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Changes in Linear Dynamics of Cerebrovascular System
After Severe Traumatic Brain Injury
M. Müller, MD; O. Bianchi; S. Erülkü; C. Stock; K. Schwerdtfeger, MD; for the Homburg Traumatic Brain Injury Group Background and Purpose—We sought to describe the dynamic changes in the cerebrovascular system after traumatic brain
injury by transfer function estimation and coherence.
Methods—In 42 healthy volunteers (meanϮSD age, 37Ϯ17 years; range, 17 to 65 years), spontaneous fluctuations of
middle cerebral artery blood flow velocity and of finger blood pressure (BP) were simultaneously recorded over a periodof 10 minutes under normocapnic and hypocapnic conditions to generate normative spectra of coherence, phase shift,and gain over the frequency range of 0 to 0.25 Hz. Similar recordings were performed in 24 patients with severetraumatic brain injury (Glasgow Coma Scale score Յ8; meanϮSD age, 50Ϯ20 years) serially on days 1, 3, 5, and 8 aftertrauma. Cranial perfusion pressure was kept at Ͼ70 mm Hg. Each blood flow velocity/BP recording was related to thepresence or absence of middle cerebral artery territory brain parenchyma lesions on cranial CT performed within a closetime frame.
Results—In controls, hypocapnia decreased coherence (0.0 to 0.20 Hz), increased phase shift (0.0 to 0.17 Hz), and
decreased gain in the frequency range of 0.0 to 0.11 Hz but increased gain at frequencies of 0.20 to 0.25 Hz (PϽ0.01for all frequency ranges reported). In patients with traumatic brain injury, 102 investigations were possible. Comparedwith controls, coherence was increased in the frequency range Ͻ0.03 Hz and between 0.13 and 0.25 Hz in bothnormocapnia and hypocapnia, irrespective of the CT findings. Gain was unchanged in normocapnia and in the absenceof a CT lesion. Gain was decreased in hypocapnia at frequencies Ͼ0.12 Hz irrespective of the presence/absence of aCT lesion. Phase shift decreased rapidly between 0.06 and 0.13 Hz under hypocapnic conditions and under normocapnicconditions in the presence of a CT lesion (PϽ0.01).
Conclusions—Use of spontaneous fluctuations of blood flow velocity and BP to assess the cerebrovascular system
dynamically requires consideration of the PaCO2 level. In different conditions, including severe traumatic brain injury,
the cerebrovascular system behaves linearly only in parts of the investigated frequency range. (Stroke. 2003;34:1197-

Key Words: cerebral circulation Ⅲ head injury Ⅲ transfer Ⅲ ultrasonography, Doppler, transcranial
Cerebral autoregulation (CA) is the ability of the cerebro- mathematically the intact system and to consider deviations vascular system to provide a constant cerebral blood as an impairment of the system involved in CA. Tiecks et al5 flow (CBF) supply to the brain in the presence of spontaneous modeled CBF velocity changes as a second-order linear blood pressure (BP) changes between 50 and 150 mm Hg differential equation describing response to a rapid BP drop (mean arterial BP). With the use of transcranial Doppler and classifying the state of CA according to the time required ultrasound (TCD), the integrity of CA is usually assessed by by CBF velocity to return to its level before the decline in BP.
2-point static measuring methods by which CBF velocity is Using transfer function analysis, other groups consider CA a measured at rest and after a challenge induced by either BP frequency-dependent filter system influencing the relation- changes, CO2, or acetazolamide application as stressor.1–3 In ship between corresponding frequencies in BP as input and recent years, the fast time resolution of TCD had made CBF velocity as output.6–8,10,11 The filter characteristics and possible the development of dynamic methods for this pur- hence the behavior of the filtering system are described by pose. These dynamic methods analyze the relationship be- phase shift, gain, and coherence. Phase shift is a correlate of tween CBF velocity changes and BP changes by using either the time delay between CBF velocity and BP; the time delay differential equations empirically4,5 or transfer function anal- is low at high frequencies, indicating that BP changes are ysis.6–9 The underlying hypothesis is to accurately model transmitted to CBF velocity; the time delay is high at low Received August 3, 2002; final revision received November 26, 2002; accepted December 9, 2002.
From the Departments of Neurology (M.M., O.B., S.E.) and Neurosurgery (K.S.), Saarland University Hospital, Homburg/Saar, and Institute for Applied Mathematics, Saarland University, Saarbrücken (C.S.), Germany.
Correspondence to Martin Müller, MD, Department of Neurology, Saarland University Hospital, Kirrberger-Strasse, D-66421 Homburg/Saar, 2003 American Heart Association, Inc.
Stroke is available at
DOI: 10.1161/01.STR.0000068409.81859.C5
frequencies, indicating that BP changes are delayed before a direct comparison between normocapnic and hypocapnic condi- they affect CBF velocity. The energy (gain) transmitted from tions in 63 arteries. Because hypoventilation is usually not used in BP to CBF velocity is increased by the system at high the treatment of acute severe TBI, we did not investigatehypercapnia.
frequencies but is clearly decreased by the system at lowfrequencies. Coherence describes the constancy over time of TBI Patients
the phase relationship between CBF velocity and BP. A low All procedures involved in the investigation of the TBI patients were coherence, as found in the low-frequency range, indicates low approved by the local ethics committee. We included 24 patients (19 phase shift stability; a high coherence, as found at higher male, 5 female; meanϮSD age, 50Ϯ20 years) with severe TBI frequencies, indicates a very stable relationship. In the (Glasgow Coma Scale score Յ8)17 whom we intended to investigate frequency-dependent model, any loss of these filter charac- repeatedly on days 1, 3, 5, and 8 after trauma using the same TCD teristics, such as lack of time delay at low frequencies, lack of device and the same probe holder and by feeding the arterial line gain increase at higher frequencies, or high coherence at low signal into the TCD device. All patients had received a SpiegelbergIII system to be used as an external ventricular drainage device and frequencies, can then be interpreted as a loss of CA.
to measure intracranial pressure (ICP). With the ICP known, cerebral A correlation exists between the dynamic CA assessment perfusion pressure as the difference between mean arterial BP and methods and the static methods,5–7,12,13 prompting sugges- ICP was maintained at Ͼ70 mm Hg with the use of catecholamines tions that the dynamic approach to assess CA may be and/or mannitol when necessary; other vasoactive substances such as clinically useful.6,8,14–16 However, clinical experience with glyceryl trinitrate or nimodipine were not used. All patients received the dynamic CA assessment methods is limited. The static regular cranial CT scan follow-ups within a close time frame with theTCD studies. At the time of investigation, the actual ICP was noted, CA assessment methods provide convincing between-method and the actual PaCO was measured by blood gas analysis. TCD comparisons. Such comparisons between different dynamic recordings were possible on 44 MCAs; the remainder were excluded models suggest that the dynamic approach to CA is poorly for reasons such as lack of a temporal bone window or TCD probe understood and provides only fair between-model reproduc- movements due to patient movement. The recording time ranged ibility.8 Such a result may lead to doubts regarding whether between 6 and 10 minutes. Although CT scanning is only a fair the dynamic approaches are truly able to test CA or may method to assess the total traumatic lesion extent, it can provide firstinsights into the relationship between brain lesion size and CA suggest that the different models investigate different aspects disturbances. To compare the CA assessment results with the of the system.8 The aim of our study was to characterize the morphological CT findings, we classified the brain parenchyma of changes in cerebrovascular system behavior after severe each MCA territory in terms of whether or not a traumatic brain traumatic brain injury (TBI) with the understanding that, if lesion was present. A traumatic subarachnoid hemorrhage (SAH) the observed changes are in agreement with similar obser- was present in 32 of 102 possible comparisons. In each SAH-positive vations in other diseases, such a model-dependent repro- CT scan, the parenchyma in the MCA territory under consideration ducibility would strengthen the assumption that the dy- showed a traumatic lesion, leading us to relate the SAH to the injuredparenchyma in each case.
namic approach can reflect the behavior of the system thatcontrols CA.
Data Preparation
For all data analyses, Matlab R12 (The MathWorks Inc) was used.
Subjects and Methods
The TCD device collects the input data with a frequency of 50 data Normal Subjects
points per second. We reduced the amount of data by averaging 100 With their written informed consent, 42 healthy subjects (23 male, 19 data points to 1 new data point every 2 seconds. The new data points female; meanϮSD age, 37Ϯ17 years; age range, 14 to 71 years) were normalized to their means [eg, (x-mean)/mean], and linear without any cerebrovascular risk factors or neurological diseases trends were removed by subtracting the straight line of best fit. A underwent simultaneous recordings of middle cerebral artery (MCA) 6-minute recording time was reduced to approximately 200 data CBF velocity (Multi DopX4, DWL; 2-MHz probe) and of BP at the points. To compare the recordings with a standard length of finger tip (Ohmeda 2300 Finapres) with the use of TCD. End-tidal observation time, the first 128 data points of each time sequence PaCO was measured with Enhancer 3000sx equipment (Diversified were used (corresponding to a time period of 256 seconds).
Diagnostic Products Inc). The volunteers were lying in the supine To calculate the coherence and the transfer function between BP position. The Doppler probes were mounted on a light metal and CBF velocity, we used Welch’s averaged periodogram method, transcranial Doppler probe holder provided by the manufacturer, and by which input (BP) and output (CBF velocity) signal sequences are both MCAs were identified according to commonly accepted crite- divided into subsets of equal length (64 seconds; thus, the lowest ria. Because of a poor temporal bone window on 1 side in 3 frequency resolution is approximately 0.015 Hz). With the use of volunteers, only 1 MCA was investigated in these subjects, while in Hanning windows, a data overlap of 50% between 2 consecutive the other subjects both MCAs were investigated, resulting in a total subsets was achieved. With the use of fast Fourier transformation, of 81 insonated arteries under normocapnic conditions. When the the power spectrum of BP [Gbpbp(f)] and of CBF velocity [Gvv(f)] subjects signaled that they were comfortable with the setting, the and the cross-spectrum between BP and CBF velocity [Gbpv(f)] recording of CBF velocity and BP began. During the 10-minute were calculated for each subset. The coherence function [Coh(f)] recording period, end-tidal PaCO values were collected every 20 seconds and summarized as a mean over the whole time period. After10 minutes the recording was stopped, and the volunteers were asked to breathe in a forced manner. When forced breathing had induced asteady state of fallen end-tidal PaCO that could be maintained Coherence values ranged between 0 and 1; 0 indicates no correlation, comfortably by the volunteers, they were asked to maintain the and 1 indicates perfect stability of the phase shift between input (BP) intensity of forced breathing, and the recording of CBF velocity and and output (CBF velocity [V]). Transferred to CA, 0 indicates that BP was started again for 10 minutes. The end-tidal PaCO values cerebral perfusion lacks any relation to BP, and 1 indicates that CBF were again collected every 20 seconds and are reported as the mean velocity follows BP changes with a perfectly stable phase shift. Such value. Nine subjects refused to hyperventilate in the setting, allowing a constant pressure-dependent perfusion is considered a total loss of Müller et al
Posttraumatic Cerebrovascular System Dynamics
CA. The complex transfer function [TF(f)] is estimated as follows: from which the gain is calculated and the phase shift is extractedfrom the real and the imaginary part of TF(f). The software we usedcalculates TF(f) according to the linear model in which the output variable y(t)ϭ(V) is modeled by the lineartransfer function G applied to the input signal u(t)ϭ(BP).
Statistical Analysis
The data are reported as meanϮSD values. Transfer function and
coherence results are plotted over the frequency range of 0 to 0.25
Hz. For simplicity of comparison, we plotted the curves of the mean
values only. In the software we used, the frequency range contains 65
defined frequency points. At each frequency point, linear regression
analysis was used to test for age and sex dependency for both normal
subjects and TBI patients. To compare the effect of the PaCO2
changes within the controls, we used the paired t test. For compar-
isons between controls and the different patient groups, we used the
unpaired t test. We considered differences to be substantial when the
t tests indicated significant differences over a broader frequency
range with the understanding that a significant t test result at one or
another frequency does not mean a physical finding. Thus, the
reported limits of a frequency range indicate that all tests in the
mentioned frequency range showed significant differences. We are
aware that the testing includes multiple comparisons. To classify
differences as substantial, we considered the level of significance for
each t test as PՅ0.01.
Normal Subjects
Under normocapnia, end-tidal PaCO2 was 34Ϯ3 mm Hg and
mean arterial BP was 88Ϯ9 mm Hg. Under hypercapnia,
PaCO2 was lowered to 21Ϯ3 mm Hg, while mean arterial BP
remained constant (89Ϯ9 mm Hg). Neither coherence, gain,
nor phase shift showed a dependence on age or sex. Hypo-
capnia substantially changed all 3 parameters: coherence
(Figure 1A) was reduced in the frequency range between 0.0
and 0.20 Hz; gain (Figure 1B) decreased between 0.0 and
0.11 Hz but increased from 0.20 to 0.25 Hz; and phase shift
(Figure 1C) was increased between 0.0 and 0.17 Hz
(PϽ0.001 over each frequency range).
TBI Patients
Of the 24 patients, 5 were investigated once, 6 twice, 5 three
times, and 8 four times. The trauma data were analyzed in
terms of 3 considerations: first, we analyzed whether the
patients were normocapnic or hypocapnic; second, recordings
were summarized regarding whether or not a CT lesion was
present, irrespective of the day of the recording; and third, the
recordings were summarized at each day of recording, irre-
spective of the CT findings. The 102 possible comparisons
Figure 1. Changes of coherence (A), gain (B), and phase shift
were recorded on day 1 (nϭ29), day 3 (nϭ29), day 5 (nϭ25), (C) during hypocapnia compared with normocapnia. Curves rep- and day 8 (nϭ19). To classify normocapnia and hypocapnia, resent mean values. Over a broad range of frequencies, coher-ence is significantly reduced and phase shift is increased. Gain we used a threshold of PaCO2 of 36 mm Hg (hypocapnia, is significantly reduced at Ͻ0.11 Hz but increased at Ͼ0.20 Hz.
Ͻ36.0 mm Hg). According to the actual PaCO2, 56 examina-tions were performed under normocapnic conditions and 46 cm in the presence of SAH. In each group (those without and under hypocapnic conditions. A traumatic SAH was present those with an SAH) there was 1 investigation during which a in 17 investigations under normocapnic conditions and in 15 slight vasospasm according to Doppler criteria (mean flow investigations under hypocapnic conditions. Mean MCA flow velocity Ͼ120 cm/s) was present. In every instance cranial velocity was 89Ϯ15 cm in the absence of SAH and 92Ϯ14 perfusion pressure was Ն70 mm Hg, and the maximum 1200
Figure 2. Trauma-induced changes of coherence, gain, and phase shift compared with controls. Findings in the trauma patients are
subdivided according to cranial CT results. For details of differences, see text. A, Coherence changes under normocapnic conditions.
B, Coherence changes under hypocapnic conditions. C, Gain changes under normocapnic conditions. D, Gain changes under hypo-
capnic conditions. E, Phase shift changes under normocapnic conditions. F, Phase shift changes under hypocapnic conditions.
Müller et al
Posttraumatic Cerebrovascular System Dynamics
recorded ICP was 30 mm Hg. None of the CA assessment peak of increase between 0.0 and 0.07 Hz, which corre- results showed a correlation with age, mean arterial BP, ICP, sponded to the gain peak of those patients without a CT lesion cranial perfusion pressure, or patient outcome 1 month after in normocapnia shown in Figure 2C. In hypocapnia, gain was trauma. Despite the fact that the TBI patients were older than substantially decreased between 0.13 and 0.25 Hz on days 1 the controls, we used the findings of the normal subjects as to 5. On day 8 there was no difference between patients and reference for comparison with the TBI patients because we controls. In both normocapnia and hypocapnia, phase shift and other investigators6 did not find the investigated linear decreased substantially between 0.05 and 0.17 Hz on all days except day 3 in normocapnia, on which phase shift was notdifferent from that of controls. The phase shift decline was of Controls Versus Presence of CT Lesions,
the same shape as shown in Figure 2E and 2F.
Irrespective of Day of Recording
Figure 2 summarizes the substantial changes of coherence,
phase shift, and gain compared with controls with respect to The cerebrovascular system regulates CBF or its first derivative CBF velocity from the input power BP. We used the frequency- In normocapnia (56 examinations, 35 with and 21 without dependent filter model to describe changes in the linear behavior a CT lesion; catecholamines were used in 21 recordings), of this system. The major findings in the normal subjects may be coherence was increased in the frequency range Ͻ0.03 Hz described as follows: (1) a hypocapnia-induced linear behavior and between 0.18 and 0.25 Hz, irrespective of the presence of of coherence and phase shift changes over a wide frequency a CT lesion. Under hypocapnic conditions (46 examinations, range; this agrees with previously reported similar linearity 30 with and 16 without a CT lesion; catecholamines were induced by hypercapnia6,7,13,18; and (2) a hypocapnia-induced used in 19 recordings), coherence was increased between 0.0 S-shaped and hence nonlinear behavior of gain as an index of the and 0.13 Hz and between 0.17 and 0.21 Hz when a lesion was manner in which the system regulates the transmission of not present; when a lesion was present, coherence was energy. To our knowledge, such behavior has not been described increased between 0.0 and 0.07 Hz and again between 0.11 previously. Zhang et al7 described, for hypercapnia, an increase of gain in the frequency range between 0 and approximately 0.15 In hypocapnia (with and without a CT lesion) and in Hz, an unchanged gain between 0.15 and 0.23 Hz, and an normocapnia with a CT lesion, gain was reduced between increased gain at Ͼ0.23 Hz, showing also a frequency range in 0.12 and 0.25 Hz. When a CT lesion was absent and the which gain does not change. From the work of Panerai et al,19 it patient was in a normocapnic state, gain was remarkably can also be assumed that the cerebrovascular system can buffer increased in the frequency range Ͻ0.05 Hz, while the gain in sudden BP changes without changing its linearity and its linear the faster frequency range did not differ from that of controls.
stability. However, such a buffering behavior argues for nonlin- Phase shift was not different from that of controls over the ear mechanisms within the system. The major finding in the TBI whole frequency range when a CT lesion was not present patients was the phase shift decrease between 0.05/0.06 Hz and under normocapnic conditions. When a CT lesion was pres- 0.15 Hz. Similar phase shift decreases in this frequency range ent, phase shift showed a rapid decline toward zero in the have been reported for patients with severe carotid artery frequency range between 0.05 and 0.16 and no difference in disease,14 arteriovenous malformations,6 and spontaneous the slower (Ͻ0.05 Hz) and the faster frequencies. In hypo- SAH.20 In addition, the phase shift decreases in this frequency capnia, phase shift was substantially decreased at Ͻ0.03 Hz range have been shown to correlate significantly with impaired and in the range between 0.06 and 0.13 Hz, irrespective of the CO2 reactivity.6,14 One third of our investigations were per- formed in the presence of a traumatic SAH. We cannot definitelyrule out that the similar phase shift behavior in our TBI patients Controls Versus Day of Recording, Irrespective of
and in those with a spontaneous SAH20 is due to SAH-mediated Presence of CT Lesions
mechanisms, but among them vasospasm did not play a role in The 102 examinations were distributed with respect to day and state of ventilation as follows: on day 1, 12 MCAs in The changes in coherence and gain agree only in part with normocapnia and 17 in hypocapnia; on day 3, 14 in normo- the results found in TBI and in other diseases.11,14,15,21 It is capnia and 15 in hypocapnia; on day 5, 16 in normocapnia still undetermined whether systemic vasoconstrictors affect and 9 in hypocapnia; and on day 8, 14 in normocapnia and 5 the behavior of the cerebral circulation.22 As stated above, phase shift decreases comparable to our results were reported Compared with controls, coherence was substantially in- in patients with severe carotid artery disease14 or arterio- creased over most of the frequencies under normocapnic and venous malformations6 in which no vasoconstrictors were hypocapnic conditions on day 1 (normocapnia, 0 to 0.25 Hz; applied at the time of the TCD examination. This seems to hypocapnia, 0.0 to 0.07 Hz and 0.13 to 0.21 Hz). On days 3 support the theory that vasoconstrictors do not affect CA to 8, coherence was increased at Ͻ0.03 Hz in normocapnia substantially. Regarding coherence, a possible explanation and at Ͻ0.05 Hz in hypocapnia and showed a second may be that the phase shift changes between 0.06 and 0.16 Hz substantially increased peak occurring around 0.20 Hz, with were too inhomogeneous to produce more consistent coher- limits ranging between 0.13 and 0.25 Hz. Gain was neither ence values. Thus, the question is whether the trauma induces increased nor decreased on days 1, 5, and 8 under normocap- phase shift changes, which interrupt the assumed linearity for nic conditions. Only on day 3 did gain show a substantial coherence found in the controls. Other possible explanations 1202
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