Inverse Bayesian Inference for Extracting Lesion Dynamics from Longitudinal Spectral CT

2026-07-25

AI Summary

This study addresses the challenge of deciphering the dynamic mechanisms driving lesion evolution from longitudinal spectral CT imaging. It introduces, for the first time in medical image analysis, an interpretable, parameterized framework based on inverse Bayesian inference, decomposing lesion dynamics into intrinsic kinetics, local tumor burden coupling, and microenvironmental state. By integrating differential equation modeling with photon-counting CT data, the method enables mechanistic inference of tumor evolution. Applied to a non-small cell lung cancer (NSCLC) metastatic cohort, it reveals competitive coupling among pulmonary lesions (B = −0.34, p < 0.05) and cooperative coupling in hepatic lesions (C ≈ +1.0, p < 0.05). Parameter recoverability is further validated using synthetic data, establishing a novel paradigm for investigating tumor evolutionary dynamics.

Abstract

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 $A_i$ 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 ($C\approx+1.0$, $p<0.05$). 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

Problem

• lesion dynamics
• longitudinal imaging
• spectral CT
• inverse inference
• dynamical parameters

Innovation

• inverse Bayesian inference
• lesion dynamics
• spectral CT
• longitudinal imaging
• dynamical modeling