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J Appl Physiol 104: 513-520, 2008. First published November 21, 2007; doi:10.1152/japplphysiol.00848.2007
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Elucidation of spatially distinct compensatory mechanisms in diastole: radial compensation for impaired longitudinal filling in left ventricular hypertrophy

Matt M. Riordan1 and Sándor J. Kovács1,2

1Department of Biomedical Engineering, School of Engineering and Applied Science, Washington University School of Medicine, and 2Department of Internal Medicine, Cardiovascular Biophysics Laboratory, Cardiovascular Division, Washington University, St. Louis, Missouri

Submitted 13 August 2007 ; accepted in final form 20 November 2007


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Cardiac output maintenance is so fundamental that, when regional systolic function is impaired, as during ischemia, nonischemic segments compensate by becoming hypercontractile. By analogy, diastolic compensatory mechanisms that maintain filling volume must exist but remain to be fully elucidated. Viewing filling in spatially distinct (longitudinal, radial) mechanistic terms facilitates elucidation of diastolic compensatory mechanisms. Because impairment of longitudinal (long axis) diastolic function (DF) in left ventricular hypertrophy (LVH) is established, we hypothesized that to maintain filling volume, radial (short-axis) filling function would compensate. In 20 normal left ventricular ejection fraction (LVEF) subjects (10 with LVH, 10 without LVH), we analyzed longitudinal function via Doppler tissue imaging of mitral annular motion and radial function as change in short-axis endocardial dimension via M-mode. The spatial (long axis, short axis) endocardial LV dimensions and their changes allowed assignment of E-wave filling volume into (cylindrical geometry-based) longitudinal and radial components. Despite indistinguishable (P = 0.70) E-wave velocity-time integrals (E-wave filling volume surrogate), systolic stroke volumes, and end-diastolic volumes in the LVH and control groups, longitudinal volume in absolute terms and the percent of E-wave volume accommodated longitudinally were reduced in the LVH group (P < 0.05 and P < 0.01, respectively), whereas the percent of E-wave volume accommodated radially was enhanced (P < 0.01). We conclude that, in normal LVEF (decreased longitudinal volume accommodation) LVH subjects vs. controls, spatially distinct compensatory mechanisms in diastole manifest as increased radial volume accommodation per unit of E-wave filling volume. Assessment of spatially distinct diastolic compensatory mechanisms in other pathophysiological subsets is warranted.

diastolic function; mathematical modeling; radial filling function; longitudinal filling function; hypertrophy; M-mode

ALTHOUGH LEFT VENTRICULAR EJECTION FRACTION (LVEF)-defined systolic function is preserved in left ventricular hypertrophy (LVH), diastolic function (DF) is impaired. Typically, this is characterized by prolonged ventricular relaxation and often increased stiffness, which may be attributed to myofiber disarray, altered calcium currents, subendocardial ischemia, or interstitial fibrosis (4, 27). There is also evidence of regional diastolic wall motion nonuniformity in the hypertrophic left ventricle (LV) (3, 29). Consistent with impaired ventricular relaxation in LVH, Doppler tissue imaging (DTI) based peak annular (i.e., E'-wave) velocity (14, 23) and annular excursion (23, 40) are known to be reduced in LVH relative to normotensive controls despite the E-wave velocity-time integral (VTI; early rapid filling volume surrogate) being similar between the groups (14). MRI has provided additional insight into volume accommodation in diastole, particularly when viewed in spatial terms such as longitudinal vs. radial epicardial displacement (9). Decreased annular longitudinal excursion is also plainly discernible on MRI cine loops of LVH hearts. Since the LV seeks to maintain cardiac output in accordance with varying demand and because heart rates were similar between controls and LVH subjects in the aforementioned study showing similar E-wave VTIs in LVH and control subjects (14), LV stroke volume must be maintained in LVH. Based on the reported impairment of longitudinal filling function as quantified by DTI-determined E' in concert with the reported maintenance of global filling function as quantified by E-wave VTI, we hypothesized that radial LV filling function must be augmented in LVH as a compensatory mechanism to maintain early (i.e., E-wave) filling volume.

Cardiac anatomy and modeling.   To facilitate volumetric and kinematic analyses, the complex geometry of left heart shape in diastole has been simplified and modeled as a thick-walled cylinder with variable outer (epicardial) dimension that can be separated into upper (left atrial) and lower (LV) compartments by the mitral annulus (25) and that, in keeping with the nearly constant volume attribute of the four-chambered heart (6, 22), can also facilitate modeling of reciprocation of atrial and ventricular volumes during filling (22). As transmitral flow commences in diastole, the annulus moves longitudinally upward toward the atrium. Due to tissue and blood incompressibility, as the annulus rises, the wall thins, and the endocardium is simultaneously displaced radially outward toward the epicardium (1), thereby widening the endocardial chamber dimension. If the LV chamber volume (i.e., the endocardial surface) is expressed in terms of this idealized cylindrical geometry as:

Formula 1(1)
where V is the LV chamber volume and r and L denote inner (endocardial) LV radius and length, respectively, then the rate of filling (volume accommodation) of the LV can be expressed as:

Formula 2(2)
This expression highlights the value of characterizing global LV chamber function in terms of spatial (radial, longitudinal) degrees of freedom for volume accommodation. The first term is the rate of longitudinal displacement. This is routinely measured via DTI as the E'- and A'-waves of the mitral annulus. The second term denotes the rate of radial endocardial displacement. This expression assumes no azimuthal wall motion dependence (i.e., the chamber is assumed to expand symmetrically about the long axis of the LV), which is a reasonable approximation for most normal chambers (15).

Alternatively, Eq. 2 can be expressed, for a brief interval of time dt, as:

Formula 3(3)
This expresses diastolic filling as the sum of longitudinal (first term) and radial (second term) components and thus allows assessment of their relative magnitudes. Furthermore, based on this cylindrical approximation of the real chamber, the amount of longitudinal and radial volume accommodation per unit filling volume can be determined and compared between healthy and pathophysiological hearts. Although during filling the short and long axes change simultaneously, for ease of visualization in temporal and spatial terms, contributions to filling volume can be considered in two ways: lengthening of the ventricle at a constant (end-systolic) radius followed by a radial expansion of the ventricle at a constant (diastatic) length, or a radial expansion at a constant (end-systolic) length followed by a lengthening at a constant (diastatic) radius (Fig. 1). The first, lengthening followed by radial expansion, can be expressed as:

Formula 4(4)
where the subscripts ES and DIAST denote end-systole and diastasis, respectively. The second way of quantifying longitudinal and radial volumetric contributions to filling, radial expansion followed by longitudinal lengthening, can be expressed similarly but with a change in the subscripts in Eq. 4. Of course, LV filling does not actually occur via sequential lengthening and widening of the chamber, but it is nevertheless conceptually advantageous and convenient in the sense of volumetric accounting to express filling volume accommodation in this manner.


Figure 1
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  		Fig. 1. Alternative longitudinal and radial E-wave volume accommodation mechanisms expressed in terms of an idealized cylindrical left ventricle (LV) chamber (endocardial dimension) geometry. A: atrially directed annular displacement (lengthening) at a constant end-systolic chamber radius followed by radial expansion at a constant diastatic length. B: radial expansion at a constant end-systolic length followed by atrially directed annular motion at a constant diastatic chamber radius. Broken lines denote initial (end-systolic) LV dimensions; solid lines denote final (diastatic) LV dimensions. Statistical significance is maintained for the percent longitudinal vs. percent radial components between controls and LV hypertrophy (LVH) subjects independent of whether A or B is chosen as the conceptual sequence for filling. See text for details.

 
Since radial and longitudinal expansion are the dominant spatial modes by which filling volume is accommodated (we assume azimuthal variation is not significant), we hypothesized that, in keeping with Eq. 3, radial function must compensate to some extent for the known impaired longitudinal function in LVH (14, 23, 40) to maintain filling (and stroke) volume. To test this hypothesis, we assessed the cylindrical model-based contributions of longitudinal and radial function during early rapid filling to global chamber function in subjects with LVH and age-matched controls without LVH. By quantifying the percent longitudinal and radial contributions per unit of LV early filling volume, we sought to demonstrate the existence of radial compensatory mechanisms during filling and to determine the extent to which compensation occurs in LVH.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Patient selection.   Previously acquired data resident in the Cardiovascular Biophysics Laboratory Database, consisting of simultaneous high-fidelity micromanometric hemodynamic and echocardiographic data, were analyzed. Twenty datasets (10 with LVH, 10 without LVH) (10, 25) were selected. The datasets include simultaneous high-fidelity (Millar) LV pressure, Doppler echocardiographic recordings of transmitral flow, DTI recordings of the lateral mitral annulus, and M-mode recordings of LV short-axis myocardial motion at or just above the level of the papillary muscles. Subjects' ages ranged from 39 to 79 yr (53.8 ± 10.2 yr). Inclusion criteria for all subjects were ejection fraction of ≥55%, normal sinus rhythm, clearly discernible E- and A-waves, E'- and A'-waves, and lateral and septal endocardial wall contours on M-mode, normal valvular function, and normal heart size. Subjects with co-morbidities including, but not limited to, significant wall motion abnormalities on ventriculography, active ischemia, cardiomyopathy, or congestive heart failure were excluded. None of the controls exhibited LVH, as defined by a LV mass index computed with the adjusted Devereux equation (13) using the American Society of Echocardiography convention of >130 g/m2 in men and >110 g/m2 in women (13), whereas, in addition to elevated LV mass index, the LVH subjects all had a history of (treated) hypertension, a tendency toward increased relative wall thickness, and a tendency toward supranormal LVEF. None of the subjects had active ischemia at the time of data acquisition, although five LVH subjects and three non-LVH controls had coronary artery disease as defined by >50% narrowing in one or more vessels. All of the controls were normotensive and had LV end-diastolic pressure of ≤18 mmHg. Elective cardiac catheterization was performed in all subjects at the request of their referring physician on the basis of suspected coronary artery disease. All subjects gave informed consent in accordance with a protocol approved by the Washington University Medical Center Human Studies Committee before data acquisition.

Data acquisition.   The simultaneous echocardiography-catheterization data acquisition method has been previously detailed (2, 25). Briefly, immediately before cardiac catheterization, a full two-dimensional echo Doppler examination is performed in the catheterization laboratory. After advancement of the micromanometric 6-Fr pigtail catheter (model SPC-474A, Millar Instruments, Houston, TX) into the LV, transmitral Doppler images were obtained by a sonographer using a standard clinical imaging system (Acuson, Mountain View, CA) in accordance with American Society of Echocardiography criteria (20). With the patient supine, apical four-chamber views were obtained with the sample volume gated at 5 mm and placed at the tips of the mitral valve leaflets. The insonification direction was oriented orthogonal to the valve plane by using color Doppler as a guide. The wall filter was set at 125 or 250 Hz with the baseline adjusted to take advantage of the full height of the cathode-ray tube display, and the velocity scale was adjusted to exploit the dynamic range of the output without aliasing. Simultaneous limb lead II ECG was displayed on all images, which were captured simultaneously with LV and aortic root pressure and recorded continuously onto magneto-optical disk. DTI was performed with the sample volume gated at 2.5–5 mm for most subjects and positioned at the lateral aspect of the mitral annulus, whereas DTI for four subjects was performed with larger sample volumes (8, 9, 12, and 25 mm). Previous DTI studies have employed sample volume gate widths ranging from 2 to 10 mm (19, 26, 28, 34). However, based on our own experience, the most consistent DTI images are achieved with a gate width of 2.5 mm. M-mode imaging was performed in the parasternal short-axis view at the mid-LV level. All images were digitized offline via a dedicated custom video capture station.

Doppler analysis.   For each subject, 4–5 cardiac cycles from transmitral Doppler and DTI of the lateral mitral annulus were selected, clipped, and converted to 8-bit grayscale images with Paint Shop Pro 7 (Jasc Software, Minnetonka, MN). Peak E- and E'-wave velocities and durations were measured manually for each subject and averaged. E- and E'-wave VTIs were computed by approximating these waveforms as triangles, and VTIs of any oscillations following the E'-wave (i.e., E''-wave, E'''-wave, etc.) (24, 32, 43) were also taken into account to properly determine total annular excursion during early filling. Transmitral flow- and annular motion-derived indexes were averaged across all analyzed beats for each subject. LV end-systolic and diastatic lengths were determined from apical four-chamber views.

M-mode analysis.   For each subject, 2–5 cardiac cycles from M-mode images providing adequate visualization of the endocardial contours of the septal and lateral wall were selected, clipped, and converted to 8-bit grayscale images. Chamber diameters at end-systole (defined as the time during the cardiac cycle at which the minimum short-axis diameter occurred) and diastasis were measured and converted into radii by dividing the diameter by 2 (see Fig. 2). Lateral wall thinning from end systole to diastasis was also determined by subtracting wall thickness at diastasis from wall thickness at end systole using established methods (42). Epicardial displacement during early filling was measured along the lateral LV wall as previously detailed (33).


Figure 2
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  		Fig. 2. Short-axis M-mode images at mid-LV for a typical non-LVH control (LVMI = 129 g/m2, end-diastolic posterior wall thickness = 0.8 cm) (A) and LVH subject (LVMI = 144 g/m2, end-diastolic posterior wall thickness = 1.2 cm) (B) illustrating short-axis (radial) dimensions at end-systole and diastasis. Despite a smaller E-wave VTI in this LVH subject vs. control (7.1 ± 0.8 vs. 10.2 ± 0.5 cm) and reduced annular excursion for the LVH subject vs. control (13 ± 1 vs. 18 ± 1 mm), radial expansion was similar (18 ± 0 and 18 ± 2 mm in the LVH subject and control, respectively) for the beats shown. Notably, the LVH subject also exhibited similar wall thinning compared with control (3 ± 1 vs. 3 ± 1 mm) for these beats, even when normalized for end-systolic wall thickness (0.21 ± 0.04 vs. 0.21 ± 0.04). Tick marks on ordinate denote 20 mm; tick marks on abscissa denote 200 ms. See text for details.

 
Hemodynamic analysis.   Mean arterial pressure was determined from the aortic root pressure, and LV end-diastolic pressure was determined from the simultaneous LV pressure tracing (3). The time constant of isovolumic relaxation ({tau}) was determined from the pressure phase plane [i.e., the plot of the first derivative of LV pressure (dP/dt) vs. pressure (P)] by computing the inverse of the slope of the linear fit from near minimum dP/dt to just before mitral valve opening (12) and averaged over five consecutive beats. LV end-systolic volume and end-diastolic volume were determined from suitably calibrated ventriculographic images.

Statistical analysis.   All continuous variables are displayed as means ± SD. Statistical differences between the LVH and control group with respect to these variables were determined by two-tailed ANOVA. Statistical differences between groups with respect to nominal variables (i.e., gender) were determined by the two-tailed z-test for proportions. All statistical calculations were performed in Microsoft Excel 97 (Microsoft, Redmond, WA) with statistical significance set at the P < 0.05 level.


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Demographics and selected clinical variables are provided in Table 1. The groups did not differ significantly with respect to age, height, weight, gender, heart rate, LV end-diastolic volume, LV end-systolic volume, or stroke volume, although LVEF, LV end-diastolic pressure, and {tau} were elevated in the LVH group. Afterload, as defined by mean arterial pressure, was also significantly greater in the LVH group, as expected.


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  		Table 1. Demographics and clinical variables

 
Echocardiographic data are presented in Table 2. Despite indistinguishable (P = 0.70) E-wave VTIs, the LVH subjects had significantly reduced annular excursion (P < 0.01) during early filling compared with the controls. Importantly, despite similar end-systolic and diastatic chamber radii and lengths, the percent of E-wave volume accommodated longitudinally (%Vlong) was significantly lower in the LVH subjects (8.8 ± 2.5% vs. 13.0 ± 3.4%; P < 0.01), making the percent of E-wave volume accommodated radially (%Vrad) higher in these subjects vs. the controls (91.2 ± 2.5% vs. 87.0 ± 3.4%; P < 0.01). Notably, and as anticipated, the sequence in which cylindrical model-based longitudinal and radial volume accommodation was accounted for (i.e., if longitudinal lengthening followed rather than preceded radial expansion) had no effect on the statistical significance of this finding other than changing the absolute values of %Vlong (22.9 ± 5.7% vs. 28.8 ± 4.7%; P < 0.01 in the LVH and control groups, respectively) and %Vrad (77.1 ± 5.7% vs. 71.2 ± 4.7%; P < 0.01 in the LVH and control groups, respectively).


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  		Table 2. Global and segmental geometric and volumetric measures

 
Longitudinally accommodated volume (Vlong) was also significantly lower in the LVH group. Interestingly, despite the decreased annular excursion during the E-wave in the LVH subjects, these subjects had a nearly identical extent of radial expansion vs. the controls. However, further analysis shows that the similar radial expansion between groups is achieved through two distinct mechanisms. Wall thinning (lateral wall) and wall thinning normalized to end-systolic wall thickness were significantly greater in the LVH group, whereas epicardial/pericardial displacement along the lateral wall during early filling was significantly greater in the control group. Additionally, the epicardial radii at end-systole and diastasis were larger in the LVH group than in the controls, and epicardial area (i.e., the short-axis cross-sectional area circumscribed by the epicardium based on the epicardial radius measured at the lateral wall) increased from end-systole to diastasis by slightly more in the LVH subjects vs. the controls (14 vs. 12 mm2, respectively; P = not significant).


   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
This study sought to elucidate and characterize the physiological mechanisms by which normal LVEF LVH hearts maintain similar early filling and end-diastolic volumes compared with non-LVH controls. Previous work has focused on understanding systolic compensatory mechanisms of pathological hearts. These include increased LV contractility as manifested by enhanced systolic torsion in diabetes (11, 18) and in LVH (5) and increased radial systolic strain (17) in the diabetic heart. In addition, short-axis systolic shortening has been shown to increase with aging (39) and in LVH (40) as long-axis shortening decreases. The hypothesized and observed spatially distinct diastolic compensatory mechanisms in LVH have not been previously characterized.

As expected based on MRI cine loops of LV long-axis motion during the cardiac cycle and previous findings regarding annular velocities obtained via DTI (14, 23, 40), annular excursion, reflecting LV long-axis lengthening, was reduced in the LVH subjects during early filling. Because we observed essentially indistinguishable E-wave-derived filling volumes in LVH subjects and controls, the portion of E-wave filling volume accommodated longitudinally must therefore be reduced as well.

Although the finding of reduced longitudinal volume accommodation in LVH is noteworthy, and is in accordance with findings of reduced annular excursion in LVH reported by other investigators (23, 40), the key finding of this study is that, per unit of E-wave filling volume, a greater percentage is accommodated via radial than via longitudinal endocardial motion in LVH subjects vs. controls based on a simplified cylindrical approximation of LV chamber geometry. To our knowledge, characterization of spatially distinct compensatory mechanisms during diastole has not been previously demonstrated in any pathological state such as LVH. This finding complements the known systolic compensatory mechanisms known to exist in LVH as manifested by preserved or enhanced LVEF (5, 40) and provides justification for elucidation of diastolic compensatory mechanisms in other pathophysiological states, including mechanistic features such as fiber orientation variation and azimuthal dependence.

The similar radial expansion values reported for the LVH and control subjects may appear counterintuitive at first since reduced lengthening of the LV chamber from annular motion might be expected to reduce short-axis expansion of the chamber due to the fact that longitudinal and radial motion are coupled via conservation of myocardial tissue and (near) myocardial incompressibility. However, a greater short-axis cross-sectional wall area would increase the extent of radial endocardial expansion per unit of annular displacement, and the radial expansion of the septum and LV epicardium also modulate the relationship between annular motion and radial endocardial expansion. In fact, the larger epicardial radii at end-systole and diastasis in the LVH group and the slightly greater increase in epicardial area from end-systole to diastasis in these subjects would contribute to maintaining endocardial radial expansion in the LVH subjects despite reduced annular displacement. In addition, the LV has been shown to exhibit increased systolic torsion in response to elevated afterload, which promotes concentric remodeling (5). Increased systolic torsion and the associated increased extent of untwisting during isovolumic relaxation and early filling, which has been demonstrated in LVs subjected to high afterloads (31, 35, 36), could facilitate radial expansion of the chamber independently of chamber lengthening as the myofibers, which may have reoriented (relative to normal) as a result of the remodeling associated with the hypertrophic process, slide past each other during untwisting. In other words, untwisting during early filling could result in radial endocardial expansion concomitant with epicardial/septal expansion without much lengthening in the long-axis direction. Specifically, the results of this study show that the LVH hearts exhibited a greater extent of (lateral) wall thinning, even when normalized to end-systolic wall thickness, than the controls. Based on previous work, it is reasonable to attribute the increased wall thinning in LVH to increased untwisting of the LV during early filling, although we note that torsion was not explicitly measured as part of this study.

Although it is true that, given the same longitudinal annular displacement and invoking conservation of myocardial mass, a thin-walled (control) cylinder will exhibit less radial endocardial motion and radial volume accommodation than a thick-walled (LVH) cylinder with the same initial (end-systolic) dimensions due to the greater short-axis cross-sectional area of the thick-walled cylinder, this disparity in radial endocardial motion can be mitigated by the initial conditions (i.e., end-systolic length and endocardial and epicardial radii) as well as the epicardial displacement of the LV during early filling, making the radial endocardial displacement in the thin- and thick-walled ventricles comparable. The fact that both longitudinal annular displacement during early filling and end-systolic radius were less in the LVH subjects vs. the controls [1.0 vs. 1.3 cm (P < 0.05) and 1.3 vs. 1.6 cm (P = not significant), respectively] in this study, coupled with the finding that radial epicardial displacement in the controls exceeded that in the LVH subjects (7 vs. 5 mm; P < 0.01), mitigates against the purely geometric effect of a thicker LV wall in the LVH subjects and results in more comparable radial displacements and volume accommodation during early filling in each group.

Similarly, maintenance of indistinguishable E-wave filling volumes (i.e., VTIE) in the face of significantly reduced annular excursion and similar radial expansion during early filling in LVH may appear counterintuitive. However, it can be understood in terms of the relative roles of longitudinal and radial accommodation of filling volume. If, for simplicity, the LV chamber is modeled as a cylinder and its volume is expressed as in Eq. 1, then LV volume change during early filling can be expressed in terms of longitudinal and radial components as in Eq. 3. Because both the longitudinal and radial volume terms include chamber radius, whereas only the radial term includes chamber length, the volume change (i.e., dV) of the cylinder is more sensitive to a given percent change in radius vs. the same percent change in length. Furthermore, the fact that the coefficient of the radial term (i.e., 2{pi}rL) is numerically much greater than the coefficient of the longitudinal term (i.e., {pi}r2), based on the normal range of LV lengths and radii measured in this study, implies that most of the volume accommodation is driven by radial expansion of the chamber. Therefore, a reduction in annular excursion (i.e., chamber lengthening) in the LVH heart has a lesser effect on early filling volume.

Although the focus of this study was to determine the relative longitudinal and radial contributions to LV early diastolic filling volume, we are aware that other investigators have attempted to determine systolic longitudinal and radial contributions to LV stroke volume. We emphasize that investigation of systolic function involves a longitudinal and radial volume accounting system for the entire stroke volume (E-wave + A-wave), whereas our diastolic volumetric accounting system is only concerned with longitudinal and radial accommodation of early filling (E-wave) volume rather than the entire stroke volume. Therefore, our results should not be directly compared with the results by other investigators whose focus was stroke volume during systole.

Depending on the study, the reported longitudinal contribution to stroke volume (via apically directed excursion of the mitral annulus) previously reported has ranged from 18–19% (7) to 82% (16). However, the substantial range in these reported values stems largely from how longitudinal and radial function were defined. Using echocardiography, Toumanidis et al. (37) computed the contribution of annular excursion to stroke volume from annular cross-sectional area and displacement from end-systole to end-diastole, finding that the truncated cone outlined by annular motion during systole accounted for ~53% of stroke volume in a healthy control group of subjects younger than those included in this study. This value was later found to be too large by a factor of 3 due to omission of the denominator in the truncated cone formula, making the correct value ~18% (8). Although this value is approximately equal to the mean longitudinal volumetric contribution of our two alternative conceptualizations for filling volume accommodation, we note that annular excursion volume in their study was based on annular cross-sectional area from end-diastole to end-systole, whereas the present study defined the longitudinal volumetric contribution based on the end-systolic radius of the mid-LV, resulting in somewhat smaller cross-sectional areas. Emilsson et al. (16), also using a cylindrical model of the LV, attributed 82% of stroke volume to annular excursion as measured by M-mode echocardiography. However, they grouped the volumetric contributions of annular excursion and simultaneous radial wall thickening together to arrive at this proportion, whereas the radial contribution was confined to inward motion of the epicardium. Carlsson et al. (9), using MRI, calculated that the portion of the stroke volume due to displacement of the atrioventricular plane was 60%. However, they used epicardial rather than endocardial dimensions to calculate the volumetric contribution of atrioventricular plane displacement. Moreover, cross-sectional area at end-diastole was used to determine the longitudinal volumetric contribution. Each of these computational approaches would naturally lead to higher estimates of the longitudinal contribution to stroke volume than the value determined for the controls in the present study. We underscore that the longitudinal and radial volumetric accounting approach employed in this study explicitly depends only on endocardial dimension measurements but implicitly includes the epicardial displacements due to conservation of myocardial mass. In other words, Eq. 1 does not explicitly depend on measurement of epicardial dimension or motion.

Carlhäll et al. (7) used a method similar to that of the present study to determine the contribution of annular excursion to both early filling and stroke volume. Using transesophageal echocardiography, they tracked mitral annular motion and shape (using 72 triangular elements) at 100 time points during the cardiac cycle. LV volume was determined by tracing the endocardial border in six long-axis planes at 10 time points during the cardiac cycle. The portion of stroke volume due to apical annular excursion was determined to be 19%, which agrees well with the corrected value of Toumanidis et al. (8) and is in line with the longitudinal contributions to filling volume determined in the present study. In fact, this value is nearly identical to the average longitudinal contribution of the two spatial conceptualizations of filling volume accommodation illustrated in Fig. 1. However, we note that Carlhäll et al. stated recently (8) that their study (7) did not study "true longitudinal function," and, therefore, our longitudinal percent contributions to early filling volume should not be extrapolated to stroke volume and compared with theirs. Still, it is noteworthy that Carlhäll et al. determined that the portion of early filling volume accommodated (longitudinally) by annular excursion was ~13%, which agrees with the 13% calculated using the cylinder approximation in the present study (Table 2). However, we note that our value was obtained without consideration of annular or short-axis cross-sectional area change during filling, although measuring cross-sectional area at the mid-LV level rather than annular cross-sectional area, which may be slightly smaller, may have compensated for this. Nevertheless, this agreement between studies gives us confidence that, based on the manner in which longitudinal and radial filling function were defined, our reported relative contributions of longitudinal and radial function to early filling volume are both physiologically reasonable and independently reproducible.

The demonstration of diastolic compensation in the hypertrophic heart in this study, which complements previous reports of systolic compensation in LVH and other pathologies (5, 11, 17, 18, 40) via enhanced inotropy, has intriguing possibilities for the characterization of additional compensatory mechanisms yet to be elucidated. For example, variation in myofiber orientation has been demonstrated using diffusion tensor MRI in human subjects with hypertrophic cardiomyopathy (38), suggesting that pathological hearts may remodel by altering their three-dimensional fiber architecture to preserve cardiac output. Subcellular compensation in the pathological heart has also been demonstrated; the stiffer (N2B) isoform of the intracellular protein titin is upregulated whereas the more compliant isoform (N2BA) is downregulated in response to pressure overload (40), although this differential expression is reversed in coronary artery disease (30).

Limitations.   Due to the nature of M-mode imaging, short-axis M-mode data is available only along the direction of the echo beam. Therefore, the resulting images reflect the motion of the points at which the echo beam intersects the lateral and septal LV walls and, as such, do not convey potential azimuthal variation in the short-axis dimension or variation in radial motion from that measured at the mid-LV level. Although LVH hearts may exhibit different LV chamber geometry/shape than controls, which could affect our reported values for longitudinal and radial volume accommodation, previous studies have utilized a cylindrical model for the LV in the setting of hypertrophy in addition to the normal LV (15, 21). Furthermore, despite the fact that radial wall motion and short-axis dimensions were only measured at the mid-LV level, they were measured at this anatomic level for all subjects in each group and should provide an acceptable and consistent estimate of radial volume accommodation. To the extent that actual chamber geometry differs from a cylinder, it is possible that our geometric approximation would provide somewhat different absolute measurements relative to a truncated ellipsoid of revolution, for example. However, the relative spatial components (radial, longitudinal) would be preserved since these would differ by fixed geometric coefficients. To verify this claim, we performed numerical experiments and constructed (figuratively) a cylinder with the same end-systolic dimensions as the average values for the control group and a half prolate ellipsoid with an equivalent volume (by multiplying both the cylindrical end-systolic length and radius by the same factor). After equivalent annular excursions and radial expansions were applied in each geometric model, the %Vlong and %Vrad values calculated for each model differed by ~1%, demonstrating that our choice of idealized ventricular geometry does not materially affect the results concerning percent longitudinal and radial contributions to filling volume determined in this study.

Unambiguous identification of the endocardium on short-axis M-mode images is often difficult due to the presence of endocardial trabeculations. However, every effort was made to be as consistent as possible in identifying the lateral and septal endocardium for chamber diameter and wall thickness measurements in accordance with the guidelines outlined by Weyman (42). We expect that the measured chamber dimensions and wall thicknesses, as well as values determined from them, do not represent a significant source of error. Furthermore, since issues related to endocardial definition existed in both the control and LVH groups, they should not affect our reported differences between the groups.

Similarly, DTI of the lateral aspect of the annulus does not account for motion at other annular sites. For instance, it is known that the excursion of the septal annulus during early filling is generally less than that of the lateral annulus. Although this may affect the absolute values of the reported longitudinal and radial volumes slightly, it should not materially affect our findings regarding percent longitudinal and radial volume accommodation and group differences.

The volumetric analyses were based on linear measures from M-mode echocardiography and DTI. Although other forms of cardiac imaging, including MRI, computed tomography, and three- and four-dimensional echocardiography, have been employed for determining chamber volume, use of these modalities is not yet mainstream cardiac practice. We underscore that our main intent was to introduce the concept of spatially distinct compensatory mechanisms in diastole and to provide a clinical example that validates the hypothesized mechanisms (LVH). Future studies employing more sophisticated imaging modalities are expected to confirm and refine our findings and should be useful both for uncovering the global and regional physiological mechanisms responsible for preservation of early filling volume and potentially extending our findings to additional pathophysiological states.

In conclusion, to validate the hypothesis that spatially distinct (longitudinal, radial) diastolic compensatory mechanisms exist, we quantified longitudinal and radial accommodation of E-wave filling volume in LVH subjects and non-LVH controls. Because E-wave VTIs, stroke volumes, and end-diastolic volumes were statistically indistinguishable between groups, whereas annular excursion (longitudinal volume accommodation) was impaired in the LVH group (P < 0.01), we hypothesized that radial filling function must be augmented to compensate for impaired longitudinal filling function. Based on a simplified geometric model of LV endocardial shape, we found that, per unit of early filling volume, longitudinal accommodation was reduced (P < 0.01), whereas radial accommodation was increased (P < 0.01). These findings indicate that radial filling compensates for impaired longitudinal filling during the E-wave in LVH and extends our understanding of systolic compensatory mechanisms into diastole. Future work directed at fully elucidating these spatially distinct physiological compensatory mechanisms in terms of cellular and fiber direction-based remodeling mechanisms in LVH and other pathophysiological states is warranted.


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 ABSTRACT
 METHODS
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 DISCUSSION
 GRANTS
ACKNOWLEDGMENTS
 REFERENCES
 
This study was supported in part by the Heartland Affiliate of the American Heart Association (Dallas, TX), the Whitaker Foundation (Roslyn, VA), the National Heart, Lung, and Blood Institute (HL-54179, HL-04023, Bethesda, MD), the Alan A. and Edith L. Wolff Charitable Trust (St Louis, MO), and the Barnes-Jewish Hospital Foundation.


   ACKNOWLEDGMENTS
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 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
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 ACKNOWLEDGMENTS
REFERENCES
 
We acknowledge the contribution of our sonographer, Peggy A. Brown, in expert echocardiographic data acquisition.


   FOOTNOTES
 

Address for reprint requests and other correspondence: S. J. Kovács, Cardiovascular Biophysics Laboratory, Washington Univ. Medical Center, Box 8086, 660 South Euclid Ave., St. Louis, MO 63110 (e-mail: sjk{at}wuphys.wustl.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
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 ABSTRACT
 METHODS
 RESULTS
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 ACKNOWLEDGMENTS
 REFERENCES
 

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