Generative Consistency Models for Estimation of Kinetic Parametric Image Posteriors in Total-Body PET

TL;DR

Dynamic total-body PET requires uncertaintyquantified parametric maps across many voxels, but traditional Bayesian methods like MCMC are impractical at this scale. The authors introduce a conditional consistency model (CM) that transforms Gaussian noise directly into posterior samples of kinetic parameters conditioned on TACs and AIF, collapsing hundreds of diffusion steps into a single forward pass with a brief refinement. Trained on 500k physiologically realistic 2TCM simulations, CM closely matches MCMC accuracy (median APE $<5\%$; median $D_{KL}<0.5$) while being more than five orders of magnitude faster, and provides voxelwise uncertainty and a posterior-based model-selection map. The framework enables routine, fully Bayesian voxelwise parametric TB-PET imaging and is readily extensible to other tracers and models, offering a practical path toward systems physiology applications.

Abstract

Dynamic total body positron emission tomography (TB-PET) makes it feasible to measure the kinetics of all organs in the body simultaneously which may lead to important applications in multi-organ disease and systems physiology. Since whole-body kinetics are highly heterogeneous with variable signal-to-noise ratios, parametric images should ideally comprise not only point estimates but also measures of posterior statistical uncertainty. However, standard Bayesian techniques, such as Markov chain Monte Carlo (MCMC), are computationally prohibitive at the total body scale. We introduce a generative consistency model (CM) that generates samples from the posterior distributions of the kinetic model parameters given measured time-activity curves and arterial input function. CM is able to collapse the hundreds of iterations required by standard diffusion models into just 3 denoising steps. When trained on 500,000 physiologically realistic two-tissue compartment model simulations, the CM produces similar accuracy to MCMC (median absolute percent error < 5%; median K-L divergence < 0.5) but is more than five orders of magnitude faster. CM produces more reliable Ki images than the Patlak method by avoiding the assumption of irreversibility, while also offering valuable information on statistical uncertainty of parameter estimates and the underlying model. The proposed framework removes the computational barrier to routine, fully Bayesian parametric imaging in TB-PET and is readily extensible to other tracers and compartment models.

Figures (10)

• Figure 1: Multistep consistency sampling for posterior kinetic parameter estimation. To draw a posterior sample, a zero-mean Gaussian vector shaped like the kinetic-parameter vector (e.g., $\mathbf{\theta}_{1,1}$) is generated and together with the measured TAC and AIF $y$ is passed through the consistency model $f_{\phi}(\cdot)$ at the highest noise level ($t = 1$), producing a coarse denoised estimate $\hat{\mathbf{\theta}}'_{0,1}$. This estimate is corrupted to the intermediate noise level ($t = 0.5$) to form $\mathbf{\theta}_{0.5,1}$, which is then fed back into $f_{\phi}(\cdot)$ to obtain the refined sample $\hat{\mathbf{\theta}}_{0,1}$. Repeating this procedure $n$ times with independent noise draws yields a posterior sample, treated as independent draws from the posterior distribution $p(\mathbf{\theta}|y)$.
• Figure 2: Architecture of the 1D U-Net used in the consistency model for kinetic‐parameter posterior estimation. The network combines three encoders: encoder A and B are dense layer-based encoders for the noisy kinetic parameter values $\mathbf{\theta}_t$ and concatenated dynamic data $y$, respectively, and the noise level $t$ is encoded by applying a Gaussian Fourier projection. Encoded $y$ and $t$ are concatenated and injected at each downsampling (blue arrow) and upsampling stage (green arrow). Skip connections (dashed blue) link corresponding encoder and decoder blocks. We use this neural network as the $f_\phi(\cdot)$.
• Figure 3: Example posterior inference for a single voxel. (a) A simulated time–activity curve is shown with the corresponding AIF. (b) The resulting posterior distributions of the kinetic parameters, predicted by the proposed consistency model (blue), are contrasted with those obtained from deep learning baselines, approximate Bayesian computation, and the reference Markov-chain Monte Carlo (MCMC) method (red). The black dashed lines represent the truth value.
• Figure 4: Quantitative evaluation on 100 simulated TACs. For each trial, a kinetic parameter vector was drawn from the pre-assumed physiological range, a noisy TAC was generated with a two-tissue compartment model, and posteriors were estimated by the proposed CM, the reference MCMC, and five baselines—ABC, DDPM, SBD, CVAE, and GAN. (a) Kullback–Leibler divergence between each method’s posterior and the MCMC posterior. (b) Absolute percentage error between the ground-truth parameter and the posterior mean. (c) Percentage error of the posterior standard deviation relative to that obtained with MCMC.
• Figure 5: Robustness of Kinetic Parameter Estimation to Tracer Arrival Delays. Analysis of estimation accuracy with respect to tracer arrival delay ($t_0$). The absolute percentage error (APE) for each kinetic parameter is plotted against the ground-truth delay time for test samples.