# Compartmental models for metabolite correction

Compartmental models can be used to model the appearance of metabolites in the plasma or blood. While Hill function or power function can fit well the plasma parent radiotracer fractions in bolus studies, those are usually not applicable in metabolite correction for bolus+infusion studies.

Huang et al. (1991) introduced general
models for metabolite correction, and
specific models for [^{18}F]FDOPA and
[^{15}O]O_{2}.
Compartmental model for metabolite correction of [^{15}O]O_{2} blood data was
simplified by Iida et al. (1993).
Several models for [^{11}C]CO_{2} have been
presented, since it is a common metabolite of ^{11}C-labelled radiotracers.
Lammertsma et al (1993) used a multi-compartmental model in metabolite analysis of
L-[^{11}C]deprenyl, but did not disclose details of the model.
Carson et al (1997) used a
two-compartmental model in metabolite analysis of
[^{11}C]raclopride. In this model, the
concentration of metabolites in plasma was calculated from total plasma activity using equation

, where *λ _{1}*≥0,

*λ*≥0,

_{2}*t*≥0, and

*λ*≠

_{1}*λ*. Here, the response function is one form of biexponential,

_{2}and its constant,
*λ _{1}λ_{2}/(λ_{2}-λ_{1})*
normalises the

*AUC*to unity. If one-compartmental model would suffice, then the biexponential response function can be replaced by surge function, with

*AUC=1*:

Gillings et al (2001) linearised
the fitting by applying Patlak plot, using parent plasma
concentration as input. Patlak plot has negative curvature if the metabolite(s) are eliminated
from the plasma, which was corrected by adding the elimination rate into the Patlak plot when
necessary. The method was applied to [^{11}C]NNC112, [^{11}C]NS2214, and
[^{11}C]PK11195 in minipigs
(Gillings et al., 2001).
A different formulation of the linear plot was previously used by the same group for
[^{18}F]FDOPA, [^{11}C]deprenyl,
[^{11}C]SCH23390, [^{11}C](S)-nicotine, and
[^{11}C]raclopride
(Cumming
et al., 1999).

When the plasma-to-blood ratio and/or the rate of
plasma-to-RBC transport is different between the parent radiotracer and its metabolites,
a compartmental model can be used to model both fractions simultaneously, as shown in
a 6-[^{18}F]fluoro-L-*m*-tyrosine study
(Asselin et al., 2002).
Wu et al. (2007) applied compartmental model
for [^{11}C]WAY-100635 when testing the
performance of different metabolite correction methods.

Model-based input methods rely on assumption that the input
function is common to all tissue regions in the PET image, and can be solved from the data
(simultaneous estimation method, SIME).
Burger & Buck (1996) have proposed using SIME
for metabolite correction, and method has been
applied for instance to [^{11}C]flumazenil
(Sanabria-Bohórquez et al., 2000).

General arterial input function model for PET was presented by Graham (1997), and while the model does not account for the appearance of label-carrying metabolites in the blood or plasma, Graham (1997) suggested combining the compartmental models for the plasma curve and metabolites. The Graham's model can be extended to account for the disappearance of the parent radiopharmaceutical from plasma pool via metabolism (Figure 1):

The metabolites formed in this model setting can be assumed to appear first in the venous/pulmonary plasma, and could be used as input for compartmental models describing the plasma kinetics of the metabolites. For a single metabolite, the compartmental model could that be defined as (Figure 2):

In this model we assume that the metabolite that appears in the *BV* compartment
(venous blood and pulmonary vascular system), possibly produced from the parent compound via
different routes, can be modelled with similar model as the parent compound (but obviously with
different rates). If there are more than one label-carrying metabolite, then each of them can have
their own compartmental model. In addition, label-carrying metabolite typically metabolises further,
and this can be modelled by using the first metabolite as the "parent" compound for the second
metabolite. These kind of models typically contain too many parameters for reliable fitting of
measured data (overdetermined), but could be useful for simulation purposes.

## See also:

- Hill function in plasma metabolite correction
- Power function in metabolite correction
- Metabolite correction
- Metabolite correction in [
^{15}O]O_{2}PET - Fractions of unchanged radiotracer in plasma
- Fitting PET input curves
- Compartmental models for input function

## References

Carson RE, Breier A, de Bartolomeis A, Saunders RC, Su TP, Schmall B, Der MG, Pickar D,
Eckelman WC. Quantification of amphetamine-induced changes in [^{11}C]raclopride binding
with continuous infusion. *J Cereb Blood Flow Metab.* 1997; 17(4): 437-447. doi:
10.1097/00004647-199704000-00009.

Lammertsma AA, Hume SP, Bench CJ, Luthra SK, Osman S, Jones T. Measurement of monoamine oxidase B
activity using L-[^{11}C]deprenyl: inclusion of compartmental analysis of plasma metabolites
and a new model not requiring measurement of plasma metabolites. In: *Quantification of brain
function: Tracer kinetics and image analysis in brain PET*. Uemura K et al., (eds.) 1993,
Elsevier, The Netherlands, p. 313-318.

Tags: Input function, Plasma, Metabolite correction, Parent fraction, Fitting, Compartmental model, Biexponential

Updated at: 2019-04-20

Created at: 2007-07-18

Written by: Vesa Oikonen