Abstract
The ellipse can be an appropriate geometry for aorta cross-section fitting on the lumen contour. However, in some regions of the aorta, such as the Sinuses of Valsalva, this approximation can suffer of a relatively high error. Thus, some authors use closed polynomial curves for a better representation of the cross section. This paper presents a detailed comparison between the use of an elliptic cross section model and a spline based model with different number of knots. We use a cohort of 32 thoracic aorta geometries (segmented triangle meshes), obtained using CT scan in the mesosystole phase of the cardiac cycle, for the assessment of both methods. We use the root mean squared error of the fitting of the studied methods to quantify their accuracy. As expected, the spline based model improves the fitting accuracy of the elliptic one and specially in complex aorta cross-sections. However, we have observed that with a high number of knots some cross sections may show high error values due to the adaption of the function to noise.
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References
Alvarez, L., et al.: Tracking the aortic lumen geometry by optimizing the 3D orientation of its cross-sections. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017, Part II. LNCS, vol. 10434, pp. 174–181. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66185-8_20
Antiga, L., Steinman, D.A.: Robust and objective decomposition and mapping of bifurcating vessels. IEEE Trans. Med. Imaging 23(6), 704–713 (2004). https://doi.org/10.1109/TMI.2004.826946
Bianchi, M., et al.: Patient-specific simulation of transcatheter aortic valve replacement: impact of deployment options on paravalvular leakage. Biomech. Model. Mechanobiol. 18(2), 435–451 (2018). https://doi.org/10.1007/s10237-018-1094-8
Cibis, M., Bustamante, M., Eriksson, J., Carlhäll, C.J., Ebbers, T.: Creating hemodynamic atlases of cardiac 4D flow MRI. J. Magn. Reson. Imaging 46(5), 1389–1399 (2017). https://doi.org/10.1002/jmri.25691. https://onlinelibrary.wiley.com/doi/abs/10.1002/jmri.25691
Cosentino, F., et al.: Statistical shape analysis of ascending thoracic aortic aneurysm: correlation between shape and biomechanical descriptors. J. Pers. Med. 10(2) (2020). https://doi.org/10.3390/jpm10020028. https://www.mdpi.com/2075-4426/10/2/28
Ghosh, R.P., Marom, G., Bianchi, M., D’souza, K., Zietak, W., Bluestein, D.: Numerical evaluation of transcatheter aortic valve performance during heart beating and its post-deployment fluid–structure interaction analysis. Biomech. Model. Mechanobiol. 19(5), 1725–1740 (2020). https://doi.org/10.1007/s10237-020-01304-9
Haj-Ali, R., Marom, G., Zekry, S.B., Rosenfeld, M., Raanani, E.: A general three-dimensional parametric geometry of the native aortic valve and root for biomechanical modeling. J. Biomech. 45(14), 2392–2397 (2012). https://doi.org/10.1016/j.jbiomech.2012.07.017. http://www.sciencedirect.com/science/article/pii/S0021929012004125
Medrano-Gracia, P., et al.: A computational atlas of normal coronary artery anatomy. EuroIntervention : J. EuroPCR Collab. Work. Group Intervent. Cardiol. Eur. Soc. Cardiol. 12(7), 845–854 (2016). https://doi.org/10.4244/eijv12i7a139
Moore, J.E., Xu, C., Glagov, S., Zarins, C.K., Ku, D.N.: Fluid wall shear stress measurements in a model of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. Atherosclerosis 110(2), 225–240 (1994)
Nerem, R.M.: Vascular fluid mechanics, the arterial wall, and atherosclerosis. J. Biomech. Eng. 114(3), 274–282 (1992). https://doi.org/10.1115/1.2891384
Romero, P., et al.: Reconstruction of the aorta geometry using canal surfaces. In: International Conference on Computational and Mathematical Biomedical Engineering (2019)
Schroeder, W., Martin, K., Lorensen, B.: The Visualization Toolkit: An Object-Oriented Approach to 3D Graphics; [visualize data in 3D - medical, engineering or scientific; build your own applications with C++, Tcl, Java or Python; includes source code for VTK (supports Unix, Windows and Mac)], 4th edn. Kitware Inc., Clifton Park (2006). oCLC: 255911428
Sedghi Gamechi, Z., et al.: Automated 3D segmentation and diameter measurement of the thoracic aorta on non-contrast enhanced CT. Eur. Radiol. 29(9), 4613–4623 (2019). https://doi.org/10.1007/s00330-018-5931-z. https://pubmed.ncbi.nlm.nih.gov/30673817. 30673817[pmid]
Shahcheraghi, N., Dwyer, H., Cheer, A., Barakat, A., Rutaganira, T.: Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J. Biomech. Eng. 124(4), 378–387 (2002). https://doi.org/10.1115/1.1487357
Tahoces, P.G., et al.: Automatic estimation of the aortic lumen geometry by ellipse tracking. Int. J. Comput. Assist. Radiol. Surg. 14(2), 345–355 (2018). https://doi.org/10.1007/s11548-018-1861-0
Tahoces, P.G., et al.: Automatic detection of anatomical landmarks of the aorta in CTA images. Med. Biol. Eng. Comput. 58(5), 903–919 (2020). https://doi.org/10.1007/s11517-019-02110-x
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Romero, P., Serra, D., Lozano, M., Sebastián, R., García-Fernández, I. (2021). Assessment of Geometric Models for the Approximation of Aorta Cross-Sections. In: Ennis, D.B., Perotti, L.E., Wang, V.Y. (eds) Functional Imaging and Modeling of the Heart. FIMH 2021. Lecture Notes in Computer Science(), vol 12738. Springer, Cham. https://doi.org/10.1007/978-3-030-78710-3_9
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