Physics-Informed Deep Learning for Improved Input Function Estimation in Motion-Blurred Dynamic [${}^{18}$F]FDG PET Images

TL;DR

Estimating the arterial input function (AIF) from dynamic mouse [${}^{18}$F]FDG PET data is invasive and error-prone with traditional methods. The authors propose PIDLIF, a physics-informed extension of FCDLIF that injects a two-tissue compartment kinetics loss during training to ground AIF predictions in physiological dynamics, enabling end-to-end AIF estimation from 4D PET data. On a dataset of 70 dynamic mouse scans, PIDLIF achieves comparable performance to the non-physics baseline on pristine data but shows markedly improved robustness to motion blur, reducing RMSE rise and maintaining higher $R^2$ under severe degradation. This approach offers a practical path toward noninvasive, robust AIF estimation in preclinical PET imaging and motivates extending physics guidance to voxel-wise kinetic analyses.

Abstract

Kinetic modeling enables \textit{in vivo} quantification of tracer uptake and glucose metabolism in [${}^{18}$F]Fluorodeoxyglucose ([${}^{18}$F]FDG) dynamic positron emission tomography (dPET) imaging of mice. However, kinetic modeling requires the accurate determination of the arterial input function (AIF) during imaging, which is time-consuming and invasive. Recent studies have shown the efficacy of using deep learning to directly predict the input function, surpassing established methods such as the image-derived input function (IDIF). In this work, we trained a physics-informed deep learning-based input function prediction model (PIDLIF) to estimate the AIF directly from the PET images, incorporating a kinetic modeling loss during training. The proposed method uses a two-tissue compartment model over two regions, the myocardium and brain of the mice, and is trained on a dataset of 70 [${}^{18}$F]FDG dPET images of mice accompanied by the measured AIF during imaging. The proposed method had comparable performance to the network without a physics-informed loss, and when sudden movement causing blurring in the images was simulated, the PIDLIF model maintained high performance in severe cases of image degradation. The proposed physics-informed method exhibits an improved robustness that is promoted by physically constraining the problem, enforcing consistency for out-of-distribution samples. In conclusion, the PIDLIF model offers insight into the effects of leveraging physiological distribution mechanics in mice to guide a deep learning-based AIF prediction network in images with severe degradation as a result of blurring due to movement during imaging.

Figures (4)

• Figure 1: Compartment model (a) for kinetic modeling with $\mathrm{[^{18}F]FDG}$ PET with rate constants describing rate of transfer between compartments. For this system, the metabolic rate of glucose is proportional to the net influx rate, $K_i \equiv K_1 \cdot k_3 / (k_2 + k_3)$, where rate constants $K_1,\ k_2$, and $k_3$ are derived from the compartment model. Example of artificial motion blur (b) split over tracer uptake phases. A motion blur kernel of size 15x15x15 are convolved with the image to simulate movement in a random direction during imaging. The columns correspond with the first 25 (peak), intermediate 9 (mid), and last 8 (tail) time-frames, respectively. The images are averaged over time within each respective segment, resulting in crisper appearence than the actual input data.
• Figure 2: Our model in context: a time series of PET images are used as input to the spatial and temporal feature extractor from salomonsen2025DLIF, which predicts the input function. We compare this with the AIF using a mean squared error loss combined with the kinetic modeling loss, computed using a two-tissue compartment model, inspired by wang2024non.
• Figure 3: Input function prediction using FCDLIF salomonsen2025DLIF: a spatial feature extractor applies 3D convolutions in a bottleneck configuration to extract a dense representation of spatial features. This is followed by a temporal feature extractor that captures temporal relationships between adjacent time frames. The final output is the regression curve predicting the input function for the associated PET-images.
• Figure 4: Results comparing the robustness of the FCDLIF salomonsen2025DLIF model with and without the physics-informed loss function to motion blur. The RMSE and $R^2$ values are shown for different levels of motion blurring denoted by the size of the kernel being convolved with the images.