# Metabolite correction in [15O]O2 PET studies

Regional metabolic rate of oxygen can be assessed with [15O]O2 PET. Inhaled [15O]O2 is distributed into tissues in red blood cells (RBCs), bound to haemoglobin. The fraction of [15O]O2 that is used in metabolism is distributed as [15O]H2O in the water space of the tissue and blood and removed via blood flow, and the fraction that is not used in metabolism is removed from the tissue in blood RBCs. In tissue that do not contain myoglobin the concentration of [15O]O2 is negligible. The different tissue distribution volume and clearance of [15O]O2 and [15O]H2O leads to different kinetics in the 15O concentration in the tissue depending on the oxygen consumption and blood flow rate. Estimation of the oxygen consumption rate requires that the input function is known, which in this case means separate concentration curves of [15O]O2 and [15O]H2O in arterial blood.

## Model

In [15O]O2 studies, the labelled water ([15O]H2O) that is formed during the study is evenly distributed between the water spaces (fw) of blood cells (RBC) and plasma (P), while [15O]O2 stays only in the blood cells, bound to haemoglobin. The ratio of [15O]H2O concentrations in blood cells and plasma equals the ratio of the water contents:

Arterial blood (B) time-activity curve (TAC), representing the total [15O], 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 haematocrit (HCT):

By combining the above two equations we can calculate the ratio of [[15O]H2O] in blood and plasma:

Arterial plasma TAC, representing [[15O]H2O], is multiplied by this ratio to achieve arterial blood TAC of [15O]H2O. If haematocrit was not measured, a fixed value for plasma-to-blood ratio can be used instead in the conversion (Lubberink et al., 2011):

In theory, [15O]O2 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 [15O]O2 curve to plasma [15O]H2O. A slightly modified model is shown in figure 1.

Figure 1. Compartment model for [15O]O2 metabolite correction. CBO denotes [15O]O2 concentration in the blood, CBW is the [15O]H2O concentration in the blood, and CEVW is the [15O]H2O concentration in extravascular (whole body) compartment.

Differential equations for the model:

In equation 6 the [15O]O2 concentration in the blood, CBO(t), is not known, but it is instead substituted with eq 5, because the total radioactivity concentration in the blood, CB(t), is measured. Resulting equation 8, together with eq 7, can be used to estimate the model parameters, and CBO(t), with nonlinear fitting.

Iida et al. (1993) simplified the model by assuming k4=0, but considering also the delayed appearance of recirculating water. Sum of parameters k1 and k3 is fitted as one parameter. Kudomi et al. (2009) showed that parameters (k3, k3/k4, and delay) can be constrained to the population averages, leaving only k1 to be fitted; this approach allows metabolite correction with only one plasma sample.

## Procedure in TPC

The plasma curve can be converted to metabolite ([15O]H2O) concentration curve in blood using program o2_p2w.

Figure 2. Example of measured arterial BTAC (black) and PTAC (red) in a [15O]O2 bolus inhalation study. [15O]H2O concentration in the blood (blue) is calculated with o2_p2w using measured haematocrit.

With these curves, the rates of formation and removal of labelled water is calculated using fit_o2bl. In the TPC data collected for 300 s the k4=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 k1=0.00127±0.00027 s-1, and k1+k3=0.0035±0.0012 s-1. The rate constants during anaesthesia (Kaisti et al., 2003) were slightly lower.

Then, the separated TACs of authentic [15O]O2 and metabolite [15O]H2O in blood can be calculated using program o2metab.

Figure 3. Example of arterial BTACs of [15O]O2 (black) and [15O]H2O (red) produced in the metabolite correction of an [15O]O2 bolus inhalation study.

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

# References:

Bigler RE, Kostick JA, Gillespie JR. Compartmental analysis of the steady-state distribution of 15O2 and H215O in total body. J Nucl Med. 1981; 22(11): 959-965.

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. doi: 10.1088/0031-9155/36/6/004.

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 CMRO2 assessment with 15O2 inhalation PET. J Cereb Blood Flow Metab. 2009; 29(2): 355-364. doi: 10.1038/jcbfm.2008.132.

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 15O-oxygen gas and dynamic PET. J Nucl Med. 2011; 52(1): 60-66. doi: 10.2967/jnumed.110.080408.

Updated at: 2019-01-05
Written by: Vesa Oikonen, Pauliina Luoto