A novel personalized time-varying biomechanical model for estimating lung tumor motion and deformation

Accurate prediction of lung tumor motion and deformation (LTMD) is essential for precise radiotherapy. However, existing models often rely on static, population-based material parameters, overlooking patient-specific and time-varying lung biomechanics. Personalized dynamic models that capture temporal changes in lung elasticity are needed to improve LTMD prediction and guide treatment planning more effectively.

This study aims to develop a patient-specific, time-varying biomechanical model to predict LTMD more accurately.

Four-dimensional computed tomography (4DCT) images from 27 patients, each with 10 breathing phases, were analyzed. A finite element model was developed, modeling lung as a hyper-elastic material and tumor as linear elastic. Lung elasticity parameters, including Young's modulus (E) and Poisson's ratio (v), were optimized for each phase using Efficient Global Optimization algorithm. Four functions were tested to model the variation of E and v across different phases. For each patient, average values of these parameters were computed, and their correlation with 11 clinical features was analyzed. The model's accuracy in predicting LTMD was evaluated using tumor center of mass motion error (ΔTCM) and volumetric Dice similarity coefficient (vDSC). Factors influencing the model's accuracy were investigated. Specifically, lung surface traction vector fields (STVFs) were calculated during the transition from end-expiration to end-inspiration phases, and their relationship with LTMD was also analyzed.

The first-order Fourier function provided the best fit among four tested functions, with average R-squared values of 0.93 ± 0.03 for E and 0.91 ± 0.03 for v. The average values of E and v were significantly correlated with patient age. The model showed a mean ΔTCM of 1.47 ± 0.68 mm and a mean vDSC of 0.93 ± 0.02. A negative correlation was found between tumor deformation vDSC and ΔTCM (r = -0.55, p < 0.05). Higher STVFs were observed near diaphragm and intercostal muscles, with correlations between STVFs and tumor motion amplitude (r ≥ 0.92, p < 0.05).

These findings offer new insights into developing personalized, time-varying motion management strategies of lung tumors.