Tracking 3-D pulmonary tree structures

Physiological measurements like branch angles, branch lengths, branch diameters and branch cross-sectional area of the 3-D pulmonary tree structures are clinically essential in evaluating the function of normal and diseased lung and during the breathing process. In order to facilitate these measurements and study relative structural changes, the 3-D lung tree volumes are reduced to a 3-D Euclidean straight line central axis tree. The central axis tree captures the branch topology and geometric features of the tree volume. Since matching 3-D tree volumes is complex, as they change in branch topology and geometry, the authors accomplish it by designing an efficient algorithm that matches their corresponding central axis trees. The algorithm takes two binary central axis trees T₁=(V₁,E₁,W₁ ) and T₂=(V₂,E₂,W₂), where W₁ and W₂ are set of tuples containing geometric attributes corresponding to the nodes in T₁ and T ₂, as inputs and returns the one-to-one matching function f of nodes in T₁ to T₂ that preserves the tree topology and closely matches the geometric attributes of these trees, i.e. branch points, branch lengths, and branch angles between mapped nodes of T₁ and T₂. Since the topology match alone could result in many choices of the mapping function f, the authors prune these choices by incorporating constraints on the geometric attributes of nodes in T₁ and T₂. The authors design a linear time algorithm that matches the branch topology and geometric features of T₁ and T₂. The authors´ algorithm produced accurate matchings on various airway data sets of a dog lung obtained from Computed Tomography under simulated breathing conditions. T₁ and T₂ are obtained by running a two-pass central axis algorithm on the tree volumes