Modelling the impact of injection time on the bolus shapes in PET-MRI AIF Conversion

With the introduction of combined PET/MRI systems, AIF conversion can be made under certain circumstances (see [1]). We propose a model that allows modification of the injection parameters in the AIF fit to account for differences caused by different injection durations [2].

Brain ¹⁸F-Choline PET and DSC-MRI data were obtained using Siemens mMR. The MR contrast agent was injected with a rate of 4ml/sec and the PET tracer was injected manually. Perfusion Mismatch Analyzer [3] was used to extract the MRI-AIF. Carotid arteries were segmented on a post contrast MPRAGE image. PET frames were registered onto this MPRAGE image using rigid registration and partial volume correction was done using the iterative Yang method [4]. The AIFs were fitted using a convolution of a ‘double Butterworth’ function, representing the injection, with a tri-exponential function representing the elimination [Eq. 1]. The bolus shape can be adjusted by changing Δτ (τ₂ - τ₁). This was tested with a population based MRI AIF [5], as well as with clinical data.

(1)

where

For the population based input function, Figure 1 shows that when Δτ was increased, lower and wider peaks were seen, and with decreased Δτ, higher but narrower peaks were observed. Figure 2 shows that the function fits both clinical PET and MRI AIFs well. Values of τ₁ and τ₂ were changed to modify the MRI-AIF and Figure 3 shows the modified MRI-AIF together with the original fitted PET-AIF, normalized to their peaks. Two AIFs have similar peak shapes but start to differ at the elimination phase as Gd-DOTA and ¹⁸F-Choline have different tissue uptake rates.

Figure 1

Simulated MRI-AIFs using Parker’s population-based input function refitted with the developed function. AIF shapes with different injection durations, Δτ is shown.

Figure 2

The double Butterworth convolution function used to fit (a) DSC-MRI data and (b) 18F-Choline PET data together with a plot where the timescale of PET-AIF was limited to MRI-AIF’s to show different bolus widths.

Figure 3

The MRI-AIF with modified τ1 and τ2 values plotted together with the PET-AIF. The MRI-AIF peak is scaled to PET-AIF’s peak.

This enables conversion of the early part of the AIFs from one modality to another even if different injection protocols are used.