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Published online before print September 24, 2001, 10.1148/radiol.2212010124
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(Radiology. 2001;221:515-522.)
© RSNA, 2001

Cardiac Imaging

Quantitative Prediction of Improvement in Cardiac Function after Revascularization with MR Imaging and Modeling: Initial Results1

John N. Oshinski, PhD, Hai-Chao Han, PhD, David N. Ku, MD, PhD and Roderic I. Pettigrew, PhD, MD

1 From the Frederik Philips MR Research Center, Department of Radiology, Emory University School of Medicine, 1364 Clifton Rd NE, Atlanta, GA 30322 (J.N.O., R.I.P.); and School of Mechanical Engineering, Georgia Institute of Technology, Atlanta (H.C.H., D.N.K.). Received December 7, 2000; revision requested January 27, 2001; revision received March 20; accepted May 1. Supported by a grant from the Whitaker Foundation. Address correspondence to J.N.O. (e-mail: jnoshin@emory.edu).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 
PURPOSE: To evaluate a model that can be used quantitatively to predict changes in postrevascularization left ventricular function based on classification of myocardial tissue as hibernating, scarred, or normal with cine magnetic resonance (MR) imaging.

MATERIALS AND METHODS: Eleven patients with chronic left ventricular dysfunction were studied before and after revascularization with cine MR imaging. Regional myocardial contractility and wall thickness were used in the model to predict postrevascularization ejection fraction (EF). The actual EF from the postrevascularization MR images was compared with the EF from the prerevascularization images predicted with the model by using regression analysis and Bland-Altman analysis.

RESULTS: Correlation between the actual EF after revascularization and the EF predicted by using the model yielded an R value of 0.98, with a standard error of 1.3 EF percentage points. Predicting changes in function in a myocardial segment was less successful because only 55% of segments classified as hibernating actually improved resting function after revascularization. In nonimproved segments, 78% were either adjacent to infarcted segments or had nontransmural wall thinning.

CONCLUSION: A simple mathematical model combined with functional information provided by MR imaging was used to predict improvements in global EF resulting from revascularization.

Index terms: Computers, diagnostic aid • Heart, MR, 511.1214 • Heart, surgery, 511.455 • Myocardium, MR, 511.1214


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 
Revascularization of myocardial tissue by using either coronary artery bypass graft (CABG) surgery or percutaneous transluminal coronary angioplasty (PTCA) is performed to relieve angina pectoris, to prevent subsequent myocardial infarction, and to improve ventricular function. Patients who undergo myocardial revascularization and have a consequential increase in ventricular function (measured by ejection fraction [EF]) have a superior prognosis compared with patients who are conservatively treated. However, patients who undergo revascularization and do not experience an increase in EF have a poor prognosis compared with patients treated conservatively (1–4). Since revascularization procedures involve morbidity and some mortality and are quite costly, a method to predict which patients will realize an increase in EF and to quantify the amount of the increase would be useful for patient treatment.

Magnetic resonance (MR) imaging has been well-established as a method of evaluating cardiac morphology and function (5–9). MR imaging also has demonstrated the ability to identify viable myocardium by being used (a) to evaluate regional wall thickness and thickening with multisection cine techniques (10–14) or (b) to image delayed enhancement after gadopentatate dimeglumine (Magnevist; Berlex Laboratories, Wayne, NJ) injection for identification of irreversibly injured myocardium (15,16).

Studies of chronic myocardial infarction with MR imaging have shown that if end-diastolic wall thickness (EDWT) is preserved in dysfunctional regions (EDWT > 5.5 mm), the myocardium is likely to be classified as hibernating (11,12). If EDWT is not preserved in the dysfunctional regions, the region is likely predominantly composed of fibrous scar tissue, which will not recover function. Therefore, by using cine MR imaging, myocardium can be classified on a regional basis as (a) normal, (b) hibernating, or (c) infarcted. Specificity for identifying hibernating myocardium can be improved further by demonstrating contractile response to dobutamine. Nonetheless, there is a high correlation between preserved EDWT in dysfunctional regions and viability assessed by using positron emission tomography (PET) with fluorodeoxyglucose fluorine 18 (FDG) in the setting of chronic infarction (11).

A priori quantification of the improvement of left ventricular function after revascularization requires some modeling of myocardial contractile properties. Finite-element modeling of the left ventricle is difficult because the three-dimensional geometrical configuration and nonisotropic properties of the myocardium have made computer analysis complex and time-consuming (17). Time constraints on obtaining clinically useful results require a model that can quickly give the physician information for patient treatment.

In this study, we propose a simple predictive model of left ventricular functional response to revascularization based on the structural and functional properties of myocardial segments determined with cine MR imaging. The model was applied to prerevascularization short-axis cine MR images to predict postrevascularization EF in 11 patients with chronic left ventricular dysfunction. All patients then underwent MR imaging a second time after revascularization, and the EF predicted by using the model was compared with the actual EF determined from the postrevascularization MR image. In addition, individual segments which were predicted to improve based on the prerevascularization MR image were examined in the postrevascularization MR image to see if they did indeed improve function.

The purpose of this study was to evaluate a model that can be used quantitatively to predict changes in postrevascularization of left ventricular function on the basis of classification of myocardial tissue as hibernating, scarred, or normal with cine MR imaging.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 
Subjects
Fifteen patients (11 men, 4 women; age range, 54–73 years) were recruited to participate in the study. Eleven of the patients completed the study, but four patients did not undergo the postrevascularization MR examination. The protocol was approved by the human investigation committee of Emory University School of Medicine, Atlanta, Ga. Informed consent was provided by all subjects after the procedure was fully explained.

All patients had chronic left ventricular dysfunction, which was demonstrated with echocardiography (EF < 45%). In the patients who had a previous myocardial infarction, the event occurred at least 2 months prior to the prerevascularization MR examination. Patients with acute myocardial infarction (<3 weeks old) were excluded from the study to eliminate potential confusion from "stunned" myocardium or recently infarcted myocardium. Stunned myocardium is tissue in which acute transient ischemia produces reversible dysfunction that will resolve without further intervention (18,19). Recently infarcted myocardium may not have had time to allow the scarring process to cause wall thinning; hence, it could be easily confused with hibernating or stunned tissue in our model. Methods that can be used to differentiate stunned, recently infarcted, and hibernating tissue exist, but they were not included in this study (20).

Nine of the patients underwent CABG surgery, and two underwent PTCA. In the patients who underwent CABG surgery, all had multivessel disease and each vessel that was suitable for bypass was treated at surgery. The two subjects who underwent PTCA also had multivessel disease. The average time between the prerevascularization MR imaging and the revascularization procedure was 2.5 days (range, 1–7 days). The average time between the pre- and postrevascularization MR imaging was 7.5 months (range, 1.5–12 months). Findings of studies indicate that as long as 1 month may be required after revascularization before function returns to hibernating tissue (21,22). In the time between the revascularization procedure and the postrevascularization MR imaging, none of the patients had evidence of restenosis, graft occlusion, or myocardial infarction.

MR Imaging
MR images were acquired with a 1.5-T imager (Philips Medical Systems, Shelton, Conn) by using a body coil for radio-frequency transmission and reception and electrocardiographic gating with a three-lead configuration. Survey MR images were obtained in three orthogonal planes. A gradient-echo electrocardiogram-gated 16-frame cine MR image of the heart was obtained in the vertical long-axis plane (parasagittal plane through the left ventricle), followed by a series of six to eight, 8–10-mm-thick (no gap), 16-frame cine MR images in the short-axis plane. A field of view of 300 mm, a matrix of 192 x 256, repetitition time msec/echo time msec of 24/11, and a flip angle of 30° were used. To ensure consistent section position for the pre- and postrevascularization MR images, image sections were always placed in the same manner. An MR image in the vertical long-axis orientation through the apex of the heart was obtained. A set of short-axis MR images was then planned perpendicular to the long axis of the left ventricle on the vertical long-axis image. The first section was planned so that the end of the section was at the epicardial border of the apex at end-diastole.

Classification of Myocardial Tissue
Short-axis cine MR images were reviewed, and borders were traced on a software program (MASS, version 2.0; AZL, Leiden, the Netherlands) by one of the authors (J.N.O.). With this program, one can then determine the systolic-to-diastolic area change for each section and use the section thickness to determine volumetric changes for the entire ventricle as well as the EF (23).

Each of the six to eight short-axis sections was radially divided into eight segments (Fig 1). Cine MR images were reviewed with the software program to identify regions that were akinetic or hypokinetic (<1.0 mm of wall thickening). In these regions of dysfunction, the reviewer characterized the myocardium as hibernating or infarcted on the basis of the following criteria (10–13): If EDWT was preserved in these dysfunctional regions (EDWT >= 5.5 mm), the myocardium was considered hibernating myocardium. If EDWT was less than 5.5 mm, the region was considered infarcted myocardium, which will not recover function.



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  		Figure 1. One frame from an electrocardiogram-gated gradient-echo cine MR image shows the left ventricle radially divided into eight segments for analysis on the short-axis view. The inferior insertion point of the right ventricle in the left ventricle (*) was used as the reference point. This point was used as the dividing line between segments 1 and 8.

 
All regions not identified as dysfunctional were considered normal myocardium. Note that there was no wall thickening in any region where EDWT was less than 5.5 mm. The criteria for hibernating myocardium do not exclude a subendocardial infarction, and this will be discussed later. An illustration of the classification procedure is given in Figure 2. The papillary muscles were excluded in wall thinning and EF measurements. The radial position (segments 1–8, Fig 1) and the long-axis position (section number) of each hibernating segment and each infarcted segment were recorded.



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  		Figure 2. MR images show end-diastole (left) and end-systole (right). Myocardial tissue was classified into either normal (N), hibernating (H), or infarcted (I) tissue on the basis of diastolic-to-systolic wall thickening and EDWT. Normal tissue has an EDWT greater than 5.5 mm and wall thickening greater than 1.5 mm, hibernating tissue has an EDWT greater than 5.5 mm and wall thickening less than 1.5 mm, and infarcted tissue has an EDWT less than 5.5 mm and wall thickening less than 1.5 mm. Arrows indicate myocardial wall thickness at end-diastole (Hdi) and end-systole (Hsi), respectively.

 
The edge detection and review procedure, when performed by experienced readers, takes approximately 15 minutes per case (23). We have previously determined the standard error for interstudy repeatability for determining EF in our laboratory to be 1.9 EF percentage points (Oshinski, JN, unpublished results, 1999).

Quantitative Modeling of Ventricular Function
In this study, a mathematical model was developed that treats the myocardium as a piecewise homogeneous circular isotropic membrane. With this model, ventricular volumes and EF can be determined from area changes in each MR image section from end-systole to end-diastole. The Appendix includes details about the model.

The major assumptions on which the model is based are as follows: (a) the longitudinal strain is unity, (b) all hibernating tissue returns to normal contractility after revascularization, (c) there is no change in contractility of normal tissue after revascularization, (d) there is no regional variation in the contractility of normal tissue, and (e) the left ventricle has a circular cross section in the short axis.

Analysis of EF Data
Three EF values were determined in each subject in the study: a presurgical EF value determined from the presurgical MR image, a predicted postsurgical EF determined with the model, and an actual postsurgical EF determined from the postsurgical MR image. The actual postsurgical EF was compared with the predicted EF determined with the model by using regression analysis. In addition, the actual improvement in EF (actual postsurgical EF minus presurgical EF) was compared with the predicted improvement in EF (predicted postsurgical EF minus presurgical EF) in each subject, again by using regression analysis.

Regional Analysis of Myocardial Segments
EF is a global indicator of left ventricular function. However, the temporal and spatial resolution provided by MR imaging allows regional functional analysis of individual myocardial segments. Therefore, all segments that were classified as hibernating on the prerevascularization MR image were reviewed on the postrevascularization image to evaluate whether they regained function. In addition, a random selection of 52 normal segments were evaluated for any postrevascularization changes.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 
EF Analysis
Eleven patients completed the pre- and postsurgical MR imaging without incident. Improvement in cardiac function was seen in 10 of 11 patients (Fig 3). In five patients, the improvement was greater than the repeatability value for determining EF in our laboratory (1.9 EF percentage points) (Table). If only the five subjects with improved EF greater than the repeatability value were considered, the improvement was significant (P < .05).



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  		Figure 3. Graph shows EF before and after revascularization in the 11 patients studied (each symbol is a separate patient). Improvement was seen in 10 of the 11 patients, and the average improvement was 3.8 EF percentage points.

 

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  		Patient Data and Results of MR Imaging and Predictions with Use of Model

 
In all 11 subjects, the mean prerevascularization EF was 42.4% ± 17.6 (SD), mean actual postrevascularization EF was 46.3% ± 17.7, and the mean predicted postrevascularization EF was 47.5% ± 18.2. Correlation between the actual and predicted postsurgery EF yielded an R value of 0.98. The mean difference between the predicted and actual EF in all subjects was 1.3 EF percentage points (range, –1.1 to 5.5). A Bland-Altman plot (Fig 4) shows that agreement between the predicted EF values and the actual EF values was 1.3 ± 3.4 (2 SDs). No degree of bias was seen in the measurements.



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  		Figure 4. Bland-Altman plot for 11 patients ({blacklozenge}) shows that the agreement between the model-predicted EF values and the actual EF values was 1.3 ± 3.4 (mean ± 2 SDs). No measurement bias on the basis of EF was observed.

 
The average predicted improvement was 5.1 EF percentage points and the actual improvement was 3.8 EF percentage points. Correlation between actual improvement in EF before and after surgery and predicted improvement in EF yielded an R value of 0.83 (Fig 5).



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  		Figure 5. Graph shows actual versus predicted improvement in EF ({Delta}EF) in 10 subjects ({blacklozenge}). Actual {Delta}EF was determined as the actual postrevascularization EF minus prerevascularization EF, and predicted {Delta}EF was determined as the predicted postrevascularization EF minus prerevascularization MR image and the mechanical model. The model can be used accurately to predict changes in EF gained from revascularization for a range of EF values. Correlation was good between the predicted and actual EF changes (R = 0.83), but several patients did not appear to show increased function.

 
Regional Analysis of Hibernating and Normal Segments
In the 11 patients, there were a total of 52 segments classified as hibernating (range, zero to nine per patient). Of these hibernating segments, 29 (55%) recovered function. In the 23 segments that were classified as hibernating but did not recover function, six were adjacent to infarcted regions, two had an EDWT between 5.5 and 8.0 mm, and 10 were both adjacent to infarcted myocardium and had an EDWT between 5.5 and 8.0 mm. This wall thickness suggests viability but was at least 1 SD less than the normal wall thickness as determined in previous studies (12). Hence, in the 23 segments that did not recover function after revascularization, 18 (78%) had wall thickness in the 5.5–8.0-mm range or were adjacent to infarcted myocardium or had both reduced wall thickness and were adjacent to infarcted tissue.

To evaluate the change in function of normal myocardium after revascularization, 52 segments that were classified as normal on the prerevascularization image were selected at random and examined on the postrevascularization image (52 normal segments were chosen to match the number of hibernating segments). None of these segments was next to an infarcted region and none had reduced wall thickness. In these normal segments, wall thickening did not change significantly after revascularization; prerevascularization wall thickening was 0.39 ± 0.11, and postrevascularization wall thickening was 0.40 ± 0.15 (P > .05).

Although there was no change in the contractility in the individual normal segments before and after revascularization, there was a change in left ventricular end-diastolic volume (LVEDV). Prerevascularization LVEDV was 126 ± 39, and postrevascularization LVEDV was 117 ± 32. Although this difference did not reach significance, this 8% difference in LVEDV would cause a change in EF between pre- and postrevascularization images. Since the postrevascularization LVEDV was not known, any change in LVEDV could not be accounted for in the model.


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
 REFERENCES
 
The use of MR imaging in combination with mathematical modeling may be a useful tool in patient treatment. It has been well documented that left ventricular EF is a very strong indicator of long-term outcome in patients with coronary artery disease. Symptomatic patients with an EF greater than 50% have a 4-year survival rate of 92%. This is in sharp contrast to a 4-year survival rate of 57% in patients with an EF less than 35% (24). Prediction of postrevascularization EF would be of great value in assessing which cardiac patients would benefit from surgery and which patients may be conservatively treated. This is particularly true since patients most likely to benefit most from revascularization are often those at greatest risk for major perioperative complications.

The decision of whether to perform surgery becomes increasingly more difficult as the EF worsens, since the surgical risk increases (25). Since definite morbidity, and some mortality, is associated with revascularization procedures, it may be desirable to perform revascularization only in patients who will show marked improvement in cardiac function or patients who will have an increase in EF greater than a threshold value, such as 50%.

Analysis of Segmental Function
A review of all segments that met the criteria for hibernating myocardium indicated that 45% of these segments did not improve function after revascularization. In these nonimproving segments, the majority (70%) were adjacent to infarcted myocardium. This observation is similar to the findings in a sheep model of chronic infarction, in which segments adjacent to infarcted tissue recovered function to only 50% of normal levels (20).

Two possible factors that may be responsible for the lack of function in the hibernating regions adjacent to infarcted tissue are tethering and cellular differences. Mechanical tethering has been shown as the underlying cause of these dysfunctional regions in acute ischemia and has been proposed as a cause in chronic infarction (26,27). The adjacent regions may also be an admixture of viable, nonviable, and differentiated cells that may not be capable of regaining function even after revascularization restores adequate perfusion. A recent study showed that regions of myocardium adjacent to chronic infarction have hypertrophied myocytes that have impaired contractile function (28). It is not clear whether the myocyte hypertrophy is a result of the mechanical tethering, which would imply that both mechanisms are responsible for reduced contractile function.

The finding that the majority (80%) of segments with reduced EDWT (5.5–8.0 mm) did not improve function after revascularization is not surprising if these regions represent regions of subendocardial infarct. Edwards et al (29) showed that ischemia in the subendocardial one-third of the wall was enough to produce a transmural loss of function. Therefore, a subendocardial infarction may prevent recovery of function in the region even if blood flow is restored to normal levels with revascularization (30).

Our finding that 45% of segments classified as hibernating did not recover function after revascularization agrees with the findings of Baer et al (31). They studied 47 patients before and after revascularization with cine MR imaging. By using criteria similar to those used in this study, they found that 40% of segments graded as viable (hibernating) did not recover function after revascularization. In these nonresponding segments, they found the mean EDWT to be significantly lower than in segments that did recover function (6 versus 9 mm). In this study, we also found that wall thickness was decreased in many segments that did not recover function.

It has also been proposed that hibernation is the result of chronic, repeated stunning and that the age of the hibernating tissue may influence its ability to respond to revascularization (16). It may be that old hibernating myocardium may not respond to revascularization because it contains patches of fibrosis and extensive structural degeneration (32). In this study, we had no way to determine the age of the hibernating myocardium, and, hence, some of the adjacent tissue may have been old hibernating tissue that could not respond to revascularization.

MR Imaging Methods for Tissue Classification
The success of the model depends on the ability of MR imaging to identify regions of hibernating myocardium. Glucose imaging with PET FDG is considered the reference technique for identifying hibernating myocardium (33). If a dysfunctional myocardial region has enhanced FDG uptake and reduced perfusion (FDG-blood flow mismatch), it indicates that the region represents hibernating myocardium, as there is preserved glucose metabolism despite decreased resting perfusion. PET studies before revascularization show that 71%–95% of myocardial regions with the FDG-blood flow mismatch improved function after surgery (1,24,33,34). Several studies indicate that MR imaging can be used to identify regions of myocardial hibernation with accuracy near that of PET. Baer et al studied 35 patients with chronic left ventricular dysfunction by using MR imaging and PET (12). With PET as the reference technique, MR imaging had a positive predictive value of 92% for the identification of hibernating myocardium. These studies indicate that MR imaging can be used to identify hibernating tissue at a level comparable to that which can be achieved with PET.

Patients did not undergo stress imaging in this study. Stress imaging is used to increase specificity in identifying regions of hibernating tissue (35). The use of stress imaging to identify hibernating tissue is critical in techniques with which EDWT cannot be accurately assessed, because the response to dobutamine is the only criterion for differentiating between infarcted and hibernating tissue (36). With MR imaging, EDWT can also be used to differentiate infarcted and hibernating tissue in the setting of chronic myocardial infarction. Nevertheless, the use of stress cine MR imaging increases the number of hibernating segments detected (12,36,37). We plan further studies with this model that will include stress cine MR imaging and response to stress as model parameters.

Recently, the use of delayed enhancement imaging after gadopentatate dimeglumine injection to determine tissue viability was demonstrated (15,16). This method is attractive because it allows identification of myocardial viability on a subendocardial basis and has high image contrast between viable and nonviable regions. The combination of delayed enhancement imaging and our model may provide a robust technique that can be applied in a clinical environment.

Limitations of the Study
This study has several limitations. First, the small number of subjects and the small changes in EF make it difficult to statistically assess the accuracy of the model. Findings of studies in our laboratory and of those by Bottini et al indicate that MR imaging can reliably and reproducibly be used to detect EF changes in the 2%–3% range (38). In this study, only five subjects had an improvement in EF that exceeded the repeatability of cine MR imaging for determining EF.

The model used is quite simple. The model treats the myocardium as a single membrane, homogeneous in the thickness direction and stepwise homogeneous in the circumferential direction. The major assumptions regarding contractility are that the longitudinal contractility is unity, there is no regional variation in normal contractility (ie, septal, lateral, or inferior wall thickening is equal in normal regions), and normal myocardium does not change contractility with revascularization. This simplicity allows rapid calculation of EF but may limit the accuracy and cause the observed overestimation in EF predictions. In a larger population with more complex cases involving extensive postinfarction remodeling, the limitations of this simple model may become more evident.

A final limitation of the study is that we were not able to assess the success of the revascularization procedure. Therefore, in some of the patients in whom the model was used to predict substantial functional improvement, which was not seen in the postrevascularization MR image, it might be that revascularization was not successful. In a study by Ragosta et al (30) of patients with chronic left ventricular dysfunction, revascularization was not successful in 16% of the cases assessed after revascularization with thallium single photon emission computed tomography.

Improvements to Model
Several improvements to the model are planned. The first is accounting for the location of hibernating regions. The location of hibernating regions may affect how much function will be recovered. If a hibernating region is located adjacent to an infarcted area, our analysis shows that recovery often is incomplete or nonexistent. Previous animal studies have shown that functional recovery of the adjacent hibernating region will be only 50% of the function seen in normal remote myocardium (20). There also may be some additional information about recovery of function to be gained by defining abnormal segments as akinetic and dyskinetic rather than simply as dyskinetic.

Another variable that may affect the recovery of contractile function after revascularization is the amount of residual EDWT in areas where a subendocardial infarct occurred. In regions where wall thickness is greater than 5.5 mm, but less than normal, there is a reduction in muscle mass, and the amount of recovery would be reduced. A subendocardial infarct with some preserved EDWT may limit left ventricular remodeling, infarct expansion, and subsequent aneurysm formation, even if function does not return after revascularization. A receiver operating characteristic curve analysis on the 5.5-mm EDWT would be useful in determining if this is the optimal cutoff value for predicting functional recovery on the basis of EDWT.

Findings of this preliminary study showed that a simple model of ventricular function in combination with cine MR imaging can be used quantitatively to predict global improvement in EF after revascularization. However, segmental analysis shows reduced functional improvement in myocardial segments adjacent to infarcted myocardium and segments with reduced EDWT. Improvements to the model and implementation of MR imaging methods to better classify the viability of myocardial tissue should improve the prognostic accuracy of the model.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
DISCUSSION
 APPENDIX
REFERENCES
 
Let the lumen cross-sectional areas of the ith sections be designated as Adi and Asi at end-diastole and end-systole, respectively. The myocardial wall thickness of the sections is designated as Hdi and Hsi. The endocardial circumferential dimensions are Pdi and Psi. Circumferential, radial, and longitudinal strains (stretch ratio) of the sections are {lambda}ci, {lambda}ri, and {lambda}li, respectively.

The incompressibility condition applied to the left ventricle dictates:

The results of both in vivo measurements and finite element analysis have shown that the longitudinal strain, {lambda}li, is quite close to unity (39,40). By neglecting the longitudinal deformation:

Since section thickness remains constant in the MR images, Hdi = Hsi = h. Heart volumes at end-diastole and end-systole will be:

and the EF is:

Assuming that the fractions of the normal, hibernating, and infarcted myocardium are {eta}N, {eta}H, and {eta}I, respectively. The circumferential strains are {lambda}N, {lambda}H, and {lambda}I, respectively. The circumferential length at end-systole would be as follows:

Converting the area to an equivalent circular cross section, we have the following equation:

Thus, the area ratio is as follows:

and the volumetric ratio is as follows:

Assuming hibernating myocardium will fully recover function to become normally contracting myocardium, its circumferential strain is equal to that of normal myocardium, {lambda}cHi = {lambda}cNi. In addition, wall thickening, {lambda}ri, is measured on the short-axis MR images. If we replace {lambda}ci with 1/{lambda}ri by using equation (A3), equation (A9) becomes the following equation:

Predicted ejection fraction, EF', for the revascularized myocardium then is as follows:


   ACKNOWLEDGMENTS
 
The authors thank Jack Peterson, PhD, Department of Radiology, Emory University, Atlanta, Ga, for his help with the statistical analysis.


   FOOTNOTES
 
Abbreviations: CABG = coronary artery bypass graft, EDWT = end-diastolic wall thickness, EF = ejection fraction, FDG = fluorodeoxyglucose fluorine 18, LVEDV = left ventricular end-diastolic volume, PTCA = percutaneous transluminal coronary angioplasty

Author contributions: Guarantor of integrity of entire study, J.N.O.; study concepts and design, J.N.O., R.I.P.; literature research, J.N.O.; clinical studies, J.N.O., R.I.P.; data acquisition, J.N.O., R.I.P.; data analysis/interpretation, all authors; statistical analysis, J.N.O.; manuscript preparation, J.N.O.; manuscript definition of intellectual content, R.I.P., J.N.O.; manuscript editing, revision/review, and final version approval, all authors.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 

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