Modeling respiratory lung motion: a biophysical approach using finite element methods

Abstract

Respiratory dynamics poses a main source of error in radiotherapy of thoracic tumors. Development and optimization of methods to adequately account for breathing motion require detailed knowledge of the dynamics and its impact on e. g. the dose delivered by radiation. Thus, computer aided modeling and model based simulation of respiratory motion gains in importance. In this paper a biophysical approach for modeling lung motion is described. Main aspects of the process of lung ventilation are identified and outlined as the starting point of modeling. They are formulated as a contact problem of linear elasticity theory. The resulting boundary value problem is solved using Finite Element Methods (FEM). 4D (= 3D+t) CT image data are used to evaluate the modeling approach. Model based three-dimensional vector fields representing respiratory motion are computed for different patients. Simulated motion patterns of inner lung landmarks like prominent bifurcations of the bronchial tree and the tumor mass center are compared with corresponding motion patterns observed in the 4D CT data. The influence of geometrical and biomechanical parameters like mesh quality and values of elasticity constants on the modeling process is investigated. Differences between model based predicted landmark positions and corresponding landmark positions identified interactively are mostly within the variability of interactive landmark positioning across multiple observers (interobserver variability). The impact of geometrical and biomechanical parameters on resulting vector fields is fairly small. Outcomes suggest that FEM state an adequate strategy to model aspects of the physiology of breathing.