Longitudinal medical imaging captures temporal evolution of lesions, yet extracting the underlying dynamical parameters governing this evolution remains challenging. We propose an inverse Bayesian framework for inferring lesion dynamics from longitudinal spectral CT. We decompose spectral feature (x) evolution into three components: \begin{equation*} \frac{dx_i}{dt} = A_i x_i + B \cdot n + C \cdot Δx_{\text{sat}} \end{equation*} where Ai captures intrinsic dynamics (lesion-autonomous evolution), B captures local environment tumour burden (organ tumour burden through satellite count coupling), and C captures environment/satellite state change (i.e., whether surrounding lesions move similarly or not). We demonstrate the framework on photon-counting NSCLC CT data from metastases, recovering distinct dynamical regimes: lung lesions exhibit significant satellite count coupling (B=−0.34, p<0.05) suggesting competitive dynamics, while liver lesions show synergistic satellite behaviour coupling (C≈+1.0, p<0.05). Synthetic validation confirms parameter recovery, and cross-coupling analysis validates that our method detects non-zero coupling when present. This work establishes inverse dynamical inference as a principled methodology for extracting interpretable parameters from longitudinal imaging, moving beyond static feature extraction toward mechanistic characterisation of lesion behaviour. The code and data are available at: https://github.com/lukasf98/inverse-bayesian-inference
This work studies lung tumor growth prediction from sparse and irregular longitudinal computed tomography (CT) observations with measurement variability. A Bayesian physics-informed neural network is developed by combining Gompertz growth dynamics with low-dimensional Bayesian inference in the log-volume domain. The framework employs a two-stage inference strategy combining maximum a posteriori (MAP) estimation and Hamiltonian Monte Carlo (HMC) sampling to estimate posterior predictive distributions and uncertainty intervals. The method was evaluated on longitudinal data from the National Lung Screening Trial (30 patients). Results show that the model captures heterogeneous tumor growth patterns while maintaining reasonable prediction accuracy under limited observations. Compared with deterministic modeling approaches, the proposed approach additionally provides calibrated uncertainty estimates. The inferred posterior parameter correlations were consistent with expected biological growth behavior. The proposed framework achieved a cohort-level log-space RMSE of approximately 0.20 together with well-calibrated 95% credible interval coverage across 30 patients. These findings suggest that Bayesian physics-informed modeling may be useful for uncertainty-aware tumor growth assessment when only limited longitudinal follow-up scans are available.
Tracking tumor lesions across serial CT scans is essential for oncological response assessment. Existing automated methods face a fundamental trade-off: end-to-end trackers achieve high automation but offer no opportunity to correct silent tracking failures, while decoupled registration-segmentation pipelines permit user verification yet discard the lesion's prior appearance, limiting accuracy in ambiguous cases. In this work, we propose a Verified Tracking paradigm: a clinician verifies a registration-proposed prompt, which the model leverages alongside the baseline lesion appearance to resolve segmentation ambiguities. We present a unified framework combining early spatial prompt fusion with latent temporal difference weighting for longitudinally-informed segmentation. To address data scarcity, we leverage large-scale synthetic pretraining, proving essential for exploiting longitudinal context, improving performance by up to 4.5 Dice points over training from scratch. Our approach secured first place in the MICCAI autoPET IV challenge. We further curate and release PanTrack, a new longitudinal pancreatic cancer benchmark, to assess out-of-distribution generalization. Experiments show that our model outperforms prior work in both fully automatic and the proposed verified tracking setting offering a clinically safe middle ground between automation and control. Code, model and dataset will be released at https://github.com/MIC-DKFZ/LongiSeg
Yannick Kirchhoff, Maximilian Rokuss, Daniel Philipp Mertens +5
Forecasting longitudinal brain lesion evolution is critical for disease monitoring and treatment planning. Existing approaches typically learn a direct mapping from a baseline image to a future observation, without explicitly modeling the physical mechanisms underlying the lesion progression. Such an entangled modeling of structural deformation and image intensity variation limits physical plausibility, model generalization, and interpretability. To address this, we propose PDF, a Physics-grounded Disentangled Flow matching framework for longitudinal brain disease forecasting. We explicitly decompose the longitudinal modeling of lesion growth into two processes, each learned by a dedicated flow matching network: morphology evolution, which captures lesion growth and structural deformation; and intensity evolution, which models signal changes driven by variations in lesion concentration. To enforce physics-grounded constraints, we introduce a PDE-regularized loss based on lesion growth dynamics, that enforces a diffusion-reaction-advection formulation for morphological evolution. Experiments on three public longitudinal datasets spanning diverse brain diseases demonstrate state-of-the-art performance, validating the effectiveness of the disentangled modeling framework and physics-grounded learning design. Code is publicly available at https://github.com/jhuldr/PDF.