This single-center study includes 33 asymptomatic PMR patients recruited between 2006 and 2010 under NHLBI Specialized Centers of Clinically Oriented Research grant (16). Primary degenerative mitral valve prolapse has echocardiographic evidence of thickened, redundant leaflets with excessive motion and prolapse. Patients were excluded for evidence of: (1) aortic valve > trace aortic regurgitation or mean gradient of > 10 mmHg, (2) mitral stenosis (mean gradient > 5 mmHg, valve area < 1.5 cm2), (3) endocarditis, (4) iatrogenic MR (ergot, radiation induced), (5) hemodialysis, (6) pregnancy, (7) presence of coronary artery disease (stenosis > 50%), (8) positive exercise tolerance test with myocardial perfusion. None of the patients were surgical candidates upon entering this study. All patients were asymptomatic and had no history or evidence of coronary artery disease, ruled out by a maximum exercise tolerance test with nuclear imaging. The Institutional Review Boards of the University of Alabama at Birmingham and Auburn University approved the study protocol. All participants gave written informed consent.

All data from patients’ baseline and return visits were obtained prospectively and recorded in electronic health data records. Asymptomatic PMR patients had Class I status, with moderate/severe PMR by color flow Echo/Doppler, LVEF > 60%, LVESD < 40 mm, leaflet thickening and prolapse, and normal maximal exercise myocardial perfusion imaging (16).

Magnetic resonance imaging was performed on a 1.5-T MRI scanner (Signa GE, Milwaukee, Wisconsin) optimized for cardiac application. Electrocardiographically gated breath-hold steady-state free precision technique was used to obtain standard (2-, 3-, and 4-chamber short-axis) views using the following parameters: slice thickness of the imaging planes 8 mm, field of view 44 44, scan matrix 256 128, flip angle 45°, repetition/echo times 3.8/1.6 ms. Three-dimensional LV geometric parameters were measured from endocardial and epicardial contours manually traced on cine-MR images acquired near end diastole and end systole. The contours were traced to exclude the papillary muscles. Cubic B-spline surfaces were fit to the endocardial and epicardial contours for each time frame (8–13). The severity of mitral regurgitation (regurgitant volume and regurgitant fraction) was obtained by: Regurgitant volume = LV – RV stroke volume and Regurgitant fraction = LV – RV stroke volume/LV stroke volume.

Tagged magnetic resonance images were acquired with repetition/echo times 8/44 ms, and tag spacing 7 mm (10, 11). Three-dimensional LV strain was measured from tagged images at end systole, which was defined by visual inspection of the image data as the time frame with maximum contraction. Strain computations were conducted using an in-house software package. Two-dimensional strain rates were measured using harmonic phase analysis. Harmonic phase analysis measures the local, 2-dimensional strain of the myocardium based on the local spatial frequency of the tag lines. During myocardial contraction, the tag lines become closer to each other and the tag frequency increases in proportion to that contraction. Strain rates were computed at mid LV segment as defined by Cerqueira et al. (17)

Three-dimensional wall thickness was computed at the same segments by measuring the distance from a point on the endocardial surface to the closest point on the endocardial surface along a line perpendicular to the epicardial surface. The radius to wall thickness ratio was computed as the reciprocal of the product of the endocardial circumferential curvature (κ) and wall thickness (T). End-systolic wall stress was computed according to the formula (10):Wallstress=0.133P2kT(1+κT2)

where P is mean arterial LV blood pressure measured by a cuff measurement at the time of the MR scan. Mean arterial pressure was calculated as: MAP = DP + 1/3(SP – DP) or MAP = DP + 1/3(PP) [systolic blood pressure 2(diastolic pressure)]/3.

The objective of this preliminary study is to develop models for predicting LVEF < 60% in the subsequent (6 month) CMR examination. Due to the limited number of patients, the study employed four features selected from our previous study (14): LVEF, LVESD, LV SI, and mid LV SR_circ measured at four time points: baseline, 6, 12, and 18 months. Predictive models were constructed to investigate the following questions: (1) Compared with the model using CMR at a single time point, does the inclusion of features recorded at multiple time points improve the prediction of LVEF < 60%? and (2) What is the optimal number of time points required for accurate prediction in this context?

The final goal of this preliminary study is to develop a predictive model for predicting LVEF < 60% in the subsequent (6 month) CMR examination. Statistical models that model repeated measurements (e.g., mixed-effect model, marginal model) require at least three time points. Thus, we utilized machine learning models to investigate the two questions. After finalizing how many time points to be included in the predictive model, both statistical and machine learning model were fitted for predicting LVEF < 60% at 18 months.

Since Random Forest (RF) showed superior performance in our previous study (14), we utilized RF to construct three predictive models to investigate the inclusion of features measured at multiple time points. RF is a nonparametric and tree-based approach that operates without assuming a specific distribution of the data. It effectively models complex relationships between variables without assuming a specific function form and is less prone to overfitting especially when dealing with high-dimensional data (18). Three RF models were used to predict whether LVEF is less than 60% at 18 month using CMR features from a) baseline only, b) baseline + 6 months, and c) baseline + 6 month + 12 month. For each model, we performed feature selection and hyperparameter tuning, and assessed the model performance via repeated cross-validation. The metrics used for model assessment include accuracy, sensitivity, specificity, and Area under the ROC curve (AUC) values.Accuracy=TP+TNTP+TN+FP+FNSensitivity=TPTP+FNSpecificity=TNTN+FPWhere TP, TN, FP, and FN are short for true positive, true negative, false positive, and false negative.

In addition to assessing the performance of the predictive models, the SHapley Additive exPlanations (SHAP) (14, 19) value was used to investigate the importance of each feature and the directional impact of each feature on predicting the drop in LVEF (i.e., a positive or negative impact on LVEF < 60% at 18 months).

With the four CMR parameters (LVEF, LVESD, LV SI, and mid LV SR_circ) obtained at baseline, 6 month, and 12 month, we also fitted the Generalized Linear Mixed-effect Model (GLMM) (20) and the Generalized Estimating Equations (GEE) (21) model, which is the marginal model, for the prediction and inference at the patient and population level, respectively. Different from RF models, the response variable in the GLMM and GEE is a length 3 vector, with each element indicating whether LVEF > 60% (coded as 0) or < 60% (coded as 1) at 6, 12, and 18 months and the predictors are the four CMR parameters recorded at baseline, 6, and 12 months.

With GLMM, the effect of the longitudinal features on individual patients is assessed (i.e., subject-level inference). To account for repeated measures within each patient, the GLMM is fitted with a random intercept. The model incorporates follow-up time as a discrete variable and interactions between the features and time to estimate the rate of progression for each feature. The determination of significant predictors and interactions are based on likelihood ratio tests, comparing the coefficient of a predictor being zero vs. non-zero.

The GEE is fitted with a similar model structure and the correlation structure being autoregressive lag 1. Different from GLMM, GEE enables group-level inference, investigating the fixed effects of the longitudinal CMR parameters on a broader population of asymptomatic PMR patients. Due to the scale differences among the four parameters, each parameter was standardized. GLMM and GEE models are assessed by the marginal R squared, which describes the proportion of variance explained by the fixed effects, and conditional R squared, which describes the proportion of variance explained by both the fixed and random effects. GLMM is not applicable to cross validation. Thus, only GEE performance was assessed via repeated cross validation and compared with the RF model. The final model was retrained using all the data, allowing for a comprehensive understanding of the model's coefficients.

Data in Table 1 are presented as number/total (%) in group or median with 25% and 75% interquartile range in parentheses.

Demographics, CMR-derived LV and LA volumes, and LV strains in 33 asymptomatic PMR patients are listed in Table 1.

The mid LV is an important point of spherical transition as LV diameter increases to a greater extent than LV length decreasing sphericity index and wall thickness/radius producing an increase in LV wall stress. LV biopsies taken at mid LV from our previous studies (10–12) demonstrate this point in our PMR patients, showing a decrease in LV SI and LV wall thickness (Figure 1A) along with a decrease in mid LV endocardial curvature (Figure 1B). The green arrow in Figure 1A at the location of our myocardial biopsies is coincident with myofibril lysis, sarcomere breakdown, and disorganized mitochondria with cristae lysis (Figure 1C). LVEDD and LVESD (Figure 1D) is the sum of 32 radially directed vectors at mid LV that is close to measurement of mid LV SR_circ. It is important to note that the location of the myocardial biopsies from our previous studies of PMR patients is in the same location of the CMR derived LVEDD and LVESD (10–12).

The 18-month outcome of 33 PMR patients with CMR baseline LVEF > 60% (n = 21) or baseline LVEF < 60% (n = 12) is presented in Figure 2. Of 21 patients with baseline LVEF > 60%, 6 patients had LVEF < 60% and 15 had LVEF > 60% at 18 months. Of 12 patients with baseline LVEF < 60%, 5 patients had an increase in LVEF > 60% at 18 months and 7 patients were asymptomatic with LVEF < 60% at 18 months. Of the 33 PMR patients, 13 had CMR LVEF < 60% by 18 months despite all presenting with a median baseline CMR-derived LVEF > 60% (Table 1) and Echo-derived LVEF >60%.

There is a wide variability of LVEF, LVESD, and mid LV SR_circ at each time point over the 18-month period (Figure 3). These indices of LV shortening are load dependent as demonstrated by the inverse relation of LVEF to mean arterial pressure at the time of imaging and a calculated LV end-systolic wall stress (Figure 4). This demonstrates the inherent physiological variability of LVEF to a changing afterload, militating for repeated measures at the four time points.

All patients had four scans (baseline, 6 month, 12 month, and 18 month). To predict the LVEF decline at 18 months, we considered using CMR features measured at baseline only (type 1 model) compared to repeated CMR features measured at two or three time points (type 2 model). In the type 2 model, we considered using baseline + 6 month CMR features and baseline + 6 month + 12 month CMR features respectively. The purpose of constructing these two types of models is to address two questions: (1) if including repeated CMR measurements can improve the prediction of the decline in LVEF at 18 months, compared with a model only using baseline measurements; (2) how many repeated measurements are needed to best predict LVEF decline at 18 months, or in other words, is it necessary to have a CMR scan every six months.

Random Forest models were constructed to predict LVEF < 60% at 18 months. The first model incorporated the four CMR features (LVEF, LVESD, LV SI, and mid LV SR_circ) identified from our previous study (14) at a single time point (i.e., baseline). The second model integrated the four features measured at two consecutive time points—baseline and 6 months. The third model encompassed the four features measured at baseline, 6, and 12 months. The RF model utilizing the four features at baseline achieved a low prediction accuracy of 64% and sensitivity of 57%, which slightly improved with the second model (72% and 63% respectively) (Table 2). Incorporating the four features (measured at baseline, 6, and 12 months) in the third model achieved highest prediction accuracy (79%) and sensitivity (85%) (Table 2).

Random Forest model was compared to GLMM and GEE statistical models for prediction of LVEF < 60% at 18 months using the same four features measured at baseline, 6, and 12 months. The coefficients of GEE and GLMM are summarized in Table 3. GEE is a marginal model that focuses on estimating the population level effects; while GLMM is the conditional model that focuses on estimating subject-specific effects. For GLMM, the marginal R squared is 0.673 and the conditional R squared is 0.673, and the variance of the subject effect is close to zero. This implies that fixed effects rather than random effects largely explain the drop in LVEF. The GEE marginal R square and conditional R square are 0.736, implying that the GEE population-averaged correlation structure fits the data better and explains more variation in the data providing a better final statistical model for the prediction of LVEF < 60%. A comparison between GEE and RF model performance (using repeated measures of the four features at baseline, 6 months and 12 months) shows that the RF model has a higher prediction accuracy and sensitivity (Table 4).

Random Forest captures the non-linear relationship between features and the response variables, and further identifies important features that have a strong impact on the LVEF < 60% in a non-linear way. The GEE model assumes a linear relationship between the features and log odds, while RF captures the interactions and combinations among features. Thus, the GEE linear model may not capture such complex relationships; while the data-driven RF model relies heavily on the patterns and information present in the provided data.

The RF model computes the importance of each variable using the four CMR features repeatedly measured at baseline, 6, and 12 months (4 features × 3 time points = 12 features) to predict LVEF < 60% at 18 months (Figure 5). The Random Forest model performance used 4 features measured at 3 time points. The RF model utilizing the top 3 features: 12 month LVEF, baseline LVEF, and 12 month mid LV SR_circ gave the best model performance in predicting 18 month LVEF < 60% with 79% accuracy and 85% sensitivity (Table 5).

The Shapley Additive exPlanations (SHAP) value (19), inspired by the Shapley value in cooperative game theory, assigns an importance value to each feature in machine learning models to explain the decision made by the model. The SHAP value constructed an overall interpretation of the RF model with the three most important features (12 month LVEF, baseline LVEF, and 12 month mid LV SR_circ) and its directional impact on prediction (a positive or negative impact on probability of LVEF < 60% at 18 months), and how each feature contributes to a prediction in each patient.

The SHAP value calculated for each patient for the top three features (y-axis) is presented in Figure 6. SHAP values quantify the contribution of each feature to model prediction on the x-axis. The sign of the SHAP value represents the directed impact on probability of LVEF < 60% at 18 months. A positive SHAP indicates high probability while a negative value indicates low probability for LVEF < 60% at 18 months. The magnitude of the SHAP value on the x-axis represents the strength of the contribution. Each dot represents an individual patient, and the color of the dot represents the feature value, high (orange) and low (purple). For baseline and 12 month LVEF, the orange-yellow dots (high LVEF) are located on the left side of the 0 SHAP (i.e., negative SHAP), indicating less probability of LVEF < 60% at 18 months. For 12 month mid LV SR_circ, the high value (orange-yellow dots) are located on the right side of the 0 (positive SHAP), therefore, a higher 12 month mid LV SR_circ (i.e., less negative), the higher chance of developing LVEF < 60% at 18 months.

To better visualize the top three features (12 month LVEF, baseline LVEF, and 12 month mid LV SR_circ), the actual value of each feature on the x axis and the likelihood of developing LVEF < 60% (red dot) or LVEF > 60% (blue dot) at 18 months is presented in Figure 7. Our data indicates that a higher absolute baseline CMR derived LVEF (> 63%), the less likely for LVEF < 60% at 18 months (negative SHAP values and mostly blue circles). Mid LV SR_circ is a negative quantity; thus, more negative values represent a greater LV SR_circ and therefore less likely to develop LVEF < 60% at 18 months.

The obvious limitation of this study is the small number of patients. In this preliminary study, we utilized the classic RF model instead of the Mixed Effects Random Forest (MERF) to model the longitudinal features. Unfortunately, we do not have blood pressure at all time points. In future studies, adding the blood pressure or end-systolic wall stress may provide additive predictive value in normalizing effects of afterload on LVEF. Compared with the classic RF, MERF considers the correlation structure within repeated measurements by incorporating random effects providing accurate predictions for each patient. However, the computational and model complexity of MERF is higher than that of RF due to the inclusion of random effects, which requires more patients. In this preliminary study with the small sample size (n = 33) classic RF is preferred over MERF.