The new two-breath CO2 method was employed to test the hypotheses that small alterations in arterial Pco2 had an impact on the magnitude and dynamic response time of the CO2 effect on cerebrovascular resistance (CVRi) and the dynamic autoregulatory response to fluctuations in arterial pressure. During a 10-min protocol, eight subjects inspired two breaths from a bag with elevated Pco2, four different times, while end-tidal Pco2 was maintained at three levels: hypocapnia (LoCO2, 8 mmHg below resting values), normocapnia, and hypercapnia (HiCO2, 8 mmHg above resting values). Continuous measurements were made of mean blood pressure corrected to the level of the middle cerebral artery (BPMCA), Pco2 (estimated from expired CO2), and mean flow velocity (MFV, of the middle cerebral artery by Doppler ultrasound), with CVRi = BPMCA/MFV. Data were processed by a system identification technique (autoregressive moving average analysis) with gain and dynamic response time of adaptation estimated from the theoretical step responses. Consistent with our hypotheses, the magnitude of the Pco2-CVRi response was reduced from LoCO2 to HiCO2 [from −0.04 (SD 0.02) to −0.01 (SD 0.01) (mmHg·cm−1·s)·mmHg Pco2−1] and the time to reach 95% of the step plateau increased from 12.0 ± 4.9 to 20.5 ± 10.6 s. Dynamic autoregulation was impaired with elevated Pco2, as indicated by a reduction in gain from LoCO2 to HiCO2 [from 0.021 ± 0.012 to 0.007 ± 0.004 (mmHg·cm−1·s)·mmHg BPMCA−1], and time to reach 95% increased from 3.7 ± 2.8 to 20.0 ± 9.6 s. The two-breath technique detected dependence of the cerebrovascular CO2 response on Pco2 and changes in dynamic autoregulation with only small deviations in estimated arterial Pco2.
- Doppler ultrasound
- brain blood flow
- autoregressive moving average
- carbon dioxide
a sensitive methodological tool that can successfully extract the independent effects of arterial Pco2 and dynamic autoregulatory responses of the cerebrovascular system is important for basic research and clinical applications, such as after acute ischemic stroke, where dynamic, but not static, cerebrovascular autoregulation is impaired (7). Approaches that have ignored potential confounding effects of Pco2 include frequency domain analyses of the effects of spontaneous fluctuations in mean arterial blood pressure (BPMCA; corrected at the level of the middle cerebral artery) on mean flow velocity (MFV) determined as the average velocity of red blood cells over a cardiac cycle by transcranial Doppler ultrasound from the middle cerebral artery or on an index of cerebrovascular resistance (CVRi = BPMCA/MFV) (2, 3, 5, 15), as well as the MFV or CVRi responses to step decreases in BPMCA after the release of thigh cuffs (1) or to oscillatory changes in BPMCA with repeated squatting (2) or deep breathing (5). In other studies, the sensitivity or the vasodilatory capacity of the cerebrovasculature was assessed with elevated levels of Pco2 (11, 18, 25). However, an increase in arterial Pco2 can significantly increase BPMCA in healthy subjects (8, 21, 27) and patients with carotid artery disease (6, 14), so the interaction of Pco2 and BPMCA should be considered.
In the present study, we employed a new method that combined brief manipulations of Pco2 by inhalation of two breaths of elevated CO2 with autoregressive moving average analysis (ARMA), a system identification technique, to extract the interactions between BPMCA and Pco2 on the cerebrovascular response (9). Three levels of end-tidal Pco2 (PetCO2), hypocapnia (8 mmHg below resting values), normocapnia, and hypercapnia (8 mmHg above resting values), were used to test the hypotheses that 1) the ARMA model provides a sensitive test to determine that the CO2 effect on CVRi depends on the Pco2 level and 2) deviations from normal Pco2 alter the magnitude and response time of the dynamic cerebrovascular autoregulatory response to fluctuations in BPMCA.
Eight healthy subjects (4 women, 21–24 yr of age) volunteered to participate. In our female subjects, we did not control for the phase of menstrual cycle, but all three conditions were tested in random order on the same day. The experiment was approved by the Office of Research Ethics at our institution, and informed consent was obtained in all cases.
Subjects reported to the laboratory 3 h after eating and after refraining from caffeine, alcohol, and heavy exercise for ≥24 h before testing. Subjects rested in a reclining chair for all tests. Data were collected on two separate days. After familiarization, the 1st day was used to determine baseline tidal volume, breathing frequency, and PetCO2. The experimental protocol was simulated with subjects breathing with an auditory signal at 24 breaths/min to drive PetCO2 to 8–10 mmHg below resting values.
On the 2nd day, subjects breathed at 24 breaths/min and the appropriate tidal volume while PetCO2 was maintained at three levels [hypocapnia (LoCO2, 8 mmHg below baseline PetCO2), normocapnia (NCO2, baseline PetCO2), and hypercapnia (HiCO2, 8 mmHg above baseline PetCO2)] with a computerized dynamic end-tidal forcing system similar to that of Robbins et al. (28). Each level was controlled for 10 min, and the order of the levels was randomized. In all cases, the first 5.5 min were used simply to allow the subject to achieve stable conditions before the data analysis section that included the two-breath series. With the use of a valve, subjects were switched to breathe two breaths of 9, 11, or 13% CO2 (21% O2, balance N2) for LoCO2, NCO2, and HiCO2, respectively, at the 6th, 7th, 8th, and 9th min of each 10-min condition to raise estimated Pco2 ∼8–10 mmHg (see Fig. 2).
Heart rate was determined from a standard three-lead electrocardiogram. MFV was measured by transcranial Doppler ultrasonography (model 500V, Multigon, Mt. Vernon, NY) of the middle cerebral artery (1). A 2-MHz Doppler probe was placed over the right temporal window and fixed by a head gear (Marc 600, Spencer Technologies, Seattle, WA) throughout collection. Arterial blood pressure was measured by noninvasive arterial tonometry (Colin, Pilot, San Antonio, TX) and corrected to estimate BPMCA. Expired Pco2 was measured continuously with mass spectrometry (MGA-1100 medical gas analyzer, Perkin-Elmer, Pomona, CA) from a face mask that allowed nose and mouth breathing to reflect normal physiological resting conditions.
Data were recorded to digital audio tape (TEAC, Montebello, CA) and then transferred to yield a data set at 100 Hz. Each cardiac cycle was marked to allow beat-by-beat assessment of MFV and BPMCA (Fig. 1). CVRi was calculated for each cardiac cycle as BPMCA/MFV. Alveolar Pco2, as an estimate of arterial Pco2, was calculated from the expired CO2 profile (Fig. 1) as described by Whipp et al. (32). This method was shown to be a good estimator of within-breath fluctuations of arterial Pco2 as determined from rapid-responding pH electrodes in the arterial blood of an anesthetized dog (32). The continuous estimate of alveolar Pco2 was then averaged over each cardiac cycle to give data for time series analysis (Fig. 1).
A two-input (BPMCA and Pco2) and one-output (MFV or CVRi) ARMA modeling procedure was applied over 5 min (including 30 s of baseline data before and after the 2-breath series) for each of the three CO2 conditions (9). ARMA represents a linear, time-invariant system, where the parameters of the model were estimated using a modified automatic, autoregressive parameter reduction algorithm described by Perrott and Cohen (24). Briefly, an overly parameterized (high-order) candidate model set was determined. The model orders for the autoregressive and moving-average parameters were then determined on the basis of the minimum description length criterion in the least squares technique (24). Final selection of the appropriate model was based on three criteria (20) from the method of Ljung (17): 1) minimal residuals, where the residuals represent the difference between the measured response and the modeled response; 2) residuals with a Gaussian distribution that did not appear to correlate with the inputs; and 3) appearance of reasonable impulse response functions. The latter two methods were based on visual inspection (Fig. 2) and on analysis of the autocorrelation of residuals from the model, including a portmanteau test (4), which confirmed white residuals for all cases. The model parameters were used to generate the output responses to maximum impulse and step transitions of the input variables to estimate system amplitude and dynamic response time and to allow comparisons with other studies (21). The impulse response for the MFV output to the input of BPMCA should be interpreted as the maximum passive response to the sudden increase in arterial pressure; the step responses for MFV and CVRi reflect the active component of the response to return MFV after the regulatory increase in CVRi.
ARMA maximum impulse and step response amplitudes and the time to 95% response were compared across the conditions (LoCO2, NCO2, and HiCO2) with a one-way ANOVA with repeated measures. If significance was obtained (P < 0.05), a Student-Newman-Keuls post hoc test was used to isolate the differences.
The intended manipulation of estimated arterial Pco2 (Table 1, Fig. 2) caused significant alterations in CVRi and MFV (Table 1, Fig. 2). As expected, HiCO2 decreased CVRi and increased MFV from NCO2, whereas LoCO2 increased CVRi and decreased MFV. The 5-mmHg increase in BPMCA during HiCO2 (Table 1) was not significant (P = 0.098). The change in MFV with the change in Pco2 was 4.4 ± 1.0%/mmHg for HiCO2 and 3.0 ± 0.8%/mmHg for LoCO2.
For an individual subject presented in Fig. 2, the two breaths of CO2 caused notable changes in CVRi and MFV in LoCO2 and NCO2 and a somewhat smaller response in HiCO2, but there was no consistent effect of the two breaths of CO2 on BPMCA. The fit to the output variables (MFV and CVRi) with the ARMA model was considered very good, yielding residuals that were small in magnitude and evenly distributed (gray lines in Fig. 2), supporting the application of a linear model to data analysis. The ARMA model solutions were used to estimate the amplitudes of the maximum impulse and step responses for BPMCA + Pco2 → MFV and BPMCA + Pco2 → CVRi under the three steady-state levels of Pco2 (Table 2). Overall, the effects of Pco2 were more evident on the relations with CVRi, rather than MFV, as the output.
The maximum impulse for BPMCA → MFV, representing the passive response to the sudden increase in BPMCA, occurred at time 0 and was significantly less in LoCO2 and greater in HiCO2 than in NCO2 (Table 2, Fig. 3A). Even though differences were detected for the passive impulse response, the active response characteristics of BPMCA → CVRi (see below) returned the MFV (Fig. 3B), so it did not differ significantly from baseline, and there were no significant differences between CO2 levels for the step response for BPMCA → MFV, although the amplitude of the step for HiCO2 tended to be different from the other conditions (P = 0.06). The maximum impulse for Pco2 → MFV was significantly greater in LoCO2 than in NCO2 and HiCO2 (P < 0.05), reflecting the different time course for the effects of CO2 on CVRi (see below). The MFV response to a calculated step transition in Pco2 was not different between the three CO2 conditions (Table 2).
The maximum impulse for BPMCA → CVRi was smallest under HiCO2, followed by NCO2 and then LoCO2, although only LoCO2 and HiCO2 differed significantly (P < 0.05; Table 2). The active regulatory process as reflected by the step response for the BPMCA → CVRi relation was significantly smaller in HiCO2 than in NCO2 or LoCO2. The dynamic response time of the BPMCA → CVRi step clearly differed under different Pco2 levels (Fig. 4A). Under LoCO2, the step response profile to a unit increase in BPMCA at time 0 showed a rapid increase and then overshoot before returning to a stable value. In contrast, the calculated step response for CVRi increased slowly under the HiCO2 condition, with the end point taken as steady state. The times at which 95% of the steady-state value was achieved were 3.7 (SD 2.8), 8.5 (SD 4.8), and 20.0 (SD 9.6) s for LoCO2, NCO2, and HiCO2, respectively. The 95% response times for LoCO2 and NCO2 differed significantly from the 95% response time for HiCO2 (P < 0.05).
The Pco2 → CVRi maximum impulse response was significantly different across the three different CO2 conditions (P < 0.05). The step response amplitude was significantly smaller for HiCO2 than for LoCO2 and NCO2 (P < 0.05; Fig. 4B). The 95% response times were similar between LoCO2 and NCO2 [12.0 (SD 4.9) and 12.8 (SD 4.0) s, respectively, P > 0.05], but only LoCO2 was significantly different from HiCO2 [20.5 (SD 10.6) s, P < 0.05]. ARMA models for BPMCA and Pco2 in HiCO2 were not found in one or two subjects, as indicated in Table 2.
This study provides new insight into the simultaneous interactions of BPMCA and arterial Pco2 on the dynamic and steady-state nature of the cerebrovascular response, and it shows the ability of a new methodology to detect small but important differences in cerebrovascular autoregulation. Consistent with the hypotheses developed from the previous observations from steady-state (10, 13), brief dynamic stimulations of BPMCA (1) and spectral analysis (8, 21), the dynamic cerebrovascular autoregulatory response depended on the steady-state level of arterial Pco2. A relatively small increase in Pco2 caused a reduction in the amplitude and a marked slowing of the CVRi response to a change in BPMCA. In contrast, a small reduction in Pco2 caused the calculated step response for CVRi to a change in BPMCA to exhibit a more rapid response with an overshoot. Also consistent with the hypotheses was that Pco2 affected the CVRi responsiveness to a step change in CO2, inasmuch as we found significantly smaller and slower responses under conditions of elevated Pco2.
The two-breath method combined with ARMA is a reproducible technique to extract the separate but simultaneous effects of changes in BPMCA and Pco2 on the cerebrovascular autoregulatory response and CO2 responsiveness (9). Unlike analysis of spontaneous baseline conditions, where there are often very small fluctuations in arterial Pco2 (9, 23), the two-breath method inserts sufficient signal strength to extract a valid solution in all but a few cases of hypercapnia. The short duration of the 8- to 10-mmHg increase in CO2 exposure avoided the complication of elevated BPMCA (2, 21, 27), which could interfere with assessment of cerebrovascular autoregulation and CO2 responsiveness.
ARMA generated the best-fit model parameters from the individual data sets that included the four exposures to two breaths of elevated CO2 and then computed maximum impulse and step responses. The random distribution of residuals shown in Fig. 2 appears to support the application of a linear model to study cerebrovascular autoregulation, rather than a nonlinear model (19, 22), and this distribution was confirmed to be random by autocorrelation analysis of the model residuals followed by the portmanteau test (4). The ARMA model generated impulse and step responses as opposed to the complex responses of the thigh cuff release, where analysis must be constrained between 1 and 3.5 s after cuff release when blood pressure was probably low (1). However, it should be anticipated after release of the thigh cuffs that there will be between-subject differences in the rate of recovery of blood pressure because of different responses of the arterial and/or cardiopulmonary baroreflexes. An additional advantage of the two-breath method is that it does not require any physical manipulation of the subject, nor is any conscious action required (the altered breathing frequency in the present study was designed to achieve different levels of Pco2 that would not be necessary for investigations of patients). The two breaths of elevated CO2 can be administered without alerting the subject. In contrast, sustained inflation of thigh cuffs for 2 min might not be suitable for patients with vascular or blood-clotting disorders.
The dynamic and the steady-state responses as computed from the ARMA model can change under different conditions (Figs. 3 and 4). These data add to information computed from the autoregulation index or the dynamic rate of regulation (1, 30) that provide only an indicator of the initial rate of change in CVRi. In addition, the ARMA model has advantages over cross-spectral analysis techniques used in the cerebrovascular literature to compute amplitude and phase relations for BPMCA and MFV (3, 5), because ARMA offers a simplistic and efficient means of accounting for potential interactions of other variables that may complicate the input and output relation. This is especially true in the low-frequency region of spectral analysis, where factors such as variation in arterial Pco2 due to spontaneous fluctuation in alveolar ventilation might contribute to the BPMCA and MFV relation (9, 23) and introduce apparent nonlinearities in autoregulation (19, 22).
In HiCO2, no ARMA solutions meeting our criteria (see methods) were found in one or two subjects. This may be attributed to the relatively small amplitudes of responses in BPMCA and Pco2. Valid ARMA solutions require the data to be “persistently exciting” (17). In addition, the magnitude of the fluctuations must be sufficient to activate dynamic autoregulatory mechanisms. Although our present research cannot confirm that the absence of solutions under HiCO2 was simply due to limitations in our technique, the progression of amplitude and time course responses from LoCO2 to HiCO2 supports the notion that, at some “high” level of CO2, all subjects might be expected to show this response, which reflects loss of autoregulation and CO2 responsiveness.
Impact of Pco2 on cerebrovascular responses.
The steady-state effects of altered Pco2 on cerebrovascular responses have been well documented and are confirmed by the present study. The trend for elevated BPMCA under hypercapnia (P = 0.098) was consistent with other studies (2, 21, 27) and could complicate interpretation of the effects of Pco2 on MFV, because CVRi would be increased as a result of autoregulation. In contrast to these studies, ventilation was maintained at a constant rate, thereby potentially limiting the sympathetic outflow and effects of the respiratory pump on BPMCA.
Aaslid et al. (1) first reported that hypocapnia accelerated and hypercapnia slowed the dynamic autoregulatory response of CVRi to a change in BPMCA induced by release of thigh occlusion cuffs. It was not clear from their results whether the elevation of arterial blood pressure under hypercapnia influenced the cerebrovascular response. In contrast, Simpson et al. (29) found no effect of Pco2 on the computed step response of MFV to a theoretical step increase or decrease in BPMCA with different levels of arterial Pco2. These apparently contradictory results are consistent with the present results and further point to the greater sensitivity of CVRi than of MFV in detecting an effect on autoregulation (8). In agreement with Aaslid et al., we observed progressive reduction in the rate at which CVRi changed in response to a theoretical step increase in BPMCA as the Pco2 increased. An observation beyond that obtained in the study of Aaslid et al. was that HiCO2 reduced the amplitude of the CVRi response to the change in BPMCA. Our finding of no significant difference in MFV to a step change in BPMCA, although there was a strong trend, was consistent with the observation of Simpson et al. The overshoot of the CVRi response during LoCO2 is consistent with the MFV overshoot observed by Aaslid et al. during hypocapnia that was twice as great as in the present study. Results from the maximum impulse reflect more the higher-frequency response that is outside the region of cerebrovascular autoregulation (3, 5, 12).
Our results are also consistent with other studies using spectral analysis to assess dynamic autoregulation under elevated levels of Pco2. Birch et al. (2), using a repeated-squat model to induce transient decreases in BPMCA under normocapnic, hypocapnic, and hypercapnic conditions, observed decreased phase between BPMCA and MFV as Pco2 increased, indicating less effective autoregulation at higher levels of CO2. In addition, Panerai et al. (21) demonstrated that 5% inspired CO2 increased the BPMCA-to-MFV coherence and gain response, while the phase delay was reduced at lower frequencies. These results also suggested that increased CO2 appears to weaken the autoregulatory response during uncontrolled, spontaneous breathing.
The two-breath method tested the sensitivity of the cerebrovascular responsiveness to brief exposures ∼8 mmHg above the prevailing PetCO2 under conditions of varied levels of CO2. The increases in MFV to this brief pulse of CO2 were ∼1.07–1.15 cm·s−1·mmHg Pco2−1, equivalent to 2.3%/mmHg in LoCO2 and 1.4%/mmHg in HiCO2. The magnitude was smaller and the direction of effect was opposite to the observations based on steady-state measurements such as reported by Poulin et al. (26) of 2.69%/mmHg in hypocapnia and 4.1%/mmHg in hypercapnia or as observed in the present study (3.0 and 4.4%/mmHg, data from Table 1). The between-method differences probably reflect the confounding effect of CO2 on BPMCA (6, 14) as well as the complex nature of CO2 equilibrium in the cerebral tissues. That is, the acute manipulation of CO2 by the two-breath test did not influence BPMCA in the present test, but it would be expected to influence the equilibrium of CO2, bicarbonate, and hydrogen ion in the extracellular fluid immediately surrounding the pial vessels. This contrasts with the longer-term application of sustained hypo- or hypercapnia, where BPMCA is often significantly affected (P = 0.098 in the present study) and the acid-base balance would be achieved throughout a larger extracellular fluid volume, allowing hydrogen ion to play its proposed role as a cerebral vessel vasodilator (16). In contrast with the divergent responses for CO2 effects on MFV, the steady-state and the two-breath method step responses of CVRi to an increase in CO2, where potential effects on BPMCA have been incorporated, showed similar directional changes, and the step response was significantly smaller in HiCO2 than in NCO2 or LoCO2. The differences in CO2 equilibrium might also explain the faster response of CVRi to a change in CO2 with the two-breath method than previously observed changes in MFV (26, 31). Taken together, these results show that cerebrovascular responsiveness to changes in CO2 or BPMCA was reduced under conditions of elevated CO2.
The two-breath technique with ARMA of the CVRi response to changes in BPMCA proved to be highly sensitive to changes in cerebrovascular autoregulation, with a progressive reduction in amplitude and a significant slowing of the CVRi response on going from hypocapnia to hypercapnia. The two-breath technique also successfully revealed impaired amplitude and rate of response of CVRi during tests of cerebrovascular reactivity to CO2 when the level of Pco2 was increased. The primary advantage of the two-breath method with ARMA is that the variation in the output variable of interest (MFV or CVRi) could be attributed independently to the input variables of BPMCA or Pco2. This contrasts with previous investigations that employed transfer function analysis (8) or leg occlusion cuff release (1), where it was unknown whether some of the variation in the output variable of interest was a function of variation in an independent input (such as spontaneous variations in Pco2) that was not accounted for in the model.
This research was supported by Heart and Stroke Foundation of Ontario Grant T4972 and the Natural Sciences and Engineering Council of Canada. M. R. Edwards was supported by a postgraduate initiative among the Canadian Stroke Network, the Heart and Stroke Foundation of Canada, the Canadian Institute for Health Research, the Institute of Circulatory and Respiratory Health, and the Canadian Institute for Health Research and Research and Development Program together with AstraZeneca Canada.
The authors thank Maria Kerigan and Eileen Hill for technical assistance.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
- Copyright © 2004 the American Physiological Society