patlak

Patlak plot, also known as Patlak graphical analysis, is a graphical method used in dynamic positron emission tomography (PET) to quantify irreversible tracer uptake in tissue. It was introduced by Patlak, Blasberg, and Fenstermacher in 1983 and has since become a standard tool in kinetic analysis of PET data.

The method relies on time-activity curves from tissue Ct(t) and plasma input Cp(t). Under the assumption of irreversible uptake (no backflux, k4 = 0) after a certain time t, the tissue concentration satisfies Ct(t)/Cp(t) = Ki ∫0^t Cp(τ)dτ / Cp(t) + V0, where Ki is the net influx rate constant and V0 represents the distribution volume of reversible compartments. By plotting Ct(t)/Cp(t) on the y-axis against ∫0^t Cp(τ)dτ / Cp(t) on the x-axis for t > t, the data should fall on a straight line. The slope of this line is Ki, and the intercept is V0.

Ki reflects the rate at which tracer is entering tissue and becoming irreversibly trapped. In practice, Patlak analysis is commonly applied to tracers such as fluorodeoxyglucose (FDG), where phosphorylation traps the tracer, enabling estimation of tracer influx and related metabolic activity. The method provides a simple, robust estimate of Ki without requiring full compartmental modeling, but it depends on accurate arterial input function, appropriate selection of the linear phase, and good data quality.

Limitations include deviations from irreversibility, noise amplification at later times, potential metabolite formation confounding Cp(t), and partial volume effects. Patlak analysis remains complementary to nonlinear kinetic modeling and is often used alongside other graphical methods, such as the Logan plot for reversible tracers.