Participants

The sample for the present study was drawn from the Framingham Original, Offspring, and Third Generation Cohorts, which have been described.^16–18 During Original Cohort examination 26 (1999–2001, N=558), Offspring examination 7 (1998–2001, N=3539), and Gen 3 examination 1 (2002–2005, N=4095), participants underwent a noninvasive assessment of central hemodynamics (successfully obtained in N=293, N=2484, and N=3921, respectively, for a total N=6698). Analysis of waveforms to extract IF measures was successfully performed in 5924 (88.4%) of the 6698 participants. Participants were further excluded for the following reasons: prevalent CVD (n=206), age<35 years (n=981), or missing laboratory or covariate data (n=37). For secondary analyses that assessed relations between IF measures and aortic stiffness, we further excluded participants with missing carotid-femoral pulse wave velocity (N=192). All participants provided written informed consent and protocols were approved by Boston University Medical Center’s Institutional Review Board.

Noninvasive Hemodynamics and Tonometry

Hemodynamic data were acquired as previously described.¹⁹ After a 5-minute rest, participants were studied in the supine position. Arterial tonometry with simultaneous electrocardiography was obtained from brachial, radial, femoral, and carotid arteries using a custom tonometer. Tonometric data were digitized during the primary acquisition and transferred to a core laboratory (Cardiovascular Engineering, Inc.) for blinded analyses. Tonometry waveforms were signal-averaged using the electrocardiographic R-wave as a fiducial point.¹⁹ Cuff systolic and diastolic blood pressures obtained at the time of tonometry were used to calibrate the peak and trough of the signal-averaged brachial pressure waveform. Diastolic blood pressure and integrated brachial mean arterial pressure were used to calibrate carotid pressure tracings, which represented central aortic pressure.²⁰ Carotid-femoral pulse wave velocity was calculated as previously described accounting for parallel transmission in the carotid artery and aortic arch.²¹

Intrinsic Frequencies

Derivation of IFs from aortic pressure waveforms, the convergence of its algorithm, and its accuracy has been described previously.^12,22 IF method is a new method (based on the sparse time-frequency representation²³) for analysis of coupled dynamical systems (See Data Supplement for more details).^12,24 IF method models a coupled dynamical system as an object rotating around an origin. The angular velocity of the rotation is the IF. In its simplest form, a coupled dynamical system is composed of 2 systems. One physiological example of a 2-coupled dynamical system is the LV-arterial system. Figure 1 is the visualization of the IF concept.²⁵ IF frequencies are operating frequencies treating the LV combined with the aorta and the remaining peripheral arteries as a coupled dynamical system (heart + aortic tree), which is decoupled upon closure of the aortic valve.^12,14,22 It is well known that sparse time-frequency representation based methods, such as IF method, are capable of handling nonlinear and nonstationary signals.^12,13,23 Using the IF method, one can extract 2 IF frequencies (ω₁ and ω₂) from a single arterial blood pressure waveform. The first IF, ω₁, describes the dynamics of the systolic phase of the cardiac cycle where the LV and aorta (vasculature) are a coupled system. Therefore, ω₁ is dominated by the dynamics of LV systolic function.^12,14 The second IF, ω₂, belongs to the diastolic phase when the aorta and vascular branches are decoupled from the LV. Hence, ω₂ is dominated by the dynamics of the aorta and the rest of the arterial system.^12,14,15

Figure 1.

Intrinsic frequency (IF) visualization. ω₁ and ω₂ are the intrinsic frequencies during systole and diastole, respectively. R_s and R_d are the envelopes of intrinsic frequencies associated with ω₁ and ω₂, respectively. dθ/dt is the instantaneous frequency. θ_s and θ_d are the intrinsic phases during systole and diastole, respectively (see the Data Supplement for details about IF and its relations to instantaneous frequency).

The IF algorithm is based on an L₂-minimization that uses a waveform to compute the IF parameters.²² The mathematical formulation is as follows:

This minimization is subject to periodicity of the waveform () and continuity at T₀ (). Here, χ (a,b) is the indicator function (χ (a,b)=1 if a ≤t≤b and χ (a,b)=0 otherwise), T₀ is the dicrotic notch time (end-systolic time), p(t) is the input waveform, and T is the duration of the cardiac cycle. A brute-force algorithm was used to solve this nonconvex and nonlinear optimization problem resulting from the aforementioned L₂ minimization formulation.^12,22 More details about the mathematical formulation of IF method, its computational procedure, and its convergence/accuracy have been provided previously.^12,14,22 Using IF algorithm, we were able to compute the 2 IFs ω₁ (IF of the coupled LV and aorta + its vascular branches) and ω₂ (IF of the decoupled aorta after the aortic valve closes; Figure 2). Since the goal of the IF method is to find the best fit dominant (single) frequency during systole and diastole (and not to find the best overall fit for the waveform data), the fit figure shows how well the first intrinsic mode functions of the IF represent the actual signal. The notch selection for IF calculation was performed using an automatic algorithm. To find the notch, a first and second derivatives were calculated for the pulse. The algorithm then performed first and second derivative analysis to determine the location of the notch by searching for zero crossings in the first derivative and peaks in the second derivative. Figure S1 in the Data Supplement shows reconstruction of IF with various values of ω₁ and ω₂ from participants overlaid on top of the original raw carotid pressure. Total frequency variation (Δω) was calculated as the difference between ω₁ and ω₂.^12,25

Figure 2.

The intrinsic frequency (IF) reconstruction of a carotid pressure waveform. The piecewise reconstruction of a representative pressure wave from a Framingham participant overlaid on top of the original raw carotid pressure waveforms (black) in arbitrary units (AU). The portions of the reconstructed waveform represented by ω₁ and ω₂ are shown in blue and red, respectively. The location of the dicrotic notch is marked by the vertical gray dotted line.

Incident CVD Outcomes

The criteria for CVD outcomes (CVD-related death, myocardial infarction, ischemic or hemorrhagic stroke, and heart failure [HF]) have been described.^26,27 Medical records were obtained for physician and hospital visits related to CVD during follow-up. All outcomes were reviewed by a committee of 3 physician investigators and were adjudicated by using a written protocol. A separate group of neurologists adjudicated cerebrovascular outcomes. Follow-up evaluations were performed on data acquired through October 17, 2014.

Clinical Evaluation and Covariates

Medical history, physical examination, and electrocardiography were performed routinely at each examination.¹⁷ Age, sex, use of antihypertensive drugs, and smoking (current versus nonsmoker) were assessed via questionnaires. Height and weight were assessed during the examination. Heart rate, systolic and diastolic blood pressures, and systolic ejection period were assessed during tonometry. Serum cholesterol levels were measured from a fasting blood test. Criteria for diabetes were a fasting glucose ≥126 mg/dL (7.0 mmol/L) or treatment with insulin or an oral hypoglycemic agent. Smoking was defined as self-reported regular use of cigarettes in the year preceding the examination. Body mass index was calculated by dividing weight in kilograms by the square of the height in meters.

Statistical Analyses

Characteristics for the study sample were tabulated. We estimated partial correlations to assess associations among the novel IFs (ω₁, ω₂, and Δω) and hemodynamic measures (heart rate, systolic ejection period, and systolic and diastolic blood pressures) accounting for age, sex, and cohort. We used Cox proportional hazards models to assess the associations between individual IFs and the time to a first major CVD event. We also assessed the associations between individual IFs and the time to event for each type of CVD event (HF, myocardial infarction, and stroke) separately. We tested the proportional hazards assumption by assessing the significance of time-dependent covariates by creating interactions of each predictor and survival time. Covariates were selected a priori and included components of the Framingham risk score²⁸: age, sex, cohort, body mass index, systolic blood pressure, diastolic blood pressure, total cholesterol, high-density lipoprotein cholesterol, smoking, diabetes, and hypertension treatment as well as additional potential confounders: heart rate and systolic ejection period. To determine whether the relations between IFs and incident CVD outcomes differed by age (segregated by median age) or sex, we included interaction terms for these variables. To further illustrate relations between IFs and CVD outcomes, IF variables that were significantly related to CVD outcomes as continuous variables were categorized into quartiles to construct Kaplan-Meier curves of cumulative probability. Non-CVD death was a censoring event; the curves of cumulative probability were not modified for competing events.

All analyses were performed with SAS version 9.4 for Windows (SAS Institute, Cary, NC). Two-tailed P<0.05 were considered statistically significant, except for the tests of interaction, where P<0.05/48 (Bonferroni-adjusted P=0.001) was considered significant.

Principal Findings

In the community-based Framingham Heart Study, we investigated relations of novel IFs (ω₁, ω₂, and Δω) derived from carotid waveforms with risk of incident CVD outcomes, including composite CVD events, myocardial infarction, stroke, and HF. In multivariable models that adjusted for traditional CVD risk factors and heart rate, higher ω₁ and Δω (the IF of the coupled heart and vascular system during systole and the total frequency variation, respectively) but lower ω₂ (IF of the decoupled vasculature during diastole) were associated with higher risk for incident composite CVD and HF events. None of the IFs were associated with incident myocardial infarction or stroke events alone. Our results are consistent with the hypothesis that IFs are cardiovascular health indicators that are associated with increased risk for HF in the community.

Recent Studies of Waveform Analysis

Novel noninvasive techniques combined with mathematical models that describe pulsatile pressure and blood flow have provided better understanding of cardiovascular pathophysiology and hemodynamics.^29–37 To model the complex interactions of the heart and systemic circulation, many investigators have relied on Windkessel and wave transmission theories, which can provide simplified models that explain changes in arterial pressure waveforms due to aging and CVD pathologies. Several recent studies used models that depend solely on assessment and analysis of arterial pressure waves, which provide parameters that are associated with CVD risk. For example, recent population-based studies have derived parameters from carotid arterial waveforms using the reservoir-wave concept, which separates pressure into Windkessel-related (reservoir) and wave-related components.^30,31 However, some studies have suggested that the reservoir-wave concept should be abandoned since it introduces error into arterial wave analysis that leads to misconceptions that violate physical principles.^38,39 Measures of vascular dysfunction such as excess pressure integral, systolic and diastolic time constants, pulse pressure amplification ratio, and wave reflection index were associated with incident composite CVD events among middle-age and elderly hypertensive patients.^30,31,40 In addition, Cheng et al³² performed pulse wave analysis on central arterial pressure waveforms in 2 large, population-based cohorts and showed that novel mechanical parameters independently predicted CVD mortality among presumably healthy participants.³² However, the aforementioned studies were inconsistent in their confounding adjustment and sample sizes. Recently, we investigated the prognostic utility of measures derived from a pressure-only Windkessel wave analysis of central waveforms in a Framingham sample.³⁶ In traditional linear models, Windkessel-derived parameters were not related to incident CVD events; however, in modified models that accounted for nonlinear pressure-dependence of systolic and diastolic time constants, Windkessel parameters were modestly related to events.³⁶

Although parameters derived from pressure-only Windkessel models may have modest utility for risk prediction in the community, they do not consider fully the implications of wave transmission at finite velocity. Therefore, their ability to represent the system dynamics of blood flow and pressure accurately is limited. Other methods for deriving novel arterial pressure parameters are based on frequency- and time-domain methodologies and rely on assessment of both pressure and flow for wave separation analysis. For example, multiple studies have shown a significant relation between backward (reflected) wave and incident CVD outcome.^9,41,42 However, these studies did not directly measure central aortic flow but instead relied on various modeling assumptions for wave separation. Previously, we performed wave separation to assess the relative contributions to CVD risk among a comprehensive panel of individual components of mean and pulsatile pressure derived from directly measured central pressure and flow.³⁷ In the forgoing study, forward pressure wave amplitude, but not backward pressure wave amplitude, predicted incident events in models that adjusted for traditional CVD risk factors. Furthermore, primary pressure wave amplitude, a pressure-only surrogate for forward pressure wave amplitude, was not associated with CVD. Thus, these studies emphasize that novel parameters derived from central pressure waveforms alone should be independent of or account for aortic blood flow.

IFs as Novel Markers of HF Risk

The arterial pressure wave is governed by dynamics of the LV, the systemic arteries, and their interactions; therefore, the pressure wave contains information about these separate systems and their optimum coupling during healthy and pathological states. For the heart and arterial system, optimum coupling occurs when minimum energy is wasted to convert LV systolic ejection to forward flow and pressure waves in the systemic circulation for perfusion. In multivariable-adjusted models, higher ω₁ (the IF of the coupled heart and arterial system during systole) and higher Δω (total frequency variation) were associated with a higher risk for incident HF. Our observation is consistent with the forgoing theoretical work, which showed that ω₁ was higher among a sample of HF patients with systolic dysfunction.¹² In addition, Pahlevan et al¹² observed that Δω was about zero among young, healthy participants with ideal ventricular-arterial coupling, but Δω was significantly higher among older individuals and among those with prevalent HF.¹² During systole, the LV-arterial coupled system has a dominant frequency about which the instantaneous frequency oscillates, which is primarily dominated by cardiac function. Both HF with reduced and preserved systolic function (HFrEF and HFpEF, respectively) are progressive pathological states of aberrant cardiac function and suboptimum ventricular-arterial coupling associated with poor outcomes, including death. In HFrEF, arterial elastance is elevated but LV systolic elastance is reduced, leading to worse ventricular-arterial coupling. For example, Ky et al⁴³ observed that worse ventricular-arterial coupling (assessed via E_a/E_es) predicted death and cardiac hospitalization outcomes among patients with HFrEF.⁴³ Unlike HFrEF, which is characterized by LV dilation (eccentric remodeling) and systolic dysfunction, HFpEF is associated with concentric remodeling, myocardial fibrosis, microvascular rarefaction, and diastolic dysfunction of the LV. In HFpEF, both arterial and ventricular elastances are elevated, which may help to preserve ventricular-arterial coupling.^44,45 However, in chronic HFpEF patients (compared with hypertensives without HF and healthy controls), Borlaug et al⁴⁶ observed impaired dynamic ventricular-arterial coupling (as assessed by E_a/E_es) during exercise. Our data suggest that elevation of ω₁ and Δω precedes HF clinical presentation and may represent preclinical markers for HF, indicating nascent impaired coupling of the ventricular-arterial system. Although distinct clinical differences among HF classifications exist, we did not distinguish by severity of HF or between HFrEF or HFpEF events. For example, Ho et al⁴⁷ showed that incident HFpEF and HFrEF are preceded by different antecedent risk factors. Thus, additional studies should assess the differential relations for IFs at different stages and between participants with and without systolic dysfunction.

After the aortic valve closes, the heart and aorta are decoupled, and the dominant frequency is dictated only by the dynamics of the arterial system. Thus, ω₂ represents the IF of the decoupled vasculature during diastole. In an adjusted multivariable model, lower ω₂ was associated with higher risk for incident HF. Since the aorta is the largest artery and is coupled directly to the LV, it dominates the wave dynamics (and pulsatile load) that the heart experiences. Pahlevan et al¹² observed lower ω₂ with increasing age among healthy individuals, and ω₂ was significantly lower among those with hypertension and peripheral artery disease (compared with healthy individuals).¹² Taken together, these data suggest that lower ω₂ may indicate early vascular remodeling associated with age, such as aortic stiffness and hypertension, which can elevate exposure of the heart to pressure pulsatility. Although pulsatile load contributes modestly to the total energy of the heart, multiple studies have shown that abnormal pulsatile load contributes to the development of ventricular remodeling and progression to HF.^19,37,48,49 Future studies should examine relations between IFs and excessive pressure pulsatility resulting from abnormal blood pressure elevation and arterial stiffness.

Appropriate and accessible clinical tools are imperative for assessment of markers that may inform clinicians about prevention, diagnosis, and progression of CVD. Deriving well-known hemodynamic measures using time and frequency domain methods is clinically challenging because it requires both pressure and flow waves directly measured at the same site simultaneously. The novel IFs presented herein are derived via a direct time-frequency signal analysis that requires only one uncalibrated arterial pressure waveform.^12,50,51 Measurement of carotid pressure via tonometry is noninvasive and easily and safely implemented in a clinical setting with relatively inexpensive equipment and modest training. Ventricular-arterial coupling can be assessed in the pressure–volume plane via analysis of pressure–volume loops. These methods, however, are invasive and limited as they do not characterize aspects of ventricular-arterial interactions, such as systolic loading sequence, that are clinically relevant for individuals at risk of HF or with prevalent HF.⁵² Thus, assessment of IFs is clinically feasible and may provide a novel method to assess HF risk.

Strengths and Limitations

Our prospective study is observational with many years of follow-up. We included a large, community-based sample consisting of men and women derived from a longitudinally followed cohort from across 3 generations of participants. Contrary to other common impedance and wave intensity methods, which require simultaneous measurement of pressure and flow waves,^50,51 our proposed modified sparse time-frequency representation method (the IF method) requires only a central arterial (carotid) pressure waveform to perform the analysis. There are also limitations of our study to consider. We did not account for multiple testing; therefore, our investigation is more susceptible to type-1 error. Finally, our findings may not be generalizable to other racial and ethnic groups since this sample was comprised primarily of white participants of Western European descent.