Ann Thorac Surg 2003;76:668-675
© 2003 The Society of Thoracic Surgeons
Original article: cardiovascular
Severe aortic insufficiency and normal systolic function: determining regional left ventricular wall stress by finite-element analysis
Brian P. Cupps, PhDa,
Pavlos Moustakidis, MDa,
Benjamin J. Pomerantz, MDa,
Giridhar Vedala, MDb,
Randall P. Scheri, MDc,
Nicholas T. Kouchoukos, MDa,
Victor G. Davila-Roman, MDb,
Michael K. Pasque, MDa*
a Division of Cardiothoracic Surgery, Department of Surgery, St. Louis, Missouri USA
b Cardiovascular Division, Department of Medicine, Washington University in St. Louis, St. Louis, Missouri USA
c Missouri Baptist Hospital, St. Louis, Missouri, USA
Accepted for publication April 1, 2003.
* Address reprint requests to Dr Pasque, Division of Cardiothoracic Surgery, One Barnes-Jewish Hospital Plaza, Suite 3103 Queeny Tower, St. Louis, MO 63110-1013, USA.
e-mail: pasquem{at}msnotes.wustl.edu
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Abstract
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BACKGROUND: Because severe aortic insufficiency in the setting of preserved left ventricular function is often associated with a long asymptomatic period and unpredictable course on medical therapy, sensitive indices of left ventricular systolic performance are necessary for the optimal direction of therapeutic intervention. Because myocardial wall stress is closely related to both pathologic cardiac remodeling and ultimately to left ventricular decompensation, an accurate description of regional wall stress distribution may improve our ability to clinically manage these patients appropriately. The objectives of this study were (1) to define sensitive, noninvasive indices of left ventricular systolic performance to assist the clinician in the serial evaluation and early detection of increased left ventricular wall stress and, therefore, inadequate left ventricular remodeling and subsequent myocardial decompensation of patients with aortic insufficiency, and (2) to quantify differences in instantaneous global and regional end-systolic wall stress between normal subjects and patients.
METHODS: Magnetic resonance imaging was performed on 23 normal volunteers and 19 patients with aortic insufficiency and normal systolic function (ejection fraction, 57% ± 6%). Finite-element analysis was used to estimate global and regional end-systolic stress.
RESULTS: End-systolic stress was significantly higher in the patient group globally (154,700 ± 31,711 versus 96,781 ± 23,185 dyne/cm2; p < 0.001) and regionally (p < 0.001 in all segments) despite normal systolic function and similar end-systolic pressures.
CONCLUSIONS: End-systolic stress as determined by magnetic resonance imaging and finite-element analysis may have considerable potential as a noninvasive, clinically applicable index of regional left ventricular function that may help in the serial evaluation, optimal management, and early identification of left ventricular decompensation in patients with aortic insufficiency.
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Introduction
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Properly selected symptomatic patients undergoing prosthetic cardiac valve replacement for aortic insufficiency (AI) generally experience relief of clinical symptoms [1, 2]. However, the natural history of chronic aortic regurgitation can often be characterized by a long asymptomatic period with a relatively unpredictable course after the onset of cardiac symptoms, making the optimal timing of aortic valve replacement difficult to determine. Moreover, among the factors responsible for poor postoperative outcomes, myocardial contractile performance appears to be a significant determinant. Accordingly, attempts have been made to identify patients with underlying myocardial dysfunction at an early stage of their illness. Earlier valve replacement may prevent further deterioration.
Aortic insufficiency almost always results in some degree of progressive left ventricular (LV) dilatation and hypertrophy. A precise description of this global and regional remodeling can improve our understanding of the mechanisms involved in this process and possibly influence therapy. Myocardial wall stress, pathologic cardiac remodeling, and LV decompensation are closely related [3], and an accurate determination of ventricular wall stress has considerable potential to characterize and quantify progression and reversal of this remodeling process. However, to date, little attention has been given to using wall stress as a means of serially following patients with chronic AI. Although studies have shown that increased LV end-systolic stress (ESS) has been associated with poor outcomes [4, 5], these studies have been limited by conflicting results, the inability to describe the regional transmural variation of stress, and the need for geometric assumptions used in the calculation of this measurement [6, 7]. Thus, improved, reliable, minimally invasive methods for consistent estimation of LV ESS are needed to determine the clinical utility of this variable in documenting the course of remodeling in this disease state.
Global and regional determination of stress has been significantly enhanced by the application of magnetic resonance imaging (MRI) and sophisticated finite-element (FE) analysis. This investigation uses both MRI and FE analysis to estimate wall stress distribution at rest in patients with chronic AI and normal ejection fraction who were referred for surgical intervention. The purpose of this study was to quantify ESS as a reflection of the degree of LV remodeling in a cohort of patients with AI and to compare these findings to similar studies performed in a group of normal volunteers. These studies are performed in hopes of defining a sensitive, noninvasive index of ventricular function that may help in the early detection of inadequate cardiac remodeling and the resultant LV decompensation. This index can then be correlated to clinical outcomes and subsequently used to assist the clinician in determination of the timing of surgical intervention in patients with chronic AI.
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Patients and methods
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Patient characteristics
The study group consisted of 19 patients (13 men and 6 women) with pure chronic severe AI and normal LV systolic function who were scheduled to undergo aortic valve surgery. The cause of AI was postinflammatory disease in 7 patients, congenital bicuspid aortic valve in 9 patients, Marfan’s syndrome in 1 patient, and prolapse of the noncoronary aortic cusp in 2 patients. The severity of aortic regurgitation was assessed by echocardiography and cardiac catheterization. All had some degree of dilatation of the aortic root and were free of coronary artery or mitral valve disease.
Control group
Twenty-three normal volunteers (12 men and 11 women) served as a control group. 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, Missouri. Informed consent was obtained from all subjects.
Magnetic resonance imaging protocol and image scanning
Imaging was performed in a 1.5-T magnetic resonance scanner (Magnetom Vision; Siemens Medical Systems, Iselin, NJ). A series of scout images was obtained to locate the heart and establish the long-axis and short-axis imaging planes. Subsequently, a set of parallel short-axis imaging planes was obtained at 8-mm intervals beginning at the level of the mitral valve and ending at a short-axis imaging plane that contained only apical myocardium and no left or right ventricular endocardium. An additional set of four long-axis imaging planes was obtained according to the following criteria: (1) orthogonal to the short-axis imaging planes, (2) intersecting the centroid of the left ventricle, and (3) oriented in a radial fashion with 45-degree separation between long-axis imaging planes.
Image acquisition
Image acquisition was synchronized with real-time electrocardiogram at the time of the MRI scanning. The R wave of the electrocardiogram signal was used to activate the MRI scanner to commence scanning. During the actual image data acquisition the subjects were instructed to hold their breath at midexpiration, and a series of images was acquired at 29-ms intervals until the approximate completion of the entire cardiac cycle at each imaging plane. Each cine sequence of images consisted of 12 to 18 images acquired during a period of 25 to 30 seconds. The end-diastolic image was chosen as the first image in sequence (Figs 1A, 1C)
and the end-systolic image was determined by choosing the smallest ventricular size in sequence (Figs 1B, 1D). Data acquisition time was about 35 minutes. Imaging settings were repetition time equal to the cardiac cycle, echo time of 29 ms, excitation angle of 15 degrees, and acquisition matrix of 256 x 256. The field of view was set to 350 x 350 mm2 and 400 x 400 mm2 for the short-axis and long-axis images, respectively.
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Fig 1. (A, C) End-diastolic image as determined by the largest ventricular diameter. (B, D) End-systolic image as determined by choosing the smallest ventricular size in the imaging sequence.
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Left ventricular pressure data
Blood pressure measurements
While they were resting in a supine position, the patients and volunteers were given at least 15 minutes to reach a steady state. Then systolic and diastolic blood pressures were measured during the MRI acquisition every 5 minutes using a Dinamap sphygmomanometric recorder (GE Medical Systems, Waukesha, WI).
Carotid pulse tracing recordings
Carotid pulse tracings were recorded simultaneously with the MRI triggering signals (Fig 2A).
A pencil-shaped Millar micromanometer probe (Micro-tip, pulse transducer SSD-779; Millar Instruments, Inc, Houston, TX) was used to acquire carotid arterial waveforms. The probe was held on the skin for a period of 3 minutes while the patient was in the MRI scanner. Simultaneous electrocardiogram tracings were obtained. Analog data were digitized at a rate of 200 data points per second using customized data-acquisition and manipulation software (LabView 4; National Instruments, Austin, TX).
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Fig 2. (A) Carotid pulse tracings, recorded simultaneously with the magnetic resonance imaging triggering signals. (B) Calculation of left ventricular end-systolic pressure. End-systolic pressure (ESP) was estimated by linear interpolation to the level of the incisura according to the formula shown. (DBP = diastolic blood pressure; SBP = systolic blood pressure.)
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Calculation of left ventricular end-systolic pressure
The method of calculating the end-systolic pressure from calibrated carotid pulse tracings has been described and validated by others [8–10]. Systolic blood pressure was determined by Dinamap measurements. Carotid pulse tracings were then calibrated by assignment of systolic blood pressure to the peak and diastolic blood pressure to the nadir of the tracing. End-systolic pressure was estimated by linear interpolation to the level of the incisura according to the following formula (Fig 2B):
Waveforms were analyzed, and the mean end-systolic pressure value was calculated for each subject.
Finite-element analysis
Image processing
Each of the short-axis imaging planes was illustrated on a four-chamber long-axis end-diastolic image. A line between the apex and the base (middle of the mitral valve) of the heart was drawn, and the distance was measured. The midventricular short-axis plane that was closest to the midpoint of that line was selected for analysis in all subjects. 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.
Mathematical model construction and finite-element solutions
Accurate nonaxisymmetric mathematical models of the LV were created from end-systolic MRI images. Details of model construction have been described previously [11, 12]. A mesh of six quadrilateral elements corresponding to the anterior, anterolateral, posterolateral, posterior, posteroseptal, and anteroseptal myocardial wall was constructed (Fig 3).
Classification and nomenclature followed the recommendations of the American Society of Echocardiography Committee on Standards, and was based on the following considerations: (1) anatomic logic, (2) easy identification of the segments using internal anatomic landmarks, and (3) relationship of the segments to known coronary arterial supply [13]. The models were loaded with pressures derived from the noninvasively obtained Millar carotid artery tracings calibrated using the brachial artery blood pressure cuff measurements (acquired during the MRI), as previously described. Forward FE solutions were obtained by treating the myocardium as an incompressible, linearly elastic, isotropic material using rigid body constraints. After model solution, the average of the maximal principal stress for each element as well as for the entire LV was calculated for each subject. Details of the p-version FE formulation may be found in Szabo and Babuska [14].
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Fig 3. Midventricular representation of the division of the ventricle into elements incorporating the influence of variation of left ventricular wall curvature and thickness, providing an accurate stress estimation on a regional basis by means of finite-element analysis. Left: normal volunteer; right: AI patient. (A = anterior; AL = anterolateral; AS = anteroseptal; P = posterior; PL = posterolateral; PS = posteroseptal.)
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Statistical analysis
Categorical data were reported as percentages and continuous data as mean ± standard deviation. Normal distribution of the data in the different groups was tested using Lilliefors and Shapiro-Wilks’ tests as well as normal probability and detrended normal plots. Homogeneity of variance and sphericity assumptions were tested by Levene’s and Mauchley’s tests, respectively. Comparisons between normal and AI groups were performed by two-tailed unpaired Student’s t test. Pathology-by-sex interaction was tested by two-way between-groups analysis of variance. Within-subjects statistical comparison among the different wall elements was performed with repeated-measures ANOVA. Age was included in the analyses as a fixed covariance. A value of p less than 0.05 was considered significant. Multiple comparisons were corrected with Bonferroni, Scheffé, and Waller-Duncan post hoc procedures. All statistical analyses were performed with Statistica (Statsoft, Tulsa, OK) and SPSS (SPSS Inc, Chicago, IL) statistical packages.
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Results
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Clinical characteristics and hemodynamic data
A total of 42 subjects were enrolled in the study. The AI group (n = 19) consisted of 13 men (68%) and 6 women (32%). The mean age was 42 ± 12 years (range, 19 to 72 years). Five (26%) were asymptomatic (New York Heart Association class I), and 14 (74%) were mildly symptomatic (New York Heart Association class II). The mean LV ejection fraction (determined by cardiac catheterization within 5 days before surgery) was 57% ± 6% (range, 50% to 71%). The control group (n = 23) consisted of 12 (52%) men and 11 women (48%); their mean age was 26 ± 6 years (range, 18 to 38 years). Hemodynamic data of both normal controls and AI patients are shown in Table 1.
There were no statistically significant differences in heart rate, duration of systole, or end-systolic pressures between the two groups.
Maximal principal end-systolic stress
Global analysis
The overall maximal principal ESS was significantly increased (Fig 4A)
in the AI group compared with the normal subjects (154,700 ± 31,711 versus 96,781 ± 23,185 dyne/cm2, p < 0.001). Women in both groups tended to have increased wall stress, although the difference within each group was not significant (p > 0.2; Fig 4B).
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Fig 4. (A) The overall maximal principal end-systolic stress was significantly increased in patients with aortic insufficiency (AI) compared with normal control subjects (154,700 ± 31,711 versus 96,781 ± 23,185 dyne/cm2, *p < 0.001 versus normal). (B) Gender differences between patients with aortic insufficiency and normal control subjects. In this subset analysis, women in both groups tended to have increased wall stress although the difference within each group was not significant (p > 0.05). Results expressed as mean ± standard deviation. (LV = left ventricular.)
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Regional analysis
Regional maximal principal end-systolic wall stress was assessed in each of the six LV regions (Table 2).
The average maximal principal stress in each of the regions was significantly increased in the AI group compared with the normal group (p < 0.001 in all cases), as shown in Figure 5.
Comparison of regional stress distribution among the different LV wall areas within each group did not demonstrate any statistically significant differences among any of the regions within each group (Fig 6). There were also no significant regional differences between men and women in each group when sex was included in the analyses (data not shown). Age as a fixed covariance did not significantly change any of the reported results. In conclusion, our data analysis suggests that the presence of AI was the only significant factor affecting the amount of wall stress, with increased global as well as regional maximal principal stress in the AI group. Figure 7
illustrates two-dimensional midventricular regional stress maps of the myocardium in a normal volunteer and an AI patient.
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Fig 5. Regional wall stress distribution. Average regional maximal principal stress in each of the ventricular elements. Patients with aortic insufficiency (striped bars) differed significantly from normal subjects (open bars) in all regions (p < 0.001).
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Fig 6. Comparison of regional stress distribution among the different left ventricular wall areas. Examination of wall stress distribution among the various left ventricular wall segments did not demonstrate any statistically significant differences among any of the segments within each group (p > 0.05). Results expressed as mean ± standard deviation. (AI = aortic insufficiency; anterior = black squares; anterolateral = open triangles; anteroseptal = open diamonds; posterior = open circles; posterolateral = black triangles; posteroseptal = black circles.)
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Fig 7. Color-coded midventricular regional and transmural end-systolic stress maps of the myocardium in a normal volunteer (A) and a patient with aortic insufficiency (B). Stress was significantly increased in the patient with aortic insufficiency in all six left ventricular wall segments. End-systolic stress was also increased in the endocardium compared with the epicardium in both subjects. (A = anterior; AL = anterolateral; AS = anteroseptal; P = posterior; PL = posterolateral; PS = posteroseptal.)
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Comment
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The surgeon’s decision to proceed with aortic valve replacement in the setting of AI is easily made when significant symptoms, significant LV dilatation, or significant deterioration of LV systolic function has been documented [15–17]. The asymptomatic patient with significant AI and preserved ventricular function, however, represents a more perplexing dilemma with regard to the timing of surgical intervention. No clinically applicable indices currently exist that can reliably signal an early warning of the onset of irreversible pathologic changes in the LV myocardium brought about by the chronic ventricular overload associated with AI. It is those exact indices that we seek in the stress/strain modeling of the LV myocardium. In this regard, the ability to accurately and reproducibly model and interpret the instantaneous LV stress state of the patient referred for aortic valve replacement carries added significance to the cardiothoracic surgeon. Objective assessment of LV architecture and the stress/strain relationship will better predict the progression of the indications for aortic valve replacement.
In chronic AI, wall stresses initially stay relatively close to normal levels (compensated volume overload) [3, 18, 19]. With progression of disease, LV dilatation can exceed the compensatory capacity of myocardial hypertrophy [20–22], resulting in marked increases in ESS and systolic dysfunction. Abnormalities in LV contractility are the predominant indicators for poor surgical outcome [16] and poor long-term prognosis after valve replacement in patients with chronic aortic regurgitation.
Complete characterization of instantaneous LV wall stress is of fundamental importance in assessing myocardial function in patients with AI. Our goal is to develop readily applicable, minimally invasive tools to assist the clinician in characterizing the status of the patient who presents with AI. Our prototype application of these methodologies to characterize regional distribution of wall stress and the pathologic remodeling process throughout the LV myocardium uses noninvasive imaging techniques, carotid tracing recordings, and p-version FE analysis. Because stress cannot be measured directly [23] in the intact, in vivo beating heart we use estimation techniques by numerical methods applied to mathematical models of cardiac geometry. In early studies, the LV was modeled with an assumed geometry [24, 25]. Although these classic analyses have provided insights into LV stress estimation on a global basis, it is now recognized that the complex geometry of the heart requires more sophisticated numerical methods. The introduction of FE techniques has allowed more accurate estimation of regional myocardial stress. Regional variations in geometry, loading, and material properties can be taken into account. This powerful method is probably the best approach for obtaining a realistic quantitative assessment of regional variations in ventricular wall stress [26]. However, applications of FE modeling to study real clinical problems are in their infancy because the FE models have only recently become sophisticated enough to truly represent in vivo mechanical behavior of the myocardium.
Solution of the FE method requires (1) an accurate mathematical description of ventricular topology, (2) a discretization or mesh, (3) boundary conditions including the ventricular pressures and in vivo constraints, and (4) myocardial material properties. The present study describes a mathematical model of the heart constructed from double oblique MRI images using spline curves to represent the endocardial and epicardial heart borders. Magnetic resonance imaging is an excellent imaging modality for generating instantaneous mathematical descriptions of LV geometry because of its high in-plane spatial resolution, excellent contrast between flowing blood and myocardium, noninvasive nature, and the ability to readily obtain images in any orientation (double oblique imaging) at specific intervals during the cardiac cycle. Additionally, the modeling approach used in this study allows a more consistent regional comparison among subjects with significantly different geometry.
Comparison with previous studies
The important role of global wall stress in the characterization of LV decompensation has been evaluated by others. Kumpuris and colleagues [27] calculated ESS in patients with chronic AI and concluded that inappropriate hypertrophy was associated with progressive increases in wall stress that eventually resulted in irreversible cardiac dilatation and failure. Siemienczuk and associates [5] reported that meridional ESS of 86,000 dyne/cm2 or more was associated with progression to aortic valve replacement and the development of LV dysfunction or symptoms after surgery. Greenberg and coworkers [28] examined the association between the exercise ejection fraction response and systolic wall stress and concluded that patients whose ejection fraction falls during exercise had elevated resting LV systolic wall stress, suggesting that LV hypertrophy has not been adequate. In another study, Percy and colleagues [6] 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 associates [4], 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. 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. 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 when nonuniform contraction may result in marked asymmetries in LV shape. Finite-element analysis, on the other hand, can incorporate the influence of variation of LV wall curvature and thickness, and clearly provides a more accurate stress estimation on a regional basis.
Clinical implications
This initial study demonstrates the utility of mathematical modeling in the clinical characterization of LV function in the setting of chronic AI. Mathematical modeling represents a potentially powerful investigative tool for both the researcher and the clinician. Specifically, the use of MRI geometry data sets combined with systolic loads acquired by carotid pulse analysis allow a noninvasive accurate characterization of the ESS of the LV when combined with the capabilities of advanced mathematical modeling and FE analysis. This methodology may allow the clinician to position the asymptomatic or minimally symptomatic patient with severe AI on the spectrum of LV decompensation and thus allow serial reassessment and judicious application of medical and surgical intervention. Patient stratification using these techniques may also allow a more appropriate comparison of the results of both medical and surgical intervention in patients with AI, as well as other patient subsets that are characterized by LV dilatation and abnormal systolic loading.
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Acknowledgments
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The authors gratefully acknowledge Glen W. Foster, RT, for his patience and expertise in performing the imaging experiments. This study was supported by National Institutes of Health grants HL64869 and HL58878 and a Fourjay Foundation grant.
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Abstract
Introduction
