of R into discretized spaces¹⁵⁰ Runs in Matlab interp1 function. Although sampling rate mismatches between clinical measurement instruments (e.g. 128 Hz for Sphymocoll CP and 1000 Hz for PulsePen) are not present in the synthetic dataset, the resampling strategy employed here can also be applied to real-world settings to harmonize signals acquired with different temporal resolutions. Performs amplitude normalization and obtains an unadjusted (normalized) signal by dividing each waveform by its range across the cardiac circulation (i.e. P-P_Min/p_Max– p_Min).

The distinct morphology of the pressure waveform at the three arterial locations is shown in Figure 2.

CNN Model Architecture

Hyperparameter tuning

The 1D convolutional neural network (CNN) receives either calibrated or unadjusted (amplitude normalized) blood pressure waveforms from three arterial locations as inputs to estimate cardiac output values, resulting in six different CNNSs (Figure 3). The input of each location-specific CNN is a set of pressure waveforms at a particular location, each waveform is an array of 150 points obtained as above. The sequential CNN model is constructed with two 1D convolutional layers, each followed by batch normalization to stabilize the training. A 1D max pooling layer is then applied to downsampling, followed by a dropout layer, reducing excess fitting. The output is planarized and a dense (fully connected) layer is used for regression. For each of the six models, Bayesian optimization is employed to define the learning rate, batch size, number of filters, kernel size, dropout rate, and the number of units in the fully connected (dense) layer. For each set of hyperparameters during Bayesian optimization, the model is evaluated with 5x cross-validation (used) stratifiedkfoldfrom Sklearn ), i.e., the dataset used for hyperparameter tuning is split into five subsets, and the model is evaluated with various combinations of training and validation sets, ensuring that all data points are used accurately once for validation. The optimal number of epochs is determined using an early stop callback function to avoid overfitting. All hyperparameters are summarized in Table S1.

Workflow

Follow the methodology proposed by Bikia et al.¹⁷The complete dataset of 3,818 samples was split into training, validation, and test sets with a ratio of 60%/20%/20% (2290/764/764 cases, respectively). To ensure generalizability of trained models, both normative and hyperdynamic groups (identified in the “Silicon population” section) are properly represented across training, validation, and test sets via layered sampling (as well as through arguments) Stratification Sklearn's “Train test split” function). Additionally, each of the six models undergoes individual hyperparameter tuning to ensure a fair comparison of model performance. Note that the Holdout (Test) set remains invisible during model training and hyperparameter adjustments. This was reserved exclusively for the final CNN performance assessment to provide a fair assessment of model performance for invisible data.

Noise injection

The synthetic waveforms are useful for proof of concept or methodology development research, but represent ideal noise-free records far away from actual blood pressure acquisition. Aplantation observation measurements at radial arteries and other locations suffer from motion and interference artifacts, resulting in baseline wandering, low- and high-frequency noise, and amplitude spikes. Introduction of noise into the synthetic pulsed waves mimics some of the frequently observed measured artifacts, allowing the noise resilience of CNN models to be evaluated.^14,17,25,26.

Given the abolition of frequency information in the preprocessing steps of the current framework (the “Pressure Waveform Preprocessing” section), we consider two sources of noise: (i) Gaussian noise, and (ii) separate random perturbations in the form of spikes. About each data point of the pressure waveform vector x = [x₁,x₂,…,x₁₅₀] Gaussian noise n_I ~ n (µ, σ²) will be added. We consider it (µ= 0. 7, σ= 1. 0) Calibrated (µ = 0, σ= 0. 1) For silent signals. The amplitude of each spike is set to 10% of the maximum value of the signal. a= 0.1・Max(x). To make the spikes positive or negative, their amplitudes are further expanded by random coefficients derived from the uniform distribution u(-1,1), brings the final spike amplitude a' ~ u (- a, a). Spikes are added at randomly selected indexes IIt consists of 20% of 150 waveform points.

Briefly:

Signal breakdown due to additive white noise and random spikes is performed after resampling of the waveform and is illustrated in Figure 4. In the case of noisy, machine learning models are trained and evaluated using noisy waveforms, keeping the model's hyperparameters the same as each noiseless case.

Statistical analysis

All statistical analyses were performed in Python. a p<-0.05 was considered statistically significant. We assessed normality using the Shapiro-Wilk test and used the non-parametric Mann-Whitney U test to assess the difference between the mean of the normal and high dynamic groups using the continuous variables (cardiac output and mean aortic pressure).

Linear regression analysis of estimated and reference data provides regression lines and p– The value of the gradient hypothesis test. Bland–Altman analysis was used to obtain biases and contract limits (LOAs) corresponding to 95% confidence intervals.

Intrasite differences between calibrated Pearson R values and normalized Pearson R values were assessed using a paired t-test followed by a Z-transformation of Fisher's R values.

We expressed relative variation in performance metrics between sites as a percentage compared to the scale-independent coefficient of variation calculated as standard deviation divided by the mean.

To assess the performance of the model, we used the following standard regression metrics: The mean absolute error (MAE) was calculated as the average of the absolute difference between the predicted and the reference (ground truth) value. The normalized root mean square error (NRMSE) was based on the RMSE and was defined as the square root of the mean of the square difference between the predicted and referenced values. NRMSE expresses RMSE as a percentage of the range (here, CO) of the target variable, allowing for scale-independent interpretation. is calculated as

nrmse = 100×rmse/(y_Max – y_Min ), here y_MaxAnd y_MinThe maximum reference and minimum values for co.