Andrew Tsao, BS

Research Assistant
Pulmonary and Critical Care
Andrew Tsao B.S.*, Pietro Nardelli Ph.D., Aaron B. Waxman M.D. Ph.D., Ruben San José Estépar, George Washko M.D. M.S., Raúl San José Estépar Ph.D., Farbod N. Rahaghi M.D. Ph.D.
Fractal Dimension Estimation Using Box-Counting to Quantify CT-Based Pulmonary Vascular Tree Simplification


Fractal dimension (FD) is a measure of self-similar complexity that shows promise in quantifying morphological changes in the pulmonary vascular tree during pulmonary arterial hypertension (PAH). In this study, we use CT imaging from patients with PAH and controls and examine the effect of arterial/venous separation and scales of analysis on estimating pulmonary vascular tree complexity using FD.


Sequential patients presenting to the dyspnea clinic with CT angiography and invasive hemodynamic testing were screened for this study. Patients with PAH were compared to patients with no evidence of pulmonary vascular disease on invasive exercise testing. 3D reconstruction of intraparenchymal pulmonary vasculature was performed using the chest imaging platform ( 3D FD was estimated using box-counting along various scales of voxel sizes.


FD was lower in the total vascular tree in patients with PAH compared to controls only when performing the analysis with very large voxel sizes (full CT). On the other hand, FD of the arterial tree was only significantly lower in PAH on the small scale (20 voxels) whereas FD of the venous tree was significantly lower in PAH regardless of scale.


Decreasing FD estimate was associated with the presence of PAH. However, separation of the tree into arterial/venous components and changes in the scale of analysis suggests the importance of methodology in estimating this quantity. This may be driven by the multifractal nature of the vascular tree and the differential changes at different scales (proximal dilation versus distal pruning) in the arterial/venous vasculatures.