INTRODUCTION

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LEFT VENTRICULAR (LV) afterload has generally been assessed by using wall stress calculated in the meridional (WS_M) or circumferential direction, neglecting the effect of radial forces. Fiber stress, as discussed by Arts et al. (3), Mirsky (19), and Regen (23, 24), takes into consideration the radially directed forces or forces generated within the wall that oppose fiber shortening. Fiber stress is, therefore, a more accurate measure of the force generated by, and acting on, the contracting myofiber. The degree to which wall stress misrepresents the forces acting on the myofiber is related to the wall thickness-to-chamber dimension (h/D) or mass-to-volume ratio (mass/volume). Hence, LV afterload is most likely understated by conventional wall stress measurements in thick-walled ventricles and overstated in dilated, thin-walled ventricles.

The magnitude of this misrepresentation is unknown, but it may have important implications in the assessment of afterload in patients with congenital or acquired heart disease known to have abnormal LV mass or abnormal mass/volume. When this is the case, it is likely that analyses of myocardial mechanics that rely on wall stress as an index of afterload are misleading. Failure of wall stress to take into account radial forces opposing fiber shortening might also contribute to the observed but incompletely explained relationship between afterload and age previously reported in normal children (8), particularly in view of the colinearity of age, wall thickness, chamber dimension, and blood pressure.

To further investigate these hypotheses, we evaluated end-systolic wall stress (WS_es) and fiber stress (FS_es) in normal subjects and in four groups of patients with varying h/D and LV mass.

	METHODS

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Normal population. Analysis of myocardial mechanics was performed in 305 normal subjects, varying in age from 10 days to 35 yr. This population has been described previously (8, 14), including the criteria for the definition of normal and a detailed description of the population. Each of the normal controls was free of evidence of heart disease, was taking no cardioactive medications, and had no history of hypertension or other systemic disorder. Data derived in these normal subjects were used to determine the normal range for each of the echocardiographic parameters and to describe age- and body surface area-related trends.

Patient population. The 52 patients with congenital aortic stenosis were aged 6-39 yr (median 12 yr) and had a Doppler-derived maximum instantaneous gradient ranging from 50 to 140 mmHg (median 76 mmHg). The 57 patients in the coarctation group were aged 1.2-32 yr (median 12 yr) and were examined 1.2-22 yr after their coarctation repair. The upper-to-lower extremity systolic blood pressure gradient ranged from 19 to 60 mmHg and was >15 mmHg in 24 patients (42%). The 51 patients in the anthracycline group were aged 3-21 yr (median 8 yr) and had received anthracycline for treatment of childhood acute lymphocytic leukemia. The 51 with severe valvar regurgitation were aged 9-24 yr (median 15 yr). Twenty-six (51%) had lesions of the aortic valve, 17 (33%) the mitral valve, and 8 (16%) both. The etiology was rheumatic in 44 (86%), aortic valve prolapse in 4 (8%), and mitral valve prolapse in 3 (6%).

Data collection. The method of echocardiographic data collection has been described in detail elsewhere (6-8). Patients <3 yr of age were sedated with 50-100 mg/kg chloral hydrate as needed. Commercially available echocardiographic equipment (Hewlett-Packard 77020, Sonos 1000 or Sonos 1500 Cardiac Imager, or Acuson 128) and transducers appropriate for body size and habitus were used for imaging. Complete two-dimensional and Doppler examinations were performed to identify additional abnormalities and to assess LV regional wall motion. High-speed (100 mm/s), hard-copy, two-dimensional echocardiographic directed M-mode recordings of the LV short axis were obtained simultaneously with an electrocardiogram, phonocardiogram, and indirect carotid artery pulse tracing (or axillary artery pulse tracing in patients <4 yr of age). Systolic and diastolic blood pressures were obtained as the average of three automated cuff recordings using a Dinamap 845 Vital Signs monitor (Criticon).

Data analysis. The indirect arterial pulse trace, the left and right ventricular endocardial borders of the septum, and the endocardial and epicardial borders of the LV posterior wall were hand digitized from the M-mode echocardiogram with the use of a microcomputer-based digitizing system and custom software (8). The pulse transmission delay was corrected by electronically aligning the dicrotic notch of the pulse tracing with the first high-frequency component of aortic valve closure on the phonocardiogram. Continuous LV internal diameter and posterior wall thickness averaged over three to six cycles were obtained from these data. Pressure during ejection was calculated by interpolation of the indirect pulse trace using the cuff blood pressure (7). From these continuous data, LV WS_M (in g/cm²) was calculated throughout ejection according to the formula of Grossman et al. (15)
where P is pressure (in mmHg), D is the LV internal chamber dimension (in cm), and h is the posterior wall thickness (in cm). Meridional fiber stress (FS_M) was calculated according to the formula of Regen (24)
where b_m is the midwall minor semiaxis expressed as
End systole was defined as the time of aortic valve closure, and end diastole as the time of the maximal LV dimension. LV mass was calculated using the formula of Devereux and Reichek (12)
where D_ed is end-diastolic D, h_ed is end-diastolic h, and S_ed is the end-diastolic septal thickness. If S_ed could not be accurately measured, LV mass was calculated by assuming septal and posterior wall thickness to be equal. h/D was calculated as the LV end-diastolic posterior wall thickness divided by the LV end-diastolic dimension.

Calculation of Z scores relative to normal population. LV dimensions, wall thickness, and mass are known to vary with body surface area. As previously reported, WS_es varies in an age-related fashion (8). To permit comparison of patients of different ages and body size, each of these variables was expressed as a Z score relative to its nonlinear distribution with respect to age or body surface area in the normal population. The Z score, or normal deviate, represents the number of SDs from the normal population mean value. Thus Z scores of 1, 0, and +1 indicate values 1 SD below normal population mean, the population mean, and 1 SD above the population mean, respectively.

Statistical analysis. t-Tests were used to compare dichotomous variables. Differences between WS_es and FS_es Z scores were further investigated by two-way repeated measures analysis of variance, comparing each patient group with the normal population and treating the afterload index (WS_es and FS_es) as the repeated variable. Linear and nonlinear regression were used to examine the interrelations between continuous variables. Results are presented as means ± 1 SD, unless otherwise specified. A P value <0.05 was considered statistically significant.

	RESULTS

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Normal population. FS_es was found to increase nonlinearly with age (Fig. 1) in a fashion similar to the relationship of WS_es to age that our laboratory has previously reported (8). Although there was a close correlation between WS_es and FS_es (r = 0.96, P < 0.001, Fig. 2A), the residuals of this regression correlated inversely with h/D (r = 0.51, P < 0.001, Fig. 2B), indicating that LV geometry contributed to the disparity between these two indexes of afterload.

View larger version (23K): [in this window] [in a new window]   Fig. 1.   Normal population. End-systolic wall stress (WSes; A) and end-systolic fiber stress (FSes; B) vs. age. SEE, standard error of estimate. Lines are population means ± 2 SDs.

View larger version (26K): [in this window] [in a new window]   Fig. 2.   Normal population. A: WSes vs. FSes. B: residuals of WSes-FSes regression vs. the end-diastolic posterior wall thickness-to-chamber dimension ratio.

Patient population. The four patient groups had widely varying values of LV mass and h/D (Table 1). Those with congenital aortic stenosis demonstrated marked concentric hypertrophy, whereas patients who had undergone coarctation repair demonstrated an increase in posterior wall thickness with increased LV mass. Although h/D in the coarctation group was normal overall, the Z score was >1 in 15 (26%) and >2 in 9 patients (16%). In the anthracycline-treated group, LV geometry was characterized by decreased wall thickness, decreased h/D, and decreased mass. Abnormalities in those with valvar regurgitation were more extreme; despite a marked decrease in h/D, LV mass was increased to a greater degree than in those with congenital aortic stenosis.

View larger version (18K): [in this window] [in a new window]   Fig. 3.   WSes and FSes Z scores for each of the 4 patient groups. Middle horizontal lines indicate the median, boxes encompass the 25th to 75th percentiles, and error bars are the upper and lower adjacent values. The shaded area indicates the normal range (Z score: 2 to +2). AS, valvar aortic stenosis; CoA, coarctation repair; ANTH, anthracycline treated; AR/MR, aortic and/or mitral regurgitation. * P < 0.05 compared with normal.

View larger version (22K): [in this window] [in a new window]   Fig. 4.   Difference between WSes and FSes Z scores vs. the end-diastolic wall thickness-to-chamber dimension ratio.

	DISCUSSION

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Recent reports have highlighted the superiority of midwall fiber shortening as a descriptor of myocardial performance in ventricles with elevated mass/volume, where endocardial indexes of shortening may be elevated (10, 11, 14, 22, 26-28). This report indicates that similar sources of bias are problematic when afterload is assessed. Wall stress, the total force in a given direction per unit area of myocardium normal to that direction, is the most commonly used index of afterload applied to the analysis of ventricular mechanics. Nevertheless, as has been pointed out by numerous authors, wall stress does not fully account for forces acting at the fiber level, because pressure in the wall transmitted from the cavity or exerted by more external fibers is included as a negative component in the calculation. Neither does it express the recoil response to stretch (3, 4, 9, 23, 24). Because of this, wall stress misrepresents afterload at the average or midwall fiber in absolute terms, and the magnitude of misrepresentation is amplified in ventricles with abnormal mass/volume characteristics. Fiber stress, which is the fiber-pulling force per unit area, accounts for the effects of ambient pressure and is, therefore, a more accurate measure of the force generated by the individual myofibrils.

A number of formulas have been used to calculate fiber stress. The method used in the present report derives average or midwall fiber stress; the minor axis (b_m) is defined as the logarithmic means of the cavity and outer semiaxes (24). Mirsky and colleagues (1, 20) have utilized a similar measure of fiber stress, which they referred to as incremental stress or stress difference, obtained by subtracting radial stress from circumferential wall stress or WS_M. Both of these methods illustrate the dependence of fiber stress on intramural pressure, wherein the fiber thickening that by necessity accompanies fiber shortening is opposed by intramural pressure. These derivations are similar in concept to the fiber stress formulas derived by Arts et al. (2, 3) and are based on a cylindrical model with varying nonradial fiber orientations similar to those of the free wall and septum of the LV. Subsequent modification by Regen and colleague (24, 25) to account for midwall volume results in a formula similar to that used in the present analysis.

In accordance with theory, we found significant differences between FS_es and WS_es. These differences were related to h/D and support the theoretical prediction that the magnitude of underestimation of afterload by wall stress is greater when wall thickness is disproportionate to chamber size (24). The magnitude of the difference between WS_es and FS_es represents a clinically important source of error in analyses of the mechanical behavior of ventricles with abnormal mass/volume characteristics. For example, previous investigators have reported WS_es to be significantly below normal in patients late after coarctation repair (17, 21). This finding is difficult to explain in that afterload is a major determinant of hypertrophy, acting as a feedback variable in a servo-controlled mechanism that can be described as "stress normalization" (18). The finding of persistently reduced afterload implies an excessive hypertrophic response. Although we also found WS_es to be persistently below normal late after coarctation repair, myocardial afterload was normal when assessed as FS_es, a measure of stress that fully accounts for the fiber shortening force per unit area. These findings suggest that previous reports of low afterload may well reflect the failure of WS_es to accurately reflect intrinsic pulling forces, particularly in patients with concentric hypertrophy. Both WS_es and FS_es were reduced in the aortic stenosis group. Reduced afterload is more readily explained in the context of aortic stenosis in which there is a marked discrepancy between peak pressure and end-systolic pressure; hypertrophy is driven by peak fiber stress so that end-systolic stress is low (5). Nevertheless, WS_es significantly overestimated the magnitude of this reduction in afterload.

In contrast, WS_es overestimated afterload in patients with severe valvar regurgitation who had a reduced h/D. Artifactual elevation of WS_es is of particular importance when evaluation of contractility is based on stress-adjusted indexes, such as the stress-velocity and stress-shortening relationships. Under these circumstances, impaired contractile function may be incorrectly classified as normal. This is of concern in a patient group in which contractile function is an important determinant of outcome (13, 29, 30).

Finally, when afterload is normal, wall stress and fiber stress are similar, as was seen in the group of patients treated with anthracycline. In addition, FS_es manifests the same pattern of age modulation in the normal population that has been previously defined for WS_es (8).

Limitations. The present study uses one-dimensional measurement of LV wall thickness and chamber dimension and assumes homogenous regional midwall fiber stress. The relationship between circumferential wall stress and fiber stress may be different from that between the respective meridional components, particularly when the long axis-to-short axis ratio is abnormal. Furthermore, there may be significant regional heterogeneity in fiber stress within the ventricle, as has been demonstrated with three-dimensional models using magnetic resonance imaging (16).

Conclusions. Wall stress significantly misrepresents fiber stress in ventricles with abnormal mass/volume characteristics. This misrepresentation is particularly important when wall stress forms the basis of an evaluation of cardiac contractility, such as stress-shortening and stress-velocity relationships.