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(Circulation Research. 2002;90:66.)
© 2002 American Heart Association, Inc.

Cellular Biology

Alterations of Myocardial Dynamic Stiffness Implicating Abnormal Crossbridge Function in Human Mitral Regurgitation Heart Failure

L.A. Mulieri, W. Barnes, B.J. Leavitt, F.P. Ittleman, M.M. LeWinter, N.R. Alpert, D.W. Maughan

From the Departments of Molecular Physiology & Biophysics (L.A.M., W.B., N.R.A., D.W.M.) and Surgery (B.J.L., F.P.I.) and the Cardiology Unit (M.M.L.W.), University of Vermont, Burlington Vt.

Correspondence to Louis A. Mulieri, PhD, Dept of Molecular Physiology and Biophysics, Given Building, University of Vermont, Burlington, VT 05405-0068. E-mail mulieri{at}physiology.med.uvm.edu

	Abstract

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Mitral regurgitation (MR) causes ventricular dilation, a blunted myocardial force-frequency relation, and increased crossbridge force-time integral (FTI). The mechanism of FTI increase was investigated using sinusoidal length perturbation analysis to compare crossbridge function in skinned left ventricular (LV) epicardial muscle strips from 5 MR and 5 nonfailing (NF) control hearts. Myocardial dynamic stiffness was modeled as 3 parallel viscoelastic processes. Two processes characterize intermediate crossbridge cycle transitions, B (work producing) and C (work absorbing) with Q₁₀s of 4 to 5. No significant differences in moduli or kinetic constants of these processes were observed between MR and NF. The third process, A, characterizes a nonenzymatic (Q₁₀=0.9) work-absorbing viscoelasticity, whose modulus increases sigmoidally with [Ca²⁺]. Effects of temperature, crossbridge inhibition, or variation in [MgATP] support associating the calcium-dependent portion of A with the structural "backbone" of the myosin crossbridge. Extension of the conventional sinusoidal length perturbation analysis allowed using the A modulus to index the lifetime of the prerigor, AMADP crossbridge. This index was 75% greater in MR than in NF (P=0.02), suggesting a mechanism for the previously observed increase in crossbridge FTI. Notably, the A-process modulus was inversely correlated (r²=0.84, P=0.03) with in vivo LV ejection fraction in MR patients. The longer prerigor dwell time in MR may be clinically relevant not only for its potential role as a compensatory mechanism (increased economy of tension maintenance and increased resistance to ventricular dilation) but also for a potentially deleterious effect (reduced elastance and ejection fraction).

Key Words: mitral regurgitation • heart failure • myocardial stiffness • crossbridge function • prerigor dwell time

	Introduction

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Heart failure in mitral regurgitation (MR) is accompanied by impaired ventricular function and altered myocardial function involving defects in excitation-contraction coupling^1,2 and in crossbridge function. The latter is evidenced by a 50% lower myofibrillar Ca²⁺-activated myofibrillar ATPase^3,4 and an 85% increased crossbridge force-time integral (FTI).⁵ Reduced ATPase suggests slowing of the rate-limiting prerigor step of the crossbridge cycle (ie, ADP release from AMADP⁶) or slowing of an earlier step (eg, the intermediate phosphate-release step from AMADPPi⁶). Consequently, we first assessed crossbridge intermediate reaction kinetics using sinusoidal length perturbation analysis in skinned MR and NF myocardium. Because preliminary experiments showed no alterations in these kinetics, the present study repeated the sinusoidal analyses in preparations that were conditioned by regular twitch activity immediately before skinning. This better complies with conditions present in our previous FTI measurements⁵ because phosphorylation levels within previously stimulated skinned strips better comply with intracellular phosphorylation levels in our previous study on excitable strips. These results also did not reveal obvious shifts in intermediate crossbridge reaction rates. However, by extending our methodology to include detection of the putative AMADP prerigor state of the crossbridge cycle, we provide evidence that increased dwell time in this state may contribute to increased crossbridge FTI in MR.

	Materials and Methods

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Patient Selection and Biopsy Procedure
Subepicardial myocardium was obtained from 4 male and 1 female patients with mitral regurgitation and New York Heart Association Class II-III heart failure symptoms, aged 66.8±7.6 years. Control subepicardial myocardium (NF) was obtained from 2 male and 3 female nonfailing coronary artery bypass patients, aged 61.6±7 years, with normal left ventricular contraction patterns. The mean ejection fraction in MR (0.67±0.03) was not significantly different than in the control group (0.69±0.03, P0.8). Medications are summarized in the online data supplement, available at http://www.circresaha.org. The committee on Human Research of the University of Vermont approved the study. Patients gave informed, written consent before participating. The anterior segment of the left ventricular free wall was biopsied shortly after cardioplegic arrest.⁷ No complications resulted from the biopsy procedure.

Muscle Strip Preparation
Biopsies were submerged in butanedione monoxime (BDM) Krebs-Ringer solution⁷ and subsequently dissected into two to four thin strips from each heart. Half of the strips from each heart were electrically stimulated at 37°C and 1 Hz for 1 hour immediately before skinning (conditioned strips) while the other half were quiescent before skinning (nonconditioned strips). For details, see the Muscle Strip Preparation section in the online data supplement, available at http://www.circresaha.org.

Apparatus
Skinned strips were suspended between a force gauge and piezoelectric motor in a muscle bath maintained at 27±0.1°C or 35±0.1°C. Length (eddy current transducer) and force (semiconductor strain gauge) signals were monitored by a strip chart recorder and oscilloscope and acquired by an A/D converter using custom software for data processing and presentation. Strips were activated by incremental increase in [Ca²⁺] by exchanging equal volumes of relaxing solution for pCa 4.5 activating solution to attain pCa values of 8, 7, 6, 5.75, 5.5, and 5. (See the online data supplement, available at http://www.circresaha.org, for solution details, and see Force Measurements and Sinusoidal Analysis section).

Sinusoidal Analysis
Small-amplitude (0.25% strip length, peak-to-peak) sinusoidal length perturbation (42 frequencies between 0.125 to 100 Hz) was used to probe strip viscoelastic properties related to crossbridge kinetics⁸ and passive viscoelasticity. Force and length changes were divided by cross-sectional area and reference length of strips, respectively, to obtain stress and strain values. We modeled the frequency-dependent dynamic modulus Y(f) ("dynamic stiffness" in normalized form) as 3 viscoelastic components in parallel (Equation 1). The first component with modulus A represents a nonenzymatic process-A; the second and third components with moduli B and C represent enzymatic process-B and process-C, respectively.^9,10

where i=-1 and =1 Hz. A, B, and C are coefficients (in Nm^-2) that characterize the modulus of each component, and b and c are characteristic frequencies (Hz) of the enzymatic processes B and C, respectively. Parameter k is a unitless exponent proportional to the phase shift, , between length change and the component of force generated by the A-process (=k/2). Components with moduli B and C are representative of enzymatic processes because their characteristic frequencies b and c have high Q₁₀s (Table). They are conventionally attributed to dynamic processes of the crossbridges.^8,9

View this table: [in this window] [in a new window]   Table 1. Tension and Stiffness Parameters*

We previously considered the term A(i2f/)^k to represent a fixed, passive viscoelastic property in cardiac strips.¹¹ This term is now expanded to include both fixed (A_nonCa) and activation-dependent (A_Ca) viscoelastic portions.¹² The A-process is present in identical form in the relaxed, active, and rigor states, with A differing only in magnitude according to changes in A_Ca. As shown later, A_Ca bears a constant relation to crossbridge activity as gauged by constancy of the ratio of A/B moduli as degree of activation is varied.

Statistics
Significance of differences between groups for each parameter was assessed using a two-tailed, paired or unpaired Student’s t test. Values are mean±SEM.

An expanded Materials and Methods section including tests of end-compliance effects and of the resolving power of our data-fitting algorithm can be found in the online data supplement available at http://www.circresaha.org.

	Results

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Myocardial Dynamic Stiffness Characteristics
The frequency dependence of total dynamic stiffness and the phase angle between force change and length change in NF are shown for an individual myocardial strip preparation in Figure 1. The average for all strips is shown in Figure 2 (left). The solid curves are fits of Equation 1 to the data points. Individual contributions to the total dynamic stiffness from the 3 viscoelastic components in Equation 1 are shown in Figure 2 (right). The negative sign of the B modulus accounts for the prominent "dip" in the total dynamic stiffness curves of Figure 1. The magnitude of the dip and the position of its nadir ("dip frequency") are controlled by the relative magnitudes of the oppositely directed B and C moduli and by the difference in their characteristic frequencies (b and c). The A-process component of Equation 1, A(i2f/)^k adds a linearly rising viscosity and constant phase angle to the total dynamic stiffness, accommodating its upward tilt as frequency increases (Figure 1).

View larger version (24K): [in this window] [in a new window]   Figure 1. Total dynamic stiffness and phase angle of a nonconditioned NF strip preparation during steady-state maximal contracture. Values () were obtained at sinusoidal length perturbation frequencies of 0.125 to 100 Hz (amplitude=0.00125 L2.1). Solid lines drawn according to least-squares fit of Equation 1. Fit parameters: A=201 kN/m2, B=-504 kN/m2, C=774 kN/m2, k=0.122, b=4.3 Hz, and c=14.5 Hz. Dimensions: L2.1=454 µm, equivalent diameter=91 µm, and pCa=5, 35°C.

View larger version (31K): [in this window] [in a new window]   Figure 2. Left, Average total dynamic stiffness and phase angle for all nonconditioned NF strips (mean±1 SEM, 9 strips, 5 hearts). Solid lines drawn according to Equation 1 using the mean-of-fit parameter values from all strips as given in the Table. Fit discrepancies arise from between-strip differences in ratios of parameter values rather than inadequacy of fitting regimen. Right, Calculated average dynamic stiffness of individual processes A, B, and C. Equation 1 was used to calculate average stiffness moduli and phase angles of the 3 viscoelastic model components. Stiffness and phase at each frequency represent the mean±SEM of the least-squares fit to each individual nonconditioned NF strip. The B curve was assigned a negative sign to facilitate plotting. Same experimental conditions as in Figure 1.

The A-process term was required to adequately fit the total dynamic stiffness data independent of whether resting, activated, or permanent rigor conditions prevailed (Figure 3). This is a key observation on which our new analysis was based. The omnipresence of the A-process supports our previous choice to associate it with parallel passive viscoelastic components, such as the extracellular collagen/elastin complex and intracellular titin. However, as shown qualitatively in Figure 3 and quantitatively in Figure 4, coefficient A increases with increased calcium concentration or rigor and this requires including other myofibrillar structures as contributors to process A.

View larger version (22K): [in this window] [in a new window]   Figure 3. Effects of calcium concentration or rigor on A- and B-process moduli. A-process stiffness (thick solid lines) retains the same frequency dependence as [Ca2+] increases from pCa 8 to pCa 5 while its A modulus doubles. The A modulus at pCa 8 is the noncalcium-dependent portion of the A-process (AnonCa). The rise in A with [Ca2+] is the calcium-dependent portion of the A-process (ACa). B-process modulus is essentially zero at pCa 8 and rises to its maximal value at pCa 5. During rigor, A rises 6-fold above the pCa 8 value while retaining a similar frequency dependence. The noncontractile epicardium strip (dots) exhibits a typical AnonCa-like stiffness but is totally insensitive to pCa or rigor conditions. Solid lines indicate same NF strip and experimental conditions as in Figure 1.

View larger version (16K): [in this window] [in a new window]   Figure 4. Codependence of A and B moduli on degree of muscle strip activation. A and B moduli increase in parallel as [Ca2+] is increased from pCa 8 to pCa 5. Least-squares linear regression line: A=52+0.28B, r2=0.96. Same strip and experimental conditions as in Figure 1.

To determine whether increases in A involve enzymatic or passive mechanisms, we measured the Q₁₀s of k and A coefficients during crossbridge cycling and during rigor. The Q₁₀ (27°C to 35°C) of k is 0.95±0.01 (n=35) during calcium activation and 0.93±0.001 (n=28; P=NS) during rigor. The corresponding Q₁₀ values for A are 0.83±0.07 and 1.02±0.001 (P=NS). The similarity of Q₁₀ values for calcium activation and rigor supports a common origin, while their near-unity values suggest a nonenzymatic process unlike the enzymatic crossbridge cycling processes B and C (Q₁₀s of b and c=3.4 to 5.2, Table). Q₁₀s near unity are consistent with associating the A-process with a passive structural phenomenon such as polymer viscoelasticity.¹³

Including our finding that A and B moduli increase proportionately as calcium concentration is raised (Figures 3 and 4 and Equation 2), we hypothesize that the calcium-dependent portion of process-A (A_Ca) reflects the viscoelastic properties of the passive portions of the crossbridge "backbone" (passive portions of S1 and S2). We neglected any possible viscoelastic compliance of the thin filaments because decreased I-band length does not increase the characteristic frequency of the B-process.¹⁴ The large increase in A modulus accompanying development of rigor (ATP withdrawal, Figure 3) is expected since all crossbridges entering the rigor state cease cycling and remain connected to actin (ie, the B modulus approaches zero).

As a test of this hypothesis, we selectively suppressed crossbridge cycling during full activation with the crossbridge inhibitor BDM¹⁵ or by actin filament depolymerization with gelsolin¹⁶ (Figure 5). These treatments leave only a calcium-independent portion of the A-process (A_nonCa) that is equal to the pretreatment, pCa 8, value of A. These observations support the proposed crossbridge origin of the calcium dependent (A_Ca) portion of the A modulus.

View larger version (17K): [in this window] [in a new window]   Figure 5. Selective abolition of ACa by BDM or gelsolin treatment. Nonconditioned NF strips were activated at decreasing levels of pCa in normal activating solution (curve 1), pCa 8 or pCa 5 activating solution with 30 mmol/L BDM (curve 2), and finally at pCa 8 or pCa 5 activating solution after depolymerization of actin filaments by gelsolin treatment (curve 3). ACa values were obtained by subtraction of A at pCa 8 from A at each pCa (ie, ApCaX-ApCa8) followed by normalization to A at pCa 5.

To explore the basis for the proportional increases in A_Ca and B with rising activation, a subset of NF myocardial strip preparations was used to evaluate the effect of [MgATP] on the slope (dA/dB) of the A versus B relation at a constant pCa 5. The slope of the A versus B relation increases as [MgATP] declines (Figure 6). The least-squares regression line for these data are given by Equation 2:

View larger version (14K): [in this window] [in a new window]   Figure 6. Dependence of A versus B slope on MgATP concentration. A and B moduli were evaluated in nonconditioned NF muscle strips (n=5) at pCa 8 and pCa 4.5 with [MgATP] varied between 10 and 0.5 mmol/L. Slope of the A versus B relation (dA/dB) was evaluated by subtraction of pCa 8 values of A and B from respective values at pCa 4.5. Slopes were normalized by their values at normal MgATP (5 mmol/L) to reduce effects of between-strip variance. Regression line fit to data: dA/dB=(0.83±0.08)+(0.9±0.07)/[MgATP], r2=0.98, P=0.001.

A rise in the slope of the A versus B relation as [MgATP] declines is consistent with transfer of crossbridges from a population undergoing the B-process to a population characterized by the A_Ca-process, since the prerigor AMADP and rigor AM states are favored at low [MgATP]. The increase in dA/dB slope can also be understood as a progressive increase in time spent by each crossbridge in the AMADP state (A_Ca-process) relative to the time spent in the AMADPPi state (B-process) (For more details, see Conceptual Scheme in the online data supplement, available at http://www.circresaha.org).

To gain further insight into the structural basis of A_nonCa, we prepared a connective tissue strip, devoid of contractile tissue, from the epicardial surface of a biopsy (See Experimental Results in the online data supplement available at http://www.circresaha.org). The epicardium strip was subjected to the same skinning, storage, and sinusoidal length perturbation as for myocardial strips. The epicardium exhibited the typical frequency dependence of the myocardial A_nonCa-process (Figure 3, filled circles). These results support associating A_nonCa with the viscoelastic properties of extracellular connective tissue.

Contractile Properties of MR Versus NF Myocardium
In both MR and NF, calcium activation saturated at pCa 5. Developed isometric tension tended to be lower in MR than in NF for both nonconditioned (by 39%) and conditioned (by 14%) preparations, but the differences were not significant (Table). Calcium sensitivity of tension was not different in nonconditioned (pCa₅₀=5.83 versus 5.77) or conditioned MR versus NF myocardium (pCa₅₀=5.83 versus 6.00). The Hill coefficient, n_H, also was not different between MR and NF myocardium both before and after being significantly reduced (see next section) by conditioning (Table).

Dynamic Stiffness Properties of MR Versus NF Myocardium
In maximally activated myocardium, although there were slight differences in the total dynamic stiffness and dip frequencies between MR and NF, none were significant in either nonconditioned or conditioned states (Table). However, unlike between-group comparisons, there were significant within-group differences in effects of conditioning in both MR and NF. The Hill coefficient of the tension-pCa relation was lowered by 1.7 (P=0.05) in NF and by 1.3 (P=0.01) in MR. Conditioning increased total dynamic stiffness in both groups at low frequency (NF: 33%, P=0.03; MR: 86%, P=0.03) but not at high frequencies. Conditioning raised dip frequency in MR (by 9%, P=0.03) but not in NF (Table). In resting myocardium, dynamic stiffness, as assessed by A-process modulus was 81±16 kN/mm² versus 100±16 kN/mm² in nonconditioned MR versus NF myocardium (P=0.4). The MR and NF resting moduli increased by 2-fold but remained not significantly different in conditioned myocardium. Phase parameter k also was not significantly different in resting MR versus NF myocardium.

The lack of significant differences between the total dynamic stiffness curves of MR and NF in both nonconditioned and conditioned states, although conditioning produced significant within-group effects, suggests there are no major effects of MR on the conventional kinetic parameters of crossbridge cycling. Comparison of the relevant model parameters (next section) confirms this.

Comparison of Viscoelastic Parameters of MR and NF Myocardium
The Table summarizes the parameters of the model fitted to the dynamic stiffness data, including the Q₁₀s of their temperature dependence. None of the 6 parameters of the fits of Equation 1 to the dynamic stiffness data from MR were significantly different than those in NF, regardless of conditioning state. Characteristic frequency b of the B-process rose 30% as pCa was lowered from 8 to 5 in both MR and NF (pCa₅₀=5.77 in NF and 5.72 in MR; n_H=2.3 in NF and 2.5 in MR). There were no significant differences in pCa dependencies of these parameters between MR and NF.

There were within-group differences in effect of conditioning on the 6 stiffness parameters corresponding to the significant effects on total dynamic stiffness of MR and NF described above. Conditioning increased the A modulus in MR (by 52%; paired, P=0.05) more than in NF (by 31%; paired P=NS) while k decreased in MR (by 10%; paired P=0.02) but not in NF (by 10%; paired P=NS). There were only insignificant effects (paired t tests) of conditioning on B and C moduli. Conditioning caused characteristic frequency b to increase slightly in both NF (by 7%) and MR (by 14%), but only the latter increase was significant (paired, P=0.03). Characteristic frequency c did not change significantly in NF or MR.

	Discussion

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Our results show that the kinetic parameters of our 6 parameter crossbridge model are not significantly altered in MR regardless of conditioning state (Table). This implies that changes in the force-generating step of the crossbridge cycle do not account for increased crossbridge FTI in MR. Therefore, we turned our attention to the possibility that a later step in the crossbridge cycle might be altered—specifically, that a prolongation of the prerigor AMADP state might account for increased FTI.

Comparison of Relative AMADP Dwell Times in MR and NF Myocardium
We used the slope of the A versus B relation (eg, Figure 4) generated by varying pCa to estimate the relative time spent by a crossbridge in the prerigor AMADP state compared with time spent in the force-generating state. The inverse relation between [MgATP] and the slope of the A versus B relation at a constant pCa (Figure 6) provides the main basis for interpreting this slope as an index of the relative dwell time of the AMADP state (see Conceptual Scheme in the online data supplement available at http://www.circresaha.org). Comparison of the A versus B slopes in MR and NF is shown for averaged data in Figure 7. These data were obtained by varying pCa. The range from pCa 8 to 5.75 was chosen to cover physiological values and to avoid departures from linearity. Increased slope consistently occurred below pCa 5.75 (see Figure 4), possibly indicating ATP depletion as this increase also occurs when [MgATP] is intentionally reduced (Figure 6).

View larger version (22K): [in this window] [in a new window]   Figure 7. Correlation of average A and B moduli in nonconditioned NF and MR myocardium at increasing levels of activation. At each pCa between 8 and 5.75, values of A and B obtained by fit of Equation 1 to the total dynamic stiffness data of each strip were averaged across all strips in each group (mean±SEM). Regression line fits were A=(86±19)+(0.20±0.04)B, r2=0.95, P=0.05 in NF (), and A=(39±4.8)+(0.35±0.03)B, r2=0.97, P=0.01 in MR ().

The linear regressions of A on B in Figure 7 were significant (r²=0.97, P=0.01 for MR; r²=0.95, P=0.05 for NF). In MR, the slope of the regression line was 75% greater (P=0.02) than in NF myocardium (0.35±0.03 versus 0.20±0.04, respectively). Thus, there is an apparent 75% increase in dwell time of the prerigor AMADP state relative to the dwell time of the force-generating state. Since there were no significant changes in B-process kinetics, most of this 75% increase in dA/dB in MR is attributable to increased AMADP dwell time alone (see last paragraph in Conceptual Scheme in the online data supplement available at http://www.circresaha.org). By prolonging the crossbridge "on-time," an increase in AMADP dwell time likely explains the increase in FTI in MR (85% at 21°C)⁵ since our observed increase in AMADP dwell time rises from 75% to 88% after correcting for the 16°C temperature difference between the two studies (Q₁₀ of dA/dB=0.75 in MR and 0.69 in NF, calculated from data used for the Table). Similarly, the previously observed 50% decrease in myofibrillar actomyosin ATPase activity in MR^4,17 can be explained by the 75% increase in AMADP dwell time (61% after temperature correction) assuming the entire ATPase turnover time is equal to the AMADP dwell time.

There is also good agreement between our estimate of the Q₁₀ of the AMADP dwell time and the Q₁₀ of FTI. In NF, the latter is 0.48 (calculated from values at 21°C⁵ and 37°C¹⁸), but unlike AMADP dwell time, this Q₁₀ is determined by the temperature sensitivities of both force (ie, crossbridge recruitment) and on-time. Removing the effect of temperature on the force component of FTI (Q₁₀ of isometric tension=1.41¹⁹) yields a Q₁₀ of 0.67 for on-time. This compares well with our Q₁₀ of 0.61±0.04 (n=9) for AMADP dwell time in NF.

Myosin changes are not likely involved in prolongation of the rate-limiting step, because our previous studies using purified myosin show that its actin-activated ATPase activity is not altered in MR.²⁰ Troponin T (TnT) isoform shifts are not likely involved either, since in contrast to the adult-to-fetal TnT isoform shift reported in dilated cardiomyopathy,²¹ none have been observed in MR.²² MR-related differences in phosphorylation of myofibrillar proteins could account for the depressed ATPase or increased FTI, but this possibility is contraindicated since appropriate conditioning effects on the crossbridge kinetics in MR did not occur (Table).

Because of the strong dependency of AMADP dwell time on [MgATP], it is tempting to speculate that changes in the energy supply system, rather than changes in contractile or regulatory proteins account for increased FTI in MR. One possible candidate is altered myofibrillar-bound creatine kinase (MBCK) since MBCK is an important component of the phosphocreatine-CK MgATP-regenerating system.²³ For example, a reduced activity or concentration of MBCK that reduces myofibrillar [MgATP] from 5 to 1 mmol/L would cause a 75% rise in dA/dB (Figure 6). Since we observed an inverse relation between A modulus and ejection fraction (see below), and others observed that declining total CK activity is inversely correlated with LV ejection fraction in MR patients,²⁴ CK depression may be the common link. If depression of MBCK activity²⁵ contributes to these correlations, it is likely that it also contributes to depressed intramyofibrillar [MgATP] and elevated A moduli in our skinned preparations, because normal MBCK activity is probably necessary to maintain saturating myofibrillar ATP levels even in the presence of exogenous CK in the skinned-strip muscle bath.²³

Clinical Relevance of Findings
Although average ejection fraction (EF) was normal in our MR patients, decreased EF and stroke work (independent of afterload) and depressed end-systolic elastance have been observed in other studies.^26,27 Since increased passive myocardial stiffness is correlated with decreased EF in MR patients,²⁸ we examined the possible role of the A modulus in contributing to variations in EF within our MR group. We found a significant inverse correlation (r²=0.84, P=0.03, n=5) between EF and A modulus, indicating a 10% decrease in EF for each 12% increase in A. In view of the quantitatively similar inverse relation between in vivo myocardial stiffness and EF reported by Corin et al,²⁸ we suggest the possibility that increases in A modulus may contribute to reduced EF. However, this speculation must be confirmed using a larger population of MR patients. Increased time spent in the force-bearing portion of the crossbridge cycle (ie, increased dA/dB, Figure 7) relative to its power stroke could increase internal resistance to sarcomere shortening and lengthening and cause internal dissipation of myocardial work output. Interestingly, our previous measurements of myosin motility in MR showed a trend toward reduced average filament sliding velocity (0.9 versus 1.2 µm/s) including a clear 90% to 100% reduction in filament velocities in the 1.7 to 2.5 µm/s range.²⁰ Thus, increased AMADP dwell time could contribute to increased internal loading, decreasing shortening velocity, and increasing myocardial stiffness in MR during ventricular ejection and filling.

Limitations of Study
The major technical limitation of this study is the uncontrolled effect of series compliance at the ends of the preparations. All stiffness moduli were obtained without compensation for differences between applied length changes and actual sarcomere length changes. Although this problem can be avoided by using an online sarcomere gauge to record actual sarcomere length change simultaneously with resulting force change (see, eg, Wannenburg et al²⁹), the apparatus used for our experiments did not have this capability. However, using a computational approach, we were able to estimate the extent to which end compliance affected our stiffness measurements.

We simulated the effects of a wide range of hidden end compliance to examine resulting errors in evaluating model parameters (see the online data supplement available at http://www.circresaha.org). The results demonstrate that the presence of a large series compliance (as much as 4 times greater than the maximum possibly present) has virtually no effect on our ability to faithfully recognize the presence of 3 parallel viscoelastic elements. Further, by assuming reasonable values of hidden end compliance determined by independent tests, we established that parameter values (A, B, C, k, b, and c) of the apparent parallel elements differed from those of the real elements by no more than 26% (range: 7% to 26%). In cases where errors are as large as 26%, it is possible that our failure to detect changes in conventional intermediate crossbridge reactions in MR myocardium are partly attributable to increased variance associated with differences in end compliance between preparations. However, it is notable that estimates of prerigor dwell time are barely affected by even large variations in hidden end compliance. Dwell-time indices are obtained from the A/B ratio, which is underestimated by only 5% in the presence of reasonable end compliance (versus up to 26% errors in absolute values).The underestimation increases to 8% if an unreasonably large end compliance is assumed.

Another potential limitation arises because of the closeness of characteristic frequencies b and c in cardiac muscle. This taxes the resolving power of the fitting algorithm. We also addressed this potential problem by computational methods. The results for simulated data in which c/b ranged from 2.8 to 5 show that possible errors in evaluating A, B, and C are less than 4%, 8%, and 8%, respectively (see the online data supplement available at http://www.circresaha.org). Since there was little difference in characteristic frequencies b or c between NF and MR myocardium, these small errors will cause even smaller errors in estimating differences between A/B ratios and dwell times in the two groups.

	Acknowledgments

 
This work was supported by National Institutes of Health Grants R01 HL54821 (D.W.M.) and R01 HL55641 (N.R.A.).

Received April 26, 2001; revision received November 15, 2001; accepted November 26, 2001.

	References

Top Abstract Introduction Materials and Methods Results Discussion References

 

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