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Ann Thorac Surg 1998;65:943-950
© 1998 The Society of Thoracic Surgeons

MRI-Radiofrequency Tissue Tagging in Patients With Aortic Insufficiency Before and After Operation

Felix F. Ungacta, MDaa, Victor G. Dávila-Román, MDa,b,ca,b,c, Michael J. Moulton, MDa,b,ca,b,c, Brian P. Cupps, PhDa,b,ca,b,c, Pavlos Moustakidis, MDa,b,ca,b,c, Douglas S. Fishman, BSa,b,ca,b,c, Ricardo Actis, PhDa,b,ca,b,c, Barna A. Szabo, PhDa,b,ca,b,c, Debiao Li, PhDa,b,ca,b,c, Nicholas T. Kouchoukos, MDa,b,ca,b,c, Michael K. Pasque, MDa,b,ca,b,c

a Division of Cardiothoracic Surgery, Department of Surgery, Washington University, St. Louis, Missouri, USA
b the Cardiovascular Division, Department of Mechanical Engineering, Washington University, St. Louis, Missouri, USA
c Department of Radiology, Washington University, St. Louis, Missouri, USA

Address reprint requests to Dr Pasque, Division of Cardiothoracic Surgery, Department of Surgery, One Barnes Hospital Plaza, 3103 Queeny Tower, St. Louis, MO 63110

Presented at the Thirty-third Annual Meeting of The Society of Thoracic Surgeons, San Diego, CA, Feb 3–5, 1997.


    Abstract
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 Appendix 1
 References
 
Background. Magnetic resonance imaging tissue tagging is a relatively recent methodology that describes ventricular systolic function in terms of intramyocardial ventricular deformation. Because the analysis involves the use of many intramyocardial points to describe systolic deformation, it is theoretically more sensitive at describing subtle differences in regional myocardial fiber shortening when compared with conventional measures of ventricular function such as wall thickening. The objectives of this study were (1) to define sensitive indices of ventricular systolic deformation to assist the clinician in the surgical evaluation of patients with aortic insufficiency, and (2) to quantify differences in regional systolic deformation before and after surgery for aortic insufficiency.

Methods. Magnetic resonance imaging with tissue tagging was performed on 10 normal volunteers and 8 patients with chronic severe aortic insufficiency. Follow-up postoperative studies (5.4 ± 1.1 months) were obtained in 6 patients who underwent Ross procedure (1 patient), David procedure (1), and St. Jude aortic valve replacement (4).

Results. There was no significant difference in fractional area change, overall circumferential shortening, or overall radial thickening among the normal group, the preoperative aortic insufficiency group, or the postoperative aortic insufficiency group. However, on a regional basis, there was a decrease in posterior wall circumferential strains in the postoperative aortic insufficiency group (29% ± 13% preoperative aortic insufficiency (n = 6) versus 24% ± 12% postoperative aortic insufficiency (n = 6), p = 0.02).

Conclusions. On regional analysis, there was a small but significant decrease in posterior wall circumferential shortening after operation. Magnetic resonance imaging tissue tagging is a sensitive and clinically applicable method of quantifying regional ventricular wall function before and after intervention for aortic insufficiency.


    Introduction
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 Appendix 1
 References
 
Chronic severe aortic regurgitation may present with normal left ventricular function with or without symptoms of heart failure. Over time, however, the response to this regurgitant lesion is ventricular dilatation with subsequent hypertrophy and, in some patients, progression to ventricular dysfunction or symptoms of heart failure, or both [1]. The exact time course for the progression to ventricular dysfunction and for the development of symptoms is unknown. It is well established, however, that surgical results are poor when valve replacement is postponed until severe left ventricular dysfunction or severe symptoms are present [13].

Analyses of ventricular function using invasive and noninvasive methods [2, 48] in patients with aortic insufficiency (AI) have been reported in an attempt to better define the nature and extent of alterations in myocardial function in response to AI. In addition, preoperative and postoperative analyses of left ventricular function have also been reported in an attempt to determine whether these preoperative alterations in myocardial function are reversed with surgical intervention [4, 9, 10].

Left ventricular chamber size and myocardial mass usually decrease after surgical intervention for chronic severe AI [1, 4, 11, 12]. The earliest and most dramatic response to aortic valve operations is a decrease in left ventricular chamber size, which usually occurs in the first few weeks after the surgical procedure [2]. A more gradual decrease in left ventricular mass occurs during the next 6 months, but this regression of ventricular hypertrophy is incomplete in many patients [13]. Improvement of impaired left ventricular pump function is difficult to predict and occurs in only about 50% of patients [13]. Preoperative and postoperative systolic deformation have been described using echocardiography; here we report our results using magnetic resonance imaging (MRI) tissue tagging with myocardial strain analysis in this clinical setting.

Currently used indices of ventricular function, such as ejection fraction and wall thickening, are gross descriptions of ventricular deformation. They measure gross global geometric changes that result from sarcomere shortening at the microscopic level. They lack the ability to describe transmurally varying myocardial deformation and are also limited by their inability to describe the different components of myocardial deformation (for example, the magnitude and direction of maximal contraction or maximal lengthening of myocardial tissue).

Previous studies using MRI tissue tagging have demonstrated regional variations in deformation in the normal heart [14, 15] and variations in several components of deformation in the hypertrophied heart [16, 17]. Because MRI tissue tagging [18] provides a noninvasive means for measuring the motion of "material points" in the myocardium, information on the transmural and regionally varying deformation throughout the myocardium is possible.

The significance of MRI-based strain analysis to describe systolic deformation is based on its more direct estimation of myocardial fiber shortening when compared with conventional echocardiographic parameters such as circumferential shortening and myocardial wall thickening. This technique uses MRI tissue tagging to alter the magnetic resonance characteristics of the myocardium in a gridlike pattern at the beginning of systole [18]. This gridlike tagged myocardium is then tracked throughout systole so that a minimum of 40 to 50 intramyocardial tag points are used in the analysis of deformation instead of only a single measurement (for example, circumference or wall thickness). Analysis of the displacements of the intersections of the radiofrequency tag lines is then used to calculate myocardial strain. Strain calculations estimate the effects of gross movements of the heart by taking the difference between the length of a line segment connecting two points in the deformed configuration (Ldef) minus its length in the undeformed state (Lundef) divided by its undeformed length (Lundef).

From this myocardial strain information, maximal shortening and maximal lengthening can then be used to estimate the magnitude and direction of "fiber" shortening on a transmural as well as on a regional basis. The strain pattern and magnitude can be represented with a color-coded strain map of the left ventricle throughout systole (Fig 1) [19]. In addition, because of the relatively short amount of time required to obtain total cardiac imaging (20 to 30 minutes), this methodology is well suited for patient evaluation.



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Fig 1. Short-axis magnetic resonance imaging (A) at end-diastole and (B) at end-systole of the heart of a normal subject. Computer-generated splines are overlayed onto the myocardial tag lines. The intersection of the splines (red circles) identifies myocardial "material points," which are used to calculate myocardial point displacement. The left ventricular borders are identified manually with two additional closed splines to represent the endocardium and the epicardium. Circumferential strain map of the left ventricle during systole demonstrating the strain patterns and magnitudes in (C) a heart with preoperative aortic insufficiency (pre-op AI) and (D) a heart with postoperative aortic insufficiency (post-op AI) in the same patient. Circumferential strain patterns demonstrate lower strains at the epicardium (red) with increasing strain towards the endocardium (yellow).

 
Previously published echocardiographic studies by Carroll and associates [20] and Burggraf and Craige [21] identified small differences in posterior wall and septal wall motion, respectively, after operations for AI in the early postoperative period. We hypothesized that MRI tissue tagging would be able to identify and quantify these differences in posterior and septal wall deformation 6 months after the surgical procedure.

The present study was undertaken to determine whether there were any distinguishing characteristics in myocardial deformation as measured by MRI tissue tagging with myocardial strain analysis in patients with severe chronic AI who were scheduled to undergo an operation when compared with a group of normal volunteers. In addition, we also sought to describe the regional and global ventricular response to surgical correction of AI. Specifically, the analysis involved two components of deformation: circumferential shortening and radial thickening.


    Material and methods
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 Appendix 1
 References
 
Patient characteristics
Eight patients with AI were studied (5 men and 3 women; age range 33 to 57 years; mean age ± standard deviation 45.3 ± 9 years) (Table 1). The cause of aortic insufficiency was congenital bicuspid aortic valve in 6 patients, Marfan’s syndrome in 1 patient, and prolapse of the noncoronary aortic cusp in 1 patient. All patients had dilatation of the aortic root. Indications for surgical procedures were either symptomatic deterioration or evidence of progressive ventricular dysfunction or dilatation, or both. Preoperative studies were performed within 2 weeks of surgery for all 8 patients and postoperative studies were obtained for 6 of 8 patients an average of 5.4 months after the operation (mean ± standard deviation 5.4 ± 1.1 months; range 3.8 to 7.0 months). Two of the 8 patients were less than 2 months after surgery at the time of this report, and thus, postoperative studies were not available. Four patients underwent aortic valve replacement with St. Jude valve, 1 patient underwent the Ross procedure, and 1 patient underwent the David procedure. All patients were free of coronary artery disease by cardiac catheterization. None had aortic stenosis and none had more than mild mitral regurgitation. All patients were in normal sinus rhythm, were in either New York Heart Association functional class I (1 patient), II (6 patients), or III (1 patient), and had no contraindications for MRI (see Table 1).


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Table 1. Aortic Insufficiency: Patient Characteristics

 
A control group of 10 healthy volunteers (5 men and 5 women; age range 21 to 63 years; mean age ± standard deviation 30.6 ± 12 years) was also studied for comparison. The study was approved by the Human Studies Committee at Washington University, St. Louis, MO.

Magnetic resonance imaging acquisition
Imaging was performed in a 1.5-Tesla MR scanner (Siemens Medical Systems, Erlangen, Germany). The true short-axis plane of the heart was first located by acquiring scout images. Once the junction of the papillary muscle with the ventricular wall was identified, a short-axis slice 6 mm basal to this level was chosen for analysis. For the selected short-axis plane, a single-slice MRI sequence was obtained consisting of a spatial modulation of magnetization (SPAMM) radiofrequency tissue-tagging preparation [22] followed by a two-dimensional fast low flip angle shot (FLASH) cine image acquisition. Imaging parameters included a slice thickness of 8 mm, a field of view (FOV) of 250 to 350 mm, a 256 x 256 pixel matrix size, 40-degree flip angle, and time echo (TE) of 40 milliseconds. Five data lines were acquired for each cine image during each cardiac cycle. Each cine sequence of images consisted of 12 to 18 images acquired over a period of 25 to 40 seconds. During the image acquisition, the subjects were instructed to hold their breath at midexpiration. Image acquisition was initiated approximately 10 milliseconds after the R wave of the electrocardiogram. The tagging sequence generated an orthogonal grid pattern of presaturations in the myocardium(Figs 1A, 1B). The end-diastolic image was chosen as the first image in sequence (Fig 1A) and the end-systolic image was determined by choosing the smallest ventricular size in sequence (Fig 1B).

Data analysis
Image processing
The files containing digitized MRI data were transferred through the network to a Silicon Graphics (Indy R-5000) computer in which the original MRI data were converted to Silicon Graphics image file format. Image processing and data analysis were performed using software developed in our laboratory on the Silicon Graphics workstation specifically for the purpose of analyzing cardiac MRI images.

Material point displacements
Finite element models were created from the short-axis images. The left ventricle was divided into four regions on the basis of the intersection of two lines: (1) a line going through the junction of the right ventricular endocardium and the septal wall and the centroid of the left ventricle, and (2) a line perpendicular to this line and intersecting it at the centroid. Four elements were then created to represent the anterior wall, lateral wall, posterior wall, and septal wall(Figs 1C, 1D).

The tagged myocardial tissue was tracked throughout systole by segmental MRI scanning at 40-millisecond intervals. The images were then processed by using a semiautomated program that overlays splines on top of the tissue tags and determines the intersection of the splines as myocardial material points (Fig 1A). These myocardial material points or spline intersections were processed for each of the MRI images, thus allowing the tracking of the intramural points at 40-millisecond intervals throughout the systolic interval to determine the overall systolic material point displacements (Fig 1B)[23].

Finite element displacement fitting
The transmural myocardial point displacement information along with the endocardial and epicardial borders was then used to construct a finite element model with four elements representing the anterior wall, lateral wall, posterior wall, and septal wall. Given the discrete myocardial displacement point information, a first-ordered fitting was performed to provide for continuous displacement information across the four left ventricular walls [19] (see Appendix 1).

Strain calculations
Myocardial material point displacement information was then used to determine deformation in terms of the principal components of myocardial strain. Lagrangian strain tensor (E) was calculated as the partial derivative of displacement in the x and y direction [24]. This information was then used to determine the direction and magnitude of maximal lengthening (radial thickening) and maximal shortening (circumferential shortening) (see Appendix 1).

All displacement fittings and strain calculations were performed using p-version finite element software (Stress Check; Engineering Software Research and Development, St. Louis, MO).

Calculation of geometric parameters
Tracings of the mid-left ventricular short-axis endocardium and epicardium were digitized and represented as splines to obtain the following: (1) total area (At) enclosed by the left ventricular epicardium and right side of the septum; (2) area enclosed by left ventricular endocardium (Ac); (3) base to apex length from the mitral valve plane to the apical endocardium (Lt), and (4) base to apex length from the mitral valve plane to the apical endocardium (Lc). These values were used to calculate the following [25]:



Statistical analysis
The two-tailed unpaired Student’s t test with unequal variance was used when comparing the normal group with the preoperative AI group. The two-tailed paired Student’s t test with unequal variance was used when comparing the preoperative AI group with the postoperative AI group.


    Results
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 Appendix 1
 References
 
Circumferential strain (shortening)
There was no difference in overall circumferential strain between the preoperative AI group (n = 8) and the normal group. There was also no difference in overall circumferential strain after operation for AI (Fig 2A). On regional analysis, however, there was a significant decrease in posterior wall circumferential strains after operation for AI (29% ± 13% preoperative AI group [n = 6] versus 24% ± 12% postoperative AI group [n = 6]; p = 0.02 by paired Student’s t test) (Fig 2C).



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Fig 2. Circumferential and radial strains are demonstrated as (A) overall circumferential shortening, (B) overall radial thickening, (C) regional circumferential shortening, and (D) regional radial thickening. Analysis of overall myocardial strains revealed no significant differences between any of the four groups in overall circumferential shortening or overall radial thickening. On regional analysis, posterior wall circumferential strains were significantly decreased in the postoperative AI group (29% ± 13% preoperative versus 24% ± 12% postoperative; *p = 0.02 by paired Student’s t test). (AI-pre = preoperative AI group; AI-post = postoperative AI group; NL = normal group.)

 
Radial strain (thickening)
There was no difference in overall radial strain or regional radial strain between the preoperative AI group (n = 8) and the normal group and no difference in overall radial strain or regional radial strain after operation for AI(Figs 2B, 2D).

Fractional area change
There was no significant difference in MRI-determined fractional area change between any of the four groups (Fig 3).



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Fig 3. Magnetic resonance imaging–determined fractional area change (FAC) from left ventricular short-axis images. There was no significant difference between the four groups. (AI-post = postoperative AI group; AI-pre = preoperative AI group; NL = normal group.)

 
Left ventricular end-systolic diameter
Left ventricular end-systolic diameter was significantly greater in the preoperative AI group when compared with the normal group (3.1 ± 0.5 cm in the normal group [n = 10] versus 3.7 ± 0.5 cm in the preoperative AI group [n = 8]; p < 0.01, unpaired Student’s t test) and significantly greater in the preoperative AI group (n = 6) when compared with the postoperative AI group (n = 6) (3.5 ± 0.5 cm versus 3.0 ± 0.5 cm, respectively; p < 0.05 by paired Student’s t test) (Fig 4A).



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Fig 4. (A) Left ventricular end-systolic diameter (LV-ESD) demonstrating significantly greater end-systolic diameters in the preoperative aortic insufficiency group (AI-pre) (n = 8) when compared with the normal (NL) group (n = 10) ({dagger}p < 0.05) and significantly greater end-systolic diameters in the AI-pre (n = 6) group when compared with the postoperative AI group (AI-post) (n = 6) (*p < 0.05). (B) Left ventricular end-diastolic diameter (LV-EDD) demonstrating significantly greater end-diastolic diameters in the AI-pre group (n = 8) when compared with the NL group (n = 10) (*p < 0.05) and significantly greater end-diastolic diameters in the AI-pre group (n = 6) when compared with the AI-post group (n = 6) ({dagger}p < 0.05).

 
Left ventricular end-diastolic diameter
Left ventricular end-diastolic diameter was significantly greater in the preoperative AI group when compared with the normal group (4.3 ± 0.5 cm in the normal group [n = 10] versus 5.2 ± 0.6 cm in the preoperative AI group [n = 8]; p < 0.01, unpaired Student’s t test) and significantly greater in the preoperative AI group (n = 6) when compared with the postoperative AI group (n = 6) (5.2 ± 0.6 cm versus 4.4 ± 0.4 cm, respectively; p < 0.01 by paired Student’s t test) (Fig 4B).

Left ventricular mass
Left ventricular mass (LVm) was significantly greater in the preoperative AI group when compared with the normal group (77 ± 7 g/m2 in the normal group [n = 10] versus 140 ± 33 g/m2 in the preoperative AI group [n = 8]; p < 0.001 by unpaired Student’s t test). There was a trend toward a lower LVm in the postoperative AI group when compared with the preoperative AI group; however, this did not reach statistical significance (144 ± 35 g/m2 in the preoperative AI group [n = 6] versus 119 ± 23 g/m2 in the postoperative AI group [n = 6]; p = 0.12) (Fig 5).



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Fig 5. Left ventricular myocardial mass indexed for body surface area (LV-Mass/BSA). The preoperative AI group (AI-pre) (n = 8) had significantly greater LV-Mass/BSA when compared with the normal (NL) group (n = 10) (*p < 0.01). The postoperative AI group (AI-post) tended toward decreased LV-Mass/BSA compared with the AI-pre group (n = 6); however, this did not reach statistical significance ({dagger}p = 0.10).

 

    Comment
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 Appendix 1
 References
 
This study used MRI-tissue tagging [18] to quantify myocardial strains before and after operation for AI. The technique uses pulse radiofrequency to modify the magnetic resonance characteristics of the myocardium in a gridlike fashion. As the heart deforms, the myocardial tags also deform. Myocardial tag line intersections can then be analyzed with computer methodology to track material points (intersection of two tag lines) and to calculate two-dimensional displacements in the myocardium. The x and y components of displacement of these discrete myocardial tag points are used to fit a first-ordered continuous displacement field for the entire myocardium. The derivative of this continuous displacement field is then used to calculate regional and transmural finite strains [23].

This study used MRI-tissue tagging with continuum mechanics methodology to describe transmural finite strains in patients with chronic severe AI. The advantage of this methodology compared with conventional measures of myocardial strain such as wall thickening or fractional shortening are as follows. Continuum mechanics allows for the description of a continuous strain field throughout the myocardium; this field describes the regional and transmural variations in myocardial strain. This characteristic of MRI-tissue tagging with continuum mechanics strain analysis is important because regional as well as transmural variations in myocardial strains in the normal heart have been demonstrated in previous studies [14, 15]. More importantly, these measures of strain and their characteristic variation throughout the myocardium have been shown to be altered in the hypertrophied heart [16, 17]. Second, in two-dimensional strain analysis there are two normal strain components (strain in the x direction, strain in the y direction) and one shearing strain (strain in the x–t direction), all of which can be calculated with the methodology used in this study. These components of strain can be determined at any number of points throughout the myocardium. From these three components of strain, principal strains can then be calculated. The principal strains are the magnitudes and directions of maximal lengthening (radial thickening) and maximal shortening (circumferential shortening). Using continuum mechanics to describe myocardial strain, a graphical representation of myocardial deformation can be generated in the form of a color-coded strain map (seeFigs 1C, 1D). Our data show the expected direction of maximal shortening, which is in the circumferential direction, and the expected variations in circumferential shortening with greater shortening at the endocardium and lesser shortening at the epicardium (seeFigs 1C, 1D) [26].

In this select group of patients with clinical and diagnostic indications for surgical repair of aortic regurgitation, the only measured parameters of ventricular function and geometry that were significantly different from the normal group of volunteers were left ventricular end-systolic diameter and left ventricular end-diastolic diameter. Magnetic resonance imaging-determined change in short-axis fractional area in the preoperative AI group was not different from that of the normal group and also was not different when compared with that of the postoperative AI group. Using strain analysis with continuum mechanics methodology, regional differences between the preoperative AI group and postoperative AI group were identified. Posterior wall circumferential shortening was decreased in the postoperative AI group when compared with the preoperative AI group (see Fig 2C).

Because of the sensitivity of MRI tissue tagging, it is possible that changes in posterior wall deformation were identified that were not seen by other methods. Carroll and associates [20] reported a trend toward decreased posterior wall thickening by two-dimensional echocardiography less than 1 month after operation for AI. This difference, however, did not reach statistical significance. Other data regarding changes in regional wall motion after operation for AI report early (<1 month) paradoxical septal wall motion [20]. Our data showed no significant differences in septal wall deformation 6 months after operation for AI.

Possible limitations of this study include the two-dimensional nature of the imaging and the strain analysis. In two-dimensional analysis of myocardial deformation, one cannot account for the effect of myocardial deformation in the third dimension (for example, contraction in the base-to-apex direction). A second problem introduced with the two-dimensional nature of this study is also a result of the fixed imaging plane used in MRI. The heart is known to move in and out of the short-axis imaging plane. Thus, the material points that one observes at end-diastole may not be the same material points that one observes at end-systole. Nevertheless, strain analysis in this framework still has higher resolution and is more well suited to the analysis of deformable bodies than conventional measures of strain such as wall thickening and circumferential shortening as determined by echocardiography, which suffer the same shortcomings of planar imaging.

To overcome the limitations as stated above, three-dimensional myocardial point displacement with three-dimensional strain analysis is necessary. With three-dimensional strain analysis, the base-to-apex contribution to myocardial wall thickening can then be described.

In summary, MRI tissue tagging was used to calculate two-dimensional myocardial strains in patients with severe chronic AI before and after operation and were compared with a group of normal volunteers. Preoperatively, there was no significant difference in MRI-determined fractional area change, overall circumferential shortening, or overall radial thickening when compared with the normal group. Similarly, there was also no significant difference in these parameters after operation for AI. Only on regional analysis was there a significant difference between the preoperative and postoperative AI groups. In the 6-month postoperative period, there was a small but significant decrease in posterior wall circumferential shortening. Magnetic resonance imaging–tissue tagging is a sensitive and quantitative methodology that is suitable for the assessment of global as well as regional ventricular function in patients before and after operation for AI.


    Acknowledgments
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 Appendix 1
 References
 
We appreciate the support and services of Glen W. Foster, RT, Nancy Nickerson, RN, Hans Lee, MD, Robert Gopler, MD, and Debbie Delano, RN, and the assistance of Richard B. Schuessler, PhD, with the statistical analysis. We also recognize Barry H. Branham and Kent Myers for their expertise and assistance in the software development aspect of the image analysis and strain analysis.


    Appendix 1
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 Appendix 1
 References
 
Finite element displacement fitting
Given a set of measured displacements at NP points, an approximation of the displacement components is performed. Let Ûx(xt,yi), Ûy(xt,yi) be the measured displacement components at points (xt,yi), i = 1,NP. We seek to determine a polynomial approximation for the displacement field in the least-square sense. Consider the approximation of the displacements as follows:


where Nj(x, y) are known polynomial functions and aj are unknown coefficients that are computed from the condition of minimizing the square of the error as follows:


where Ux(x1, y1), Uy(x1,y1) are the predicted displacement components at the points (x1, y1), i = 1,NP. This results in two systems of simultaneous equations of size NV, where NV is the number of variables in the expansion of Ux and Uy.

Strain calculation
The components of strain are first calculated in a rectangular cartesian coordinate system. In two dimensions this results in the three components of strain as follows:



The two principal strains E1 (maximal strain) and E2 (minimal strain) are the eigenvalues of E and the corresponding directions in which they act are the eigenvectors of E [24]. These principal strains represent the maximum and minimum deformation (elongation and contraction) experienced by the myocardial tissue at that point. In the normal heart, E1 is positive and represents maximal elongation, and E2 is negative and represents maximal contraction. E1 is referred to as radial thickening and E2 is referred to as circumferential shortening in this article.


    References
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 Appendix 1
 References
 

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