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 parameter was 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.

Ventricular function is one of the fundamental components of cardiovascular health in children with congenital and acquired heart disease. It follows that the ability to detect ventricular dysfunction is critical for clinicians in guiding the treatment, management, and prognosis of children with cardiovascular disease. The transthoracic echocardiogram is the primary imaging modality for assessing the anatomy and function of the heart (Cheitlin et al 2003, Lai et al 2006). However, echocardiography requires specialized training to perform and interpret, limiting the settings where an echocardiogram can be obtained. While physicians and parents of children with heart disease are taught to recognize symptoms of heart failure (HF), many of these symptoms, such as tachypnea, are nonspecific (Price 2019). Children with HF are also known to have higher rates of emergency department utilization, health care costs, and rates of admission (Shamszad et al 2013, Price et al 2016, Mejia et al 2018). In resource-limited health care settings, such as rural communities, and in the home, an urgent need exists for a simple, non-invasive, and inexpensive method of screening for left ventricular (LV) dysfunction to determine if a patient needs further medical evaluation.

A newly developed wireless smartphone-based handheld device, the Vivio, uses the intrinsic frequency (IF) method to quickly and non-invasively measure LV function (Pahlevan et al 2014, Pahlevan et al 2017b, Armenian et al 2018, Rinderknecht et al 2020). The Vivio is an optical tonometer and phonogram that can quickly capture arterial waveforms (Rinderknecht et al 2020). This device is non-invasive, inexpensive, easy to use, ultra portable, and compatible with Bluetooth-capable smartphones and tablets (Rinderknecht et al 2020). We recently demonstrated the practicality and reliability of the Vivio device in capturing carotid arterial waveforms and deriving IFs in children with normal cardiovascular function (Miller et al 2020).

The IF method is a new systems-based mathematical method that considers the arterial network as a dynamic system coupled to the LV during systole and uncoupled during diastole. Intrinsic frequencies (IFs) are operating frequencies that are physically and mathematically different than resonance-type frequencies, such as Fourier frequencies (Pahlevan et al 2014, Tavallali et al 2015, Alavi et al 2021). The IF method can extract information about LV function, vascular dynamics, and the interaction between the LV and arterial system (LV-arterial coupling) from pressure waveforms (Pahlevan et al 2014, Pahlevan et al 2017b, Tavallali et al 2018, Mogadam et al 2020). Previous clinical studies have shown that the IF method can be applied to carotid artery waveforms measured by Vivio or a smartphone (an iPhone) to compute LV ejection fraction (LVEF), the most common measure of global LV systolic function (Pahlevan et al 2017b, Armenian et al 2018). In a recent clinical study based on the Framingham Heart Study (FHS) data, it was shown that IFs derived from a custom tonometer (functionally similar to the Vivio) could be used to predict HF events in adults (Cooper et al 2021). Detecting decreased LVEF in pediatric patients early via IF screening would similarly be clinically useful, as ventricular dysfunction has been associated with morbidity and mortality in children admitted with a variety of conditions including sepsis and cardiomyopathy (McMahon et al 2004, Fisher et al 2005).

In this study, we explored the use of a non-invasive, inexpensive, easy to use, ultra-portable device (Vivio) in pediatric patients with normal cardiac anatomy and depressed LV systolic function, as assessed by transthoracic echocardiogram and cardiac magnetic resonance imaging (MRI). Our goal was to demonstrate that a novel IF-based machine learning (ML) method (focusing on IFs that are linked to LV systolic function such as and ) applied on carotid waveforms measured by Vivio can distinguish between normal and reduced (abnormal) LVEF in pediatric patients.

Study design

The study was conducted at Children's Hospital Los Angeles (CHLA). Patients ages 0 to 21 years who had undergone an echocardiogram or cardiac MRI for clinical purposes were invited to participate in the study. The only exclusion criterion was known vascular disease that would interfere with obtaining a carotid artery pulse. Informed consent was obtained from participants, or their legal guardians for those who were minors. Patients underwent LVEF measurement by either echocardiogram or cardiac MRI. On the same day, patients had a carotid artery waveform recorded using the Vivio device. The study was approved by the CHLA Institutional Review Board (CHLA-17-00377).

Echocardiograms were performed at CHLA using either an IE33 or Epiq 7 ultrasound system (Philips, Best, Netherlands). Studies were performed according to American Society of Echocardiogram guidelines (Lai et al 2006, Lopez et al 2010). LV systolic function was evaluated by LVEF. IntelliSpace Cardiovascular Workstation (Philips) was used to calculate end-systolic and end-diastolic volumes using the modified Simpson's method in apical 4 and apical 2 chamber views. LVEF was then calculated as: LVEF = 100*(LV end diastolic volume—LV end systolic volume)/(LV end diastolic volume) (Lopez et al 2010).

Cardiac MRI studies were performed at CHLA using a 1·5 Tesla Achieva system (Philips, Best, Netherlands). Images were obtained using a balanced steady state free procession sequence without use of a contrast agent. Each dataset consisted of 15 short-axis slices covering the left ventricle from base to apex with 30 frames per cardiac cycle. Typical scan parameters were slice thickness 6–10 mm, in-plane spatial resolution 1·5–2 mm2, repetition time 3–4 ms, echo time 1·5–2 ms, and flip angle 60 degrees. Images were obtained with the patients free breathing; 3 signal averages were obtained to compensate for respiratory motion. Manual image segmentation was performed using Circle cvi42 v.5.10 software (Circle Cardiovascular Imaging Inc., Calgary, Canada). Endocardial contours were drawn on end-diastolic and end-systolic images. LVEF was then calculated from these contours as above.

A trained physician positioned each patient's head to expose the carotid triangle by rotating their head laterally 30–60 degrees and up 30 degrees. After palpating the common carotid artery pulse, the physician then used the Vivio device to record the carotid pulse waveform. Waveforms were recorded for one minute to ensure that high-quality tracings were obtained over multiple cardiac cycles. All patients were studied at rest. After the waveforms were collected, cardiac cycles were selected by a researcher blinded to study participant clinical history and LVEF data. For each patient, three to five cardiac cycles deemed good signal quality were selected from the Vivio carotid waveforms. The selected cycles were used to calculate the IF parameters (see the next section) and the IF parameters from the selected cycle were averaged to serve as the final IF analysis result for the individual (each patient has only one set of IF parameters). A picture of the Vivio device and sample waveforms measured by it are provided in figure 1.

Figure 1. The wireless Vivio system for cardiovascular monitoring. (A) The Smartphone-based device (Vivio). (B) The user interface for real-time patient monitoring of the mobile application for the Vivio.

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Intrinsic frequencies are operating frequencies based on the Sparse Time-Frequency Representation (STFR) (Hou and Shi 2011), treating the LV combined with the aorta and the remaining peripheral arteries as a coupled dynamical system (heart + aortic tree), which decouples upon closure of the aortic valve (Pahlevan et al 2014, Tavallali et al 2015, Pahlevan et al 2017b). The IF method models a dynamical system as an object rotating around an origin. The angular velocity of the rotation is the intrinsic frequency (see figure 2). In the LV-arterial system, the average angular velocity during systole and diastole are ω1 and ω2, respectively. The first IF, ω1, describes the dynamics of the systolic phase of the cardiac cycle, where the LV and aorta are a coupled dynamical system (Pahlevan et al 2014, Tavallali et al 2015, Pahlevan et al 2017b). The second IF, ω2, is dominated by the dynamics of the vasculature (Petrasek et al 2015, Pahlevan et al 2017b, Tavallali et al 2018). Further details about the physics and mathematics of IF can be found in previous publications (Pahlevan et al 2014, Tavallali et al 2015, Alavi et al 2021). The IF mathematical formulation is:

Here, p(t) is the carotid arterial waveform and is the indicator function ( if and otherwise). The initial phases (and ) and envelopes (and ) can be computed from Here, is the tangent inverse function. and are the initial phase shifts (or intrinsic phases) associated with and respectively. and are the envelopes of IFs related to and respectively. Reconstruction of an arterial pulse with IF method and visualization of IFs during systolic and diastolic phases are provided in figure 2.

Figure 2. Illustration of intrinsic frequency (IF) method. (A) Reconstruction of arterial pulse with IF method. (B) Visualization of IFs. and are the IFs during systole and diastole, respectively. and are the envelopes of IF components associated with and respectively. and are the phase shifts (or intrinsic phases) of the IF components associated with and respectively. Ts is the systolic time, and it is equal to T0. Td is the diastolic time, and it is equal to T–T0.

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Previous clinical studies have indicated that IF systolic parameters (e.g. ) extracted from carotid waveforms can reflect LV systolic function (Pahlevan et al 2017b, Mogadam et al 2020). Hence, and which delineate LV systolic function, were considered as physiologically relevant metrics for classifying low LVEF. In this study, was also corrected for LV ejection time. Since heart rates (HR) normally change with age in children (Finley and Nugent 1995), we also considered the index, denoted as which is normalized with respect to the HR. We expected that would provide supplementary information to for predicting low LVEF in our pediatric cohort across all ages.

We previously reported that there was a significant difference in among different age groups (Miller et al 2020); particularly, of the age group from 0 to 4 years old showed significant difference from the that of the adult cohort (Miller et al 2020). Therefore, we divided the study population into three age groups: 0–6 years old, 7–13 years old, and 14–20 years old. Then, we compared the and between patients with LVEF <50% and LVEF ≥50% in each age group. To grasp the classification ability of and intuitively, we also used the Beeswarm plots to inspect the scattering and distribution of and for the low LVEF and normal LVEF patients in age-separated groups.

In our analysis we adopted a hybrid IF- Machine Learning (IF-ML) method by applying physiologically relevant IF parameters (i.e. and ) as inputs to Decision Tree classifiers. Decision Tree is a well-established machine learning approach that exhibits good interpretability through generating a set of if-then-else decision rules which can be visualized as a binary tree (Lewis 2000, Song and Ying 2015). The decision tree technique can facilitate the exploration and development of classification criteria for clinical decision making based on relevant IF-derived parameters and their physiological connotation.

We used the IF-ML method to identify low LVEF in our pediatric cohort (N = 50) based on the physiologically relevant feature space composed of and age. The threshold for low LVEF was chosen as <50%, and positive labels were assigned for patients with low LVEF. The Statistics and Machine Learning Toolbox of MATLAB (The MathWorks, Inc., Natick, Massachusetts) was used to create the binary decision trees using the standard CART algorithm (Lewis 2000). To illustrate the exemplary decision rules based on the novel IF parameters for classifying low LVEF, we presented the tree structures developed based on the whole dataset set. To strive for concision of the decision tree and mitigate overfitting, we set the constraints that the maximal number of the tree splits cannot be greater than (1 + number of predictors), and that the samples in the splitting nodes should be greater than 10.

We employed leave-one-out cross-validation (LOCCV) in our dataset to evaluate the classification performance. Considering the sample size, we chose the leave one out cross-validation (LOOCV) for fair comparisons between different feature combinations. LOOCV does not overestimate test error rates and it gives the same estimate because the partitions are not chosen randomly. The analysis metrics include the area under curve (AUC) in receiver-operating characteristic (ROC) analysis, sensitivity, specificity, and accuracy, which are defined as:

Patient cohort

Figure 3 summarizes patient enrollment. A total of 71 pediatric patients' guardians were consented (1/3/18 to 11/6/19) for this study. Due to their young age, twelve patients did not cooperate with recording of their carotid pressure waveforms with the Vivio device. Acceptable carotid tracing measurements were not achieved in nine patients (low signal quality and severe distortion of carotid waveforms due to body motion or respiratory motion). For the remaining consented patients, signal quality was confirmed manually by one of the study investigators (N.M.P.) before any analysis and calculations of intrinsic frequencies. Thus, 50 patients were included in the study analysis. Table 1 summarizes the demographic characteristics of the patient cohort. No patients had significant aortic valve disease, aortopathy, or hypertension. Forty-six had LVEF measured by echocardiogram and 4 had LVEF measured by cardiac MRI. Of the patients evaluated by echocardiogram, 32/46 (70%) had normal LVEF and 14/46 (30%) had abnormal LVEF. Of those evaluated by cardiac MRI, 2/4 (50%) had normal LVEF and 2/4 (50%) had abnormal LVEF.

Figure 3. The flowchart of patient enrollment process.

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Table 1. Demographics of patient cohort.

 Total (n = 50)Normal LVEF (n = 34)Abnormal LVEF (n = 16)Sex, N (%)   Male22 (44%)18 (53%)10 (63%)Female28 (56%)16 (47%)6 (37%)Race/Ethnicity, N (%)   Asian/Pacific Islander3 (6%)3 (9%)0 (0%)Black/African American3 (6%)2 (6%)1 (6%)Hispanic29 (58%)17 (50%)12 (75%)Non-Hispanic White12 (24%)10 (29%)2 (13%)Other3 (6%)2 (6%)1 (6%)Age at examination, years (median, IQR)9·9 (5·1–14·5)9·2 (3·4–13·5)12 (6·2–16·9)BMI at examination, kg/m2 (median, IQR)18 (15·3–24·1)17·2 (15·5–23·3)19·3 (14·9–26·7)Diagnosis, N (%)   Normal20 (40%)20 (59%)0 (0%)Status post cardiac transplant7 (14%)6 (18%)1 (6%)Status post chemotherapy9 (18%)8 (23%)1 (6%)Dilated cardiomyopathy14 (28%)0 (0%)14 (88%)Comorbidities, N (%)   Moderate-severe mitral valve disease2 (4%)0 (0%)2 (13%)Diabetes1 (2%)0 (0%)1 (6%)Obesity11 (22%)6 (18%)5 (31%)LVEF (median, IQR)59·1% (48–64·5%)62·5% (58·9%–67%)40·7% (21%–48%)Receiving heart failure medications, N (%)18 (36%)6 (18%)12 (75%)

Reconstruction of sample waveforms from IF analysis (the systolic phase is the red curve and the diastolic phase is the blue curve) with the corresponding raw pulse waveforms (black curve) are shown in figure 4 for patients in different age brackets. The Beeswarm plots in figure 5 show the distribution of and in different age groups and EF levels. The supplementary predictive power of to can be perceived from figure 5. We can observe that there is a larger discrepancy of