Visualizing the spatiotemporal pattern of yolk sac membrane vascular network by enhanced local fractal analysis

To establish methods for providing a comprehensive and detailed description of the spatial distribution of the vascular networks, and to reveal the spatiotemporal pattern of the yolk sac membrane vascular network during the angiogenic procedure.

Addressing the limitations in the conventional local fractal analysis, an improved approach, named scanning average local fractal dimension, was proposed. This method was conducted on 6 high-resolution vascular images of the yolk sac membrane for 3 eggs at two stages (E3 and E4) to characterize the spatial distribution of the complexity of the vascular network.

With the proposed method, the spatial distribution of the complexity of the yolk sac membrane vascular network was visualized. From E3 to E4, the local fractal dimension increased in 3 eggs, 1.80 ± 0.02 vs. 1.85 ± 0.02, 1.72 ± 0.03 vs. 1.83 ± 0.02, and 1.77 ± 0.03 vs. 1.82 ± 0.02, respectively. The mean local fractal dimension in the most distal area from the embryo proper was the lowest at E3 while the highest at E4. At E3, the most peaks of the local fractal dimension were located in the vein territories and shifted to artery territories at E4.

The spatial distribution of the complexity of the yolk sac membrane vascular network exhibited diverse patterns at different stages. In addition from E3 to E4, the increment of complexity at the intersection areas between arteries and sinus terminalis was with the most advance. This is consistent with the physiologic evidence. The present work provides a potential approach for investigating the spatiotemporal pattern of the angiogenic process.