blood flow, fractional oxygen extraction, and oxygen uti lisation. These last two ... higher than those reported using arteriovenous difference techniques.
Journal of Cerebral Blood Flow and Metabolism 3:416-424 © 983 Raven Press, New York
1
Correction for the Presence of Intravascular Oxygen-15 in the Steady-State Technique for Measuring Regional Oxygen Extraction Ratio in the Brain: 1. Description of the Method
Adriaan A. Lammertsma and Terry Jones MRC Cyclotron Unit, Hammersmith Hospital, London, England
Summary: The oxygen-I5 steady-state inhalation tech
for this intravascular component utilising a measurement
nique provides quantitative values of regional cerebral
of regional cerebral blood volume. The statistical penalty
imposed as a result of this correction is defined. Key
blood flow, fractional oxygen extraction, and oxygen uti lisation. These last two, however, have been found to be
Words: Oxygen-I5 steady-state model-Positron emis
higher than those reported using arteriovenous difference
sion tomography-Regional cerebral blood flow-Re
techniques. On theoretical grounds, this overestimation
gional cerebral blood volume-Regional cerebral oxygen
is due to the signal from nonextracted intravascular ox
extraction ratio-Regional cerebral oxygen utilisation.
ygen-I5. In this paper, a method is presented to correct
pIing (Frackowiak et aI. , 1980b; Baron et aI. , 1981c). Lammertsma et ai. (1981a) have shown that, on theoretical grounds, an overestimation oc curs due to the signal from non extracted haemo globin-bound oxygen-IS in the 15 02 scan. In the steady-state model this intravascular component is assumed to be negligible. However, if rOER and/or rCBF are low, the tissue signal arising from the gen eration of labelled metabolic water is small, and the contribution of the vascular, unextracted activity becomes important. A correction for this back ground vascular signal requires an additional mea surement of regional cerebral blood volume (rCBV) (Lammertsma et aI. , 198Ia). This article develops the theory of this correc tion, a model of the influence of background signals from both arterial and venous blood, and the statis tical properties of the correction.
Positron emission tomography (PET) permits the absolute measurement of the distribution of posi tron-emitting radionuclides within the human body. This has been used to measure regional cerebral oxygen-IS concentration while a subject continu ously inhales tracer amounts of oxygen-IS-labelled carbon dioxide and molecular oxygen. From this data it has been possible to obtain measurements of regional cerebral blood flow (rCBF), oxygen ex traction ratio (rOER; the fraction of oxygen ex tracted from the arterial blood), and oxygen utili sation (rCMR02). This technique has been used to study both normal brains and cerebral disease (Frackowiak et aI. , 1980a, 1981; Ackerman et aI. , 1981; Baron et aI. , 1981a,b; Ito et aI. , 1982; Lenzi et aI. , 1982; Wise et aI. , 1983). The reported absolute values for normal rOER (and therefore for normal rCMR02) are, however, higher than those obtained with arteriovenous sam-
OXYGEN-IS STEADY-STATE MODEL Address correspondence and reprint requests to Dr. Lam
rOER is calculated from two separate scans. The first is obtained during the continuous inhalation of C1502, and the second during 1502 inhalation (Frac kowiak et aI. , 1980a). In the simplified model used for clinical studies it is assumed that the tissue/blood partition coeffi-
mertsma at MRC Cyclotron Unit, Hammersmith Hospital, Du cane Road, London Wl2 OHS, England. Abbreviations used: PET, Positron emission tomography; rCBF, regional cerebral blood flow; rCBV, regional cerebral blood volume; rCMR02, regional cerebral oxygen utilisation; rOER, regional oxygen extraction ratio (fraction of oxygen ex tracted from arterial blood).
416
417
rCBV CORRECTION IN 150 STEADY-STATE TECHNIQUE: METHOD
cient of water and the extraction fraction of water
Nonexchanging tissue (bone or cerebrospinal
are unity. Although both assumptions are not com
fluid space) is excluded, and the small capillary
pletely true,errors from these simplifications,when
blood volume is assumed to be distributed over the
applied to the human brain,are small (Lammertsma
arterial and venous compartments. This article de
et a!., 1981a).
fines the extended form of the tracer model, which
During inhalation of C1502, the 150 label is rap
describes the influence of the vascular compart
idly transferred in the lungs to H21S0 (West and
ments and how they may be accounted for in the
Dollery, 1962). This results in a continuous arterial
calculation of rOER and rCBF. The volume of distribution for extracted water
supply of H2150. In the steady-state model, if blood
(Vd) is now given by
volume is neglected, the activity Aw in a volume V of cerebral tissue will be given by
Aw =
CF' F'I
;+
(4) (1)
'A
Therefore, in the case of CI502 inhalation, the activity Aw in a volume V is actually given by (see
where Cw is the arterial concentration of H2ISO, 'A
Appendix A)
is the decay constant for oxy gen-15, and F' is the apparent blood flow through volume V.
CwF
Aw =
During continuous inhalation of 1502, the aero
FIVa + 'A
bically respiring cerebral tissue extracts 150 and
b
CoE F'
+
C' F' F'I
;+
+ 1
)
(5)
From Eqs. 1 and 5 it follows that
tivity Ao in the same volume V is given by
F'IV + 'A
FlVa FIVd + 'A
where F is the actual flow through volume Yd'
forms H2150 of metabolism. The steady-state ac
Ao =
(
(2)
'A
where Co is the arterial concentration of haemo globin-bound molecular 1502, C!.v is the arterial con
In the same way, during IS02 inhalation, the ac
centration of recirculating H21S0 (of metabolism),
tivity Ao in a volume V is given by (see Appen
b is the apparent oxygen extraction ratio.I
and E
dix A)
From measurements of Aw and Ao with PET and values of Cw, C!.v and Co, obtained from well
b
counting of arterial blood samples, E
F Ao = ---FIVa + 'A
is obtained
from Eqs. 1 and 2. It is this quantity, together with
F'IV (Eq. 1), which has been measured in most of
(
EoCoFIVa FIVd + 'A
Co(l - Eo)FIVa
the clinical studies to date.
FIVy + 'A
C!.vFIVa
+ ------"-
---"---- +
FIVd + 'A -
+ C0 + C'w
)
(7)
EFFECT OF INTRAVASCULAR OXYGEN-IS
where Eo is the actual oxygen extraction ratio, as
In this simplified model, the volume V is consid
b
opposed to E , which is computed from the sim
ered to be 100% cerebral tissue. In fact,this volume
plified model (Eqs. 1 and 2).
is composed of both tissue and vascular spaces:
V = Vt + Vy + Va = Vt + Vb
+ Eo
From Eqs. 1,2,5,and 7, the relationship between
(3)
FIVd + 'A
)
F1Va
Eo and E '
Eo -
1
where Vt is the tissue volume, Vy is the venous blood volume, Va is the arterial blood volume, and
Vb is the total blood volume (i.e., Va + Vy).
_
(
b can be derived, by solving for AoIAw, as
FIVd + 'A FIVy + 'A
+
FIVd + 'A
)
F1Va (8)
FIVd + 'A
FIVy + 'A
b
Because E
� I, it follows that Eo
� E . This
b
mathematically illustrates the fact that nonex tracted activity in the venous blood and activity in the arterial blood act as background signals in the
J Equation 2 is independent of capillary haematocrit because the product CoP' is constant due to conservation of red cell flow.
1502 scan, and result in an overestimation of rOER. From Eqs. 6 and 8 it is clear that a complete
J each Blood FloI\' Me/abol, Vol. 3, No.4, 1983
418
A. A. LAMMERTSMA AND T. JONES
solution of FIVd and Eo can only be calculated if both the venous volume (Vy) and the arterial volume (Va) are known. Methods exist for mea suring the total regional blood volume (Vb)' but no techniques are available that distinguish between the arterial and venous volumes of the brain. From Eq. 6 and, especially, Eq. 8, it follows that the terms incorporating Va are small, if Va itself is small. It is generally accepted that the arterial fraction consti tutes 20-3 0% of the systemic circulation (Mel lander and Johansson, 1968). This has been con firmed for the cerebrocortical blood volume (L. M. Auer, personal communication). From Eq. 6 it can be calculated that for values of Va up to 6% of the total brain volume V and flow values up to 100 mIl 100 ml/min, F'IV and FIVd are essentially the same (Fig. 7). In Fig. 1, the relationship between Eo and E� for a variable arterial fraction a of the total blood volume Vb is shown. For normal blood volume and all values of blood flow, the arterial fraction is un important (Fig. 1). In these considerations it has been assumed that all arterial blood in the total volume V is nutrient to the tissue within that same volume. If, however, larger arterioles crossing to adjacent regions of brain or arteriovenous shunts are present, the two compartment model presented in Appendix A will not strictly apply. This situation is discussed in de tail in Appendix B, in which an alternative constant background model is presented. It has been shown in Appendix B that, for the vast majority of cases, both models would give the same results. If the sit uation of a constant background (Appendix B) is more appropriate, there will be a slight overesti-
mation in the measurement of rCBF when using the simplified model of Eq. 1. In reality, a combination of both models will exist, resulting in only a minor error in the measurement of rCBF. The relationship between real and measured rOER is even less de pendent on the arterial fraction of the total blood volume. In a situation in which the model of Ap pendix B is the most appropriate for a particular study, and rCBF is extremely low and both rCBV and the arterial fraction of rCBV are high, then rOER will have a very slight dependency on the arterial fraction. CORRECTION METHOD
For practical purposes, a first-order approxima tion, therefore, would neglect the arterial volume completely and consider all the blood volume signal to be at venous concentration. Thus
Va Vb Vd FIVd
Eo" I .0 Eo" . 90
.9
Eo=.80
.8
Eo=.70
.7
Eo" . 60 .6 Eo=.50 '0
w
.5 Eo" .40 .4
Eo=.30
.3
Eo=.20
.2
Eo=. 10
.1
Eo=O .0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1 .0
ex
FIG. 1. Relationship between uncorrected oxygen extraction ratio E� and arterial fraction ex of total blood volume rCBV for different real oxygen extraction ratios (Eo); rCBF = 50 mil 100 ml/min and rCBV = 5%. J
Cereb Blood Flow Me/abol, Vol. 3, No, 4, 1983
0 Vy V F'IV
(9) (10) (11) (12)
In considering the calculation of rCBF from Eq. 5, no correction in the flow calculation from Eq. 1 has to be performed if the arterial blood volume is assumed to be negligible. This is because the ex traction of water is assumed to be complete and the (venous) blood volume is, therefore, part of the total volume of distribution of the (extracted) water. Finally, from Eqs. 8-12, assuming all the blood volume to be venous, the corrected rOER is giv en by
Eo 1.0
= = = =
and
X =
FIVd + A FIVy + A
_ -
E� 1
-
-
F'IV + A F'IVb + A
X X
(13) rCBF/l OO + A rCBR/rCBV + A (14)
with rCBF and rCBV expressed per 100 ml of brain. In Figs. 2 and 3, the relationship between Eo , E�, FIVd (or F'IV), and Vb is shown. For normal values of rCBF, the correction depends principally on the blood volume and the value of the rOER itself. However, Eq. 13 depends on rCBF, and it can be seen from Figs. 2 and 3 that for low flow values and low or normal rOER the percentage correction be comes large. This is due to the fact that the amount of activity (labelled metabolic water) residing within the parenchymal tissues depends on the product of flow and rOER. The effect of the intravascular, unextracted activity becomes important in the 1502 scan, because of the limited accumulation of signal within the tissues at low flows.
rCBV CORRECTION IN 150 STEADY-STATE TECHNIQUE: METHOD Eo= I .0
1 .0
.55
Eo'.90
.9 .e
419
�
.525
Eo'.80 Eo'.70
.7
.5
Eo'.60
.6
Eo' .50 '0
W
.5
'0
W
Eo' .40
cev= I 0.0%
.4 75
cev= 9.0% CBV= e .o%
.4
CBV= 7 .0%
Eo=.30 .3
.45
CBV= 6 .0% CBV= 5 .0%
Eo'.20
CBV= 4 .0%
.2
Eo' . 10
CBV= 3 .0%
.425
CBV= 2 .0%
.1
Eo'0 .0
10
20
30
CBF
40
50
60
70
(mill 0 0 milmin)
80
90
CBV= 1 .0%
10
100
20
30
CBF
40
50
60
70
(mill 0 0 milmin)
eo
90
100
FIG. 2. Relationship between uncorrected oxygen extraction ratio E� and rCBF for different real oxygen extraction ratios (Eo) and a blood vol ume rCBV = 5%.
FIG. 3. Relationship between uncorrected oxygen extraction ratio Eo and rCBF for different blood volumes (rCBV) and a real oxygen extraction ratio Eo = DAD.
The effect of the blood volume correction and uncertainties in the arterial/venous ratios in situa tions of extremely low flow (as, for example, that encountered in peripheral tissues) will be described elsewhere (T. J. Spinks et aI. , in preparation). In conclusion, if rCBV is known, it is possible to calculate Eo from Eqs. 13 and 14, assuming the blood volume is entirely venous. For the purpose of calculating Eo, this assumption is justified, be cause, in most conditions, the applied correction is not sensitive to a change in distribution of the blood over arterial and venous compartments. The correction is valid, irrespective of how rCBV is measured. It requires first the calculation of un corrected rOER, followed by the correction to ob tain corrected rOER. However, if rCBV is mea-
mllmllmin) and white (rCBF = 0. 2 mllm1lmin) matter, a maximum underestimation of 18% for the mean rCBF was found (Lammertsma et aI. , 1981b). It is therefore of interest to estimate the expected error in the corrected rOER, since in the correction the measured value of rCBF is used (Eq. 14). It is important to realise that tissue heterogeneity will affect both 1502 and CI502 scans in the same manner. Because uncorrected rOER (E�) is ob tained basically by dividing the two scans (Eq. C. 7, Appendix C) there will be only a negligible effect. In addition, rCBV will not be affected, because rCBV is linearly dependent on pixel counts (Phelps et aI. , 1979). Therefore, from Eqs. 13 and 14 it can be derived that
11..EO =
Eo
�(1 - E � )rCBV
(E�
- rCBV)rCBF - ACI
sured by use of continuous inhalation of C150, it is possible to calculate corrected rOER directly. Equations for this calculation are given in Appen dix C. TISSUE HETEROGENEITY
In the correction method (Eqs. 13 and 14) it is assumed that the tissue sampled is homogeneous. However, in practice, due to the finite spatial res olution, heterogeneous brain areas will often be en countered. It has been shown previously that, due to the nonlinear character of Eq. 1, an underesti mation of the measured "mean" flow will occur, compared to the true "mean" flow for the region. For example, for a mixture of grey (rCBF = 0. 7
-
IlrCBF Eo')rCBV
rCBF
(15)
with rCBF and rCBV expressed per milliliter of brain. Substitution into Eq. 15 of the example given above (Lammertsma et ai. , 1981b), with E� = 0. 5 and rCBV = 5%, shows that even the maximum underestimation of 18% in rCBF will result in a final error in the corrected rOER of
