Timeresolved tracking of the atrioventricular plane displacement in Cardiovascular Magnetic Resonance (CMR) images
 Felicia Seemann^{1, 2, 3}View ORCID ID profile,
 Ulrika Pahlm^{1},
 Katarina StedingEhrenborg^{1, 4},
 Ellen Ostenfeld^{1},
 David Erlinge^{5},
 JeanLuc DuboisRande^{6},
 Svend Eggert Jensen^{7},
 Dan Atar^{8},
 Håkan Arheden^{1},
 Marcus Carlsson^{1} and
 Einar Heiberg^{1, 3}Email author
DOI: 10.1186/s1288001701895
© The Author(s). 2017
Received: 2 July 2016
Accepted: 16 February 2017
Published: 28 February 2017
Abstract
Background
Atrioventricular plane displacement (AVPD) is an indicator for systolic and diastolic function and accounts for 60% of the left ventricular, and 80% of the right ventricular stroke volume. AVPD is commonly measured clinically in echocardiography as mitral and tricuspid annular plane systolic excursion (MAPSE and TAPSE), but has not been applied widely in cardiovascular magnetic resonance (CMR). To date, there is no robust automatic algorithm available that allows the AVPD to be measured clinically in CMR with input in a single timeframe. This study aimed to develop, validate and provide a method that automatically tracks the left and right ventricular AVPD in CMR images, which can be used in the clinical setting or in applied cardiovascular research in multicenter studies.
Methods
The proposed algorithm is based on template tracking by normalized crosscorrelation combined with a priori information by principal component analysis. The AVPD in each timeframe is calculated for the left and right ventricle separately using CMR longaxis cine images of the 2, 3, and 4chamber views.
The algorithm was developed using a training set (n = 40), and validated in a test set (n = 113) of healthy subjects, athletes, and patients after STelevation myocardial infarction from 10 centers. Validation was done using manual measurements in end diastole and end systole as reference standard. Additionally, AVPD, peak emptying velocity, peak filling velocity, and atrial contraction was validated in 20 subjects, where timeresolved manual measurements were used as reference standard. Interobserver variability was analyzed in 20 subjects.
Results
In end systole, the difference between the algorithm and the reference standard in the left ventricle was (mean ± SD) 0.6 ± 1.9 mm (R = 0.79), and −0.8 ± 2.1 mm (R = 0.88) in the right ventricle. Interobserver variability in end systole was −0.6 ± 0.7 mm (R = 0.95), and −0.5 ± 1.4 mm (R = 0.95) for the left and right ventricle, respectively. Validation of peak emptying velocity, peak filling velocity, and atrial contraction yielded lower accuracy than the displacement measures.
Conclusions
The proposed algorithm show good agreement and low bias with the reference standard, and with an agreement in parity with interobserver variability. Thus, it can be used as an automatic method of tracking and measuring AVPD in CMR.
Keywords
Atrioventricular plane displacement Automated tracking Normalized crosscorrelation Principal component analysis Cardiac valve displacementBackground
The atrioventricular (AV) plane is a fibrous region containing the cardiac valves, separating the atria from the ventricles. During a heartbeat the AVplane moves as a piston pump, towards apex during systole and back to the initial position during diastole [1, 2]. The atrioventricular plane displacement (AVPD) has been shown to account for 60% of the left ventricular (LV) stroke volume, and 80% of the right ventricular (RV) stroke volume [3, 4] and is an indicator of both systolic and diastolic function [5, 6]. A reduced AVPD is associated with disease and aging [7–10], while regular exercise has been shown to increase AVPD in young male athletes [11] and maintain AVPD at a level similar to young subjects in male master athletes [10].
In echocardiography, it is clinical standard to measure AVPD [9, 12] and a reduced longaxis function has been shown to have prognostic significance for future clinical events [13–17]. Mitral annular plane systolic excursion (MAPSE) is easily used as a good marker for left ventricular function [14], and current guidelines suggest the quantification of tricuspid annular plane systolic excursion (TAPSE) for determining RV function [12, 18]. A number of algorithms has been proposed in order to automatically measure valve displacement with echocardiography [19–21].
In cardiovascular magnetic resonance (CMR) imaging, longaxis cine images, acquired in clinical routine, can be used for measuring AVPD. However, currently AVPD is rarely evaluated in a clinical setting and is not implemented in the consensus document for CMR assessment [22]. When AVPD is assessed in CMR, the required method is often manual measurements in the end diastolic and end systolic timeframe [3, 4, 10, 11, 17, 23–26]. These measurements are applicable for quantification of the maximum displacement over a cardiac cycle. However, it does not carry any information about the temporal distribution of the displacement throughout a heartbeat. Timeresolved measurements allow computation of the AVPD over the whole cardiac cycle, thus creating an AVPD curve. However, manual timeresolved measurements are time consuming and observer dependent. Derived from the AVPD curve, velocity at peak emptying and peak filling can be calculated. These velocities can be considered in parity to the peak systolic and diastolic annular velocity known from echocardiography. Furthermore, atrial contraction can also be derived from the AVPD curve. Automatic tracking of the AVPD reduces the subjectivity of different observers, as well as the time spent on manual image analysis.
A few semiautomatic methods for tracking valves in CMR images have been presented [27–32]. However, no previous method has presented an algorithm using standard clinical CMR images, and that only require manual input in a single timeframe to track the AVplane in both the left and the right side of heart.
Therefore, the aim of this study was to develop and validate a method that use manually placed input points in a single timeframe and thereafter automatically track the left and right ventricular AVplane motion in CMR images. This will be useful in the clinical setting as well as in applied cardiovascular research in multicenter studies.
Methods
Study population
A total of 153 subjects, who underwent CMR imaging in three previous studies, were included in this study. Subjects consisted of 32 elite athletes [33], 14 elderly normal subjects [10], 81 patients with first time STelevation myocardial infarction from the multicenter clinical cardioprotection trial MITOCARE [34], and 26 normal controls [33]. Ten centers participated in data inclusion. Each subject underwent CMR scanning in a 1.5 T scanner using a steadystatefree precession (SSFP) sequence with retrospective ECG gating under endexpiratory breath hold. Scanners were from Philips (Philips Healthcare, Best, The Netherlands), Siemens (Siemens Healthcare, Erlangen, Germany) or GE (GE Healthcare, Waukesha, WI, USA). Longaxis cine images of the 2chamber, 3chamber, and 4chamber views were acquired. In all vendors, typical pixel resolution was 1.5 × 1.5 mm, 8 mm slice thickness, 30 timeframes per cardiac cycle. For Philips, MR sequence parameters ranges were: repetition time 2.6–4.0 ms; echo time 1.3–2.0 ms; flip angle 60°; field of view 151–430 mm; matrix size (92–336) × (92–336). For Siemens ranges were: repetition time 2.6–3.4 ms; echo time 1.1–1.4 ms; flip angle 47–80°; field of view 129–430 mm; matrix size (73–256) × (79–256). For GE: repetition time 3.1–4.0 ms; echo time 1.3–1.7 ms; flip angle 45–70°; field of view 143–400 mm; matrix size (166–512) × (166–512).
Subjects were divided into a training set for algorithm development and optimization (n = 40), and a test set for validation (n = 113). A subset of the test set (n = 20) was used for timeresolved validation while the whole test set was used for validation of the maximum AVPD. The training set consisted of 16 patients, 9 athletes, and 15 healthy controls and was selected manually prior to looking at the images of the included subjects. The timeresolved test set consisted of 7 patients, 6 athletes, 2 elderly normal subjects, and 5 normal controls. Additionally, a subset of n = 20 patients from the training set was used for interobserver variability analysis in end diastole and end systole.
All studies were approved by the local ethical committees, and written informed consent was obtained from each individual.
Automatic tracking algorithm
Training of statistical model
The algorithm was developed and optimized using the timeresolved manual measurements in the training set (n = 40). The amount of timeframes in CMR images differs between the subjects. Hence, all measurements were interpolated to 30 timeframes and normalized by the curve amplitude. For each of the 8 input points, the data was stored as a matrix representation of size 40x30. Rows consisted of the input point displacement perpendicular to the AVplane in mm for 40 subjects, columns represented the 30 timeframes. Principal component analysis is a method that find underlying structures of the data it is applied to, using statistics and eigenvalue decomposition. Each eigenvector represents a component of the underlying structures, a principal component, and have a corresponding eigenvalue that represent the variance of the structure. In PCA, the largest eigenvalue corresponds to the most dominant principal component of the data. By performing PCA decomposition on the constructed matrix with AVPD data, a statistical model describing the shape of an AVPD curve was constructed. This transforms the matrix into linearly uncorrelated principal components, enabling the information about AVPD from the training set to be represented in 30 dimensions. When analyzing the 30 eigenvalues yielded by the PCA, the sum of the 5 largest eigenvalues accounted for 99% of the sum of all eigenvalues. Hence, the AVPD curve shape and behavior could be reconstructed from 5 coefficient dimensions, using the eigenvectors corresponding to the 5 most significant eigenvalues of the data covariance matrix.
The mean displacement for each point was reconstructed using this model, in order to define a position prediction curve. The prediction points are used by the algorithm as an initial guess of where the input point tracked is located in each timeframe. Reconstruction is also applied on the algorithm tracking result, as a physiological filtering method that smooth the displacement of each tracked point.
Tracking and reconstruction process
Step 1: AVplane definition
Only the perpendicular movement in relation to the AVplane in end diastole is accounted for. The AVplane is defined in each longaxis view. In the 2chamber and 4chamber view, the AVplane is defined as the line where the residuals between the input points and plane are minimized. In the 3chamber, the plane intersects the lateral input point of the LV and pass between the input points in septum and RV. This is illustrated in Fig. 1.
Step 2: tracking with a priori position prediction
The position of the input point throughout the cardiac cycle is predicted by placing prediction points in each timeframe, according to the prediction curves obtained in the training process. Prediction points are positioned perpendicular to the AVplane, and interpolated according to the duration of the cardiac cycle.
Around this tracked point, a new ROI is extracted and a ROS is extracted around the prediction point in the next timeframe, and normalized crosscorrelation is applied again. The procedure is repeated twice for each input point. First, the tracking is initiated in end diastole, proceeding forward to the next timeframe until reaching the last timeframe. The tracking is then repeated according to the same principle, but instead of forward tracking, the input points in end diastole are tracked backwards.
Step 3: curve shape reconstruction
Displacement curves from the forward and backward tracking are calculated and merged as a weighted sum of the curves. The forward tracking displacement is weighted linearly from 1 to 0, assigning the displacement in the first timeframe the weight 1 and the last timeframe the weight 0. Accordingly, the displacement in the first timeframe from backward tracking has the weight 1, and the last timeframe the weight 0. To ensure a smooth and physiologically behaving curve, the merged displacement curve for each point is projected using PCA weights and the 5 most significant eigenvectors.
Each of the 8 input points are tracked separately, hence step 2–3 are repeated 8 times before the fourth processing block is executed. The corresponding position of each input point is visualized in every timeframe in Segment.
Step 4: calculation of AVplane displacement
After tracking, the total LVAVPD and RVAVPD curves are calculated according to Carlsson et al. [3, 4]. The total LVAVPD is the mean displacement curve of the 6 tracked points located in the left side of heart. The sum of the displacement curves of the 2 tracked points in the right side of heart, plus the mean of the displacement curves of the 2 points in septum, divided by 3 gives the total RVAVPD. End systole is defined as the timeframe where the AVPD curve is at its minimum, that is, where the AVplane is the farthest away from the starting point in end diastole.
A 3 dimensional (3D) AVplane was defined for comparison to the 2 dimensional (2D) planes defined in step 1. The 3D plane was defined by the best fit in the least square sense between the input points in all long axis views, using the 3D coordinate system from the MR scanner.
Parameter optimization
The sizes of the region of interest, ROI, and region of search, ROS, for all 8 input points were optimized by using the timeresolved measurements in the training set as reference. The training set (n = 40) consisted of 16 patients, 9 athletes, and 15 healthy controls. The size of each ROI and ROS in mm was optimized over a range of combinations using 10fold crossvalidation. Correlation R value, bias, and standard deviation, SD, was calculated between manual and tracked AVPD in the end systolic timeframe for each parameter combination in an exhaustive search. Also, the 2norm of the difference between the manual and tracked AVPD curves was calculated for each subject, as a measure of similarity between the manual and automatic AVPD curves, where the value 0 would indicate that the two curves are identical. The ROI and ROS size for each input point was chosen by optimizing the combination of the mean of R value, bias, SD, and 2norm difference for each fold. The parameter combination yielding the minimum SD was sought out, combined with the requirement that constraints defined for R, bias, and 2norm were fulfilled. The constraint for R was all parameter combinations yielding an R value above the 75^{th} percentile of all calculated R. For bias, the constraint was parameter combinations yielding a bias below the 25^{th} percentile. The 2norm constraint was parameter combinations yielding a 2norm value below the 75^{th} percentile. For 2 out of 8 parameter combinations, the constraints were fulfilled for the global minimum of all calculated standard deviations. The same ROI and ROS sizes are used for the forward and the backward tracking and are presented in Additional file 1.
Validation
The AVplane displacement was measured manually by expert readers in all subjects. The automatic tracking algorithm was validated against manual measurements of the total displacement in mm from end diastole to end systole in the whole test set (n = 113), as well as separately in the patient (n = 65), healthy control (n = 24), and athlete (n = 24) populations. For the timeresolved subset of the test set (n = 20), the AVPD resulting from the automatic tracking algorithm in each timeframe was compared to manual measurements. In the timeresolved test set, the minimum velocity at peak emptying (cm/s), the maximum velocity at peak filling (cm/s), and the atrial contraction (%) was compared for the automatic tracking algorithm and manual measurements. The distance between the manual and automatic AVPD curves was assessed by taking the 2norm of the difference of the manual and automatic curves in each timeframe. Interobserver variability of the AVPD in end systole was performed in a subset of 20 patients with first time myocardial infarction.
Since the starting point for the algorithm is the 8 input points provided by the user in the end diastolic timeframe, different input points will result in different tracking results, even if placed only slightly differently. In order to ensure that the same points were compared, the automatic tracking was provided the exact same input points in end diastole as in the manual measurements. To measure how the algorithm results may differ due to different positions of the input points, interobserver analysis of the algorithm was analyzed. For the interobserver analysis, both of the algorithm and for manual measurements, the input points in end diastole were placed separately for each observer. All manual measurements were verified by a second observer.
Statistical analysis
Comparisons were performed using modified BlandAltman plots with manual measurements as reference standard (mean with limits of agreement (±2SD)) [38], and linear regression analysis (correlation coefficient).
Automatic tracking of the LVAVPD and RVAVPD was compared to manual measurements in end systole for the test set (n = 113). In the timeresolved test set (n = 20), the displacement in the automatic tracking was compared to timeresolved manual measurements of the displacement in each timeframe. Also, the peak emptying velocity, peak filling velocity, and atrial contraction was compared in the timeresolved test set. Interobserver variability in end systole was assessed.
Results
An example of a tracked AVPD curve together with the corresponding manual curve is shown in Fig. 4, showing high similarity of the curves in amplitude and phase. Three movies are available as additional files illustrating typical tracking results in a 2chamber (Additional file 2), 3chamber (Additional file 3), and 4chamber longaxis view (Additional file 4).
Additional file 2:Tracking in a 2chamber longaxis view.
Additional file 3:Tracking in a 3chamber longaxis view.
Additional file 4:Tracking in a 4chamber longaxis view.
Displacement results. Manual and automatic measurement results of atrioventricular plane displacement (AVPD) as mean ± SD in the left (LVAVPD) and right ventricle (RVAVPD). Comparison of automatic tracking vs manual measurements as correlation R value and bias ± SD of the AVPD. In the timeresolved measure, the AVPD in each timeframe is compared for n = 20 subjects. The validation in end systole was performed on n = 113 subjects
Measure  Manual  Automatic  R  Bias ± SD 

LVAVPD in end systole [mm]  −13 ± 3  −12 ± 3  0.79  −0.6 ± 1.9 
RVAVPD in end systole [mm]  −18 ± 4  −18 ± 4  0.88  −0.8 ± 2.1 
Timeresolved LVAVPD [mm]      0.93  −0.6 ± 2.0 
Timeresolved RVAVPD [mm]      0.95  −0.5 ± 2.2 
Population based end systolic displacement results. Manual and automatic measurement results of atrioventricular plane displacement (AVPD) in end systole as mean ± SD in the left (LVAVPD) and right ventricle (RVAVPD) for patients (n = 65), healthy controls (n = 24), and athletes (n = 24). Comparison of automatic tracking vs manual measurements as correlation R value and bias ± SD of the AVPD
Measure  Manual  Automatic  R  Bias ± SD 

LVAVPD in patients [mm]  −11 ± 2  −11 ± 2  0.81  −0.6 ± 1.3 
RVAVPD in patients [mm]  −17 ± 4  −15 ± 3  0.83  −1.0 ± 2.2 
LVAVPD in healthy controls [mm]  −14 ± 3  −14 ± 2  0.49  0.0 ± 2.5 
RVAVPD in healthy controls [mm]  −20 ± 4  −20 ± 3  0.88  −0.4 ± 1.7 
LVAVPD in athletes [mm]  −16 ± 2  −15 ± 2  0.44  −1.3 ± 2.3 
RVAVPD in athletes [mm]  −22 ± 3  −21 ± 2  0.77  −0.7 ± 2.2 
Results for automatically calculated peak velocities and atrial contraction. Manual and automatic measurement results of automatically calculated peak emptying velocity, peak filling velocity, and atrial contraction as mean ± SD in the left and right side of the heart. Comparison of automatic tracking vs manual measurements as correlation R value and bias ± SD. The validation was performed on n = 20 subjects. The atrial contraction is given in % of the atrioventricular plane displacement (AVPD) in end systole
Measure  Manual  Automatic  R  Bias ± SD 

Left peak emptying velocity [cm/s]  −57 ± 12  −49 ± 8  0.63  −7.6 ± 9.0 
Right peak emptying velocity [cm/s]  −77 ± 18  −77 ± 12  0.74  −0.4 ± 12.0 
Left peak filling velocity [cm/s]  72 ± 29  49 ± 15  0.74  23.0 ± 20.4 
Right peak filling velocity [cm/s]  79 ± 28  68 ± 23  0.85  10.8 ± 14.8 
Left atrial contraction [%]  31 ± 11  32 ± 7  0.49  −1.5 ± 9.9 
Right atrial contraction [%]  38 ± 9  35 ± 7  0.39  3.3 ± 9.0 
Interobserver variability for manual measurements in end systole (n = 20) was −0.6 ± 0.7 mm, R = 0.95, for the LVAVPD and −0.5 ± 1.4 mm, R = 0.95, for the RVAVPD. Thus, interobserver variability was similar to the difference between manual and automatic algorithm measurement of AVPD. Interobserver variability of the algorithm in end systole (n = 20) was 0.2 ± 1.4 mm, R = 0.69, for the LVAVPD and 0.0 ± 0.7 mm, R = 0.98, for the RVAVPD. The average time for tracking and calculation of the AVPD for both the left and the right heart was 0.6 s per subject, using a standard laptop computer.
Comparison of tracking results using 2D and 3D AVplanes in the timeresolved test set (n = 20) showed a low variability and strong correlation. LVAVPD results was −0.1 ± 0.5 mm, R = 0.99. RVAVPD results was −0.1 ± 0.6 mm, R = 1.00.
Discussion
In this study, an automatic algorithm for timeresolved tracking of the AVPD from standard longaxis CMR cine images has been developed and validated. The algorithm is based on template tracking by normalized crosscorrelation and a priori information by principal component analysis, and yield the position of the AVplane in all timeframes. The input needed by the user is the marking of the AVplane in end diastole at eight points. The validation of the algorithm in 113 subjects from multicenter and multivendor studies showed low bias and high correlation to expert manual measurements.
Forward template tracking can be quite unstable. If the tracking fails in one timeframe, the error will propagate since another point than the intended will be tracked in the coming timeframes. This might occur at any timeframe for various reasons such as poor image quality, or a region of search (ROS) that does not cover the intended match. This problem has previously been approached in different ways. In the method presented by Wu et al. [29], the user was encouraged to interactively adjust unsatisfactory tracking results, and then run the algorithm again based on the corrections. In the work by Leng et al. [28], stability is obtained by placing input points in several timeframes, and tracking is performed in the timeframes between these input points. In the method presented by Maffessanti et al. [27], manual input is required in the end diastolic and end systolic timeframes. A novelty in the presented algorithm compared to previous approaches is that input points are only required in the end diastolic timeframe and merges the tracking results from both forward and backward tracking in order to approach the stability issues with forward tracking. In case the template tracking drifts off at some point, the weighted sum of the two displacement curves aids in improving the final AVPD curve. Also, the use of a priori information specific to each input point tracked is used as a prediction for the tracking, thus always placing the ROS in a region where the match is expected, which stabilizes the forward tracking. The prediction adapts according to the number of timeframes in the data set, varying heart rates, and the parameter optimization of ROI and ROS sizes in mm allow the algorithm to adapt to different spatial resolutions. The incremental value of merging two tracking results, using position prediction and curve shape reconstruction can be seen in Fig. 10, suggesting that these steps improves the tracking results comparing to only performing forward tracking without any position prediction.
Other researchers have implemented valve tracking for different purposes than to quantify AVplane displacement per se. Quantification of mitral valve displacement and velocity in 4chamber view cine images was presented by Saba et al. [30], and a similar method quantifying the tricuspid valve displacement and velocity has been described by Ito et al. [31]. The method by Saba et al. [30] was later on expanded to a threedimensional volume tracking method, based on semiautomated tracking of the mitral valve in the 2, 3, and 4chamber views [29]. Also, Westenberg et al. implemented retrospective valve tracking in order to measure threedimensional blood flow in CMR [32]. The presented algorithm in this study aimed to quantify the AVplane displacement in both the left and the right side of the heart, using cine images of the 2, 3, and 4chamber view that are acquired as clinical standard. To the best of our knowledge, this approach of using images acquired as clinical standard to quantify both the left and right ventricular AVPD has not be published before.
Manual interobserver variability in end systole was performed on 20 subjects and showed a low bias and variability, and manual measurements were used as reference standard. The interobserver variability of the algorithm in end systole had a similar agreement as for the manual interobserver variability in the right side of the heart. In the left side of the heart, the algorithm interobserver had a lower correlation R value than for the manual interobserver, but low bias and SD. Hence, the overall algorithm performance varies about as much as manual measurements vary for different observers. Also, the displacement results of the algorithm had an agreement in parity with the manual interobserver variability, and bias was below pixel resolution for both automatic and manual displacement measurements. The end systolic results for both the LVAVPD and the RVAVPD were interchangeable with the interobserver variability. In the three population groups (consisting of patients, healthy controls, and athletes), similar displacement results were obtained, although the correlation R value was stronger in the LVAVPD for patients compared to healthy controls and athletes.
The AVplane determined in 2D, by defining a line in each long axis view, was compared to an approach where the AVplane was defined in 3D, by a best fit all input points in a least square sense. The comparison showed a strong correlation, low bias and variability between both methods. Images were acquired during endexpiratory breath hold and the apex is essentially stationary during the heart beat [39], hence the global heart movement was minimized during the data collection. However, in case the subject move during the MR scan, the 3D coordinate system from the MR scanner might not correspond well to the obtained long axis image positions. Therefore, the 2D implementation was used in this study.
Peak emptying and peak filling are usually calculated from ventricular volume curves and reported as a volumetric flow rate in ml/s. In this study the velocity of the AVplane at peak emptying and peak filling are quantified in cm/s. Since the AVPD accounts for 60% of the stroke volume in the left side of the heart and 80% in the right side [4], the AVplane velocity could be an indirect measure of the emptying and filling of the ventricles. A study by Leng et al. showed a good correlation between early diastolic filling from tissue Doppler echocardiography and CMR measures of the AVplane velocity which would support this [28]. The derivative of a distance curve must be calculated in order to determine velocity estimations. The tracking yields a timeresolved AVPD curve, and even though the curve shape is reconstructed and smoothed using PCA eigenvectors, this curve can appear noisy in between the timeframes. Also, difficulties are to be expected since CMR cine images can be rather noisy in the timeframes where the peak emptying velocity and peak filling velocity occur. Therefore, taking the numerical first order derivative of the AVPD curve results in an even noisier velocity curve, where it is hard to extract an accurate maximum and minimum velocity. Hence, taking the moving average of the displacement curves prior to differentiating them, and calculating the slope of the straight line over the timeframes where the maximum and minimum velocity occur was considered a more stable approach in this study. The results for the peak emptying velocity have an agreement for manual and automatic measurements in the left and the right side of the heart. When comparing the results of the peak filling velocity, the automatic measurements tends to underestimate the velocities and both bias and SD are quite large.
In general, it is difficult to automatically determine the atrial contraction in the AVPD curve, since the duration of the diastasis can vary from about 20% of the cardiac cycle for low heart rates, to nonexisting for high heart rates [40]. The proposed algorithm is programmed to calculate atrial contraction to be the difference in AVPD between end diastole and where the absolute value of the second derivative of the AVPD curve is at its minimum, but the user might change the interval by observing the tracked curve. By design, the algorithm forces the AVPD curve to return to its original position at the end of the cardiac cycle. Hence, if the AVPD tracking is far away from the original position at diastasis, the atrial contraction will be represented as a very steep segment in the AVPD curve. This might explain why the SDs of the atrial contraction was large. Also, the diastasis can be hard to detect for high heart rates.
An underestimation can be seen for large displacements in both the end systolic and timeresolved AVPD measurements (Figs. 5 and 6), as well as in the results of high peak velocities and large atrial contractions (Figs. 7, 8 and 9). The cause of this underestimation is unknown. However, one source for the underestimation could be an effect of overtraining of the algorithm. In order to evaluate if overtraining could be a cause, the proportion of subjects in the training and test sets were compared. The proportion of healthy controls in the training set was 38% whereas in the test set it was 21%, thus the training set included more subjects with a higher AVPD compared to the test set. The proportion of athletes in both the training and test set were the same (23% and 21%, respectively). This should rather be a source for overestimation than underestimation. Another potential source of error might be that the algorithm has difficulties in tracking the AVplane when it is moving at high velocities. On the other hand, the overall tracked displacement curve has a good agreement to manual measurements, according to the timeresolved displacement validation and the low distance between the automatic and manual AVPD curves, measured by the 2norm.
Limitations
Limitations of this study comprises that patients included in the training and test set were only patients with first time STelevation myocardial infarction. The algorithm is based on a priori information extracted from manual measurements in the training set. Hence other patient categories and anatomic variations may have been missed when constructing the AVPD prediction model, such as patients with very low AVPD. Including such patients might be necessary for the algorithm to track very low AVplane motions, but it might also reduce the accuracy of the tracking results in healthy subjects if the prediction curve is reduced in amplitude. On the other hand, the lower limit of agreement of LVAVPD was 7 mm, why this limitation might be of less significance.
The algorithm is not expected to work on prospective ECG gated CMR data, since the backward tracking, PCA prediction, and curve shape reconstruction are designed on data comprising the whole cardiac cycle. All images in this study were acquired during endexpiratory breath hold. In images acquired during breathing, the calculation of the AVPD might be obfuscated by the chest movement.
The input points to be tracked are chosen by the user, and variations in placements of these input points may result in some points being hard to track for the algorithm. Heart sizes impacts the amplitude of the AVPD curve, where for example athletes have larger hearts and therefore are expected to have a larger AVPD, while elderly and different patient groups often have a reduced AVPD. The amplitude of the tracking predictor is not scaled according to the specific subject, and even though the size of the ROS’s for each input point has been optimized for a large range of AVPD amplitudes, the true match may not be present in the ROS for varying heart sizes. The curve shape reconstruction ensures that the AVplane trajectory is transformed to a smooth and physiological movement. If the chosen input point does not move as physiologically expected, for example due to anatomical variations, severe disease, or an incorrect input by the user, the calculated displacement may not represent the true AVPD. Therefore, manual monitoring and manual corrections are important for research and clinical use, as for any automatic image analysis algorithm. The same applies to the estimated peak emptying velocity, peak filling velocity, and atrial contraction, where the user should check that the interval of the lines defining the measures are placed in agreement with the appearance of the AVPD curve. The use of the proposed automatic tracking algorithm will reduce time input and user variability, which are important aspects for clinical use. Also, this allow the researcher or clinician to observe not only the total AVPD in end systole, which is the commonly used reference standard today, but also the whole AVPD trajectory throughout the whole cardiac cycle.
Future work
Atrial contraction results were not satisfactory, comprising many outliers (Fig. 9). Further studies of the algorithm can verify if this is a recurring issue.
In order to implement a fully automatized algorithm for AVPD tracking, the 8 manually placed input points in the end diastolic timeframe may possibly be replaced by automatic input point detection. The tracking algorithm predict the position of each input point in the next timeframe, using a priori information gathered from normal controls, athletes and patients with first time myocardial infarction. Gathering information from other physiological variations and patient groups might improve the prediction model. An automatic adaptive approach to scale the prediction curve based on the physiology of each individual data set could also increase the robustness of the algorithm and yield more accurate results for displacement, peak velocities, and atrial contraction.
Conclusion
The developed automatic algorithm performs timeresolved tracking of the AVDP in CMR images using normalized crosscorrelation and a priori information based on principal component analysis. The algorithm performs well with regards to displacement against manual measurements in healthy controls of a wide age spread, athletes, and first time myocardial infarction patients from multicenter and multivendor data. Further, the algorithm yields displacement results in parity with interobserver variability.
Therefore, an algorithm based on normalized crosscorrelation and principal component analysis may be introduced as a method for measuring the atrioventricular plane displacement in CMR imaging.
Abbreviations
 AV:

Atrioventricular
 AVPD:

Atrioventricular plane displacement
 CMR:

Cardiovascular magnetic resonance
 LV:

Left ventricle
 LVAVPD:

Left ventricular atrioventricular plane displacement
 MAPSE:

Mitral annular plane systolic excursion
 PCA:

Principal component analysis
 ROI:

Region of interest
 ROS:

Region of search
 RV:

Right ventricle
 RVAVPD:

Right ventricular atrioventricular plane displacement
 SD:

Standard deviations
 TAPSE:

Tricuspid annular plane systolic excursion
Declarations
Acknowledgements
Not applicable.
Funding
This study was founded by the Swedish Research Council (2012–4944), The Swedish Heart Lung Foundation (20140624) and the Region of Scania, Sweden. Funding for the MITOCARE trial was received from the European Commission within the 7^{th} Framework Program for RTD – Project MITOCARE – Grant Agreement HEALTH2010261034. The inclusion of elderly normal subjects was funded by Novo Nordisk and the Swedish Heart Association.
Availability of data and materials
The implemented software will be made freely available to researchers provided that they properly cite the current paper describing the method.
Authors’ contributions
FS developed and implemented the algorithm, analyzed the results, performed timeresolved manual measurements in the training and test set, the interobserver analysis, drafted the manuscript, and helped conceive the study. UP contributed by performing manual measurements of the patient data, and second observer analysis on the timeresolved measurements in the training and test set, and in the interobserver analysis. KE included healthy subjects and athletes, and performed manual measurements in them. EO performed the interobserver analysis. DE, SJ, and JR collected patient data. DA was responsible for the collection of patient data. HA helped in conceiving the study. MC contributed to the design of the algorithm and conceived the study. EH contributed to the design of the study, the algorithm design, and conceived the study. Further, FS, EH, UP, EO, KE, MC contributed with intellectual discussion and consensus definition of the AVplane. All authors have revised the manuscript and approved the final version.
Competing interests
EH is the founder of Medviso AB, Lund, Sweden, which sells a commercial version of the software Segment. HA is a shareholder of Imacor AB, Lund, Sweden, which performs core lab analysis of CMR images. HA and MC have been parttime consultants to Imacor AB. The other authors declare that they do not have any competing interests.
Consent for publication
Not applicable.
Ethics approval and consent to participate
All images were previously included in 3 different studies [10, 33, 34]. All studies were approved by the local ethical committees at the inclusion sites, and written informed consent was obtained from each individual. No additional ethics approval or informed consent was needed for the algorithm development presented in this current study.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
References
 Henein MY, Gibson DG. Normal long axis function. Heart. 1999;81:111–3.View ArticlePubMedPubMed CentralGoogle Scholar
 Henein MY, Gibson DG. Long axis function in disease. Heart. 1999;81:229–31.View ArticlePubMedPubMed CentralGoogle Scholar
 Carlsson M, Ugander M, Mosen H, Buhre T, Arheden H. Atrioventricular plane displacement is the major contributor to left ventricular pumping in healthy adults, athletes, and patients with dilated cardiomyopathy. AJP Heart Circ Physiol. 2006;292:H1452–9.View ArticleGoogle Scholar
 Carlsson M, Ugander M, Heiberg E, Arheden H. The quantitative relationship between longitudinal and radial function in left, right, and total heart pumping in humans. AJP Heart Circ Physiol. 2007;293:H636–44.View ArticleGoogle Scholar
 Willenheimer R, Israelsson B, Cline C, Rydberg E, Broms K, Erhardt L. Left atrioventricular plane displacement is related to both systolic and diastolic left ventricular performance in patients with chronic heart failure. Eur Heart J. 1999;20:612–8.View ArticlePubMedGoogle Scholar
 Carlhäll CJ, Lindström L, Wranne B, Nylander E. Atrioventricular plane displacement correlates closely to circulatory dimensions but not to ejection fraction in normal young subjects. Clin Physiol. 2001;21:621–8.View ArticlePubMedGoogle Scholar
 Willenheimer R, Cline C, Erhardt L, Israelsson B. Left ventricular atrioventricular plane displacement: an echocardiographic technique for rapid assessment of prognosis in heart failure. Heart. 1997;78:230–6.View ArticlePubMedPubMed CentralGoogle Scholar
 Wandt B, Bojö L, Wranne B. Influence of body size and age on mitral ring motion. Clin Physiol. 1997;17:635–46.View ArticlePubMedGoogle Scholar
 Caballero L, Kou S, Dulgheru R, Gonjilashvili N, Athanassopoulos GD, Barone D, Baroni M, Cardim N, Gomez de Diego JJ, Oliva MJ, Hagendorff A, Hristova K, Lopez T, Magne J, Martinez C, de la Morena G, Popescu BA, Penicka M, Ozyigit T, Rodrigo Carbonero JD, Salustri A, Van De Veire N, Von Bardeleben RS, Vinereanu D, Voigt JU, Zamorano JL, Bernard A, Donal E, Lang RM, Badano LP, et al. Echocardiographic reference ranges for normal cardiac Doppler data: results from the NORRE Study. Eur Hear J Cardiovasc Imaging. 2015;16(9):1031–41.
 StedingEhrenborg K, Boushel RC, Calbet JA, Åkeson P, Mortensen SP. Left ventricular atrioventricular plane displacement is preserved with lifelong endurance training and is the main determinant of maximal cardiac output. J Physiol. 2015;593:5157–66.View ArticlePubMedPubMed CentralGoogle Scholar
 StedingEhrenborg K, Carlsson M, Stephensen S, Arheden H. Atrial aspiration from pulmonary and caval veins is caused by ventricular contraction and secures 70% of the total stroke volume independent of resting heart rate and heart size. Clin Physiol Funct Imaging. 2013;33:233–40.View ArticlePubMedGoogle Scholar
 Lang RM, Badano LP, MorAvi V, Afilalo J, Armstrong A, Ernande L, Flachskampf FA, Foster E, Goldstein SA, Kuznetsova T, Lancellotti P, Muraru D, Picard MH, Rietzschel ER, Rudski L, Spencer KT, Tsang W, Voigt JU. Recommendations for cardiac chamber quantification by echocardiography in adults: an update from the american society of echocardiography and the european association of cardiovascular imaging. J Am Soc Echocardiogr. 2015;28:1–39. e14.View ArticlePubMedGoogle Scholar
 Sanderson JE. Left and right ventricular longaxis function and prognosis. Heart. 2008;94:262–3.View ArticlePubMedGoogle Scholar
 Hu K, Liu D, Herrmann S, Niemann M, Gaudron PD, Voelker W, Ertl G, Bijnens B, Weidemann F. Clinical implication of mitral annular plane systolic excursion for patients with cardiovascular disease. Eur Heart J Cardiovasc Imaging. 2013;14:205–12.View ArticlePubMedGoogle Scholar
 Kalam K, Otahal P, Marwick TH. Prognostic implications of global LV dysfunction: a systematic review and metaanalysis of global longitudinal strain and ejection fraction. Heart. 2014;100:1673–80.View ArticlePubMedGoogle Scholar
 Galiè N, Humbert M, Vachiery JL, Gibbs S, Lang I, Torbicki A, Simonneau G, Peacock A, Vonk Noordegraaf A, Beghetti M, Ghofrani A, Gomez Sanchez MA, Hansmann G, Klepetko W, Lancellotti P, Matucci M, McDonagh T, Pierard LA, Trindade PT, Zompatori M, Hoeper M. 2015 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertension. Eur Respir J. 2015;46:903–75.View ArticlePubMedGoogle Scholar
 Rangarajan V, Chacko SJ, Romano S, Jue J, Jariwala N, Chung J, FarzanehFar A. Left ventricular long axis function assessed during cinecardiovascular magnetic resonance is an independent predictor of adverse cardiac events. J Cardiovasc Magn Reson. 2016;18:35.View ArticlePubMedPubMed CentralGoogle Scholar
 Rudski LG, Lai WW, Afilalo J, Hua L, Handschumacher MD, Chandrasekaran K, Solomon SD, Louie EK, Schiller NB. Guidelines for the echocardiographic assessment of the right heart in adults: a report from the american society of echocardiography. J Am Soc Echocardiogr. 2010;23:685–713.View ArticlePubMedGoogle Scholar
 Nevo ST, van Stralen M, Vossepoel AM, Reiber JHC, de Jong N, van der Steen AFW, Bosch JG. Automated tracking of the mitral valve annulus motion in apical echocardiographic images using multidimensional dynamic programming. Ultrasound Med Biol. 2007;33:1389–99.View ArticlePubMedGoogle Scholar
 Behar V, Adam D, Lysyansky P, Friedman Z. The combined effect of nonlinear filtration and window size on the accuracy of tissue displacement estimation using detected echo signals. Ultrasonics. 2004;41:743–53.View ArticlePubMedGoogle Scholar
 Eto Y, Yamada H, Shin JH, Agler DA, Tsujino H, Qin JX, Saracino G, Greenberg NL, Thomas JD, Shiota T. Automated mitral annular tracking: a novel method for evaluating mitral annular motion using twodimensional echocardiography. J Am Soc Echocardiogr. 2005;18:306–12.View ArticlePubMedGoogle Scholar
 SchulzMenger J, Bluemke DA, Bremerich J, Flamm SD, Fogel MA, Friedrich MG, Kim RJ, von KnobelsdorffBrenkenhoff F, Kramer CM, Pennell DJ, Plein S, Nagel E. Standardized image interpretation and post processing in cardiovascular magnetic resonance: Society for Cardiovascular Magnetic Resonance (SCMR) board of trustees task force on standardized post processing. J Cardiovasc Magn Reson. 2013;15:35.View ArticlePubMedPubMed CentralGoogle Scholar
 Arvidsson PM, Toger J, Heiberg E, Carlsson M, Arheden H. Quantification of left and right atrial kinetic energy using fourdimensional intracardiac magnetic resonance imaging flow measurements. J Appl Physiol. 2013;114:1472–81.View ArticlePubMedGoogle Scholar
 Stephensen S, StedingEhrenborg K, Munkhammar P, Heiberg E, Arheden H, Carlsson M. The relationship between longitudinal, lateral, and septal contribution to stroke volume in patients with pulmonary regurgitation and healthy volunteers. AJP Heart Circ Physiol. 2014;306:H895–903.View ArticleGoogle Scholar
 Jorstig S, Emilsson K, Lidén M, Thunberg P. A study to determine the contribution to right ventricle stroke volume from pulmonary and tricuspid valve displacement volumes. Clin Physiol Funct Imaging. 2015;35:283–90.View ArticlePubMedGoogle Scholar
 Ostenfeld E, Stephensen SS, StedingEhrenborg K, Heiberg E, Arheden H, Rådegran G, Holm J, Carlsson M. Regional contribution to ventricular stroke volume is affected on the left side, but not on the right in patients with pulmonary hypertension. Int J Cardiovasc Imaging. 2016;32(8):1243–53.
 Maffessanti F, Gripari P, Pontone G, Andreini D, Bertella E, Mushtaq S, Tamborini G, Fusini L, Pepi M, Caiani EG. Threedimensional dynamic assessment of tricuspid and mitral annuli using cardiovascular magnetic resonance. Eur Heart J Cardiovasc Imaging. 2013;14:986–95.View ArticlePubMedGoogle Scholar
 Leng S, Zhao XD, Huang FQ, Wong JI, Su BY, Allen JC, Kassab GS, Tan RS, Zhong L. Automated quantitative assessment of cardiovascular magnetic resonancederived atrioventricular junction velocities. Am J Physiol Heart Circ Physiol. 2015;309:H1923–35.View ArticlePubMedGoogle Scholar
 Wu V, Chyou JY, Chung S, Bhagavatula S, Axel L. Evaluation of diastolic function by threedimensional volume tracking of the mitral annulus with cardiovascular magnetic resonance: comparison with tissue Doppler imaging. J Cardiovasc Magn Reson. 2014;16:71.View ArticlePubMedPubMed CentralGoogle Scholar
 Saba SG, Chung S, Bhagavatula S, Donnino R, Srichai MB, Saric M, Katz SD, Axel L. A novel and practical cardiovascular magnetic resonance method to quantify mitral annular excursion and recoil applied to hypertrophic cardiomyopathy. J Cardiovasc Magn Reson. 2014;16:35.View ArticlePubMedPubMed CentralGoogle Scholar
 Ito S, McElhinney DB, Adams R, Bhatla P, Chung S, Axel L. Preliminary assessment of tricuspid valve annular velocity parameters by cardiac magnetic resonance imaging in adults with a volumeoverloaded right ventricle: comparison of unrepaired atrial septal defect and repaired tetralogy of fallot. Pediatr Cardiol. 2015;36:1294–300.View ArticlePubMedGoogle Scholar
 Westenberg JJM, Roes SD, Ajmone Marsan N, Binnendijk NMJ, Doornbos J, Bax JJ, Reiber JHC, de Roos A, van der Geest RJ. Mitral valve and tricuspid valve blood flow: accurate quantification with 3D velocityencoded MR imaging with retrospective valve tracking. Radiology. 2008;249:792–800.View ArticlePubMedGoogle Scholar
 Steding K, Engblom H, Buhre T, Carlsson M, Mosén H, Wohlfart B, Arheden H. Relation between cardiac dimensions and peak oxygen uptake. J Cardiovasc Magn Reson. 2010;12:8.View ArticlePubMedPubMed CentralGoogle Scholar
 Atar D, Arheden H, Berdeaux A, Bonnet JL, Carlsson M, Clemmensen P, Cuvier V, Danchin N, DuboisRande JL, Engblom H, Erlinge D, Firat H, Halvorsen S, Hansen HS, Hauke W, Heiberg E, Koul S, Larsen AI, Le Corvoisier P, Nordrehaug JE, Paganelli F, Pruss RM, Rousseau H, Schaller S, Sonou G, Tuseth V, Veys J, Vicaut E, Jensen SE. Effect of intravenous TRO40303 as an adjunct to primary percutaneous coronary intervention for acute STelevation myocardial infarction: MITOCARE study results. Eur Heart J. 2015;36:112–9.View ArticlePubMedGoogle Scholar
 Heiberg E, Sjögren J, Ugander M, Carlsson M, Engblom H, Arheden H. Design and validation of Segmentfreely available software for cardiovascular image analysis. BMC Med Imaging. 2010;10:1.View ArticlePubMedPubMed CentralGoogle Scholar
 Lewis JP. Fast normalized crosscorrelation. Vis interface. 1995;10(1):120–23.
 Pearson K. LIII. On lines and planes of closest fit to systems of points in space. Philos Mag Ser 6. 1901;2:559–72.View ArticleGoogle Scholar
 Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;1:307–10.View ArticlePubMedGoogle Scholar
 Carlsson M, Cain P, Holmqvist C, Stahlberg F, Lundback S, Arheden H. Total heart volume variation throughout the cardiac cycle in humans. Am J Physiol Heart Circ Physiol. 2004;287:H243–50.View ArticlePubMedGoogle Scholar
 Chung CS. Duration of diastole and its phases as a function of heart rate during supine bicycle exercise. AJP Heart Circ Physiol. 2004;287:H2003–8.View ArticleGoogle Scholar