INTRODUCTION

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IT IS WELL KNOWN THAT cerebral blood flow decreases with hypocapnia (11, 20, 32, 34, 35). However, measurements of cerebral blood flow a few hours after the induction of hypocapnia suggest that there is some secondary recovery of cerebral blood flow over time. The time course associated with this is uncertain. One report suggests that there is an adaptation of carotid artery flow to both hyper- and hypocapnia over 20 min (10), but in a previous study we were unable to reproduce that finding for hypercapnia in the middle cerebral artery, where blood flow remained constant after the initial rise (27).

To address the question of the time course of adaptation over time with sustained hypocapnia, two particular methodological problems have to be addressed. First, a stable level of hypocapnia has to be obtained, and, second, a continuous measure of cerebral blood flow has to be employed. In this study, the technique of combining hyperventilation with dynamic end-tidal forcing (16, 33) has been employed to address the first issue. To obtain continuous measurements of cerebral blood flow, transcranial Doppler ultrasound has been employed, suitably modified to allow for any changes in cross-sectional area that might occur (27, 28).

Thus the purpose of the present study is to examine the dynamics of the middle cerebral artery blood flow in response to 20 min of euoxic hypocapnia, in particular to determine the time course of any adaptation in cerebral blood flow over time. To quantify the dynamics of the response, a simple model was fit to the data to provide gain terms, time constants, and a pure time delay for the response to the onset and relief of hypocapnia as well as a gain term and a time constant for a second slower component.

	METHODS

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Glossary

VP	Instantaneous (10-ms) value for the velocity associated with the maximum frequency of the Doppler shift
VIWM	Instantaneous (10-ms) value for the velocity associated with the intensity-weighted mean frequency of the Doppler spectrum
P	Instantaneous (10-ms) value for the total power (arbitrary units) of the Doppler spectrum
P · VIWM	Instantaneous (10-ms) product of VIWM and P
P	Mean for VP averaged over the cardiac cycle
IWM	Mean for VIWM, averaged over the cardiac cycle
	Mean for P, averaged over the cardiac cycle
IWM	Mean for P · VIWM, averaged over the cardiac cycle

Subjects

Protocols

Two protocols were employed: the control protocol (protocol I) and the hypocapnic protocol (protocol II). On each day, either one or two repeats of each protocol were undertaken. During both protocols, subjects hyperventilated throughout, and PET_CO2 and end-tidal PO₂ (PET_O2) were controlled by using the dynamic end-tidal forcing technique.

In protocol I, PET_O2 was held at 100 Torr and PET_CO2 was held 1.5 Torr above the subject's normal value for 40 min. Protocol II started with an 11-min period when PET_O2 was held at 100 Torr and PET_CO2 was held 1.5 Torr above the subject's natural value as determined on that day. Then, PET_CO2 was decreased rapidly (over a few breaths) by 15.0 Torr (i.e., by 13.5 Torr below the subject's normal value), while PET_O2 continued to be held at 100 Torr and maintained constant for 20 min. Finally, PET_CO2 was returned (within 1 or 2 breaths) to its initial near-eucapnic value and maintained constant for a further 10 min.

Hyperventilation and Control of PET_CO2

Accurate control of the end-tidal gases was achieved by using the technique of dynamic end-tidal forcing (16, 33). At the start of the experiment, a controlling computer generated the inspired partial pressures predicted to give the desired end-tidal partial pressures by using a fast gas-mixing system (16). The controlling computer receives feedback of the measured end-tidal partial pressures on a breath-by-breath basis as the experiment progresses. These measured end-tidal values are compared with the desired values, and the computer then adjusts the initial predicted inspired gas mixture by using an integral proportional feedback algorithm based on the deviations of the measured end-tidal values from the desired end-tidal values.

Measurement of Cerebral Blood Flow

The middle cerebral artery was identified by an insonation pathway through the right temporal window just above the zygomatic arch by using search techniques described previously (1, 24). Optimization of the Doppler signals from the middle cerebral artery was performed by varying the sample volume depth in incremental steps and, at each depth, varying the angle of insonance to obtain the best-quality signals for the Doppler frequency shifts that corresponded with the maximum power signal. The probe was secured in a headband device (Müller and Moll Fixation, Nicolet Instruments) to ensure optimal insonation position and angle for the duration of the experiment.

For each cardiac cycle, mean values for the velocity associated with the maximum frequency of the Doppler shift _P), the intensity-weighted mean velocity (_IWM), signal power (), and the product of the 10-ms values for these variables (_IWM) were calculated. The total power of the signal is proportional to cross-sectional area (3), and so the proposed index (_IWM) allows for any changes that occur in the cross-sectional area of the vessel. Additionally, taking the product of the 10-ms values to obtain the index (_IWM) allows for any systematic change in diameter throughout the cardiac cycle.

Modeling Cerebral Blood Flow Responses to Hypocapnia

(1)

(2)

The differential equation (Eq. 1) may be solved to provide a difference equation that supplies a series of values for _f on a beat-by-beat basis, provided that we assume that the input function can be regarded as constant over any single heartbeat. _f for the n + 1 beat may be calculated from _f for the nth beat, together with the value for the input function for this beat, and we may write

(3)

and

(4)

In the present study the data suggest that a second compartment is required in the model (see RESULTS). This equation can be written as

(5)

where _s is the slow component of the middle cerebral artery flow in response to changes in PET_CO2, _s is a time constant, and g_s is a gain term. The total flow is given by

(6)

The differential equation (Eq. 5) may be solved to provide a difference equation that supplies a series of values for _s on a beat-by-beat basis and we may write

(7)

Finally, middle cerebral artery flow for the n + 1 beat may be calculated as

(8)

Parameter Estimation Process

Eight of the parameters (g_f,on, g_f,off, g_s, _f,on, _f,off, _s, MC, and MC) were estimated by using a routine for minimizing a sum of squares. The ninth parameter (T_d) was determined by minimizing the sum of squares for the other eight parameters for a set of fixed pure delays ranging between 0 and 20 s in steps of 1 s. The estimated pure delay is the value that is associated with the lowest value for the sum of squares from these minimization procedures.

The model input was the breath-by-breath PET_CO2. Values at times between breaths were obtained by linear interpolation. The model output was compared with the data on a beat-by-beat basis to determine the residuals, and no averaging was employed. A single set of parameter values was determined for each repetition for a single subject by minimizing the sum of squared residuals for each repetition. For each repetition, this totaled between ~2,000 and 3,000 residuals (1 for each heartbeat). The data employed for parameter estimation included a 2-min prehypocapnic period, the 20-min hypocapnic period, and the 10-min recovery period.

The particular routine employed for the minimization was taken from the Numerical Algorithms Group (Oxford, UK) FORTRAN library, subroutine E04FDF. This routine is designed to minimize a nonlinear function of a number of variables when that function takes the special form of a sum of squares. All parameters (except the gain of the slow component) in the cost function were constrained to be positive. The routine required initial guesses to be made for the parameters of the model. The guesses were based partly on visual inspection of the data and partly on a knowledge of the range of likely values where previous information was available. A number of such starting points was employed in each case to try to determine whether there were multiple minima. In every case, only a single minimum was detected.

	RESULTS

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General

After each experimental test, subjects completed a short questionnaire on symptoms associated with hypocapnia. Symptoms, rated on a six-point scale (from 0 = absent to 5 = severe), included sweating, chest pains, tingling fingers/toes, tingling lips, muscle cramps, light-headedness, dizziness, headache, warmth, cold, effort of breathing, irritability, and drowsiness. On the six-point scale, two symptoms, tingling fingers/toes and light-headedness, were rated significantly higher during hypocapnia (1.6 and 2.5, respectively) than during eucapnia (0.1 and 0.0, respectively), with paired t-tests.

Table 1 lists the individual values and the group mean for the depth of the Doppler sample volume at which the main segment of the middle cerebral artery was insonated. Small variations in depth among subjects are attributable to differences in skull size (24). Small variations in depth within each subject represent day-to-day differences in the experimenter's determination of the best-quality Doppler signals because the optimization of signals was performed on each visit without any reference to results from previous visits. The test-to-test individual variations in _P and _IWM, together with the associated PET_CO2, are listed in Table 2.

Quality of Input Stimuli

View larger version (22K): [in this window] [in a new window]   Fig. 1.   Typical results for 1 repetition of each protocol for 1 subject (subject 951). A: control (). B: hypocapnia (). PETCO2, end-tidal PCO2; PETO2, end-tidal PO2; IWM, middle cerebral artery velocity; IWM, middle cerebral artery flow. Power () and IWM are expressed as percentage of average value for 5-min period preceding time 0. Data for PETCO2, PETO2, IWM, , and IWM are averaged over 15-s periods.

Figure 2 shows ensemble averages of the time-related changes in PET_O2 and PET_CO2 for each subject and for each protocol. Each profile represents an average of six repetitions. Figure 2 shows that good control over the end-tidal gases was achieved, although some minor imperfections in the desired PET_O2 and PET_CO2 can be detected at the onset and relief of hypocapnia.

View larger version (21K): [in this window] [in a new window]   Fig. 2.   Ensemble averages of time-related changes in PETO2 and PETCO2 for each subject (subjects 951, 964, 966, 967, 971, and 1009). , Control; , hypocapnia. Each symbol represents a 30-s mean.

General Features of Cerebrovascular Responses

Figure 3 shows ensemble averages of the responses for _IWM, , and _IWM for each subject and for each protocol. and _IWM have been expressed as a percentage of a 5-min baseline immediately preceding time 0. First, the eucapnic control data show relatively stable values for _IWM, , and _IWM throughout the experimental period. For the hypocapnic data, the profiles for the power signal appear to not change much from baseline values of 100%, although in general there appear to be slight increases in the power associated with initial period of hypocapnia. The most striking observation is that there are marked changes in _IWM and _IWM associated with the hypocapnia, the changes in _IWM and _IWM being similar against the background of relatively constant values for . Apart from the rapid and consistent changes at the onset and relief of hypocapnia, there appears to be adaptation throughout the period of hypocapnia, which is a consistent finding across all subjects. This adaptation process also appears to be present in the period after the relief of hypocapnia.

View larger version (27K): [in this window] [in a new window]   Fig. 3.   Ensemble averages of IWM, , and IWM responses for each subject. Symbols and subjects are defined as in Fig. 2. Each symbol represents a 15-s mean.

Average values for a range of variables obtained from the Doppler signals (both as absolute and as normalized values) are given in Table 3 for the 5 min preceding the induction of hypocapnia, the first 2 min of hypocapnia, the last 2 min of hypocapnia, and the last 2 min of the recovery period, together with the matching values for the eucapnic control data. For the eucapnic control data, there is little variation over these time periods. For the hypocapnic data, apart from the obvious fall in velocity with the induction of hypocapnia, there is a small rise in power that is nevertheless significant (P < 0.001, ANOVA). Similarly, after the relief of hypocapnia, there is a persistent, small reduction in power compared with control, which again is significant (P < 0.001, ANOVA).

The small change in power at the onset of hypocapnia is reflected in small but significant (P < 0.001, paired t-test) differences in the percent reductions in _IWM and _P compared with _IWM. No differences in the percent reductions between _IWM and _P were detected.

Dynamics of MCAF Responses to Hypocapnia

View larger version (34K): [in this window] [in a new window]   Fig. 4.   IWM responses to hypocapnia (), model fit (solid horizontal line), and 95% confidence intervals (CI) for associated residuals for each subject. Subjects are same as in Fig. 2. Each data set represents an ensemble average of data from all repetitions for each subject. Beat-by-beat data are interpolated over 0.5-s intervals.

The individual values and group means for the estimated model parameters are listed in Table 4. The _IWM responses to hypocapnia start after an estimated delay of 3.9 s. The time constant for the on-response is more than two times faster than the time constant for the off-response, and this difference is significant. The gain term for the on-response is significantly smaller than the gain term for the off-response, and this difference is significant. The baseline before the response is significantly smaller than that after the off-response, and this difference is significant. Once the initial transient is over, there appears to be a slow increase in _IWM that persists for the remainder of the 20-min hypocapnic exposure. This slow adaptation in _IWM has a gain of 1.26%/Torr and a time constant of 426.9 s; the gain is significantly different from zero (Table 4).

	DISCUSSION

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Major Findings

Adaptive Nature of Cerebral Blood Flow Response

In a previous study, Ellingsen et al. (10) measured blood flow velocity in the internal carotid artery (by using Doppler ultrasound) in response to both step increases and step decreases in alveolar PCO₂ and reported progressive changes in cerebral blood flow over 20 min for both types of experiments. However, in a previous study (27) we were unable to reproduce the adaptation that was reported for hypercapnia from the study by Ellingsen et al. (10). Because actual PET_CO2 values were not reported in the study by Ellingsen et al., it is difficult to determine how well the end-tidal values were controlled. In fact, the authors did report some difficulties in controlling end-tidal values and noted that "the detailed time course of these experiments depended on how the subject aimed on the predetermined alveolar PCO₂ value." Although the results of our previous study were not consistent with those of Ellingsen et al. for hypercapnia, the results of our present study of an adaptation of cerebral blood flow with hypocapnia are consistent with their results for hypocapnia.

Adaptation of cerebral blood flow has been reported previously with exposures to hypocapnia of substantially longer duration than those of Ellingsen et al. (10) and of the present study. Raichle et al. (30), in unanesthetized voluntarily hyperventilating men, reported a 40% decrease in cerebral blood flow after 30 min of hypocapnia (PET_CO2 = 15-20 Torr), with a return of cerebral blood flow to 90% of its prehypocapnic value after 4 h of hyperventilation, and a calculated overshoot of 31% over control values when eucapnia was restored. Similar reports have appeared of longer term adaptation in total cerebral blood flow over periods of 2 and 6 h for unanesthetized piglets (12) and goats (2), respectively.

The underlying mechanism for the slow component of the cerebrovascular response to hypocapnia remains unclear. However, it is reasonably well accepted that pH is one of the main regulators of the cerebral blood flow response to CO₂ (22). With prolonged hypocapnia, there is an initial increase in extracellular pH, with the maximal value being reached from within 30 min (2, 26) to a few hours (5, 23, 30) after the onset of hypocapnia. Although the reported time to maximal pH differs considerably among studies, most studies agree that the initial increase is then followed by a decrease in extracellular pH toward normal values (2, 5, 23, 26, 30). It is thought that the subsequent decrease in pH is due to a progressive increase in brain lactate (2, 8, 19), although the time course over which the change in lactate occurs remains uncertain, with studies reporting times from 1 to 6 h after the onset of hypocapnia before the maximum response in lactate is observed (2, 19, 25). These variations may be related to species differences (25).

Sensitivity of Cerebral Blood Flow Response to Hypocapnia

The presence of an adaptive process may be one reason why there is uncertainty as to whether the cerebral blood flow sensitivity is linear, with variations in PET_CO2. Some studies have been consistent with a linear response across both a hypo- and hypercapnic range (13, 14), whereas other studies have not (6, 31), with some suggesting that the relationship is better described by an exponential (18, 21, 36) or sigmoid (32) function.

One way to avoid the influence of the adaptive process on the measurement of sensitivity is to determine instead whether the gain of the fast component of the response, g_f, varies over the physiological range of PET_CO2. By using our data and technique, the hypocapnic values for g_f from the present study can be compared with the hypercapnic values for g_f from Poulin et al. (27). The value for g_f in hypocapnia (2.69%/Torr) was significantly smaller (34%; unpaired t-test, P < 0.01) than the value for g_f in hypercapnia (4.1%/Torr). Four of the six subjects were common to both studies, and to highlight further the differences observed between hypercapnia and hypocapnia, their gains for the fast component at the onset of hypercapnia [taken from Poulin et al. (27)] and for the fast component at the onset of hypocapnia (taken from the present study) are presented in Fig. 5. The differences on an individual basis are consistent with the statistical results for the two groups as a whole. Also shown in Fig. 5 are the values for g_f  g_s for each subject. These show that the appearance of nonlinearity will be enhanced in those studies that take longer to determine the response of cerebral blood flow to hypocapnia.

View larger version (33K): [in this window] [in a new window]   Fig. 5.   Comparison of gain of cerebral blood flow response (% /Torr) to onset of hypercapnia (solid bars) with fast (gf; open bars) and fast minus slow (gf  gs; hatched bars) components of cerebral blood flow response to hypocapnia. Hypercapnic data were taken from a previous study (27).

Speed of Rapid Response to Onset and Offset of Hypocapnia

Our study finds significant asymmetry between the response of cerebral blood flow to the onset and relief of hypocapnia. We were unable to find any related results in the literature for hypocapnia. However, the asymmetry observed in hypocapnia does show some qualitative similarities to that observed in hypercapnia (27). In both conditions, the time constant of the cerebral blood flow response to a step decrease in CO₂ is less than the time constant of the cerebral blood flow response to an increase in CO₂. However, some quantitative differences are observed: the time constants for the step decreases in CO₂ were similar (6.8 ± 4.7 s in hypocapnia and 6.1 ± 1.3 s in hypercapnia), but the time constants for the step increases in CO₂ were significantly different (14.3 ± 13.0 s in hypocapnia and 45.3 ± 32.9 s in hypercapnia; P = 0.05).

Changes in Doppler Power