# Dispersion of 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 add to this dispersion effect. Dispersion affects the shape of the blood curve, especially at the bolus infusion peak time, but at late times the AUC of blood curve is not biased. Therefore, dispersion correction is necessary only when very fast kinetics are measured, for example perfusion measurement with radiowater.

In theory, input function is the same for all organs and can be measured from arterial blood, but since dispersion effect differs for the measured and true input function to the region of interest, this is not strictly true, unless dispersion correction is applied. Venous blood sampling causes additional dispersion and biases.

Figure 1. Physiological processes cause distortion (dispersion and delay) of plasma TAC. Sample withdrawal and measurement apparatus may distort the TAC even more.

## Dispersion correction

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). Munk et al. (2004 and 2008) proposed a dispersion correction method with less noise problem. Although certain automatic blood sampling systems are MR-compatible (Breuer et al., 2010), most are not, requiring long tubing with PET-MR systems. Long tubing increases the dispersion error; O’Doherty et al. (2015) have shown that dispersion correction can be successful even with 3 m arterial sampling tubing.

Dispersion correction should be done before time delay correction, or simultaneously (Meyer, 1989).

### 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; Senda et al., 1988; Weinberg et al., 1988).

A separate β-microprobe placed close to the arterial catheter could be used to measure the shape of the blood curve without most of the dispersion effects of the main detector system and blood tubing (Seki et al., 1998). Microprobe system could also work without the pump, relying only on the impedance of the system to control the blood flow (Wollenweber et al., 1996).

### 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). Liver is especially difficult case with dual input (Keiding, 2012).

### 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.

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 would be:

disp4dft off uo268blo.kbq 2.5 uo268ab.kbq

## References:

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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.

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O’Doherty J, Chilcott A, Dunn J. Effect of tubing length on the dispersion correction of an arterially sampled input function for kinetic modeling in PET. Nucl Med Commun. 2015; 36(11): 1143-1149. doi: 10.1097/MNM.0000000000000374.

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Updated at: 2018-11-24
Written by: Vesa Oikonen