Finite element analysis in the modeling of the heart and aorta structures
Authors: Smirnov A. A. , Ovsepyan A. L. , Kvindt P. A. , Paleev F. N. , Borisova E. V. , Yakovlev E. V. 
Published: November 2021

Rationale: 3D modeling of various anatomical structures has recently become a separate area of topographical, anatomical, and biomechanical studies. Current in vivo visualization methods and quantitative analysis in silico allow to perform the precise modeling of these processes aimed at investigation into the pathophysiology of cardiovascular disorders, risk prediction, planning of surgical interventions and virtual refinement of their separate stages.

Aim: To develop tools for elaboration, analysis and validation of personalized models of various structures of the heart and aortal arch taking into account their morphological characteristics.

Materials and methods: We used the results of 14 computed tomography studies from randomized patients without any disease or anomaly of the heart, aortic valve and aortal bulb. The analysis and subsequent transformation of the images were done with Vidar DICOM Viewer, SolidWorks 2016, VMTKLab software. For the FSI modeling of the aortic arch based on the results of functional multiaxial computed (MAC) coronarography (a female patient of 55 years) we developed a personalized model of the ascending aorta and aortic arch at the beginning of the systole. Using HyperMesh software (Altair Engineering Inc., USA) we have built a network of finite element of the luminal area, adventitia, and aortic media. To model mechanical properties of the aortic structures we used an anisotropic hyperelastic material model by Holzapfel – Gasser – Ogden. Material modeling, choice of the limiting antecedents, and analysis of fluid-structure interaction were performed with Abaqus CAE 6.14 software (Simulia, Johnston, USA). Adaptive image meshing by Young was used to elaborate the finite element template of the left ventricle. The algorithm was realized within the IDE PyCharm software media in Python 3.7. The algorithm was realized based on the open-source libraries OpenCV, NumPy, Matplotlib, and SciPy.

Results: The first stage of the development of the aortic valve model included the design of its virtual 3D template. Thereafter, a cohesive geometric model was elaborated. Subsequent stage of the work included the transformation of the aortic valve geometric model into the parametric one. This was done through the use of the “Equations” tool within the SolidWorks. No problems with geometry of the model during its deformation were identified. Aortic segment modeling was based on the data obtained by functional MAC coronarography. Based on this and on Inobitec Dicom Viewer software, we generated a multiplane reconstruction of the zone of interest including anatomical structure of the heart and aortic valve. With the resulting set of contours, we created a 3D model, which then was converted into a polygonal stereolithographic model. We developed an algorithm for adaptive meshing to elaborate a polygonal template capable of deformation that can be used for registration both with the net methods (B-Spline) and based on the image characteristics (homologous pixels).

Conclusion: The resulting parametric 3D model of the aortic valve anatomical structures is capable of adequate transformation of its geometry under external factors. It can be used in simulators of endovascular cardiosurgical procedures.