On the convergence and accuracy of the cardiovascular intrinsic frequency method

Detecting elevated left ventricular end diastolic pressure from simultaneously measured femoral pressure waveform and electrocardiogram

Objective.Instantaneous, non-invasive evaluation of left ventricular end-diastolic pressure (LVEDP) would have significant value in the diagnosis and treatment of heart failure. A new approach called cardiac triangle mapping (CTM) has been recently proposed, which can provide a non-invasive estimate of LVEDP. We hypothesized that a hybrid machine-learning (ML) method based on CTM can instantaneously identify an elevated LVEDP using simultaneously measured femoral pressure waveform and electrocardiogram (ECG).Approach.We studied 46 patients (Age: 39-90 (66.4 ± 9.9), BMI: 20.2-36.8 (27.6 ± 4.1), 12 females) scheduled for clinical left heart catheterizations or coronary angiograms at University of Southern California Keck Medical Center. Exclusion criteria included severe mitral/aortic valve disease; severe carotid stenosis; aortic abnormalities; ventricular paced rhythm; left bundle branch and anterior fascicular blocks; interventricular conduction delay; and atrial fibrillation. Invasive LVEDP and pressure waveforms at the iliac bifurcation were measured using transducer-tipped Millar catheters with simultaneous ECG. LVEDP range was 9.3-40.5 mmHg. LVEDP = 18 mmHg was used as cutoff. Random forest (RF) classifiers were trained using data from 36 patients and blindly tested on 10 patients.Main results.Our proposed ML classifier models accurately predict true LVEDP classes using appropriate physics-based features, where the most accurate demonstrates 100.0% (elevated) and 80.0% (normal) success in predicting true LVEDP classes on blind data.Significance.We demonstrated that physics-based ML models can instantaneously classify LVEDP using information from femoral waveforms and ECGs. Although an invasive validation, the required ML inputs can be potentially obtained non-invasively.

A reliable evaluation approach for multichannel signal denoising algorithms based on a novel arterial pulse acquisition system

Background

Tactile sensors are utilized to measure multichannel pulse signals in pulse wave analysis (PWA). Owing to noise interferences, researchers have applied various denoising algorithms on multichannel pulse signals. To comprehensively assess these algorithms, numerous evaluation metrics have been proposed. However, these studies did not investigate the noise mechanisms in depth and lacked reference pulse signals, thus making the evaluations insufficiently objective.

Materials and methods

An applicable denoising evaluation approach for multichannel pulse signal algorithms based on an arterial pulse acquisition system is established by superimposing real-world multichannel noise to the reference signals. The system, comprising a SphygmoCor and a uniaxial noise acquisition device, allows us to acquire single-reference pulse signals as well as real-world multichannel noise.

Results

We assess eight popular denoising algorithms with three evaluation metrics, including amplitude relative error (ARE), mean square error (MSE) and increased percentage signal-noise ratio (SNR%). Our proposed approach provides accurate and objective evaluations of multichannel pulse signal denoising. Notably, classic algorithms for single-channel denoising are not recommended for multichannel denoising. Comparatively, RPCA-based algorithms can denoise pulse signals independently for each channel.

Conclusion

This study sets the stage for the establishment of accurate and objective pulse signal denoising evaluations and provides insights for data-driven clinical diagnoses in cardiovascular medicine.

A machine learning approach for computation of cardiovascular intrinsic frequencies

Analysis of cardiovascular waveforms provides valuable clinical information about the state of health and disease. The intrinsic frequency (IF) method is a recently introduced framework that uses a single arterial pressure waveform to extract physiologically relevant information about the cardiovascular system. The clinical usefulness and physiological accuracy of the IF method have been well-established via several preclinical and clinical studies. However, the computational complexity of the current L2 optimization solver for IF calculations remains a bottleneck for practical deployment of the IF method in real-time settings. In this paper, we propose a machine learning (ML)-based methodology for determination of IF parameters from a single carotid waveform. We use a sequentially-reduced Feedforward Neural Network (FNN) model for mapping carotid waveforms to the output parameters of the IF method, thereby avoiding the non-convex L2 minimization problem arising from the conventional IF approach. Our methodology also includes procedures for data pre-processing, model training, and model evaluation. In our model development, we used both clinical and synthetic waveforms. Our clinical database is composed of carotid waveforms from two different sources: the Huntington Medical Research Institutes (HMRI) iPhone Heart Study and the Framingham Heart Study (FHS). In the HMRI and FHS clinical studies, various device platforms such as piezoelectric tonometry, optical tonometry (Vivio), and an iPhone camera were used to measure arterial waveforms. Our blind clinical test shows very strong correlations between IF parameters computed from the FNN-based method and those computed from the standard L2 optimization-based method (i.e., R≥0.93 and P-value ≤0.005 for each IF parameter). Our results also demonstrate that the performance of the FNN-based IF model introduced in this work is independent of measurement apparatus and of device sampling rate.

Assessment of Aortic Characteristic Impedance and Arterial Compliance from Non-invasive Carotid Pressure Waveform in The Framingham Heart Study

The primary goal of this study was to test the hypothesis that a hybrid intrinsic frequency-machine learning (IF-ML) approach can accurately evaluate total arterial compliance (TAC) and aortic characteristic impedance (Zao) from a single noninvasive carotid pressure waveform in both women and men with heart failure (HF). TAC and Zao are cardiovascular biomarkers with established clinical significance. TAC is lower and Zao is higher in women than in men, so women are more susceptible to the consequent deleterious effects of them. Although the principles of TAC and Zao are pertinent to a multitude of cardiovascular diseases, including HF, their routine clinical use is limited because of the requirement for simultaneous measurements of flow and pressure waveforms. For this study, the data were obtained from the Framingham Heart Study (n = 6,201, 53% women). The reference values of Zao and TAC were computed from carotid pressure and aortic flow waveforms. IF parameters of carotid pressure waveform were used in ML models. IF models were developed on n = 5,168 of randomly selected data and blindly tested the remaining data (n = 1,033). The final models were evaluated in patients with HF. Correlations between IF-ML and reference values in all HF and HF with preserved ejection fraction for TAC were 0.88 and 0.90, and for Zao were 0.82 and 0.80, respectively. The classification accuracy in all HF and HF with preserved ejection fraction for TAC were 0.9 and 0.93, and for Zao were 0.81 and 0.89, respectively. In conclusion, the IF-ML method provides an accurate estimation of TAC and Zao in all subjects with HF and in the general population.

Screening left ventricular systolic dysfunction in children using intrinsic frequencies of carotid pressure waveforms measured by a novel smartphone-based device

Objective.Children with heart failure have higher rates of emergency department utilization, health care expenditure, and hospitalization. Therefore, a need exists for a simple, non-invasive, and inexpensive method of screening for left ventricular (LV) dysfunction. We recently demonstrated the practicality and reliability of a wireless smartphone-based handheld device in capturing carotid pressure waveforms and deriving cardiovascular intrinsic frequencies (IFs) in children with normal LV function. Our goal in this study was to demonstrate that an IF-based machine learning method (IF-ML) applied to noninvasive carotid pressure waveforms can distinguish between normal and abnormal LV ejection fraction (LVEF) in pediatric patients.Approach. Fifty patients ages 0 to 21 years underwent LVEF measurement by echocardiogram or cardiac magnetic resonance imaging. On the same day, patients had carotid waveforms recorded using Vivio. The exclusion criterion was known vascular disease that would interfere with obtaining a carotid artery pulse. We adopted a hybrid IF- Machine Learning (IF-ML) method by applying physiologically relevant IF parameters as inputs to Decision Tree classifiers. The threshold for low LVEF was chosen as <50%.Main results.The proposed IF-ML method was able to detect an abnormal LVEF with an accuracy of 92% (sensitivity = 100%, specificity = 89%, area under the curve (AUC) = 0.95). Consistent with previous clinical studies, the IF parameterω1was elevated among patients with reduced LVEF.Significance.A hybrid IF-ML method applied on a carotid waveform recorded by a hand-held smartphone-based device can differentiate between normal and abnormal LV systolic function in children with normal cardiac anatomy.

A Multiple Linear Regression Model for Carotid-to-Femoral Pulse Wave Velocity Estimation Based on Schrodinger Spectrum Characterization

In this paper, a multiple linear regression model for estimating the Carotid-to-femoral pulse wave velocity (cf-PWV) from a single non-invasive peripheral pulse wave, namely blood pressure or photoplethysmography, is proposed. The training and testing datasets were extracted from in-silico, publicly available, pulse waves and hemodynamics data. The proposed model relies on a preprocessing and features extraction steps, which are performed using a semi-classical signal analysis (SCSA) method. The obtained results provide more evidence for the feasibility of machine learning and the SCSA method as a smart tool for the efficient assessment of the cf-PWV.

Effects of vessel wall mechanics on non-invasive evaluation of cardiovascular intrinsic frequencies

Intrinsic Frequency (IF) is a systems-based approach that provides valuable information for hemodynamic monitoring of the left ventricle (LV), the arterial system, and their coupling. Recent clinical studies have demonstrated the clinical significance of this method for prognosis and diagnosis of cardiovascular diseases. In IF analysis, two dominant instantaneous frequencies (ω₁ and ω₂) are extracted from arterial pressure waveforms. The value of ω₁ is related to the dynamics of the LV and the value of ω₂ is related to the dynamics of vascular function. This work investigates the effects of vessel wall mechanics on the accuracy and applicability of IFs extracted from vessel wall displacement waveforms compared to IFs extracted from pressure waveforms. In this study, we used a computational approach employing a fluid-structure interaction finite element method for various wall mechanics governed by linearly elastic, hyperelastic, and viscoelastic models. Results show that for vessels with elastic wall behavior, the error between displacement-based and pressure-based IFs is negligible. In the presence of stenosis or aneurysm in elastic arteries, the maximum errors associated with displacement-based IFs is less than 2%. For non-linear elastic and viscoelastic arteries, errors are more pronounced (where the former reaches up to 11% and the latter up to 27%). Our results ultimately suggest that displacement-based computations of ω₁ and ω₂ are accurate in vessels that exhibit elastic behavior (such as carotid arteries) and are suitable surrogates for pressure-based IFs. This is clinically significant because displacement-based IFs can be measured non-invasively.

Scalability of cardiovascular intrinsic frequencies: Validations in preclinical models and non-invasive clinical studies

AIMS

Cardiovascular intrinsic frequencies (IFs) are associated with cardiovascular health and disease, separately capturing the systolic and diastolic information contained in a single (uncalibrated) arterial waveform. Previous clinical investigations related to IF have been restricted to studying chronic conditions, and hence its applicability for acute cardiovascular diseases has not been explored. Studies of cardiovascular complications such as acute myocardial infarction are difficult to perform in humans due to the high-risk and invasive nature of such procedures. Although they can be performed in preclinical (animal) models, the corresponding interpretation of IF measures and how they ultimately translate to humans is unknown. Hence, we studied the scalability of IF across species and sensor platforms.

MATERIALS AND METHODS

Scaled values of the two intrinsic frequencies ω1 and ω2 (corresponding to systolic and diastolic dynamics, respectively) were extracted from carotid waveforms acquired either non-invasively (via tonometry, Vivio or iPhone) in humans or invasively in rabbits and rats.

KEY FINDINGS

The scaled IF parameters for all species were found to fall within the same physiological ranges carrying similar statistical characteristics, even though body sizes and corresponding heart rates of the species were substantially different. Additionally, results demonstrated that all non-invasive sensor platforms were significantly correlated with each other for scaled IFs, suggesting that such analysis is device-agnostic and can be applied to upcoming wearable technologies.

SIGNIFICANCE

Ultimately, our results found that IFs are scalable across species, which is particularly valuable for the training of IF-based artificial intelligence systems using both preclinical and clinical data.

Intrinsic Frequencies of Carotid Pressure Waveforms Predict Heart Failure Events: The Framingham Heart Study

Supplemental Digital Content is available in the text.

Intrinsic frequencies (IFs) derived from arterial waveforms are associated with cardiovascular performance, aging, and prevalent cardiovascular disease (CVD). However, prognostic value of these novel measures is unknown. We hypothesized that IFs are associated with incident CVD risk. Our sample was drawn from the Framingham Heart Study Original, Offspring, and Third Generation Cohorts and included participants free of CVD at baseline (N=4700; mean age 52 years, 55% women). We extracted 2 dominant frequencies directly from a series of carotid pressure waves: the IF of the coupled heart and vascular system during systole (ω₁) and the IF of the decoupled vasculature during diastole (ω₂). Total frequency variation (Δω) was defined as the difference between ω₁ and ω₂. We used Cox proportional hazards regression models to relate IFs to incident CVD events during a mean follow-up of 10.6 years. In multivariable models adjusted for CVD risk factors, higher ω₁ (hazard ratio [HR], 1.14 [95% CI], 1.03–1.26]; P=0.01) and Δω (HR, 1.16 [95% CI, 1.03–1.30]; P=0.02) but lower ω₂ (HR, 0.87 [95% CI, 0.77–0.99]; P=0.03) were associated with higher risk for incident composite CVD events. In similarly adjusted models, higher ω₁ (HR, 1.23 [95% CI, 1.07–1.42]; P=0.004) and Δω (HR, 1.26 [95% CI, 1.05–1.50]; P=0.01) but lower ω₂ (HR, 0.81 [95% CI, 0.66–0.99]; P=0.04) were associated with higher risk for incident heart failure. IFs were not significantly associated with incident myocardial infarction or stroke. Novel IFs may represent valuable markers of heart failure risk in the community.

Proof-of-concept for a non-invasive, portable, and wireless device for cardiovascular monitoring in pediatric patients

Measurement of cardiac function is vital for the health of pediatric patients with heart disease. Standard tools to measure function including echocardiogram and magnetic residence imaging are time intensive, costly, and have limited accessibility. The Vivio is a novel, non-invasive, handheld device that screens for cardiac dysfunction by analyzing intrinsic frequencies (IF) ω₁ and ω₂ of carotid artery waveforms. Prior studies demonstrated that left ventricular ejection fraction can be derived from IFs in adults. This study 1) studies whether the Vivio can capture carotid arterial pulse waveform data in children ages 0–19 years old; 2) tests the performance of two sensor head geometries, one larger and smaller than the standard size used in adults, designed for the pediatric population; 3) compares the IFs between pediatric age groups and adults with normal function. The Vivio successfully measured a carotid artery waveform in all children over 5 years old and 28% of children under the age of five. The small head did not accurately measure a waveform in any age group. One-way analysis of variance (ANOVA) demonstrated a difference in the IF ω₁ between the adult and pediatric cohorts (F = 7.3, Prob>F = 0.0001). Post host analysis demonstrated a difference between the adult cohort (ω₁ = 99 +/- 5 bpm) and the cohorts ages 0–4 (ω₁ = 111 +/- 2 bpm; p = 0.0006) and 15–19 years old (ω₁ = 105 +/-5 bpm; p = 0.02). One-way ANOVA demonstrated a difference in the IF ω₂ between the adult and pediatric cohorts (F = 4.8, Prob>F = 0.003), specifically between the adult (ω₂ = 81 +/- 13 bpm) and age 0–4 cohorts (ω₂ = 48 +/- 8 bpm; p = 0.002). These results suggest that the Vivio can be used to capture carotid pulse waveform data in pediatric populations and that the data produced can be used to measure intrinsic frequencies.

Cardiac Triangle Mapping: A New Systems Approach for Noninvasive Evaluation of Left Ventricular End Diastolic Pressure

Noninvasive and practical assessment of hemodynamics is a critical unmet need in the treatment of both chronic and acute cardiovascular diseases. Particularly, the ability to monitor left ventricular end-diastolic pressure (LVEDP) noninvasively offers enormous benefit for managing patients with chronic congestive heart failure. Recently, we provided proof of concept that a new cardiac metric, intrinsic frequency (IF), derived from mathematical analysis of non-invasively captured arterial waveforms, can be used to accurately compute cardiovascular hemodynamic measures, such as left ventricle ejection fraction (LVEF), by using a smartphone. In this manuscript, we propose a new systems-based method called cardiac triangle mapping (CTM) for hemodynamics evaluation of the left ventricle. This method is based on intrinsic frequency (IF) and systolic time interval (STI) methods that allows computation of LVEDP from noninvasive measurements. Since the CTM method only requires arterial waveform and electrocardiogram (ECG), it can eventually be adopted as a simple smartphone-based device, an inexpensive hand-held device, or perhaps (with future design modifications) a wearable sensor. Such devices, combined with this method, would allow for remote monitoring of heart failure patients.

Intrinsic Frequency Analysis and Fast Algorithms

Intrinsic Frequency (IF) has recently been introduced as an ample signal processing method for analyzing carotid and aortic pulse pressure tracings. The IF method has also been introduced as an effective approach for the analysis of cardiovascular system dynamics. The physiological significance, convergence and accuracy of the IF algorithm has been established in prior works. In this paper, we show that the IF method could be derived by appropriate mathematical approximations from the Navier-Stokes and elasticity equations. We further introduce a fast algorithm for the IF method based on the mathematical analysis of this method. In particular, we demonstrate that the IF algorithm can be made faster, by a factor or more than 100 times, using a proper set of initial guesses based on the topology of the problem, fast analytical solution at each point iteration, and substituting the brute force algorithm with a pattern search method. Statistically, we observe that the algorithm presented in this article complies well with its brute-force counterpart. Furthermore, we will show that on a real dataset, the fast IF method can draw correlations between the extracted intrinsic frequency features and the infusion of certain drugs.

Artificial Intelligence Estimation of Carotid-Femoral Pulse Wave Velocity using Carotid Waveform

In this article, we offer an artificial intelligence method to estimate the carotid-femoral Pulse Wave Velocity (PWV) non-invasively from one uncalibrated carotid waveform measured by tonometry and few routine clinical variables. Since the signal processing inputs to this machine learning algorithm are sensor agnostic, the presented method can accompany any medical instrument that provides a calibrated or uncalibrated carotid pressure waveform. Our results show that, for an unseen hold back test set population in the age range of 20 to 69, our model can estimate PWV with a Root-Mean-Square Error (RMSE) of 1.12 m/sec compared to the reference method. The results convey the fact that this model is a reliable surrogate of PWV. Our study also showed that estimated PWV was significantly associated with an increased risk of CVDs.

On the convergence and accuracy of the cardiovascular intrinsic frequency method

In this paper, we analyse the convergence, accuracy and stability of the intrinsic frequency (IF) method. The IF method is a descendant of the sparse time frequency representation methods. These methods are designed for analysing nonlinear and non-stationary signals. Specifically, the IF method is created to address the cardiovascular system that by nature is a nonlinear and non-stationary dynamical system. The IF method is capable of handling specific nonlinear and non-stationary signals with less mathematical regularity. In previous works, we showed the clinical importance of the IF method. There, we showed that the IF method can be used to evaluate cardiovascular performance. In this article, we will present further details of the mathematical background of the IF method by discussing the convergence and the accuracy of the method with and without noise. It will be shown that the waveform fit extracted from the signal is accurate even in the presence of noise.