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Gjedde-Patlak plot

Principles of Gjedde-Patlak analysis

The original idea of Patlak and Blasberg was to create a model independent graphical analysis method: whatever the tracer is facing in the tissue, there must be at least one irreversible reaction or transport step, where the tracer or labeled product cannot escape.

It is assumpted that all the reversible compartments must be in equilibrium with plasma, i.e. the ratio of the concentrations of tracer in plasma and in reversible tissue compartments must remain stable. In these circumstances only the accumulation of tracer in irreversible compartments is affecting the apparent distribution volume. In practise, this can happen only after the initial sharp concentration changes when the plasma curve descends slow enough for tissue compartments to follow.

pic/patlak_model_independent.gif (15877 bytes) Gjedde-Patlak plot is model-independent: it can be used when there are any number of reversible compartments and at least one irreversible compartment.

When the equilibrium is achieved, the Gjedde-Patlak plot becomes linear. The slope of the linear phase represents the net transfer rate Ki (influx constant). To make it simple, Ki represents the amount of accumulated tracer in relation to the amount of tracer that has been available in plasma.

The y axis of plot contains apparent distribution volumes, i.e. the ratio of concentrations of tracer in tissue and in plasma. On x axis is normalized plasma integral, i.e. the ratio of the integral of plasma concentration and the plasma concentration.

pic/patlak_plot.gif (15164 bytes)

Gjedde-Patlak plot without plasma sampling

Inbrain studies it may be possible to have a reference region where irreversible compartment does not exist: e.g. cerebellum in FDOPA studies. In FDG studies it is not possible because all regions consume glucose. Reference region contains only reversible compartments, which also achieve an equilibrium with plasma. The reference region can be included in the model, and the plasma curve is ‘cancelled out’ [Patlak and Blasberg 1985]. In practise, the only difference in the calculation is that plasma curve is replaced with reference region curve.

pic/patlak_plot_ref.gif (4107 bytes) An example of a Gjedde-Patlak plot with reference tissue input.

The result is not the same when reference input is used instead of plasma input. In the terms of the traditional three-compartmental model, Ki=K1*k3/(k2+k3) with plasma input, but Kiref=k2*k3/(k2+k3) with reference input.

pic/patlak_summary.gif (11373 bytes)

Gjedde-Patlak plot with late imaging only

Gjedde-Patlak plot can be calculated even when PET imaging is not started at the time of injection. Analysis can be done with a few time frames from the later times where equilibrium is achieved, if the slope can be reliably determined from the remaining plot. If only one (late) time frame is available (static imaging), Gjedde-Patlak plot cannot be used, but its slope can be approximated with FUR.

Fractional uptake rate (FUR)

If just one time frame is available(static imaging), fractional uptake rate (FUR, previously sometimes called retention index Ri) can be calculated as a ratio of concentration of tracer in tissue, CT, at time T, and integral (AUC) of its metabolite corrected plasma concentration, CP, from 0 to T [Ishizu et al. 1994, Thie 1995]. FUR is an approximation to the Gjedde-Patlak slope Ki, to the extent that at large T (late time after injection) the effective distribution volume term in Gjedde-Patlak analysis is not important (y axis intercept is assumed to be 0) [Thie 1995]. The unit of FUR is min-1. Also FUR and SUV are proportional, related by plasma clearance rate and a dimensionless initial distribution volume [Thie 1995].

Although only static late imaging is needed, the metabolite corrected plasma curve must always be measured from the beginning of the study to the end.

pic/fur.gif (13365 bytes)

Metabolic rate of glucose

[18F]FDG and glucose compete for a common carrier on the cell membrane (blood-brain barrier in the brain) for transport from plasma to tissue. Inside the tissue cells they compete either for the carrier for transport back from tissue to plasma or for the enzyme hexokinase, which phosphorylates [18F]FDG and glucose to 6-phosphates. The labeling of deoxyglucose instead of glucose has an advantage: While glucose-6-phosphate is metabolized further, eventually to carbon dioxide, [18F]FDG-6-PO4 is not metabolized further in considerable amounts during the first 60 min in the brain and muscle. Therefore, [18F]FDG-6-PO4 accumulates in the tissue where it is formed, resulting in PET images of good quality and easy modelling.

pic/patlak_fdg.gif (19008 bytes)

The recommended LC for brain [18F]FDG studies is 0.65, if irreversible uptake is assumed (3-parameter model or Gjedde-Patlak plot without kLOSS), and LC=0.81, if dephosphorylation is considered (4-parameter model or Gjedde-Patlak plot with kLOSS)  [Wu et al. 2003].

Ishizu K, Nishizawa S, Yonekura Y, et al. Effects of hyperglycemia on FDG uptake in human brain and glioma. J Nucl Med 1994; 35:1104-1109.

Patlak CS, Blasberg RG. Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Generalizations. J Cereb Blood Flow Metab. 1985; 5:584-590.

Thie JA. Clarification of a fractional uptake concept. J Nucl Med 1995; 36:711-712.

Wu H-M, Bergsneider M, Glenn TC, Yeh E, Hovda DA, Phelps ME, Huang S-C. Measurement of the global lumped constant for 2-deoxy-2-[18F]fluoro-D-glucose in normal human brain using [15O]water and 2-deoxy-2-[18F]fluoro-D-glucose positron emission tomography imaging: a method with validation based on multiple methodologies. Mol Imaging Biol 2003; 5: 32-41.