Single-voxel delay map from long-axial field-of-view PET scans

Abstract

Objective: We present an algorithm to estimate the delay between a tissue time-activity curve and a blood input curve at a single-voxel level tested on whole-body data from a long-axial field-of-view scanner with tracers of different noise characteristics.

Methods: Whole-body scans of 15 patients divided equally among three tracers, namely [¹⁵O]H₂O, [¹⁸F]FDG and [⁶⁴Cu]Cu-DOTATATE, which were used in development and testing of the algorithm. Delay times were estimated by fitting the cumulatively summed input function and tissue time-activity curve with special considerations for noise. To evaluate the performance of the algorithm, it was compared against two other algorithms also commonly applied in delay estimation: name cross-correlation and a one-tissue compartment model with incorporated delay. All algorithms were tested on both synthetic time-activity curves produced with the one-tissue compartment model with increasing levels of noise and delays between the tissue activity curve and the blood input curve. Whole-body delay maps were also calculated for each of the three tracers with data acquired on a long-axial field-of-view scanner with high time resolution.

Results: Our proposed model performs better for low signal-to-noise ratio time-activity curves compared to both cross-correlation and the one-tissue compartment models for non-[¹⁵O]H₂O tracers. Testing on synthetically produced time-activity curves showed only a small and even residual delay, while the one-tissue compartment model with included delay showed varying residual delays.

Conclusion: The algorithm is robust to noise and proves applicable on a range of tracers as tested on [¹⁵O]H₂O, [¹⁸F]FDG and [⁶⁴Cu]Cu-DOTATATE, and hence is a viable option offering the ability for delay correction across various organs and tracers in use with kinetic modeling.

Keywords: delay correction; delay map; dynamic whole-body PET; kinetic modeling; one-tissue compartmental modeling.

Figure 1

Summing the TACs cumulatively eliminates most of the noise and hence increases robustness of the fit using Equation (2).

Figure 2

Example TAC from a voxel in the arm of injection (green), cumulatively summed TAC (blue), and IDIF (yellow). Possible partial volume effects in the early part of the TAC creates double spikes as the tracer passes tissue twice (venous pass and a later arterial pass). This creates plateaus in the summed TAC.

Figure 3

Parameter maps for the proposed model (left column), cross-correlation (middle column) and one-tissue compartment model (right column) showing the residual delay (difference between the actual delay and estimated delay) for synthetic TACs created from a one-tissue compartmental model using an IDIF of the tracer [¹⁵O]H₂O as $C_A(t)$ in Equation (5), across combinations of $K_1$ (horizontal axis) and $k_2$ (vertical axis), linearly spaced in the range $1\frac{\mathrm{ml}}{100\mathrm{g}\cdot \min }\le K_1\le 350\frac{\mathrm{ml}}{100\mathrm{g}\cdot \min }$ and $0.05\mathrm{mi}{\mathrm{n}}^{-1}\le k_2\le 3\mathrm{mi}{\mathrm{n}}^{-1}$. Shown here for two levels of noise (low noise: A, C, and E; and high noise: B, D, and F) and for an actual delay between input function and tissue TAC of 0 s, as the parameter maps do not change significantly between different actual delays.

Figure 4

Histograms of the parameter maps in Figure 3 across a range of noise levels, $0\le \sigma \le 0.5$, downward, for the three models tested: proposed (A), cross-correlation (B), and one-tissue compartment model (C). Note that the x-axis is bounded in a range from −8 s–+8 s, and that the residual delay of cross-correlation mainly lies below this range.

Figure 5

Coronal slice of whole-body delay maps for the proposed model (left column/subfigures A, D, and G), cross-correlation (middle column/subfigures B, E, and H) and a one-tissue compartment model with delay included (right column/subfigures C, F, and I), across the tracers [¹⁵O]H₂O (top row), [¹⁸F]FDG (middle row) and [⁶⁴Cu]Cu-DOTATATE (bottom row).

Figure 6

Delay distributions of selected organ for the tracers [¹⁵O]H₂O (left/subfigure A), [¹⁸F]FDG (center/subfigure B) and [⁶⁴Cu]Cu-DOTATATE (right/subfigure C).

Figure 7

Parametric images showing the blood flow {K₁, [ml blood/(100 g tissue * min)]} of an axial slice of brain in a patient with carotid stenosis on their left side (the right side in the images) receiving the tracer [¹⁵O]H_sO. (A) is delay corrected using the mean organ time activity curve, while (B) uses voxel-wise delay correction with delay correction, and (C) shows the relative difference between the two.