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 parameter ω1 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.


Introduction
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 ω 1 and φ 1 ) 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).

Lvef measurement
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 mm 2 , 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.

Noninvasive carotid artery waveform measurement using Vivio
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.

Intrinsic frequency method
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 ω 1 and ω 2 , respectively.The first IF, ω 1 , 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, ω 2 , 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 χ (a, b) is the indicator function (χ (α, β) = 1 if α ⩽ t ⩽ β and χ(α, β) = 0 otherwise).The initial phases (φ 1 and φ 2 ) and envelopes (R s and R d ) can be computed from a Here, tan −1 is the tangent inverse function.φ 1 and φ 2 are the initial phase shifts (or intrinsic phases) associated with ω 1 and ω 2 respectively.R s and R d are the envelopes of IFs related to ω 1 and ω 2 respectively.Reconstruction of an arterial pulse

Parameter selection and analysis
Previous clinical studies have indicated that IF systolic parameters (e.g.ω 1 ) extracted from carotid waveforms can reflect LV systolic function (Pahlevan et al 2017b, Mogadam et al 2020).Hence, ω 1 and φ 1 , which delineate LV systolic function, were considered as physiologically relevant metrics for classifying low LVEF.In this study, ω 1 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 ω 1 index, denoted as ωi 1 , which is ω 1 normalized with respect to the HR.We expected that ωi 1 would provide supplementary information to ω 1 for predicting low LVEF in our pediatric cohort across all ages.
We previously reported that there was a significant difference in ω 1 among different age groups (Miller et al 2020); particularly, ω 1 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 ω 1 and ωi 1 between patients with LVEF <50% and LVEF ⩾50% in each age group.To grasp the classification ability of ω 1 and ωi 1 intuitively, we also used the Beeswarm plots to inspect the scattering and distribution of ω 1 and ωi 1 for the low LVEF and normal LVEF patients in age-separated groups.

Hybrid IF-machine learning algorithm
In our analysis we adopted a hybrid IF-Machine Learning (IF-ML) method by applying physiologically relevant IF parameters (i.e.ω 1 , φ 1 , and ωi 1 ) 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 andYing 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 ω 1 , φ 1 , ωi 1 , 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.

Validation and analysis
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-

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.

Discussion
In this study we demonstrated that IFs derived from a carotid artery waveform captured by the Vivio device can be used to discriminate between normal and abnormal LVEF in children with normal cardiac anatomy.Overall, we observed that in all age groups, higher ω 1 and ωi 1 were associated with low LVEF on echocardiogram or cardiac MRI.We then tested several decision tree models that combined the different IFs and clinical variables to develop a hybrid machine learning (ML) model to predict if a patient had normal or abnormal LVEF.Our hybrid IF-ML method was able to detect an abnormal LVEF with an accuracy of up to 92% (sensitivity = 89%, specificity = 100%, AUC = 0 The interpretation and usage of our IF-ML models are straightforward.When age and φ 1 were used along with ω 1 , ω 1 <107•6 was indicative of normal LVEF regardless of age and the value of φ 1 .However, ω 1 >107•6 only confirmed abnormal LVEF in patients older than 6 years.For children younger than 6 years, abnormal LVEF was confirmed via reduced φ 1 .

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For this age bracket (younger than 6 years), only those with high ω 1 (>107) and low φ 1 (< −0•65) had abnormal LVEF.It is noteworthy, that the age of 6 years as a branching point was not pre-enforced, but was deduced by the algorithm itself.Although using only ω 1 and age created an accurate (88%) classification of LVEF with AUC of 0•87, as shown in table 2, both accuracy and AUC were improved when φ 1 was added as a classifying parameter.
However, the accuracy was slightly reduced under leave-one-out validation analysis when φ 1 was included.This may suggest that the augmented classification ability by φ 1 could be unstable to dataset/training population and it will require a larger dataset for further investigation.
As demonstrated in figure 7  Given the hemodynamic, physiologic, and anatomical differences between infants, toddlers, school age children, and teenagers, making standardized or predictive models can be difficult for pediatric patients.It is common, if not expected, for other diagnostic studies such as echocardiogram, plain film radiography, and blood tests to need adjustment for age to interpret results (Gutgesell et al 1977, Dallaire et al 2016, Cantinotti et al 2020).
While not a comprehensive diagnostic modality such as an echocardiogram or cardiac MRI, the Vivio device and IF method can potentially serve as a powerful adjunctive tool in a variety of clinical scenarios.In resource limited settings, rural clinics, or at home, if a child with heart disease becomes sick, the decision to wait and see if a child improves or seek advanced cardiac care may be influenced if abnormal LV function is detected.The explosion of telehealth services in the past year has also created the need for new technology (Burke andHall 2015, Sasangohar et al 2018).Several patients and family members in our study expressed enthusiasm and interest in having the device at home.Home use of the Vivio device based on the proposed ML-based IF model could allow cardiologists and families to remotely monitor a child's cardiac function, providing more valuable care via telehealth.
Similar to other tonometry devices, the Vivio is a virtually risk-free diagnostic modality.Empirically, we observed that the Vivio device was minimally intimidating and well tolerated in this pediatric population.In addition, capturing the carotid waveform is a quick and painless process.While we collected 1 min of arterial waveforms during our study and computed IFs for multiple cardiac cycles, only one cardiac cycle is needed to instantaneously estimate LVEF qualitatively.Comparatively, an echocardiogram would take a technician on average 30 min to perform bedside, not including the time needed to physically transport the equipment or patient to and from the scan, and additional time for the study to be interpreted by a cardiologist (Lai et al 2006). 2 The ease of use of the device also allows parents and non-cardiac medical providers to be taught how to use the device.Our proposed ML-derived IF method combined with the Vivio device may also become a cost-effective screening tool in patients who need serial assessments of LV function, such as children who have undergone heart transplantation.Critical care is another area where the Vivio and IF measurement estimations of LVEF would be very useful.Similar to the utility of continuous arterial blood pressure monitoring, continuous monitoring of LVEF, derived from IF calculations from these same arterial blood pressure tracings, could be of great utility in detecting early improvement or worsening of cardiac function.This information would help guide providers whether other studies such as echocardiogram are indicated, if cardiac support should be increased, or if cardiac support could safely be weaned.In future studies, we will also examine a larger cohort of pediatric patients with LV dysfunction, in addition to different cardiac anatomies, to further evaluate additional biometrics such as body mass index, clinical variables, and factors such as respiration and motion artifacts that may influence the predictive value of IFs.We will also investigate the classification performance with blinded testing.

Limitations
While there is known discrepancy between LVEF measurements by echocardiogram compared to cardiac MRI, the majority of the patients in this study had LVEF measurement by echocardiogram.Of the small number who had LVEF measured by cardiac MRI, an even number had normal versus abnormal LVEF.Thus, the difference in LVEF calculation between the two modalities is unlikely to have significantly affected our decision tree analysis of normal versus abnormal LVEF.Also, statistical significance tests were not performed due to limited sample size in some age subgroups and EF categories.

Conclusion
Our study demonstrated that intrinsic frequencies calculated from a carotid artery waveform recorded by a hand-held smartphone-based device (the Vivio) can be used to differentiate between normal and abnormal LV systolic function (as measured by LVEF) in children with normal cardiac anatomy.Overall, the IF-ML model based on ω 1 and ωi 1 provided the best accuracy, AUC, and leave-one-out analysis AUC for all pediatric ages.The classification results indicate that IF can serve as a simple and sensitive tool for indicating risk of low LVEF.The proposed method can be done quickly, non-invasively, and easily, allowing for its use in multiple settings by both medical professionals and family members.This makes the IF method and Vivio device a potentially useful screening tool and valuable accessory to standard cardiac testing modalities.In the future, more diagnostic and prognostic information can be obtained from the IF method and smartphone-based devices such as Vivio as the hybrid IF-ML method is refined in pediatric patients by developing models for accurate LVEF quantification across all ages.This approach could be immensely useful for home monitoring or in resource limited medical settings where pediatric cardiac care is not readily available.This same methodology could also be adapted to calculate LVEF continuously from standard arterial blood pressure monitoring for critically-ill children in the hospital setting.The flowchart of patient enrollment process.

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Health Research Alliance Author Manuscript Beeswarm plots for the scattering of ω 1 and ωi 1 in different age groups and LVEF (EF).
The cross overlying the scattering dots indicates the mean value ± standard deviations for the group of samples.Unit of ω 1 is beats per minutes (bpm).ωi 1 is unitless.

Figure 7 (
Figure7(A) shows the decision tree for LVEF classification using ω 1 and ωi 1 .The results indicate that ω 1 = 107•6 bpm still serves as the top-level splitting boundary.ωi 1 further subdivided each branch as shown in figure7(A).According to the decision boundary visualized in figure7(B), the upper right region highlighted in red is classified as low LVEF, which is associated with high ω 1 and ωi 1 , as compared to the blue region, classified as normal LVEF.The ROC curve for the decision tree with ω 1 and ωi 1 as the predictors is depicted in figure7(C).The AUC was 0•95, as shown in figure7(C).
•95).Consistent with previous clinical studies (Pahlevan et al 2014, Pahlevan et al 2017b, Mogadam et al 2020), ω 1 was elevated among patients with reduced LVEF (figure 5); hence, it played a dominant role in IF-ML models for low LVEF detection as expected.

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.

Figure 2 .
Figure 2. Illustration of intrinsic frequency (IF) method.(A) Reconstruction of arterial pulse with IF method.(B) Visualization of IFs.ω 1 and ω 2 are the IFs during systole and diastole, respectively.R s and R d are the envelopes of IF components associated with ω 1 and ω 2 respectively.φ 1 and φ 2 are the phase shifts (or intrinsic phases) of the IF components associated with ω 1 and ω 2 respectively.T s is the systolic time, and it is equal to T 0 .T d is the diastolic time, and it is equal to T-T 0 .

Figure 4 .
Figure 4. Representative raw carotid waveforms (black curve) measured by Vivio, and IF reconstructed waveforms (red curve: systolic phase; blue curve: diastolic phase) in different ages.(A) sample IF reconstruction waveform for a 5 year old patient.(B) sample IF reconstruction waveform for a 9 year old patient.(C) sample IF reconstruction waveform for a 19 year old patient.

Figure 6 .
Figure 6.Decision tree analysis for low LVEF (EF) classification (<50%) with IF parameters and age.(A) The decision tree for classifying low EF (<50%) using ω 1 and age.(B) Visualization of the decision boundary and classification result based on ω 1 and age.(C) The expanded branch from the node of patients with ω 1 ⩾107•6 and age <6 (N = 10) for leveraging φ 1 for further classification of low EF patients.(D) Visualization of the decision boundary based on φ 1 for classifying low EF patients with ω 1 ⩾107•6 and age <6.(E) The ROC of decision tree classifier based on the predicting features of ω 1 and age (black line), and the predicting features of ω 1 , φ 1 , and age (blue line).The units for ω 1 is bpm (beats per minute).φ 1 is in radian.

Figure 7 .
Figure 7. Decision tree analysis for low LVEF (EF) classification (<50%) with IF parameters only.(A) The decision tree for classifying low LVEF (<50%) using ω 1 and ωi 1 .(B) Visualization of the decision boundary and classification result based on ω 1 and ωi 1 .(C) The ROC of decision tree classifier based on the predicting features of ω 1 and ωi 1 .The units for ω 1 is bpm.ωi 1 is unitless.
(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: validation 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.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 figure4for patients in different age brackets.The Beeswarm plots in figure5show the distribution of ω 1 and ωi 1 in different age groups and EF levels.The supplementary predictive power of ωi 1 to ω 1 can be perceived from figure5.We can observe that there is a larger discrepancy of ωi 1 in the age group of [0, 6] (years) between the normal and abnormal low EF groups.boundarybasedon ω 1 and age is depicted as the black line in figure6(B).It can be seen in this figure that no decision rule was grown for the low LVEF for patients younger than 6 years old.By integrating φ 1 into the tree structure, an expanded branch with φ 1 as the splitting node grew for patients (N = 10) with ω 1 > 107•6 and age <6. Figure 6(C) visualizes the branch with φ 1 as the splitting node with φ 1 = −0•65 as the decision boundary.The ROC curves for the decision trees based on the predictor sets [ω 1 ,age] and [ω 1 ,age, φ 1 ] are demonstrated in figure 6(E).
1 developed for the whole study population (N = 50).The splitting boundary for ω 1 and age are 107•6 bpm and 6 years old (extracted by the IF-ML algorithm), respectively.The decision

Table 2
summarizes the classification performance of the decision trees when different systolic IF features are selected.Sensitivity, specificity, accuracy, and AUC for IF-ML analyses are provided in this table.The leave-one-out validation analyses of the IF-ML models are also presented in this table.While the addition of φ 1 can further improve the performance as compared to the feature set of [ω 1 , age] in full sample analysis, it does not hold in the leave-one-out validation analyses.The feature set of [ω 1 , ωi 1 ] produces the best classification performance in terms of AUC in both full sample and leave-one-out validation analyses.This is further discussed in the Discussion section.
and table 2, the IF-ML algorithm was able to create a more accurate, more specific, and more sensitive model for LVEF classification when ω 1 and ωi 1 were considered.The model's robustness is evident by its simplicity, symmetry, and high AUC under leave-one-analysis validation test.Based on this model, ωi 1 >1•6 and ωi 1 < 1•22 indicate abnormal LVEF and normal LVEF, respectively.For values of ωi 1 between 1•6 and 1•22, classification of LVEF is decided by the value of ω 1 , where ω 1 >107•6 corresponds to low LVEF (note that this ω 1 threshold is the same as the previous model where age and φ 1 were used).The IF-ML model based on ω 1 and ωi 1 was universal for all pediatric ages.This was achieved by incorporation of HR (a strong correlate of age among pediatric population) through ωi 1 .
(Pahlevan et al 2017a, 2017b, Armenian et al 2018)umber of patients enrolled in each age bracket.Since each age bracket has its own normal heart rate, they will have different dynamical states.Consequently, each age bracket has its own IF equation that estimates LVEF quantitively.Future studies will be aimed at deriving IF equations that can estimate LVEF (as opposed to only classifying it as normal versus abnormal) similar to what has been done with the Vivio device or the iPhone camera in adults(Pahlevan et al 2017a, 2017b, Armenian et al 2018).Howeverthis will require enrolling a larger number of patients in each age bracket.
Sasangohar F, Davis E, Kash BA and Shah SR 2018 Remote patient monitoring and telemedicine in neonatal and pediatric settings: scoping literature review J. Med.Internet Res 20 e295 [PubMed: 30573451] Shamszad P, Hall M, Rossano JW, Denfield SW, Knudson JD, Penny DJ, Towbin JA and Cabrera AG 2013 Characteristics and outcomes of heart failure-related intensive care unit admissions in children with cardiomyopathy J. Cardiac Failure 19 672-7 [PubMed: 24125105] Song Y-Y and Ying L 2015 Decision tree methods: applications for classification and prediction Shanghai Archives Psychiatry 27 130 Tavallali P, Hou TY, Rinderknecht DG and Pahlevan NM 2015 On the convergence and accuracy of the cardiovascular intrinsic frequency method R. Soc.Open Sci 2 150475 [PubMed: 27019733] Tavallali P, Razavi M and Pahlevan NM 2018 Artificial intelligence estimation of carotid-femoral pulse wave velocity using carotid waveform Sci.Rep 8 1014 [PubMed: 29343797]

Table 2 .
The classification performance of IF-based decision trees for low LVEF.
Physiol Meas.Author manuscript; available in PMC 2024 May 06.