DeepVesselNet: Vessel Segmentation, Centerline Prediction, and Bifurcation Detection in 3-D Angiographic Volumes

We present DeepVesselNet, an architecture tailored to the challenges faced when extracting vessel trees and networks and corresponding features in 3-D angiographic volumes using deep learning. We discuss the problems of low execution speed and high memory requirements associated with full 3-D networks, high-class imbalance arising from the low percentage (<3%) of vessel voxels, and unavailability of accurately annotated 3-D training data—and offer solutions as the building blocks of DeepVesselNet. First, we formulate 2-D orthogonal cross-hair filters which make use of 3-D context information at a reduced computational burden. Second, we introduce a class balancing cross-entropy loss function with false-positive rate correction to handle the high-class imbalance and high false positive rate problems associated with existing loss functions. Finally, we generate a synthetic dataset using a computational angiogenesis model capable of simulating vascular tree growth under physiological constraints on local network structure and topology and use these data for transfer learning. We demonstrate the performance on a range of angiographic volumes at different spatial scales including clinical MRA data of the human brain, as well as CTA microscopy scans of the rat brain. Our results show that cross-hair filters achieve over 23% improvement in speed, lower memory footprint, lower network complexity which prevents overfitting and comparable accuracy that does not differ from full 3-D filters. Our class balancing metric is crucial for training the network, and transfer learning with synthetic data is an efficient, robust, and very generalizable approach leading to a network that excels in a variety of angiography segmentation tasks. We observe that sub-sampling and max pooling layers may lead to a drop in performance in tasks that involve voxel-sized structures. To this end, the DeepVesselNet architecture does not use any form of sub-sampling layer and works well for vessel segmentation, centerline prediction, and bifurcation detection. We make our synthetic training data publicly available, fostering future research, and serving as one of the first public datasets for brain vessel tree segmentation and analysis.

A nonlinear optimization shooting method for bifurcation tracking of nonlinear systems

A continuation method for bifurcation tracking is presented based on the proposed optimization problem formulation which is designed to locate the bifurcation periodic solution. The bifurcation detection problem is formulated as a constrained optimization problem. The nonlinear constraints of the optimization problem are imposed on the shooting function and bifurcation conditions derived from the Floquet theory whereas the objective function associated with the pseudo-arclength correlation equation is devised to solution continuation. The proposed optimization formulation is integrated with the prediction–correction strategy to achieve bifurcation tracking. Two numerical examples about the Jeffcott rotor and the nonlinear tuned vibration absorber are illustrated to validate the effectiveness of the proposed methodology. Numerical results have demonstrated that the proposed method offers a convenient scheme to follow bifurcation periodic solution.

Bifurcation analysis and damage detection in mechanical structures

Bifurcation and damage are two phenomena prompting any structure to unpredicted failure. Their early detection is crucial to maintaining structural health and integrity. In this work, we investigate two topics in bifurcation and damage detection. Trusses with geometric and loading symmetries have been used in many structures to reduce complexity design. Here, bifurcation analysis has been conducted for a two-bar truss and a shallow arch structure with seven bars. Two program packages Gesa and Ansys based on the finite elements method (FEM) have been used to detect the symmetry breaking bifurcation points. The theoretical examination uncovers that the bifurcation prompts a much lower critical load in the presence of little asymmetry in comparison to the symmetric case. The outcomes of bifurcation detection by using Gesa program in Matlab for fully nonlinear analysis and Ansys commercial program show the two programs give results close to the results acquired from the theoretical analysis. Our study opens the door for the researcher to use the two programs for more complicated structures for bifurcation detection analysis since analytically will be hard to use. As for damage detection, the residual error method has been used. This is a technique that relies on observing the residual error in the equation of motion specified for free vibration analysis so as to reveal any changes in the structural dynamic characteristics. The method has been applied on bar, beam and plate to demonstrate its validity. Several numerical simulations with different damage scenarios are presented to assess the robustness and limitations of the method. The sensitivity of the method to noise has been tested with different noise levels as well. Results obtained with the residual error method are compared with those obtained from the absolute difference mode shape curvature (ADMSC) method. The comparison demonstrates that the residual error method can detect and locate damage in the simulated structures with low level of noise.