Introduction

In-vivo mitral valve strain estimation has historically been performed using surgically implanted localized markers, such as sonomicrometry and radiopaque tantalum markers [1,2,3]. While these in-vivo techniques have provided valuable insight into mitral valve physiology and pathophysiology particularly in animal models, image-based non-invasive strategies for in-vivo strain estimation are critical to application in humans within a clinical setting. As a response to this challenge, recent studies have described non-invasive techniques for mitral valve strain estimation from real-time 3D echocardiographic (rt-3DE) images [4, 5]. These algorithms are significant steps towards building clinically applicable mitral valve strain assessment tools, but a critical challenge is that they are reliant on image segmentations. Likewise, research in mitral valve repair simulation and finite element modeling requires detailed image-derived valve reconstructions [7,8,9,10,11]. Finite element modeling has been used to study valve physiology and related medical device design. Mechanical modeling of the mitral valve relies on assumptions and identification of parameters for constitutive models. The earliest FEM models have assumed an idealized geometry of the mitral valve and have evolved to include more detail derived from patient-specific imaging. Algorithms have also included thickness modeling from computed tomography [6] and require assumptions related to the dynamics of the mitral valve and chordal tension forces. Therefore, the ability to automatically segment and geometrically model the mitral valve from clinical images, especially from rt-3DE which is frequently used in pre-operative surgical planning, is essential for implementing mitral valve tissue mechanics analyses for surgical planning and decision making.

Towards this end, several studies have explored 4D mitral valve segmentation and modeling. In [12], the mitral valve is first segmented in a diastolic 3DE image using graph cuts and the resulting mesh evolves under a set of data-driven and regularization forces to capture valve shape in the other images in the series. Application-specific regularization includes forces that tether the leaflet free edges into the left ventricle, enforce a physiological strain on the leaflets, and prevent collision along the leaflet free margin. In [13], a landmark-based deformable model of the mitral and aortic valves is first initialized in two frames in the cardiac cycle. For all other frames, landmark motion is predicted using manifold learning and clustering and then updated by an optical flow tracker and boundary detection. The result is a full 4D surface model of both valves. A drawback of these methods is that they do not generate volumetric segmentations that distinguish the atrial and ventricular surfaces or capture locally varying thickness of the leaflets, which is an important material property in studying valve tissue mechanics [14].

The development of a 4D automated tool that allows for consistent landmarking and modeling of the mitral leaflets can aid in solving clinical dilemmas such as whether to treat ischemic mitral regurgitation with repair or replacement. Ischemic mitral regurgitation (IMR) is a condition in which the mitral valve becomes incompetent due to ischemic disease of the left ventricle. Transesophageal rt-3DE is the standard of care for preoperative assessment of IMR in many major medical centers. Given the high recurrence rate of moderate to severe IMR after valve repair surgery (33% in the first year [15]), there is a great need to identify patients at elevated risk of recurrence, for whom alternative surgical approaches (complete valve replacement) may provide better long-term outcomes. Recently, 3D morphological features extracted from intra-operative rt-3DE of the diseased valve were shown to predict post-repair IMR recurrence [16]. Static features, such as leaflet tethering angles, have demonstrated promising predictive value but only take advantage of rt-3DE data at a single phase of the cardiac cycle. Since the etiology of IMR is functional left ventricular disease, it is likely that features of mitral valve dynamics could potentially bolster recurrence prediction. Towards this end, we have developed an automated spatiotemporal image analysis algorithm that can be used to quantitatively describe mitral valve shape and motion in normal and IMR subjects.

In this work, we build upon the work presented in [17] and present a 4D segmentation method that combines the benefits of atlas-based segmentation and deformable modeling with medial axis-based representation, which produces topologically consistent volumetric models of the mitral valve. The former uses expert knowledge of valve image appearance to label the target rt-3DE series and the latter establishes geometric correspondences across subjects and facilitates statistical shape analysis. Temporal coherence is enforced in the segmentation stage by employing a groupwise implementation of multi-atlas label fusion, which updates segmentations of individual 3DE frames using information from its temporal neighbors in the same image series. Temporal consistency is also enforced during the modeling phase by using the Kalman filter to smooth the trajectories of deformable models fitted to the label fusion results. In contrast to previous work [12, 13], this method is validated against label maps of the valve at every frame in the rt-3DE series. Moreover, it demonstrates the ability to compare functional valve measurements in subjects with normal mitral valve function and in subjects with severe IMR.

Materials and Methods

Image Data and Manual Segmentation

The iE33 imaging platform (Philips Medical Systems, Andover, MA) was used to acquire ECG-gated rt-3DE images of the mitral valve from 28 patients: 14 with normal mitral valve structure and function and 14 with severe IMR. Images were obtained over four consecutive cardiac cycles with a 2–7 MHz matrix-array transesophageal transducer. The rt-3DE acquisitions over consecutive cardiac cycles were obtained at end-expiration during positive pressure ventilation in anesthetized patients to eliminate motion caused by respiration. Each subject’s rt-3DE image series consisted of 10–37 frames (temporal resolution of 18–40 Hz) showing the mitral valve over one cardiac cycle beginning at early systole. The images were exported in Cartesian format with nearly isotropic resolution ranging from 0.4 to 0.8 mm. All data series, totaling 613 individual 3DE images, were manually segmented in ITK-SNAP, an interactive medical image segmentation tool [18]. An expert observer separately labeled the anterior and posterior leaflets in each 3DE image. The manual segmentations served as atlases for multi-atlas label fusion and as references for cross-validation of automated segmentation.

Automated Image Analysis

Automated 4D mitral valve segmentation requires a reference atlas set consisting of manually traced images at each phase of the cardiac cycle, and a deformable model of the valve. The only manual interaction required to segment a new unseen target image series is the identification of several temporal and physical landmarks in the target series, described below. First, the series is segmented using a groupwise implementation of multi-atlas label fusion. Then, a mitral valve model in the form of a medial axis representation is deformed to the groupwise segmentation result with enforcement of temporal coherence. The combination of these techniques facilitates standardized automated measurements of mitral valve dynamics in rt-3DE data. Figure 1 illustrates an overview of this pipeline and Figs. 2, 3 and 4 demonstrate the specifics of each step of the pipeline.

Fig. 1
figure 1

Summary of the image analysis pipeline for automatic segmentation and modeling. The user identifies 2 temporal landmarks and 5 spatial landmarks. Groupwise multi-atlas label fusion is used to generate temporally coherent segmentations of all frames in an image series. Deformable continuous medial representation (cm-rep) is then used to generate topologically consistent volumetric models of the mitral valve from the segmentation results. Temporal consistency is enforced with a Kalman filter. The final output is a 4D patient-specific mitral valve model that can be used for shape analysis

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Fig. 2
figure 2

a Example of landmarking in a cross-section of a 3DE image, from left to right: midpoint of posterior annulus, midpoint of the coaptation line, and the anterior aortic peak of annulus. b Anatomical representation of five manually identified mitral valve landmarks, from top to bottom: anterior aortic peak of the annulus, two commissures, the midpoint of the coaptation line, and the midpoint of the posterior annulus

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Fig. 3
figure 3

Intra- and inter-cardiac phase registration within the target image series. Intra-phase registrations: all pairs of 3D images within a cardiac phase are registered to each other. Inter-phase registrations: mid-systolic frame I2 is registered to the mid-diastole frame I6, which is registered to the transitional frame I4

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Fig. 4
figure 4

Summary of groupwise multi-atlas label fusion. A set of reference 3D images is assigned to each frame within a target image series. Multi-atlas joint label fusion is performed independently on each 3DE image in the series. The multi-atlas segmentations are then iteratively updated using the image’s temporal neighbors as pseudo-atlases, in addition to the initially assigned reference images. An example of a groupwise segmentation update for frame 2 is shown. Here, I denotes a 3D image within the target series, S denotes a 3D segmentation, and A denotes a 3D atlas from other subjects’ data sets. The numbered subscripts indicate frame numbers

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Cardiac Phase Detection and Landmark Initialization

Given an unseen target rt-3DE image series to segment, a user first identifies two frames in the cardiac cycle: mid-systole and mitral valve opening. As illustrated in Fig. 2, the user identifies five landmarks in the mid-systolic image: the anterior aortic peak of the annulus, two commissures, the midpoint of the coaptation line, and the midpoint of the posterior annulus. The purpose of the landmarks is to roughly initialize the affine transformation needed to align the atlas and target images. Because the utility of landmarking is used for rough initialization rather than for final measurements, inter-user variability does not likely have a strong impact on the final patient-specific geometric model, especially if the landmarks are within several millimeters [19]. Similar approaches to initialization using either automated landmarking or manual tracing have been used in other valve segmentation tools [12, 13, 20]. While it may be possible to automate this step using convolutional and recurrent neural networks as in [21], which applies to landmark magnetic resonance imaging data sets, it requires a much larger dataset especially for echocardiography where the contrast is not as high.

Intra-subject registrations

The spatial landmarks identified in the mid-systolic frame are first propagated to the other frames in the rt-3DE series in order to accurately initialize multi-atlas segmentation of each individual frame. Landmark propagation is achieved by deformable registration between pairs of 3D images within the target image series. Figure 3 illustrates that all pairs of images within the same phase of the cardiac cycle are registered to one another, both for landmark propagation and for groupwise multi-atlas segmentation as described below. In addition to these intra-phase registrations, the mid-systole frame is registered to the mid-diastole frame, and the mid-diastole frame is registered to the transitional frame (i.e., mitral valve opening). This allows for the mid-systole landmarks to be propagated to all frames within the target rt-3DE image series. The intra-subject registrations also facilitate groupwise iterations of multi-atlas segmentation as described below. All deformable registrations are performed with the open-source Advanced Normalization Tools (ANTs) toolkit [22].

Groupwise Multi-Atlas Segmentation

Given the relatively small number of cases and the consistency in mitral valve appearance in 3D TEE, we take advantage of multi-atlas label fusion (MALF) [23] as an alternative to machine learning techniques that require very large training data sets. Multi-atlas label fusion (MALF) uses a set of expert-labeled images, referred to as atlases, to generate individual candidate segmentations of a target image. Each candidate segmentation is created by performing deformable registration between the target and atlas image, and then warping the atlas labels to the target image space. Registration is initialized with the user-identified landmarks described above. Since the candidate segmentations may not be accurate on their own, they are merged into a higher quality segmentation using a consensus-seeking strategy called label fusion, which uses spatially varying intensity-based weighted voting to combine the candidates into a consensus label map [24]. In order to extend 3D MALF to the spatiotemporal domain, we use a groupwise adaptation of MALF [25]. First, each 3DE image in the series is independently segmented with MALF using other subjects’ atlases. Once an initial segmentation is generated for each frame, the series of segmentations is iteratively updated using both the original reference atlases and the MALF segmentations of neighboring 3DE images as “pseudo” reference atlases. By weighting the “pseudo” atlases equal to or more than the original atlas set, the iteratively updated segmentations become more coherent with one another, capturing the similarity in the segmentations of the same structure moving over time.

A challenge of using groupwise MALF (GW-MALF) for 4D valve segmentation is that performing within-subject deformable registration between the valve at systole and diastole often produces poor results because the temporal resolution of image acquisition is not sufficient to provide many intermediate images of the leaflets during rapid valve opening. To overcome this challenge, GW-MALF is performed separately in overlapping cardiac phases: systole, transition, and diastole. Figure 4 illustrates that for each 3D image In in a sample target series, a set of atlases \( \left\{{A}_f^s\right\} \) is selected from the same cardiac phase and a neighboring cardiac phase of other subjects’ data sets. Each 3DE image In in the target series then has an independent atlas set \( \left\{{A}_f^s\right\} \). Here, f denotes a set of frame numbers and s denotes a set of subject identifiers. In the first round of MALF, each In is segmented using only the reference atlas set \( \left\{{A}_f^s\right\} \). In the subsequent groupwise iterations, the segmentation of In is updated using the segmentations of In − 1and In + 1 as pseudo atlases, along with the original atlas set \( \left\{{A}_f^s\right\} \).

Deformable Medial Modeling

Once a series of valve segmentations is obtained, a deformable model in the form of a continuous medial representation (cm-rep) [26] is warped to the GW-MALF results. This step imposes a fixed topology on the final segmentation, establishes correspondences on different patients’ segmentations, and facilitates automated morphological measurement. An advantage of combining label fusion and deformable medial modeling is that medial modeling can geometrically correct segmentation artifacts such as holes and over-segmentation. Cm-rep describes the valve in terms of its medial axis geometry and is parameterized by {m, R} ∈ ℝ3 × ℝ+, where m is a continuous medial manifold and R is a radial thickness field defined over the medial manifold. Numerically, the medial manifold and leaflet surfaces are represented by triangulated meshes that can be sequentially Loop subdivided to a desired vertex density. The template medial mesh, shown in Fig. 5b, is generated using a method similar to that described in [27] and is deformed to maximize its overlap with the target segmentation while imposing soft regularization constraints to ensure mesh regularity and validity of medial axis geometry as described in [28]. Figure 5a summarizes these definitions. In brief, the template is generated by co-registering a population of mitral valve segmentations to generate a unbiased template segmentation that is then manually meshed as described in [27]. The resulting triangulated template is used to model the mitral valve in each 3D frame in each data series.

Fig. 5
figure 5

a Overview of continuous medial representation (cm-rep) adapted from [27]. b Example of the cm-rep template being fitted to a GW-MALF segmentation in order to generate a patient-specific cm-rep model

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Kalman Filtering

Dynamic measurements derived from cm-reps that are independently fitted to each frame in the output GW-MALF segmentations are inherently noisy. To impose spatiotemporal smoothness on the model series, a Kalman filter [29] is used to recursively estimate the true state of the system (the valve’s configuration and motion), which cannot be observed directly but can be estimated by combining noisy observations with the predictions of kinematic equations. Let xt denote the true system state at time t and let \( {\hat{\mathbf{x}}}_{t\mid t-1} \) be the a priori estimate of the system’s state at time t with variance Pt ∣ t − 1. The vector \( {\hat{\mathbf{x}}}_{t\mid t-1} \) is determined by applying kinematic equations to the state estimate at t − 1. Let zt be observations of the system made at time t. The goal of the Kalman filter is to combine the a priori estimate \( {\hat{\mathbf{x}}}_{t\mid t-1} \) and measurements zt to generate an a posteriori prediction of the state at time t, denoted by \( {\hat{\boldsymbol{x}}}_{t\mid t} \).

In this work, the sought “true” system state is defined by \( {\mathbf{x}}_t=\left[\genfrac{}{}{0pt}{}{x_t}{{\dot{x}}_t}\right] \), where xt denotes vertex coordinates that comprise the medial surface m and \( {\dot{x}}_t \) denotes their velocities at time t. We treat the cm-rep models fitted independently to different rt-3DE frames as the noisy observations zt. With a medial mesh consisting of np nodes, the total number of state variables is nv = 6np. The recursive filter begins by initializing \( {\hat{\mathbf{x}}}_{0\mid 0}={\mathbf{z}}_0 \) as the medial node coordinates and velocities of the medial model fitted to the first frame of the rt-3DE series. Its covariance is initialized as \( {\mathbf{P}}_{0\mid 0}={\mathbf{0}}_{n_v} \). For each subsequent frame, the state is predicted to evolve according to \( {\hat{\mathbf{x}}}_{t\mid t-1}={\mathbf{F}}_t{\hat{\mathbf{x}}}_{t-1\mid t-1}+{\mathbf{w}}_t \), where Ft is a transition matrix that displaces the nodes with constant velocity and \( {\mathbf{w}}_t\sim \mathcal{N}\left(0,{\mathbf{Q}}_t\right) \) is zero-mean Gaussian distributed process noise with covariance Qt. The a priori covariance is updated as \( {\mathbf{P}}_{t\mid t-1}={\mathbf{F}}_t{\mathbf{P}}_{t-1\mid t-1}{\mathbf{F}}_t^T+{\mathbf{Q}}_t \). Noisy measurements of the state at time t are modeled as zt = Htxt + vt, where Ht is the identity matrix \( {\mathbf{I}}_{n_v} \) and \( {\mathbf{v}}_t\sim \mathcal{N}\left(0,{\mathbf{R}}_t\right) \) is zero-mean Gaussian distributed measurement noise with covariance Rt. Assuming that the process noise and measurement errors are uncorrelated, the a posteriori state estimate is given by:

$$ \genfrac{}{}{0pt}{}{{\hat{\boldsymbol{x}}}_{t\mid t}={\hat{\boldsymbol{x}}}_{t\mid t-1}+{\mathbf{K}}_t\left({\mathbf{z}}_t-{\mathbf{H}}_t{\hat{\mathbf{x}}}_{t\mid t-1}\right)}{{\mathbf{P}}_{t\mid t}={\mathbf{P}}_{t\mid t-1}-{\mathbf{K}}_t{\mathbf{H}}_t{\mathbf{P}}_{t\mid t-1}} $$
(1)

where Kt is the Kalman gain defined by \( {\mathbf{K}}_t={\mathbf{P}}_{t\mid t-1}{\mathbf{H}}_t^{\mathrm{T}}{\left({\mathbf{H}}_t{\mathbf{P}}_{t\mid t-1}{\mathbf{H}}_t^{\mathrm{T}}+{\mathbf{R}}_t\right)}^{-1} \). In this study, \( {\mathbf{R}}_t={\mathbf{I}}_{n_v} \) remains constant over time. Since the state evolution equations assume a constant velocity, which does not accurately reflect the nonlinear motion of the valve, we employ a time-varying process noise covariance that increases in magnitude at ttrans, the transition time in the cardiac cycle when the valve opens:

$$ {\mathbf{Q}}_t=\alpha (t){\mathbf{I}}_{n_v},\mathrm{where}\ \alpha (t)=\Big\{{\displaystyle \begin{array}{c}0.1,\kern0.5em t<{t}_{trans}\\ {}1.0,\kern0.5em t\ge {t}_{trans}\end{array}}\operatorname{} $$
(2)

The time-varying Qt allows the model fittings to have a stronger influence on the state estimation when the valve accelerates. Once the Kalman filter is applied to the entire series of medial models, measurements of valve dynamics are computed.

Statistical Analysis

To assess the smoothing effect (noise reduction) of the Kalman filter, a cubic polynomial was fitted to each set of dynamic measurements before and after Kalman filtering, and the root mean square residuals between the measurements and the cubic polynomial was calculated. The mean of these residuals was calculated for each patient for each measurement, resulting in two sets of 28 residuals per measurement. A paired Student’s t test was used to test whether the difference in residuals before and after Kalman filtering was significant for each measurement. In addition, the absolute percent difference between the measurements before and after filtering was calculated to determine if a smoothing effect is achieved with minimal measurement alteration.

To test for inter-group differences in valve dynamics, an independent t-test was used to compare IMR and control group measurements at each time point of the cardiac cycle. A Dunn-Sidak correction (α = 0.0014) was used to account for multiple-hypothesis testing. The testing was performed after interpolation to ensure that an equal number of time points in both the IMR and normal groups were assessed.

Results

Valve segmentation and modeling were evaluated in a leave-one-out experiment using manual image segmentation for comparison. For each target image series, the atlas set for each 3D frame consisted of 10 randomly selected frames from the other 13 subjects’ data sets within the same sub-group (normal and IMR). Of these 10 randomly selected frames, 8 were from the same phase of the cardiac cycle as the target image and 2 were from the transition phase. For target images in the transitional phase, the atlases consisted of 1 from systole, 8 transitional, and 1 from diastole. The series of segmentations were updated with one groupwise iteration. A representative segmentation result is shown in Fig. 6, and the Kalman-filtered model fittings for the same dataset are illustrated in a supplemental video file. The accuracy of GW-MALF and model fitting relative to manual tracing for all subjects are given in Table 1. Segmentation accuracy was assessed using the mean boundary error (BE) metric, a symmetric measurement of distances between meshes as defined in [27]. Given two meshed shapes P and Q, the MBE is defined as the average of the distances between the two meshes P and Q and Q and P as follows:

$$ MBE=\frac{1}{2}\left(d\left(P,Q\right)+d\left(Q,P\right)\right) $$
(3)

The distance between the two meshes is given by:

$$ d\left(P,Q\right)\cong \frac{1}{A_P}\underset{x\in P}{\int }{\operatorname{inf}}_{y\in Q}\left\Vert x-y\right\Vert\ dA $$
(4)

where x is a point on mesh P and y is a point on mesh Q and Ap is the surface area of mesh P.Table.

Fig. 6
figure 6

a Manual segmentations overlaid on 3DE slices. b MALF results for a subject with ischemic mitral regurgitation. c GW-MALF results for the same IMR subject. The anterior leaflet is red and posterior leaflet is green. The cm-rep models fitted to the GW-MALF segmentations in (c) are presented in a supplemental video file

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Table 1 Segmentation accuracy based on the symmetric mean boundary error (BE) metric. Mean BE is averaged across all time points within the indicated cardiac phases
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Dynamic geometric measurements listed in Table 2 were extracted from (1) cm-reps fitted to the GW-MALF segmentations and (2) cm-reps fitted to the GW-MALF segmentations followed by Kalman filtering. Deformable modeling with cm-rep establishes geometric correspondences across all subjects and across all time points in the rt-3DE images, enabling automatic computation of the same valvular features from all subjects at all frames of the rt-3DE data. Without cm-rep model fitting, the measurements in Table 2 could not be computed from the segmentation results in a straightforward manner. To assess the smoothing effect (noise reduction) of the Kalman filter, a cubic polynomial was fitted to each set of dynamic measurements before and after Kalman filtering, and the residual between the measurements and the cubic polynomial was calculated. To evaluate if noise reduction substantially changed the magnitude of the measurements, the average percent difference between the measurements before and after filtering was calculated (Table 2).

Table 2 Root mean square residual (RMSR) in dynamic measurements relative to their best-fit cubic polynomials before and after Kalman filtering of the groupwise multi-atlas segmentation (GW) results. The p value refers to comparison of the residuals for each measurement before and after Kalman filtering. The percent difference between the measurements before and after Kalman filtering is reported
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For the normal and IMR subgroups, the septolateral diameter (SLD), intercommissural width (ICW), annular bending angle, annular area, posterior and anterior annular circumferences, and total annular circumference were plotted as a function of time, normalized to the cardiac cycle. Bending angle is a measure of flatness of the mitral annulus, with a larger angle signifying a flatter annulus. Figure 8 shows the IMR measurements in blue and normal valve measurements in red. Early systole measurements of septolateral diameter were significantly different between subgroups (α = 0.0014), after Sidak correction for multiple hypothesis testing.

The geometric correspondences established by deformable modeling with cm-rep also enable direct comparison of spatially varying valve features between subjects at different phases of the cardiac cycle. To demonstrate this capability, Fig. 8 illustrates a comparison of leaflet thickness between two different cardiac phases: mid-systole and end-diastole.

Discussion

The proposed 4D mitral valve segmentation pipeline combines the attractive properties of multi-atlas segmentation and deformable medial modeling to create descriptive, quantifiable representations of mitral valve dynamics from rt-3DE images. Exemplified in Fig. 6, the output models are visually consistent with the images throughout the cardiac cycle. In addition, the accuracy metrics presented in Table 1 demonstrate that in each cardiac phase, automated segmentation performs on par with user-guided segmentation (0.40 ± 0.32 mm [30]) and compares favorably to other automated 4D segmentation algorithms (0.59 ± 0.49 mm [12] and 1.54 ± 1.17 mm [13]). The pipeline’s novelty is its extension of MALF and cm-rep into the spatiotemporal domain by enforcing temporal consistency during both the segmentation and modeling stages. From Table 1, even a single iteration of GW-MALF shows improvement in the quality of multi-atlas segmentations, especially with respect to the mean BE during systole and diastole, as well as the maximum BE. The improvement in temporal consistency of the segmentations is also visually observed in Fig. 6, where GW-MALF can be seen to reduce artifacts in the posterior leaflet. Kalman-filtered cm-reps produce dynamic measurements that are less noisy than those fitted directly to GW-MALF segmentations. This observation is supported by the low p values (p < 10−6) reported in Table 2. Moreover, the low percent differences between the measurements computed before and after Kalman filtering suggest that the noise reduction does not substantially change the magnitude of the measurements.

Another important observation in this study is the identification of differences in valve dynamics in patients with normal mitral valve function and in patients with severe IMR. Overall, the dynamics of annular area are consistent with some of the early sonomicrometry ovine studies that described annular dilation at diastole [31]. Figure 7 demonstrates differences in annular dynamics in the normal and IMR subgroups. Increased septolateral diameter and annular bending angle in IMR patients suggest annular dilatation and flattening, which are common features of IMR. Moreover, Fig. 7 suggests that annular dynamics, particularly changes in septolateral diameter, annular area, and annular circumference, may be less pronounced over the cardiac cycle in IMR patients relative to normal mitral valves. Interestingly, this may be due to differing dynamics in the posterior annulus of the IMR and normal subgroups during systole. While the anterior and posterior annular segments of normal mitral valves increase in length over the cardiac cycle (Fig. 7g), the posterior annular segment decreases in length during diastole in the IMR subgroup. In addition to annular dynamics assessment, the image analysis method is able to measure regional leaflet velocities. The free edges of the leaflet were divided into 6 scallops corresponding to the A1, A2, A3, P1, P2, and P3 Carpentier segments, and the average velocity of each segment was calculated over the cardiac cycle. As observed for all leaflet segments, Fig. 7 demonstrates that velocities of the free edge of the A3 and P3 segments rapidly increase with valve opening during diastole. While this behavior seems to be similar for both normal and IMR patients, increasing the number of patients may yield interesting finding regarding especially when stratifying the IMR patients based on the pathophysiology of annular dilatation vs leaflet tethering.

Fig. 7
figure 7

Comparison of (a) A3 leaflet velocity, (b) P3 leaflet velocity, (c) septolateral diameter (SLD), (d) intercommissural width (ICW), (e) annular bending angle, (f) annular area, (g) anterior annular circumference, (h) posterior annular circumference, and (i) annular circumference in subjects with normal mitral valves (red) and severe IMR (blue) over one cardiac cycle. The error bars represent one standard deviation from the mean. * indicates significant difference between IMR and normal subjects for the given time point

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For valve mechanics applications, automated image-based segmentation and geometric modeling of the mitral valve over the cardiac cycle can allow for improved, detailed understanding of mitral valve geometry and motion. In particular, the ability to capture regional thickness over time is important for finite element simulations. In a study by Rausch and colleagues [14], finite element simulation was shown to be highly sensitive to parameters such as thickness. Underestimating or overestimating thickness led to different simulated behaviors of the mitral valve leaflets such as larger or smaller deflections of the leaflets into the atrium. Modeling the distribution of thickness is also critical. For example, assuming a uniform thickness distribution overestimates the stiffness of the leaflets towards the free edge and underestimates the stiffness near the annulus [32]. The ability to model thickness throughout the cardiac cycle provides information that can be incorporated into these simulations as well. As seen in Fig. 8, the anterior leaflet appears to be thicker during end diastole when compared to mid systole, suggesting that leaflet stretch may impact leaflet thickness. The ability to capture leaflet velocity is also useful for tissue mechanics simulation by helping to estimate the amount of deflection and restriction of the leaflets. In addition, fluid mechanics and dynamics modeling [33] may have improved accuracy and patient specificity with advanced 4D image-based modeling. It is well known that the anterior leaflet affects vortex formation and transmittal, which in turn reduces energy loss [34]. However, current methods are limited by standardized geometries. Furthermore, the utilization of detailed 4D mitral valve modeling may improve our understanding of how changes in mitral valve dynamics impact cardiac function, and thereby lead to new insight and advancement in surgical and interventional therapies for diseases like mitral regurgitation. For example, a recent study [35] used finite element and fluid structure interaction modeling to demonstrate that the changes in geometry caused by the popular MitraClip procedure may lead to changes in left intraventricular hemodynamics, such as dissipation of the anterior vortex [36] and higher energy loss [37].

Fig. 8
figure 8

Mean thickness maps for all subjects combining the normal and IMR subgroups at mid-systole and end-diastole, demonstrating the ability to compare geometric features across time points by using continuous medial axis-based representations. Areas of greater of thickness are indicated in dark red

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While the proposed pipeline only requires manual identification of two key frames in the cardiac cycle and five valve landmarks at mid-systole, future work will focus on full automation of the algorithm. In this study, the use of a Kalman filter with a constant velocity model and time-varying process noise provide meaningful time series smoothing. A physical model that better captures the valve’s non-linear dynamics could further improve temporal coherence in the output 4D model. Finally, although differing trends in annular dynamics and spatially varying leaflet thickness can be appreciated in the normal and IMR subgroups in Figs. 7 and 8, a larger patient population is needed to verify these interesting findings. The development of this 4D automated segmentation and modeling tool is a step towards better understanding the functional mechanisms underlying IMR progression and post-operative disease recurrence, and can provide patient-specific input to biomechanical simulations that guide surgical simulation and decision making.

Conclusions

Automatic 4D segmentation and modeling allow for reliable physiological, non-invasive reconstruction of the mitral valve over the cardiac cycle. This study demonstrates its application to comparison of mitral annular and leaflet dynamics in pathological and normal mitral valves. The method may help inform finite element modeling by decreasing assumptions about input parameters related to regional mitral valve thickness, geometry, and motion. Future studies can apply this algorithm to a range of cardiovascular mechanics applications, including patient-specific strain estimation, fluid dynamics simulation, inverse finite element analysis, risk stratification of surgical treatment, and development of minimally invasive therapies for valve disease.