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Purpose: Dynamic or 4D imaging of the thorax has many applications. Both prospective and retrospective respiratory gating and tracking techniques have been developed for 4D imaging via CT and MRI. For pediatric imaging, due to radiation concerns, MRI becomes the de facto modality of choice. In thoracic insufficiency syndrome (TIS), patients often suffer from extreme malformations of the chest wall, diaphragm, and/or spine with inability of the thorax to support normal respiration or lung growth (Campbell et al., 2003, Campbell and Smith, 2007), as such patient cooperation needed by some of the gating and tracking techniques are difficult to realize without causing patient discomfort and interference with the breathing mechanism itself. Therefore (ventilator-supported) free-breathing MRI acquisition is currently the best choice for imaging these patients. This, however, raises a question of how to create a consistent 4D image from such acquisitions. This paper presents a novel graph-based technique for compiling the best 4D image volume representing the thorax over one respiratory cycle from slice images acquired during unencumbered natural tidal-breathing of pediatric TIS patients., Methods: In our approach, for each coronal (or sagittal) slice position, images are acquired at a rate of about 200-300ms/slice over several natural breathing cycles which yields over 2000 slices. A weighted graph is formed where each acquired slice constitutes a node and the weight of the arc between two nodes defines the degree of contiguity in space and time of the two slices. For each respiratory phase, an optimal 3D spatial image is constructed by finding the best path in the graph in the spatial direction. The set of all such 3D images for a given respiratory cycle constitutes a 4D image. Subsequently, the best 4D image among all such constructed images is found over all imaged respiratory cycles. Two types of evaluation studies are carried out to understand the behavior of this algorithm and in comparison to a method called Random Stacking - a 4D phantom study and 10 4D MRI acquisitions from TIS patients and normal subjects. The 4D phantom was constructed by 3D printing the pleural spaces of an adult thorax, which were segmented in a breath-held MRI acquisition., Results: Qualitative visual inspection via cine display of the slices in space and time and in 3D rendered form showed smooth variation for all data sets constructed by the proposed method. Quantitative evaluation was carried out to measure spatial and temporal contiguity of the slices via segmented pleural spaces. The optimal method showed smooth variation of the pleural space as compared to Random Stacking whose behavior was erratic. The volumes of the pleural spaces at the respiratory phase corresponding to end inspiration and end expiration were compared to volumes obtained from breath-hold acquisitions at roughly the same phase. The mean difference was found to be roughly 3%., Conclusions: The proposed method is purely image-based and post-hoc and does not need breath holding or external surrogates or instruments to record respiratory motion or tidal volume. This is important and practically warranted for pediatric patients. The constructed 4D images portray spatial and temporal smoothness that should be expected in a consistent 4D volume. We believe that the method can be routinely used for thoracic 4D imaging., (Copyright © 2016 Elsevier B.V. All rights reserved.)