ORIGINAL ARTICLE 
Anna]s of Nuclear Medicine Vol. 9, No.4, 191-198, 1995 
Validation of noninvasive quantification of rCBF compared with dynamic/integral method by using positron emission tomography and oxygen-15 labeled water 
H WATABE,* M. ITOH,** M. MEJIA R.,** T. FUirwARA,** T. JONES*** and T. NAKAMURA** 
*Department of Investigative Radiology. National Cardiovascular Center Research Institute, Osaka, Japan **Cyclotron and Radioisotope Center, Tohoku University, Sendai, Japan ***MRC Cyclotron Unit. Hammersmith Hospital, London, U.K. 
This study proposes a new solution for the quantification of rCBF pixel-by-pixel using PET and 150-H2O. The method represents an application of weighted integration that uses PET image only, requiring no input function of arterial blood. It generates the rCBF image quickly and automatically. Simulation studies revealed that the calculation of rCBF was fairly stable as long as a relatively shorter scan frame time and longer scan time were selected. Calculated images of actual PET study by this method correlated significantly with those identified by the dynamic/integral method. Because this procedure could detect whole brain CBF change between different studies as accurately as by the dynamic/integral method, this procedure may be the most suitable for brain activation studies. 
Key words: 15O-labeled noninvasive quantification water, reglonal cerebral blood flow, positron emission tomography, 
INTRODUCTION 
INVESTIGATORS have devised several techniques for calculating rCBF by means of PET i.e. , steady-state, 1 weighted integration,2 autoradiographic3' 4 and build-up technique,5. 6 but in these models repeated arterial blood sampling in which the value is 1O0-200 ml in several runs is necessary to obtain absolute blood flow. The continuous measurement of arterial blood by tube, with a radio-counting device (p detector), should take into account delay and dispersion in the blood curve obtained relative to the brain data.7 This procedure creates unnecessary complications for both subjects and examiners. Our study proposes a new numerical solution for rCBF calculation by using PET and O-15 labeled water. 
In this paper, results of simulation studies and PET studies are presented. The theory of this method is shown in the appendix. 
MATERIAL AND METHODS 
Simulations With the following equation, tissue time-activity curves (TACs) were generated by using actual arterial input function and having the distribution volume fixed at 0.95: 
Blood flow of 50 ml/1OO g/min was used for Region 1 , and by varying flow values from 20 to 1OO ml/1OO g/min, TACs for Region 2 were generated. Computation of Eq. (13) and (15) for the TACs of Region I and Region 2 gave estimations of flow for Region 2. 
The accuracy and effects of scan protocol were evaluated by comparing the calculated values with the original ones used to generate tissue data. 
In order to evaluate the effects of total scan time on the calculated rCBF, sequential tissue data at 5 sec interval in Regions 1 and 2 were generated up to 300 sec for flow values from 20 to 100 ml/lOO g/min. With these tissue data, rCBF values at Region 2 were calculated by means of Eq. (14) (Fig. 2).  In order to evaluate the effects of the frame time, it was varied from 5 sec to 100 sec. After generating tissue data at Region 2 for flow values from 20 ml/1OO g/min to 80 ml/ lOO g/min, we calculated rCBF in Region 2 with the PET scan time fixed at 90 sec, 150 sec and 300 sec. 
The evaluation of the effect of the fixed distribution volume has been done. Tissue data in Region 2 were generated with a flow range from 1 to 100 ml/100 g/min with three different Vd Values: 0.85, 0.95 and 1.05. Scan frame time and scan time were fixed at 5 and 150 sec, respectively. 
To evaluate the effect of noise on PET data, the random noise in the +- 30% range was added to the tissue data for each second for Regions 1 and 2. The rCBF was calculated for Region 2 with a 10 sec frame time. 
The simulations were carried out on a workstation (SparcStation IPX; Sun Microsystems, Mountain View, CA, U.S.A.). 
PET studies 
In order to validate the method, a comparison between the present method and the dynamic/integral method6 was carried out with actual PET data. PET studies with Cl5O2 inhalation on 17 normal volunteers (age: 20-59, mean 40.8 +- 14) were performed. Data were acquired with an ECAT 931 -08/12 (CTI, Knoxville, TN, U.S.A.) positron emission scanner.10 
Before 2 min dynamic Cl5O2 scan, a transmission scan was performed with external 67Ge/68Ga ring sources for tissue attenuation correction purposes. Dynamic scans were collected by means of the following protocol: l (background) frame of 30s, 4 of 5s, and 16 of lOs. Subjects inhaled a constant supply of Cl5O2 for a period of 2 min beginning at the start of the second frame through a face mask. Arterial blood radioactivity was measured with an on-line detection system. Blood was withdrawn continuously through a radial artery cannula at a speed of 5 ml/min with polyethene tubing (length 65 cm from cannula to scintillation crystal) with an internal diameter of 1 mm and a wall thickness of 0.5 mm. For each study scanning started when all tubing components were filled with blood after blood had been withdrawn. Four minutes after the start of scanning, one 2 ml calibration sample was collected through a three-way tap positioned directly behind the BGO scintillator. Following the collection of this calibration sample, the whole-blood circuit (includ-ing the cannula) was flushed with heparinised saline. All emission scans were reconstructed with a Hanning filter with a cut-off frequency of 0.5 of maximum, which resulted in a spatial resolution of 8.4 x 8.3 x 6.6 mm full width at half-maximum at the center of the field of view. Io 
Image processing 
The reconstructed dynamic images were transferred to the SparcStation for image processing. 
Programs were developed which calculated rCBF by pixel-base for the two different methods-the present method and the dynamic/integral method. The steps in our method are as follows: 
Another set of rCBF images were calculated by the dynamic/integral method.6 Whole-brain ROIs were de-fined on planes 6 to 10 of the 15 planes of integrated images, created by summing counts of all frames over the 2 min inhalation period. By projecting these ROIs on the 21 dynamic frames and averaging over the 5 planes, the time activity curve of the whole-brain was generated. This curve was used to determine delay and dispersion of the arterial whole-blood curve.6 ArCBFvs Ct lookup table was generated by using the determined delay (d), disper-sion (p), and fixed Vd(0.95) as follows 5: 
where  denotes the operation of convolution, Tl is frame start time. T2 is frame end time and Cm(t) is the measured arterial curve. The rCBF images were generated by using this lookup table. 
RESULTS 
An evaluation was made of the effects of total scan time on the calculated rCBF. At shorter scan time calculated flows were overestimated when the flow value was lower than the flow in Region 1 (50 ml/lOO g/min) and underes-timated when flow value was higher than 50 ml/lOO gl min, but amounts of over- or underestimation were lower than 1 %, and rCBF values became asymptotic after a lO sec scan. These trends were similar for all flow values. 
The effects of the frame time are shown in Figure 3. As shown in Figure 3 errors were increased with longer scan frame time. In the case of 20 ml/1OO g/min (lower than the flow in Region l) calculated flows were overestimated. On the other hand, in the case of 80 ml/lOO g/min calculations were underestimated. When scan time was longer, the calculation gave a better estimation of flow less dependent on the scan frame time. For example at a 50 sec frame time, errors in calculation for flow 20 ml/1OO g/min were 16% (90 sec scan time), 1.7(~o (150 sec scan time) and O. 1% (300 sec scan time). 
The effect of the fixed distribution volume is shown in Figure 4. Figure 4 illustrates the rCBF errors due to incorrect distribution volume. The distribution volume of 0.85 generates singular values around 50 ml/lOO g/min (flow value in Region l), although appropriate agree-ments were obtained between true and calculated values at a lower flow level. With a higher flow, the calculated values tended to be higher than the true values (calculated values were 4.4% higher on average than true values at a flow level of 60 to 100 ml/100 g/min). A Iarger distribution volume, for example 1.05, underestimates the flow, especially in a higher flow region (1.O% underestimation of flow at 60-lOO ml/lOO g/min). Singular deviations were also found around 50 ml/1OO g/min.  
The noise effect has been examined in Figure 5. A higher noise level produced larger errors in the calculated values, as shown in Figure 5, but the longer scan time and lower flow regions were less dependent on noise. 
For each subject, the images obtained with both methods were compared by plotting rCBF values for regions of 4 x 4 pixels in all planes against each other. Regression curves and correlation coefficient were calculated for all studies and are shown in Table l. The mean value was calculated by averaging all individual pixels in all slices. In order to remove the pixels out of the brain from the calculation of mean value, the transmission images were used for masking the brain field. The mean value was slightly lower than the typical value, 50 ml/lOO g/min, because some pixels are outside of the brain. Figure 6 shows the mean CBF values calculated by both methods for all subjects. When data for pl644, p1657 and p183l were excluded, the correlation coefficient was 0.788, with a significant correlation between the two methods (paired t test p < 0.0005). 
DISCUSSION 
The present technique is based on weighted integration,s and has the following characteristics: 
¥ The method is noninvasive, requiring no arterial input function and hence corrections for dispersion and time delay. No arterial counting devices are necessary.
¥ The method produces pixel-by-pixel, functional images of rCBF with short calculation time. 
¥ The calculations proceed automatically without the operator's intervention. 
Once the feasibility of mapping human brain function by means of PET was established, numerous research designs were developed. The localization of cortical centers for the processing of stimuli such as tactile, visual, auditory, etc. was a prime focus, but since PET measurement studies require a relatively long time period to complete (in the order of minutes), the state of attention relative to habituation has became problematic. The subject's psychological state is often disturbed. Arterial blood sampling taken during PET studies can be stressful, so that it is often omitted and replaced by the standard input function; but this simplified method cannot give absolute flow changes before and after stimulation. The standard input function can be a good estimation of true individual input only when the time difference or time delay between the standard and brain curve is correctly known. Moreover, the difference in circulation time of H20 in large vessels in individual subjects easily distorts the profile of the arterial curve. This technique may therefore sometimes enhance the non-lineality of the PET count further. The present noninvasive procedure was developed to solve the above problems simultaneously and practically with the additional advantage of efficient, automatic calculation. 
The method presented in this paper is based on the weighted integration methods, which uses two types of PET data-one, decay-corrected and the other without decay-correction. The weighted integration method was originally utilized by Huang et al . 8 and Alpert et al . 11 Their purpose was to shorten calculation time while improving accuracy. Their techniques required arterial input function. Our report may therefore be the first that uses true, noninvasive CBF measurement with 15O-water. 
Gambhir et al.12 reported that CBF values derived by the integrated projection technique depended on scan time, implying that delay and dispersion were not taken into account in the measured arterial blood curve. Our technique is, in principle, free from these problems. According to our first simulation, the rCBF value did not depend on the PET scan time. Errors in calculation with a shorter scan time may be due to errors in numerical integrations caused by discrete data sampling. It is known that the trapezoidal rule of integration sometimes produces errors, especially in the ascendant phase of curve formation . 
This technique calculates rCBF in two regions simulta-neously, in which input functions in both regions are assumed to be the same. Region 1 was fixed at in certain area as a reference and the flow in Region 2 (each of the all pixels) was compared with that in Region 1 . One of the problems is the selection of the reference region. Because it is better to work with homogeneous tissue, such as gray matter, 10% maximum counts of the integrated image were selected. With this setting, the program can proceed automatically . Optimization of the selection of the referece region must be done. 
The assumption is that all brain tissue has the same distribution volume. As indicated in the simulation, this assumption leads to large errors, especially in the calculation of flow that is close to that of Region 1 . Subtractions as  in the denominatorin equations such as Eq. (15) may induce relatively larger errors from minor errors in Cf(t). This may explain the oscillation around the flow value of 50 ml/100 /min in Figure 4. 
In spite of the above problems, correlation between our method and the dynamic/integral method in PET studies was fairly good except for tree excluded data (Fig. 6). We have not found the differences between the three excluded data and others in Figure 6. Further studies will be required . 
The results of simulations revealed that a shorter scan frame time could reduce errors in calculation, but by a choosing longer scan time this error can be canceled. By limiting the injected dose as well as limiting the sensitivity of the PET scanner, it is possible to select an optimum scan time and scan intervals to make possible precise measurement of rCBF. 
In conclusion, this procedure proposes a new solution for rCBF calculation by using 15O-water injection. The method is noninvasive since no blood sampling is required. The calculation is relatively simple and can generate the rCBF image quickly on completion of PET scans. 
APPENDIX 
The model applied the single compartment model originally developed by Kety,9 in which the differential equation for the tissue radioactive concentration and arterial input function as follows: 
(Note: Where Ct(t) and Cu(t) reflect the tissue radioactive concentration values at time t in the brain and arterial blood respectively, f is the regional cerebral blood flow, Vd is the distribution volume of water and  is the physical decay constant for 15O-half life is 122 sec). Another differential equation for the decay-corrected data is: 
the data with the superscripted asterisks are decay corrected. Choosing any 2 regions called Regions 1 and 2 in the brain, Eq. (1) and (2) can be applied to Region 1 or Region 2, as follows: 
The data with the subscripted numbers are from the specified regions. It is reasonable to assume that the input function Cu(t) was the same for all brain regions, and the distribution volume Vd may be fixed for every pixel at 0.95 ml/g. 6 Thus, two time integrations of the four equations above, during time O to T yield: 
From Eq (11) and Eq (12), flow f1 and f2 for Regions l and 2, respectively, can be rewritten: 
With positron tomography, the counts are the integrals   Samplingthedatawithoutdecay correction, the decay corrections were carried out numerically on reconstracted images. The double integrations  Cf and  Cf were calculated by means of the numerical integrations by applying the trapezoidal rule. For the actual calculation, Region 1 (reference region) was selected as 10% of the maximum value for integrated images. By taking each of the brain pixels as those for Region 2, the flows for Region I were obtained by Eq. (13). The actual rCBF value for Region 1 was estimated by averaging these values for each pixel . Then the flow for each pixel (p) was calculated from the following equation derived from Eq. (12). 
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