Harmonic Distortion of Blood Pressure Waveform as a Measure of Arterial Stiffness

Abstract

Aging and disease alter the composition and elastic properties of the aortic wall resulting in shape changes in blood pressure waveform (BPW). Here, we propose a new index, harmonic distortion (HD), to characterize BPW and its relationship with other in vitro and in vivo measures. Using a Fourier transform of the BPW, HD is calculated as the ratio of energy above the fundamental frequency to that at the fundamental frequency. Male mice fed either a normal diet (ND) or a high fat, high sucrose (HFHS) diet for 2-10 months were used to study BPWs in diet-induced metabolic syndrome. BPWs were recorded for 20 s hourly for 24 h, using radiotelemetry. Pulse wave velocity (PWV), an in vivo measure of arterial stiffness, was measured in the abdominal aorta via ultrasound sonography. Common carotid arteries were excised from a subset of mice to determine the tangent modulus using biaxial tension-inflation test. Over a 24-h period, both HD and systolic blood pressure (SBP) show a large variability, however HD linearly decreases with increasing SBP. HD is also linearly related to tangent modulus and PWV with slopes significantly different between the two diet groups. Overall, our study suggests that HD is sensitive to changes in blood pressure and arterial stiffness and has a potential to be used as a noninvasive measure of arterial stiffness in aging and disease.

Keywords: blood pressure waveform; harmonic distortion; pulse wave velocity; radio telemetry; tangent modulus.

FIGURE 1

(A) A gel-filled pressure catheter is surgically inserted in the left common carotid artery of a mouse, with the pressure-sensing region (4 mm) resting in the aortic arch. (B) Example of in vivo BPWs over 1 s time period measured using radiotelemetry.

FIGURE 2

(A) A triangular wave (solid line) and a normalized BPW from radiotelemetry (dashed line). (B) The normalized power spectrum, calculated as the squared fraction of Fourier coefficients at integer multiple of the fundamental frequency of the waveforms in (A) at 1 Hz.

FIGURE 3

(A) Representative bimodal probability density distribution of SBP over a 24-h period for a 2-months ND and a 3-months HFHS mouse. Solid and dashed lines are Gaussian distributions fit to the data. The low and high pressure values of the bimodal SBP distribution for each age and diet groups were averaged and showed in (B,C) for the low and high pressure means, respectively, for the age and diet groups (^* p < 0.05; ^** p < 0.01).

FIGURE 4

(A) HD values of individual BPW are plotted as a function of the corresponding wave’s SBP. (B) Mean HD values within evenly spaced BP bins for the 8-months ND group (n = 5). Different symbols represent different mice in the group. The solid line represents a weighted linear regression (r ² = 0.78) to the data from the group. (C) Linear regressions between HD and luminal SBP for the 7 age and diet groups. The linear relationships consistently trend upward with increasing age and HFHS diet.

FIGURE 5

Representative results of (A) in vitro pressure-outer radius curves from biaxial extension-inflation test; (B) circumferential stress-stretch curves; and (C) tangent modulus vs. pressure of a carotid artery sample of a 4-months ND mouse with model parameter c = 20.540 kPa, $c_1^1$ = 3.742 kPa; $c_2^1$ = 0.030; $c_1^2$ = 11.267 kPa; $c_2^2$ = 0.043; $c_1^{\mathrm{3,4}}$ = 0.008 kPa; $c_2^{\mathrm{3,4}}$ = 1.373 kPa, and α = 46.352° (Gkousioudi et al., 2022).

FIGURE 6

Harmonic distortion from in vivo spectral analysis as function of tangent modulus measured by in vitro biomechanical testing for the 4-months (A) and 10-months mice (B), normal (circles and solid line) and HFHS diet (triangles and dashed line). Linear regressions from each group are also displayed. (C) Average slopes of the harmonic distortion vs. tangent modulus linear fitting for the age and diet groups.

FIGURE 7

Average HD at 115 mmHg (A), 135 mmHg (B), and 155 mmHg (C) is plotted as a function of the group’s corresponding average PWV, collected via Doppler ultrasound, for each age and diet group.