Lumped constant (LC)
The lumped constant for formulated by Sokoloff et al. (1977), based on the biochemical principles of competitive substrate kinetics. It accounts for the differences in transport and phosphorylation rates between D-glucose and 2-fluoro-2-deoxy-D-glucose, and is used to transform the [18F]FDG uptake rate to glucose uptake rate.
The concept of lumped constant can be used with any metabolism PET tracer which competes with a natural substrate, for example to estimate the rates of amino acid and and fatty acid uptake.
LC of [18F]FDG
A common assumption in FDG PET studies is that lumped constant is uniform over the whole brain and in all subject and patient groups, but this is not strictly true: Hexokinase favours glucose over FDG, and transport favours FDG over glucose. Although there are several different estimates on the normal value of LC in the brain, the estimates are always less than 1.0, representing that in normal condition the phosphorylation is the rate-limiting step in glucose uptake. In supply limited conditions (hypoglycemia and ischemia) LC increases as shown by Crane et al. (1981) and Hawkins et al. (1981).
Lumped constant is a function of the rate constants (Sokoloff et al. 1977). The variability of LC results primarily from changes in k3/k2 for glucose and for FDG (k3*/k2*) as is expressed in below (Phelps et al. 1983):
Phelps et al. (1983) used values p=0.50 and q=1.67 (q/p=3.34) to estimate the changes in LC between normal and ischemic brain regions. This equation was used by Sasaki et al. (1986) to estimate whether LC is uniform over the whole brain.
Kuwabara and Gjedde (1990; 1991) derived equation for LC which is independent of the model used:
, where Ki* is the unidirectional clearance from the circulation to the metabolic compartment (net influx rate), τ is the ratio between FDG and glucose clearances (K1*/K1), and φ is the phosphorylation ratio between FDG and glucose (k3*/k3). Kuwabara and Gjedde (1991) used estimates τ=1.10 and φ=0.30. Before that, Crane et al. (1983) have used estimates τ=1.67 and φ=0.55 in rat studies.
In irreversible 2-tissue compartment model Ki=K1*k3/(k2+k3), and thus (Gejl et al., 2012)
Recommended values for using as LC
The recommended LC for brain [18F]FDG studies is 0.65, if irreversible uptake is assumed (3-parameter model or Patlak plot without kLOSS), and LC=0.81, if dephosphorylation is considered (4-parameter model or Patlak plot with kLOSS) (Wu et al. 2003). Graham et al. (2002) obtained value LC=0.89±0.08 for normal brain, and 0.78±0.11 for cerebellum, using reversible two-tissue compartmental model, but, in comparison to other studies, suggested that 0.80 should be used.
In rat brain studies, lumped constant of 0.71 is recommended (Tokugawa et al., 2007; Krohn et al., 2007).
LC for [18F]FDG in myocardium is dependent on the serum insulin concentration (Bøtker et al., 1997 and 1999). Values for τ and φ in myocardium in humans were determined to be 2.26 and 0.43, respectively (Bøtker et al., 1997), and these values have been used later by the same group (Wiggers et al., 1999; Bøtker et al., 2000; Gejl et al., 2002). In isolated working rat hearts values were 1.73 and 0.15, respectively (Bøtker et al., 1999). If LC is not determined from the dynamic FDG PET data, the recommended LC for Patlak and FUR analysis of heart FDG studies is 1.
Peltoniemi et al. (2000) measured the LC in skeletal muscle to be 1.16.
LC in human adipose tissue is 1.14 (Virtanen et al., 2001).
LC in the liver of pigs is close to one (Iozzo et al., 2007).
LC of [18F]FTHA
Lumped constant for [18F]FTHA represents the ratio of the probability that arterial tracer molecule, [18F]FTHA, will be activated to [18F]FTHA-CoA, to the probability that an arterial long-chain fatty acid (palmitate and other FFAs) molecule will undergo activation to fatty acyl-CoA. If the kinetics of the tracer and of the average native compound would be identical, LC would equal 1.
Because LC is difficult to measure in human subjects, it is often assumed to equal 1. This may cause bias in results and should be taken into account in interpretation of the results.
Alternatives to LC
Correction using Michaelis constant
Williams et al. (2012a; 2012b) have proposed an alternative method to traditional measure of metabolic rate of glucose (MRgluc). In this method, the metabolic rate is extrapolated to the hypothetical condition of glucose saturation:
This method has been shown in mice studies to provide results with smaller variation than the traditional method. Michaelis-Menten constant KM=130 mg/dL was used in the mice studies.
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Created at: 2009-01-09
Updated at: 2018-08-17
Written by: Vesa Oikonen