Statistical Modeling of 4D Respiratory Lung Motion Using Diffeomorphic Image Registration

Abstract

Modeling of respiratory motion has become increasingly important in various applications of medical imaging (e.g., radiation therapy of lung cancer). Current modeling approaches are usually confined to intra-patient registration of 3D image data representing the individual patient's anatomy at different breathing phases. We propose an approach to generate a mean motion model of the lung based on thoracic 4D computed tomography (CT) data of different patients to extend the motion modeling capabilities. Our modeling process consists of three steps: an intra-subject registration to generate subject-specific motion models, the generation of an average shape and intensity atlas of the lung as anatomical reference frame, and the registration of the subject-specific motion models to the atlas in order to build a statistical 4D mean motion model (4D-MMM). Furthermore, we present methods to adapt the 4D mean motion model to a patient-specific lung geometry. In all steps, a symmetric diffeomorphic nonlinear intensity-based registration method was employed. The Log-Euclidean framework was used to compute statistics on the diffeomorphic transformations. The presented methods are then used to build a mean motion model of respiratory lung motion using thoracic 4D CT data sets of 17 patients. We evaluate the model by applying it for estimating respiratory motion of ten lung cancer patients. The prediction is evaluated with respect to landmark and tumor motion, and the quantitative analysis results in a mean target registration error (TRE) of 3.3 ±1.6 mm if lung dynamics are not impaired by large lung tumors or other lung disorders (e.g., emphysema). With regard to lung tumor motion, we show that prediction accuracy is independent of tumor size and tumor motion amplitude in the considered data set. However, tumors adhering to non-lung structures degrade local lung dynamics significantly and the model-based prediction accuracy is lower in these cases. The statistical respiratory motion model is capable of providing valuable prior knowledge in many fields of applications. We present two examples of possible applications in radiation therapy and image guided diagnosis.

A 4D Statistical Shape Model for Automated Segmentation of Lungs with Large Tumors

“…This is achieved by propagating M pseudo-landmarks from an automatically landmarked atlas to all other shapes of the training set. After the generation and landmarking (by means of a surface triangulation and curvature-based mesh simplification) of an average lung shape atlas, landmark propagation is done by using non-linear transformations obtained from atlas-patient and intra-patient registrations of the images performed with a non-linear diffeomorphic registration method [8].…”

Estimating the 4D Respiratory Lung Motion by Spatiotemporal Registration and Building Super-Resolution Image

“…The advantages of using temporal fibers include: 1) The modeling of temporal motion is much easier on the particular temporal fiber φ(x i , t) than on the entire motion field φ(x, t); 2) The spatial correspondence detection and temporal motion regularization are unified along the temporal fibers. Here, we model the motion regularization on each temporal fiber as the kernel regression problem with kernel function ψ: (2) Energy Function of Spatiotemporal Registration-The energy function in our spatiotemporal registration method is defined as: (3) where L s (f s ) is the bending energy for requiring the deformation field f s to be spatially smooth [8]. λ 1 and λ 2 are the two scalars to balance the strength of spatial smoothness L s and temporal consistency L T .…”

“…However, the respiratory motion is the significant source of error in radiotherapy planning of thoracic tumors, as well as many other image guided procedures [1]. Therefore, there is increasing growth in investigating the methods for accurate estimation of the respiratory motion in 4D-CT [2][3][4].…”

“…Image registration plays an important role in the current motion estimation methods by establishing temporal correspondences, e.g., between the maximum inhale phase and all other phases [3,4]. However, there are some critical limitations in these methods.…”

“…Since the modern CT scanner can only scan a limited region of human body at each couch position, the final 4D-CT has to be assembled by sorting multiple free-breathing CT segments w.r.t. the couch position and tidal volume [3]. However, due to the patient's free breathing during scan, no CT segment can be scanned exactly at the particular tidal volume.…”