Graph-based retrospective 4D Image construction from free-breathing MRI slice acquisitions

4D or dynamic imaging of the thorax has many potential applications [1, 2]. CT and MRI offer sufficient speed to acquire motion information via 4D imaging. However they have different constraints and requirements. For both modalities both prospective and retrospective respiratory gating and tracking techniques have been developed [3, 4]. For pediatric imaging, x-ray radiation becomes a primary concern and MRI remains as the de facto choice. The pediatric subjects we deal with often suffer from extreme malformations of their chest wall, diaphragm, and/or spine, as such patient cooperation needed by some of the gating and tracking techniques are difficult to realize without causing patient discomfort. Moreover, we are interested in the mechanical function of their thorax in its natural form in tidal breathing. Therefore free-breathing MRI acquisition is the ideal modality of imaging for these patients. In our set up, for each coronal (or sagittal) slice position, slice images are acquired at a rate of about 200-300 ms/slice over several natural breathing cycles. This produces typically several thousands of slices which contain both the anatomic and dynamic information. However, it is not trivial to form a consistent and well defined 4D volume from these data. In this paper, we present a novel graph-based combinatorial optimization solution for constructing the best possible 4D scene from such data entirely in the digital domain. Our proposed method is purely image-based and does not need breath holding or any external surrogates or instruments to record respiratory motion or tidal volume. Both adult and children patients' data are used to illustrate the performance of the proposed method. Experimental results show that the reconstructed 4D scenes are smooth and consistent spatially and temporally, agreeing with known shape and motion of the lungs.