Clinical management of foot pathology requires accurate and robust measurement of the anatomical angles. In order to measure a 3D angle, recent approaches have adopted a landmark-based local coordinate system to establish bone angles used in orthopedics. These measurement methods mainly assess the relative angle between bones using a representative axis derived from the morphological feature of the bone and therefore, the results can be affected by bone deformities. In this study, we propose a method of deriving a global frame-of-reference to acquire consistent direction of the foot by extracting the undersurface of the foot from the CT image data. The two lowest positions of the foot skin are identified from the surface to define the base plane, and the direction from the hallux to the fourth toe is defined together to construct the global coordinate system. We performed the experiment on 10 volumes of foot CT images of healthy subjects to verify that the proposed method provides reliable measurements. We measured 3D angles for talus-calcaneus and talus-navicular using facing articular surfaces of paired bones. The angle was reported in 3 projection angles based on both coordinate systems defined by proposed global frame-of-reference and by CT image planes (saggital, frontal, and transverse). The result shows that the quantified angle using the proposed method considerably reduced the standard deviation (SD) against the angle using the conventional projection planes, and it was also comparable with the measured angles obtained from local coordinate systems of the bones. Since our method is independent from any individual local shape of a bone, unlike the measurement method using the local coordinate system, it is suitable for inter-subject comparison studies.
Clean bone segmentation is critical in studying the joint anatomy for measuring the spacing between the bones. However, separation of the coupled bones in CT images is sometimes difficult due to ambiguous gray values coming from the noise and the heterogeneity of bone materials as well as narrowing of the joint space. For fine reconstruction of the individual local boundaries, manual operation is a common practice where the segmentation remains to be a bottleneck. In this paper, we present an automatic method for extracting the joint space by applying graph cut on Markov random field model to the region of interest (ROI) which is identified by a template of 3D bone structures. The template includes encoded articular surface which identifies the tight region of the high-intensity bone boundaries together with the fuzzy joint area of interest. The localized shape information from the template model within the ROI effectively separates the bones nearby. By narrowing the ROI down to the region including two types of tissue, the object extraction problem was reduced to binary segmentation and solved via graph cut. Based on the shape of a joint space marked by the template, the hard constraint was set by the initial seeds which were automatically generated from thresholding and morphological operations. The performance and the robustness of the proposed method are evaluated on 12 volumes of ankle CT data, where each volume includes a set of 4 tarsal bones (calcaneus, talus, navicular and cuboid).
Optical diffraction tomography (ODT) is an interferometric microscopy technique capable of measuring 3-D refractive index (RI) distribution of transparent samples. Multiple 2-D holograms of a sample illuminated with various angles are measured, from which 3-D RI map of the sample is reconstructed via the diffraction theory. ODT has been proved as a powerful tool for the study of biological cells, due to its non-invasiveness, label-free and quantitative imaging capability. Recently, our group has demonstrated that a digital micromirror device (DMD) can be exploited for fast and precise control of illumination beams for ODT. In this work, we systematically study the precision and stability of the ODT system equipped with a DMD and present measurements of 3-D and 4-D RI maps of various types of live cells including human red blood cells, white blood cells, hepatocytes, and HeLa cells. Furthermore, we also demonstrate the effective visualization of 3-D RI maps of live cells utilizing the measured information about the values and gradient of RI tomograms.