Info
Background:
PET occupancy studies are widely used to estimate in vivo drug–target engagement and apparent affinity (EC50). Conventional analyses assume spatial homogeneity and yield a single regional estimate [1], whereas voxel-wise extensions such as the Lassen Plot Filter (LPF) enable spatially resolved occupancy and EC50 imaging [2, 3]. However, voxel-wise LPF introduces statistical challenges, including correlated measurement error between regression axes and sensitivity to noise propagation through image reconstruction and kinetic modeling, potentially leading to biased occupancy and EC50 estimates..

 

Hypothesis/Objective:
This study aimed to quantitatively characterize bias in voxel-wise LPF-derived occupancy and EC50 images under controlled simulation conditions and to develop a decorrelated LPF formulation (dcLPF) to mitigate regression-induced bias.

 

Methods:
A 4D digital phantom with heterogeneous ground-truth EC50 values (5–150 ng/mL) was generated using a two-tissue compartment model. Sixteen plasma concentrations were simulated, producing paired baseline and post-drug dynamic PET datasets to mimic the output of a standard PET-occupancy experiment. The quantitative pipeline included voxel-wise VT estimation using multilinear analysis (MA1), LPF-based occupancy estimation, and voxel-wise Emax modeling.

Bias was evaluated across four conditions: (i) noise-free digital phantom, (ii) OSEM reconstruction from noiseless sinograms , (iii) image-space noise (Gaussian approximation to Poisson fluctuations; CV = 5%), (iv) sinogram-space Poisson noise with iterative OSEM reconstruction using the YRT-PET package [4, 5], and errors in occupancy and EC50 estimates were quantified using median percent bias and normalized RMSE across the full image and region-specific analyses.

Three regression approaches to the LPF were compared: conventional LPF with ordinary least squares (LPF-OLS), total least squares (LPF-TLS), and a decorrelated LPF formulation (dcLPF-TLS) in which baseline and post-drug VT were used as X and Y variables to reduce axis correlation.

 

Results:
Under noise-free conditions, all methods demonstrated negligible bias (occupancy <0.3%, EC50 <0.6%), confirming no intrinsic bias in the LPF framework itself.

Once noise was introduced into image-space, PET and VT estimates remained unbiased (<0.5% bias), but occupancy bias increased substantially for LPF-OLS (14.2%) and LPF-TLS (10.0%), propagating to negative bias in EC50 (−14.0% and −8.9%, respectively). In contrast, dcLPF-TLS reduced occupancy bias to 1.9% and EC50 bias to 4.5%.

Under sinogram-space noise and reconstruction, bias was further amplified (Figure 1). Whole-image occupancy bias reached 26.5% (LPF-OLS) and 24.0% (LPF-TLS), with corresponding bias in EC50 of −33.1% and −30.4%. The dcLPF-TLS method reduced occupancy bias to 7.9% and EC50 bias to −7.7%.

Bias was strongly occupancy-dependent, reaching >70% in very low-occupancy regions for conventional LPF, while remaining substantially lower with dcLPF. Reconstruction-only experiments demonstrated that iterative reconstruction alone introduced moderate positive occupancy bias (~5–6%) despite negligible PET and VT bias.

Across all conditions, EC50 bias tracked with occupancy bias in magnitude but in the opposite direction, indicating that errors in EC50 estimation are primarily driven by bias in voxel-wise occupancy estimation.

 

Conclusion:
Voxel-wise LPF introduces substantial, noise-dependent bias in occupancy and EC50 imaging despite unbiased PET and kinetic modeling stages. This bias arises from errors-in-variables effects and is amplified by sinogram-level noise and image reconstruction. The proposed decorrelated LPF (dcLPF) significantly reduces bias across all simulation conditions, improving the reliability of spatially resolved EC50 images. These findings establish a validated framework for bias characterization and mitigation in quantitative PET occupancy studies and support the use of dcLPF for robust voxel-wise pharmacodynamic imaging.

 

Image/Figure:
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Image/Figure Caption:
Figure 1: Bias propagation in occupancy and EC50 estimation across LPF methods under realistic noise conditions. Emax fits of true and estimated occupancy under sinogram-space Poisson noise and iterative reconstruction. Each row corresponds to an occupancy estimation method (LPF-OLS, LPF-TLS, and dcLPF-TLS), and columns correspond to Pass1, estimating both occupancy and VND (left) and Pass2, fixing VND to median VND from Pass1 (right). For ROI 2 (high occupancy; blue) and ROI 8 (lower occupancy; orange), solid curves denote the ground-truth Emax relationship, while square markers represent the median estimated occupancy across voxels within each ROI at each plasma concentration. Shaded bands indicate the IQR of voxel-wise estimates. Vertical dashed lines denote the estimated EC50 (median), with shaded vertical bands representing the EC50 IQR interval.

 

Author
Alaaddin Ibrahimy
Yale University