Introduction
Cardiovascular abnormalities are a major cause of disease in the present day. In addition to causing significant problems to the affected patients, treatment and further follow up after heart failure impose heavy expenses on the health care system. Identifying individuals at significant risk of developing heart failure is therefore of paramount importance.
Various imaging modalities can be used to assess global ventricular function through measures such as ejection fraction, end-systolic volumes etc. that give important information about the overall functioning of the heart [
1]. These measures, though being strong predictors of cardiovascular disease, are often insensitive to regional myocardial dysfunction; for example, regional dysfunction can often be masked by a normal ejection fraction [
2]. On the other hand, abnormalities in heart wall motion, often an indicator of ischemia caused by the occlusion of the coronary arteries, are a sensitive indicator and can be seen much before other symptoms set in [
3,
4].
In general, heart wall motion abnormalities are considered to be life threatening. Several techniques, including tagged MRI, can provide robust quantification of such abnormalities and hence facilitate diagnosis. Thus regional performance markers such as quantification of strain and torsion have emerged as more accurate predictors of myocardial disease. This has further been validated by many studies that have found consistent differences in regional strains, strain rates and torsion between healthy and diseased myocardium [
5,
6]. In addition to quantifying regional myocardial abnormalities, the inferred heart wall motion can also be used to model forces in the heart wall for realistic simulations of cardiac motion.
Currently, cardiovascular magnetic resonance (MR) is the gold standard for assessing global as well as regional heart function due to its high spatial and temporal resolution [
7]. Various MR-based techniques have been proposed to infer cardiac deformation. The Displacement Encoding with Stimulated Echoes (DENSE) method relies on the modulation of phase according to position [
8]. On the other hand, feature-tracking techniques [
9,
10] track myocardial boundaries and other distinct landmarks to estimate displacements. Zerhouni et al. (1988) [
11] introduced an MR based noninvasive method for imaging called tagged MRI (tMR). The tags, which are regions of reduced signal intensity in the images caused by the saturation of magnetic field in selective planes, act as intrinsic tissue markers. Since then, tMR techniques have shown great potential for measuring the local mechanical wall function and other cardiac abnormalities [
12‐
19]. Despite these successful advances, tMR has not been adopted in everyday clinical use, partly because of the complicated post processing. Harmonic Phase analysis (HARP) [
20] is currently the most widely used technique for quantifying myocardial motion from tMR images. The HARP method analyzes motion by filtering harmonic peaks in the frequency domain of the image and computes a dense displacement map of tag lines by tracking their phase changes over time.
In the well-established experimental technique called Particle Image Velocimetry (PIV) in experimental Fluid Mechanics, a fluid flow is typically seeded randomly with micron-size glass particles (in water) or oil droplets (in air). These particles are illuminated using a laser light sheet, and visualized in images acquired using a high-speed camera. Pulsed lasers are often used if the flow velocities are large or flow time scales are small. The patterns of the intensity distribution in the time series images are then tracked using correlation image velocimetry (CIV) to quanitatively estimate the velocity field in the flow [
21]. Here, tracking tag lines and their intersections in tMR images is reduced to the problem of tracking patterns in the intensity distribution over successive images, performed using CIV. More details on CIV are given in the CIV Implementation subsection of the “
Methods” section, and the Additional file
1: Appendix. We adapt an existing Matlab-based PIV tool called
UVMAT [
22] to calculate a dense myocardial displacement field in cardiac tMR images.
In this paper, we aim to adapt correlation image velocimetry to estimate displacements and strain fields from tagged-MRI images. Furthermore, we verify that the estimated displacement and strain fields compare favorably with ground truth and HARP, respectively using a publicly available database of 15 healthy individuals. Our specific objectives in this paper are:
-
To demonstrate the first-time use of CIV with extracted tag lines as input to quantitatively estimate cardiac deformation fields from tMR images,
-
To characterize the errors in displacement and strain estimation using synthetic and phantom grids and identify the optimum CIV algorithm parameters to minimize error,
-
To validate the CIV-estimated dense displacement and strain fields via comparisons with ground truth and HARP, respectively.
Discussion
One of the reasons for tMR not being used in routine clinical practice is the lack of easy-to-use tools for image analysis and strain mapping. In this paper, we have presented the performance analysis of a CIV algorithm, used often in experimental fluid mechanics, applied to tMR image analysis. We first characterized the accuracy of the CIV algorithm using simulated displacement fields, and then tested it on the STACOM 2011 data set. The algorithm was able to recover the simulated displacement fields superimposed on a synthetic 2D grid as well as on phantom and patient images. The errors in the estimation of the displacement field were found to be within the limits of error reported widely in literature.
The CIV algorithm requires the values of C
B
(the correlation box size) and S
B
(the search box size) as inputs for estimating the displacement field. Using simulated displacement fields imposed on synthetic and phantom images, we determined the error in the estimated displacement fields as a function of C
B
and S
B
. Our approach was shown to accurately estimate displacements of 3 pixels or more in 512 × 512 grid-like images, thus requiring us to choose time points in the cardiac cycle that are within the sensitivity limits of the algorithm. Depending on the imaging sequence, tag, grid and overall image sizes, a calibration study as described in this paper would be required to determine the optimum values of C
B
and S
B
that correspond to least errors. In addition to validating the method on simulated displacement fields, we tracked individual points in the myocardium across the cardiac cycle using CIV to find near-perfect agreement with the expert tracked ground truth.
Following validation and appropriate input parameter selection, we estimated displacement fields from patient data. The estimated displacement fields capture the periodic physiologic motion of the heart accurately. The smoothness of the estimated displacement fields indicate the effectiveness of the outlier rejection techniques and smoothing techniques implemented in UVMAT. The displacement vectors were estimated on 100x100 points on the overall grid and later interpolated for pixel-wise fields. It is also possible to increase the density of points on which the displacement fields are estimated, but at the cost of increased computational time.
The estimated Eulerian strain trends are consistent with physiology, i.e. predominantly negative (positive) circumferential (radial) strain in the entire cardiac cycle starting at end diastole, thus making our approach potentially useful for diagnosis. The strain curves are determined in sixteen segments of the AHA 17-segment model of the heart. Despite the noise arising due to finite difference approximation in the Eulerian strain estimate, post-processing of the estimated displacement field allows us to determine strain curves from different segments of the heart.
An important pre-processing step is myocardial segmentation. For high throughput it is essential to have an algorithm that can provide a 3D segmentation mask for all volumes in the cardiac cycle. A novel technique exploiting dynamic programming and image based cues has been developed recently [
28]. However, in this work, a manual over-segmented mask is used to delineate the myocardium excluding the LV blood pool. An oversegmenting mask is defined so that it can be used on all cross sections of the heart and across the entire cardiac cycle.
The segmentation step can have an impact on the estimated displacement fields especially at the edges of the epicardium and endocardium because of the presence of discontinuities. Since the mask we used could include non-myocardial regions in some of the frames, and hence track unphysical deformation of the tag lines, it would be prudent to manually define (preferably by an expert) an accurate mask for every frame. We note, however, that accurate circumferential strain estimates in most regions of the heart indicate that an oversegmented mask does not have a serious impact in regions of large strain magnitudes. Radial strain estimates, however, are impacted by the boundary effects.
The results in this paper suggest that CIV is a viable tool for cardiac deformation analysis. A few shortcomings, however, have to be addressed before it can be used in a clinical setting. Though the circumferential strains are accurately estimated by CIV, radial strains (shown in Fig.
9) are underestimated. This could be due to (i) the thinness of the ventricular wall, owing to which the number of grid points in the radial direction is small in the region, and (ii) relatively smaller displacements in some segments, which leads to larger errors in the CIV estimates. The accuracy of the strain estimates also depend on the extent of smoothing done during the CIV processing and the treatment of data close to the domain boundaries; these processing protocols have to be suitably optimized for clinical applications. Interestingly, an underestimation of the radial strains have been reported for other methodologies too [
23]. Also, the processing pipeline can be optimized to minimize the computational time. Currently, on a standard laptop (8 GB RAM, Processor: Intel Core i5-3230M CPU @ 2.6 GHz), HARP takes around 5–10 s to perform calculations over an entire cardiac cycle for a single slice on a single patient; in comparison, our technique takes around 45 s to perform the same calculations. We would like to point out that the software UVMAT is implemented on Matlab, and there is certainly scope for improvement in our computational times. In addition, the segmentation of the myocardium can be automated using algorithms similar to what is described in [
28]. Furthermore, parallelization of the implementation of CIV is another avenue for reducing overall processing times. A clinical trial of patients with variable heart function would be required before routine clinical use.
Conclusion
In this paper, we have demonstrated the ability of the CIV algorithm to estimate cardiac deformation from tMR images, and the resulting displacement and strain fields were found to be physiologically consistent. Our circumferential strain estimates are in good agreement with those of HARP in most regions of the heart, but the radial strains are underestimated. Our method fundamentally differs from HARP wherein the displacement fields are directly estimated from the phase image. Here we use the harmonic phase image to extract the grid into a grayscale image in successive time frames and then estimate the grid deformation using the CIV algorithm. It is noteworthy that we neither require a shape template nor a numerically complicated registration optimization algorithm.
With regards to our other specific objectives, we have
-
extracted the grid from tMR images using Fourier techniques and used it as input to CIV algorithms. Our grid extraction algorithm was found to be robust by successful implementation on synthetic, phantom and patient images,
-
identified that (C
B
,S
B
)=(25,55) pixels represent the optimum CIV algorithm parameters that result in less than 4% error for pixel displacements larger than 3 pixels on a 512 × 512 pixels image,
-
shown that the estimated displacements of individual landmarks in patient images agree with expert raters to within 1 pixel on an average,
-
demonstrated agreement with HARP on circumferential strain rates in most of the AHA model segments. The radial strain rates, however, were underestimated in comparison with HARP.
An analysis of the strain curves in arbitrarily defined segments of the myocardium would be relevant for clinical trials, particularly in quantifying the difference between healthy and diseased hearts. We have presented a 2D analysis of cardiac deformation even though the motion in 3D in nature. Despite the 2D nature of the analysis the method offers the flexibility to analyze multiple views (sagittal, coronal) thus enabling a pseudo-3D analysis. The extension of this method to fully 3D analysis will be the subject of future work.
Acknowledgements
We would like to thank Dr. Joel Sommeria for his inputs and discussions regarding UVMAT. The help from Myocardial Solutions in providing us with an evaluation version of the HARP software is gratefully acknowledged. We would also like to acknowledge Dr. HSN Murthy for enabling this collaborative work.