Coherence and Coupling Functions Reveal Microvascular Impairment in Treated Hypertension

Abstract

The complex interactions that give rise to heart rate variability (HRV) involve coupled physiological oscillators operating over a wide range of different frequencies and length-scales. Based on the premise that interactions are key to the functioning of complex systems, the time-dependent deterministic coupling parameters underlying cardiac, respiratory and vascular regulation have been investigated at both the central and microvascular levels. Hypertension was considered as an example of a globally altered state of the complex dynamics of the cardiovascular system. Its effects were established through analysis of simultaneous recordings of the electrocardiogram (ECG), respiratory effort, and microvascular blood flow [by laser Doppler flowmetry (LDF)]. The signals were analyzed by methods developed to capture time-dependent dynamics, including the wavelet transform, wavelet-based phase coherence, non-linear mode decomposition, and dynamical Bayesian inference, all of which can encompass the inherent frequency and coupling variability of living systems. Phases of oscillatory modes corresponding to the cardiac (around 1.0 Hz), respiratory (around 0.25 Hz), and vascular myogenic activities (around 0.1 Hz) were extracted and combined into two coupled networks describing the central and peripheral systems, respectively. The corresponding spectral powers and coupling functions were computed. The same measurements and analyses were performed for three groups of subjects: healthy young (Y group, 24.4 ± 3.4 y), healthy aged (A group, 71.1 ± 6.6 y), and aged treated hypertensive patients (ATH group, 70.3 ± 6.7 y). It was established that the degree of coherence between low-frequency oscillations near 0.1 Hz in blood flow and in HRV time series differs markedly between the groups, declining with age and nearly disappearing in treated hypertension. Comparing the two healthy groups it was found that the couplings to the cardiac rhythm from both respiration and vascular myogenic activity decrease significantly in aging. Comparing the data from A and ATH groups it was found that the coupling from the vascular myogenic activity is significantly weaker in treated hypertension subjects, implying that the mechanisms of microcirculation are not completely restored by current anti-hypertension medications.

Keywords: aging; cardiovascular regulation; coherence analysis; coupling functions; heart rate variability; hypertension; microvascular blood flow oscillations; non-linear oscillator.

Figure 1

Schematic representation of the interactions between respiratory, cardiac and vascular activity, together with the corresponding recordings: respiratory effort signal (RES), electrocardiogram (ECG), and laser Doppler flowmetry (LDF).

Figure 2

Decomposition into oscillatory modes. (A) Typical time windows of the signals, their wavelet transforms, and their averaged power spectra. The central frequency of each oscillation is shown for ECG (red) and respiration (orange). (B) A 250-s window of the LDF signal from the same subject is shown in the top panel. The time-frequency evolutions of the modes extracted by NMD (second panel) are indicated by color with heart-rate red, respiration orange, and myogenic brown. The time evolutions of the extracted modes are plotted below, with the same color-code.

Figure 3

Examples of the similarity index for (A) high and (B) low similarity. The form obtained numerically from a unidirectionally coupled system, shown with a red grid, is shifted along the coupling function obtained from measured data, shown in gray, to detect the highest similarity modulus $\overline{\left|\rho \right|}$. The arrow in the polar plot has a modulus equal to $\overline{\left|\rho \right|}$ and a phase $\langle \overline{\rho }\rangle$ corresponding to the phase-shift of the red grid.

Figure 4

Wavelet power: (A) Time-averaged wavelet power of blood flow, means over groups. Brown shading indicates significance between A and Y, red shading between ATH and A, and yellow shading between Y and ATH. (B) Box-plots showing the cardiac, respiration and myogenic oscillations and the total power in the LDF signal within these three intervals. The Y group is represented in gold, A in brown, and ATH in red.

Figure 5

Phase coherence: (A) Typical SBF and R-R interval (RRI) signals from each group of subjects. PU – perfusion units; (B) Wavelet phase coherence (minus surrogate thresholds) between R-R intervals and SBF, mean over groups, where gold shading indicates significant difference between the Y and A groups and brown shading – between the A and ATH groups; (C) Time-localized wavelet phase coherence for individuals typical of the three subject groups. Note how the coherence within the myogenic interval is diminished almost to vanishing point in the ATH group.

Figure 6

Group-averaged coupling functions in the central network (top row) compared with equivalent results from the peripheral network (bottom row). In each case the color coding is: Y (gold), A (brown), ATH (red), and surrogates (gray). (A–C) Show the coupling functions $q_C^{R,C}$ between the phases of centrally measured respiratory ϕ_R and cardiac ϕ_C oscillations, and (E–G) Show the equivalent quantity $q_c^{r,c}$ between the phase of respiratory ϕ_r and cardiac ϕ_c oscillations in the peripheral network. (D,H) show the surrogate coupling functions computed to check the validity of the results presented in each row. The polar plot in the top-right corner of each figure indicates the similarity index ρ for the average form (colored arrow) and for the individual subjects (gray arrows). Note how, with aging, the forms lose amplitude in the central network and resemble the variability of surrogates in the peripheral network.

Figure 7

As in Figure 6 except that (A–C) represent the coupling functions $q_C^{m,C}$ between the phase of myogenic ϕ_m and cardiac ϕ_C oscillations in the central network and (E–G) show $q_c^{m,c}$ between the phases of myogenic ϕ_m and cardiac ϕ_c oscillations in the peripheral network. Plots (D,H) are from the corresponding surrogates. Again, the forms lose amplitude with aging in the central network, and with hypertension, resemble the variability of surrogates in the peripheral network.

Figure 8

Statistics for coupling parameters. (A) Table showing the median values for the coupling strength σ and modulus of similarity |ρ| for groups of Y, A, ATH subjects, and surrogates, with median values not significantly different from surrogates are shown in gray. Box-plots picturing the distributions of the similarity modulus |ρ| within each group, using the same color map as Figure 4. The relation between respiration and cardiac for the (B) central and (C) peripheral networks and of myogenic and cardiac for the (D) central and (E) peripheral networks.

Figure A1

Schematic representation of the interactions between respiratory, cardiac and vascular activity, together with the corresponding recordings: respiratory effort signal (RES), electrocardiogram (ECG), laser Doppler flowmetry (LDF) and pulse plethysmography (PPG). In the resting state, the concentration of red blood cells can be considered constant, and so a Doppler shift in the velocity signal provides a measure of microvascular flow. In contrast, the finger PPG provides a measure of changes in arterial volume proportional to changes in arterial blood pressure.

Figure A2

Typical time series: (A) Skin blood flow measured by the LDF (also referred to as SBF); (B) RR interval (RRI); and (C) PPG signals from each group of subjects. PU stands for perfusion units, and AU for arbitrary units.

Figure A3

Comparison of RR-PPG, (A,B) with the corresponding RR-LDF, (C,D) phase coherences. Panels (A,C) show time-localized phase coherence obtained as a average for each group. Panels (B,D) show the time-averaged wavelet phase coherence (minus surrogate thresholds), and then averaged over groups; gold shading indicates significant difference between the Y and A groups, gray shading between Y and ATH, and brown shading between the A and ATH groups. Note how the coherence within the myogenic interval is higher in the Y than in the A and ATH groups in (B) and that it is diminished almost to vanishing point in the ATH group in (D).