On the simulation of mitral valve function in health, disease, and treatment

Abstract

The mitral valve (MV) is the heart valve that regulates blood ?ow between the left atrium and left ventricle (LV). In situations where the MV fails to fully cover the left atrioventricular ori?ce during systole, the resulting regurgitation causes pulmonary congestion, leading to heart failure and/or stroke. The causes of MV insuf?ciency can be either primary (e.g. myxomatous degeneration) where the valvular tissue is organically diseased, or secondary (typically inducded by ischemic cardiomyopathy) termed ischemic mitral regurgitation (IMR), is brought on by adverse LV remodeling. IMR is present in up to 40% of patients and more than doubles the probability of cardiovascular morbidity after 3.5 years. There is now agreement that adjunctive procedures are required to treat IMR caused by lea?et tethering. However, there is no consensus regarding the best procedure. Multicenter registries and randomized trials would be necessary to prove which procedure is superior. Given the number of proposed procedures and the complexity and duration of such studies, it is highly unlikely that IMR procedure optimization will be achieved by prospective clinical trials. There is thus an urgent need for cell and tissue physiologically based quantitative assessments of MV function to better design surgical solutions and associated therapies. Novel computational approaches directed towards optimized surgical repair procedures can substantially reduce the need for such trial-and-error approaches. We present the details of our MV modeling techniques, with an emphasis on what is known and investigated at various length scales.

Fig. 1

A graphical illustration of how myocardial infarction induces IMR by tethering of the MV. Reproduced from Ref. [2].

Fig. 2

Real-time 3D echocardiographic images of the human mitral valve. In (a), the prerepaired state is shown, where the regurgitant jet in the left atrium can be clearly seen. In (b), the postrepaired state is shown with the valve clearly competent. In ((c) and (d)), the pre- and post-repaired states are shown for a flailed leaflet, which produces a different disease presentation but treated using the same methods.

Fig. 3

Multiscale hierarchical structure for the heart system and the associated computational paradigm for modeling the functional MVs with integration of tissue-, layer-, and cellular-level mechanical responses into the organ-level macroscopic simulation

Fig. 4

(a) Modular left heart simulator for acquiring micro-CT images of native ovine MVs, (b) 3D reconstruction of the MV organ-level geometry (green) based on high-resolution micro-CT images with representative slices for illustrations of how the FE model was constructed: (c) atrial and ventricular MV leaflet surfaces were extracted from the 3D reconstructed MV geometry, whereas the median leaflet surfaces (white dashed lines) were determined and spatially varied thicknesses were computed for the developed FE model; (d) representative landmark points, denoted by white crosses, were determined for idealization of the MVCT; and (e) the CSA associated with each MVCT landmark point as identified in (c) was measured based on the encompassed pixels (purple), and segmentation of the fiducial markers (in orange) was performed via a separate mask with a brighter grayscale threshold. Reproduced from Ref. [20].

Fig. 5

Final segmented ovine mitral valve derived from micro-CT imaging data shown in Fig.4

Fig. 6

MV leaflets: (a) parameterization, conventional regional demarcation analogous to the aortic valve in both the (b) anatomic, and (c) 2D mapped configurations

Fig. 7

The results of multiresolution reconstruction are shown for five ovine MVs. The simplistic superquadric model (a) is enhanced by adding the DC frequency to reconstruct a basic model of the atrial and ventricular surfaces in (b). Integrating more frequencies in the reconstruction recovers more geometric details as shown in (c) and (d). The original geometry that is input to our pipeline is shown in (e) for comparison. Overall, the results show that spectral analysis of geometric attributes allows controlling the level of detail in model development.

Fig. 8

From images to Reeb graphs: a segmented surface of representative chord is shown in (a), from which we extracted a curve-skeleton representation (b) and then linearized (c) to identify fiducial locations. In (d), we define the angular quantities used for 3D orientation analysis: bifurcation angle and nonplanarity angle. These two angles quantify the symmetry and nonplanarity of each branching incidence, respectively. Reeb graph models (e) illustrate the topology: connectivity pattern between the natural fiducial points.

Fig. 9

((a)–(d)) Population results for the major geometrical characteristics of all ten ovine MVCT, revealing a degree of consistency at the population level. (e) Pooled MVCT leaflet insertion map for five MV, revealing clear regional variations.

Fig. 10

The four major layers of the mitral valve leaflet shown of the transverse-radial section of the center region of the MV anterior leaflet (Top), and multiphoton microscopy of the ventricularis (V), fibrosa (F), spongiosa (S), and atrialis (A) layer of the anterior leaflet (Bottom). The histological section shows the relative thickness of each layer, and the multiphoton microscopy shows the orientation or collagen (red) and elastin (green) fibers in each layer. Reproduced from Ref. [37].

Fig. 11

The net stress contribution from each ECM component from each layer for the equibiaxial stress protocol is shown for the circumferential (left) and radial (right) direction of the anterior (top) and posterior (bottom) leaflets. Here, the contributions from the layers are ventricularis (V), fibrosa (F), spongiosa (S), and atrialis (A). Interestingly, while the fibrosa layer is dominant circumferential directions in both leaflets, the atrialis also contributes substantially in the radial direction. Elastin clearly contributes minimal stress comparing to collagen, but it forms the bulk of the response in the toe region. Reproduced from Ref. [37].

Fig. 12

A schematic diagram of the our FE computational framework for modeling the MV with the following four key ingredients: (i) anatomically accurate organ-level geometry obtained from high-resolution images, (ii) constitutive models for MV components, (iii) fiber morphological architecture incorporated with the FE model, and (iv) applicable boundary conditions. Reproduced from Ref. [20].

Fig. 13

Results of the mapped fiber structure for the MV FE mesh at the pressure loaded state (top panel) and at the unloaded/reference state (bottom panel). Dashed lines denote element-based local material axis direction and the color contour represents the strength of fiber splay. Note that here the normalized orientation index (NOI) was defined as percentile scale, where 0% and 100% represent randomly oriented and perfectly aligned collagen fiber networks, respectively. Reproduced from Ref. [20].

Fig. 14

Predicted NOI values of the MV leaflets at various transvalvular pressure levels. Reproduced from Ref. [20].

Fig. 15

Comparison of the (a) predicted von Mises stress and (b) predicted collagen fiber NOI of the MV leaflets considering different stress–strain response curvatures at 100 mmHg transvalvular pressure. Reproduced from Ref. [20].

Fig. 16

(a) The complete second-generation MV modeling pipeline. (b) The sequence of calibration starting with the unloaded state, then to the loaded state done by ensuring matching of the fiducial marker positions, with the full MVCT and transition zones. Note that this allows for the development of a complete, full fidelity MV model that includes the MVCT.

Fig. 17

(a) Second-generation model results for a single MV, showing the responses for both the leaflet and the MVCT. Effects of anatomic variation on the: (b) circumferential stresses, ((c) and (d)) the computed membrane tension (stress/local tissue thickness) mean responses, and (e) CD scores. See Sec. 4.2.4 for details.

Fig. 18

Illustration of the key differences in the predictions of the stresses, strains, and fiber recruitment values between the low fidelity and high fidelity models. This result suggests that while organ-level simulations can utilize simplified material models, detailed downscaled studies will clearly need greater model fidelity.

Fig. 19

(a) Differences in the annular boundary conditions to simulate the in vivo MV state using the MV in vitro model. Notice the distinct difference in the flatness of the annular shapes. (b) The resulting simulation CD scores, which clearly indicated that the midleaflet segments A2 and P2 undergo the greatest change in variance as a result of annular dilation. See Sec. 4.2.6 for details.

Fig. 20

(a) Schematic of physiological MV with corresponding diagram of the position of the five sonocrystals and an MV during flat-ring surgical repair. Heart valve schematics acquired from Ref. [52]. (b) Ovine in vivo tissue-level circumferential (solid lines) and radial strains (dotted lines) during ventricular systole for physiological (green) and surgically repaired valve (blue). Flat-ring surgical repair leads to a decrease in the maximum circumferential strain, whereas the radial strain remains relatively constant. (c) Schematic diagrams of the MVIC microenvironment model with tissue-level deformations prescribed as boundary conditions, whereby cells are included in the tissue model as ellipsoidal inclusions.

Fig. 21

MVIC deformation as a major driver for cellular mechanoregulation. A maximum fibrosa NAR that is less than 3.28 is bracketed as hypo-physiological, an NAR between 3.28 and 4.92 is bracketed as physiological, and an NAR above 4.92 is hyper-physiological (adapted from Ref. [51]).

Fig. 22

The in vivo MV mesh development pipeline, showing the in vivo image, interactively traced contours, and the three-step sequence to convert the segmented image to a FE mesh

Fig. 23

Comparison of ground-truth (i.e., marker-based) directional stretches with results from our noninvasive stretch estimation method, which relies only on overall MV leaflet shape. Arrows denote local circumferential and radial directions. Reproduced from Ref. [26].

Fig. 24

Results of a noninvasive analysis of the post-MI induced deformations in the diastolic (open) configuration at 8 weeks post-IMR. (Top) Method used to map the annular and free-edge boundaries from the normal to 8 week post-IMR states. (Bottom row) IMR produced large, highly anisotropic responses, with mainly circumferential stretch occurring in the posterior leaflet, whereas mainly radial stretch occurred in the posterior leaflet. This underscores the complexity of the post-IMR response.

Fig. 25

(a) MVAL directional stretches under 200 kPa, pre- and post-MI. (b) Correlation between MR grade and MVIC NAR.

Fig. 26

(a) Geometric representations of the native (top left) and various MVCT resolution models utilized to represent the effective subvalvular apparatus (i.e., MVCT network). (b) FE simulations using these MVCT network integrated into the MV leaflet model clearly demonstrate that a functionally equivalent MVCT network can be developed.

Fig. 27

Representative FE simulation results for a different MV, illustrating the accuracy of our functionally equivalent MVCT not only in the normal (calibrated) configuration but also in the dilated and repaired states used for validation