Physics-Based Patient-Specific Coronary Models

• Physics-based patient-specific coronary models are computational frameworks that integrate imaging data, physical laws, and topology extraction to simulate blood flow and myocardial risk.
• They employ advanced methods like constrained Delaunay triangulation and medial axis extraction to fuse vessel and myocardium segmentation for precise regional mapping.
• These models enable personalized treatment planning and multi-scale simulations, enhancing diagnostic accuracy and optimizing interventional strategies in ischemic heart disease.

Physics-based patient-specific coronary artery models are computational frameworks that use physical laws, patient-derived anatomical data, and computational algorithms to quantitatively represent the structure and function of coronary arteries. These models are employed to simulate blood flow, vessel wall biomechanics, and their interaction with the myocardial tissue, enabling patient-specific diagnosis, risk stratification, treatment planning, and the virtual evaluation of interventions in ischemic heart disease and related cardiovascular conditions.

1. Geometric and Topological Modeling of Coronary Arteries

The foundation of physics-based models is the accurate reconstruction of an individual’s coronary artery anatomy from medical imaging (CT, CCTA, IVUS, or OCT). Segmentation pipelines extract the vessel lumen and wall structures and generate 3D triangular or hexahedral meshes suitable for downstream simulation.

A key advancement is the extraction of the arterial medial axis—the "curve-skeleton"—from these meshes, which provides both a topological map and a basis for geometric partitioning. The process typically involves:

• Constrained Delaunay triangulation (CDT), which divides the vessel volume into tetrahedral elements, each with a circumsphere center.
• Construction of an adjacency graph with nodes at circumsphere centers, connecting tetrahedra that share faces.
• Pruning to create an adjacency tree, done via shortest path algorithms to preserve the anatomical tree structure.
• Refinement steps such as removal of outlying nodes, deletion of minute subtrees ("shaving hairs"), and straightening of “bumpy” nodes through vector difference analysis (using measures such as $\|u_{23} - u_{12}\| > \alpha_1$).

This detailed medial axis is then used as the core skeleton for segmenting both the coronary arteries and myocardium, supporting physiologically meaningful mapping and further computational analysis (Chaa et al., 2017).

2. Fused Segmentation and Structure–Function Mapping

Fused segmentation refers to the simultaneous partitioning of the coronary artery and the myocardium (typically modeled as the left ventricle, LV) so that each ventricular or coronary region is assigned to its closest medial axis node.

This procedure is extended to a discrete optimization framework, where, for each tetrahedral cell in the myocardium or in the CA mesh, assignment to a medial axis node minimizes the Euclidean distance:

$\min_{x_{ij}} \sum_i \sum_j D(c_i, n_j) x_{ij}$

subject to

$\sum_j x_{ij} = 1,\;\; x_{ij} \in \{0,1\}$

where $c_i$ is a cell’s centroid and $n_j$ a medial axis node. The solution provides a bijective correspondence between myocardial subregions and supplying coronary branches. This precise mapping enables the quantification of regional myocardium-at-risk, enhancing the accuracy of ischemia prediction well beyond schematic models like the AHA 17-segment framework.

3. Algorithmic Implementation and Computational Complexity

Physics-based segmentation and quantification algorithms are implemented in software pipelines such as VoroHeart, which consume triangular mesh models of CA and LV provided by patient imaging. Key algorithmic stages include:

• CDT computation for both artery and myocardium.
• Graph-based skeleton extraction and pruning via forward/backward shortest path expansion.
• Fused assignment/segmentation as an integer linear programming problem.

Theoretical analysis shows that the most expensive step—cycle removal in adjacency graphs—has complexity $O(|N||L| + |N|^2 \log |N|)$, where $N$ and $L$ are the number of graph nodes and links. Empirical validation (20 clinical CT-derived datasets) demonstrates the approach is both computationally feasible and yields segmentation accuracy that matches expert manual annotation (Chaa et al., 2017).

4. Patient-Specific Clinical Applications and Advantages

Integrating arterial geometry, topology, and myocardial supply domains offers several clinical advantages:

• Patient-specific risk stratification: Quantifying the precise volumetric extent of myocardium subtended by an obstructed branch allows direct estimation of infarct risk in event of vessel occlusion.
• Enhanced ischemia assessment: Spatial correspondence enables computations of both ischemic extent and severity from imaging, supporting non-invasive functional diagnosis.
• Personalized treatment planning: Morphometrics such as branch lengths, cross-sectional areas, and regional myocardium volumes can optimize stent selection, bypass graft targets, or regenerative therapies.
• Data for optimization and modeling: The fused segmentations form the foundation for optimization models in cardiac systems—e.g., personalized computational simulations or automated interventional planning (Chaa et al., 2017).

A notable distinction is the tailored mathematical linkage between topological coronary distribution and the regional myocardium—in contrast to conventional static models.

5. Integration with Multi-Scale Modeling and Diagnostic Workflows

Physics-based patient-specific coronary models serve as the basis for multi-scale simulation cascades, often coupling to physiological flow models (1D, 3D CFD) or lumped parameter boundary conditions. The segmented and skeletonized anatomy allows:

• Downstream CFD or FSI simulations with patient-specific boundary conditions, capturing blood flow dynamics and wall deformation under realistic coronary pressure loads.
• Extraction of computational metrics such as wall shear stress, pressure drops, and derived indices (e.g., FFR), which are central to non-invasive assessment of functional lesion severity (Blanco et al., 2018).
• Facilitation of data-driven or reduced-order modeling methods for real-time evaluation and clinical deployment.

The use of fused segmentation is also compatible with downstream uncertainty quantification and multi-physics models, which can propagate input or material property uncertainties through the patient-specific pipeline, providing confidence intervals for clinically relevant outputs (Seo et al., 2019).

6. Limitations, Validation, and Prospective Directions

While physics-based, medial axis-driven approaches overcome many limitations of schematic segmentation, several considerations remain:

• Accuracy depends on the quality of input 3D segmentations from imaging, and non-calcified plaque or imaging artifacts can introduce errors.
• The approach assumes that the coronary artery is topologically a tree, which holds for most but not all coronary morphologies.
• Integer-programming-based assignment can become computationally intensive for very high-resolution meshes, although current algorithms remain practical for clinical datasets.
• Future work may extend segmentation and mapping frameworks to include right ventricular myocardium, adaptive models in pathologies (e.g., coronary anomalies), or direct integration with machine learning pipelines for automated, real-time diagnosis.

Overall, physics-based patient-specific coronary artery models, particularly those employing fused segmentation via medial axis extraction and assignment, represent a substantial advance in linking anatomy and function for individualized cardiovascular medicine. Their theoretical rigor, computational tractability, and compatibility with downstream simulation and optimization frameworks render them foundational tools for modern patient-specific diagnostic and interventional workflows (Chaa et al., 2017).