Imaging of the appearance time of cerebral blood using [¹⁵O]H₂O PET for the computation of correct CBF

Quantification of cerebral blood flow (CBF) is important for the understanding of normal and pathologic brain physiology. Parametric CBF images can be quantitatively measured using positron emission tomography (PET) with ¹⁵O-labeled water (H₂ ¹⁵O) or carbon dioxide (C¹⁵O₂), and several quantitative approaches have been developed to obtain CBF images for clinical assessment, such as the bolus administration of H₂ ¹⁵O or C¹⁵O₂ with autoradiography (ARG) [1, 2] and dynamic protocols [3–5]. The ARG protocol applies the integration method from the bolus administration of C¹⁵O₂ or H₂ ¹⁵O [1, 2], while the dynamic protocol applies optimization procedures such as the basis function method (BFM) [4], allowing the simultaneous estimation of multiple parameters, including uptake and washout rate constants of tracer and vascular volume.

Recently, Kudomi et al. developed a dual-tracer approach with the basis function method (DBFM) [6] for images of CBF as well as oxygen extraction fraction (OEF) and metabolic rate of oxygen (CMRO₂). In the report, the authors demonstrated differences in sensitivity between the ARG and BFM computation algorithms due to error factors in input functions such as delay and dispersion. These errors resulted from the over- or underestimation of estimated parametric values, suggesting that the difference in the estimated parameters can be utilized as information regarding the degree of error in the error factors. Thus, the delay time in the input function, namely the appearance time of cerebral blood (ATB) (or tracer), may be estimated on a pixel-wise basis.

In this study, we estimated the ATB in brain regions using a pixel-wise approach based on the differences in estimated CBF values derived from the ARG and BFM using clinical C¹⁵O₂ PET data. The feasibility of this method was tested by comparing the estimated ATB to that derived using a region-based analysis. On the basis of estimated ATB, CBF images were recomputed by shifting the time in tissue time-activity curves (TACs). The sensitivity of the ATB and resulting CBF, as well as the feasibility of our methodology, were tested in a simulation study.

In the present study, we estimated the ATB in the brain in an image-based fashion, from the sensitivity differences of different computation methods, including the ARG, BFMF, and BFMP. On the basis of the estimated ATB, CBF values were computed using the BFMAT by shifting the time in tissue TACs. The ATB obtained in image-based analysis was not significantly different from that obtained by ROI-based analysis. Significantly later appearance was found in the cerebellum compared to the other regions in all three groups. In the regions where CBF was reduced due to occlusive lesions, the estimated ATB was 0.2 ± 1.2 s, which was significantly delayed compared to the value of −0.6 ± 1.3 s in the unaffected contralateral regions. In our simulation study, estimated CBF was insensitive to errors in appearance time and dispersion time constant. With regard to the variation of the partition coefficient, systematic errors in CBF persisted after ATB correction. However, the degree of error was smaller than that computed by BFMF and was the same as that computed by ARG. As a whole, this study suggests a method for visualizing the ATB in the brain and correcting CBF that is less sensitive to the error sources in PET examination.

The computation of CBF using bolus inhalation of C¹⁵O₂ or injection of H₂ ¹⁵O generally requires the determination of the common zero time between the measured arterial blood and brain tissue curves in every study using appropriate procedures [8]. However, the accuracy of computed regional CBF is still affected by regional differences in the ATB. For further correction for regional time differences, the present study used an image-based approach to estimate the ATB. None of the ATB values obtained from images of the parietal, frontal, temporal, deep gray matter, occipital, or cerebellar cortical regions were significantly different from those derived using the ROI-based analysis. The ATB for different brain regions varied from −1.0 to 2.0 s from the zero times obtained from whole-brain TACs (Table 1) in group 0, 1, and 2 subjects. The ATB in the cerebellar cortical region varied from around 1.5 to 2.0 s and was significantly delayed compared to that in the other regions. A previous study has demonstrated similar time differences of around ±2-s variation and 2-s delay in the cerebellum [8]. In anatomical terms, vascular supply patterns are basically subject to individual variation, and it may not be possible to define universal ATB patterns in the brain. However, there are still frequent and dominant patterns identifiable in the human brain [16]. The finding of no significant differences in the ATB in the parietal and frontal regions (territory of the terminal branches of the anterior cerebral artery (ACA)), the temporal region (territory of the middle cerebral artery (MCA)), the occipital (territory of the posterior cerebral artery (PCA)), and the deep gray (the territory of penetrating branches of the ACA, MCA, and PCA), all supplied from the internal carotid artery, may suggest a similar degree of blood transit time supply. However, the significant difference in ATB in the cerebellar region, which is the territory of the posterior inferior cerebral artery through the vertebral artery, suggests that the transit time could be longer.

In the regions with reduced CBF, i.e., those affected by occlusive lesions, the ATB was significantly delayed, and that delay can be clearly seen in the ATB image (Figure 3). These findings suggest that the ATB measure could be of interest for identifying occluded areas or as a pathophysiological indicator in patients with occlusive lesions. It may be of interest to compare the ATB with the OEF in the occlusive area. The present study focused on ATB and CBF, so only the C¹⁵O₂ PET scan and data analysis procedures were presented. Since the PET protocol was originally designed to obtain CBF, CBV, OEF, and CMRO₂ [8], it was possible to compare the ATB and OEF. We determined the correlation between these two measures and found that it was slight, i.e., r = 0.25 for all ROIs drawn in group 2 subjects and r = 0.45 for CBF-reduced regions (data not shown). This slight correlation might be due to the structure of the cerebral circulation system; specifically, variation in the ATB due to cerebral location may obscure the delayed appearance in the occlusive areas. Further study to determine the possibility of ATB as a clinical indicator, taking into account the cerebral circulation structure, is warranted.

The present experimental study showed that the regional variation in the ATB was around ±1.5 s, which caused errors in computed CBF values that depended on the computation method used (Figure 4). As the present simulation showed, the difference of ±1.5 s led to errors of 3%, 3%, and 7% in CBF computed by ARG, BFMF, and BFMP, respectively (Figure 5C). To correct for the error in delay and reduce the degree of error in the CBF value, the present method was used to determine the pixel-wise ATB within a reasonable computation time of approximately 85 s. While determining the ATB, the accuracy could be affected by framing of PET data and by noise in tissue TAC. The present simulation, assuming the same framing condition as the clinical data, showed that the mean ATB reproduced the shift time, and the SD was 1.7 s. This relatively improved temporal resolution was achieved because the ATB was estimated from difference in CBF values, which is dependent on the computation method and independent of the framing, particularly with the ARG. We applied ROI-based analysis to the noisy TACs after summing 50 of the noise-added TACs. The estimated SD of ATB was 2.5 s, suggesting that the present pixel-wise method, depending on CBF accuracy, may provide more accurate shift time than the ROI-based method in the present clinical setup.

Additionally, the estimated mean CBF value was identical to the assumed CBF value, independent of shift time; and particularly, the magnitude of noise on CBF was not enhanced in comparison to the method without ATB correction, i.e., BFMF. The noise on CBF was not enhanced by either ARG or BFMP with ATB correction (data not shown). The lesser enhancement of noise in CBF following ATB correction might be due to the three CBF values competing with each other as additional information and thus decreasing noise, although ATB correction enhanced noise to the same degree.

The CBF value was affected by errors in the applied dispersion time constant in the input function. The simulation performed here revealed that the estimated ATB was affected by the error in the dispersion time constant; however, the error in the estimated CBF after correction was negligible compared to the error in both the time constant and the appearance time (Figure 5C). The CBF and ATB values were also affected by errors in the partition coefficient. For the error in the partition coefficient, both the ATB and CBF were affected when calculated by BFMAT; however, the degree of error in CBF was smaller than that computed by BFMF and the same as that by ARG (Figure 5D). The partition coefficient obtained using BFMP and that obtained after ATB correction were around 0.80 ml/g which did not change significantly with ATB correction, except for the cerebellar region, and was identical to the fixed value for ARG, BFMF, and BFMAT. The significant difference in the cerebellar region could be partly derived from the significant delay of the appearance time, although the obtained appearance time was identical between the image-based and ROI-based analyses. The computed CBF value after ATB correction was identical among ARG, BFMF, and BFMP; and to determine the final CBF value, the present study applied BFMF because this method was less affected by noise than BFMP, was useful in determining arterial blood volume (Va), and did not require the partition coefficient. When the partition coefficient is required, BFMP with ATB correction is available.

A previous approach suggested around ±2 s of regional variation in the appearance time of the tracer [8]. For dispersion, a corresponding difference in the time constant (Δτ) could be roughly estimated as Δτ = ±0.6 s for ±2-s appearance time difference if we apply the relationship between the time difference (Δt) and the constant as Δτ = 0.31Δt − 0.30 [17]. Additionally, the effect might be smaller in the cerebral capillary circulation system since dispersion is assumed to be caused by laminar flow [18], and the degree of dispersion in small vessel would therefore be small. Thus, we presume that the effect of variation in appearance time is larger than that of dispersion, and on the basis of this, we developed the computation strategy for ATB. The estimated CBF computed using BFMAT, which is important for clinical diagnosis and research purposes, was less sensitive to variations in both appearance time and dispersion time constant, as demonstrated by the simulation we performed.

In a previous report, the authors demonstrated differences in sensitivity between the ARG and BFM computation algorithms due to delay in input functions [6]. In the present study, ATB was estimated using the difference in estimated CBF values from the different computation methods, i.e., differences between ARG and BFMF and between BFMP and BFMF. For practical estimation, we represented the difference as the ratio of two CBF values. Additionally, it was not guaranteed that the degree of error in CBF was independent of the CBF value, although the look-up tables generated showed similar ATB values independent of CBF values (Figure 1). Thus, we created the tables as a function of the mean and ratio of the estimated CBF values. In our preliminary assessment, the look-up table created for estimation was dependent on the input function applied. Thus, a table was created for every data computation applied. In creating the table, the means and ratios of CBF values were obtained by shifting the times of the input function applied. The shifted time corresponds to the ATB. There could be multiple ATB values as an element on a table, or there could be no data. In the former case, the mean of multiple values was inputted as the element. In the latter case, the interpolation of adjacent elements was inputted. In both cases, accuracy could be deteriorated, and this may have appeared as a fluctuation of the table value (Figure 1) and thus of the estimated ATB (Figures 4 and 5A,B). However, the degree of fluctuation does not seem to be large.

The method used in the current study generated arterial blood volume images after ATB correction. The Va contains only the arterial blood volume rather than the total arterial and venous blood volume that can be determined using a C¹⁵O PET scan [6]. For Va images derived using the BFMF formula without ATB correction, qualitative and quantitative accuracy suffered from noise and from further systematic error in the measured and corrected input functions. Specifically, the error magnitude of the Va value, propagated from errors in the input function such as delay and dispersion corrections, was quite large [19]. The present algorithm allows for the correction of regional variation in the ATB based on the estimated ATB and, thus, may reduce the systematic error in the estimated Va value, although the estimated Va could still be affected by dispersion in input function. The procedure can be extended to another approach for the DBFM method [6], for additional OEF, CMRO₂, and V ₀ images, where the V ₀ contains both the arterial and venous blood volume. Further studies should be carried out to evaluate the significance of the Va and V ₀ parameters by applying the present procedure.

The present simulation study revealed that the computed CBF after ATB correction was less sensitive to errors in the input function, such as delay and dispersion. The errors in CBF due to these delay and dispersion factors may also reduce accuracy when obtaining image-derived input functions [20] because errors in both measured and image-derived input lead to differences in CBF values. The present CBF computing procedure avoids such effects and, thus, may contribute to the further development of methods for image-derived input.

In conclusion, this study suggests the possibility of visualizing the ATB in the brain and correcting CBF so that it is less sensitive to the error sources inherent in PET examination.