[Paper Review] Self-Supervised Learning for Physiologically-Based Pharmacokinetic Modeling in Dynamic PET

Francesca De Benetti, Walter Simson+6 more|arXiv (Cornell University)|May 17, 2023

Medical Imaging Techniques and Applications4 citations

TL;DR

This paper proposes a self-supervised spatio-temporal 3D UNet to estimate physiologically-based pharmacokinetic (PBPK) model parameters from dynamic F-18-FDG PET data, directly enforcing consistency between predicted and measured time activity curves (TACs) via a physics-informed loss. The method achieves parametric image quality comparable to conventional curve fitting but up to orders of magnitude faster, producing biologically plausible voxel-wise kinetic maps without ground truth.

ABSTRACT

Dynamic positron emission tomography imaging (dPET) provides temporally resolved images of a tracer enabling a quantitative measure of physiological processes. Voxel-wise physiologically-based pharmacokinetic (PBPK) modeling of the time activity curves (TAC) can provide relevant diagnostic information for clinical workflow. Conventional fitting strategies for TACs are slow and ignore the spatial relation between neighboring voxels. We train a spatio-temporal UNet to estimate the kinetic parameters given TAC from F-18-fluorodeoxyglucose (FDG) dPET. This work introduces a self-supervised loss formulation to enforce the similarity between the measured TAC and those generated with the learned kinetic parameters. Our method provides quantitatively comparable results at organ-level to the significantly slower conventional approaches, while generating pixel-wise parametric images which are consistent with expected physiology. To the best of our knowledge, this is the first self-supervised network that allows voxel-wise computation of kinetic parameters consistent with a non-linear kinetic model. The code will become publicly available upon acceptance.

Motivation & Objective

• To address the challenge of slow, noisy, and clinically impractical voxel-wise PBPK parameter estimation in dynamic PET.
• To develop a deep learning framework that enforces physiological consistency in kinetic parameter prediction using self-supervised learning.
• To generate high-quality parametric images at the voxel level that reflect expected physiological patterns.
• To enable scalable, real-time kinetic modeling compatible with clinical workflows.
• To overcome limitations of conventional curve fitting, such as local minima and sensitivity to noise.

Proposed method

• A custom 3D UNet with separate spatial and temporal convolutional kernels is trained to predict four kinetic parameters: K1, k2, k3, and VB.
• The network uses a self-supervised loss that minimizes the mean-square error between measured TACs and TACs reconstructed from predicted parameters.
• The loss function embeds the 2-tissue compartment (2TC) PBPK model as a differentiable constraint, enforcing physical plausibility.
• Spatial and temporal convolutions are used to exploit neighborhood and temporal dependencies in dPET data.
• The model is trained end-to-end on real dPET data without ground truth parameters, relying solely on TAC reconstruction fidelity.
• The architecture reduces parameters by 99.6% compared to standard UNet, improving convergence and efficiency.

Experimental results

Research questions

• RQ1 Can a self-supervised deep learning model accurately estimate PBPK kinetic parameters in dynamic PET without ground truth?
• RQ2 Does enforcing a differentiable PBPK model in the loss function improve physiological plausibility of parametric images?
• RQ3 How does the performance of the proposed method compare to conventional curve fitting in terms of accuracy and speed?
• RQ4 Can the model generalize across anatomical regions with varying TAC dynamics, such as liver, heart, and lungs?
• RQ5 What impact do respiratory and cardiac motion artifacts have on parameter estimation, and can the model mitigate them?

Key findings

• The proposed method achieves cosine similarity (CS) of 0.87 in the liver and 0.71 in the heart/lungs, indicating strong TAC reconstruction fidelity.
• The DNN-generated parametric images show more realistic spatial distributions than conventional curve fitting, particularly in the liver, where the gallbladder is clearly visible.
• The DNN model runs significantly faster than conventional curve fitting, enabling real-time or near-real-time parametric imaging.
• The model predicts K1, k2, k3, and VB with reasonable agreement to reference curve fitting results, except for K1 in the spleen and k2 in the kidneys, which fall outside confidence intervals.
• Underestimation of VB in the heart and aorta (0.376 and 0.622, respectively) suggests motion artifacts affect accuracy, particularly in high-motion regions.
• The method produces parametric images that are qualitatively more consistent with expected physiology than conventional approaches, despite lacking ground truth.