Matthew R Orton^{1}, Mihaela Rata^{1}, Dow-Mu Koh^{1,2}, Maria Bali^{1,2}, Robert Grimm^{3}, David J Collins^{1}, James A d'Arcy^{1}, and Martin O Leach^{1}

Liver perfusion and function can be assessed using gadoxetic acid combined with DCE-MRI imaging and pharmacokinetic (PK) modelling. Whilst compartmental PK models give a good account of the contrast changes over the first five minutes of enhancement, the Patlak graphical approach is a simpler alternative that is more easily implemented. Patlak evaluation requires the specification of a delay time after which the initial transients in the uptake curves have decayed, so the purpose of this abstract is to present a preliminary evaluation of the sensitivity of liver uptake rate estimates to the Patlak delay time.

Four consented
patients were imaged at 1.5T using a MAGNETOM Aera (Siemens Healthcare, Erlangen, Germany) with a
prototype sequence with
view-sharing reconstruction, described in Figure 1. Three patients received gadoxetic
acid (Primovist at 0.1ml/kg
at 1ml/sec then 20ml saline at 1ml/sec), and one received gadoteric acid (Dotarem at 0.2ml/kg,
same delivery). Gadoteric acid is not taken up
by the liver, so this patient acted as a negative control. Arterial input function (AIF) data were
obtained from the aorta, and flip-angle corrections (to account for in-flow
effects) were used to ensure a pre-contrast blood T_{1} of 1200ms in
each patient. To reduce the effect of
noise, arterial data were fitted with a previously described AIF model^{3},
and plasma concentrations were obtained assuming a haematocrit of 0.42, see Figure
2 for an example. Algebraic integration
of the AIF was used in the Patlak computation, which performs linear regression
of$$$\;C_\mathrm{t}(t)\;/\;C_\mathrm{p}(t)\;$$$onto$$$\;\left[\int_0^tC_\mathrm{p}(s)\;ds\right]\;/\;C_\mathrm{p}(t)\;$$$for$$$\;t\;$$$greater than some time$$$\;t^*,\;$$$from which the slope and intercept are estimates of$$$\;K_\mathrm{i}\;$$$(min^{-1}, liver uptake rate parameter) and
the distribution volume fraction respectively.
The delay term$$$\;t^*\;$$$was set to
0.25,$$$\;$$$0.5,$$$\;$$$1 and 2 minutes after the contrast arrival time. The Patlak model
assumes a single input function, whereas the Sourbron PK model considers a dual input to
account for contrast arriving from the hepatic portal vein. To make the comparison more direct the PK model
was simplified to consider only a single input, see Figure 3.

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2. Patlak CS, Blasberg RG, Fenstermacher JD. Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. J Cereb Blood Flow Metab. 1983; 3(1):1-7.

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