Uncertainty-Aware Prediction of Lung Tumor Growth from Sparse Longitudinal CT Data via Bayesian Physics-Informed Neural Networks

2026-05-13

AI Summary

This study addresses the challenge of predicting lung tumor growth and quantifying uncertainty from sparse, irregular longitudinal CT scans by proposing a Bayesian physics-informed neural network that integrates Gompertzian growth dynamics. The model operates in log-volume space and employs a two-stage inference strategy combining maximum a posteriori (MAP) estimation with Hamiltonian Monte Carlo (HMC) sampling. To the best of our knowledge, this is the first application of Bayesian physics-informed neural networks to tumor growth forecasting from sparse CT sequences. The approach yields well-calibrated uncertainty estimates and uncovers parameter correlations consistent with known biological behavior. Evaluated on data from 30 NLST patients, the model achieves an RMSE of approximately 0.20 in log space and demonstrates strong 95% credible interval coverage, effectively capturing inter-patient heterogeneity in tumor growth trajectories.

Abstract

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.

Problem

• lung tumor growth
• sparse longitudinal data
• uncertainty quantification
• CT imaging
• Bayesian inference

Innovation

• Bayesian physics-informed neural networks
• tumor growth prediction
• uncertainty quantification
• Gompertz model
• longitudinal CT data