Computer models for computation and verification of bronchial morphology

Accurate physiological measurements of the parameters like branching angles, branch lengths and diameters of bronchial tree structures help in addressing the mechanistic and diagnostic questions related to obstructive lung disease. In order to facilitate these measurements, bronchial trees are reduced to a central axis tree. The approach we take employs first setting up a theoretical computerized tree structure, and then applying a three dimensional analysis to obtain the required anatomical data. A stick model was set up in 3D, with segment endpoints and diameters as input parameters to the model generator. By fixing the direction in which the slices are taken, a stack of 2D images of the generated 3D tree model is obtained, thereby simulating bronchial data sets. We design a two pass algorithm to compute the central axis tree and apply it on our models. In the first pass, the topological tree T is obtained by implementing a top-down seeded region growing algorithm on the 3D tree model. In the second pass, T is used to region grow in a bottom-up manner starting from the terminal branches, in order to ensure region growth along the axes of the branches. As the 3D tree model is traversed bottom-up, the centroid values of the cross sections of the branches are stored in the corresponding branch of T. At each bifurcation, the branch point and the three direction vectors along the branches are computed, by formulating it as a non-linear optimization problem that minimizes the sum of least squares error of the centroid points of the corresponding branches. By connecting the branch points with straight lines, we obtain a reconstructed central axis tree which closely corresponds to the input stick model. We also studied the effect of adding external noise to our tree models and evaluating the physiological parameters. We conclude with the results of our algorithm on real airway trees.