Aging is Associated With an Earlier Arrival of Reflected Waves Without a Distal Shift in Reflection Sites.

BACKGROUND: Despite pronounced increases in central pulse wave velocity (PWV) with aging, reflected wave transit time (RWTT), traditionally defined as the timing of the inflection point (TINF) in the central pressure waveform, does not appreciably decrease, leading to the controversial proposition of a "distal-shift" of reflection sites. TINF, however, is exceptionally prone to measurement error and is also affected by ejection pattern and not only by wave reflection. We assessed whether RWTT, assessed by advanced pressure-flow analysis, demonstrates the expected decline with aging. METHODS AND
RESULTS: We studied a sample of unselected adults without cardiovascular disease (n=48; median age 48 years) and a clinical population of older adults with suspected/established cardiovascular disease (n=164; 61 years). We measured central pressure and flow with carotid tonometry and phase-contrast MRI, respectively. We assessed RWTT using wave-separation analysis (RWTTWSA) and partially distributed tube-load (TL) modeling (RWTTTL). Consistent with previous reports, TINF did not appreciably decrease with age despite pronounced increases in PWV in both populations. However, aging was associated with pronounced decreases in RWTTWSA (general population -15.0 ms/decade, P<0.001; clinical population -9.07 ms/decade, P=0.003) and RWTTTL (general -15.8 ms/decade, P<0.001; clinical -11.8 ms/decade, P<0.001). There was no evidence of an increased effective reflecting distance by either method. TINF was shown to reliably represent RWTT only under highly unrealistic assumptions about input impedance.
CONCLUSIONS: RWTT declines with age in parallel with increased PWV, with earlier effects of wave reflections and without a distal shift in reflecting sites. These findings have important implications for our understanding of the role of wave reflections with aging.

Introduction

Pulsatile arterial hemodynamics is highly relevant for cardiovascular disease associated with aging and various disease states.1 Several studies have demonstrated that both aortic pulse wave velocity (PWV) and measures of wave reflections are independently predictive of cardiovascular disease.2, 3, 4, 5, 6 Pulse waves generated by the heart travel forward in the arteries at a finite PWV and undergo partial reflections at sites of impedance mismatch (such as points of branching or changes in wall diameter or material properties along the arterial tree). Innumerable reflections effectively merge into a discrete reflected wave, as seen from the aortic root, increasing aortic pulse pressure and left ventricular pulsatile afterload.

With increasing PWV, the speed of forward and backward wave travel increases, which is logically expected to result in an earlier arrival of wave reflections. However, the increased large artery PWV with aging has been reported to be associated with unremarkable changes in the time of the inflection point (TINF) of the central pressure waveform in mid‐ to late adulthood, traditionally defined as reflection timing.3, 7, 8 If TINF is interpreted as a surrogate of reflected wave transit time (RWTT), this combination would appear to represent an increase in effective reflective distance. Along with the observation that there is little increase in medium‐sized (muscular artery) PWV with aging in the setting of increased large artery PWV, the lack of change in TINF with aging has motivated the controversial9 proposition that aging is associated with impedance matching of central and peripheral arteries and a distal shift of reflection sites.10, 11, 12 This proposition has been advanced as a key mechanism for aging‐related microvascular disease. However, it challenges established principles of pulse wave transmission and reflection8, 13, 14, 15 and is based on the untenable assumption that “PWV matching” is equivalent to impedance matching.16 Furthermore, the inaccuracy of relying on TINF (a high‐frequency pressure‐only characteristic point exceptionally prone to measurement error) as a surrogate of RWTT has been demonstrated in humans17 and modeling studies.18 TINF is also highly dependent on factors other than arterial wave reflection timing, including the pattern of LV contraction.19, 20 Therefore, it remains unclear whether aging is indeed associated with an earlier arrival of wave reflections, an issue that has important implications for our understanding of the role of wave reflections and microvascular disease with aging.

The aim of the present study was to assess whether aging is indeed associated with a distal shift in reflecting sites (as suggested by previous studies that utilized TINF), using appropriate pressure‐flow analyses. We also aimed to critically assess underlying assumptions and limitations of various techniques to compute RWTT and their implications for the assessment of aging‐related changes in RWTT and effective reflective distance.

Methods

Study Population

We performed 2 substudies.

Substudy in adult participants from an unselected population. We enrolled a sample of adult volunteers (n=48, median age 49 years) at the University of Pennsylvania and the University of Iceland as part of the control population for the Penn‐Iceland Sleep Apnea Study. Participants were adults without overt cardiovascular disease who were on stable medications (no changes in the 2 months prior to enrollment). We excluded subjects with a history of obstructive sleep apnea or any sleep disorder, a body mass index >40 kg/m2, a positive urine toxicology screen, routine consumption of >2 alcoholic beverages per day, current/recent illicit drug use, excessive caffeine use (>10 caffeinated beverages per day), active infection, malignancy, chronic inflammatory disorders, atrial fibrillation, or inability to undergo a cardiac MRI. Women with a positive pregnancy test or who were receiving hormone replacement therapy were excluded from the study.

Substudy in an older clinical population. Given that the impact of pulsatile hemodynamics and the proposition of a distal shift of reflecting sites with aging are particularly relevant for older patients with cardiovascular risk factors or established cardiovascular disease, we also studied a population of older adults (n=164, median age 61 years) with established or suspected cardiovascular disease referred for a cardiac MRI examination at the Corporal Michael J. Crescenz Veterans Affairs Medical Center (VAMC) or the Hospital of the University of Pennsylvania.

The institutional review boards of the VAMC, University of Pennsylvania, and University of Iceland approved the parent studies, and all subjects provided written informed consent.

MRI Examinations

We measured ascending aortic flow with phase‐contrast MRI, using 1.5‐T Avanto or Espree systems (Siemens Medical Solutions). A phase‐contrast gradient‐echo pulse sequence with through‐plane velocity encoding was applied during free breathing using retrospective gating, in a plane perpendicular to the long axis of the proximal ascending aorta. Maximal velocity encoding was set at 150 cm/s, adjusted as needed to avoid aliased velocity measurements. Other typical parameters were slice thickness 6 mm, matrix 192×192, and repetition time ≈10 milliseconds. Images were analyzed using the freely available software Segment.21 Flow‐time integrals were scaled to stroke volume measured with cine steady‐state free precession (SSFP) images of the left ventricle (short‐axis stack) in order to minimize errors introduced by phase‐offset and eddy currents. Carotid‐femoral PWV was measured with a SphygmoCor EM3 device (AtCor Medical, Sydney, Australia), with sequential tonometry recordings of the carotid and femoral pulse, using the QRS complex as a fiducial time point.

Reflected Wave Transit Time

We utilized 3 methods to compute RWTT.

Method 1. TINF was calculated as the time from the foot of the carotid pressure waveform to the inflection point (Figure 1A) as identified by the SphygmoCor platform (C_T1R variable).

Figure 1

Assessment of T (A) and of RWTT via WSA (B) and TL modeling (C). In WSA, forward and backward waves are computed from pressure‐flow data, and the time delay between the point at which backward (red) and forward (green) pressure waves start adding to mean pressure (zero crossing) is considered as the RWTT. TL modeling utilizes the entire pressure and flow information to assess the 1‐way wave transit time (τ) to the reflection site (which is complex and frequency dependent, as indicated in the shaded red region); RWTT was obtained as twice the value of τ.

Method 2. Wave separation analysis (WSA) was performed on time‐aligned pressure and flow signals using standard methods.22 Briefly, arterial input impedance (Zin) was derived using Fourier analysis as the ratio of pressure to flow harmonics in the frequency domain. Aortic characteristic impedance (Zc) was estimated by averaging the modulus of Zin for harmonics 3 to 15. Only harmonics with flow magnitudes >5% of the fundamental harmonic flow magnitude were included in the averaging process to minimize the effects of noise.23 Forward (Pf) and backward (Pb) pressure waves were obtained from the relations Pf=(P+QZc)/2 and Pb=(P−QZc)/2. Time‐varying Pf and Pb waveforms were obtained through inverse Fourier transformation. Because the “foot” of Pf and Pb is generally not well defined and particularly susceptible to sources of high‐frequency noise (eg, measurement, Zc estimation method), RWTTWSA was calculated as the time delay between the zero crossings of Pf and Pb as previously described17 (Figure 1B), due to better definition of the landmarks. Despite improved definition of zero crossings over the “foot” of Pb and Pf, a small subset of cases had poorly defined zero crossings (Figure S1).

Method 3 (TL modeling). The arterial system was modeled as a finite PWV system represented by a lossless tube terminating in a complex frequency‐dependent load (Figure 1C).24, 25 Tube‐based models with complex loads have been previously validated and applied to various animal species25, 26, 27, 28 and humans29, 30 for the purpose of studying arterial wave reflections. The TL model used here is fully characterized by tube characteristic impedance (Z0), peripheral resistance (Rp), load compliance (Cl), and 1‐way wave transmission time to the effective reflection site (τ). Rp was calculated as the ratio of mean pressure to mean flow. With measured aortic flow as input to the model, an optimal set of parameters (Z0, Cl, τ) was obtained after minimizing the normalized root mean square error (NRMSE) of predicted and measured pressure; a unique set of parameters can be identified if τ multiplied by a measurement of PWV is within the dimensions of the body.31 NRMSE was calculated as the square root of the mean squared error normalized by mean arterial pressure. RWTTTL was computed as twice the value of τ, to account for roundtrip travel, allowing for direct comparisons with TINF and RWTTWSA.

Effective Reflection Distance

Combining RWTT with measured carotid‐femoral PWV allows for calculation of an effective reflection distance (ERD). If wave reflections, as seen from the proximal aorta, were to be summarized and abstracted by a theoretical single discrete reflection site from which all reflections effectively originate, ERD represents the distance to this site. ERD was calculated as 0.5×RWTT×PWV.

Assumed Input Impedance Spectra of TINF and TL Modeling

The computation of an ERD from TINF and PWV relies on the assumption that a uniform tube, terminated in a peripheral resistance (ie, a real reflection coefficient), represents a suitable approximation of the arterial system.32, 33, 34, 35 This model's input impedance (Zin,INF) can be fully specified by 3 parameters (see Data S1): aortic Zc, 1‐way tube transit time (0.5×TINF), and Rp. We used this model, as well as TL modeling (Method 3) to generate input impedance spectra for each decade of age in order to assess the correspondence of each model with the known age‐related changes to input impedance patterns.

Statistical Analysis

Continuous variables are reported as mean±standard deviation or median and interquartile range (IQR), as appropriate. Proportions are expressed as percentages. Changes with age are presented as point estimates and 95% confidence intervals (CIs) for each decade of life. We used linear regression analysis to compute the mean change per decade of age in RWTT and ERD, as estimated by each of the 3 methods described above. Statistical significance was defined as a 2‐tailed α<0.05. Statistical analyses were performed using SPSS (SPSS Inc, Chicago, IL).

Results

Tables 1 and 2 list the clinical and hemodynamic characteristics, respectively, of study subjects in the general sample and the clinical sample.

Table 1

Clinical Characteristics of Subjects Enrolled in Both Substudies

	General Sample (n=48)	Clinical Sample (n=164)
Age, y	49 (43, 54)	61 (54, 66)
Male	79 (38)	152 (93)
BMI, kg/m2	26.8 (24.9, 29.5)	29.8 (26.3, 33.9)
Height, cm	175 (169, 182)	175 (170, 183)
Hypertension	11 (23)	134 (82)
Current smoking	10 (21)	53 (32)
Diabetes mellitus	4 (8)	76 (46)
CAD	0 (0)	67 (41)
HF	0 (0)	68 (41)
ACE‐I	4 (8)	79 (48)
ARB	3 (6)	21 (13)
β‐Blocker	1 (2)	93 (57)
Long‐acting nitrate	0 (0)	21 (13)
CCB	1 (2)	41 (25)

Values reported as median (IQR) or proportions expressed in percentage. ACE‐I indicates angiotensin‐converting enzyme inhibitor; ARB, angiotensin receptor blocker; BMI, body mass index; CAD, coronary artery disease; CCB, calcium channel blocker; HF, heart failure.

Table 2

Hemodynamic Characteristics of Study Subjects

	General Sample (n=48)	Clinical Sample (n=164)
MAP, mm Hg	88 (84, 97)	103 (94, 113)
Central SBP, mm Hg	114 (109, 122)	135 (123, 150)
Central PP, mm Hg	46 (41, 51)	53 (45, 68)
Heart rate, BPM	66 (62, 71)	62 (55, 71)
Cardiac output, L/min	6.6 (5.3, 7.5)	5.01 (3.7, 6.4)
SVR, dynes·s/cm5	1162 (955, 1346)	1632 (1315, 2170)
Zc, dynes·s/cm5	81.0 (66.6, 93.1)	103 (80, 140)
Reflection coefficient magnitude, |Γ1|	0.48 (0.41, 0.53)	0.50 (0.41, 0.56)
Reflection coefficient phase θ1, deg	−60.3 (−71.2, −49.5)	−45.4 (−56.9, −35.6)
PWV, m/s	7.0 (6.1, 7.8)	9.6 (7.8, 11.4)

Values reported as median (IQR). BPM indicates beats per minute; MAP, mean arterial pressure; PP, pulse pressure; PWV, pulse wave velocity; SBP, systolic blood pressure; SVR, systemic vascular resistance; Zc, aortic characteristic impedance.

Changes in PWV, RWTT, and ERD With Aging

Figure 2 demonstrates trends of PWV as well as RWTT and ERD computed by the 3 methods for the general sample (Figure 2A) and the clinical sample (Figure 2B). We observed the well‐known increase in PWV across decades of age (Figure 2A and 2B, top row), with a mean per‐decade increase of 0.80 m/s (95% CI=0.48‐1.12; P<0.001) in the general population sample and 1.34 m/s (95% CI=0.85‐1.82; P<0.001) in the clinical sample. Similarly, consistent with previous reports, TINF exhibited minimal changes across decades of age in either the general sample (Figure 2A; ß=−5.41 ms per decade; 95% CI=−1.07 to −0.15; P=0.044) or the clinical sample (Figure 2B; ß=−0.34 ms per decade; 95% CI=−0.380 to −0.312; P=0.85). TINF remained within a very narrow range in both samples after the fourth decade of life (Figure 2A and 2B, middle panels). For instance, in the clinical sample, it decreased from a mean of 152 milliseconds for subjects <40 years old to 145 milliseconds for subjects aged 70 to 79 years old, representing a 4.6% decrease in timing despite a 67.0% increase in carotid‐femoral PWV. As a result, apparent ERD computed by the inflection point timing (ERDINF) increased with age in both the general (ß=5.46 cm/decade; 95% CI=1.86‐9.06; P=0.004) and clinical samples (ß=9.27 cm/decade; 95% CI=5.70‐12.8; P<0.001; Figure 2A and 2B, bottom panels), consistent with previous reports that relied on TINF as a surrogate for RWTT.

Figure 2

Change in carotid‐femoral PWV with aging (top), RWTT (middle), and ERD (bottom) in the general population sample (A, left panels) and the clinical sample (B, right panels).

Results were, however, markedly different when methods derived from pressure‐flow data were used to estimate reflection timing. WSA and TL modeling demonstrated pronounced and significant reductions in RWTT across decades of age (Figure 2A and 2B, middle panels). RWTTWSA decreased by −15.0 milliseconds per decade of age (95% CI=−2.142 to −8.7; P<0.001) in the general sample and −9.07 milliseconds (95% CI=−14.9 to −3.2; P=0.003) in the clinical sample, with the latter sample demonstrating consistently lower times (ie, earlier wave reflections) across the age spectrum than the general population sample. Similarly, TL modeling indicated that RWTT decreased by −15.8 milliseconds per decade of age (95% CI=−2.11 to −1.04; P<0.001) in the general sample and by −11.8 milliseconds (95% CI=−15.3 to −8.2; P<0.001) in the clinical sample, with the clinical sample demonstrating consistently lower times across the age spectrum than the general population sample. The overall decrease in RWTT with aging across the life span was pronounced. In the clinical sample, for instance, RWTTTL decreased by 62.7% from <40 years old to 70 to 79 years.

Given that the reduction in RWTTWSA was concordant with the increase in PWV, ERD computed by this method was found to not significantly increase with age in either the general sample (ß=0.78 cm/decade; 95% CI=−2.4 to 4.0; P=0.63) or the clinical sample (ß=3.0 cm/decade; 95% CI=−1.47 to 7.44; P=0.19), with values consistently in the range of ~50 cm. Given the pronounced reduction of RWTTTL with age (Figures 2 and 3), aging was associated with a decrease in ERDTL in both the general population sample (ß=−2.37 cm per decade; 95% CI=−4.63 to −0.17; P=0.04) and the clinical sample (ß=−2.96 cm per year decade 95% CI=−4.77 to −1.16; P=0.001).

Figure 3

Estimated change in carotid‐femoral PWV (blue bars), RWTT (green bars), and ERD (red bars) per decade of life, assessed by different methods, in the general population sample (A, left panels) and the clinical sample (B, right panels). The green‐shaded area represents assessments from the inflection point timing (T). The red‐shaded area represents assessments from the use of WSA. The blue area demonstrates estimates from use of TL modeling.

Interpretations of Reflection Timing and ERD

Figure 3 summarizes the competing interpretations of wave reflection timing and effective reflection distance for the general population and the clinical samples. Each point corresponds to the mean change in the variable per decade of age, with error bars denoting 95% CIs. In both populations, PWV increases with age, particularly in the clinical sample. The green region demonstrates analyses based on pressure only (TINF), which demonstrates a very small decrease in TINF with age in the general sample and a nonsignificant change in the clinical sample. When interpreted in the context of the markedly increased PWV, the apparent ERD by this method increases, suggesting a distal shift of reflecting sites, consistent with previous reports.7, 10, 11, 12 These results, however, are not supported by analyses that use pressure and flow data. The red‐shaded region shows results from WSA, demonstrating significant decreases in RWTTWSA concordant with the increase in PWV in both samples, without significant changes to ERDWSA, which is inconsistent with a distal shift of reflection sites with age. Furthermore, TL modeling (blue‐shaded region) demonstrates pronounced decreases in RWTTTL, with a decreased ERDTL with age (ie, effective reflection sites move closer, rather than further away from to the heart with aging).

Assumptions of TINF as a Surrogate of RWTT for Assessments of ERD

Input impedance patterns per decade of age implied by use of TINF and PWV for the calculation of ERDINF are shown in Figure S2A for the clinical sample and Figure S3A for the general sample. The figures demonstrate markedly unrealistic impedance patterns, based on known input impedance patterns reported in the literature, with apparently high reflections occurring in the higher frequencies. In sharp contrast, input impedance patterns implied by the TL model (Figures S2B and S3B) in the same populations are highly consistent with the well‐known human input impedance patterns and their changes with aging, including a shift to higher frequencies of the magnitude minima and the zero crossover of the phase angle of input impedance. Two examples for comparison of the time‐domain pressure‐flow relationships implied by the models are shown in rows I and II of Figure 4. It is clear that use of TINF as a surrogate for the arrival of reflection waves is highly inconsistent with the relationship between measured pressure and flow; predicted pressure waveforms are highly oscillatory and are nonphysiological. Because losses in the large arteries are small, similar results are obtained when the tube is viscoelastic.36

Figure 4

Model‐predicted pressure waveforms when measured aortic flows are used as input into the underlying models assumed by the quarter‐wavelength formula used with T as reflection timing (INF) and TL modeling. The vertical dashed lines indicate T as identified by the SphygmoCor system.

Discussion

In this study, we assessed whether aging is associated with an increased ERD (ie, a distal shift in reflection sites), as suggested by studies that used TINF as a surrogate of RWTT. In line with these previous reports, we found that carotid‐femoral PWV increases markedly with aging, without an appreciable decrease in TINF, falsely suggesting an increase in ERD. However, given the important limitations of TINF as a surrogate of RWTT, and in contrast with previous studies that suggested a distal shift of reflecting sites, we quantified RWTT based on pressure‐flow analyses. We demonstrate that RWTT markedly declines with age as PWV increases, with an earlier arrival of wave reflections and without a distal shift in reflecting sites. In fact, consistent with physiologic insights, TL modeling (which accounts for phase shifts associated with wave reflections), suggests that the ERD actually decreases (ie, reflections effectively move closer to the heart) as PWV increases with age.17, 35 We further demonstrate that TINF is a misleading surrogate of RWTT with aging and would be reliably related to the latter only under highly unrealistic assumptions about human aortic input impedance patterns. We therefore reconcile the apparent paradox introduced by misinterpretation of TINF as a surrogate of RWTT, disproving the proposition of a distal shift in reflecting sites with aging. Our findings have important implications for our understanding of the role of wave reflections on changes in arterial pulsatile hemodynamics with aging and their role in target organ damage and microvascular disease.

As shown in previous studies,3, 7, 10, 12, 17 we found that TINF in the central pressure waveform demonstrates unremarkable changes with age. Our estimates of TINF essentially reproduce the pattern reported by Mitchell et al,7 in which TINF is constrained within tight limits across the adult age spectrum despite the sharp increase in carotid‐femoral PWV. This has been interpreted as a distal shift of reflection sites10, 12 under the assumption that TINF represents RWTT. Given the proposed central role of this distal shift on microvascular damage, carefully assessing this issue with appropriate methods is of great importance. Our findings demonstrate that TINF is a poor measure of RWTT. There are several reasons for this. First, this characteristic point is dependent on high frequencies, which are most susceptible to measurement noise. In addition, TINF is highly dependent on factors other than arterial wave reflection timing, including the pattern of LV contraction.19, 20 This is consistent with recent data demonstrating that the augmentation index (which is computed based on the pressure at the inflection point) is influenced by various factors other than wave reflections and is not a robust predictor of cardiovascular risk.5, 37

The primary derivation of the inflection point as a surrogate for RWTT explicitly assumed an arterial system model as a uniform tube terminated with a pure resistance.33 The profound limitations introduced by this assumption are often unrecognized. When implied input impedances from such a model are produced across the life span from measured parameters, its poor resemblance to the arterial system becomes readily apparent, with impedance patterns that show pronounced/unrealistic oscillations in both magnitude and phase spectra. These patterns are inconsistent with well‐known patterns of human aortic input impedance,33, 38, 39 characterized by modulus values settling around aortic Zc as well as increasing frequency of the magnitude minimum and phase zero crossing with increasing age.35, 40, 41 The assumption that TINF can be used to infer ERD also implies a real reflection coefficient at the effective reflection site, which is inconsistent with the complex (and frequency‐dependent) reflection coefficients that occur in vivo.40, 42, 43 For instance, in the femoral arteries, reflection coefficients have frequency‐dependent magnitudes, with the highest magnitudes in lower frequencies and magnitudes settling toward lower nonzero values in the higher frequencies.40, 44, 45, 46

To avoid these important limitations, we used the TL model, which is terminated with a complex frequency‐dependent load. We found that input impedance patterns derived from this model (using parameters obtained from both studied populations) display the well‐known characteristics of human input impedance (Figures S2B and S3B), with a shift of the modulus minimum and phase zero crossing to increasing frequency with increasing age and impedance modulus settling around Zc with increasing frequency. We also found that wave reflections already begin to exert subtle effects on central pressure and flow as early as ~30 milliseconds into systole in the clinical sample. It is worth noting that this timing precedes time of peak aortic flow and the inflection point observed on the aortic pressure waveforms, as supported by previous studies that utilized invasive measurements24, 26, 47, 48, 49 (discussed in more detail in Data S2). Consistent with these invasive studies, we demonstrate that when the timing of arterial wave reflections is assessed using pressure and flow measurements along with a suitable arterial system model, there is neither theoretical support for a reflectionless state until the time of peak flow nor a need to make such an assumption.

RWTTWSA is a more reliable method than TINF because of its reliance on both pressure and flow data, leading to anticipated relationships with age in the setting of increased PWV. However, this method does not implicitly model the phase shift associated with wave reflections, producing higher absolute values for RWTT and longer values for ERD than the TL modeling, as discussed in Data S2 (Figures S4 and S5). Whereas both TL and WSA demonstrated a reduction of RWTT and the lack of a distal shift of reflection sites with aging, absolute values of RWTT were different. This is not surprising and is explained by the fact that WSA assumes a uniform tube terminated in a pure resistance (as is also the case for TINF), whereas TL does not make this restrictive assumption because it can model complex and frequency‐dependent reflection coefficients as encountered in vivo. A uniform tube terminated in a pure resistance emerges only as a special case of TL if there exists no physical vascular compliance or wave transmission outside the aorta. WSA is therefore unable to capture changes in the complex part of reflection coefficients (which captures physical vascular compliance and pulse wave transmission beyond the aorta). TL emerges as the most robust and physiologic model to assess RWTT.

Despite the differences between WSA and TL modeling, findings from both methods are inconsistent with the previously proposed paradigm10, 11 regarding age‐related impedance matching of central‐to‐peripheral arteries and distal shifting of reflection sites. The motivation for this paradigm was based on a flawed method for reflection timing (TINF) along with the untenable assumption that “PWV matching” is equivalent to impedance matching (Figure S6). The amount of reflection at a given interface (due to conditions downstream) is dependent on the relationship between characteristic impedance of the parent vessel and the complex input impedance of the distal system, rather than being dependent on the relationship between the proximal and distal PWV.16 The interpretation that matching of carotid‐femoral and carotid‐brachial PWV denotes impedance matching is inappropriate because it neglects the strong effects of arterial size on wave reflections at the interfaces of elastic and muscular arteries. Furthermore, this interpretation is overly simplistic and does not account for the innumerable sources of wave reflections present in vivo at multiple points of the arterial tree and the complex nature of the input impedance at various arterial beds supplied by individual muscular arteries.45

The paradigm of a distal shift of wave reflections has been extended to suggest a “protective” role of reflections at single interfaces between large and muscular arteries that supply target organs (such as the aorta‐carotid interface).50 Mitchell et al proposed that progressive impedance matching at this interface with aging favors the penetration of power to the central nervous system due to a reduction in the local reflection coefficient. This interpretation neglects the fact that impedance matching for forward wave travel in individual first‐order bifurcations is already nearly optimized in the natural arterial system because of the anatomical (size) relationship between parent and branch arteries.45, 51 Data reported by Mitchell et al indicate that 95% of the values of reflection coefficients (RC) at this interface across the life span lie in the range of 0% to 15%. Although not reported, it can be readily inferred from standard physics formulas52, 53, 54 that these RCs correspond to power transmission coefficients (=1−RC2) of 97.75% to 100%. Therefore, only a very small proportion (0‐2.25%) of power penetration is prevented by this local reflection, in line with the presence of impedance matching at first‐order bifurcations across the adult life span in the native arterial system.40, 45, 51 In fact, despite its negligible effects on power penetration, positive reflection coefficients at this interface would induce a positive effect on pulse pressure amplification of the transmitted forward‐traveling wave.16, 53 More importantly, in contrast to the weak effects of the local reflection on power transmission to the carotid, the effect of innumerable reflections from the lower body produces a substantial composite backward wave, which would penetrate the carotid interface as a forward wave (considerably increasing carotid pulsatile pressure, flow, and power) due to the favorable conditions for forward transmission present at this interface.45, 51 This phenomenon underlies the strong positive (rather than negative) correlation between late systolic carotid pressure and flow augmentation and the concordant increase in carotid pressure and flow augmentation with increasing age.55

It should also be noted that, as wave reflections return to the aortic root earlier due to increased PWV, they are re‐reflected at the heart and rectified, effectively contributing to (ie, becoming part of) the forward wave independently of aortic root properties.30, 40, 51, 56, 57 Furthermore, the increased pulsatile load from wave reflections has been shown to cause diastolic dysfunction, myocardial hypertrophy, and fibrosis in animal models.58, 59 Similarly, human studies have shown a relationship between wave reflections and worse longitudinal LV function,60, 61 LV hypertrophy,62 a higher risk of incident new‐onset HF,5, 63 and a higher readmission risk after an episode of established acute decompensated HF.64 Available evidence therefore strongly supports that wave reflections, which arrive earlier to the proximal aorta as PWV increases with aging, are deleterious for target organs, including the heart and the brain.35, 55, 65, 66 We note that this study did not aim to compare the general population and the clinical samples. Rather, we aimed at assessing prevalent values of RWTT across the adult age spectrum in both the general population and a clinical setting. We demonstrate highly consistent trends with aging in the 2 populations.

Our study should be interpreted in the context of its strengths and limitations. Strengths include consistency of results between both the unselected and clinical cohorts, which supports the generalization of the TL model previously validated in animals.24, 31 Furthermore, in contrast to the studies that use left ventricular outflow tract flow as a surrogate of aortic flow,10, 39 our study uses ascending aortic flow, which more closely obeys the requirements for assessing aortic input impedance.35, 40, 41, 67 Limitations of our study include the use of carotid tonometry to obtain a surrogate of aortic pressure, which carries some potential for operator dependency. However, this technique is widely accepted for central hemodynamic assessment68 and is the same technique used in a number of human population studies.7, 35, 39 Whereas each of the 2 substudies included a wide age range of age (~4 decades), with an overall span of ~5 decades, the addition of younger individuals to the clinical sample and older individuals to the general sample would have strengthened our study. The TL model employed is necessarily a reduced representation of the arterial system that does not inform on regional aortic stiffening/dilation; identification of regional changes that occur with aging would require a more complex and validated model (eg, modified asymmetric T‐tube26) and should be a focus for future studies.

Perspectives

In contrast to studies that relied on TINF, the application of appropriate methods based on pressure‐flow analyses demonstrates that increased PWV with aging is associated with an earlier arrival of wave reflections at the proximal aorta, without a distal shift of reflecting sites. Our findings reconcile the apparent paradox introduced by misinterpretation of TINF as a surrogate of RWTT, which is incompatible with standard hemodynamic theory and falsely suggests a distal shift in reflection sites. The assumption that “impedance matching” leads to a distal shift in reflection sites is therefore disproven. Wave reflections arriving earlier to the proximal aorta as PWV increases with aging are deleterious for target organs, including the heart and the brain. Strategies at reducing early wave reflections should be tested as a potential strategy to reduce the burden of cardiovascular disease in older age.

Sources of Funding

This research was funded by NIH grants R56 HL‐124073‐01A1 (Chirinos), 5‐R21‐AG‐043802‐02 (Chirinos), and PPG: 1P01‐1HL094307 (Pack).

Disclosures

Dr Chirinos is a consultant to Bristol‐Myers Squibb, OPKO Healthcare, Fukuda Denshi, Microsoft, and Merck. He received research grants from National Institutes of Health, American College of Radiology Imaging Network, Fukuda Denshi, Bristol‐Myers Squibb, Microsoft, and CVRx Inc, and a device loan from AtCor Medical. He is named as inventor in a University of Pennsylvania patent application for the use of inorganic nitrates/nitrites for the treatment of Heart Failure and Preserved Ejection Fraction. The other authors do not have any disclosures.

Data S1. Supplemental methods.

Data S2. Supplemental discussion.

Figure S1. Example of a case in which the zero crossing of Pb is poorly defined. Due to the presence of noise, particularly on high‐frequency features of pressure and flow waveforms, single‐point landmarks (eg, zero crossing, “foot”) may be ambiguous. Note that there is no apparent “foot” to the backward wave (due to the presence of multiple reflection sites in vivo). Empirically imposing a “foot” to Pb may amplify the significance of high‐frequency artifacts (eg, due to pressure‐flow alignment processes, use of surrogate waveforms, etc).

Figure S2. Arterial input impedance implied by (A) TINF and the quarter‐wavelength formula, and (B) TL modeling with a complex and frequency‐dependent load for each decade of age in the clinical sample. Vertical lines correspond to the frequencies of impedance modulus minimum and phase angle zero crossings.

Figure S3. Arterial input impedance implied by (A) TINF and the quarter wavelength formula, and (B) TL modeling with a complex and frequency‐dependent load for each decade of age in the general sample. Vertical lines correspond to the frequencies of impedance modulus minimum and phase angle zero crossings.

Figure S4. Aortic input impedance from the model‐based study. The vertical red and purple lines correspond to the frequencies at which the impedance modulus is minimal and the phase angle crosses 0 degrees, respectively. As generally encountered in vivo, these 2 frequencies are not identical.

Figure S5. A, Aortic pressure and flow waveform from the model‐based study. B, Aortic pressure separated into its forward and backward traveling components. The vertical dashed green and red lines correspond to the zero crossings of the forward and backward waves, respectively.

Figure S6. Carotid‐radial PWV measurements were available in the clinical population sample. The reported15 trend of carotid‐femoral PWV surpassing muscular artery PWV is reproduced in our clinical sample. Contrary to the age‐related impedance‐matching interpretation of this PWV‐gradient crossover, pressure‐flow analyses reveal earlier effects of reflection.

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