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Changes in cerebral blood flow velocity (CBFV) pulse latency reflect pathophysiological changes of the cerebral vasculature based on the theory of pulse wave propagation. Timing CBFV pulse onset relative to ECG QRS is practical. However, it introduces confounding factors of extracranial origins for characterizing the cerebral vasculature. The present work introduces an approach of reducing confounding influences on CBFV latency. This correction approach is based on modeling the relationship between CBFV latency and systemic arterial blood pressure (ABP) pulse latency. It is tested using an existing data set of CBFV and ABP from 14 normal subjects undergoing pressure cuff tests under both normoxic and acute hypoxic states. The results show that the proposed CBFV latency correction approach produces a more accurate measure of cerebral vascular changes with an improved positive correlation between beat-to-beat CBFV and the CBFV latency time series, e.g., correlation coefficient raised from 0.643 to 0.836 for group-averaged cuff-deflation traces at normoxia. In conclusion, the present work suggests that subtraction of systemic ABP latency improves CBFV latency measurements, which in turn improves characterization of cerebral vascular changes.
Continuous assessment of the structural and functional status of the human cerebral vasculature is highly desirable in managing cerebral vascular diseases. A prototypical clinical condition requiring a continuous cerebral vascular assessment is cerebral vasospasm (pathological narrowing of cerebral arteries), which is a frequent and devastating complication after subarachnoid hemorrhage (Mayberg et al. 1994). In current clinical practice, standard surveillance methods based on sporadic transcranial Doppler (TCD) measurements of blood flow velocity in major cerebral vessels may delay or even miss the detection of important changes in cerebral hemodynamics before cerebral ischemic damage (Aaslid 2002; Sloan et al. 1989).
To develop clinically viable tools capable of continuously assessing the cerebral vasculature, a focus of our laboratory has been to explore novel methods of extracting physiological information by analyzing continuously acquired signals of an intracranial origin (Hu et al. 2007; Hu et al. 2008). In a recent work (Hu et al. 2008), we have postulated that the latency of the onset a vascular pulse relative to an extracranial timing signal (i.e. time delay between the electrocardiogram (ECG) QRS peak and the initial inflection in the resulting blood pressure pulse) is a function of several variables of relevance to the cerebral vasculature including its radius, stiffness, and wall thickness. Our theoretical foundation for postulating that the latency of a pulsatile intracranial signal as a cerebrovascular index is based on the premise that the Moens-Korteweg equation, Pulse Wave Velocity , establishes a deterministic relationship between the velocity that a blood pressure or a flow velocity pulse travels through the cerebral vasculature and the basic properties of this vascular route including Young's elastic modulus (E), internal radius (R), and wall thickness (h). The underlying relationship is that changes in PWV should manifest with reciprocal changes in pulse waveform latency. Of the various vascular-related intracranial waveforms available for study, we have previously investigated the latency of the onset of an intracranial pressure (ICP) pulse relative to QRS peak (Hu et al. 2008), primarily from the perspective of developing an algorithm to reliably extract latency measure.
One of the inherent problems with measuring intracranial waveform latency, relative to the QRS peak, is that there are both extracranial and intracranial components to this latency value. From the viewpoint of assessing the cerebrovascular influence on pulse latency, physiological changes occurring anywhere from the cardiac sinus node to the skull base could confound the ability to infer intracranial-only changes. For example, changes in the pre-ejection period (PEP), which is the delay comprised of both the electromechanical delay and the period of isovolumic contraction, could affect the latency of the ascending aorta flow waveform, which would obviously affect a measure taken downstream. The confounding effect of PEP on using pulse transit time for indirectly characterizing PWV has been reported previously (Payne et al. 2006).
On the positive side, choosing ECG QRS peak as a timing signal is of practical value for developing a clinically friendly tool for continuously assessing the cerebral vasculature. Therefore, we sought to develop methods to extract the component of the pulse latency referable to the intracranial pulse propagation that would therefore reflect changes originating in the cerebral vasculature. Our approach involves a nontrivial subtraction of latency of a systemic arterial blood pressure (ABP) pulse from the measured intracranial latency. This effort furthers our previous methodological development of the ICP latency extraction algorithm. In a larger context, although extensive applications of the concept of PWV in studying systemic arterial systems have been undertaken (Chang et al. 2006; Davies and Struthers 2003; Foo and Lim 2006; Foo et al. 2005; Nichols and Singh 2002; Willum-Hansen et al. 2006), few studies of its application in the cerebral circulation have been pursued (Giller and Aaslid 1994; Hu et al. 2008).
The main objective of the present work is to investigate the proposed subtraction approach of reducing extracranial influence on intracranial latency. We collaborated with a team of researchers at the University of Colorado Altitude Research Center who were conducting a study of CBFV changes associated with sudden changes in systemic hemodynamics. We adapted our previous latency methodology, which was applied to ICP waveforms, to CBFV measurements. We reasoned that the CBFV in the major cerebral arteries, as measured by the TCD (Aaslid et al. 1982), would similarly serve as an excellent candidate hemodynamic signal for pulse latency analysis. Fundamentally, many of the same principles in terms of latency detection, analysis, and interpretation should apply to both ICP and CBFV pulse waves. We hypothesized that subtraction of ABP latency would enhance the application of CBFV latency in cerebral hemodynamic assessment.
Before proceeding with detail methods and data analysis, we provide a summary of the study design here. In the Colorado study, subjects had CBFV (via TCD), systemic ABP, and ECG recordings during a test in which thigh pressure cuff was inflated and then suddenly deflated using the well established protocol (Aaslid et al., 1989). With abrupt deflation, volumetric redistribution leads to arterial hypotension and subsequent systemic and intracranial hemodynamic responses. We utilized our previously developed algorithm (Hu et al. 2008) to extract latencies of CBFV pulse measured at the middle cerebral artery (MCA) and ABP pulse that was measured noninvasively at the radial artery. The proposed subtraction approach was then applied to these two pulse latency measurements to extract a “corrected” CBFV latency measure. The algorithm was then tested by comparing the original and this corrected CBFV latency with regard to their abilities in capturing the acute changes in the cerebral vasculature by cuff inflation and cuff deflation during both normoxic and hypoxic states.
The data set used in this study was obtained from a study on the influence of hypoxia on CBF autoregulation conducted at the Altitude Research Center at the University of Colorado Denver. Following approval from the institutional review board, fourteen healthy individuals (7 men & 7 women; 24-40 yrs) volunteered and gave written informed consent to participate in the study. All subjects completed a thorough medical examination and were included only if shown to be free of known disease.
Testing for each individual took place during a single experimental session. Subjects underwent continuous monitoring of ABP utilizing a tonometer placed over the left radial artery (Colin Medical Instruments Corp., TX: Model 7000 San Antonio), and CBFV in the ipsilateral middle cerebral artery isonnated through the temporal window using a 2MHz Transcranial Doppler (DWL Electronic Systems, Model Multi Dop T2, Singen, Germany). Signals including ABP, ECG, CBFV, and cuff pressure indicator were synchronized and recorded simultaneously at a sampling rate of 400 Hz (Powerlab 16SP, ADInstruments, Colorado Springs, CO).
Subjects were studied in a supine position with their left arm abducted to avoid hydrostatic differences in ABP between the radial and middle cerebral arteries. In a single blinded design, medical grade hypoxic (12% O2) or normoxic (21% O2) gas was delivered under normobaric conditions (625 mmHg) using compressed gas tanks, a 15 L breathing reservoir and Hans Rudolph 2 way valve (Hans Rudolph, St. Louis, MO) connected in line. Each subject completed a total of six 10-minute trials breathing either hypoxic (3 trials) or normoxic (3 trials) gas using a Latin squares design to control for order effects. Following a 6-minute period of resting data collection, large pneumatic cuffs placed around both thighs were inflated to 30 mmHg above systolic pressure to occlude blood flow to the lower extremities. After 3 minutes of occlusion the cuff pressure was rapidly released (<0.1 second) and changes in ABP and CBFV were followed for the next 60 seconds. Subjects rested and breathed ambient air 5 minutes between trials. In summary, each of the 14 subjects had three recordings collected under normoxic state and three recordings collected under hypoxic state totaling 84 recordings.
Figure 1 illustrates a schematic representation of the components of ABP latency (LTBP) and CBFV latency (LTFV). The LTBP value was decomposed into two components termed LTC and LTR, where LTC represents the time interval from the ECG QRS to the time when blood pressure pulse reaches the juncture point between the extra- and intracranial components. LTC is thus a shared latency component common to both the ABP and CBFV waveforms (anatomically, roughly the origin of the common carotid arteries). LTR represents the traveling time of blood pressure pulse from the terminal point of the LTC to the radial artery assessment point. Likewise, LTFV was decomposed into LTC and LTI where LTI represents the traveling time of blood pressure pulse to reach the site of CBFV measurement from the juncture point. LTI also includes the intrinsic phase difference between pressure and flow velocity pulse measured at the same site (Nichols et al. 2005), which should be a negative value given the fact that flow velocity pulse usually leads pressure pulse. We were of course most interested in determining the LTI value, since it should be the closest to reflect the status of the cerebral vasculature as defined by the Moens-Kortweg equation.
Based on the above decomposition, we have the following equations
If given just one sample of LTBP and LTFV, these two equations will not be sufficient to recover LTI since we have only two known measurements for three unknown variables. However, a relationship between LTC and LTR can be derived by using the following equation
where DC is the length of the vascular segment from the heart to the origin of the juncture node; DR is the length of the vascular segment from this juncture node to the location of the radial artery where ABP is measured; vC and vR are the pulse wave velocities at these two vascular segments, respectively; α is a constant ratio between vR and vC. Combining Equations 3) through 5), we have the following
By defining and , Equation 6) leads to
By combining and re-arranging the above equations, we obtain the following:
Suppose we are given a set of paired samples of LTBP(i) and LTFV(i) where i = 1,2,… is merely a symbol for indexing samples so that Equation 8) can be written as
where we separate LTI into two components: that does not change from sample to sample and that varies from sample to sample. Equation 9) indicates that a set of samples of LTFV and LTBP can be potentially related through a straight line if k0 and k1 do not vary with sample index i and that variation of LTI is small in these samples. Furthermore, will be the slope and will be the intercept of this straight line.
With the above theoretical setup, we can proceed to discuss the situation where samples of LTFV and LTBP are from the same subject. Given and , it is fairly valid to expect that k0 and k1 should be constant for samples obtained in a short period of time. Therefore, a linear relation between the measured LTFV and LTBP would indicate a cerebrovascular steady-state (CV-SS) condition where is small. On the other hand, the deviation of the relationship between LTFV and LTBP from a linear one would suggest the occurrence of large changes in the cerebral vasculature from the branching node to the measurement site of CBFV. We designate this as the cerebrovascular dynamic state (CV-DS).
Based on the above analysis, it can reasoned that samples of ABP and CBFV latency recorded in a CV-SS could be used to estimate the slope and the intercept coefficient in Equation 9. These model coefficients can then be applied to samples recorded in a CV-DS state to derive sample-by-sample variations of LTI, i.e., . Particularly, Equation 9 can be rearranged to derive a corrected CBFV latency, cLTFV(i), in the following way
Equation 10 resembles a subtraction procedure where scaled systemic pulse latency and a constant term were extracted from the measured CBFV latency. Although a positive linear relationship between CBFV latency and ABP latency samples used in the model fitting process is required, the applicability of Equation 10 does not depend on this prerequisite. Indeed, the essence of this correction is to look for variations that deviate from a linear model. Based on our modeling analysis, this corrected CBFV latency represents the information more directly related to the sample-to-sample changes in the cerebral vasculature by essentially removing extracranial confounding influence.
Figure 2 illustrates the notations used in the present work for denoting different segments of data from the start of measurement to the end. We manually mark the start points of cuff inflation (t0) and deflation (t0) based on the pressure indicator signal recorded. Based on t0 and t1, a recording was segmented into four segments denoted as I, II, III, and IV, respectively. Of interest to the present work include Segment I, III and IV. Segment I includes data from the start of recording to t0. A fifty-second segment after t0 and t1 were considered as cuff-inflation (II) and cuff-deflation period (IV), respectively. Acute changes in cerebral vasculature are expected to occur during II and IV.
An ECG-aided pulse detection algorithm (Hu et al. 2008) was used to delineate each pulse of ABP and CBFV using Lead II of ECG. In addition, each detected pulse was saved and visualized using the custom software developed in-house to screen obvious noise or artifacts so that only clean beats were further processed. Algorithm parameters for the pulse detection were the same as those used for ICP in (Hu et al. 2008). ECG QRS detection was performed using a previously published algorithm (Afonso et al. 1999) on lead II of the ECG.
We calculated an autoregulation index (ARI; Aaslid et al. 1989) for each trial of cuff-deflation. We report the average value of this index and conduct an inter-subject correlation analysis of ARI and FVLT. In addition, we used the FFT-based method to calculate critical closing pressure (CCP) and resistance area product (RAP) (Panerai 2003). CCP is reported as one of hemodynamic variables in Results. We also report the correlation analysis of corrected CBFV latency and RAP.
Latency was derived for beats of ABP and CBFV that pass the screen test mentioned above. Latency was measured from the onset of each pulse relative to ECG QRS. The onset was automatically located using the tangent intercept method (Chiu et al. 1991).
To derive cLTFV, pairs of ABP and CBFV latency samples extracted from the beats of Segment I of each trial were used to fit a linear model to estimate the slope and the intercept coefficients following Equation 9. A total of 84 linear models were obtained for the whole data set. Then cLTFV of a trial was calculated, using Equation 10, for each trial's Segments of II and IV using the estimated coefficients from the corresponding Segment I of the same trial.
Group average of data from all subjects was obtained by first fitting a cubic spline to the beat-by-beat time series of a variable to unify the time axis. The resulting time series were then re-sampled at 2 Hz starting from t0 and t1 for Segments II and IV, respectively. Then the group average can be readily obtained from these re-sampled time series with effective anchor points at t0 and t1. Two different physiological states within the same individuals were investigated. Data were analyzed separately since hypoxia was expected to impose mild cardiovascular stress, including increased heart rate (decreased R-R interval) and cardiac output.
The present work focuses on correlating changes in CBFV after cuff inflation/deflation with those in the uncorrected and corrected CBFV latency because CBFV changes depict clearly the physiological response of the cerebral vasculature to cuff inflation/deflation. This is advantageous for investigating whether the corrected CBFV latency could describe the same cerebral vascular process in a way compatible to what is shown by CBFV. Therefore, we chose the correlation coefficient between group-averaged CBFV latency and CBFV after cuff inflation/deflation as a measure of the fidelity of the reflection of the CBFV change pattern by CBFV latency extracted using different methods. The significance of the difference in the correlation coefficient will be tested by a method of comparing in-sample correlation coefficient proposed in (Cohen and Cohen 1983).
Figure 3 shows a scatter plot of ABP latency and CBFV latency extracted from the pulses in Segment I for one of the three normoxia recordings of each subject. A rectangle was used to enclose scatter plot of each subject. It can be seen from this figure that, in general, a strong linear correlation exists between ABP latency and CBFV latency. An average correlation of 0.791 ±0.104 was achieved for measuring the intra-patient correlation of the beat-by-beat time series of these two variables shown in the figure.
Figure 4 shows the group average of beat-by-beat mean ABP and CBFV time series for Segment II, which correspond to cuff-inflation, and Segment IV, which correspond to cuff-deflation. Average was done on all 42 traces of normoxic and hypoxic states, respectively. To help assess the timing of the signals, a vertical line is positioned at the peak of ABP for the cuff inflation cases and positioned at the nadir of ABP for the cuff deflation case. The plots in Fig.2 represent typical responses that have been reported in literature (Aaslid et al. 1989). A clear earlier start of the return of CBFV towards baseline, as compared to that of ABP, is demonstrated in all panels. This has been considered as a signature pattern of cerebral blood flow autoregulation (Aaslid et al. 1989).
Table 1 lists mean and standard deviation of basic hemodynamic variables and the four parameters obtained from using Equation 9 to fit samples of CBFV latency and ABP from data Segment I. In addition, we compared the mean values of these variables at the normoxic and the hypoxic states using the paired t-test. Hemodynamic variables that are significantly different at the two states include systolic blood pressure, heart rate, end-tidal CO2, and both latency measures. We did not obtain a significant correlation between ARI and CBFV latency with a value of 0.07 for the normoxic state and a value of -0.0136 for the hypoxic state.
The four parameters from the model fitting include the goodness of fit (R2), Pearson correlation coefficient (ρ), the slope coefficient and the intercept coefficient in Equation 9. R2 and ρ are significantly higher for the hypoxic data with a p value of 2.1E-4 and 4.4E-4, respectively. However, no significant difference of slope and intercept parameters was detected between the normoxic and hypoxic states. It should also be noted that the intercept parameters of most subjects are negative. This is possible because of the intrinsic negative phase difference between the pressure pulse and the flow velocity pulse that are measured at the same site as discussed in Section 2.2.1.
As a typical example, figure 5 shows the group averaged CBFV in panel A, RAP in panel B, LTBP in panel C, LTFV in panel D, and cLTFV in panel E for normoxia traces aligned at the starting point of cuff deflation. A vertical line is positioned at the nadir of the CBFV so that timing of different signals can be readily assessed. It can be seen that an apparent delay exists between the first start of CBFV increase after initial drop and the start of CBFV latency increase. However, this delay was significantly reduced when comparing CBFV and cLTFV traces. This is a consistent pattern for all hypoxia and cuff inflation cases as well. This reduction of delay improved the correlation between the corrected CBFV latency and the CBFV as shown in Table 2 where the linear correlation coefficients between the trace of CBFV and those of original and corrected CBFV latencies are listed. The results in Table 2 suggest that the corrected CBFV latency measures correlate better with the CBFV than the original CBFV latency does in a statistically significant manner (p value « 1E-6).
Similar patterns also exist in Fig.5 when comparing the timing of the start of RAP decrease with the timing of the start of the latency increase, i.e., cLTFV trace shows a much smaller lag between the two as compared to LTFV. CBF autoregulation after cuff deflation is usually considered to start at the point when RAP starts decreasing. Because of this shortening of the lag, the cLTFV time series, beginning at the starting point of RAP decrease, have a negative correlation with the corresponding RAP time series while LTFV has a positive correlation with RAP. Quantitative results of this correlation analysis are also shown in Table 2. However, correlation of RAP with both cLTFV and LTFV after cuff-inflation is both negative and close to each other.
Pathological changes in cerebral vasculature, such as development of cerebral vasospasm, are not unusual during the intensive care of stroke and brain trauma patients. Therefore, the state of cerebral vasculature should ideally be monitored in a continuous fashion to support timely clinical treatment and management of critical conditions related to cerebral vasculature changes. In the current clinical practice, intermittent assessments of cerebral hemodynamics using transcranial Doppler or cerebral blood flow measurement are often used for such a purpose, but may miss important hemodynamic events. The sound physics and physiology behind the concept of pulse wave velocity and its many successful applications in systemic circulation support the potential usefulness of the signal processing technique of extracting beat-to-beat latency of cerebral hemodynamic signals developed in our previous work. Timing latency relative to ECG QRS is of practical value, but unavoidably confounded by influences of extracranial origins. The main motivation behind the present work was therefore to develop an algorithm to improve PWV analysis in the cerebral circulation.
As shown in Fig.3, there is in general a strong positive linear correlation between CBFV latency and ABP latency. Based on the modeling analysis presented in Section 2.2.1 and Equation 9, a positive linear correlation between intra-patient samples of ABP latency and CBFV latency is expected if sample-to-sample variation of the pulse propagation time from the extracranial/intracranial juncture node to the site of CBFV measurement is small. Despite this high positive correlation between ABP latency and CBFV latency, it was also observed that CBFV latency could change in an opposite direction to that of ABP latency in the initial seconds after cuff deflation as evidenced in Fig. 5 (comparing panels B and C). This demonstrates the power of simultaneous measurement of CBFV latency and ABP latency for detecting changes that cannot be explained by alternations in the common components of both latency measures. This observation is indeed supportive of the concepts of cerebral vascular steady state (CV-SS) and cerebral vascular dynamic state (CV-DS). A positive linear relationship between CBFV latency and ABP latency exists at CV-SS while such relation may not hold at CV-DS.
The challenge was then to reduce the extracranial confounding influence on CBFV latency by exploring the relationship between ABP latency and CBFV latency as modeled in Section 2.2.1. This modeling process led to a practical CBFV latency correction algorithm as proposed in Section 2.2.2. Using a set of ABP and CBFV signals from thigh cuff test experiment, we were able to collect evidence supportive of the validity of the proposed algorithm. The correlation between beat-to-beat CBFV and corrected CBFV latency time series is greater than the correlation between CBFV and original CBFV latency. This improvement of correlation was mostly achieved by reducing the time delay between the start of the CBFV recovery and the start of latency increase, which is demonstrated for the cuff-deflation case shown in Fig. 5 where it shows a large time delay existed between the start of CBFV recovery and the start of CBFV latency recovery.
CBFV recovery is presumably caused by a vasodilatation in the cerebral vasculature to compensate for the decrease of cerebral blood perfusion pressure caused by cuff deflation, which would have also led to a decrease of pulse wave velocity in the cerebral vasculature and thus an increase in CBFV latency. However, increase in CBFV latency may be masked by a simultaneous decrease of LTc due to an increase of systemic blood pressure that increases pulse wave velocity in systemic arterial vasculature (Nichols et al. 2005). This explanation is supported by the observation that the period of decreasing ABP latency overlaps that of decreasing CBFV latency as shown in Fig. 5. Improved correlation between the corrected CBFV latency and CBFV also occurs for the cuff-inflation data as well as for both normoxic and hypoxic states as reported in Table 2.
When replacing CBFV with an existing cerebral vascular resistance metric RAP for conducting the correlation analysis with latency, we observed that CVR started to decrease before LTFV started to increase after cuff deflation while this time lag was greatly reduced by using the cLTFV. This observation basically lends further support to the conclusion from analyzing the results from correlation analysis of CBFV and latency because the start of RAP decrease should ideally coincide with the start of CBFV latency increase indicating a slower PWV due to the vasodilatation.
The present work focuses on correlating changes in CBFV and RAP after cuff inflation/deflation with those in CBFV latency extracted by different methods. In future work, several existing cerebral vascular indices including cerebral critical closing pressure, RAP, CBFV pulsatility index (PI) should be studied more thoroughly together with CBFV latency because there exist a large body of literature on their role as cerebrovascular indices (Czosnyka et al. 1999; Hsu et al. 2004; Michel et al. 1997 Panerai, 1999 #114; Panerai 2003; Panerai et al. 1993), which would provide additional corroboration needed for further illustrating whether CBFV (or ICP) latency may be a useful for characterizing pathological cerebral vascular changes. In addition, it will be worthwhile to further derive CBF autoregulation indices from latency measure and to evaluate them with established scores such ARI. As we briefly reported, LTFV and ARI are not correlated. This is not surprising because LTFV reflects changes in the cerebral vasculature while an autoregulation index such as ARI reflects how effective the cerebral vascular changes are at stabalizing the CBF. Therefore, directly correlating latency measures with ARI is not expected to reveal a correlation. Instead, metrics have to be derived from latency time series to quantify the amount or the speed of latency changes, which may be more appropriate for comparing with autoregulation indices.
Some remaining issues need to be taken into consideration when interpreting the results obtained in the present work. No effort has been made to account for the individual difference of the distance from the branching node in Fig.1 to the MCA before taking group-average of latency measures. In addition, the assumption of stability of PEP from beat-to-beat is needed for fitting a straight line to obtain the model coefficient in Equation 9. Furthermore, the assumption of a constant PEP is also needed for the applicability of the model coefficients estimated using data Segment I to data Segments II and IV. This may not pose a serious problem to the current data set because the duration of the whole experiment is about 10 minutes. In such a short period, these assumptions may not be seriously violated given the reported coefficient of variation of PEP is about 8.3% (Payne et al. 2006). However, for the intended use as a continuous cerebral vasculature indicator over a long period of time, the validity of these assumptions has to be checked for corrected CBFV latency by inspecting the adequacy of model fitting. Alternatively, one would resort to using a different signal other than the ECG QRS as a timing landmark, e.g., the second heart sound to directly measure PEP in a beat-by-beat fashion.
In conclusion, CBFV latency alone (relative to ECG QRS peak) is inadequate as an indicator for characterizing cerebral vascular changes due to the extracranial confounding influence on this measure. However, we demonstrated that CBFV latency can be used to track continuously cerebral vascular changes for an individual patient in situations where continuous ABP latency or latency of a systemic pulse is available. This allows the cerebral vascular dynamic state to be detected by simultaneously monitoring both cerebral pulse and systemic pulse latency. In addition, the extracranial confounding influence on CBFV latency was reduced using the proposed correction method. Future studies will be required to determine whether the results regarding using CBFV latency and ABP latency to derive a corrected latency measure can be extrapolated to ICP latency as well.
The present work is partially supported by NINDS R21 awards NS055998, NS055045, and NS059797 and R01 awards NS054881 and HL070362.