Dispersion of the input function

The measured blood curve after a radiotracer bolus is smeared out, because of inhomogeneous velocity fields in the vessels and in the catheter and detector assemblies. Also sticking of radiotracer to the tubing may a add to this dispersion effect, which differs for the measured and true input function to the region of interest.

Dispersion correction with traditional methods adds noise to the blood curve. Regardless of that, dispersion correction should not be accompanied by smoothing (Wollenweber et al., 1997).

Dispersion in the detector system

External dispersion of the input function can be determined by measuring the rising/falling edges of the detector system's response to an input step function (Iida et al., 1986).

Internal dispersion

The internal (physiological) dispersion (caused by human vascular system) between the radial artery and the brain is 4-6 sec (Iida et al., 1986).

Dispersion correction in Turku PET Centre

In Turku PET Centre, when the dispersion correction is necessary, it is usually done automatically by the blood data processing software: first, the external dispersion is corrected, and secondly the internal dispersion is corrected, if an estimate of internal dispersion time constant is available.

In Turku PET Centre, the external dispersion time constant has been estimated to be 2.5 sec for the assemblies that are currently in use. If tubing is changed, the dispersion time constant should be measured again, or asked from the PET physicists.

Internal dispersion time constant of 5 sec has been used for the brain studies.

The corrections are done using disp4dft. To continue with the above example, the command could be:
disp4dft off uo0268blo.kbq 2.5 uo0268ab.kbq

References:

Iida H, Higano S, Tomura N, Shishido F, Kanno I, Miura S, Murakami M, Takahashi K, Sasaki H, Uemura K. Evaluation of regional difference of tracer appearance time in cerebral tissues using [¹⁵O]water and dynamic positron emission tomography. J Cereb Blood Flow Metab. 1988; 8: 285-288.

Iida H, Kanno I, Miura S, Murakami M, Takahashi K, Uemura K. Error analysis of a quantitative cerebral blood flow measurement using H₂¹⁵O autoradiography and positron emission tomography, with respect to the dispersion of the input function. J Cereb Blood FlowMetab. 1986; 6: 536-545.

Meyer E. Simultaneous correction for tracer arrival delay and dispersion in CBF measurements by the H215O autoradiographic method and dynamic PET. J Nucl Med. 1989; 30:1069-1078.

Munk OL, Keiding S, Bass L. A method to estimate catheter dispersion and to calculate dispersion-free blood time-activity curves. J Nucl Med. 2004; 45(5): 392P-393P.

Munk OL, Keiding S, Bass L. A method to estimate dispersion in sampling catheters and to calculate dispersion-free blood time-activity curves. Med Phys. 2008; 35(8): 3471-3481.

Oikonen V. Model equations for the dispersion of the input function in bolus infusion PET studies. TPCMOD0003.

van den Hoff J, Burchert W, Müller-Schauenburg W, Meyer G-J, Hundeshagen H. Accurate local blood flow measurements withdynamic PET: fast determination of input function delay and dispersion by multilinear minimization. J Nucl Med. 1993; 34:1770-1777.

Wollenweber SD, Hichwa RD, Ponto LLB. A Simple on-line arterial time-activity curve detector for [O-15]water PET studies. IEEE Trans Nucl Sci. 1997; 44(4): 1613-1617.