Cerebrovascular reactivity (CVR) has become an increasingly recognized clinical and research tool for assessing vascular function in the brain. In short, CVR is a measure of the change in cerebral blood flow (CBF) in response to a vasoactive stimulus, such as carbon dioxide (CO₂). The standard mathematical expression for CVR is shown in Equation 1. In MRI, the most common technique for detecting CBF changes for CVR is with BOLD imaging, as it is a robust clinical sequence that provides high spatial sensitivity and temporal resolution [1]. However, the response of cerebral blood vessels to alterations in arterial partial pressures of CO₂ is physiologically limited by both a temporal lag and a period of transient increase before the plateau [2,3] (Figure 1). The temporal lag can be partially corrected with appropriate time shifting of data, but the non-linear CBF response can influence the correlation between BOLD and CO₂ data. Recently, a method for incorporating the various temporal delays into CVR analysis was introduced, known as transfer function analysis (TFA) [3]. Instead of a direct temporal correlation, TFA performs a frequency analysis on the primary harmonic to create Gain and Phase maps that can account for time-delay inhomogeneities across the brain. This approach is potentially useful in cerebrovascular diseases as vessel response time may be affected, leading to artificially lowered CVR measures. In this study, we investigated the application of TFA compared to standard temporal correlation for BOLD-CVR calculation in children with sickle cell disease (SCD) as they have known cerebrovascular impairment [4]. We hypothesize that the Gain maps computed with TFA will exhibit higher CVR than with standard correlation, and this improvement will be more pronounced in the SCD data compared to healthy controls.

$$CVR = \frac{CBF_{hypercapnia} - CBF_{baseline}}{CO_{2,hypercapnia} - CO_{2,baseline}}\hspace{3cm}\tt{(Equation\hspace{0.2cm}1)}$$

Data from 62 children with SCD (age 10 to 18 years) and 35 age matched healthy controls were retrospectively analyzed for this study. Each subject was scanned on a 3T clinical MRI (MAGNETOM Tim Trio, Siemens Healthcare, Erlangen Germany) with a 32-channel head coil. BOLD data was acquired using a gradient-echo EPI (TR/TE=2000/30ms, FOV=220mm, matrix=64×64, slices=25, slice=4.5mm, volumes=240, time=8min) in synchrony with a CO₂ stimulus. The gas stimulus was delivered to the subject via a facemask connected to a computer-controlled gas sequencer, which also sampled the end-tidal partial pressures of CO₂ and O₂ (P_ETCO₂ and P_ETO₂) of each exhaled breath. The stimulus paradigm alternated between 60 seconds of normocapnia (P_ETCO₂=40mmHg, P_ETO₂=100mmHg) and 45 seconds of hypercapnia (P_ETCO₂=45mmHg, P_ETO₂=100mmHg). In addition, a high resolution MPRAGE anatomical scan was performed for tissue classification. The MRI and CO₂ data were transferred to an independent workstation for post-processing and analysis. BOLD images were corrected for motion using FSL and the P_ETCO₂ waveforms were resampled to 2 second intervals before performing TFA. Using the TFA tool, the BOLD and P_ETCO₂ data were temporally aligned and voxel-wise Gain and Phase maps were generated. Standard CVR maps were also calculated using temporal correlation for comparison. The anatomical images were skull-stripped and segmented into grey and white matter masks using FSL. CVR, Gain, and Phase maps for each subject were co-registered to the corresponding anatomical scan and then averaged across grey and white matter regions, as defined by the masks. Group differences were determined with a Student's t-test. A linear regression analysis was performed between CVR and Gain and we tested for significant differences between slopes in the patient data versus control data using a z-test [5]. A p-value<0.05 was considered statistically significant.Representative slices from CVR, Gain, and Phase maps for a SCD patient are provided in Figure 2. We see that CVR maps underestimate the CBF response compared to the Gain maps, especially in the white matter where the Phase maps indicate a delayed response. Group averages comparing CVR and Gain exhibit the same pattern in both groups, as shown in Table 1. Figure 3 plots CVR versus Gain for patients and controls, showing that the slope for patients is significantly higher in both grey and white matter with p<0.01 in both cases.Using the TFA method, a more robust measure of CVR can be obtained as it is less sensitive to small variations in BOLD response time. This is reflected in the results as the Gain maps computed with TFA, on average, are higher than CVR maps computed with standard temporal correlation. We found that the difference is more prominent in children with SCD compared to healthy controls, suggesting that the disease may be affecting the response time of the cerebral vasculature.