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Passive Stiffness of Isolated Cardiac and SkeletalMyocytes in the Hamster

Daniel Fish, Jan Orenstein, and Sherman BloomFrom the Department of Pathology, George Washington University Medical Center, Washington, D.C.

SUMMARY. Single cardiac myocytes and skeletal myocyte fragments, devoid of interstitialcollagen but with intact glycocalyx, were prepared by mechanical disaggregan'on of hamsterventricular myocardium and caudal gracilis muscle, respectively. Passive stiffness was studied byexamining the sarcomere length-tension relationship over the approximate Eulerian stress rangeof 0-20 mN/miTr for cardiac myocytes and 0-120 mN/mm2 for skeletal myocytes. Creep andstress-relaxation became apparent only when cells were stretched to sarcomere lengths close to,or exceeding, 2.2 pm for the cardiac myocytes, and 2.7 /zm for the skeletal myocytes. Stress-relaxation and creep occurred simultaneously, suggesting that the sarcomere is at least one of thestructural components responsible for viscoelasticity. The differential strain stiffness constant wascalculated from the regression of natural stress [Ln(mN/mm2)] against differential strain [(L-Lo)/Lo] and found to be 7.48 ± 1.73 for the ventricular myocytes and 5.77 ± 0.87 for the skeletalmyocyte fragments. The natural strain stiffness constant was obtained from the regression ofnatural stress against natural strain [Ln(L/Lo)]. The natural strain stiffness constant was 30-50%higher than the differential strain constant. The high correlation coefficients obtained for bothregressions indicate that the length-tension relationships for these isolated cardiac and skeletalmyocytes can be very closely fitted to the single exponential function, a = C-exp[K(<)]. The length-tension curves obtained for the skeletal myocyte fragments are qualitatively and quantitativelysimilar to those obtained by others with intact skeletal muscle. The cardiac myocyte length-tension curves are qualitatively, but not quantitatively, similar to those obtained with cardiacmuscle. Isolated ventricular myocytes are stiffer than similarly isolated skeletal myocytes. Thesefindings suggest that cellular structures contribute to myocardial stiffness in the hamster. (CircRes 54: 267-276, 1984)

PASSIVE stiffness at long sarcomere lengths is muchgreater in cardiac muscle than in skeletal muscle,and may function to limit excessive diastolic stretch-ing (Braunwald et al., 1976). This restriction of dia-stolic stretching is a critical function, inasmuch as,without it, pathological ventricular dilation wouldoccur. On the other hand, excessive stiffness is un-desirable because it reduces contraction velocity(Pollack, 1970; Mirsky et al., 1981; Natarajan et al.,1979). The sites of the stiffness-inducing structuresin cardiac muscle are unknown. Many intracellularanatomic sites have been suggested as candidates,including the sarcolemma, residual actomyosincrossbridges, actin-dependent 'intracellular struc-tures," actin links across the H zone (S filaments),myosin-Z-line connections (C filaments), and Z-Iine-to-Z-line connections. These studies have been re-viewed by Sonnenblick (1974).

Recent studies have reported the isolation andcharacterization of an intracellular elastic protein,connectin, thought to be the source of the parallelelastic element (PE) which is responsible for cardiacstiffness at long sarcomere lengths (Maruyama etal., 1977a, 1977b; Fabiato and Fabiato, 1978). Fa-biato and Fabiato showed that the passive mechan-ical properties of 'skinned" cardiac myocytes (sar-colemma removed) are highly variable, depending

on the particular species of animal under study.Their results suggest an intracellular site for the highresting stiffness of intact rat cardiac muscle, whereasfrog and dog cardiac muscle stiffness depends moreon elements in either the cell surface complex orextracellular connective tissue.

Interstitial collagen is attractive as a source ofdiastolic stiffness (Borg et al., 1981a, 1981b), espe-cially in view of the physical properties of collagenand its widespread function in loadbearing (Fung,1981). However, the intersntium does not show ananatomic arrangement that suggests a specific rolein generating diastolic stiffness. That is, there is noclear longitudinal component to the system of inter-stitial collagen fibers. If collagen were the PE, itsrole would be mechanically complex, and dependon longitudinal stress vectors of nonlongirudinalfibers.

Data concerning the correlation between age, col-lagen content, and various indices of intrinsic myo-cardial stiffness tend also to be species dependent(Mirsky et al., 1976; Kane et al., 1976; Weisfeldt etal., 1971). The observed increase in ventricular dis-tensibility with increasing age in the rat (Mirsky etal., 1981) is interesting, in light of the fact that anelevated level of connective tissue in the heart ofthe old male rat has been well established (Gay and

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Johnson, 1967; Weisfeldt et al., 1971; Borg et al.,1981a, 1981b). Also, passive stiffness may be normalor elevated in ventricles of patients with aortic ste-nosis (Gaasch et al., 1982; Mirsky et al., 1974) inwhich the collagen content is known to be increased.These studies suggest that the strategic distributionof collagen or other elastic elements, rather thansimply the amount, may relate more directly tooverall cardiac muscle stiffness.

A component of the cell-surface complex thatcould be a source of passive stiffness is the systemof unbanded fibrils, or 'cell-surface cables," that arepresent on the surface of heart muscle cells (Oren-stein et al., 1980). These cables are partially buriedin the glycocalyx, and, in contrast to interstitialcollagen, are largely parallel to the long axis of thecell. The orientation of these cables suggests thatthey could contribute to diastolic stiffness.

The mechanical disaggregation procedure, bywhich cells were prepared in this study, has beenshown to yield cells with an intact glycocalyx (Or-enstein et al., 1980). Cell surface cables, roughlyparallel to the long axis, and partially embedded inthe glycocalyx, are abundant. Interstitial collagen,however, is absent, except for rare random strands.Although the glycocalyx appears intact, the cellsbehave as though their membranes are leaky, in thatthey present no permeability barrier to calcium ormany other substances, ionic and non-ionic (Bloomet al., 1974; Tsokos et al., 1977). This leakiness maybe due to occasional physical defects in the cellsurface, or to biochemical factors. The importantpoint is that, although the cells are leaky, the cellsurface complex is morphologically intact. For thisreason, cells prepared by mechanical disaggregationmight be suitable for testing the hypothesis that thePE resides within hamster cardiac myocytes or theirimmediate surface coat, rather than the interstitium.An intact glycocalyx is also present on skeletal my-ocytes obtained by this method (Caced et al., 1981).Therefore, comparison of the mechanical propertiesof these two myocyte preparations is justified.

In an attempt to further narrow the range ofpossible choices for the anatomic locus of the PE,we have studied the passive mechanical propertiesof single cardiac myocytes and skeletal myocytefragments in the hamster. The aim of this work wasto determine whether single myocytes, with intactglycocalyx, but devoid of interstitial collagen, pos-sess passive mechanical properties similar to thoseof intact cardiac muscle in the hamster. The passivemechanical properties displayed by these isolatedmyocytes that are of interest in intact muscle includethe nonlinear length-tension relationship, a linearrelationship between natural stress and natural ordifferential strain, stress-relaxation, and creep. Thepassive mechanical properties of intact cardiac mus-cle appear to be qualitatively but not quantitativelyreflected in isolated cardiac myocytes. An intracel-lular site which contributes, at least in part, to thestiffness of hamster myocardial tissue is thereforesuggested.

Circulation Research/Vol. 54, No. 3, March 1984

TerminologyAt this point, it is appropriate to define the terms

employed in this study, since much confusion andmisinterpretation of data stem from the use of in-consistent terminology.

Stress (ff) is defined as force per unit cross-sec-tional area of a material, and is a measure of theintensity of force. Units commonly employed aremN/mm2, g/cnr, mg/mm2, etc. The terms "stress"and "tension" are interchangeable.

Strain (e) is the fractional or percent dimensionalchange of a stressed elastic material from its originalor unstressed shape. It is a dimensionless quantity.Both Lagrangian and Eulerian strain are used inmuscle mechanics. Lagrangian strain assumes(among other things) a constant cross-sectional areafor materials subjected to variable amounts of stress.Eulerian strain assumes that for large deformations,defined as greater than 0.2%, the physical dimen-sions of stressed materials undergo significant alter-ation. Therefore, Eulerian stress-strain relationshipsare evaluated on the basis of instantaneous cross-sectional area. Eulerian theory is particularly appli-cable in studies such as this, since muscle undergoeslarge deformation over the range of load applied.Values of stress calculated using either Lagrangianor Eulerian strain are referred to as Lagrangian orEulerian stress, respectively.

Two different mathematical expressions for strainare used in this study and the results are compared.

(L-Lo)/Lo: "differential strain' (DS)Ln(L/Lo): "natural strain" (NS)Either of these expressions of strain are applicable

to the study of both Eulerian and Lagrangian stress-strain relationships.

MethodsHeart muscle cells were prepared from Syrian golden

hamsters, as previously described (Orenstein et al., 1980).The same method was applied to skeletal muscle cellsobtained from the caudal portion of the gracilis muscle.The hamsters were male, random bred, 100-130 g, and2-5 months old. In brief, about 500 mg of left ventricularmyocardium were homogenized in a Virtis-45 homoge-nizer in 25 ml of ice-cold homogenization medium (HM)containing, in mmol/liter: KG, 135; Tris buffer at pH 7.1,50; MgCl2, 2; ATP, 2; Na+, 1. The homogenate was passedthrough a 100-mesh stainless steel screen in a 2.5-cmSwinnex filter holder (Millipore Filter Corp.) to removelarge fragments and sedimented once at 150 g for 30seconds to remove subcellular debris. The cell pellet wasresuspended in 30 ml of HM and kept at 0°C. A drop ofthis homogenate, containing many cells, was transferredto a plexiglass flow cell. A single cell was selected, impaledat each end with glass needles, and superfused at aconstant flow rate of 0.33-0.66 ml/min with HM contain-ing 2 rriM EGTA (HM-EGTA) at 25°C. The calculated[Ca"1"*] of HM-EGTA was 10~8 M, assuring complete relax-ation. Cells were selected for impalement on the basis ofregularity and clarity of the sarcomere pattern and overallappearance. The glass needles used for impalement wereprepared from capillary tubing, using an electrode puller.The needle tips were curved into hooks with a de Fon-brune microforge.

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Fish et al. /Stiffness of Isolated Cardiac and Skeletal Muscles 269

One glass needle, mounted on a motorized microma-nipulator (Eric Sobotka Co.), served as a mechanical an-chor. The other needle was attached to a high-sensitivitysmall displacement force transducer (Ade Corp.) mountedon a micromanipulator fashioned from a microscope base.The transducer was calibrated with wisps of thread ofknown mass. Transducer compliance did not influence themeasurements reported here, since direct measurement ofsarcomere length was used. For the same reason, highcompliance at the sites of impalement would not influencethe results. Tension was recorded on a strip-chart recorder.The entire experimental apparatus rested on a Micro-gvibration isolation table (Technical Manufacturing Corp.).This, in turn, was surrounded by a wind-screen, and waslocated in a room with minimal forced-air ventilation.

The flow cell was located on the stage of a Leitz Diavertinverted microscope equipped for 35-mm photography. Apneumatic shutter release and automatic film advance,selected for minimum vibration, were used. After impale-ment, cells were photographed to determine the sarcomerelength at zero tension. Then the impaling microneedleswere moved further apart, to produce a length and tensionincrement. Another photograph was taken and the tensionagain raised. This was continued until a set of photographswas obtained, one for each of a series of tensions. Thelength of the preparation was generally adjusted by hand-controlled movements of the transducer micromanipula-tor. Sarcomere length was determined by projecting 35-mm negative images of cells onto a surface where meas-urements could be accurately made. These were comparedto a projected scale obtained from the photographic imageof a stage micrometer. For cardiac and skeletal myocytes,the average sarcomere length at each tension incrementwas obtained by measuring groups of 3-40 consecutivesarcomeres and dividing by n (n = 20-150). For somecells, more than one set of sarcomeres was counted. Hence,the average number of sarcomeres counted per cell exceedsthe maximum number present in any one consecutiveseries. Sarcomeres close to attachment sites were not in-cluded in the stress-strain analysis, due to optical interfer-ence from the microneedles, and the higher probabilitythat these areas had sustained internal structural damageduring the impalement process.

The stiffness constant, K, was taken from the equation:

Ln(<r) = Ln(C)

where: (<r) = stress in mN tension/mm2 of x-sectionalarea

(t) = either natural strain [Ln(L/Lo)] or differ-ential strain [(L-Lo)/Loj

L = mean sarcomere length at any given tensionLo = mean sarcomere length at zero tensionC = a constant

K was calculated as the slope of the regression of Ln(stress)against either Ln(L/Lo) or (L-Lo)/Lo. We use the notationK(NS) or K(DS) to indicate K calculated by natural ordifferential strain, respectively.

The stress-strain relationships described here are notvalid when stress is zero. That is, Ln(stress) does not equalzero when Ln(strain) is zero. However, this expression isotherwise in conformity with the fundamentals of elastic-ity theory. Values for instantaneous stress at 2.2 and 2.6urn were obtained for each cell (Tables 1 and 2) bysubstituting the appropriate sarcomere lengths into thenatural or differential expressions for strain

<J = C • exp[K • Ln(L/Lo)]

or

a = C • exp(K • [(L-Lo)/Lo])and solving for a. Each of these equations permits calcu-lation of Eulerian stress, since, in both instances, instan-taneous values of cross-sectional area were employed ateach level of load. The cross-sectional area of the cell wascalculated from the measured cell diameter, assuming thecell was circular in cross-section. Results are stated asmean ± SD. Student's t-test was used for the comparisonof mean values. The concentration of ionized calcium inthe medium was calculated by the Newton-spontaneousoverrelaxation method (Ortega and Rheinboldt, 1970).

After completion of the length-tension recording, thecell was superfused with HM-EGTA containing 2.5% glu-taraldehyde for 45 minutes and rinsed with HM-EGTAfor 5 minutes. Cells then were carefully extricated fromthe needles and transferred with a 10-/*l micropipet to a6 x 6 mm coverslip pretreated by a modification of themethod of Sanders et al. (1975). We applied a thin film ofpoly-L-lysine to an acid-alcohol washed coverslip, andallowed this to dry in room air. This provided a surface towhich the cells would adhere tightly for processing. Thesuspended cells were allowed to settle onto the coverslipsovernight, at 4°C, prior to processing for scanning electronmicroscopy (SEM).

Cells were prepared for SEM as previously described(Orenstein et al., 1980). In brief, the coverslips were passedthrough increasing concentrations of ethanol up to dessi-cated 100%, and critical-point dried with a Samdri critical-point drier (Tousimis Research Corporation). After critical-point drying, the coverslips were mounted on aluminumstubs with cyanoacrylic cement and silver paint. The stubswere then coated with 150-200 A of 60:40 gold:pallidium,using a Denton evaporation unit and tilting omni stage(Denton Vacuum Incorporated), and scanned in a JEOLJSM-35 SEM equipped with a tungsten filament. Imageswere recorded, at magnifications of 20x-30,000x, onPolaroid P/N 55 film.

ResultsThe sarcomere length of ventricular myocytes sus-

pended in HM-EGTA and photographed immedi-ately after impalement (Lo) was 1.74 ± 0.09 jtm(Table 1). This measurement was made with notension load on the cells. In fact, care was taken toprovide a small amount of slack. This sarcomerelength was much greater than was noted in cellssuspended in HM and not impaled for mechanicalstudies (Orenstein et al., 1980). This is due to thelow [Ca++] of HM-EGTA, calculated to be about10~H M. In comparison, the [Ca++] of HM is about10"6 M (Bloom et al., 1974). The long, load-freesarcomere length of impaled cells [Lo (Tables 1 and2)] indicates that the contractile apparatus wasquiescent, as would be expected at this low ionizedcalcium level (Fabiato et al., 1976). In several earlyexperiments, the medium was briefly changed toHM, to verify that the cardiac myocytes would showspontaneous contractile activity. This was, in fact,observed for every cell thus tested.

Cardiac myocytes selected for impalement had amean diameter of 29.2 ± 6.3 /xm. Whereas we donot have prior data on the diameter of isolatedhamster ventricular myocytes, this value is not sig-

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nificantly different from that reported for rat cells.These have been found to be 12-40 fjm in diameter(Bishop and Drummond, 1979; Carlson et al., 1978;Moses and Kasten 1979; Powell et al., 1978). Theappearance of impaled cells, by both light micros-copy and SEM (Figs. 1 and 2) was that of mechani-cally disaggregated heart muscle cells, as previouslydescribed (Orenstein et al., 1980). Transmission elec-tron microscopy of cells embedded in plastic directlyfrom the coverslip, where they had been attachedfor SEM, revealed that selected cells were singlecells. Skeletal myocyte fragments selected for im-palement had a mean diameter of 62 ± 14 pm.

Cells recovered after impalement showed scantevidence, at the SEM level, of injury by the glassmicrotools. For cardiac myocytes, the only evidenceof prior impalement was a small, barely recognizablehole in the cell surface at the impalement site (Fig.2, c and d). Although it is obvious that impalementmust produce local injury, and probably a region ofhigh compliance, the absence of a conspicuous rentin the cell, or distortion of the sarcomere pattern,implies that the injury was not as severe as antici-pated. At one impalement site, however, there wasdenudement of the cell surface complex distal to thesite of impalement (Fig. 2d), revealing the underly-ing myofilaments. This change was not observed atany other impalement site examined. It appearedthat this membrane was avulsed at the time the cellwas removed from the glass microneedles.

A typical tension recording is shown in Figure 3,which is a photocopy of an actual experiment (cellno. 1, Table 1). The sarcomere length, obtained fromphotographs taken at the indicated times, is also

Circulation Research/Vol. 54, No. 3, March 1984

given, together with the simultaneous tension, inmN/mm . It is apparent, from this figure, that thereis a substantial amount of stress-relaxation and creepobservable at sarcomere lengths approaching2.2 jtin, and above. Since our view of the cells understudy is limited to one focal plane or optical section,our observations are, clearly, incomplete. In additionto sarcomere length variation along the length ofthe cell, variation in the transverse plane must alsobe considered. That is, there may be some radialvariation in strain, since the angular relationshipamong sarcomeres did show some variation acrossthe cell width (Fig. 1). However, this could not beestimated with sufficient reliability to justify an at-tempt at quantification. We would anticipate thatradial variation in strain is randomly distributed,and is not a significant source of error.

The sarcomere length-tension curves obtained forisolated hamster ventricular myocytes (Figs. 4a and5) are similar to those obtained previously withcardiac muscle and whole heart preparations (Spiroand Sonnenblick, 1964; Spotnitz et al., 1966;Winegrad, 1974). The skeletal myocyte length-ten-sion curves (Figs. 4a and 5) are similar to thoseobtained previously with intact skeletal musclepreparations (Spiro and Sonnenblick, 1964; Lanner-gren and Noth, 1973; Moss and Halpern, 1977).These data are also similar to those obtained withintact heart and skeletal muscle preparations, in thatthey demonstrate a linear relationship between nat-ural stress [Ln(mg/mm2)] and both NS and DS (Fig.4b). This technique for linearization of length-ten-sion data has been discussed in detail (Mirsky andParmley, 1973; Natarajan et al., 1979).

1

FIGURE 1. Light micrograph obtained using bright-field illumination of a skeletal myocyte fragment during stress-strain analysis. H-zones areseen here, as they were with all skeletal myocyte fragments at sarcomere lengths greater than 199 p.m. Sarcomere length here is 3.82 )im for 138sarcomeres. Bar ~ 40 fim; 410*.

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FIGURE 2. Part a: cardiac myocyte held with two microneedles for tension recording. Sarcomere length is 2.16 + 0.14 pm for 51 sarcomeres. Thecell was fixed at this level of tension and processed for SEM (bar =10 nm). Part b: scanning electron micrograph of the cell shown in part a.Surface undulations can be seen, but surface cables are not visible at this magnification. Part c: high magnification of the impalement siteindicated on the left, in part b. Four mitochondria are seen at the edge of the elongated defect. Undulations and surface cables (arrow) areapparent. Part d: high magnification of the impalement site indicated on the right in part b. This defect is smaller. The surface complex has beenremoved distal to the defect, exposing myofilaments. Magnifications: part a, 540x, bar = 10 fim; part b: 585X, 30° tilt; part c: 10,000x, 30° tilt,bar = 1 nm; part d: lO.OOOx, 30° tilt.

TJX

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272 Circulation Research/Vo/. 54, No. 3, March 1984

2 99

3.

(mN/mm'l

FIGURE 3. Recording of a length-tension curve obtained with an isolated hamster cardiac myocyte (cell no. 1, Table 1). Sarcomere length, m urn,is indicated along with the simultaneous tension, in mN/mm1. Arrows indicate points along the tension recording where photographs were takenfor sarcomere length determination. At the end of the experiment, a repeat baseline recording was made. This has been moved to the left toconserve space.

TABLE 1

Stress-Strain Parameters of Cardiac Myocytes

Cellno

12345678

MeanSD

Lo

1.451.621.801.851.771.801.661.74

1.740.09

Cellwidth(Mm)

35.930.229.333.037.723.024.320.4

29.26.3

A.

K(NS)

8.487.98

12.0910.78

7.6613.869.58

10.14

10.072.14

Calculated

r

0 9710.9880.9610.9820.9860.9800.9910.994

0.9820.011

using Ln(L/Lo)

Stress(mN/mm2)

2.2 Mm

0.620.720.170.821.020.381.441.83

0.880.55

2 6 Mm

2.572.711.304.943.673.837.159.86

4.502.78

B.

K(DS)

5.285.848.718.856.44

10.406.787.58

7.481.73

Calculated

r

0.9610.9890.9500.9860.9890.9870.9940.995

0.9810.017

using (L-Lo)/Lo

Stress(mN/mm2)

2.2 Mm

0.560.630.600 740.970.371.391.79

0.880.48

2.6 Mm

2.392 664.155.004.163.697.04

10.20

4.912.58

K, r, stress at 2.2 (im, and stress at 2.6(NS) or differential strain (DS).

were calculated from the regression of natural stress [Ln(mN/mm2)] against either natural

TABLE 2

Stress-Strain Parameters of Skeletal Myocytes

Cellno.

12345

MeanSD

Lo(jim)

2.342.632.161.982.15

2.250.25

Cellwidth(Mm)

42.578.371.757.660.4

62.113.8

A.

K(NS)

8.817.06

10.048.238.67

8.561.08

Calculated

r

0.9970.9810.9980.9820.997

0.9910.007

using Ln(L/Lo)

Stress(mN/mm2)

2.2 Mm

0.280.330.100.270.19

0.250.06

2.6 Mm

1.201.070.521.060.79

1.020.15

B.

K(DS)

5.735.227.005.125.81

5.770.87

Calculated

r

0.9920.9800.9950.9880.998

0.9910.007

using (L-Lo)/Lo

Stress(mN/mm2)

2.2 Mm 2.6 Mm

0 63 1.670.60 1.330.19 0.670.39 1.110.28 0 83

0.44 1.200.16 0.36

K, r, stress at 2.2 Mm, and stress at 2.6 Mm were calculated from the regression of natural stress [Ln(mN/mm2)] against either natural(NS) or differential strain (DS).

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Fish et a/./Stiffness of Isolated Cardiac and Skeletal Muscles 273

Table 3 summarizes some of the information givenin Tables 1 and 2. Here, we can see an explicitcomparison of the parameters of passive mechanicalproperties calculated from experimental data, using

4aoHRT M CELL1.TBL 1•SKELM CELL-3. TBL2

20 25Svcomef* Length Cl*n)

4b• SKEL M CELL [LN(L/Lo|]• SKEL M CELL QL-Lo]/Ldo HUT M CELL U-N(L/Lo)]• HRT U CELL QL-Lo|/Lo]

Strain [(L-U>|/Lo or LN|L/Lo| ]

FIGURE 4. Part a: sarcomere length-tension curve obtained for thecardiac myocyte experiment shown in figure 3 and for a skeletalmyocyte fragment (cell no. 3, Table 2). Part b: plot of stress-straindata for the same isolated cardiac and skeletal myocytes shown inpart a. For natural strain, the broken line describes the equation,Ln(a) = 8.48-Ln(L/1.45) + Ln(0.60), for the cardiac myocyte, andLn(o) = 10.04-Ln(L/131) + Ln(2.76), for the skeletal myocyte frag-ment. For differential strain, the solid line describes the equation,Ln(a) = 5.28(L - 1.45)/1.45 + Ln(0.60), for the cardiac myocyte, andUi(o) = 7.00-[(L - 2.3V/2.31] + Ln(3.25), for the skeletal myocytefragment.

20.0-,

z

io.o-

1 2 3

Sarcomere Length (/jm)

FIGURE 5. Composite length-tension curve for eight cardiac myocytesand five skeletal myocyte fragments.

either natural or differential strain. The use of nat-ural or differential strain significantly affects thecalculated K, but has less of an effect on the calcu-lated stress. For the data shown in Table 3, the useof NS vs. DS had no effect on calculated values ofstress, except for skeletal myocytes at a sarcomerelength of 2.2 nm. The data in Table 3 can also beused to compare cardiac and skeletal myocytes inregard to these same parameters. Since skeletal mus-cle is known to be more compliant than cardiacmuscle, a one-tailed f-test was used for calculationof the P values. Comparison of stiffness constantsand calculated stress at sarcomere lengths 2.2 and2.6 Mm shows that cardiac myocytes are more stiffthan skeletal myocytes. The difference between val-ues of K(NS) is not significant, but it is highly

TABLE 3

Summary and Comparison of Calculated Parameters

K(NS)K(DS)P

Stress at2.2 /rai

NSDSP

Stress at2 6 pm

NSDSP

Cardiacmyocytes

10.07 ±2.147.48 ± 1.73

<0.02

0 88 ± 0.550.88 ±0.48

*

4.50 ±2.784.91 ±2.58

*

Skeletalmyocytes

8 56 ± 1.085.77 ± 0.87

<0.002

0.25 ± 0.060.44 ± 0.16

<0.05

1.02 ± 0 151.20 ± 0.36

P

<0.086<0 031

<0.014<0.037

<0.009<0.005

Abbreviations: NS, natural strain; DS, differential strain. Unitsof stress: mN/mm2.

* Indicates not significant, or P > 0.05.

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suggestive. This difference in K would probably besignificant if the range of stress for the skeletalmyocyte fragments (0-120 mN/mm2) was limitedto the same range obtained for the cardiac myocytes(0-20 mN/mm"). In general, comparisons of musclestiffness (K) must be made over the same range ofstress. In spite of this discrepancy, the skeletal my-ocyte K(DS) is significantly less than the cardiacmyocyte K(DS). The values of stress at sarcomerelengths 2.2 and 2.6 nm are clearly higher for thecardiac than for the skeletal myocytes.

The correlation coefficients (r) indicate a tightclustering of data points around the calculatedregression lines (Table 1). The values of K(NS) andK(DS) were calculated using only 'peak* tensionvalues obtained from stress-strain curves of isolatedcells. To evaluate the effect of the observed viscoe-lasticity, a worst-case calculation was performed inwhich only "plateau* or 'steady state* length andtension values were used for the natural strainregression analysis of the cardiac myocytes. Thiscalculation yielded a mean K(NS) for the eight cellsof 9.23 ± 0.71 (mean ± SEM). This was significantlydifferent from K(NS) calculated using the peak val-ues (P < 0.05).

DiscussionThe data shown here are similar to those obtained

by others, in that the cardiac and skeletal musclelength-tension data can also be interpreted as beingbilinear or biexponential, resulting from differentstiffness elements dominating the high and lowstress ranges of the curve. The same data can be,and usually are, interpreted as being uniexponential.The high r values for the regression of Eulerianstress against either NS or DS for all cells studied(Tables 1 and 2) indicate that uniexponential linear-ization is appropriate. This suggests that a singlestiffness element is operative throughout the fullrange of both the cardiac and skeletal myocytelength-tension curves.

The high r values also suggest that both expres-sions of strain (NS and DS) are equally valid forlinearization of the sarcomere length-tension curves.However, as shown by Mirsky and Parmley, (1973),values of K are dependent on the particular mathe-matical expression of strain employed. This indicatesthat care must be exercised when comparing indicesof stiffness obtained from length-tension or pres-sure-volume studies. Our results show (Tables 1 and2; Fig. 4b) that NS increases more slowly withincreases in sarcomere length than DS, resulting ina 30-50% higher value of K(NS). K(NS) obtainedfor the cardiac myocytes (10.07 ± 2.14) is similar tothe K obtained indirectly from pressure-volume data(10.93 ± 0.51; mean of nine age groups, from 1 to24 months ± SEM) by Kane et al. (1976) with intacthamster ventricles. However, DS was the definitionof strain used by Kane et al., who obtained K byplotting the slope of the length-tension curve at a

Circulation Research/Vol. 54, No. 3, March 1984

given value of strain, as a function of strain at thatpoint on the curve. K(DS) is therefore more compa-rable to the K obtained by Kane et al., and can morereliably be compared to length-tension data ob-tained by others who have also used DS. It shouldbe noted that, as L approaches Lo, NS approachesDS. Although the Y-intercepts for the NS and DSmethods are slightly different in Figure 4b, they aretheoretically identical, and observed to be not sig-nificantly different.

Comparison of the cardiac myocyte K(DS) (7.48± 1.73) with the K obtained by Kane et al. indicatesthat the isolated ventricular myocytes are not as stiffas the wall of the intact left ventricle. Furthermore,K(DS) is comparable to a K (6.12) similarly obtainedfor isolated, intact frog atrial myocytes (Tarr et al.,1979). The atrial cells studied by Tarr et al., werefound to be more compliant than intact frog atrialtrabeculae studied by Winegrad (1974). Using DS,we linearized the data of Winegrad [(1974) Fig. 5]and obtained a K of 11.7 with a stress at 2.2 /xm of5.1 mN/mm2. This stress is 5-10 times higher thanour mean value of stress at 2.2 /*m (0.88 ± 0.55mN/mm2) for the ventricular myocytes. However,it should be noted that trabecular preparations havenot been proven to be entirely representative ofventricular myocardium in general (Sonnenblick andSkelton, 1974).

Values of stress at 2.2 Mm for hamster intactmyocardial preparations are not available for com-parison. However, studies involving mammalian in-tact cardiac preparations have reported a stress at2.2 ^m which is considerably higher than valueslisted for frog trabecular preparations. These include14.0 mN/mm2 for cat papillary muscle (Julianand Sollins, 1975), 15.7 mN/mm2 for the 11- to 12-month-old rat (Weisfeldt et al., 1971), up to 58.0mN/mm2 for dog papillary muscle (Kitabatake andSuga, 1978), with a mean of about 30.0 mN/mm2

for all reported values (Spiro and Sonnenblick, 1964;Spann et al., 1967; Natarajan et al., 1979; Kruegerand Pollack, 1967). We have conducted preliminarylength-tension studies on trabecular muscle prepa-rations isolated from the hamster right ventricle(data not shown). These studies indicate that stressat 2.2 ^m for hamster trabeculae is approximately3.0-8.0 mN/mm2 compared with 15.7 mN/mm2 inthe rat (Weisfeldt et al., 1971). This appears to bereasonable, since rat myocardium, at all ages, isconsiderably more stiff than hamster myocardium(Borg and Caulfield, 1981a).

For the skeletal myocyte fragments, the DS regres-sion gave a stress at 2.3 fim of 0.56 ± 0.19 mN/mm2. This value is comparable to a range of 0.46-0.77 mN/mm2 at 2.3 Mm for frog isolated twitchmuscle fibers (Lannergren and Noth, 1973) and 0.29± 0.02 mN/mm2 at 2.25 jim for whole semitendi-nosus muscle (Moss and Halpern, 1977). Comparedwith the skeletal myocyte fragments, the stress at2.30 Mm for the cardiac myocytes (1.34 ± 0.73 mN/mm2) is higher. Furthermore, the stress at 2.35 Mm

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Fish et al. /Stiffness of Isolated Cardiac and Skeletal Muscles 275

for the cardiac myocytes (1.67 ± 0.90 mN/mm2) ishigher than a Lagrangian stress at 2.35 nm (0.60mN/mm2) obtained by Tarr et al. (1979) with singleintact frog atrial cells. The cells studied by Tarr etal. were enzymatically isolated, so that the glycoca-lyx was probably absent (Bishop and Drummond,1979; Carlson et al., 1978; Moses and Kasten, 1979).At any rate, the length-tension curve obtained byTarr et al. is shifted considerably to the right, com-pared with those obtained with frog atrial trabeculae(Winegrad, 1974). In contrast, the composite length-tension curves obtained here for cardiac myocytesand skeletal myocyte fragments (Figs. 4a and 5) arequalitatively similar to curves obtained by otherswith isolated muscle and whole heart preparations(Braunwald et al., 1976). Our cardiac myocytelength-tension curves are also qualitatively compa-rable to curves obtained with isolated, 'skinned"ventricular myocytes of the rat (Fabiato and Fabiato,1978). Stress at 2.2 ^m is not obtainable for skinnedrat cells, since the length-tension curve obtained byFabiato and Fabiato employed percent tension ratherthan force/area plotted against sarcomere length.

One possible source of error in a study such asthis would be mistaking two cells for one. A rangefor .hamster cardiac cell width has not been estab-'lished in the literature. Values reported for rat ven-tricular cells range anywhere from 12 to 40 nm(Bishop and Drummond, 1979; Carlson et al., 1978;Moses and Kasten, 1979; Powell et al., 1978). Ourcell diameters were within this range (Table 1). Ifsome of our cardiac myocytes had been 2 cells thick,there might have i>een an increase in stiffness dueto the presence of interstitial matrix. However, trans-verse sections of two myocytes, examined by trans-mission electron microscopy (data not shown)showed them to be actually one cell thick. Further-more, the three lowest calculated values of K(DS)for the ventricular myocytes (5.28, 5.84, and 6.44)were obtained with the three widest cells (35:9,30.2,and 37.7 /im, respectively). There was no significantcorrelation between cell (diameter and the stiffnessconstant, K. It is apparent that wide cells were notmore stiff than thin cells.

The simplest representation of diastolic stiffnessis the sarcomere length-tension curve. The curvesobtained in this study suggest that the resting stiff-ness of hamster cardiac tissue, like that in the rat, isdue at least in part to inrracellular structural ele-ments. Since it has not been shown conclusively thattrabecular preparations accurately reflect ventriclewall stiffness, data from future length-tension stud-ies of isolated ventricle wall should be comparedwith the ventricular myocyte data. This comparisonwould more reliably reflect the interstitial contribu-tion to wall stiffness. The model used here seemsappropriate for further studies of this type. Futureapplications might also include studies of hyper-trophic changes at the cellular level during cardiachypertrophy. Likewise, studies dealing with the im-pact of exercise, nutrition, and aging on cardiac

muscle function at the cellular level can be envi-sioned.

We would like to express our appreciation to Philip Rutlcdge forphotographic assistance; also, our thanks to Susan Garrctt and ViannPowers for assistance in the manuscript preparation.

This research was supported by Grant PCM-8020968 from theNational Science Foundation.

Address for reprints: Department of Pathology, George WashingtonUniversity, Medical Center, 2300 Eye Street, Washington, D.C 20037.

Received January 21, 1983; accepted for publication January 11,1984.

ReferencesBishop SP, Drummond JL (1979) Surface morphology and cell

size measurement of isolated rat cardiac myocytes. j Mol CellCardiol 11: 423-433

Bloom S, Brady AJ, Langer G (1974) Calcium metabolism andactive tension in mechanically disaggregated heart muscle. JMol Cell Cardiol 6: 137-147

Borg TK, Caulfield JB (1981a) The collagen matrix of the heart.Fed Proc 40: 2037-2041

Borg TK, Ranson WF, Moslehy FA, Caulfield JB (1981b) Structuralbasis of ventricular stiffness Lab Invest 44: 49-54

Braunwald E, Ross J, Sonnenblick EH (1976) Mechanisms ofContraction of the Normal and Failing Heart, ed 2. Boston,Little, Brown and Company, pp 41-43

Caceci T, Orenstein JM, Bloom S (1981) Surface cables of verte-brate muscle cells. Scan Electron Microsc 3: 115-123

Carlson EC, Grosso DS, Romero SA, Frangakis CJ, Byus CV,Bressler R (1978) Ultrastructural studies of metabohcally activeisolated adult rat heart myocytes. J Mol Cell Cardiol 10: 449-459

Fabiato A, Fabiato F (1976) Dependence of calcium release,tension generation and restoring forces on sarcomere length inskinned cardiac cells. Eur J Cardiol 4 (suppl): 13-27

Fabiato A, Fabiato F (1978) Myofilament-generated tension oscil-lations during partial calcium activation and activation depend-ence of the sarcomere length-tension relation of skinned cardiaccells. ] Gen Physiol 72: 667-699

Fung YC (1982) Biomechanics: Mechanical Properties of LivingTissues, ed 1. New York, Springer-Verlag, pp 203-214

Gaasch WH, Bing OHL, Mirsky I (1982) Chamber complianceand myocardial stiffness in left ventricular hypertrophy. EurHeart J 3 (suppl A). 139-145

Gay WA, Johnson EA (1967) An anatomical evaluation of themyocardial length-tension diagram Circ Res 21: 33-43

Julian FJ, Sollins MR (1979) Sarcomere length-tension relationsin living rat papillary muscle. Circ Res 37: 299-308

Kane RL, McMahon TA, Wagner RL, Abelmann WH (1976)Ventricular elastic modulus as a function of age in the Syriangolden hamster. Circ Res 38: 74-80

Kitabatake A, Suga H (1978) Diastolic stress-strain relation ofnonexrised blood-perfused canine papillary muscle. Am J Phys-iol 234: H416-H420

Krueger JW, Pollack GH (1975) Myocardial sarcomere dynamicsduring isometric contraction. J Physiol (Lond) 251: 627-643

Lannergren J, Noth J (1973) The effect of bathing solution tonicityon resting tension in frog muscle fibers. J Gen Physiol 62: 737-755

Maruyama K, Matsubara S, Natori R, Nonomura Y, Kimura S,Ohasi K, Marajami F, Handa S, Eguchi G <1977a) Connectin,an elastic protein of muscle: Characterization and function. JBiochem 82: 317-337

Maruyama K, Kimura S, Kuroda M, Handa K (1977b) Connectin,an elastic protein of muscle: Its abundance in cardiac myofibrils.J Biochem 82: 347-350

Mirsky I, Krayenbuchl HP (1981) The role of wall stress in theassessment of ventricular function. Herz 6: 288-299

Mirsky I, Parmley W (1973) Assessment of passive elastic stiffness

by guest on May 23, 2018

http://circres.ahajournals.org/D

ownloaded from

276 Circulation Research/Vol. 54, No. 3, March 1984

for isolated heart muscle and the intact heart. Circ Res 33: 233-243

Mirsky 1, Cohn PF, Levine JA, Gorlin R, Herman MV, Kreulen T,Sonnenblick EH (1974) Assessment of left ventricular stiffnessin primary myocardial disease and coronary artery diseaseCirculation 50: 128-136

Moisescu DG, Thieleczek R (1979) Sarcomere length effects onthe SR++ and Ca++ activation curves in skinned frog-musclefibers. Biochim Biophys Acta 546: 64-76

Moses RL, Kasten FH (1979) Ulrrastructure of dissociated adultmammalian myocytes. J Mol Cell Cardiol 11: 161-172

Moss RL, Halpern W (1977) Elastic and viscous properties ofresting frog skeletal muscle. Biophys J 17: 213-238

Natarajan G, Bove AA, Coulson RL, Carey RA, Spann JF (1979)Increased passive stiffness of short-term pressure-overload hy-pertrophied myocardium in cat. Am J Physiol 237: H676-680

Orenstein J, Hogan D, Bloom S (1980) Surface cables of cardiacmyocytes. J Mol Cell Cardiol 12: 771-780

Ortega JM, Rheinboldt WC (1970) Iterative Solution of NonlinearEquations with Multiple Variables, ed 1. New York, AcademicPress, pp 181-218

Pollack GH (1970) Maximum velocity as an index of contractilityin cardiac muscle: Critical evaluation. Circ Res 26: 111-127

Powell T, Steen EM, Twist VW, Woolf N (1978) Surface charac-teristics of cells isolated from adult rat myocardium. J Mol CellCardiol 10: 287-292

Sanders SK, Alexander EL, Braylon RC (1975) A high yieldtechnique for perparing cells fixed in suspension for scanningelectron microscopy J Cell Biol 67: 476-480

Sonnenblick EH (1968) Correlation of myocardial ulrrastructure

and function Circulation 38: 29-44Sonnenblick EH, Skelton LC (1974) Reconsideration of the ultra-

structural basis of cardiac length-tension relations. Circ Res 35:517-526

Spann JF, Buccino RA, Sonnenblick EH, Braunwald E (1967)Contractile state of cardiac muscle obtained from cats withexperimentally produced ventricular hypertrophy and heartfailure. Circ Res 21: 341-354

Spiro D, Sonnenblick EH (1964) Comparison of the ultrasrxucruralbasis of the contractile process in heart and skeletal muscle.Circ Res 15: 14-37

Spornitz HM, Sonnenblick EH, Spiro D (1966) Relation of ultra-structure to function in the intact heart: Sarcomere structurerelative to pressure-volume curves in the intact left ventricle ofdog and cat. Circ Res 18: 49-66

Tarr M, Trank JW, Leiffer P, Shepherd N (1979) Sarcomerelength-resting tension relation in single frog atrial cardiac cells.Cue Res 45: 554-559

Tsokos J, Sans R, Bloom S (1977) Ca++ uptake by hyperpermeablemouse heart cells: Effects of inhibitors of mitochondrial func-tion. LifeSci 20: 1913-1921

Weisfeldt ML, Loeven WA, Shock NW (1971) Resting and activemechanical properties of trabeculae carnae from aged malerats. Am J Physiol 220: 1921-1927

Winegrad S (1974) Resting sarcomere length-tension relation inliving frog heart. J Gen Physiol 64: 343-355

INDEX TERMS: Cardiac myocytes- • Skeletal myocytes • Me-chanics • Length-tension • Passive stiffness • Scanning electionmicroscopy • Cell-surface cables • Ultrastructure

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D Fish, J Orenstein and S BloomPassive stiffness of isolated cardiac and skeletal myocytes in the hamster.

Print ISSN: 0009-7330. Online ISSN: 1524-4571 Copyright © 1984 American Heart Association, Inc. All rights reserved.is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231Circulation Research

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