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Macroparameters

Combination of model parameters can be computed with better reproducibility from lesser data than the separate rate constansts.

Irreversibly binding radiotracers

One general method of this type is graphical analysis, or Gjedde-Patlak plot [Patlak and Blasberg 1985]; the slope of the resulting straight line represents the net influx rate constant K_i=K₁k₃/(k₂+k₃) of the irreversibly trapping tracer.

While the graphical analysis is easier to apply than compartment models, the influx constant K_i is a function of blood flow(perfusion) as well as the enzyme activity or receptor concentration. Difficulties are most apparent in tissue having low blood flow and high enzyme activity or receptor concentration. In these cases it may be necessary to fit the compartment model to estimate the blood flow and plasma protein binding independent rate constant k₃. However, a macroparameter λ*k₃ (where λ=K₁/k₂) can be calculated as an alternative, which is independent of blood flow and non-specific binding in tissue, but is dependent on plasma protein binding [Fowler et al. 1999; Logan et al. 2002]. This parameter can be calculated e.g. using equation λ*k₃=K_i*K₁/(K₁ -K_i).

Reversibly binding radiotracers

For reversible tracers, another linearization method, so called Logan plot [Logan et al. 1990], can be used to provide estimations of distribution volumes of tracers, DV=(K₁/k₂)*(1+k₃/k₄). As linear models, these can be applied pixel-by-pixel to produce parameteric images.

If there exists a "reference region" with no specific binding of radiotracer (k₃=k₄=0), then the binding potential BP can be calculated as BP=DV^roi/DV^ref-1.

Fowler JS, Volkow ND, Cilento R, Wang G-J, Felder C, Logan J. Comparison of brain glucose metabolism and monoamine oxidase B (MAO B) in traumatic brain injury. Clin Pos Imag 1999; 2:71-79.

Logan J, Fowler JS, Volkow ND, Wolf AP, Dewey SL, Schlyer DJ, MacGregor RR, Hitzemann R, Bendriem B, Gatley SJ, Christman DR. Graphical analysis of reversible radioligand binding from time-activity measurements applied to [N-¹¹C-methyl]-(-)-cocaine PET studies in human subjects. J Cereb Blood Flow Metab 1990; 10: 740-747.

Logan J, Fowler JS, Ding Y-S, Franceschi D, Wang G-J, Volkow ND, Felder C, Alexoff D. Strategy for the formation of parametric images under conditions of lowinjected radioactivity applied to PET studies with the irreversible monoamine oxidase A tracers [¹¹C]clorgyline and deuterium-substituted [¹¹C]clorgyline. J Cereb Blood Flow Metab 2002; 22: 1367-1376.

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.