Visualization of myocardial strain-rate tensors from time-resolved 3D cine phase contrast MRI. Pernilla Selskog1, Einar Brandt2, Lars Wigström2, Matts ...
Visualization of myocardial strain-rate tensors from time-resolved 3D cine phase contrast MRI Pernilla Selskog1, Einar Brandt2, Lars Wigström2, Matts Karlsson1
1Linköping University, Department of Biomedical Engineering, Linköping, Sweden; 2Linköping University, Department of Medicine and Care, Linköping, Sweden; Introduction During the cardiac cycle the myocardium undergoes large elastic deformations as a consequence of the active muscle contraction along the muscle fibers and their relaxation, respectively. A 4D mapping (3D+time) of myocardial strain-rate would help to describe the mechanical properties of the myocardium, which are believed to affect important physiological factors such as the pumping performance of the ventricles. Strain-rate imaging using echo-Doppler has been suggested as a clinical tool1. Strain-rate has previously also been calculated from 2D MRI2. However, this assumes that myocardial motion only occurs in one direction (ultrasound) or in one plane (2D MRI), respectively. We have presented a method for quantification of myocardial strain-rate using 3D cine phase contrast MRI3. 3D strainrate is represented by a 3x3 tensor and a tensor visualization method is therefore needed to visualize complete strain-rate. Here we present a method for visualization of strain-rate in the myocardium that displays the 3D characteristics of the tensors. Methods The velocity measurements were performed on a 1.5 T imaging system using a 3D cine phase contrast pulse sequence4 (TR=27 ms, TE=8 ms, VENC=18 cm/s). This provides velocity vector information in a 3D spatial grid during the whole cardiac cycle (32 time frames reconstructed, spatial resolution 1x4x4 mm). The phase contribution from concomitant gradient (Maxwell) terms and eddy current effects were subtracted. Saturation pulses were used to reduce the signal from the blood. The calculations were performed on data from a healthy volunteer. The 3x3 velocity gradient tensor L was calculated according to Lij = ∂vi /∂xj. Rigid body motion should not contribute to a proper measurement of deformation rate and strain-rate was therefore calculated as the strain-rate tensor D=½(L+LT). The eigenvalues and eigenvectors of the strain-rate tensor represent the principal values and the principal directions of strain-rate in the myocardium. This makes it possible to image both magnitude and direction of the instantaneous deformation. The sign of the eigenvalues represents positive and negative material stretching in the direction of the corresponding eigenvector. The strain-rate tensor is visualized as an ellipsoid in each data point5. The three axis of the ellipsoid represent the eigenvectors of the tensor and the length of the axis represent the three eigenvalues, respectively. In the presented results, the eigenvalues have been normalized so that the magnitude of the largest eigenvalue is 1. This makes all ellipsoids visible while preserving the ratio between the eigenvalues. Results Since the directions of the eigenvectors are the principal directions of the strain-rate tensor, the major axis of the ellipsoids represent the main direction of instantaneous deformation. The ellipsoids may then also be colored according to, for example, the sign of the largest eigenvalue representing stretch or compression in the main direction.
Figure 1 shows a surface in the left ventricular myocardium (left) and the strain-rate tensor in a region of interest on this surface (right) in an end-diastolic time-frame. In the example region of interest, there is a principally uniform main direction of stretch, see Figure 1 (right).
Figure 2. The strain-rate tensor in a short-axis image of the left ventricle (left-right approximately septal-lateral) Since the strain-rate tensor is known in the complete data volume, strain-rate can be visualized in any plane. Figure 2 shows, as an example, the strain-rate tensor in a short-axis slice of the left ventricle myocardium in end diastole. The myocardium was extracted using a threshold in the magnitude image. The results also show through-plane main strain-rate directions, which implies that a 3D method is needed for correct calculation and representation of myocardial strain-rate. Discussion Myocardial strain-rate is three-dimensional and should therefore be displayed by visualization of the strain-rate tensor. The eigenvalues and the eigenvectors of that tensor provide full information of both magnitude and direction of the instantaneous deformation of the myocardium. The presented method displays the strain-rate tensor, revealing the main direction of deformation rate without any assumptions of myocardial motion directions in the calculation of strain-rate. The results, as well as the method, are three-dimensional and an interactive 3D visualization program is needed to study strain-rate in the complete data volume and to make the large amount of result data more comprehensible. References 1. Voigt JU et al, Assessment of regional longitudinal myocardial strain rate derived from doppler myocardial imaging indexes in normal and infarcted myocardium. J Am Soc Echocardiogr, 2000;13(6):58898. 2. Wedeen VJ, Magnetic resonance imaging of myocardial kinematics. Magn Reson Med, 1992;27:52-67. 3. Selskog P et al, Quantification of myocardial strain-rate from 3D cine phase contrast MRI, Proceedings ESMRMB p.83, Paris, France, 2000 4. Wigström L et al, Temporally resolved 3D phase contrast imaging. Magn Reson Med, 1996;36:800-803. 5. Westin C-F, A tensor framework for multidimensional signal processing, Dissertation No 348, Linköping 1994.
Figure 1. The strain-rate in a region of interest (circle) on a surface in the left ventricular myocardium.
Proc. Intl. Soc. Mag. Reson. Med 9 (2001)
1870
Proc. Intl. Soc. Mag. Reson. Med 9 (2001)
1870
