3D Coronary Artery Model Registration via Convex Optimization
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Solution Overview
Problem
Current methods for registering 3D models with 2D projections, particularly in coronary artery procedures, face challenges in achieving accurate alignment due to the non-trivial task of finding inter-modal correspondences and the nonlinear optimization involved, which hampers the visualization and guidance during percutaneous coronary interventions, especially for Chronic Total Occlusion cases.
Innovation Solution
A computer-implemented method using convex optimization programs to register a 3D centerline model of coronary arteries with multiple 2D fluoroscopic images, optimizing the correspondence and transformation between the 3D model and 2D images through rotation matrices and permutation matrices, allowing for efficient global optimization and alignment.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional 2D/3D registration methods are used to align 3D coronary artery models with 2D fluoroscopic images, then the alignment accuracy can be improved, but the computational complexity and optimization difficulty increase significantly due to the nonlinear nature of the correspondence problem
Solution Approach 1:
The patent transforms the nonlinear optimization problem into a convex optimization problem by changing the parameter space representation. Specifically, it formulates the registration problem as a semidefinite programming problem where the rotation matrix is represented through its vectorization, converting the non-convex objective function into a convex one that can be solved efficiently with standard solvers.
Solution Approach 2:
The patent replaces the traditional iterative nonlinear optimization approach (which relies on gradient-based methods and initial guesses) with a convex optimization framework. This substitution eliminates the need for complex optimization algorithms and initializations, using instead semidefinite programming techniques that guarantee convergence to the global optimum.
2Measurement precision
If iterative optimization algorithms are used to register 3D models with 2D images, then alignment accuracy can be achieved, but the computation time and processing speed decrease due to the iterative nature of the algorithms
Solution Approach 1:
The patent substitutes iterative gradient-based optimization algorithms with a direct convex optimization approach. By formulating the problem as semidefinite programming, it eliminates the need for repeated iterations, achieving both accuracy and speed by solving the optimization problem in a single execution using standard conic programming solvers.
3Measurement precision
If complex optimization algorithms are employed to handle the nonlinear correspondence problem, then registration accuracy improves, but the ease of operation and implementation deteriorates due to sensitivity to initial conditions and algorithm configuration
Solution Approach 1:
The patent changes the mathematical formulation from a nonlinear optimization problem to a convex optimization problem. This parameter change in the problem space allows the use of standard, well-tested convex optimization solvers that are less sensitive to initial conditions and algorithm parameters, significantly easing implementation while maintaining accuracy.
Solution Approach 2:
The patent replaces complex iterative optimization algorithms with a convex optimization framework. This substitution uses standard conic programming software that handles the optimization automatically, eliminating the need for custom algorithm development and fine-tuning of initialization parameters, thereby greatly simplifying implementation.
Data Source
AI summary
A method of registering a 3-dimensional (3D) model of a coronary artery tree with 2-dimensional (2D) images includes solving for matrices R, Pi, i=1, . . . , N, that minimize a cost function Σi=1N∥ΨiRX−IiPi∥2,1 subject to constraints that R∈conv(SO(3)), Pi∈[0,1]n<sub2>i</sub2>×m, and Pi1≦1, 1TPi=1, for i∈{1, N}, where N is a number of 2D images, R is a rotation matrix, conv(SO(3)) denotes a convex hull of the special orthogonal group in 3 dimensions, X denotes a 3D centerline model of a coronary artery tree, Ii denotes the ith 2D image, Ψi denotes a transformation between the 3D centerline model X and the ith 2D image Ii, 1 is an all-ones vector, Pi is a permutation matrix, and rounding a solution R to a nearest orthogonal matrix R* in SO(3), where R* aligns the 3D centerline model X of the coronary artery tree with 2D fluoroscopic images acquired during a percutaneous coronary intervention procedure.