Ann Thorac Surg 2006;82:840-846
© 2006 The Society of Thoracic Surgeons
Original article: Cardiovascular
Left Ventricular Wall Stress in Patients With Severe Aortic Insufficiency With Finite Element Analysis
Jason R. Wollmuth, MDa,
Douglas R. Bree, MDa,
Brian P. Cupps, PhDa,
Marc D. Krock, MDa,
Benjamin J. Pomerantz, MDa,
Robert P. Pasquea,
Analyn Howells, RNa,
Nader Moazami, MDa,
Nicholas T. Kouchoukos, MDb,
Michael K. Pasque, MDa,*
a Divisions of Cardiothoracic Surgery, Department of Surgery, and Cardiology, Department of Medicine, Washington University School of Medicine, Barnes-Jewish Hospital, St. Louis, Missouri
b Missouri Baptist Hospital, St. Louis, Missouri
Accepted for publication March 30, 2006.
* Address correspondence to Dr Michael Pasque, One Barnes-Jewish Hospital Plaza, Suite 3103 Queeny Tower, St. Louis, MO 63110-1013 (Email: pasquem{at}wustl.edu).
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Abstract
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BACKGROUND: Severe aortic insufficiency (AI) with preserved left ventricular (LV) function may be associated with a long asymptomatic period and unpredictable course on medical therapy. Since myocardial wall stress is closely related to both pathologic cardiac remodeling and ultimately to LV decompensation, a more accurate description of regional wall stress may improve our ability to appropriately manage these patients. The objective of this study was to define differences in instantaneous global and regional three-dimensional end-systolic maximum principal stress (ESS) between normal patients and patients with AI, both before and after aortic valve replacement (AVR) using magnetic resonance imaging (MRI) and finite element analysis (FEA).
METHODS: Magnetic resonance imaging was performed on 20 normal volunteers and 14 patients with moderate to severe AI with normal systolic function (ejection fraction: 57 ± 0.6) before and after AVR. Finite element analysis was utilized to estimate global and regional ESS.
RESULTS: Both global (p < 0.001) and regional (p < 0.001 in all segments) ESS were significantly higher in the preoperative AI patients when compared with their postoperative values and normal controls. Postoperative ESS was significantly lower than the normal controls (p = 0.002).
CONCLUSIONS: Three-dimensional regional and global end-systolic LV wall stress can be determined by MRI and finite element analysis. Values of ESS in patients with chronic AI were elevated prior to AVR and normalized after AVR. This method may have considerable potential as a noninvasive, clinically applicable index of regional LV geometry and function that may help with the serial evaluation of patients with AI.
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Introduction
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Patients with chronic aortic insufficiency (AI) experience myocardial remodeling leading to an alteration in myocardial wall stress. Increased left ventricular (LV) end-systolic stress (ESS) has generally been associated with worse clinical outcomes [1–3]. Unfortunately, the clinical assessment of ESS has been limited by the geometric assumptions that are necessary when echocardiographic tools are utilized to assess ventricular dimensions and by a lack of consistency in regional anatomic definition [4–6]. Magnetic resonance imaging (MRI)-based finite element analysis may overcome these limitations and aid in the early identification of patients who develop an increase in ESS prior to significant changes in ejection fraction (EF) or ventricular dimensions. More precise knowledge of stress-state evolution in this disease process may allow identification of progression of irreversible LV dysfunction in otherwise asymptomatic patients [7].
In the present study we used MRI with finite element analysis (FEA) to determine three-dimensional (3D) full LVESS in patients with chronic AI who were asymptomatic or minimally symptomatic and had normal EF, prior to and after aortic valve replacement (AVR). These results were compared with a large control group of normal volunteers with normal myocardial function. It was hypothesized that 3D MRI with FEA could be utilized to obtain consistent regional and global ESS values that would be elevated in patients with chronic AI prior to AVR. We further hypothesized that the values assessed in preoperative AVR patients with chronic AI would normalize postoperatively.
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Patients and Methods
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Patient Population
Patients referred for AVR to Washington University were screened for inclusion. Patients with pacemakers, claustrophobia, or a history of ventricular tachycardia, atrial fibrillation, or other arrhythmias were excluded from the study. Patients with other significant cardiac problems, such as coronary artery disease, LV dysfunction, or other valvular abnormalities, were excluded. The study group consisted of 14 patients (12 men and 2 women) with isolated chronic severe AI and normal LV systolic function (EF > 0.50). Standard transthoracic echocardiography was used to assess the severity of AI and all patients underwent cardiac catheterization prior to AVR. Baseline MRI images were performed less than one month before AVR and follow-up was scheduled to be approximately two years after AVR (mean 28 ± 11 months after AVR). Three patients enrolled into the study had preoperative scans but were lost to follow-up and were not included in this analysis. In addition, one patient was not included because of significant ectopy during scanning that resulted in poor image quality. The etiology of the AI was secondary to a bicuspid aortic valve (eight patients), rheumatic disease (three patients), and aortic root dilating-aneurysm (three patients). Four patients underwent a Ross procedure, five patients had AVR with bovine pericardial bioprosthetic valves, and five patients had AVR with St. Jude mechanical valves (St. Jude Medical, Inc, St. Paul, MN).
The control group consisted of 20 normal volunteers. All of these subjects had normal physical and electrocardiographic findings and no history of heart disease. The study was approved by the Human Studies Committee at Washington University, St. Louis, MO. Informed consent was obtained from all subjects.
MRI Protocol
Imaging was performed with the subjects at rest in a 1.5 Tesla MR scanner (Magnetom Vision, Siemens Medical Systems, Iselin, NJ). A full description of the imaging protocol has been previously published [8]. To summarize, a series of parallel short axis images and an additional set of long axis images intersecting the centroid of the LV were obtained. Image acquisition was synchronized with electrocardiogram monitoring. Total MRI data acquisition time was about 60 minutes.
Left Ventricular Pressure Data
Noninvasive blood pressure measurements and carotid pulse tracings were obtained in all subjects according to our previously published methods [8]. The method of calculating the end-systolic pressure from calibrated carotid pulse tracings has been described and validated by others [8–11].
Finite Element Analysis
Image processing
The end-diastolic image was the first image obtained and the image with the smallest LV chamber area was selected as the end-systolic geometry corresponding to the dicrotic notch on the carotid pulse waveform. The most basal image was the first image in which the LV endocardial and epicardial boundaries were visible from diastole to end-systole. The most apical was the image that had visible endocardium at end-diastole but not at end-systole.
Mathematical Model Construction and Finite Element Solutions
Mathematical models of the LV were created from end-systolic images [12, 13]. Endocardial and epicardial boundaries were manually identified on each of the short axis images (Fig 1A). Contours from the individual images were used to construct a spline surface representation of the endocardial and epicardial surfaces (Fig 1B). Utilizing the anterior and posterior junction points between the right ventricular free wall and LV septum as anatomic markers, a mesh of twelve hexahedral elements (anterior, anterolateral, posterolateral, posterior, posteroseptal, and anteroseptal myocardial walls at the base and mid-LV regions) and four pentahedral elements (anterior, lateral, posterior, and septal at the apex) was constructed (Fig 2). Classification and nomenclature followed the recommendations of the American Society of Echocardiography Committee on Standards. The models were loaded with pressures derived from the noninvasively obtained Millar carotid artery tracings (Millar Instruments, Houston, TX) calibrated using the brachial artery blood pressure cuff measurements (acquired during the MRI), as previously described. Forward FE solutions were obtained treating the myocardium as a linearly elastic, isotropic material using elastic constraints. After model solution, the average values of maximum principal stress for each element, as well as for the entire model, were calculated for each subject. Details of the p-version FE formulation may be found in Szabo and Babuska [14].
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Fig 1. (A) Spline curve representations of the endocardial and epicardial boundaries from short axis images and (B) the resulting spline surfaces.
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Fig 2. Finite element model of the left ventricle (LV). Models are subdivided into six elements representing the anteroseptal (AS), anterior (A), anterolateral (AL), posterolateral (PL), posterior (P), and posteroseptal (PS) regions. In the apical region, the model has four segments, with the AS and PS constituting the apical septal segment and the AL and PL constituting the apical lateral segment.
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Left Ventricular Geometric Measurements
A line between the apex and the base (middle of the mitral valve) of the heart was drawn and the distance was measured. The short axis plane that was closest to the midpoint of that line was selected for measurement of LV end-systolic and end-diastolic diameter. Endocardial and epicardial boundaries on all short axis images were identified at end-diastole and end-systole. The endocardial boundaries were used to calculate the area of each short axis image and this was translated to volumetric data summing up all the area measurements and multiplying this by the spacing between slices. Left ventricular EF (LVEF) was calculated as left ventricular end-diastolic volume–left ventricular end systolic volume/left ventricular end-diastolic volume ([LVEDV–LVESV]/LVEDV). Stroke volume was calculated as LVEDV–LVESV and cardiac output was obtained by multiplying stroke volume and average heart rate during scanning. Ventricular mass was determined at end-diastole by epicardial LVEDV–endocardial LVEDV multiplied by 1.05 g/cm2.
Statistical Analysis
Categoric data were reported as percentages and continuous data as mean ± standard deviation. Statistical analysis was carried out using SPSS software (SPSS Inc, Chicago, IL). Ventricular volumes, hemodynamic parameters, and ventricular diameters were compared using a Student t test. Stress values from the three groups were compared using analysis of variance with post-hoc testing using the Fischer least significant difference test. In all cases a p value less than 0.05 was considered significant.
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Results
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Clinical Characteristics and Hemodynamic Data
The AI group (n = 14) consisted of 12 men (86%) and 2 women (14%). The mean age was 42 ± 12 years (range, 22 to 79). Seven (50%) were asymptomatic (New York Heart Association [NYHA] class I) and 6 (43%) were mildly symptomatic (NYHA class II) with one patient in NYHA class III. The mean LVEF determined by cardiac catheterization within 5 days before surgery was 57 ± 6 (range, 50 to 71) and the mean LVEF by echocardiography was 54 ± 6%. The control group (n = 20) consisted of 8 (40%) men and 12 women (60%); their mean age was 29 ± 8 (range, 20 to 51) years. There were no statistically significant differences in end-systolic pressures between the control group and the study group, either preoperatively or postoperatively. As expected in patients with severe AI, diastolic blood pressure significantly increased after surgery from 66.9 ± 9.8 mm Hg to 82.7 ± 8.9 mm Hg (p < 0.002). There was no significant difference in systolic blood pressure (p = 0.11) or heart rate (P = 0.39) before and after surgery. The AI group had a significantly higher preoperative systolic blood pressure (136 ± 21 mm Hg vs 119 ± 10 mm Hg, p = 0.02) and postoperative diastolic BP (83 ± 9 mm Hg vs 72 ± 10 mm Hg, p = 0.003) compared with the control group. All other hemodynamic parameters were not significantly different.
Left Ventricular Measurements
Preoperatively, patients with AI had an average echocardiographic EF of 54.1 ± 0.084 and an average left ventricular end-diastolic diameter (LVEDD) of 6.7 ± 1.0 cm. Preoperative MRI-obtained end-diastolic and end-systolic diameters were 6.0 ± 1.0 cm and 4.3 ± 0.7 cm, respectively. Preoperatively, the AI patients had an average EF of 56.0 ± 0.07 by MRI, which was not significantly different than preoperative echo values (p = 0.54). As expected, LV dimensions, end-diastolic volume, and mass all decreased significantly after surgery (Table 1). Despite the normalization of LV dimensions, mass remained significantly greater in the AI group postoperatively compared with the normal controls (199.0 ± 41.7 vs 140.4 ± 41.2, p < 0.001), presumably secondary to LV hypertrophy in the AI group. A nonsignificant increase in EF to 60.7 ± 0.076 was seen after surgery (p = 0.097). Stroke volume and cardiac output both decreased significantly after AVR (Table 1).
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Table 1. Mean Values of Hemodynamic and Left Ventricular Geometric and Performance Measures Before and After Aortic Valve Replacement
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End-Systolic Stress
Global analysis
The overall ESS was significantly increased in the preoperative AI group compared with the normal control group (1.06E+05 ± 1.65E+04 vs 9.12E+04 ± 1.72E+04 dynes/cm2; p < 0.026). After AVR, stress decreased significantly compared with preoperative values (7.08E+04 ± 2.03E+04, p < 0.001). In addition, postoperative stress was significantly lower than normal controls (7.08E+04 ± 2.03E+04 vs 9.12E+04 ± 1.72E+04, p = 0.002).
Regional analysis
End-systolic maximum principal stress was assessed in each of the 16 LV regions. In addition, comparison was made between the six basal regions, the six mid-LV regions, and the four apical regions. As expected, ESS increased from the apex to the base of the heart in all three study groups (Fig 3). The results of the regional analysis were similar to those for the global analysis and are shown in Figures 4,5, and 6.
In the basal regions (Fig 4), ESS in the preoperative group was significantly greater than the normal controls in all but the anterolateral region (p = 0.135 in the anterolateral region, p < 0.05 for others). Stress values decreased significantly after AVR in all regions (p < 0.001) compared with preoperative stress values. In addition, postoperative stress values were less than normal controls in all but the posterior region (p = 0.066 for the posterior region, p < 0.05 for others).
In the mid-LV regions (Fig 5), ESS in the preop AI group was significantly greater than in normals in the anterior and posterolateral regions only. After AVR, ESS in the AI patients was significantly less than the preoperative values in all regions (p 
0.002) and less than the normal controls in five of six regions (p 0.05). In the four apical regions (Fig 6), postoperative ESS was significantly less than both the AI preoperative and normal ESS in all regions (p 0.001). There were no differences between the AI preoperative group and the normal controls. Figure 7
illustrates 3D ventricular regional stress maps of the myocardium in a normal volunteer (A), an AI patient preoperative (B), and postoperative (C).
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Fig 7. Three-dimensional ventricular regional stress maps of the myocardium in a normal volunteer (A) and an aortic insufficiency patient preoperative (B) and postoperative (C). Areas of red indicate increased maximal principal stress and are prominent in the preoperative example (B) and demonstrate a return to near-normal values in the postoperative example (C). (A = anterior; AL = anterolateral; AS = anteroseptal; P = posterior; PL = posterolateral; PS = posteroseptal.)
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Comment
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This study documents the prospective acquisition of full LV three-dimensional regional and global ESS in patients with chronic AI, utilizing FEA applied to highly accurate MRI-based, patient-specific ventricular geometry. This enhanced technique demonstrated that LV end-systolic wall stress in patients with chronic AI was elevated prior to AVR and returned to values lower than healthy volunteers after AVR. The important role of global wall stress in the characterization of LV decompensation has been evaluated by others utilizing less exacting techniques[1, 3, 15]. Kumpuris and colleagues [3] calculated ESS in patients with chronic AI and concluded that inadequate hypertrophy was associated with progressive increases in wall stress that eventually resulted in irreversible cardiac dilatation and failure. Siemienczuk and colleagues [15] reported that meridional ESS of 8.60E+04 dynes/cm2 or more was associated with progression to AVR and the development of LV dysfunction or symptoms after surgery. Percy and colleagues [5] addressed the prognostic significance of LV wall stress for outcome prediction in asymptomatic patients with AI. The authors reported that ESS was a significant discriminator between patients that remained unchanged clinically at follow-up and those that progressed to decompensated LV volume overload or death related to aortic valve disease. A similar conclusion was reached by Gaasch and colleagues [2] who demonstrated that patients with chronic AI and high systolic wall stress preoperatively, had a higher incidence of postoperative heart failure and were less likely to achieve substantial reduction in LV size after surgery. Likewise, patients in our study with a higher ESS preoperatively had a trend toward larger postoperative LVEDD and left ventricular end-systolic dimension (LVESD). Greenberg and colleagues [1] showed the association between the exercise EF response and systolic wall stress and concluded that patients whose EF falls during exercise had elevated resting LV systolic wall stress, suggesting that LV hypertrophy had not been adequate. Furthermore, the three groups studied by Greenberg and colleagues had similar, near normal end-systolic dimensions and abnormal ESS, suggesting the possibility that ESS might in fact be independent of dimensions at some time in the spectrum of disease. Taking the composite of the literature on ESS in chronic AI patients, elevated ESS appears to predict a poorer mechanical and clinical prognosis that may be independent of the customary parameters such as LV systolic function and LV dimensions.
Although data from these studies address the significant role of global wall stress in the pathophysiology and progression of the disease, the ESS calculations were based on simplified spherical geometric shape assumptions [6]. Such an approach is limited in its accuracy because idealized geometry models are unable to account for regional changes in curvature and regional variation in wall thickness. These regional inaccuracies are heightened at end-systole where nonuniform contraction may result in marked asymmetries in LV shape. This may be of particular importance in dilatation of the ventricle associated with volume-overload secondary to valvular regurgitation, where changes from an elliptical shape to a more spherical, globular geometry are well known. The complex geometry of the heart requires highly accurate geometric assessment combined with more sophisticated numerical methods. The MRI-based finite element analysis can incorporate the influence of variation of LV wall curvature and thickness, and thus provides more accurate stress estimation on a regional basis. Magnetic resonance imaging also offers accurate determination of LV volumes and performance measures as well as myocardial strain. In addition, dobutamine MRI can also be performed to determine change in ESS from rest to exercise, which has also been shown to be predictive of outcome in patients with AI [4].
The results of this study represent the continuing evolution of this MRI modality to image, accurately, the ventricle. We have expanded upon the two-dimensional analysis previously published [8] to now provide a 3D assessment of the entire LV with the results presented in this study. The presented data serve as a companion to our previously published finding in this group of patients that post-AVR strain values were significantly decreased from both pre-AVR and normal controls. Interestingly, the strain values in the pre-AVR cohort and the normal controls showed no significant difference [16]. Therefore, to summarize both studies, patients with chronic AI were shown to have increased wall stress in the setting of ventricular dilatation, but normal values for strain in the preoperative period. In the postoperative period the AI patients had significantly reduced strain values, and wall stress values that decreased to less than the normal controls in the setting of normalization of ventricular chamber size. Further study is necessary to ascertain the reason for these findings, but these observations may implicate a change in loading conditions from a volume-overload state to a pressure-overload state induced from the residual gradient across the valve prosthesis.
Our finding that postoperative ESS values were significantly lower than healthy volunteers deserves special comment. Our results in chronic AI patients demonstrated an increase in LV mass over healthy volunteers, suggestive of LV hypertrophy, which did not return to normal after AVR. This residual LV hypertrophy after AVR could have contributed to the decreased wall stress documented in the postoperative population.
Study Limitations
While this study demonstrates that abnormal preoperative stress values decrease postoperatively, it lacks a true longitudinal clinical comparison with ESS values over a more complete spectrum of AI patients, especially before an increase in LV dimensions. This study was done on a limited subset of chronic AI patients, which represents a narrow observational window into the natural course of this disease. We are currently evaluating patients being treated medically in an attempt to more accurately define the early natural history of ESS in patients with severe AI.
The use of finite element analysis to characterize LV wall stress during systole is limited by the lack of an accurate characterization of systolic ventricular myocardial material properties. The material properties of myocardium during diastole have been quantified previously [17]; however, diastolic material property descriptions obtained during passive ventricular filling are not directly applicable to the actively contracting myocardium. Ventricular systole simply cannot be characterized as a passive state where loads are acting on the myocardium with resulting deformation. Instead, we must be satisfied to hold as a constant the material property description in the setting of changing patient-specific end-systolic load and LV geometry to obtain a "snapshot" of the influence of ventricular geometry at a single point at the end of contraction. In this regard, the primary advantage of MRI imaging with FEA is the ability to incorporate highly accurate regional geometry information into the solution. Assumptions of uniform geometric shape limit other stress quantification methodologies as LV geometry undergoes changes in sphericity and may be irregular and asymmetrical in the setting of pathological influences, such as AI, that induce abnormal ventricular remodeling. Although currently limited by an inadequate systolic material property description, our methodology nonetheless provides clinically meaningful information regarding the influences of geometry changes on wall stress before and after such interventions as AVR in the setting of chronic AI. Clearly, a dilated ventricle with thinned walls and globular shape will have higher wall stress (all other things being equal) than the ventricle with normal chamber dimensions and elliptical geometry. We know of no other clinically applicable modality that is capable of "quantifying" the influence of the critical geometric changes that characterize pathological ventricular remodeling. The accurate characterization of true LV wall stress throughout the active state of ventricular systolic contraction awaits the development of an active contraction stress formulation.
Clinical Implications
When combined with the capabilities of advanced mathematical modeling and finite element analysis, the use of MRI-geometry data sets with systolic loads acquired by carotid pulse analysis allows a noninvasive, highly accurate characterization of global and regional end-systolic stress of the LV. Patient stratification using these techniques may allow a more appropriate comparison of the results of both medical and surgical intervention in patients with AI, as well as other patient subsets (eg, ischemic cardiomyopathic patients) that are characterized by LV dilatation and abnormal systolic loading.
The decision of the clinician to proceed with AV in the setting of aortic insufficiency is more easily made when significant symptoms, significant LV dilatation or significant deterioration of LV systolic function has been documented [18–20]. The asymptomatic or minimally symptomatic patient with significant AI and preserved ventricular function, however, continues to represent a more perplexing dilemma in regard to the timing of surgical intervention. No clinically applicable indices currently exist which can reliably signal the onset of irreversibility in the pathological changes in the LV myocardium. Elevation of ESS in AI patients may represent an early indication of decompensation of the myocardium prior to changes in conventional measurements of LV size and performance or the onset of symptoms. In this regard, the ability to accurately and reproducibly model the instantaneous LV stress state of the patient with severe AI using MRI techniques may be helpful in the clinical characterization of these patients.
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Acknowledgments
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We would like to thank Richard Scheussler, PhD, for his assistance with the statistical analysis and Glenn Foster, RRT, and Rich Nagel, RRT, for their assistance in acquiring the data used in this manuscript. This research was supported by NIH Grant RO1 HL64869.
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Abstract
Introduction
p < 0.05 vs aortic insufficiency [AI] postoperative; 
= normal; 
= preoperative AI; 
= postoperative AI.)
