Population-Averaged Geometric Model of Mitral Valve From Patient-Specific Imaging Data1 (2015)

The mitral valve (MV) is one of the atrioventricular heart valves and regulates the blood flow between the left atrium and ventricle during the cardiac cycle. Its anatomical structure is comprised of anterior and posterior leaflets, chordae tendineae, and papillary muscles. The main function of the MV is to prevent blood flow regurgitation back into the left atrium during systole. Abnormalities in geometry of MV can lead to mitral insufficiency disorder, which requires either valve replacement or surgical repair to restore proper MV coaptation. Annually, over 40,000 patients in the U.S. alone are treated for MV disorders [1]. In the past two decades, the emphasis in MV treatment has been shifting from replacement toward repair due to lower morbidity and mortality of the latter approach [2]. However, the natural anatomical variability of human MV geometry precludes the use of single or simplified geometries for the simulation of surgical repair.One of the ways to address this issue is by using patient-specific diagnosis and modeling [3], or population-averaged geometric models of MV. The existing approaches for characterization and reconstruction of the cardiovascular organ-level geometry include fitting of predefined sets of nonuniform rational B-splines (NURBS) to the imaging data [4], and using spheroidal harmonics representations [5]. Even though it is possible to construct average geometric models this way, the analysis of anatomical shape variations becomes difficult in this setting because of the confounding of dimensional and shape descriptors. At the same time, none of the existing methods allow integration of the high-fidelity in vitro data with lower-resolution in vivo imaging in a consistent manner.In this work, we formulate the framework for building the population-averaged geometric model of MV, which lends to straightforward analysis of dimensional and anatomical variations. In the sections to follow, we discuss the procedure and advantages of this method for the development of robust medical devices and treatment procedures.Imaging of MV geometry was acquired from Siemens Inveon microcomputed tomography (μCT) system (Siemens AG, Munich, Germany) configured to 80 keV energy, 500 μA intensity, 650 ms integration time, and 39 μm resolution with isotropic voxels. All scans were performed for the fully open state of MV, corresponding to the left ventricular diastole.The segmentation and filtering of μCT images were performed in simpleware scanip (Simpleware Ltd., Exeter, UK) software to obtain volumetric representation of the MV geometry. In the next step, the volumetric data were rotated to align MV central axis with the major axis calculated using principal component analysis. Rotational slices around the MV central axes were exported into matlab (MathWorks, Natick, MA) for tracing the contours of exterior (ventricular) and interior (atrial) surfaces of the leaflets. The point clouds corresponding to ventricular and atrial surfaces were imported into Geomagic Studio (3D Systems, Inc., Rock Hill, SC) to construct the tessellated median surface representation with the corresponding pointwise thickness field. Chordae insertion points, medial axes, and pointwise diameters were manually processed in a similar fashion and stored for separate geometric analysis (not discussed in this paper due to the differences in topology).The median surface is analyzed using a two-scale geometric model. At the macroscale, the model is defined as a superquadric surface with the implicit form [6](1)[(xa1)2/ɛ2 + (ya2)2/ɛ2]ɛ2/ɛ1 + (za3)2/ɛ1=1where a1, a2, a3 are the dimensional parameters, and ε1,ε2 are the shape parameters. At the finer scale, the model is specified in the spectral form as 2D discrete Fourier reconstruction.The parameters of the fitted superquadric surface are obtained by a nonlinear optimization set to minimize the squared residuals of the data from the implicit surface defined by Eq. (1). The spectral reconstruction of the fine-scale features is calculated by nonuniform discrete Fourier transform of the normal deviations of point cloud data from the fitted surface.The population-averaged MV geometry was derived by taking the arithmetic mean of the superquadric surface parameters (corresponding to the mean macroscale shape), and arithmetic averaging of fine-scale Fourier spectra (corresponding to the mean fine-scale features). Finally, the population-averaged model is used to build a NURBS surface.The proposed data processing and geometry averaging method was applied to build an ovine population-averaged MV based on five MV specimens. An example of the filtered μCT data is shown in Fig. 1. Tracing of the leaflet surface contours is illustrated in Fig. 2. Figure 3 depicts the calculated median surface and the geometric averaging procedure. The results of the superquadric surface fitting (Fig. 3(a)) demonstrate the robustness of optimization algorithm to capture the macroscale geometry of the MV. The scalar field shown in Fig. 3(b) represents the pointwise normal deviations of the point cloud points from the fitted surface. The Fourier transform was applied to the deviations dataset to obtain the spectral representation of the fine-scale features. An example of the population-averaged NURBS surface is illustrated in Fig. 4.We presented a method for robust population-averaging of the MV geometry. In this framework, the average model preserves the anatomical structure through decoupling of the geometry reconstruction into fitting of the shape descriptor template (superquadric surface) and spectral representation of the feature descriptor field (Fourier transform of the surface deviations). Spectral representation of the fine-scale features allows for straightforward filtering of the spatial noise and enables control of the smoothness level in the reconstructed surface. The final population-averaged NURBS model is suitable for finite element modeling with the adaptive level of discretization and isogeometric modeling approaches.The proposed characterization of the MV geometry provides a unified framework for describing physiological and dimensional variations. In turn, this allows to investigate dimensional differences independently from the physiological variations and study their interaction. Integration of this framework into the medical device design process has a potential to improve robustness of the final products and designed intervention procedures by combining the population-averaged geometry (representative template) with the bounds for the expected statistical variations.Future work will extend this framework to include detailed chordae structure analysis and development of population-averaged finite element models for simulating the biomechanical behavior of MV under different loading conditions.Research reported in this publication was supported by National Heart, Lung, and Blood Institute of the National Institutes of Health under Award No. R01HL119297. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. Andrew Drach gratefully acknowledges the financial support provided by the ICES Postdoctoral Fellowship.