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Altered oscillatory work by ventricular myofilaments from a rabbit coronary artery ligation model of heart failure

David J Miller, Niall G MacFarlane, Gayle Wilson
DOI: http://dx.doi.org/10.1016/j.cardiores.2003.09.032 94-104 First published online: 1 January 2004


Objectives: Understanding the changed ability of cardiac myofilaments to produce pump work requires knowledge of kinetics of crossbridge function as well as more widely studied parameters such as Ca-sensitivity and isometric force development. We tested the hypothesis that altered crossbridge kinetics contribute to reduced myofilament work in early-stage heart failure (left ventricular dysfunction, LVD). Methods: The sinusoidal oscillation technique can yield insights into crossbridge function. Dynamic stiffness, oscillatory work and power were assessed in chemically skinned, Ca-activated trabeculae from rabbit ventricles in early-stage failure, 8 weeks after infarction induced by coronary artery ligation (LIG). Results were compared with sham-operated controls (SH). LVD was assessed by echocardiography. Results: Ca-activated force and myofilament Ca-sensitivity were not significantly altered at this early stage of LVD. In maximally Ca-activated preparations, the frequency of minimal dynamic stiffness (fmin) was 23% lower in LIG. fmin increases by >80% between pCa 5.8 and 4 in SH but not in LIG. Maximal phase lead and lag angles (between length and tension) were lower in LIG at frequencies near fmin, lowering oscillatory work and power. The Lissajous figures (oscillatory work loops) of imposed length vs. tension are often asymmetric near fmin. The degree of asymmetry was greater in LIG. Conclusions: Reduced capacity for mechanical power, consistent with depressed haemodynamic performance in LVD hearts, is only partially attributable to crossbridge slowing; changes in the phase relationship will also contribute. These changes are not readily attributable to known alterations in contractile protein isoforms. Some deductions are drawn about which steps in the crossbridge cycle are modified in this model of LVD. Altered cardiac myocyte Ca-transients, reported to be associated with LVD, will be translated into pump work by a contractile machinery that is functionally altered, even though isometric force and myofilament Ca-sensitivity might remain near-normal at this stage.

  • Heart failure
  • Contractile function
  • e–c coupling
  • Ventricular function
  • Rabbit

1 Introduction

Contractile dysfunction, although one of many, is perhaps the defining symptom of heart failure (reviewed in Ref. [1]). It is characterised by reduced pump function as well as slowed contraction and relaxation [2]. While much work has addressed whether dysfunction results from altered intracellular Ca2+ handling and E–C coupling, crossbridge dysfunction may contribute significantly. This paper questions whether cardiac work and power are reduced by myofilament alterations early in heart failure.

Studies of contractile dysfunction generally focus on isometric force reduction, or slowing of tension development and relaxation. However, isometric ‘contraction’ means no (external) work is done. By contrast, studies with isolated myocytes often measure unrestrained shortening; again, no external work is involved. Myocyte isolation necessarily disrupts cell-to-cell coupling and the extracellular matrix, removing structures relevant to mechanical function in vivo. Against that, the mechanical complexity of multicellular cardiac vs. skeletal muscle preparations has minimised information about work and power characteristics for failing myocardium, particularly from the myofilaments.

We have used the sinusoidal analysis technique to study crossbridge properties. This method applies small, sinusoidal length perturbations to probe attached crossbridges [3], avoiding many of the difficulties highlighted above. It can inform about dynamic properties revealed in parameters such as fmin, the frequency at which dynamic stiffness is at a minimum [4–6], oscillatory work and power.

We have examined myofilament function in a rabbit coronary artery ligation model of heart failure (CHF) to establish whether work potential diminishes and thus could contribute to reduced contractile performance. It is also essential to define whether the alterations to Ca2+ transients in failure reported by others, e.g. [7], are translated into pump function by a defective myofilament system.

Preliminary results have been published [8].

2 Methods

2.1 Animal model and assessment of left ventricular dysfunction (LVD)

This LVD model, detailed previously [7,9], is described briefly here. The left anterior descending coronary artery was ligated in anaesthetised New Zealand White rabbits (LIG). Animals developed early signs of CHF over the subsequent 8 weeks. Echocardiography (animals under light sedation) was done on all animals. Sham-operated animals (SH) were treated identically, except for the ligation. All procedures were performed under license in accordance with the UK Animals (Scientific Procedures) Act, 1986 and the animals cared for in accordance with NIH published guidelines.

2.2 Isolated ventricular trabeculae experiments

Rabbits were killed by Euthatal overdose (1.0 ml/1.4 kg i.v.), hearts excised and placed in standard Ringer's solution (20 °C) with 30 mM 2,3-butanedione monoxime (BDM) to facilitate further preparation. Free-running trabeculae were isolated, mostly from near the AV valves of the right ventricle, from viable, non-infarcted regions where compensatory hypertrophy is evident. Our group has reported cellular remodelling in these tissues [7]. Preparations, typically elliptical in cross-section, were 1.34±0.07 vs. 1.54±0.08 mm (length) by 162.1±6.7 vs. 173.4±7.2 μm (diameter; SH vs. LIG, mean±S.E.M., n = 25 for each group). Similarity in trabecular dimensions between SH and LIG is partially due to preparation selection to meet optimal size criteria. Thus, we cannot judge whether remodelling alters trabecular dimensions. For isometric force measurement and length perturbation, trabeculae were mounted between an Akers AE 875 force transducer and a lever system (Cambridge Technology, Watertown, MA. USA, Series 300B Lever System) as detailed elsewhere [8,9,11].

Sarcomere length in chemically ‘skinned’, relaxed preparations, was set at 2.1-2.2 μm under direct microscopy [10]. Any distortion of sarcomere pattern, usually appearing as hypercontracture, was restricted to the end-snares, typically representing <2% of preparation length overall. Thus, ‘end’ damage and ‘end compliance’ are minimal with this mounting method [10]. Preparation length was measured between the snares that form sharply defined ‘end’ perpendicular to the trabecula's long axis. Preparation width and depth was measured at several points.

2.3 Solution composition

Table 1 shows solution composition. Trabeculae were chemically ‘skinned’ (30-min exposure to solution B with 1% v/v Triton X-100). Methods for calculating free [Ca2+], other ionic conditions and solution exchange have been reported elsewhere [10]. Experiments were done at 20–21 °C.

View this table:
Table 1

Composition of basic solutions (in mM except where stated; pH 7.0, 20 °C)

  • Potassium ions as KCl and KOH. The [Ca2+]total in all solutions was approximately 0.005–0.01 mM due to Ca2+ contamination, except solution A where it was set at 10 mM (as CaC03 in the CaEGTA stock solution with CO2 driven off by mild heating).

  • Magnesium ions as 1 M MgCl2; free Mg2+=2.1–2.5 mM in solutions A, B and mixtures of these solutions.

  • Sodium ions from the salts Na2ATP and Na2CrP.

  • § 0.1 mM Ca, as CaCl2, was added to aliquots of solution A to yield a ‘full activating’ solution (pCa 4.0). Total Cl-concentrations varied from about 110 to 120 mM.

  • HDTA (diaminohexane tetraacetic acid 9.8 mM) was added to solution C to maintain the ionic strength, but at greatly reduced Ca2+ buffering power.

2.4 Data handling and analysis

Muscle tension (F) and length (l) signals were generally low-pass filtered (50 Hz; roll-off 18 dB decade−1), well above any frequencies relevant here, and digitised at appropriate rates (400 Hz during oscillations, to preclude aliasing, otherwise 40 Hz, MacLab 8). Analysis and graphical output employed Igor Pro software (Wavemetrics, ver. 3.16). Some preparations yielded valid stiffness measurements but with a signal-to-noise ratio inadequate for reliable phase-shift quantification.

2.5 Statistical analysis

Data are reported as mean±S.E.M. for n animals. Significance of difference (paired or non-paired Student's t-test) was taken at the P<0.05 level (NS=difference not significant).

2.6 Sinusoidal length change experiments

The lever system was controlled with in-house software via a 12-bit A-D/D-A card. The sinus-form length changes typically comprised 200–300 steps peak-to-peak.

Compliance at the transducer and lever-arm ends was equivalent to length changes of approximately 0.05% and 0.01% of initial length, respectively, assuming a preparation 1.40 mm long producing 0.06 mN tension oscillation (ΔF, typical values). No compliance correction was made, so the ratio minimum/maximum stiffness at different frequencies (e.g. Fig. 1) is slightly underestimated. The assembly's first resonant frequency was about 240 Hz, 10 × the highest frequencies relevant here.

Fig. 1

Frequency plots of dynamic stiffness (●) and phase angle (○) obtained from sinusoidal perturbation of a maximally Ca-activated trabecula.

Small-amplitude, sinusoidal oscillations were applied (Δl, generally ±0.25% of initial muscle length) at several frequencies (0.125–12.5 Hz, see Ref. [11]). This is considered small enough to avoid stretching most attached crossbridges beyond their working stroke, which, although controversial, is generally reported to be 4-20 nm. Stiffness varies with oscillation frequency because crossbridge cycle kinetics are strain dependent (e.g. [12]). In preliminary tests, dynamic stiffness was generally maximal at 7.5 Hz or greater and minimal at 0.5–2 Hz. The test-frequency sequence did not affect mechanical behaviour. Stiffness vs. frequency plots typically have two maxima with a lesser one slightly below fmin, on which most of our interest has focused (see Section 4.6). Resting and Ca-activated muscles, plus those in ATP withdrawal-induced rigor in some preparations, were tested.

2.7 Muscle stiffness

The ratio ΔFl defines dynamic muscle stiffness (M). Tension responses typically stabilised well within one Δl cycle (see Fig. 2), even at higher frequencies. Δl was standardised, therefore, results are plotted simply as ΔF representing M as a function of oscillation frequency. During Ca-activation, the plot has a characteristic minimum at a frequency termed fmin (Fig. 1), an index of mean crossbridge cycling kinetics (see Section 4). Control experiments concentrating more test frequencies around fmin confirmed that the data reported give sufficient resolution for present purposes.

Fig. 2

Oscillation frequency transition between 7.5 and 1.88 Hz in a fully Ca-activated preparation (tension normalised to the level at 7.5 Hz, length excursion=±0.25% lo—see Section 2). (A) Experimental trace showing length and tension vs. time; the tension waveform stabilises within one cycle after the frequency transition. (B) Enlargement of the transition shown in A. Here the length waveform after the transition has been normalised (thicker line) to the maximum tension amplitude (thinner line) to make the phase shift clearer.

For a range of submaximal activations, active stiffness relates linearly to isometric tension (r = 0.933, 4 SH and 4 LIG preparations), as anticipated if the proportion of crossbridges activated is Ca-dependent. Dynamic stiffness at 7.5 Hz for submaximal activations was normalised to that at pCa 4. Protocol experiments revealed that fmin was detectably affected by the degree of Ca-activation in SH but not LIG (see later, Fig. 3). Thus, to ensure maximal crossbridge rates, trabeculae were usually maximally Ca-activated.

Fig. 3

Effect of [Ca2+] on fmin. Panel A shows fmin (Hz, mean±S.E.M.) for SH (○) and LIG (●) trabeculae. Panel B shows data from the same experiments normalised to the maximum rate in each case to reveal the relative effect of Ca. **P<0.05 SH vs. LIG. §P<0.05 SH vs. own maximum (paired t-test).

In resting and rigor muscle, M should be virtually independent of frequency, with phase shift virtually zero, e.g. [3,13]. This was routinely confirmed. Resting M was checked since a high value indicates that much of the preparation was not functional myocardium. Resting and Ca-activated M were proportionate at two amplitudes of Δl, with due allowance for system compliance, confirming a Hookean elastic characteristic (data not shown).

2.8 Phase shift

The phase shift (φ, reported in degrees) between tension and length was examined (Fig. 1). Phase relationships stabilised, regardless of the frequency step, within about 0.25 wavelengths. For this study, we arbitrarily measured φ at the mid-point of the length waveform's rising phase (the ‘stretch’ phase). We have defined its value as: (i) positive φ, quantifying phase lag of tension behind length, (ii) negative φ, phase lead, or (iii) zero φ where the tension and length sinusoids were in phase. (Other authors have defined phase lag as negative (e.g. Refs. [3,4]). Since one considers external work associated with phase lag as ‘positive’, we have termed phase lag as positive, for convenience.)

2.9 Oscillatory work and power

Net oscillatory work at a given frequency, Wf, and the associated power, Pf, output of the muscle can be calculated [4]:

Embedded Image(1) Embedded Image(2)

where f denotes frequency, φf phase shift (in radians) and Mf dynamic stiffness. The frequency at which fmin occurs, or at which maximum work (fw) or power (fp) is found, have all been employed by others as indicators of significant crossbridge kinetic properties [4,14–16].

2.10 Work and power units

The results reported concerning work and power derived from Eqs. (1) and (2) show no units. To facilitate comparisons between different trabeculae, dynamic stiffness was normalised to maximum tension. For a typical preparation generating 0.60 mN Ca-activated tension, dynamic stiffness at fmin would be about 5% of maximum tension, i.e. 0.03 mN. The total length change was 0.5%, i.e. 7.5 μm for a 1.5-mm preparation. Thus, oscillatory work=tension × distance × sin φ[rad]=3 × 10−5 N × 7.5 × 10−6 m × sin [rad 13.6°]=0.053 nJ. At 1 Hz, this is equivalent to 0.053 nW oscillatory power.

2.11 Quantifying oscillatory work and power

The tension waveform was not always a perfect sinus, in contrast to the imposed length waveform. Thus, φf is not constant throughout a given cycle, especially near fmin, although consistent at a given frequency. Eq. (1) would be inaccurate in those cases.

The ‘ideal’ form, assuming constant phase shift throughout a cycle, yields an elliptical length vs. tension Lissajous figure. The (signed) area within an oscillatory work loop represents the work done (clockwise=work ‘absorbed’ or dissipated, anticlockwise=external work done) the latter analogous to pressure–volume loops defining cardiac pump work. Fig. 4A exemplifies how loops differed from this pattern. If they differed, φ on the falling (=shortening) and rising (=stretching) phases was generally of the same sign (Fig. 4A). Rarely, φ reversed sign between the rising and falling phase (Fig. 4B); the loop crosses over (see also Refs. [14–16]).

Fig. 4

Examples of the phase relationship between length (thinner trace) and tension (thicker trace) illustrating that the shift may consistently differ between the ascending and descending limbs. (Ai) Phase shift is much larger on the ascending limb. (Bi) Phase-shift changes sign on the ascending limb. (Aii and Bii) The same data shown as tension vs. length loops. Broken line shows line of equality (=zero phase shift), arrows indicate time sequence.

We have quantified these deviations as a correction factor at each frequency for each preparation. Actual loop area was divided by that for the regular ellipse predicted by φf. This ‘loop factor’ conveniently quantifies the extent of length vs. tension loop asymmetries at relevant frequencies, providing a further parameter characterising kinetic behaviour and rescaling work and power values obtained simply from Eqs. (1) and (2).

3 Results

3.1 Animals used in this study

This ‘heart failure’ model produces a range of infarct sizes, LVD and ejection fractions (%, EF, assessed by echocardiography). Thus, it was decided before analysis that LIG animals would only be included with EF≤50% and SH controls with EF≥65%. Characteristics are summarised in Table 2. Otherwise, the haemodynamic and morphological adaptations have been well characterised by our group [7,9,18]. Left ventricular and right atrial end diastolic dimension (Table 2), liver and lung weights (as %body weight) and left ventricular end diastolic pressure (from invasive haemodynamic monitoring) all increase in LIG [7,9,18]. EF (Table 2), left ventricular systolic pressure and cardiac output are reduced in LIG.

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Table 2

Echocardiographic data

LVEDD (mm)17.5±0.319.9±0.2
LAD (mm)11.2±0.215.3±0.2
EF (%)73.7±1.846.1±1.1
HR (bpm)211±2.4236±2.5
  • LVEDD: left ventricular end diastolic dimension, LAD: left atrial end diastolic dimension, EF: ejection fraction, HR: heart rate (beats per minute).

    Comparison (mean±S.E.M.) of some echocardiographically determined cardiac dimensions and functional properties indicative of left ventricular dysfunction in a representative sample of animals used in this study.

    All differences SH vs. LIG are significant (P<0.05).

3.2 Protocols

Preliminary experiments established reproducibility and a suitable protocol. Time controls confirmed that fmin or φ are consistent, despite repetitions. Maximum dynamic stiffness and isometric tension are well maintained.

3.3 Preparation dimension, tension generation

There were no significant differences in the lengths or cross-sectional areas (CSA) of preparations utilised, or in resting stiffnesses (Table 3 and see Section 2.2). Maximum Ca-activated tension correlates with trabecular CSA, as expected, for both SH and LIG (data not shown). In the absence of differences, alterations in fmin or φ observed in LIG tissue can thus be attributed to alterations in the contractile proteins.

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Table 3

Mechanical properties of trabeculae

Maximum Ca-activated force (mN)1.19±0.141.09±0.13
Ca-activated force/CSA (mN mm−2)60.8±4.661.9±6.0
Resting stiffness/CSA (mN mm−2)0.049±0.016 (n = 25)0.056±0.011 (n = 25)
Hill coefficient3.33±0.36 (n = 5)2.82±0.33 (n = 6)
fmin (Hz)0.910±0.07 (n = 25)0.705±.05* (n = 25)
  • Comparison of some mechanical properties of trabeculae from Sham-operated (SH) and coronary artery ligated (LIG) rabbits (mean±S.E.M.).

    CSA=preparation cross-section area (see Section 2), pCa50=pCa necessary to evoke half-maximal steady-state tension, fmin=frequency at which dynamic stiffness (see Fig. 1) was minimal.

  • * Only fmin is significantly different between LIG and SH (P<0.05).

3.4 Dynamic stiffness

fmin was significantly lower in LIG (0.705±0.05 Hz, n = 25) than SH (0.910±0.07 Hz, n = 25, P<0.05). (Results were included only where the full protocol was completed without 7–10-Hz stiffness or steady-state tension fall-off exceeding 10%.) Pooled frequency spectra are shown in Fig. 5. Fig. 4A shows data normalised to maximum Ca-activated force, Fig. 4B reports a subset of these preparations, as normalised for each preparation to maximum dynamic stiffness with the minimum defined as zero. For this group, to validate a comparison of the shape of the stiffness vs. frequency relationships, only preparations with max/min dynamic stiffness >4 were included. (n = 14 SH, n = 15 LIG, mean fmin for these subgroups 0.933±0.095 (SH), 0.734±0.053 (LIG), P<0.05). The relationship is significantly shifted to lower frequencies in LIG (P<0.01 from 0.63 to 5 Hz, mean frequency for half-maximal stiffness derived from individual logistic curve best-fits was 1.63±0.096 (LIG) vs. 2.17±0.226 Hz (SH), P<0.05).

Fig. 5

Dynamic stiffness (mean±S.E.M.) as a function of oscillation frequency for SH (○) and LIG (●) groups. Panel A shows data normalised to maximum Ca-activated tension (n = 25 in each). In order to compare the shape of the relationship between SH and LIG, Panel B shows data normalised to individual maximum stiffness with minimum stiffness taken as zero (for preparations where max/min >4—see text for details). **=P<0.05 for differences between means. The paired means differ significantly across the frequency range 0.63–5 Hz (P<0.01). Mean±S.E.M. of half-max values derived from individual curves are plotted (▪ LIG, □ SH). NB Individual minima are obscured by averaging for both these plots.

3.5 Ca2+-sensitivity

As reported previously [9], LIG showed no significant differences in the pCa-tension relationship (Table 3). However, fmin proved sensitive to the degree of Ca-activation in SH but not LIG (Fig. 3). Four or five submaximally activating pCas were tested, evoking 11% to 96% of maximum tension, plus that at 100% (at pCa 4). fmin rises significantly with [Ca2+] in both absolute (Fig. 3A) and relative (Fig. 3B) terms in SH, but not in LIG. The mean maximum fmin (at pCa 4) was again significantly lower in LIG for this subset.

3.6 Phase shift

Oscillatory work and power can be calculated from the phase relationship between length and tension sinusoids. The φ vs. frequency plot looks similar to that of dynamic stiffness (Figs. 1 and 6). For an individual preparation (Fig. 1), φ at lower frequencies was generally close to zero (but usually positive, even if only marginally in the LIG group), increasing slightly to a maximum at a frequency immediately below fmin. Just above fmin, φ abruptly changes to negative values (i.e. tension leads length). φ progressively increases with frequency, becoming positive again. This form, particularly around fmin, is somewhat obscured when mean φ is plotted (Fig. 6). Nevertheless, mean positive φmax at two frequencies just below fmin and one for negative φmax above it (at 1.88 Hz) is significantly lower in LIG. Table 4 presents means of the individual maxima from each experiment, regardless of the frequency at which they occurred. The maximum positive φ (just below fmin) is significantly lower in LIG, as is the negative φmax.

Fig. 6

Mean phase shift between length and force waveforms over a range of frequencies. Positive values indicate phase lead (length leading force), negative values indicate phase lag. *P<0.05, **P<0.005, ***P<0.001 for LIG (n = 24) vs. SH (n = 22).

View this table:
Table 4

Summary of mean phase-shift data

Max. positive, phase shift (°)13.58±1.026.74±1.06**
Max. negative, phase shift (°)−70.08±3.89−49.88±4.89*
  • Values in this table are obtained by taking the maximum values of phase shift (positive and negative) independent of the frequency at which this occurs. (LIG vs. SH.

  • ** P<0.001.

  • * P<0.01.

Fig. 7 shows examples of length vs. normalised tension loops for both positive and negative work from SH and LIG. Anti-clockwise loop area represents positive (external) oscillatory work, clockwise loops denotes ‘negative’ (i.e. absorbed or dissipated) work. For this and all preparations, maximum work dissipated was thus far greater than that generated (at frequencies just above and just below fmin, respectively).

Fig. 7

Positive and negative work loops for SH and LIG preparations. (A) Examples of work loops for a typical SH preparation. The arrows denote the direction around the loop. (i) Positive work loop which rotates anti-clockwise (at 0.25 Hz) and (ii) a negative work loop which rotates clockwise (at 1.5 Hz). (B) Examples of work loops for a typical LIG preparation (i) and (ii) as described for the sham animal. Depending upon the direction the loop rotates, the area under the loop represents the positive or negative work performed by the preparation. The rising phase shift, determined as in Section 2, is reported on each panel.

Work and power values were corrected for variations in φ (see Fig. 4 and text) by multiplying them by the relevant loop correction factor. Mean correction factors (Table 5) differed significantly, SH vs. LIG. Thus, values derived without correction would over estimate the actual work and power output in both groups, but more so in LIG.

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Table 5

Work and power results

(n)Mean max. work performedMean max. work absorbedMean max. power performedMean max. power absorbed
Loop factor0.68±0.02*1.05±0.010.68±0.02*1.05±0.01
Loop factor0.37±0.020.99±0.010.31±0.020.99±0.05
  • Maximum work and power results after loop correction.

    For explanation of units, see Section 2, for loop factor, see text and Fig. 7.

  • * P<0.05 SH vs. LIG.

Mean sinusoidal work was significantly lower in LIG (Table 5). Additionally, whereas 5 of 16 LIG preparations did not generate positive work just below fmin, all SH tissues did. In each preparation, fw (SH: 0.61±0.07, LIG: 0.56±0.02 Hz, difference NS) was fractionally lower than fmin. Negative work tends to be lower in LIG, but this did not reach 95% significance (Table 5). In both groups, the mean frequency for maximum negative work (SH: 2.17±0.02, LIG 1.99±0.08 Hz, difference NS) is significantly faster than fmin (P<0.001).

3.7 Oscillatory power

Oscillatory power is the product of net work and oscillation frequency. The results match the statistical outcome for oscillatory work presented earlier. Small differences are attributable to those instances where the frequencies of positive or negative power generation are slightly different from those for maximal work (data not shown).

3.8 Resting and rigor muscle

For resting muscle (pCa∼7), both LIG and SH at all frequencies, loops are virtually flat (compare with Fig. 4Aii and Bii), but rotate clockwise, confirming that some work is dissipated, as expected for a passive visco-elastic body. Similar results were observed in eight preparations in rigor, albeit at much higher absolute dynamic stiffness. Importantly, these observations confirm that loop areas in Ca-activated conditions reflect kinetic properties associated with active crossbridges and are not attributable to methodological artefacts.

4 Discussion

4.1 Evidence of LVD in LIG animals

Reduced LV EF is commonly used as an index of fibre shortening to assess CHF. However, preload and the afterload change in failure and EF is afterload-sensitive. Although imperfect, it remains the best single index we have for assessing LVD. Changes to chamber dimensions and heart rate (Table 2) are further clinical signs of early-stage heart failure with clear LVD in LIG animals. Other characteristics of LVD in LIG animals have been presented by our group [7,9,18].

4.2 Significance of fmin and its slowing in LVD hearts

The frequency of minimum dynamic stiffness (fmin) is of interest as a mechanical property that might alter in LIG. Evidence for fmin as a reliable indicator of crossbridge kinetics is reviewed in Ref. [16]. A resonance-like phenomenon exists between the tension developed in the crossbridge cycle and the length perturbation imposed. Several groups have used sinusoidal analysis or pseudo-random binary noise-modulated perturbation (PRBN) techniques to examine cardiac muscle [4,13,19,20]. A detailed analysis by Rossmanith and Tjokorda [16] reveals the steps in the crossbridge cycle which most influence fmin.

fmin is derived under quasi-isometric conditions, possibly relevant for myocardium in vivo (discussed below). The dynamic stiffness vs. frequency plot produces characteristic spectra (Fig. 1), comparable with those reported for cardiac muscle in various species, e.g. [5,6,16]. Present values (near 1 Hz, Table 3) were obtained at 20 °C, consistent with those of Rossmanith et al. [21] for rat with the V3 myosin isoform or of Ruf et al. [6] for human myocardium. These rates would approach 10 Hz at 37 °C, assuming a Q10 of about 3, but still appear to be slow, superficially at least. However, crossbridge kinetics are well known to be strain-dependent [12]. Thus, fmin cannot readily be related to shortening velocities observed during auxotonic conditions, just as isometric tension cannot predict more physiological (often auxotonic) contractions.

Rossmanith and Tjokorda [16] concluded that Vmax is particularly sensitive to changes of detachment rate in crossbridges being unloaded (i.e. shortening). While ktr (the rate of tension redevelopment after release and restretch) is sensitive to attachment rate (f in A.F. Huxley's crossbridge kinetic terms f and g), Vmax and fmin are not. By contrast, fmin proves to be more sensitive than Vmax to the forward rate of the power stroke, as well as detachment rate, for the crossbridge subject to stretch, but not release. It is generally accepted that the rate of the detachment step after the power stroke dominates the rate of relaxation. Thus, our finding that the maximum relaxation rate is slowed in LIG tissues, when the decline of [Ca2+] itself is not limiting [23], provides further evidence about where LIG crossbridge kinetics differ. According to this analysis, fmin is sensitive to this rate for lengthening steps only. This condition might well apply during rapid relaxation because this effectively stretches those crossbridges still attached as relaxation proceeds.

4.3 Ca-sensitivity of fmin

Studies of papillary muscles and myocytes reveal that [Ca2+] affects maximal shortening velocity (Vmax), e.g. [24] or ktr [25] in addition to the proportion of crossbridges activated. Sinusoidal analysis of skinned fibres allows kinetic measurements to be made at different [Ca2+]. We found that the degree of activation (isometric tension) relates linearly to dynamic stiffness, consistent with an increase of active, uniform crossbridges. Fig. 3 shows that Ca also affected fmin in normal (SH) cardiac tissue, in contrast to reports by Rossmanith et al. [16,22] and Hancock et al. [26] for cardiac muscle from other species. However, the change (Fig. 3B) is less than two-fold, whereas Wolff et al. [25] found a three- to five-fold increase for the rate of tension recovery (ktr) after quick release. To be consistent with Rossmanith and Tjokorda's analysis [16], the kinetics of both quasi-isometric and de novo crossbridges must be significantly Ca-sensitive. This implicates events in the weak-to-strong state transition, as well as attachment rate (f), given the relative sensitivity of fmin and ktr to these rates. This conclusion agrees with the findings of Wannenburg et al. [20] that revealed Ca-sensitive crossbridge kinetics from a transfer function-based sinusoidal analysis of rat myocardium. One reading of Fig. 3A is that this element of Ca-regulation is virtually lost in LIG, accounting for the difference in fmin for fully Ca-activated tissues (Fig. 3 and Table 3).

4.4 Myofilament protein changes?

Some elements of crossbridge kinetics are slower in LIG (e.g. Fig. 5, Table 3), consistent with reports for human CHF [6,13]. Several features argue against known myofilament isoform alterations causing this change in adult rabbit or human. fmin correlates with the ratio of the V1 to V3 myosin, slowing as V3 increases (e.g. Ref. [21]). Myosin isoform shifts are well documented in cardiac pathological and maturational states in several species, but slow V3 is already predominant in human and adult rabbit ventricle. The minor V1 fraction (detected as protein or mRNA) may diminish in disease states, but no consistent change has been reported ([27–29], but see Ref. [6], Section 4.2). However, reduction of an already small fraction of V1 myosin reportedly has little effect on filament sliding velocity [29], so an effect on fmin is not anticipated.

The phosphorylation status of MLC2 has been implicated in the aetiology of failure. However, selective phosphorylation of cardiac MLC2 by endothelin affect neither fmin nor maximum Ca-activated tension [5]; Morano et al. [30] found no MLC2 phosphorylation differences in human ischaemic myopathy. Increases in ventricular atrial MLC1 associated with some disease state increased Ca-sensitivity [30]. Alterations in TnT isoforms may underlie depressed myofibrillar ATPase in CHF, but correlate with reduced tension production in familial hypertrophy [31]. Finally, TnI phosphorylation is reported [32] to increase fmin, but this is associated with reduced Ca-sensitivity. Given no significant alteration in Ca2+-sensitivity or maximum tension in LIG (Table 3), we conclude such TnI, MLC or TnT changes are not significant for the present observations.

We have previously reported that fmin was reduced in both SH and LIG tissue by oxygen-derived free radicals (ROS), such HOCl (hypochlorite) and superoxide [11,17]. This is also true for phase shifts (data not shown). Chronic exposure of myofilament proteins to ROS, in vivo after ligation, could contribute to the kinetic alterations reported here.

4.5 Crossbridge properties

Hasenfuss et al. [33] found reduced isometric tension-dependent heat in human LVD, indicating decreased crossbridge number. We found that LIG maximum stiffness is not significantly altered, nor was the stiffness vs. tension relationship. If fewer in number, active crossbridges would have to be stiffer in LIG, but a decrease in maximum Ca2+-activated tension would be expected. This was not found (Table 3).

Average crossbridge tension-time integral, reflecting crossbridge attachment time, increased ∼33% in human failing myocardium [33], consistent with the slowing we observed (mean fmin is 23% lower in LIG, Table 3). Increased attachment time can manifest two different outcomes for cardiac function. From the energy-economy perspective, it may seem favourable that greater tension is generated per ATP, especially since diseased hearts have reduced energy reserves, e.g. [13]. However, prolonged attachment time will decrease relaxation rate, the scope for developing power and thus pump function.

4.6 Sinusoidal work

Phase relationships between length and tension from sinusoidally perturbed striated muscle reveal information about its mechanical properties [3,14,15]. In LIG, maximum positive and negative φ were reduced (Table 4), like fmin, and sinusoidal work and power correspondingly. However, first we consider the nature of the phase-shift data. Although phase relationships stabilise quickly after frequency changes (Fig. 2), φ is often far from constant throughout a single cycle, particularly near fmin (see Figs. 2, 4 and 7). Similar deviations reported for skeletal fibres [15] were not due to sarcomere inhomogeneity. Rossmanith and Tjokorda [16] found that such deviations can be predicted from crossbridge kinetics and are sensitive to the oscillation amplitude. Their analysis predicts the largest distortions centre on fmin, as observed here (e.g. Table 5).

We quantified phase-shift variation as a ‘loop factor’ (Section 2, Fig. 7, Table 5), potentially valuable since loop asymmetries probably reflect crossbridge conversion of chemical to mechanical energy [3,34]. For phase lead, the loop factor was close to unity for both groups. However, for phase lag (external work generated), the loop factor was significantly smaller, meaning greater phase angle variation during each loop (both groups, see Table 5). For LIG, loops obtained near fmin were consistently different on the shortening sector, i.e. during concentric contraction (compare Fig. 7A and B). This implies, as concluded earlier (Sections 4.2 and 4.3), that certain strain-related kinetic features of crossbridge action [12] are selectively compromised in LVD.

Decreased contractility in CHF is well documented but difficult to assess clinically. Pressure–volume loops provide one approach [35] analogous to sinusoidal work loops. Our findings reveal that, beyond the biophysical characterisation of crossbridge function, sinusoidal analysis helps to assess functionally critical attributes of myocardium. Normally, fw is marginally slower than fp and, in turn, than fmin. Insofar as these parameters relate to overall crossbridge cycle rate, this meets the adaptive functional optimisation first suggested by Hill [36]. fmin, fw and fp are all slower in LVD, yet the relationship among them is maintained. This may reflect an adaptive response to stress.

We considered the frequencies near fmin because they relate best to those experienced by crossbridges in vivo. The perturbation of active myocardium will principally be at frequencies generated by the component myofilaments. Any crossbridge, or cell, being stretched by stronger and/or faster contracting neighbours can ‘resist’ such stretch to an extent far greater than the stress it generates itself (thus maximum negative power exceeds maximum positive power near fmin; Table 5). It may be significant that the loop factor reduction in LIG is mostly due to a deficit on the shortening side (Fig. 7). Nevertheless, most LIG preparations could produce net positive work, at least at one frequency or, in the five worst cases, only just fail to exceed zero (Figs. 5 and 6). By contrast, Iwamoto [15] reported many frog fast twitch skeletal fibres failed to generate positive sinusoidal work (thus termed ‘idler’ fibres), attributing this to ‘greater nonlinearity’ in kinetic properties (broadly equivalent to the loop asymmetries discussed here). No doubt the muscles in that study, as well as the present one, would generate external work physiologically (i.e. undergoing significant shortening while under load). The lack of oscillatory work merely indicates that protocol details are critical.

4.7 Physiological implications of reduced sinusoidal work and power

Myocardium generally works submaximally, leaving a ‘contractile reserve’ to match greater haemodynamic demands. In heart failure, a reduced reserve is revealed as ‘exercise intolerance’. Our results show that myofilament (oscillatory) work and power, even with optimal activation, are reduced in early-stage LVD. These properties will amplify deficits in E–C coupling, upstream from contraction.

To clarify the functional implications, consider cardiac mechanics in vivo. Early-phase ventricular contraction is isovolumic, roughly analogous to isometric experimental conditions, producing no external (pump) work. However, cycling crossbridges always accomplish localised movements across the ventricle walls and work internal to the sarcomere. In this brief phase, the ability to absorb work might be highly relevant. If cells or segments initially being stretched are able to shorten within a brief enough time, the visco-elastic work stored in the strained crossbridges can be released mechanically rather than dissipated as heat [37]. This is a process akin to the ‘thermal ratchet’ described by Maughan et al. [34]. Once sufficient pressure has developed, the exit valves open, and ejection begins (auxotonic conditions). The rate at which the blood is ejected is influenced by power rather than work characteristics and thus, intimately related to heart rate [38].

The development of quasi-isometric tension (isovolumic pressure) in vivo requires component segments both to develop tension and sustain it. For quasi-isometric tension, those crossbridges (or sarcomeres, cells, or groups of cells) too weak to shorten must at least resist being lengthened, otherwise, tension and pressure will dissipate. While isometric tension is unchanged in this model of LVD (see Table 3), the capacity to work, that is to move that tension even through small distances, is significantly reduced. Quasi-isometric tension development can be compromised even if truly isometric tension is not. This deficit becomes prominent during ejection, slowing systolic pressure rise. This could be compensated for if the myocardium generated sufficient power, but that is also reduced. These deficits lead to decreased EF and cardiac output, as observed [7,9]. Work and power deficits are exacerbated in vivo, since the LVD heart generally pumps against a greater afterload. However, failing heart cannot accommodate this demand, placing it under further stress.

Finally, myofilament function in LVD myocardium might alter homogeneously or heterogeneously; the trabeculae studied here probably include sub-endocardial and M-cell types, as reported for canine trabeculae [39]. Our group has already found heterogeneity in both Ca-transients [7] and electrophysiological characteristics [40] in this model. Any heterogeneity at the myofilament level exacerbates the E–C coupling heterogeneity upstream and thus any pump dysfunction, as described above.


We are grateful to the Medical Research Council and the British Heart Foundation for the financial support. GW was an MRC Research Scholar.


  • Time for primary reviews 23 days


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View Abstract