# Metabolite correction in [^{15}O]O_{2} PET studies

## Model

In [^{15}O]O_{2} studies, the labeled water ([^{15}O]H_{2}O)
that is formed during the study is evenly distributed between the water spaces (f^{w}) of
blood cells (RBC) and plasma (P), while
[^{15}O]O_{2} stays only in the blood cells, bound to hemoglobin.
The ratio of [^{15}O]H_{2}O concentrations in blood cells and
plasma equals the ratio of the water contents:

Arterial blood (B) time-activity curve (TAC), representing the total [^{15}O],
is measured using blood pump and on-line detector and processed
as usual, or computed from a VOI drawn on heart LV cavity in
dynamic PET image.

For metabolite analysis, plasma must be separated from arterial blood samples and its radioactivity concentration is measured. Concentration in blood is the sum of concentrations in blood cells and plasma, weighted by hematocrit (HCT):

By combining the above two equations we can calculate the ratio of
[[^{15}O]H_{2}O] in blood and plasma:

Arterial plasma TAC, representing [[^{15}O]H_{2}O], is multiplied by this ratio
to achieve arterial blood TAC of [^{15}O]H_{2}O. If hematocrit was not measured,
a fixed value for plasma-to-blood ratio can be used instead in the conversion
(Lubberink et al., 2011):

In theory, [^{15}O]O_{2} concentration in arterial blood can then be calculated
by simply subtraction:

However, in practise only few arterial plasma samples can be measured.
Therefore, further input modelling steps are needed to produce continuous and reliable input TACs
for calculation of oxygen consumption.
A compartmental model by Huang et al. (1991) describes the kinetics of converting blood
[^{15}O]O_{2} curve to plasma [^{15}O]H_{2}O.
A slightly modified model is shown in figure 1.

**Figure 1.**Compartment model for [

^{15}O]O

_{2}metabolite correction.

*C*denotes [

_{B}^{O}^{15}O]O

_{2}concentration in the blood,

*C*is the [

_{B}^{W}^{15}O]H

_{2}O concentration in the blood, and

*C*is the [

_{EV}^{W}^{15}O]H

_{2}O concentration in extravascular (whole body) compartment.

Differential equations for the model:

In equation 6 the [^{15}O]O_{2} concentration in the blood,
*C _{B}^{O}(t)*, is not known, but it is instead substituted with eq 5,
because the total radioactivity concentration in the blood,

*C*, is measured. Resulting equation 8, together with eq 7, can be used to estimate the model parameters, and

_{B}(t)*C*, with nonlinear fitting.

_{B}^{O}(t)Iida et al. (1993) simplified the model by assuming *k _{4}*=0, but considering
also the delayed appearance of recirculating water.
Sum of parameters

*k*and

_{1}*k*is fitted as one parameter. Kudomi et al. (2009) showed that parameters (

_{3}*k*,

_{3}*k*, and delay) can be constrained to the population averages, leaving only

_{3}/k_{4}*k*to be fitted; this approach allows metabolite correction with only one plasma sample.

_{1}## Procedure in TPC

The plasma curve can be converted to metabolite ([^{15}O]H_{2}O) concentration
curve in blood using program o2_p2w.

**Figure 2.**Example of measured arterial BTAC (black) and PTAC (red) in a [

^{15}O]O

_{2}bolus inhalation study. [

^{15}O]H

_{2}O concentration in the blood (blue) is calculated with o2_p2w using measured hematocrit.

With these curves, the rates of formation and removal of labeled water is calculated using
fit_o2bl.
In the TPC data collected for 300 s the *k _{4}*=0, and option

`-model=k3`

should be used. Also delay can be fixed to the population median, but the value is dependent on
the sample collection protocol.
In a group of healthy young men (Kaisti et al., 2003) the mean parameters were
*k*=0.00127±0.00027 s

_{1}^{-1}, and

*k*=0.0035±0.0012 s

_{1}+k_{3}^{-1}. The rate constants during anaesthesia (Kaisti et al., 2003) were slightly lower.

Then, the separated TACs of authentic [^{15}O]O_{2} and metabolite
[^{15}O]H_{2}O in blood can be calculated using program
o2metab.

**Figure 3.**Example of arterial BTACs of [

^{15}O]O

_{2}(black) and [

^{15}O]H

_{2}O (red) produced in the metabolite correction of an [

^{15}O]O

_{2}bolus inhalation study.

To measure oxygen consumption in the brain, it is usually not necessary to correct the input curve for labeled water. If metabolite correction is required, individual measurements may sometimes be replaced by rate constants determined for a similar group.

# References:

Huang SC, Barrio JR, Yu DC, Chen B, Grafton S, Melega WP, Hoffman JM, Satyamurthy N,
Mazziotta JC, Phelps ME. Modelling approach for separating blood time-activity curves in
positron emission tomographic studies. *Phys Med Biol.* 1991; 36(6): 749-761.

Iida H, Jones T, Miura S. Modeling approach to eliminate the need to separate arterial plasma
in oxygen-15 inhalation positron emission tomography. *J Nucl Med.* 1993; 34: 1333-1340.

Kaisti KK, Långsjö JW, Aalto S, Oikonen V, Sipilä H, Teräs M, Hinkka S, Metsähonkala L,
Scheinin H. Effects of sevoflurane, propofol, and adjunct nitrous oxide on regional cerebral
blood flow, oxygen consumption, and blood volume in humans.
*Anesthesiology* 2003; 99(3): 603-613.

Kudomi N, Hayashi T, Watabe H, Teramoto N, Piao R, Ose T, Koshino K, Ohta Y, Iida H.
A physiologic model for recirculation water correction in CMRO_{2} assessment with
^{15}O_{2} inhalation PET.
*J Cereb Blood Flow Metab.* 2009; 29(2): 355-364.

Lubberink M, Wong YY, Raijmakers PGHM, Schuit RC, Luurtsema G, Boellaard R, Knaapen P,
Vonk-Noordegraaf A, Lammertsma AA. Myocardial oxygen extraction fraction measured using bolus
inhalation of ^{15}O-oxygen gas and dynamic PET.
*J Nucl Med.* 2011; 52(1): 60-66.

Tags: Oxygen, Input function, Blood, Plasma, Metabolite correction

Updated at: 2016-02-29

Written by: Vesa Oikonen, Pauliina Luoto