Am J Physiol Heart Circ Physiol 289: H1826-H1833, 2005.
First published June 17, 2005; doi:10.1152/ajpheart.00442.2005
0363-6135/05 $8.00
Three-dimensional systolic kinematics of the right ventricle
Idith Haber,1
Dimitris N. Metaxas,2
Tal Geva,1 and
Leon Axel3
1Departments of Cardiology and Cardiac Surgery, Children's Hospital, Boston, Massachusetts; 2Computer Science Department, Rutgers University, Piscataway, New Jersey; and 3Department of Radiology, New York University, New York, New York
Submitted 2 May 2005
; accepted in final form 16 June 2005
 |
ABSTRACT
|
|---|
The right ventricle (RV) of the heart is responsible for pumping blood to the lungs. Its kinematics are not as well understood as that of the left ventricle (LV) due to its thin wall and asymmetric geometry. In this study, the combination of tagged MRI and three-dimensional (3-D) image-processing techniques was used to reconstruct 3-D RV-LV motion and deformation. The reconstructed models were used to quantify the 3-D global and local deformation of the ventricles in a set of normal subjects. When compared with the LV, the RV exhibited a similar twisting pattern, a more longitudinal strain pattern, and a greater amount of displacement.
magnetic resonance imaging; myocardial contraction; three-dimentional motion
THE RIGHT VENTRICLE (RV) plays an important role in normal and abnormal hemodynamics because it receives deoxygenated blood from the right atrium and pumps it into the pulmonary circulation for oxygenation. The onset of RV dysfunction can also adversely affect the left ventricle (LV) and can lead to heart failure (2). A potentially important means of detecting and evaluating RV dysfunction is to quantitatively analyze changes in its motion. However, because of its thin wall and asymmetric geometry, the normal three-dimensional (3-D) motion and deformation of the RV are not yet well understood.
Early studies (4, 5, 14, 19, 20, 24) used implanted radiopaque markers to provide limited knowledge about RV motion, mostly in animals. Recently, imaging modalities, such as echocardiography, computed tomography, and conventional magnetic resonance imaging (MRI), have provided a noninvasive means of studying the RV (3, 7, 12). However, observation or measurement of wall motion using these techniques is difficult due to the lack of trackable landmarks in the RV wall, as well as its relative thinness and complex geometry. The noninvasive MRI tissue-tagging technique generates trackable landmarks by nullifying a portion of the MR signal before imaging. Several researchers have used planar tagged MRI to establish the in-plane deformation of the RV free wall (6, 12, 16, 17) and septum (6). The dependence of these studies on the location of image slices, and on the choice of regional demarcation within the slice, results in difficulties with reproducing or comparing measurements. One preliminary study (25) used MRI tags to provide a qualitative description of the 3-D motion of a midwall portion of the RV free wall.
The current study describes the use of tagged MRI and image analysis to provide a 3-D quantitative description of RV, septal, and LV motion. Information about 3-D motion was obtained by using multiple imaging views and a specialized 3-D motion reconstruction technique (9). This method provided a dense set of 3-D motion data from which both global and local deformation was quantified. Regional analysis allowed us to compare corresponding regions of the RV, septum, and LV. Unlike previous methods, the current technique enables direct comparison of 3-D displacement and twisting of the RV with corresponding regions in the LV. Furthermore, 3-D strain measurements provide information about both the magnitude and orientation of shortening. This is the first study reporting normal values for the full 3-D motion of the RV.
|
METHODS
|
|---|
Tagged MRI acquisition.
We studied six normal volunteers aged 18 to 43 yr. With the MR tagging technique, a set of radiofrequency pulses and magnetic field gradient pulses is used to saturate tissue magnetization in parallel planes before imaging. Images acquired perpendicular to these planes have dark lines at the intersection of tag and image planes (Fig. 1). For each tag plane orientation, the perpendicular component of motion is provided by the displacement of the tag lines because the tags move with the underlying tissue. To capture 3-D information about motion, two perpendicular tagged MR image sets covering the volume of the ventricles were acquired (Fig. 2). A stacked set of transverse, or short-axis, images provided information on tag motion in two mutually perpendicular directions. Another set of longitudinal, or long-axis, images provided the information on motion in the third perpendicular direction. The images were acquired on a Signa 1.5 T clinical MR system (GE Medical Systems, Milwaukee, WI), using an ECG-gated gradient echo imaging sequence with the following parameters: field of view (22–26 cm, approximately 1-mm spatial resolution), repetitive time (6–7 ms), and echo time (2.3–2.6 ms). Slice thickness was 6 mm, slice spacing was 6–7 mm, and tag spacing was 6–7 mm. Because 5–8 images were acquired through systole, the temporal resolution was 40–60 ms.
View larger version (182K):
[in this window]
[in a new window]
|
Fig. 1. Tagged magnetic resonance (MR) images have noninvasively created dark bands that could then be used to track motion of myocardium. Top: long-axis four-chamber view at end diastole and end systole. Bottom: short-axis images with superimposed two-dimensional active contours used to track motion through systole. Light-colored points fall within the ventricular walls. RV, right ventricle; LV, left ventricle; RA, right atrium.
|
|
View larger version (16K):
[in this window]
[in a new window]
|
Fig. 2. Tagged MR image plane orientation. Schematic biventricular unit with representative image planes. Short-axis image planes are parallel to one another, whereas long-axis image planes are rotated about LV base-to-apex direction.
|
|
3-D motion reconstruction.
Images were analyzed by using a custom-made software package (SPAMMVU) (13). Endocardial and epicardial borders of both the RV and LV were defined by using active contours (11). In addition, a semiautomatic algorithm was used to identify and track two-dimensional (2-D) tag motion in each image plane over time (Fig. 1B).
The 3-D motion of the RV was reconstructed from multiple image views using a previously described and validated method (8, 9). The technique can be separated into geometry definition and 3-D fitting of motion data. First, a 3-D volumetric finite element model was generated from contours extracted from end-diastolic images. As shown in Fig. 3, a biventricular model was defined to allow comparisons between ventricles. The geometric model was then fit to tag and contour data extracted from the 2-D images. The model was deformed over time using spring-like pseudoforces calculated between the model and image data. The finite element stiffness of the finite elements ensures smoothing and continuity. It should be noted that the forces and smoothing are not meant to replicate actual heart tissue properties. The model was updated by using modified equations of motion and adaptive Euler integration. The fitting process was applied between each consecutive pair of images until the full systolic RV motion was recovered.
View larger version (67K):
[in this window]
[in a new window]
|
Fig. 3. Ventricular finite element model used to reconstruct three-dimensional RV-LV motion. LV and RV endocardial walls are shown as shaded surfaces.
|
|
Motion analysis.
The 3-D motion reconstruction provided a dense displacement data set interpolated over the volume of the finite elements. Because of the complex shape of the RV, a local wall-based coordinate system was defined for each element (Fig. 4). Vectors perpendicular to the model walls were calculated to determine the local normal direction. The projection of the long axis of the LV onto the plane of the model wall determined the longitudinal direction. The tangential direction was defined as perpendicular to the normal and longitudinal vectors. The components of displacement were resolved according to the local coordinate system. The twisting motion of the RV was defined relative to the long axis of the LV to enable comparison with the septal and LV free-wall twisting.
View larger version (19K):
[in this window]
[in a new window]
|
Fig. 4. Wall-based coordinate systems. A: schematic ventricles with cutaway of surface of wall showing wall-based axes. z, longitudinal; t, tangential; n, normal. B: angle that minimum principal direction makes with tangential-normal plane ( E3) (shaded area).
|
|
The local deformation of the RV, septum, and LV were derived from the 3-D motion data. A useful quantitative description of the degree of muscle deformation due to contraction is the Lagrangian strain (21). Given the initial and final positions of a point in the material (X and x, respectively), the deformation gradient tensor (F) is defined as:
 | (1) |
where the subscripts p and q range from 1 to 3 and denote one of the 3-D Cartesian coordinates. The tensor F includes both the rotation and deformation around a point in the material. It can be shown that the Lagrangian strain tensor E only includes the deformation of the material and is related to F as follows (21):
 | (2) |
where FT is the transpose of matrix F, and I is the identity matrix. The Lagrangian strain formulation describes systolic deformation relative to an end-diastolic reference configuration.
The finite element formulation was used to numerically compute strains. The derivatives in Eq. 1 were found by using the chain rule:
 | (3) |
where 
i is a component of the local finite element coordinate system.
The eigenvalues of E are the principal strains where a positive value indicates lengthening, whereas a negative value indicates shortening (21). Each principal strain is associated with a corresponding principal direction along which the deformation occurs. The principal direction associated with E3 (the greatest shortening) was measured relative to the wall-based coordinate system. We calculated the parameter E3, the angle that the E3 direction makes with the tangential-normal plane (Fig. 4B). Because the tangential-normal plane represents a cross-sectional cut across the ventricular wall, E3 varied between 0° and 90°. A value of 0° indicated a tangential shortening direction, and a value of 90° indicated longitudinally oriented shortening.
Data analysis.
To investigate the spatial variation in motion and deformation, the RV, septum, and LV were separated into regions. Anatomical landmarks were selected from the original images to divide the RV into four regions and the other walls into three regions. First, the outflow tract was separated from the rest of the RV free wall by identifying the parietal and septal bands. A septal long axis was defined between the basal septum and the insertion of the RV into the LV at the epicardial apex. The normalized height along the septal axis was used to demarcate regions of the remaining free wall, the septum, and the LV (Fig. 5). Deformation and displacement were calculated for each region as the volume-weighted average of the strains in the elements belonging to those regions.
Repeated-measures ANOVA was used to test differences between regions within each wall and between regions in the same longitudinal position (e.g., basal) across the three walls of the heart. Bonferonni adjustment was used in multiple comparisons with P < 0.05 considered as significant.
|
RESULTS
|
|---|
Global motion.
All subjects exhibited similar qualitative global motion. Figure 6 shows the motion of the model over all time phases for a typical normal study. The path of points in the center of each wall is plotted along with a color plot of point displacement on the endocardial wall. The motion of most points in the RV free wall is directed anterior and toward the apex.
View larger version (62K):
[in this window]
[in a new window]
|
Fig. 6. Motion through systole shown with endocardial walls shaded gray for visualizing amount of displacement (mm) (scale provided). Paths of points located in centers of each wall are shown from end diastole (light) to end systole (dark). Top row: RV free wall coded with LV uniformly shaded. Middle row: Septal view of endocardial wall of RV cavity is gray coded. Bottom row: LV free wall gray coded with RV uniformly shaded.
|
|
Table 1 shows regional total displacements as well as displacement components relative to the local wall-based coordinate system. The RV free wall showed a significantly greater total (P < 0.002), longitudinal (P < 0.02), and tangential (P < 0.04) displacement compared with the septum and the LV. In addition, the apical septum exhibited significantly smaller tangential displacement and larger normal displacement than the LV apex. The greatest amount of both total and axial displacement in the biventricular unit occurs in the basal free wall of the RV. The outflow tract, on the other hand, shows a smaller value in all displacement measures compared with the RV base. Linear regression was used to establish the relationship between displacement and axial position (base-apex) in the RV free wall (excluding outflow tract) and in the septum. Both total (R = 0.724) and longitudinal displacement (R = 0.931) increased with distance from the apex. An apex-to-base increase in axial displacement was also found in the septum (R = 0.918).
Figure 7 shows the angular displacement of points in the RV and LV for equally spaced transverse cross sections. The angular displacements were measured relative to LV long axis for the RV, septum, and the LV. Within each cross section, the angular displacement was similar for the RV and LV free walls, except at the apex where angular displacement in the RV was less than that in the LV (P < 0.05). Initially, all cross sections rotated clockwise, followed by a counterclockwise rotation of the base relative to the apex.
View larger version (24K):
[in this window]
[in a new window]
|
Fig. 7. Angular motion about LV long axis in three cross sections [reference (A), base (B), midsection (C), and apex (D)] of RV (solid line), septum (sep, dashed line), and LV (dotted line). Angular position is plotted as function of normalized systolic time with counterclockwise positive. End-systolic angular displacement of RV apex was significantly less than that of LV (*P < 0.05).
|
|
Regional deformation.
To assess local deformation, we calculated the principal strains from the strain tensor. The three principal eigenvalues were sorted from largest (E1) to smallest (E3). These strains are shown in Table 2. Because the sign of E3 was consistently negative, it indicated muscle shortening from which we infer contraction. Figure 8 shows a gray-shaded plot on the endocardial surfaces of E3 at end systole for a representative normal subject. The associated principal directions are plotted at the midventricular surface with lengths scaled according to the maximum shortening at those locations. These directions were approximately aligned within planes parallel to the endocardial and epicardial walls. The average angles between the wall-based tangential-longitudinal plane and the E3 direction were 10.8 ± 2.2, 12.9 ± 2.2, and 10.7 ± 1.0 in the RV, septum, and LV, respectively.
View larger version (30K):
[in this window]
[in a new window]
|
Fig. 8. End-systolic configuration of representative study with endocardial walls shaded gray for visualizing E3 (scale provided provided). View is provided of RV free wall (A), RV septal wall (B), and LV free wall (C). Lines are minimum principal strain directions drawn with lengths scaled to strain magnitude.
|
|
When comparing regional E3 within each wall, we found that basal |E3| was significantly smaller than other regions in the septum, RV, and LV (P < 0.04). In addition, the septal |E3| was significantly different among all levels, with a gradient from base to apex (P < 0.001). No difference in E3 was detected in the RV outflow tract versus the rest of the RV. The value of E3 remained approximately constant when comparing the same levels across the three walls, except for a significantly greater |E3| in the midsection of the RV versus the septum and LV (P < 0.01).
The intermediate principal strain (E2) in all regions of the heart was found to be negative. Basal |E2| was on average smaller than midsectional and apical |E2| and significantly smaller in the septum and LV (P < 0.03). In the RV wall, midsectional |E2| was significantly greater than at the apex (P < 0.05). In comparing regions across walls, RV apical |E2| was less than septal and LV |E2| (P < 0.04).
Finally, the maximum principal strain E1, which was consistently positive, indicated the greatest expansion in the muscle wall. The average E1 was lower in the basal regions, with a significantly smaller magnitude found the LV base versus apex (P < 0.05). In comparing the same region across the heart walls, septal E1 was less in the RV and LV in both the midsection and the apex (P < 0.04).
As stated earlier, the eigenvector corresponding to the minimum principal strain (E3) indicated the direction of maximum shortening. The angle of this vector with respect to the tangential wall-based direction is shown in Table 3. RV basal and midsection E3 was significantly greater than corresponding regions in the septum (P < 0.02), and apical E3 was greater than that found in the LV apex (P < 0.01). Furthermore, within the septum, E3 was significantly smaller in the base than in the midsection.
|
DISCUSSION
|
|---|
Tagged MRI was used to reconstruct and analyze both the global and local 3-D motion of the biventricular unit. Globally, the RV cavity volume decreases during systole due to a combination of the following mechanisms: motion of the free wall toward the septum, motion of the base toward the apex, and the bulging of the septal wall into the cavity (2). Here, we have quantified the global motion of the RV and compared it to that of the septum and LV free wall. The greatest total and longitudinal displacement in both ventricles was found to occur in the RV freewall. Longitudinal displacement was greatest at the base of the RV, similar to other finding (23, 25).
Although angular displacement of the LV has previously been documented (1, 15, 26), little has been reported regarding the angular displacement of the RV. The recovered 3-D motion of the biventricular unit showed that the pattern of angular displacement about the LV long axis was similar for all walls of the heart. The biventricular unit exhibited initial clockwise rotation, followed by twisting of the base with respect to the apex. A previous study (12) limited to short-axis images found a similar order of magnitude in tangential-normal displacement but no twisting of the RV base relative to the apex. Because the RV is coupled to the LV at the insertion points, it is possible for it to exhibit a similar angular motion, as shown in a previous qualitative study (25).
In addition to global motion, we calculated the 3-D principal strains and their orientations. Similar to the findings of Young et al. (25), the minimum principal strain (E3) was found to be oriented mainly within the plane of the RV wall. We found significantly less shortening in the RV base versus the midsection and the apex. An increasing gradient in the magnitude of E3 toward the apex was also observed by Waldman et al. (24), who implanted a matrix of beads onto the epicardial surface. Other studies (6, 12) measuring uniaxial deformation have found a general base-to-apex increase in one-dimensional (1-D) shortening as well.
We also compared RV free wall E3 to that found in the septum and LV. Except for the midsection of the RV, where E3 was greater, no difference was found with the LV strain. In the septum, the magnitude of E3 was found to be similar to those of previous 3-D motion reconstruction studies of the LV (26). However, our E3 values were less than those found in the LV using yet another 3-D motion reconstruction method (15).
The intermediate principal strains (E2) were negative in the RV as well as the LV. This phenomenon, where 1-D muscle fiber contraction leads to two directions of shortening (negative deformation), is evidence of the cross-fiber shortening phenomenon (10). Because the RV wall is thinner and has different myofiber architecture (18), it is interesting to note that cross-fiber shortening occurred in the RV as well as the LV.
The maximal principal strain E1 indicates the greatest amount of extension and was approximately perpendicular to the muscle wall. We found that septal E1 was lower in the midsectional and apical regions. No difference was found in regional E1 in other studies (15, 26). This may be the case because, as in our study, E1 has the greatest standard error. Our 3-D method produces values with the smallest standard error along directions where the most tag data lie. The maximal principal strain, on the other hand, relies on both tag and less-reliable contour data to guide the 3-D motion reconstruction.
The angle E3 of the minimum principal strain direction was greater in all regions of the free wall compared with the septum and LV. In the LV, muscle fiber orientation is known to vary by about 160° from endocardium to epicardium, with 10 times as many fibers oriented in the tangential-normal plane (0 ± 22.5°) than otherwise (18, 22). In contrast, the fiber orientation in the RV free wall does not exhibit such transmural variation (18), and the RV is likely to have fewer tangential fibers in its thinner wall. It has also been noted that twisting of the RV due to LV coupling may lead to a change in the angle of greatest shortening (25). The longitudinal orientation of minimum principal strain can also explain the greater amount of RV versus LV displacement with no notably significant differences in shortening between respective regions: the contraction of the RV contributes mainly to its long-axis deformation, whereas the tangential component of displacement is larger due to LV coupling.
Our methods have been limited by the complex geometry and thin wall of the RV. Because normally only one tag falls within the thickness of the RV wall, we had to use contour data as well as tag data to reconstruct the 3-D motion. In addition, the finite element model geometry used did not include portions of the outflow tract lying above the most basal short-axis image. This may explain why no major differences were found between outflow tract deformation and the rest of the RV.
In conclusion, we have reconstructed and analyzed the 3-D motion of the RV using tagged MRI. By quantifying 3-D strain, we were able to show that the orientation of shortening is different in the RV than in the LV and septum. Not only has the overall 3-D motion been quantified for the first time, angular displacement of the RV relative to the LV long axis has been quantified. The normative data presented in this study should open the way for studying alterations in regional RV motion in various types of heart disease.
|
FOOTNOTES
|
|---|
Address for reprint requests and other correspondence: I. Haber, Children's Hospital, Dept. of Cardiology, 300 Longwood Ave., Bader-2, Boston, MA 02115 (e-mail: idith.haber{at}tch.harvard.edu)
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
|
REFERENCES
|
|---|
- Arts T, Meerbaum S, Reneman RS, and Corday E. Torsion of the left ventricle during the ejection phase in the intact dog. Cardiovasc Res 18: 183–193, 1984.[ISI][Medline]
- Barnard D and Alpert JS. Right ventricular function in health and disease. Curr Probl Cardiol 12: 422–429, 1987.
- Boxt LM. Radiology of the right ventricle. Radiol Clin North Am 37: 379–400, 1999.[CrossRef][ISI][Medline]
- Chin KW, Daughters GT, Alderman EL, and Miller DC. Asynergy of right ventricular wall motion in man. J Thorac Cardiovasc Surg 97: 104–109, 1989.[Abstract]
- Chuong CJ, Sacks MS, Templeton G, Schwiep F, and Johnson RL Jr. Regional deformation and contractile function in canine right ventricular free wall. Am J Physiol Heart Circ Physiol 260: H1224–H1235, 1991.[Abstract/Free Full Text]
- Fayad ZA, Victor Ferrari A, Kraitchman DL, Young AA, Palevsky HI, Bloomgarden DC, and Axel L. Right ventricular regional function using MR tagging: normals versus chronic pulmonary hypertension. Magn Reson Med 39: 116–123, 1998.[ISI][Medline]
- Geva T, Powell AJ, Crawford EC, Chung T, and Colan SD. Evaluation of regional differences in right ventricular systolic function by acoustic quantification echocardiography and cine magnetic resonance imaging. Circulation 98: 339–345, 1998.[Abstract/Free Full Text]
- Haber I. Three-Dimensional Motion Reconstruction and Analysis of the Right Ventricle From Planar Tagged MRI (PhD thesis). Philadelphia, PA: Univ. of Pennsylvania, 2000.
- Haber I, Metaxas DN, and Axel L. Three-dimensional motion reconstruction and analysis of the right ventricle using tagged MRI. Med Image Anal 4: 335–355, 2000.[CrossRef][ISI][Medline]
- Hexebert E, Homans DC, and Bache RJ. Interpretation of systolic wall thickening. Can thickening of a discrete layer reflect fiber performance? Circ Res 29: 16–21, 1995.
- Kass M, Witkins A, and Terzopoulos D. Snakes: active contour models. Int J Comput Vision 1: 321–331, 1987.
- Klein SS, Graham TP Jr, and Lorenz CH. Noninvasive delineation of normal right ventricular contractile motion with magnetic resonance imaging myocardial tagging. Ann Biomed Eng 26: 756–763, 1998.[CrossRef][Medline]
- Kraitchman DL, Young AA, Chang CN, and Axel L. Semi-automatic tracking of myocardial motion in MR tagged images. IEEE Trans on Med Imaging 14: 422–433, 1995.[CrossRef]
- Meier GD, Bove AA, Santamore WP, and Lynch PR. Contractile function in canine right ventricle. Am J Physiol Heart Circ Physiol 239: H794–H804, 1980.[Abstract/Free Full Text]
- Moore CC, Lugo-Olivieri CH, McVeigh ER, and Zerhouni EA. Three-dimensional systolic strain patterns in the normal human left ventricle: characterization with tagged MRI. Radiology 214: 453–466, 2000.[Abstract/Free Full Text]
- Nagel E, Stuber M, Fischer SE, Hess OM, and Boesiger P. Regional wall motion analysis of the right ventricle. In: Proceedings of the SMR (3rd Annual Meeting). Nice, France: Society for Magnetic Resonance, 1995, p. 252.
- Naito H, Arisawa J, Harada K, Yamagami H, Kozuka T, and Tamura S. Assessment of right ventricular regional contraction and comparison with the left ventricle in normal humans: a cine magnetic resonance study with presaturation myocardial tagging. Br Heart J 74: 186–91, 1995.[Abstract/Free Full Text]
- Nielsen PMF, Le Grice IJ, Smaill BH, and Hunter PJ. Mathematical model of geometry and fibrous structure of the heart. Am J Physiol Heart Circ Physiol 260: H1365–H1378, 1991.[Abstract/Free Full Text]
- Raines RA, LeWinter MM, and Covell JW. Regional shortening patterns in canine right ventricle. Am J Physiol 231: 1395–1400, 1976.[Abstract/Free Full Text]
- Santamore WP, Meier GD, and Bove AA. Contractile function in canine right ventricle. Am J Physiol Heart Circ Physiol 239: H794–H804, 1980.[Abstract/Free Full Text]
- Spencer AJM. Continuum Mechanics. London: Longman, 1980.
- Streeter DD, Spotnitz HM, Patel DP, Ross J, and Sonnenblick EH. Fiber orientation in the canine left ventricle during diastole and systole. Circ Res 24: 339–347, 1969.[Abstract/Free Full Text]
- Stuber M, Nagel E, Fischer SE, Scheidegger MB, and Boesiger P. Systolic long-axis contraction of the human myocardium. In: Proceedings of the SMR (3rd Annual Meeting). Nice, France: Society for Magnetic Resonance, 1995.
- Waldman LK, Allen JJ, Pavelec RS, and McCulloch AD. Distributed mechanics of the canine right ventricle: effects of varying preload. J Biomech 29: 373–381, 1996.[Medline]
- Young AA, Fayad ZA, and Axel L. Right ventricular midwall surface motion and deformation using magnetic resonance tagging. Am J Physiol Heart Circ Physiol 271: H2677–H2688, 1996.[Abstract/Free Full Text]
- Young AA, Kramer CM, Ferrari VA, Axel L, and Reichek N. Three-dimensional left ventricular deformation in hypertrophic cardiomyopathy. Circulation 90: 854–867, 1994.[Abstract/Free Full Text]
This article has been cited by other articles:
|
|
|
|
 
P. P. Sengupta, A. J. Tajik, K. Chandrasekaran, and B. K. Khandheria
Twist Mechanics of the Left Ventricle: Principles and Application
J. Am. Coll. Cardiol. Img.,
May 1, 2008;
1(3):
366 - 376.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
E. Pettersen, T. Helle-Valle, T. Edvardsen, H. Lindberg, H.-J. Smith, B. Smevik, O. A. Smiseth, and K. Andersen
Contraction Pattern of the Systemic Right Ventricle: Shift From Longitudinal to Circumferential Shortening and Absent Global Ventricular Torsion
J. Am. Coll. Cardiol.,
June 26, 2007;
49(25):
2450 - 2456.
[Abstract]
[Full Text]
[PDF]
|
|
|
Copyright © 2005 by the American Physiological Society.
TOP
ABSTRACT
METHODS
h < 0.35; midventricle (M), 0.35