Noninvasive Quantification of rCBF Using Positron Emission Tomography

Journal of Cerebral Blood Flow and Metabolism 16:311-319 © 1996 The International Society of Cerebral Blood Flow and Metabolism Published by Lippincott-Raven Publishers, Philadelphia

Noninvasive Quantification of rCBF Using Positron Emission Tomography

H. Watabe, M. Itoh, *V. Cunningham, *A. A. Lammertsma, *P. Bloomfield, M. Mejia, T. Fujiwara, tAo K. P. Jones, *T. Jones, and T. Nakamura

Cyclotron and Radioisotope Center, Tohoku University, Sendai, Japan, *MRC Cyclotron Unit,

Hammersmith Hospital, London, and tRheumatic Diseases Centre, Hope Hospital, Manchester, England

Summary: This study proposes a new method for the pixel-by-pixel quantification of regional CBF (rCBF) with positron emission tomography and Hi50 by using a ref­erence tissue region, No arterial blood is required. Sim­ulation studies revealed that the calculation of rCBF was fairly stable provided that the frame time was relatively short compared with total scan time. In practice, calcu-

Several methods for the measurement of regional CBF (rCBF) using H�50 and positron emission to­mography (PET) have been described. These in­clude steady-state (Frackowiak et aI., 1980), weighted integration (Huang et aI., 1982, 1983; Alp­ert et aI., 1984), autoradiographic (Raichle et aI., 1983; Kanno et aI., 1984), buildup (Lammertsma et aI., 1989), and dynamic/integral techniques (Lam­mertsma et aI., 1990). These methods require arte­rial blood sampling to obtain absolute blood flow values. To measure the time course of the radioac­tivity concentration in arterial blood accurately, an external detection device is required. However, this measurement should take into account delay and dispersion of the measured blood curve relative to the brain data (Iida et aI., 1986). The total amount of blood withdrawn, which can amount to 100-200 ml for a study of several runs, is not small. The present study proposes a new numerical solution for the calculation of rCBF. The method uses time-activity curves of two different brain regions and has the following characteristics:

Received January 20, 1995; final revision received June 20, 1995; accepted June 20, 1995.

Address correspondence and reprint requests to Dr. H. Watabe at National Cardiovascular Center, Osaka, Japan.

Abbreviations used: PET, positron emission tomography; ROls, regions of interest; BGO, Bi4Ge3012.

311

lated CBF images correlated significantly with those ob­tained with the dynamic/integral method. Because the method accurately detects changes in CBF, it is particu­larly suitable for brain activation studies. Key Words: Re­gional cerebral blood flow-Positron emission tomogra­phy-Noninvasive quantification.

• The method is noninvasive, requiring no arterial input function and, hence, no corrections for dis­persion and time delay are required. More impor­tantly, no arterial cannulation is needed.

• The method produces pixel-by-pixel, functional images of rCBF with short calculation times.

• The calculations proceed automatically without operator's intervention.

The results of simulation and PET studies are presented as well as the theory. The present tech­nique is related to the technique developed by Mejia et ai. (1994), which corrects the nonlinearity of CBF and produces the relative CBF image.

THEORY The method is based on the single compartment

model originally developed by Kety ( 195 1), in which the differential equation between tissue ra­dioactivity concentration and arterial input function can be described as follows:

( 1)

where Clt) and Ca(t) reflect the tissue radioactive concentration values at time t in the brain and ar­terial blood, respectively, f is the rCBF, and V d is

312 W. WATABE ET AL.

the distribution volume of water. Both Cit) and Ca(t) are decay corrected.

Choosing any two regions called Regions 1 and 2 in the brain, Eq. 1 can be described for both regions as:

dCdt) h -d - = fzCa(t) - -

V Ct2(t) (3)

t d2

where the subscripts denote the respective regions. It is assumed that the input functions Ca(t) is the same for all brain regions.

Integrating both Eqs. 2 and 3 twice from time 0 to T results in

II fcT fcl - -

V dt CII(s)ds

dl 0 0

12 fcT fcl - - dt Cds)ds

Vd2 0 0

(4)

(5)

where T is the time of the last frame for PET scan. The arterial input function C a can be eliminaed

from Eqs. 4 and 5:

[T II [T Jo CII(t)dt = h. Jo Cdt)dt

II fcT fcl + -V

dt Cds)ds d2 0 0

II fcT fcl - -

V dt Ctl(s)ds

dl 0 0 (6)

For a PET scan with n frames, n data sets for Eq. 6 are obtained:

II [T, [I } - Vdl Jo dt Jo CII(s)ds i=I ... n (7)

To calculate CBF on a pixel-by-pixel basis, a two­step computational strategy was developed. In the first step, the whole brain was defined as Region 1

J Cereb Blood Flow Metab, Vol . 16, No.2, 1996

and all pixels within 10% of the maximum counts as Region 2. The integrated image from time zero to T was created and made the histogram for distribution of pixel counts. Pixels within 10% of the maximum counts were defined as the pixels being in the higher 10% of the histogram. Using the corresponding time-activity curves, whole-brain CBF if!) and dis­tribution volume of water (Val)' together withI2 for Region 2 were fitted using standard non-linear re­gression techniques. To reduce the number of pa­rameters, the distribution volume of water for Re­gion 2 (V d2) was fixed to 0.86 ml/ml (Lammertsma et al., 1992).

In the second step,jl and Vd1 were fixed to these fitted values and each pixel was, in turn, used for Region 2. For each pixel 12 was calculated accord­ing to

JoT

CaCt)dt

h = ------------------------------

- I� [T Ctl(t)dt + -vi [T dt

[I CI1(s)ds -IJO dl Jo Jo

I fcT fcl -V

dt CaCs)ds d2 0 0

(8)

which can be derived from Eq. 6. In this calcula­tion, V d2 was also fixed to 0.86 mllml.

MATERIAL AND METHODS Simulations

To evaluate the accuracy and limitations of the method, computer simulations were performed to examine (a) the effects of the total study duration, (b) the effects of single­frame duration, (c) the effects of noise, (d) the effects of flow in Region 2, (e) the effects of an incorrect assumed distribution volume (V d) ' and (D the effects of heteroge­neity of gray and white matter.

U sing the following equation, tissue time-activity curves [C,(T)] of Region I and Region 2 were generated:

-(LH)T T (LH)I CI(T;) = exp Vd ' • I' fo ' Ca(t) . exp Vd dt

(9)

where Ca(t) is an arbitrary measured arterial input function. In these simulations, two typical input curves were used, one for a 2-min inhalation of C

l502 (Input 1) and one of a I-min infusion of H�50 (Input 2) (Fig. 1).

In each simulation, flows of Regions 1 and 2 and Vd of Region 1 were estimated using Eq. 7 and stan­dard non-linear regression analysis.

The simulations were carried out on a worksta­tion (SparcStation IPX; Sun Microsystems, Moun­tain View, CA, U.S.A.).

NONINVASIVE QUANTIFICATION OF rCBF WITH PET 313

0.40

"8 0- 0.30 :ll

0.20

0.10

0.00 0.0

.�--'-----�- .. -�---." .... -. -.� 1.0 2.0 3.0

Time (min)

FIG. 1. Input functions of Input 1 (2-min C1502 inhalation study, solid line) and Input 2 (1 min H�50 infusion study, dotted line). These curves were used in the simulation stud­ies. The tissue response curves for Regions 1 and 2 were calculated with these input functions.

PET studies To validate the method, a comparison between the

present method and dynamic/integral method (Lam­mertsma et aI., 1990) were carried out with actual PET data. PET studies with C I502 inhalation on 17 normal volunteers (ages: 20-59, mean 40.8 ± 14) were per­formed. Data were acquired using an ECA T 93 \ -08/12 (CT!, Knoxville, TN, U.S.A.) positron emission tomo­graph (Spinks et aI., \988).

Before a 2-min dynamic C I502 scan, a transmission scan was performed using external 67Ge/68Ga ring sources for tissue attenuation correction purposes. Dynamic scans were collected using the following protocol: \ (background) frame of 30 s, 4 of 5 s, and 16 of 10 s. Subjects inhaled a constant supply of C I502 for 2 min beginning at the start of the second frame. Arterial blood radioactivity was measured using an on-line detection system. Blood was withdrawn continuously through a ra­dial artery cannule at a speed of 5 mllmin using 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, blood withdrawal was started first and scanning commenced when all tub­ing components were filled with blood. Four minutes af­ter start of scanning, one 2-ml calibration sample was collected through a three-way tap positioned directly be­hind the BGO scintillator. After the collection of this cal­ibration sample, the whole-blood circuit (including can­nula) was flushed with heparinized saline.

All emission scans were reconstructed using a Hanning filter with a cutoff 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 (Spinks et aI., 1988). Image processing

The reconstructed dynamic images were transferred to a SparcStation IPX (Sun Microsystems, Mountain View, CA, U.S.A.) for image processing. Whole-brain regions of interest (ROIs) were defined on planes 6-10 of the 15 planes of integrated images, created by summing counts of all frames during the 2-min inhalation period. By pro-

jecting these ROIs on the 21 dynamic frames and averag­ing over the 5 planes, the time-activity curve of the whole brain was generated. This time-activity curve was used for both methods. For the present method, these data were used directly in the process of fitting of Eq. 7. For the dynamic/integral method, this curve was used to de­termine delay and dispersion of the arterial whole-blood curve (Lammertsma et aI., 1990).

A computer program was developed for the pixel-by­pixel calculation of rCBF using the present method. The procedure steps were as follows.

1. To fit for II' V dl J2 in Eq. 7 and to calculate rCBF for each pixel using Eq. 8, single and double integrals, i.e., J C" J J C, were calculated numerically. Sampling the data without on-line decay correction, data were numer­ically corrected for decay using the reconstructed images of each frame. The double integration J J C, for each pixel was calculated numerically using the trapezoidal rule.

2. Pixels within 10% of the highest value in the inte­grated images were determined and averaged to create the time activity curves in the (Region 2) (Ct2). 3. Using Eq. 7, best estimates for the three parameters II' V dl' 12 were obtained by fitting.

4. Fixingil and Vdl to the values obtained in step 3,f2 was calculated for each pixel using Eq. 8.

Another set of rCBF images was calculated by the dy­namic/integral method (Lammertsma et aI., 1990) to com­pare with the present method.

RESULTS Simulations

An evaluation was made of the effects of total scan time on the calculated rCBF. Sequential tissue data were generated for Regions 1 and 2 using 5-s frames and total study duration up to 300 s. CBF was assumed to be 50 mlldl/min in Region 1 and 100 mlldllmin in Region 2 with corresponding Vd values of 0.6 ml/ml and 0.86 mllml, respectively (0.6 mllml for Region 1 was chosen because of the tissue het­erogeneity. It will be examined at the last simula­tion study). Using these tissue data,jl' Vdl, andI2 were estimated. Figure 2 illustrates that CBF of Re­

gions I and 2 were generally overestimated, whereas V d of Region 1 was underestimated when the study time was shortened. However, the estimation of Vd was more stable than that of CBF. Although the general pattern was the same, for Input 1 (C1502 inhalation) a shorter study duration was required than for Input 2 (Hi50 infusion). For Input 1 the error in II was <5% after only 75 s, whereas for Input 2 a study duration of 110 s was required.

The effects of frame duration are shown in Figure 3. The frame time was varied from 1 to 30 s. Tissue curves for a total scan duration of 120 s were gen­erated for Regions 1 and2 using the same parameter values as for the previous simulation. As shown in Fig. 3, errors in estimated CBF values increased with increasing frame time. The estimations of Vdl were more independent of frame time than the es-

J Cereb Blood Flow Metab. Vol. 16. No.2. 1996

314 W. WATABE ET AL.

100.0 nr 80.0 1\

60.0 \ \ 1\ 40 0

\ \ I \ 20 0 1 \ � \�

i�: 1 1 . .. �-- I � 100.0 I I �-+--.1 � 80.0 � II

E r II

� :: [t\/f\� \ I

g I v \ w 20.0 � \ "#. "'-

oo f �

'20.0 I -40.0 L � --... � .. �C-::C:-=----�--:-�C":-::-�:-C:-:-

0.0 40.0 80.0 120.0 160.0 200.0 240.0 280.0 Scan time (sec)

FIG. 2. The effects of total study duration on the calculations of rCBF. The upper graph shows the results for Input 1, and the lower graph those for Input 2. Percentage of error in estimated CBF for Region 1 (solid line), estimated Vd for Re­gion 1 (dotted line) and estimated CBF for Region 2 (dashed line) are plotted against study duration with a fixed frame length of 5 s.

timations of CBF. For Input 2, a stronger influence of frame time was observed. According to these results, a frame length of 9 s was required for Input

1 to reduce the error to <5%, whereas for Input 2 a frame length of 6 s is required.

Random noise with a variance of up to 30% was added to every point of the tissue curves for Re­gions 1 (flow: 50 ml/dllmin, Vd: 0.6 mllml) and 2 (flow: 100 ml/dllmin, Vd: 0.86 mllml). The rCBF for Regions 1 and 2 and V d for Region 1 were calculated with 5-s frame, 120-s study duration. These simula­tions were carried out 100 times with different ran­dom noise and the data obtained were averaged. Higher noise levels produced larger errors in the calculated values as shown in Fig. 4. Calculations of V dl were more stable with respect to noise in the PET data than the calculations of CBF. Again, In­put 1 resulted in smaller errors than Input 2.

To evaluate the relationship between flow at Re­gion 1 and flow at Region 2, tissue data were gen­erated for Region 1 (flow 50 mlldllmin, Vd: 0.6 mIl ml) and Region 2 (Vd: 0.86 ml/ml). Flow of Region 2 was varied from 60 to 120 mlldl/min. Figure 5 indicates that as flow of Region 2 approached that of Region 1, there was a slight increase in the esti-

J Cereb Blood Flow Metab, Vol. l6, No.2, 1996

mation of CBF. Tendencies for estimated flow and Vd between Input 1 and Input 2 are similar for Input 1 and Input 2.

The effect of the fixed distribution volume in Re­gion 2 is illustrated in Fig. 6. Tissue data for Region 2 were generated with a flow of 100 ml/dllmin and a Vd ranging from 0.69 to 1.03 mllml. Tissue data for Region 1 were the same as before. Frame and study duration were fixed at 5 and 120 s, respectively. Vd for Region 2 was fixed to 0.86 ml/ml in the fitting process. Figure 6 illustrates the errors obtained due to this incorrect assumed distribution volume. If ac­tual V d was smaller than 0.86 mllml, estimated flows and V dl were overestimated. The opposite was true for larger actual V dS, although the effect of a smaller Vd was more pronounced in absolute terms.

To assess the effects of tissue heterogeneity, tis­sue data of gray matter (CBF = 80 ml/dllmin; Vd =

1.02 mllml) and white matter (CBF = 20 ml/dllmin; V d = 0.88 ml/ml) were generated. The tissue time­activity curves of Region 1 with different fractions of gray and white matter were created using weighted averages of the stimulated gray and white matter curves. The tissue data of Region 2 were also generated as CBF = 100 mlldl/min; Vd = 0.86 mllml). Study and frame duration were fixed to 120

100.0 I 80.0 e

60.0

40.0

20.0

"if. 100.0

-50.0 L � __ �_' 0.0 5.0 10.0 15.0 20.0 25.0 30.0

Frame duration (sec)

FIG. 3. The effects of frame duration on the calculation of rCBF and Vd. The upper graph shows the results for Input 1, and the lower graph those of Input 2. Percentage error in estimated CBF at Region 1 (solid line), estimated Vd for Re­gion 1 (dotted line) and estimated CBF at Region 2 (dashed line) are plotted as a function of frame duration.

NONINVASIVE QUANTIFICATION OF rCBF WITH PET 315

100.0 r--�-- �� .. � .. -. �-------,

� "0 c OS

80.0

I 60.0

40.0

20.0

0.0

� 100.0 r----+----+-�----+--�--+--�-+-�---+-�_____________! () "0 -¥J 80.0

E ti II> 60.0 � '0 I g 40.0 W

20.0

, r '

� �

-2::: ,::--�----="::-------+--:-----,'-c---�--�--�J 0.0 5.0 10.0 15.0 20.0 25.0 30.0

% Error in PET data

FIG. 4. Simulation of errors due to statistical noise. Random noise with a variance of 1-30% was added to tissue counts. The upper graph shows the results for Input 1, and the lower graph for Input 2. Percentage errors of estimated CBF for Region 1 (solid line), estimated Vd for Region 1 (dotted line), and estimated CBF for Region 2 (dashed line) are plotted against noise level.

and 5 s, respectively. Figure 7 demonstrates the effect of tissue heterogeneity on estimated values of flows and V dl' It can be seen that all fitted values were underestimated. Estimations of flows were af­fected more by tissue heterogeneity than by V dl'

PET studies To validate the present method, it was compared

with the dynamic/integral method (Lammertsma et aI., 1990) on the same subjects.

Figure 8 presents examples of functional CBF im­ages obtained with both methods together with the corresponding summed images. The images ob­tained with the present method were very similar to those obtained with the dynamic/integral method, and the contrast of both sets of images was en­hanced compared with the summed images.

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. One example of such a plot is shown in Fig. 9. Regression curves and correlation coefficient were calculated for all studies and are shown in Table 1. The mean value was calculated by averag­ing over all individual pixels in all slices. The mean

value was slightly low because some pixels were outside the brain. Figure 10 shows the mean CBF values calculated by both methods for all subjects. To get rid of pixels outside of the brain, the trans­mission images were used for masking the brain field. The correlation coefficient was 0.749, with a significant correlation between two methods (paired t test, p < 0.0005).

DISCUSSION

Once the feasibility of mapping human brain function with PET and H�50 was established, nu­merous research protocols were developed. How­ever, because PET measurements are relatively long, the state of attention relative to habituation has become a point of concern. The subject's psy­chological state is often disturbed. In particularly, the presence of an arterial cannula can be a source of unwanted stimulation. Therefore, often activa­tion studies with PET are carried out without arte­rial sampling. However, this procedure cannot give absolute flow values before and after stimulation. The present noninvasive technique was developed to provide quantitative functional CBF pixel-by-

MI l 3.0, I . I

i-------�-�- - - -.�-'--===--==-- - -I 10 I ,

-1.0 r � I � 5 0 �� ----+- --+1------+-----1 "0 I �-

� 3.0

Ii

----=--� - - - .- -

.� II>

'0 g 1.0 W '#-

-1.0

-3.0 L......_� __ ____+_ _____ � __ �_ 60.0 80.0 100.0 120.0

Flow of Region 2 (ml/dl/min) FIG. 5. The effects of rCBF of Region 2. The upper graph shows the results for Input 1 , and the lower graph those for Input 2. Percentage error of estimated CBF for Region 1 (solid line), estimated Vd for Region 1 (dotted line), and esti­mated CBF for Region 2 (dashed line) are plotted against flow value of Region 2.

J Cereb Blood Flow Me/ab, Vol. 16, No.2, 1996

316 W. WATABE ET AL.

75.0 F��------ -----�---,

50.0 f

25.0 ��-__ i - - �-� I �

0 0 � !

I

-25.0 L ____ c _____ __ �_ ____��� �-��1 � M M 1�

Actual Vd value of Region 2 FIG. 6. Errors due to incorrect distribution volume. The up­per graph shows the results for Input 1, and the lower graph those for Input 2. Percentage error of estimated CBF for Re­gion 1 (solid line), estimated Vd for Region 1 (dotted line) and estimated CBF for Region 2 (dashed line) are plotted against actual distribution volume value of Region 2.

pixel maps without arterial sampling. This tech­nique calculates rCBF at two regions simulta­neously, assuming the input function to both re­gions to be the same and difference in arrival to be relatively small (lid a et aI., 1988).

The main weakness of the proposed method is that it relies on PET data of two regions simulta­neously. Inaccuracies in both regions will affect the final result. In particular, for Region 2 V d is as­sumed to be 0.86 mllml. From Figure 6 it follows that potentially large errors may result if the actual value of V d is very different. However, a large vari­ation in V d for this region is unlikely. Lammertsma et al. ( 1992) found for a similar region a coefficient of variation was <5% (n = 12). If the CBF value for Region 2 is too close to that for Region 1, the error sensitivity will increase (Figure 5). Again, by choos­ing a whole brain ROI and an ROI containing only the maximum 10% of the pixel values, this situation is unlikely in practice. The present method is also affected by tissue heterogeneity. It is interest to note, however, that in contrast to the dynamic! integral method (Lammertsma et aI., 1990), in the present method there was no difference in effect of tissue heterogeneity between flow and Vd (Fig. 7).

J Cereb Blood Flow Metab, Vol. 16, No.2, 1996

The model that uses fixed Vd for Region 1 had been applied to calculate flow of Region 1 in Eq. 6, and the results obtained were not as good as in the present method because of the tissue heterogeneity. In the current implementation, the whole brain was used for Region 1 and all pixels that were within 10% of the maximum integrated count for Region 2. Further studies will be required to optimize the se­lection of Regions 1 and 2.

According to the results shown in Figs. 2 and 3, both a too-short total study duration or a too-long frame time resulted in significant errors, probably due to numerical errors related to integration over discrete data points. There is the alternative method of integration to solve Eq. 6, namely, integrating over each of the n scan frames rather than integrat­ing from 0 time to the end of the nth scan frame. Since the early frames after injection of 150 may contain errors due to low counts of the PET detec­tor, the integration was carried out from 0 time to the end of the nth scan frame. To reduce such nu­merical errors, it is desirable to select shorter frame times and a longer total study duration. However, as shown in Fig. 5, noise propagation errors should

� � c ttl LL (D ()

� ttl E � Q) '0

10.0 -. --

0.0

-10.0

\ \

\

'''''"'''--...:.----------

.-.--- ---- .��

I / ./

/ �./

./ ./

//'1 / 1 //

10.0 '-, ---+---�--+------<-�--+---�__1

0.0

-10.0

-20.0 -_. 0.0 20.0 40.0 60.0

% of Gray Matter 80.0 100.0

FIG. 7. The effects of tissue heterogeneity in Region 1 for different fractions of gray matter on estimations of flow and distribution volume. The upper graph shows the results for Input 1, and the lower graph those for Input 2. Percentage error of estimated CBF for Region 1 (solid line) estimated Vd for Region 1 (dotted line) and estimated CBF for Region 2 (dashed line) are plotted against percentage of gray matter.

FIG. 8. First row depicts summed images (from 2 to 15 frames) of 2-min C1502 inhala­tion study of normal volunteer. Second row is functional rCBF images calculated by the dynamic/integral method. Third row depicts functional rCBF images calculated by the present method.

also be taken into account. These errors become more pronounced for shorter time frames. Further studies will be required to select the optimal frame duration, taking into account the two effects al­ready mentioned.

The simulation studies that are shown in this ar­ticle only evaluate the relationship between Region

1 and Region 2. In practice, one is more interested in the flows in individual pixels obtained by Eq. 8 rather than the values obtained for flow in these reference regions. As shown in Table 1 and Fig. 9, the correlation coefficient is fairly good (most are 1) between our method and the dynamic/integral method, which suggests that the process to calcu­late each pixel's flow associated with Eq. 8 is equiv­alent to the process of the dynamic/integral method.

80.0 � � ii i [ SO.O

� I �

i 40.0 !: � /

20.0 /' // /

,/ 0.0 0.0 20.0 40.0 SO.O 80.0 100.0 rCBF (mI/dlImin) by dynamic/integral method

FIG. 9. Comparison of rCBF values calculated by the dy­namic/integral method (abscissa) and the present method (ordinate). Each plotted point represents 4 x 4 pixels.

50.01

i � ' f � ! ."

i � 30.0 � I � • � 20.0 l

1 0 .o L����------=-c'-::����· 10.0 20.0 30.0 40.0 50.0 rCBF (mWl/mln) by dynamic/integral method

FIG. 10. Comparisons of mean rCBF values of 17 subjects calculated by the dynamic/integral method (abscissa) and the present method (ordinate) with a regression curve. The dotted line is the line of identity.

FIG. 11. Error surface image generated by simulation data.

318 W. WATABE ET AL.

TABLE 1. Comparison of two methods

Run no. Mean" Meanb Corr. coef. Slope Intercept

p1414 26.8 27.7 1.00 1.04 -0.119 p1474 28.7 26.3 1.00 0.909 0.167 pl597 24.9 24.8 1.00 0.985 0.0061 p1634 29.3 28.3 1.00 0.958 0.275 p1639 25.7 26.7 1.00 1.05 -0.128 pl644 36.7 28.0 1.00 0.745 0.659 pl657 33.1 27.2 1.00 0.808 0.470 p1672 26.9 30.9 1.00 1.16 -0.384 pl770 23.4 25.2 1.00 1.08 -0.172 pl803 22.5 22.8 1.00 1.01 -0.0867 pl831 37.8 33.0 1.00 0.861 0.449 p1852 24.5 25.8 1.00 1.06 -0.108 p1865 25.2 25.0 1.00 0.990 0.0144 pl949 27.7 26.9 1.00 0.969 0.0308 p2018 35.3 35.4 1.00 1.00 -0.0098 p2037 33.1 34.8 1.00 1.06 -0.159 p2122 33.4 29.5 1.00 0.875 0.319

Average 29.1 28.1 1.00 0.974 0.0720 SD 4.8 3.6 1 x 10-4 0.107 0.277

a Mean CBF value (ml/dl/min) of whole brain image by dy-namic/integral method.

b Mean CBF value (ml/dl/min) of whole brain image by the present method.

The simulation studies which evaluate Eq. 8 and the relative relationship between flows in Region 1 and Region 2 have been carried out by Mejia et al. (1994).

The main problem of the present method is shown in Fig. I I . This error surface was created as follows.

U sing simulated tissue data (frame and total study duration were 5 and 120 s, respectively) of Region 1 (CBF = 50 ml/ml/min; Vd = 0.6 ml/ml) and Region 2 (CBF = 100 ml/ml/min; Vd = 0.86 mllml), sums of squares of the right side of Eq. 7 were calculated for different combinations of fl and

f2.fl was varied from 30 to 70 dIlmIlmin andf2 from 80 to 120 dllml/min. Results were plotted as an im­age with highest pixel value for the lowest sums of squares. This error surface image demonstrates that, although there is a solution at the center ([I =

50 dl/mllmin;f2 = 100 dIlml/min, the brightest point in the image), the error surface broadens from low­flow to high-flow area, that is, this solution is very near to singular. The error surface is somewhat shallow when noise is added within the actual PET data; local minima could give rise to solutions that are dependent on the starting values in the fitting routine. The disagreement between the two meth­ods in the high-flow study in Fig. 10 may represent this problem. It is important that the scanning pro­tocol be optimized (see previous discussion) to ob­tain better-defined solutions. In addition to frame duration and selection of reference region, attention

J Cereb Blood Flow Metab, Vol. 16, No.2, 1996

should be paid to the input function. From the sim­ulation it follows that a 2-min administration period performs better than a I-min period. Again, this needs to be further optimized.

Despite the problems already discussed, in prac­tice, good results were obtained. In particular, the intra- and inter-subject correlations with the dy­namic/integral method (Figs. 9 and 10) are promis­ing and warrant further investigation of the method.

The major advantage of the proposed new tech­nique is that it does not require blood sampling. In addition, the calculation is relatively simple and can generate rCBF images quickly after completion of the PET scans.

REFERENCES

Alpert NM, Eriksson L, Chang JY, Bergstrom M, Litton JE, Correia JA, Bohm C, Ackerman RH, Taveras JM (1984) Strategy for the measurement of regional cerebral blood flow using short-lived tracers and emission tomography. J Cereb Blood Flow Metab 4:28-34

Frackowiak RSJ, Lenzi GL, Jones T, Heather JD (1980) Quan­titative measurement of regional cerebral blood flow and oxygen metabolism in man using 150 and positron emission tomography: theory, procedure, and normal values. J Com­put Assist Tomogr 4:727-736

Huang SC, Carson RE, Phelps ME (1982) Measurement of local blood flow and distribution volume with short-lived iso­topes: A general input technique. J Cereb Blood Flow Metab 2:99-108

Huang SC, Carson RE, Hoffman EJ, Carson J, MacDonald N, Barrio JR, Phelps ME (1983) Quantitative measurement of local cerebral blood flow in humans by positron computed tomography and 150-water. J Cereb Blood Flow Metab 3: 141-153

Iida H, Kanno I, Miura S, Murakami M, Takahashi K, Uemura K (1986) Error analysis of a quantitative cerebral blood flow measurement using HJ50 autoradiography and positron emission tomography, with respect to the dispersion of the input function. J Cereb Blood Flow Metab 6:536--545

Iida H, Higano S, Tomura N, Shishdo F, Kanno I, Miura S, Murakami M, Takahashi K, Sasaki H, Uemura K (1988) Evaluation of regional differences of tracer appearance time in cerebral tissues using C50]water and dynamic positron emission tomography. J Cereb Blood Flow Metab 8:285-288

Kanno I, Lammertsma AA, Heather JD, Gibbs JM, Rhodes CG, Clark JC, Jones T (1984) Measurement of cerebral blood flow using bolus inhalation of CI502 and positron emission tomography: description of the method and its comparison with the CI502 continuous inhalation method. J Cereb Blood Flow Metab 4:224-234

Kety SS (1951) The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacal Rev 3: 1-41

Lammertsma AA, Frackowiak RSJ, Hoffman JM, Huang SC, Weinberg IN, Dahlbom M, MacDonald NS, Hoffman EJ, Mazziotta JC, Heather JD, Forse GR, Phelps ME, Jones T (1989) The CI502 build-up technique to measure regional cerebral blood flow and volume of distribution of water. J Cereb Blood Flow Metab 9:461-470

Lammertsma AA, Cunningham VJ, Deiber MP, Heather JD, Bloomfield PM, Nutt J, Frackowiak RSJ, Jones T (1990)

NONINVASIVE QUANTIFICATION OF rCBF WITH PET 319

Combination of dynamic and integral methods for generating reproducible functional CBF images. J Cereb Blood Flow Metab 10:675--686

Lammertsma AA, Martin AJ, Friston KJ, Jones T (1992) In vivo measurement of the volume of distribution of water in cere­bral grey matter: effects on the calculation of regional cere­bral blood flow. J Cereb Blood Flow Metab 12:291-295

Mejia MA, Itoh M, Watabe H, Fujiwara T, Nakamura T (1994) Simplified non-linearity correction of oxygen-15-water re-

gional cerebral blood flow images without blood sampling. J Nucl Med 35: 1870-1877

Raichle ME, Martin WRW, Herscovitch P, Mintun MA, Markham J (1983) Brain blood flow measured with intrave­nous Hi'O. II. Implementation and validation. J Nucl Med 29:241-247

Spinks TJ, Jones T, Gilardi MC, Heather JD (1988) Physical performance of the latest generation of commercial positron scanner. IEEE Trans Nucl Sci NS35:72I-725

J Cereb Blood Flow Metab, Vol. 16, No. 2, 1996