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Beyond Conventional Parametric Modeling: Data-Driven Framework for Estimation and Prediction of Time Activity Curves in Dynamic PET Imaging

Niloufar Zakariaei, Arman Rahmim, Eldad Haber

TL;DR

This paper tackles the difficulty of accurately estimating Time-Activity Curves (TACs) in Dynamic PET when conventional $2$-tissue and $3$-tissue compartment models fail to capture non-linear, spatially varying kinetics. It introduces a data-driven reaction-diffusion neural network that embeds the imaging data into a high-dimensional state $\mathbf{u}(\mathbf{x},t)$ and learns diffusion coefficients $\boldsymbol{\kappa}$ and a nonlinear reaction term $R(\mathbf{u},t;\boldsymbol{\theta})$, discretized with an IMEX scheme and time embeddings. Training uses early frames to predict later frames by minimizing the $L^2$ loss with the Adam optimizer on seven patients with [18F]DCFPyL PET, and is benchmarked against nonlinear least-squares fitting of $3$-TCM. The results show improved TAC predictions across organs, suggesting a physically motivated, scalable framework for PK/PD quantification in quantitative nuclear medicine and potential applicability to next-generation radiopharmaceuticals.

Abstract

Dynamic Positron Emission Tomography (dPET) imaging and Time-Activity Curve (TAC) analyses are essential for understanding and quantifying the biodistribution of radiopharmaceuticals over time and space. Traditional compartmental modeling, while foundational, commonly struggles to fully capture the complexities of biological systems, including non-linear dynamics and variability. This study introduces an innovative data-driven neural network-based framework, inspired by Reaction Diffusion systems, designed to address these limitations. Our approach, which adaptively fits TACs from dPET, enables the direct calibration of diffusion coefficients and reaction terms from observed data, offering significant improvements in predictive accuracy and robustness over traditional methods, especially in complex biological scenarios. By more accurately modeling the spatio-temporal dynamics of radiopharmaceuticals, our method advances modeling of pharmacokinetic and pharmacodynamic processes, enabling new possibilities in quantitative nuclear medicine.

Beyond Conventional Parametric Modeling: Data-Driven Framework for Estimation and Prediction of Time Activity Curves in Dynamic PET Imaging

TL;DR

This paper tackles the difficulty of accurately estimating Time-Activity Curves (TACs) in Dynamic PET when conventional -tissue and -tissue compartment models fail to capture non-linear, spatially varying kinetics. It introduces a data-driven reaction-diffusion neural network that embeds the imaging data into a high-dimensional state and learns diffusion coefficients and a nonlinear reaction term , discretized with an IMEX scheme and time embeddings. Training uses early frames to predict later frames by minimizing the loss with the Adam optimizer on seven patients with [18F]DCFPyL PET, and is benchmarked against nonlinear least-squares fitting of -TCM. The results show improved TAC predictions across organs, suggesting a physically motivated, scalable framework for PK/PD quantification in quantitative nuclear medicine and potential applicability to next-generation radiopharmaceuticals.

Abstract

Dynamic Positron Emission Tomography (dPET) imaging and Time-Activity Curve (TAC) analyses are essential for understanding and quantifying the biodistribution of radiopharmaceuticals over time and space. Traditional compartmental modeling, while foundational, commonly struggles to fully capture the complexities of biological systems, including non-linear dynamics and variability. This study introduces an innovative data-driven neural network-based framework, inspired by Reaction Diffusion systems, designed to address these limitations. Our approach, which adaptively fits TACs from dPET, enables the direct calibration of diffusion coefficients and reaction terms from observed data, offering significant improvements in predictive accuracy and robustness over traditional methods, especially in complex biological scenarios. By more accurately modeling the spatio-temporal dynamics of radiopharmaceuticals, our method advances modeling of pharmacokinetic and pharmacodynamic processes, enabling new possibilities in quantitative nuclear medicine.
Paper Structure (5 sections, 6 equations, 5 figures, 2 tables)

This paper contains 5 sections, 6 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Deriving a reaction diffusion neural network for the modeling of TACs
  3. Training the network and Dataset
  4. Numerical Results and Evaluation
  5. Discussion and Conclusions

Figures (5)

  • Figure 1: Dynamic liver images captured at eight distinct time points.
  • Figure 2: The average of the TAC curve over the liver, along with its standard deviation. Data is fitted using a three-tissue compartment model (3TCM) based on the early 6 time frames.
  • Figure 3: The reaction diffusion network architecture: An opening layer takes the input image into a higher embedded dimension, where a reaction diffusion network with learned diffusivity and reaction operates. In the example above, 3 channels are utilized to open the image.
  • Figure 4: A selected slice of one of the patients, showcasing the latest time points predicted by our proposed model versus the 3TCM and the original images.
  • Figure 5: Predicted vs. actual [18F]DCFPyL concentrations over time in 3 patients. Training data are shown with solid markers, test data with hollow markers. Predictions from the reaction diffusion model and traditional 3TCM are compared with original test. Trend lines connect data points, showing our model's enhanced accuracy in capturing distribution dynamics.