Virtual Shape-Editing of Patient-Specific Vascular Models Using Regularized Kelvinlets

Cardiovascular diseases, and the interventions performed to treat them, can lead to changes in the shape of patient vasculatures and their hemodynamics. Computational modeling and simulations of patient-specific vascular networks are increasingly used to quantify these hemodynamic changes, but they require modifying the shapes of the models. Existing methods to modify these shapes include editing 2D lumen contours prescribed along vessel centerlines and deforming meshes with geometry-based approaches. However, these methods can require extensive by-hand prescription of the desired shapes and often do not work robustly across a range of vascular anatomies. To overcome these limitations, we develop techniques to modify vascular models using physics-based principles that can automatically generate smooth deformations and readily apply them across different vascular anatomies.

We adapt Regularized Kelvinlets, analytical solutions to linear elastostatics, to perform elastic shape-editing of vascular models. The Kelvinlets are packaged into three methods that allow us to artificially create aneurysms, stenoses, and tortuosity.

Our methods are able to generate such geometric changes across a wide range of vascular anatomies. We demonstrate their capabilities by creating sets of aneurysms, stenoses, and tortuosities with varying shapes and sizes on multiple patient-specific models.

Our Kelvinlet-based deformers allow us to edit the shape of vascular models, regardless of their anatomical locations, and parametrically vary the size of the geometric changes.

These methods will enable researchers to more easily perform virtual-surgery-like deformations, computationally explore the impact of vascular shape on patient hemodynamics, and generate synthetic geometries for data-driven research.