INTRODUCTION

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RECENT STUDIES USING TRANSFER function analyses have shown that the relationship between arterial pressure (AP) and transcranial Doppler-derived cerebral blood flow velocity (CBFV) oscillations during resting conditions can be used to predict the CBFV response to a sudden blood pressure reduction during leg-cuff deflation (14, 20). This analytic approach may be particularly useful in elderly patients if it can identify those at risk of cerebral hypoperfusion during orthostatic hypotension. If elderly people have impairments in cerebral autoregulation that allow changes in AP to be passively transferred to CBFV, then the resting transfer function relating these signals may be a particularly good predictor of the CBFV response to orthostasis in these individuals.

Normal cerebral autoregulation acts like a high-pass filter (6) and blunts the transfer of low-frequency (LF) AP oscillations (<0.2 Hz) onto CBFV. Therefore, we hypothesized that the transfer function describing the dynamic relationship between AP and CBFV would yield poor predictions of the LF CBFV response to posture change in healthy young subjects. Moreover, in the higher frequency range of the cardiac cycle (0.7-1.4 Hz), where cerebral autoregulatory mechanisms are presumably not operative, we postulated that the transfer function would provide a good prediction of the CBFV response to orthostasis. Accordingly, in this study, we computed the transfer function between resting AP and CBFV, used the corresponding impulse-response function to predict the CBFV response to sudden pressure changes during standing, and compared the predicted and observed responses between groups of healthy young and healthy elderly subjects.

	METHODS

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This study evaluated data obtained from 10 healthy young subjects (age 24 ± 1 yr) and 10 healthy elderly subjects (age 72 ± 3 yr), who have been described elsewhere (9). Subjects were recruited from among laboratory personnel, volunteers responding to newspaper advertisements, and members of the Harvard Cooperative Program on Aging subject registry. The subjects were carefully screened with a medical history, physical examination, and electrocardiogram (ECG) to exclude acute and chronic medical conditions and focal neurologic abnormalities or carotid bruits. The presence of carotid and/or cerebral vascular disease was excluded by the absence of stroke or transient ischemic attack (TIA) by previous history. No subjects took medications or smoked cigarettes. Subjects were also evaluated for an adequate temporal window for insonation of the middle cerebral artery (MCA). The study was approved by the Hebrew Rehabilitation Center for Aged (HRCA) hospital institutional review board, and all subjects provided informed consent.

Experimental Protocol

Instrumentation. Subjects reported to the Cardiovascular Laboratory at the HRCA in the postabsorptive state, at least 2 h after their last meal. Three ECG leads were attached to the chest for measurement of the R-R interval, and the finger cuff of a photoplethysmographic noninvasive AP monitor (Finapres, Ohmeda, CO) was placed on the middle finger of the right hand to measure beat-to-beat AP. The hand was supported by a sling at the level of the right atrium to eliminate hydrostatic pressure effects. Finapres measurements were initially corroborated by standard measurements of AP with an oscillometric cuff on the upper arm (Dinamap, Critikon, FL). To assess breathing frequency and tidal volume during the protocol, respiration was measured continuously with an inductive plethysmograph (Respitrace, Ambulatory Monitoring, NY) attached to two elastic respiratory transducer bands, one around the midchest and the other around the abdomen.

Standing Protocol

Data Processing and Analysis

To compute power spectra for the sitting AP and CBFV time series, the Welch algorithm for averaging periodograms was used (2, 17). The time series were low-pass filtered with a cut-off frequency of 4 Hz (Fig. 1) and then divided into six equal overlapping segments. Each segment was detrended, Hanning-windowed, and fast-Fourier transformed. The periodograms were averaged to produce the spectrum estimate. The calculations were carried out using MATLAB software.

View larger version (48K): [in this window] [in a new window]   Fig. 1.   Time series of arterial pressure (AP) and cerebral blood flow velocity (CBFV) before and after posture change (the beginning of posture change is indicated by an arrow) for a single young subject. AP and CBFV frequency spectra and the coherence, gain, and phase relating these signals are shown for the 5-min period of sitting for the same subject. Both AP and CBFV have significant power in low-frequency (0.05-0.2 Hz) and heartbeat-frequency (0.7-1.4 Hz) ranges. The power near 0.25 Hz is due to paced respiration. Inset: power spectrum for the low-frequency range for clarity.

Transfer function analysis quantifies the extent to which the input signal, AP, is reflected in the output signal, CBFV. Knowledge about the transfer function also enables one to predict the output for any given input. The transfer function H(f) is computed as follows (15)
where S_pp is the autospectrum of changes in AP, S_pv is the cross-spectrum between AP and CBFV, and f is frequency.

The transfer function magnitude |H(f)| and phase spectrum (f) were expressed as the real [H_R(f)] and imaginary parts [H_I(f)] of the complex transfer function as

The magnitude reflects the degree to which AP oscillations at a discrete frequency become manifest in CBFV oscillations, i.e., it provides a measure of the gain between AP and CBFV.

For each subject, the coherence [MSC(f)] between AP and CBFV signals was calculated across all frequencies from 0 to 1.5 Hz using the following formula
where S_vv is the autospectrum of changes in CBFV. The coherence is a statistical measure of the linearity of the input/output relationship and thus the reliability of the transfer function.

All but 1 of the 20 subjects had >10% variability in the mean AP signal, and all but two subjects had coherence values above 0.5 in the frequency ranges of interest, which were considered necessary criteria for applying the transfer function analysis (13). Because exclusion of the two subjects not meeting these criteria did not alter the results, their data are included in the analysis.

To predict the changes in CBFV during posture change, the AP during posture change was convolved with the impulse-response function obtained as the inverse Fourier transform of the transfer function estimated under sitting steady-state conditions. The predicted changes in CBFV were then compared with the measured changes in CBFV using Pearson correlation coefficients (R), which give the degree of prediction (7).

We tested the reliability of the impulse-response analysis by deriving the transfer function from the first 150 s of sitting steady-state data, then we used it to predict the next 45 s of sitting steady-state CBFV. The average correlations between predicted and actual data were 0.87 for elderly and 0.80 for young subjects.

To study the effect of different rates of change of AP on our ability to predict change of CBFV, we computed impulse responses over different physiological frequency ranges. From previous studies using transfer-function approaches (8, 9, 14, 15, 20, 21), it appears that cerebral autoregulation operates most effectively (i.e., the transfer gain between AP and CBFV is lowest) from 0 to 0.05 Hz, then gradually becomes ineffective (i.e., the gain gradually increases) from 0.05 to 0.3 Hz. Cerebral autoregulation is not known to operate over higher frequency ranges. Separate analyses were carried out over the following frequency ranges: 1) LF from 0.05 to 0.2 Hz (corresponding to cerebral autoregulation), 2) heartbeat frequency (HBF) from 0.7 to 1.4 Hz (corresponding to the heart rate), and 3) both LF and HBF. The above frequency regions were selected because only these frequency ranges (except 0.2-0.3 Hz) satisfied the conditions of sufficient power in AP and CBFV signals and an average coherence >0.5. The frequency range between 0.2 and 0.3 Hz was excluded to avoid the effects of paced respiration. To obtain the impulse responses, the transfer function was filtered to isolate the LF, HBF, or both LF and HBF ranges, then the inverse Fourier transform was applied. The results from the young and elderly subjects were compared using t-tests. P < 0.05 was considered statistically significant. All data are reported as means ± SE. To account for the possibility of nonnormal distributions for some of the data, a nonparametric Wilcoxon rank-sum test was also performed (10). The P values obtained from the t-test and Wilcoxon rank-sum test did not differ significantly; therefore, the t-test results are presented.

	RESULTS

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Subject Hemodynamic Characteristics

Basal sitting conditions. There was no significant difference in systolic blood pressure (116 ± 4 vs. 123 ± 5 mmHg), diastolic blood pressure (69 ± 3 vs. 68 ± 4 mmHg), or heart rate (69 ± 3 vs. 62 ± 1 beats/min), respectively, between young and elderly groups. There was no significant difference in mean AP (MAP) between young (94.1 ± 2.2 mmHg) and elderly (87.2 ± 2.9 mmHg) subjects, but the mean CBF velocity (MCBFV) was significantly higher in the young subjects (52.2 ± 2.2 cm/s) compared with elderly subjects (35.5 ± 2.3 cm/s; P < 0.05).

Response to standing. At the onset of standing, MAP fell by 24.3 ± 2.1 mmHg in the young subjects and by 21.0 ± 2.2 mmHg in the elderly subjects; this decline was more rapid in the young (6.8 ± 1.9 s) compared with the elderly (10.4 ± 3.0 s; Table 2). The rate of decline was significantly different between groups (P < 0.004). The MAP recovery time (time taken to reach steady state from nadir) was also significantly less in the young subjects compared with the elderly subjects (P < 0.004). The fall in MCBFV was greater in the young (10.1 ± 1.1 cm/s) than in elderly (5.3 ± 1.2 cm/s) subjects (P < 0.05), but the rate of fall was not significantly different between the groups (Table 2). The MCBFV recovery time was greater in the elderly (11.1 ± 2.1 s) than in the young subjects (6.0 ± 1.3 s; P < 0.00001).

View this table: [in this window] [in a new window]   Table 2.   in heart rate, MAP, and MCBFV and average time taken (in s) for MAP and MCBFV to reach their nadir and to recover to steady state from the nadir during standing for young and elderly subjects

View larger version (51K): [in this window] [in a new window]   Fig. 2.   Time series of AP and CBFV before and after posture change (the beginning of posture change is indicated by an arrow) for an elderly subject. Note that the widening of pulsatility in CBFV is less pronounced at the onset of standing for this subject than for the young subject in Fig. 1.

Predicting the CBFV Response to Posture Change

LF response (0.05-0.2 Hz). The coherence and gain in the LF range during steady-state sitting conditions for both young and elderly subjects are shown in Table 3. Average coherence and transfer gain, respectively, were similar for both groups (Table 3). The LF impulse-response function was convolved with the observed AP during posture change to obtain the predicted CBFV during posture change. In this frequency range, the mean observed and predicted CBFVs were used in the calculation of the Pearson correlation coefficients. For both young and elderly groups, the correlations between the observed and predicted CBFV were poor and not statistically significant (Table 3).

HBF response (0.7-1.4 Hz). All subjects demonstrated higher coherence and similar gain between AP and CBFV in the HBF range (Table 3) compared with the LF range. There was no significant difference in coherence or gain, respectively, between the two groups. The 0.7- to 1.4-Hz impulse-response function successfully predicted the high-frequency response to posture change in elderly subjects (R = 0.65 ± 0.23) but not in the young (R = 0.19 ± 0.35). There was a significant difference in the degree of prediction (R) between the groups (P < 0.003, Table 3).

Frequency range 0.05-0.2 and 0.7-1.4 Hz. The impulse-response function containing frequency ranges 0.05-0.2 and 0.7-1.4 Hz was also used to predict CBFV during posture change. In this frequency range, the prediction was higher for the elderly subjects (R = 0.49 ± 0.26) than for the young subjects (R = 0.18 ± 0.29), and the difference between the groups was statistically significant (P < 0.03). An example of the predicted and measured CBFV response for an elderly subject is shown in Fig. 3.

View larger version (46K): [in this window] [in a new window]   Fig. 3.   Comparison of observed and predicted CBFV for an elderly subject. The CBFV is predicted from the impulse response for frequencies 0.05-0.2 and 0.7-1.4 Hz. The correlation coefficient between the observed and predicted data is 0.69.

	DISCUSSION

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The results of this study elucidate several important aspects of pressure-flow relationships in the MCA circulation and their alterations in healthy elderly subjects. First, with the use of transfer-function analyses, it is evident in young subjects that the linear relationship between AP and MCA blood flow velocity during sitting steady-state conditions is altered during orthostatic stress across a wide range of physiological frequencies. This finding suggests that various regulatory responses to transient hypotension during standing blunt the transmission of AP changes onto cerebral blood flow. Moreover, it suggests that the mechanisms governing pressure-flow relationships during basal conditions are different from those engaged during a perturbation such as standing. The mechanisms called into play during active standing include LF (<0.2 Hz) vascular responses (18) in the peripheral cerebral circulation (e.g., autoregulatory myogenic vasodilitation) and systemic circulation (vasoconstriction) as well as HBF (0.7-1.4 Hz) systemic hemodynamic responses [e.g., cardiovagal baroreflexes that increase heart rate (5)].

Second, our analysis suggests that in healthy elderly subjects, LF cerebral autoregulation remains intact, but higher frequency regulatory mechanisms affecting cerebral blood flow velocity are altered. Thus HBF-AP oscillations are passively transmitted to cerebral blood flow in supine and upright positions without intervening adaptive responses. This finding may reflect vascular stiffening in the older subjects, leading to more passive transmission of pressure onto CBFV. Furthermore, the increase in cerebral blood flow pulsatility (4) seen in young subjects during posture change (Fig. 1) may reflect rapid circulatory adjustments in the cerebral vasculature, which loses compliance with advancing age. The increased systolic pulse-wave amplification observed in the young group may be due to greater cardioacceleration (3, 12). Elderly subjects have impaired cardioacceleration during orthostatic stress that may be responsible for diminished pulse amplification (5).

Third, our study suggests that a linear model may not be appropriate to predict changes in cerebral blood flow during orthostatic stress. The simple linear relationship between pressure and flow that describes the resting state may not be adequate to describe the multiple interacting control mechanisms that maintain blood pressure and cerebral blood flow during posture change.

The results of our transfer-function analysis in the LF range may appear to conflict with the work of Zhang et al. (20) and Panerai et al. (14), who reported good correlations between measured and predicted CBFV after thigh-cuff deflation in healthy subjects. This discrepancy may be due to a different stimulus used in our study to induce transient changes in AP. In our study, posture change was used, rather than thigh-cuff deflation, to reproduce a hypotensive stress encountered in everyday life. An important difference lies in the time taken for AP to reach its nadir during these two hypotensive stresses. With the thigh-cuff method, AP appeared to reach its nadir in <5 s (20), whereas after posture change, AP reaches its nadir in ~7-10 s (Table 2). Because AP reached its nadir over a longer time interval in our protocol, there was ample time for autoregulation to blunt the transmission of AP changes onto CBFV. Previous studies using the thigh-cuff method may have achieved such rapid blood pressure changes that autoregulatory mechanisms were not engaged. Furthermore, in our study, impulse-response functions were computed only in physiological frequency ranges where there was adequate power and coherence between the AP and CBFV signals. These ranges are readily apparent in the time-series data for these signals (Figs. 1-3), where LF trends and beat-to-beat oscillations are visible.

In conclusion, the present study suggests that although both young and elderly subjects have intact cerebral autoregulatory mechanisms that reduce the transmission of LF AP changes onto CBFV during posture change, there is a deterioration of HBF regulatory mechanisms in the elderly. This loss of rapid adaptive responses to posture change may make elderly individuals vulnerable to transient cerebral hypoperfusion during beat-to-beat fluctuations in AP. A clinical study of elderly patients with cerebrovascular disease and healthy controls showed a relationship between increased short-term blood pressure variability determined by 24-h monitoring and vascular dementia (19). This lends support to the notion that short-term fluctuations in blood pressure may predispose elderly individuals to cerebral ischemia.

Perspectives