Studies were conducted at the Autonomic Nervous System Laboratory at the Department of Neurology at The Ohio State University and at the SAFE (Syncope and Falls in the Elderly) Laboratory at the Beth Israel Deaconess Medical Center at Harvard Medical School. All subjects signed informed consent, approved by the Institutional Review Boards. Subjects in the stroke and non-stroke groups were recruited from the Neurology Stroke Service and through advertisement. Demographic characteristics are summarized in Table 1.

The experiments were done in the morning or > 2 hours after the last meal. The electrocardiogram was measured from a modified standard lead II or III using a Spacelab Monitor (SpaceLab Medical Inc., Issaquah, WA). Beat-to-beat BP was recorded from a finger with a Finapres device (Ohmeda Monitoring Systems, Englewood CO), which is based on a photoplethysmographic volume clamp method. During the study protocol, BP was verified by arterial tonometry. With finger position at the heart level and temperature kept constant, the Finapres device can reliably track intraarterial BP changes over prolonged periods of time 13. Respiratory waveforms were measured with a nasal thermistor. CO₂ was measured from a mask using an infrared end tidal volume CO₂ monitor (Datex Ohmeda, Madison WI). The right and left MCAs were insonated from the temporal windows, by placing the 2-MHz probe in the temporal area above the zygomatic arch using a transcranial Doppler ultrasonography system (MultiDop X4, DWL Neuroscan Inc, Sterling, VA). Each probe was positioned to record the maximal BFV and fixed at a desired angle using a three-dimensional positioning system attached to the light-metal probe holder. Special attention was given to stabilize the probes, since their steady position is crucial for reliable, continuous BFV recordings. BFV and all cardiovascular analog signals were continuously acquired at 200 Hz and exported at 50 Hz for off-line post-processing. Data were visually inspected and occasional extrasystoles and outlier data points were removed using linear interpolation. Fourier transform of the Doppler shift (the difference between the frequency of the emitted signal and its echo (frequency of reflected signal) was used to calculate BFV. BFVs in the MCA correlate with invasive measurements of blood flow with xenon clearance 14, laser Doppler flux 15 and positron emission tomography 16. Since MCA diameter is relatively constant under physiological conditions, BFV can be used for blood flow estimates 17.

To quantify the dependency between cerebral blood flow and systemic pressure, we developed a novel computational procedure, called multimodal pressure-flow (MMPF) analysis. The MMPF analysis implemented the Hilbert-Huang transformation 12 technique to measure the coupling between two nonstationary signals. This method was motivated by the fact that the original BP and BFV signals are recorded over time. However, different subjects vary in the amount of time spent in each stage of the VM. Therefore, it is essential to find an alternative coordinate system for both BP and BFV signals that allows for a meaningful, non-time dependent cross referencing of these two signals. Since the complete VM cycle can be treated as a full cycle of BP oscillation, the oscillatory phase of the BP modulation during the VM can serve as such a useful coordinate system.

To implement this approach, we first need to calculate how BP phase changes as a function of time. Then we can map the original time-varying BP and BFV signals to the new axis of reference, namely BP oscillatory phase. To precisely calculate the BP phase, we need to extract the characteristic (dominant) BP oscillation induced by the VM. We applied the empirical mode decomposition (EMD) technique developed by Huang et al. 12 The EMD algorithm decomposes complex signals such as BP and BFV into multiple empirical modes. Each mode represents the frequency-amplitude modulation at a specific time scale. Figure 1A shows the original BP waveform, which is modulated by multiple frequencies corresponding to the systolic peak, dicrotic notch, heart rate, respiratory frequency and BP fluctuations induced by the VM. Figure 1B shows the decomposed empirical modes (1–10) of the original BP signal. Empirical modes 1–5, corresponding to the faster frequencies, were removed from the signal. The remaining lower frequency BP signal, termed the "residual BP" or BP_R (shown as thick curve in Figure 1A), was used to identify the maximum and minimum values during the VM. The empirical mode best representing the dominant BP profile during the VM, denoted as BP_VM (mode 6 in this example, plotted as the thick line in Figure 1B), was visually identified and used for subsequent phase analysis. We followed the same procedure to obtain the residual BFV signal, denoted as BFV_R.

In the next step of the MMPF analysis, we applied the Hilbert transform to the BP_VM signal to calculate its instantaneous phases. This phase was then used as a reference coordinate both for BP and BFV signals. From this point on, the term phase refers to the phase of the BP_VM oscillation during the VM. Unlike the Fourier transform, the Hilbert transform does not assume that signals are composed of superimposed sinusoidal oscillations of constant amplitude and frequency. Real-world biological fluctuations, such as BP and BFV, are not stationary and are better described by analytical methods that can quantify variations of amplitude and frequency.

Mathematically, the first two steps of the MMPF algorithm can be summarized in the following way: Any complex signal s(t) can be represented as the superimposition of more basic (simpler) components: S(t) = ∑_k S_k (t), where S_k are empirical modes that fulfill certain criteria of the original signal 12. For each empirical mode, its Hilbert transform is defined as:

where the Cauchy principal value is taken in the integral. Instantaneous amplitude, A_k (t), and instantaneous phase, φ_k (t), can be calculated by

The BP_VM profile from the first peak at the beginning of the VM to the subsequent BP_VM maximum forms a complete phase cycle from 0–360° over 30–40 seconds. We assigned the first peak at the beginning of the VM to phase 0°, the BP_VM minimum during the VM to phase 180° and the subsequent BP_VM maximum to phase 360°. To quantify the relationships between BP and BFV signals, we measured the BP-BFV phase shift, defined as the difference between the phase at the BP_R minimum (maximum) value and the phase at the BFV_R minimum (maximum) value. We have calculated phase values for all data points in this interval and, in principle, we can measure the phase shift at all point of the VM cycle. However, for simplicity, we only calculated the phase shift at the minimum and maximum of these two signals for statistical analysis. Since these BP-BFV phase shifts reflect dynamical changes in peripheral and cerebral vascular tone over the course of the VM, they can be used as a sensitive index of cerebral autoregulation dynamics in normal and pathological conditions.

We also assessed autoregulation using a standard index, calculated using the second-order differential equation model proposed by Tiecks et al5 This model assumes a linear flow-pressure relationship and a constant cerebral perfusion pressure over the course of a sudden BP reduction, such as occurs during thigh cuff deflation. This technique can be also applied to the sudden BP decline during the VM. The autoregulation index ranges from 0 = "no autoregulation" to 9 = "the fastest autoregulation;" value 5 reflects "normal autoregulation." We also calculated the "rate of autoregulation" (RoR) using the slope of the linear regression fitted to the original BP and BFV waveforms signals during the period between the baseline and the BP minimum (descending slope) and between BP minimum and maximum (ascending slope).

We used one-way analysis of variance for between-group comparisons of baseline, minimum and maximum BP_R and BFV_R values and phases. Two-way analysis of variance was used for side-to-side comparisons of BFV between groups (JMP-5.0 SAS Institute, Cary, NC). For the group comparisons, we used the BFV_R in the right and left MCAs for the normotensive and hypertensive groups compared to the BFV_R in the stroke-side and non-stroke side MCA in the stroke group. Age was different between the groups (p < 0.003). However, age and stroke subtypes had no significant effects when included as co-variants in the analysis. Data are presented as mean ± SE.

Figure 3A shows the group averages of BFV_R values and the phases at the BFV_R minimum and maximum values for the right MCA in the normotensive and hypertensive groups and for the non-stroke side MCA in the stroke group. Figure 3B shows the BFV_R values and the phases for the left MCA in the normotensive and hypertensive group, and the stroke side MCA in the stroke group. Mean BP_R values and corresponding phases are shown in panel C. The phase at BFV_R minimum was different between groups for the right (non-stroke side) (p = 0.0005) and left (stroke side) (p = 0.004) MCAs. In the normotensive group, the phase at BFV_R minimum was shorter than the phase at BP_R minimum. In the stroke group, the phase at BFV_R minimum was similar to the phase at BP_R minimum. The phase at BFV_R minimum was greater in the non-stroke (p = 0.002) and stroke (p = 0.03) MCAs, compared to the normotensive group. In the hypertensive group, the phase at BFV_R minimum was also greater for the right (p = 0.0007) and left (p = 0.006) MCAs compared to the normotensive group. No significant differences were found between the stroke and hypertensive groups.

The phase at BP_R minimum was similar between groups (normotensive group = 172.7 ± 3.9°, hypertensive group = 178.6 ± 2.0°, stroke group = 178 ± 1.9°). Average BP_R values were higher in the stroke and hypertensive groups compared to the normotensive group at baseline (p = 0.001), at BP_R minimum (p = 0.054) and at BP_R maximum (p = 0.0001) (Figure 3C). Average BFV_R values at baseline, at BFV_R minimum and maximum, and BFV_R change from baseline were not different among groups. Average BP_R change and percent change from baseline to BP_R minimum and maximum were not different. Average BFV_R change and percent change from baseline to BFV minimum and maximum were also not different.

In the normotensive group, the phase at BFV_R maximum preceded the phase at BP_R maximum (Figure 3). The phase at BFV_R maximum was different between groups for the right (non-stroke side) (p = 0.009) and left (stroke side) (p = 0.003) MCAs. In the stroke group, the phase at BFV_R maximum was similar to the phase at BP_R maximum. The phase was greater for the non-stroke side (p = 0.008) and stroke side (p = 0.03) MCAs, compared to the normotensive group. In the hypertensive group, the phase at BFV_R maximum was also greater for the right (p = 0.005) and left (p = 0.009) MCAs compared to the normotensive group. The phase at BP_R maximum was similar among groups (normotensive group = 354 ± 4.7°, hypertensive group = 360.1 ± 2.2° stroke group = 364.1 ± 4.3°).

Figure 4A summarizes the differences between the phases at BP_R and BFV_R minimum and between the phases at BP_R and BFV_R maximum for the right MCA in normotensive and hypertensive groups and for the non-stroke side MCA in the stroke group. The BP-BFV phase shifts at the minimum points were smaller in the stroke and hypertensive groups compared to the normotensive group (p = 0.009). The BP-BFV phase shifts at the maximum points were smaller in stroke and hypertensive groups compared to the normotensive group (p = 0.03). Figure 4B shows the phase shift for the left MCA in normotensive and hypertensive groups and for the stroke-side MCA in the stroke group. The BP-BFV phase shifts at the minima and maxima were also smaller in the stroke and hypertensive groups compared to the normotensive group (p = 0.0002). The BP-BFV phase shifts at the maxima were smaller in the stroke and hypertensive groups compared to the normotensive group (p = 0.008). In the stroke group, the BP-BFV phase shift at the maxima was greater compared to the phase shift at the minima for the non-stroke MCA (p = 0.02). The BP-BFV phase shifts at the minima and maxima for the stroke MCA did not reach statistical significance (p = 0.08). The BP-BFV phase shifts between the stroke and non-stroke MCA at the minima and maxima were not different. In the normotensive group, the phase difference between BP_R and BFV_R minima was about 60 degrees corresponding to a time difference of about 3.6 seconds. In contrast, in the stroke and hypertensive groups, the time difference between BFV and BP phases was < 0.5 second.

The standard autoregulation index was not different between groups and between MCAs in both hemispheres (Table 2). The rate of autoregulation (RoR) of BFV responses to BP reduction and increases during the VM were also not different (Table 2).

In a subset analysis, we separated stroke-normotensive (N = 6) and stroke-hypertensive subjects (N = 9) and compared them to the non-stroke normotensive and hypertensive groups. For the non-stroke side MCA, the phases at BFV_R minima (p = 0.01) and maxima (p = 0.04) were greater in the stroke-normotensive group compared to the normotensive group. For the stroke side MCA, the phases at BFV_R minima (p = 0.04) and maxima (NS, p = 0.08) were greater in the stroke-normotensive group compared to the normotensive group. The phases at BFV_R minima and maxima were not different between the stroke-hypertensive and hypertensive groups for both MCAs. No significant differences were found between the stroke and non-stroke side MCA.