Image-based modeling is an active and growing area of biomedical research that utilizes medical imaging to create patient-specific simulations of physiological function. Under this paradigm, anatomical structures are segmented from a volumetric image, creating a geometric model that serves as a computational domain for physics-based modeling. A common application is the segmentation of cardiovascular structures to numerically model blood flow or tissue mechanics. The segmentation of medical image data typically results in a discrete boundary representation (surface mesh) of the segmented structure. However, it is often desirable to have an analytic representation of the model, which facilitates systematic manipulation. For example, the model then becomes easier to union with a medical device, or the geometry can be virtually altered to test or optimize a surgery. Furthermore, to employ increasingly popular isogeometric analysis (IGA) methods, the parameterization must be analysis suitable. Converting a discrete surface model to an analysis-suitable model remains a challenge, especially for complex branched structures commonly encountered in cardiovascular modeling. To address this challenge, we present a framework to convert discrete surface models of vascular geometries derived from medical image data into analysis-suitable nonuniform rational B-splines (NURBS) representation. This is achieved by decomposing the vascular geometry into a polycube structure that can be used to form a globally valid parameterization. We provide several practical examples and demonstrate the accuracy of the methods by quantifying the fidelity of the parameterization with respect to the input geometry.

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