Patient-specific mitral valve closure prediction using 3D echocardiography

Abstract

This article presents an approach to modeling the closure of the mitral valve using patient-specific anatomical information derived from 3D transesophageal echocardiography (TEE). Our approach uses physics-based modeling to solve for the stationary configuration of the closed valve structure from the patient-specific open valve structure, which is recovered using a user-in-the-loop, thin-tissue detector segmentation. The method uses a tensile shape-finding approach based on energy minimization. This method is employed to predict the aptitude of the mitral valve leaflets to coapt. We tested the method using 10 intraoperative 3D TEE sequences by comparing the closed valve configuration predicted from the segmented open valve with the segmented closed valve, taken as ground truth. Experiments show promising results, with prediction errors on par with 3D TEE resolution and with good potential for applications in pre-operative planning.

Figure 1

Flow chart of system studied. The valve anatomy is first recovered via preliminary segmentation using structure tensor and k-means. The model is vetted and corrected by an expert for missing or erroneous features. A mesh is created. A parameter estimation process allows the estimation of tether length, which cannot easily be done via imaging only. This consist of finding the chordal lengths that minimize the prediction error between actual and predicted closed configuration. After estimation of the patient specific parameters, the mesh is virtually modified be modified in a way that would reflect possible surgical options and the resulting post-operative closure is predicted. These last processes, indicated in green, are not covered in this manuscript.

Figure 2

Our Saint Venant-Kirchho elasticity model (yellow) is tuned to approximate the mean MV behavior (magenta) found empirically in (May-Newman and Yin, 1998) for 15% strain, equibiaxial stretching case (circumferential and radial stretches are equal), anterior leaflet. Stress parallel to the fiber direction (σ_aa) is plotted versus strain parallel to the fiber direction (ε_aa). Curves represent hyperelastic model with particular parameter sets, May Newman-Yi specimens CP01 through CP08 (black, dark gray, light gray, blue, dark blue, green, red, and dark red respectively), and “mean” (cyan), Holzapfel law (magenta) (Prot et al., 2007)

Figure 3

Elastic stress-strain relationship: off-biaxial case (the MV radial stretch is 1.5 times the circumferential stretch).

Figure 4

Elastic stress-strain relationship: strip-biaxial case (the circumferential stretch is fixed at 15% and the radial stretch is varied).

Figure 5

Elastic stress-strain relationship: strip-biaxial case (the radial stretch is fixed at 15% and the circumferential stretch is varied).

Figure 6

An exampled of a 3D thin tissue detection of MV leaflets (left) long axis/four chambers view and (right) long axis/two chambers view.

Figure 6

An exampled of a 3D thin tissue detection of MV leaflets (left) long axis/four chambers view and (right) long axis/two chambers view.

Figure 7

Examples of segmentation open and closed valve for case 10. (left) output of the preliminary segmentation and (right) after manual semi-automated segmentation.)

Figure 7

Examples of segmentation open and closed valve for case 10. (left) output of the preliminary segmentation and (right) after manual semi-automated segmentation.)

Figure 7

Examples of segmentation open and closed valve for case 10. (left) output of the preliminary segmentation and (right) after manual semi-automated segmentation.)

Figure 7

Examples of segmentation open and closed valve for case 10. (left) output of the preliminary segmentation and (right) after manual semi-automated segmentation.)

Figure 8

Example papillary muscle and chordae placement (case 1) from three views: (a) looking up at the mitral valve from within the ventricle, and (b-c) side views of the mitral valve. Papillary muscles are depicted as red balls, chords appear as pink lines, and chordal insertion points are represented as pink dots on the valve mesh. A portion of the annulus and atrium are shown but not clearly marked. Otherwise, the blue portion of the mesh represents the anterior mitral valve leaflet, while the red portion of the mesh represents the posterior mitral valve leaflet. Note that chordae attach to both the tip of the mitral valve leaflets as well as slightly lower on the basal portion of the leaflets; these represent the marginal and basal chordae.

Figure 8

Example papillary muscle and chordae placement (case 1) from three views: (a) looking up at the mitral valve from within the ventricle, and (b-c) side views of the mitral valve. Papillary muscles are depicted as red balls, chords appear as pink lines, and chordal insertion points are represented as pink dots on the valve mesh. A portion of the annulus and atrium are shown but not clearly marked. Otherwise, the blue portion of the mesh represents the anterior mitral valve leaflet, while the red portion of the mesh represents the posterior mitral valve leaflet. Note that chordae attach to both the tip of the mitral valve leaflets as well as slightly lower on the basal portion of the leaflets; these represent the marginal and basal chordae.

Figure 8

Example papillary muscle and chordae placement (case 1) from three views: (a) looking up at the mitral valve from within the ventricle, and (b-c) side views of the mitral valve. Papillary muscles are depicted as red balls, chords appear as pink lines, and chordal insertion points are represented as pink dots on the valve mesh. A portion of the annulus and atrium are shown but not clearly marked. Otherwise, the blue portion of the mesh represents the anterior mitral valve leaflet, while the red portion of the mesh represents the posterior mitral valve leaflet. Note that chordae attach to both the tip of the mitral valve leaflets as well as slightly lower on the basal portion of the leaflets; these represent the marginal and basal chordae.

Figure 9

Sequence of computed configurations taken at various intermediary iterations, top views (case 1).

Figure 9

Sequence of computed configurations taken at various intermediary iterations, top views (case 1).

Figure 9

Sequence of computed configurations taken at various intermediary iterations, top views (case 1).

Figure 9

Sequence of computed configurations taken at various intermediary iterations, top views (case 1).

Figure 9

Sequence of computed configurations taken at various intermediary iterations, top views (case 1).

Figure 9

Sequence of computed configurations taken at various intermediary iterations, top views (case 1).

Figure 9

Sequence of computed configurations taken at various intermediary iterations, top views (case 1).

Figure 9

Sequence of computed configurations taken at various intermediary iterations, top views (case 1).

Figure 10

Initial open valve configuration from TEE segmentation and closed configuration predicted using mechanical modeling (case 1).

Figure 10

Initial open valve configuration from TEE segmentation and closed configuration predicted using mechanical modeling (case 1).

Figure 11

Error map showing the prediction error distribution (in mm) for the MV (case 1).

Figure 12

Sensitivity of solution to tether lengths. The mean absolute prediction error (in mm) is shown as a function of various values of the tether lengths. In these plots, the x axis is a scaling factor multiplying the end diastole chordal length (EDCL), taken to be the distance between papillary muscles and chordal insertion points. A value of 1 corresponds to using the tether length at end diastole, other values of the x-axis correspond to multiplicative factors of the EDCL ranging from 0.6 to 1.4. These plots are interesting from a sensitivity analysis perspective, but they also inform the method as to the estimated patient-specific length of the chords, found as those that minimize the prediction error.

Figure 13

Annulus at diastole and systole.

Figure 13

Annulus at diastole and systole.