Maximal Twitch Tension in Intact Length-Clamped Ferret Papillary Muscles Evoked by Modified Postextrasystolic Potentiation
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65
Maximal Twitch Tension in Intact
Length-Clamped Ferret Papillary Muscles
Evoked by Modified Postextrasystolic
Potentiation
Ferdinand Urthaler, Alfred A. Walker, David N.S. Reeves, and Lloyd L. Hefner
A modified test of postextrasystolic potentiation achieved with a brief episode of rapid pacing followed
by a 6-second pause (RPP maneuver) was used to evoke maximal force in isolated intact ferret right
ventricular papillary muscles. Maximal RPP tensions were examined under length-clamped conditions
and compared with the steady-state forces obtained when further increases in [Ca2+]0, did not further
increase force and to the tensions recorded at the point of saturation of force when similarly
length-clamped muscles were subjected to caffeine-induced tetanization. The results show that the
calculated maximal twitch tension achieved with RPP is comparable to the 25-35 g/nun2 observed in
intact single skeletal muscle fibers. The study also shows that the beat-to-beat decay of the potentiated
contraction is exponential. While the amount of the constant fractional beat-to-beat decay is a function
of [Ca^L, it is not influenced by length. During the decay of potentiation, the ratio of the potentiation
of any beat divided by that of the previous beat is a constant, called (x). With certain assumptions,
it is shown that (x) is a measure of the fraction of activator calcium taken up by the sarcoplasmic
reticulum in each beat and, in the steady state, the fraction of activator calcium that comes from the
sarcoplasmic reticulum. The (x) amounted to 33%, 50%, and 65% when [Ca 2+ ], was 1.25, 2.50, and
5.0 mM, respectively. Thus, at 1.25 mM [Ca2+]., some two thirds of the total calcium required to
activate the myofilaments comes from the extracellular compartment during excitation and only one
third is contributed via release from the sarcoplasmic reticulum. In the region of optimal myofilament
overlap, RPP force-length curves are remarkably shallow and almost indistinguishable from the
sarcomere length-tension relation observed in skinned single cardiac cells. Tetanus plateau tensions
are significantly smaller than RPP forces at any length, and the slope of the tetanus force-length curves
is greater than that obtained with RPP. Thus, and by exclusion, we also suggest that caffeine may exert
significant downstream inhibitory effects. (Circulation Research 1988;62:65-74)
ytosolic free calcium concentration, [Ca2+],,
C
In the present study, we have used a modified test of
modulates the contraction and relaxation of postextrasystolic potentiation to achieve maximal
myocardial myofibrils, and the resting [Ca2*], force. We have measured these maximal tensions under
of 0.05-0.5 /xM will increase by one or two orders of length-clamped conditions and compared the magni-
magnitude when the cells are electrically or chemically tude of these peak twitches with the amplitude
stimulated.1 To examine the relation between [Ca2+]; of the beats recorded when further increases in extra-
and force, steady-state levels of calcium activation of cellular calcium, [Ca 2+ ] o , did not cause further in-
contractile proteins must be achieved. Since in the creases in force and with the tensions recorded at
normally beating heart the duration of the contraction- the point of saturation of force when similarly length-
relaxation cycle is too brief to allow such steady state controlled muscles were subjected to caffeine-induced
to develop,2 various investigators5"" resorted to studies tetanization.
of the pCa-force relation in hyperpermeable3"* or The results show that the calculated maximal twitch
mechanically9"" skinned cardiac muscle fibers. More tension that can be achieved in an intact length-clamped
recently, rapid repetitive stimulation (tetanization) of papillary muscle with a modified postextrasystolic
ryanodine-pretreated but otherwise intact papillary potentiation is comparable to the peak tensions of
muscles1213 was successfully used to achieve both 25-35 g/mm2 observed in intact single skeletal muscle
steady contractile activations and maximal calcium- fibers.l413 These forces, also observed by others,16"" are
activated force.1213 considerably larger than the maximal calcium-activated
forces observed in either mechanically skinned cardiac
From the Division of Cardiology, Department of Medicine,
University of Alabama at Birmingham, Birmingham, Ala. fibers6 or pharmacologically pretreated intact muscle
Supported by the National Heart, Lung, and Blood Institute, HL during tetanization.'213 The study also shows that the
31310 and SCOR on Ischemic Heart Disease Grant 5P50HL17667. beat-to-beat decay of the force after the potentiated
Address for reprints: Ferdinand Urthaler, MD, Division of contraction is exponential and that the amount of the
Cardiology, Department of Medicine, University of Alabama at
Birmingham, Birmingham, AL 35294. constant fraction of beat-to-beat decay is a function of
Received February 26, 1987; accepted July 28, 1987. [Ca 2+ ] 0 .
Downloaded from http://circres.ahajournals.org/ by guest on March 6, 201566 Circulation Research Vol 62, No 1, January 1988
Materials and Methods that 1.5%. In the few muscles with larger angles of
Right ventricular papillary muscles (cross-sectional rotation as estimated visually, the pins are readjusted.
areaUrthaler et al Maximal Force of Intact Cardiac Muscle 67
Modified Post-Extrasystolk Potentiation puting p values.24 Throughout each repeated measures
12
analysis of variance, we chose a conservative estimate
of p, as reflected by the Geisser-Greenhouse value.23
Results
8- fca'+lo: 2.50 Paired Pacing Versus Modified Postextrasystolic
Temp: 25* Potentiation
CSL: 0.98L m a x
Twitch tensions evoked by maximally effective
paired pacing (PP) were compared with the potentiated
— 4
contractions achieved with the rapid pace pause (RPP)
>
© maneuver. Each muscle (n = 5) was studied at two
central segment lengths (0.900 and0.984% of L J and
exposed to three increasing [Ca2+]0 (Table 1). At low
length and 1.25 mM Ca, the control force averaged
I IiiIi iiI I
2.34 ± 0.52 g/mm2. PP and RPP increased the force by
400 800 1200 1600 0 400 800 1200 179% and 216%, respectively, above control. At 2.5
Time in msec
mM Ca, these increments were 98% and 102%, and at
FIGURE 1. Example of modified postextrasystolic potentiation 5.0 mM Ca, the respective potentiations were 44% and
(PC) achieved with rapid pace pause (RPP) maneuver. Control 48% above control. At 0.984% of 1 ^ and 1.25 mM
steady-state twitch (left) generates 4.1 glnvn2 offorce. Appli- Ca, the control force averaged 3.94 ± 1.18 g/mm2. PP
cation of 10 repetitive stimuli (short vertical bars) beginning at and RPP increased the force by 128% and 130%,
time of half relaxation of steady-state beatfollowed by 6-second respectively, above control. With exposure to 2.5 mM
pause leads to PC of 11.6 g/mnf. Ca, PP and RPP increased twitch tension by 64% and
70%, respectively, and at 5.0 mM Ca, the increments
of force still averaged 31% and 33%, respectively.
consists of a series of rapid stimuli beginning at half Except for one paired comparison between PP and RPP
relaxation time of the control steady-state beat, fol- evoked potentiations (see low length and 1.25 mM Ca,
lowed by a pause (Figure 1). The pause is terminated Table 1, there were no significant differences between
by the potentiated beat. In addition to the interval PP and RPP beats at any length or [ C a ] o .
between the stimulus of the preceding beat and the On instituting paired pacing, the magnitude of the
onset of rapid repetitive stimulation at half relaxation, potentiated contractions first typically increases over
we selected 10 stimuli (5-msec stimulus duration) some 4 - 8 beats before reaching a peak and then
delivered at a frequency of 10-15 Hz followed by a stabilizes some 6-12 beats after onset of PP at a level
pause of 6 seconds. The actual execution of this slightly lower than peak. In contrast, the RPP elicited
modified postextrasystolic potentiation using the preset maximal potentiation is always achieved with the first
parameters requires a single keyboard command. beat after the pause, and it can easily be repeated with
Reference control beats (usually two), the potentiated less than 5% variability. Thus, twitch potentiation
contraction, and at least 10 consecutive beats fol lowing evoked with RPP is a convenient and ideally suited
the PC were routinely recorded and stored by the intervention whenever a reliable, immediate, and
computer for subsequent analysis. rapidly reversible potentiation of contractile perfor-
mance is desired.
Statistics
The results are expressed as means ± S D . The Maximal Twitch Tension
repeated measures analysis of variance, section P2V, Using bicarbonate-phosphate buffer. In four other
Biomedical Data Package (BMDP), was used for com- length-clamped muscles (0.989 L ^ ) , [Ca 2+ ] 0 was
Table 1. Effects of Length and [Ca3*], on Standard and Modified Postextrasystolic Potentiations Studied in
Five Ferret Papillary Muscles
Central segment length (% L,^)
0.900 0.984
DVLT PP RPP DVLT PP RPP
[Ca- + ] 0 (g/mm2) (g/mm2) (g/mm2) (g/mm2) (g/mm2) (g/mm2)
1.25 mM 2 .34±0.52 6 .52±1.44 7.40+1.37 3.94±1.18 8.97 ±1.80 9.10±1.79
2.50 mM 4 .38±0.53 8.66 ±1.08 8.86±0.96 6.29±1.10 10.32±1.37 10.72± 1.29
5.00 mM 6 .66±0.87 9 .60±1.40 9.86±1.30 8.54±0.73 11.20+1.50 11.40±1.49
DVLT, steady-state developed tension; PP, postextrasystolic potentiation evoked by paired pacing; RPP, modified
postextrasystolic potentiation evoked by rapid pace pause maneuver. Repeated measures analysis of variance for all the
above conditions (3 x 2) indicates that there is no significant difference between PP and RPP except at low length and
1.25 mM Ca.
Downloaded from http://circres.ahajournals.org/ by guest on March 6, 201568 Circulation Research Vol 62, No 1, Janua
Effect of [Ca* + ] o 0n Steady State Forces and RPP Evoked Potentiated Contractions Decay of potentiated contraction. At any
12 [Ca 2+ ] o (0.625-5.0 mM), the potentiated cont
decays fractionally with each beat. Figures 3
illustrate such a characteristic decay. At low [
(0.625 mM) (n = 5), return to steady-state controlforce
required 2-3 beats, while 6-10 beats were nee
return to control at 5.0 mM [Ca 2+ ] o (n = 8). The n
of beats rather than time is the critical determin
this decay. Thus, whether paced at 12-24 beats/
any other rate between 6 and 30 beats/min, it ta
any of the [Ca 2+ ] 0 studied, the same number o
for the potentiated contraction to return to contr
fractional decay of each beat was then further
acterized by plotting on semilogarithmic pap
difference between the potentiated force and the c
FIGURE 2. Maximal potentiated contraction evoked with RPP force versus the number of the beat (Figu
(twitches without hatching) is observed at 5 mM [Ca2*],, both Irrespective of the [ C a ] 0 , each of these plots a
in HEPES and in phosphate-bicarbonate-containing buffer. imates a straight line indicating that the decay o
Maximal steady-state twitch tensions (hatched twitches) are potentiated contractions is exponential. The low
achieved when [Ca1*], is increased to 14 mM. Peak twitch [ C a ] 0 , however, the steeper the slope. Thus
tensions achieved with RPP are consistently, although slightly, possible to directly determine from these grap
higher than maximal steady-state twitch tensions. rate constant, K, which is the number of
required for the potentiated contraction to decay
or =Urthaler et al Maxima) Force of Intact Cardiac Muscle 69
Effect of Low and High [Ca' + ] 0 on the Beat-Dependent
Decay of Potentiated Contraction
FIGURE4. Effect of low (0.625 mM)andhigh (5.0
mM) [Co2*], on normalized beat-dependent decay
of RPP-induced potentiated contraction (PC).
Rate: 12
Temp: 25* C
x-Axis, beat numberfollowing PC; y-axis, ratio of
ADVLT/bDVLT^; &DVLT, developed tension
minus control steady-state tension; SDVLT^,
developed tension ofPC minus control steady-state
tension.
2 3
Beat Number
Effect of length on maximum twitch tension evoked relations in this region of lengths. In the tetanized
with RPP maneuver. The results of this study are caffeine-pretreated muscles at 5.0 mM [Ca2+]o, the
summarized in Table 2. In 7 muscles exposed to 5 mM normalized increase in force is still 26% with a slope
Ca, twitch tension elicited with the RPP maneuver of 3.1 (r = 0.95). In contrast, the effect of length on the
steadily increased by some 14% when length was RPP-potentiated contraction at 5.0 mM [Ca2+]0 showed
incremented from 0.900 to 0.986 L ^ , although at L ^ , a 12% increase in force with a slope of 1.6 (r = 0.99),
an increase in [Ca2+]o from 5.0 to 8.0 mM had no which is significantly less (/?70 Circulation Research Vol 62, No 1, January 1988
Table 2A. Effect of Length on Amplitude of Tetanic Plateau Force (n=12)
Central segment length (% L . , ) 0.907 0.926 0.943 0.964 0.986
2
Tetanus plateau tension (g/mm ) 7.04±1.86 7.63 ±1.85 8.27+1.97 8.86 + 2.20 9.58±2.59
Table 2B. Effect of Length on Maximum Twitch Tension Evoked With RPP Maneuver (n = 7)
Central segment length (% 0.900 0.930 0.950 0.950 0.986
RPP maximum twitch tension (g/mm2) 10.69 ±1.08 11.43±0.81 11.76±0.75 11.76 ± 0.75 12.14±0.77
Discussion different experimental approaches. Developed force
Maximum Twitch Tension increases steadily and directly with increases in [Ca2+]0.
The present study shows that the maximum uncor- Maximum twitch tensions areregularlyachieved when
rected twitch tension of an intact ferret right ventricular [Ca2+]ois raised to 11-14 mM. Similar peak forces are
papillary muscle, length-clamped at 0.99 L^, and obtained from the frequency-potentiated contractions
contracting 12 times per minute at 25° C, is about 12 of the RPP maneuver at 5 mM [Ca2+]0. Under condi-
g/mm2. After taking into consideration the ratio of tions of maximal steady-state contractility (L,,^ and
cellular-to-total volume, which amounts to 0.6 accord- 11-14 mM [Ca2+]0, further increases in [Ca2+]0 led to
ing to Page,2* the maximum corrected twitch tension is a fall in developed tension. The same declines in peak
about 20 g/mm2. This peak developed force compares force also occurred when muscles underwent RPP
favorably with the maximal calcium-activated isomet- testing, provided the [Ca2+]0 is 5 mM or more. Hence,
ric tension of mechanically skinned skeletal muscle by definition, the muscles exhibited calcium over-
fibers,272* which have variably been reported to average load .M It has recently been shown that calcium overload
about 11 g/mm2 u or 14 g/mm2 w or to vary between 15 is related to a diastolic release of calcium from the
and 20 g/mm2.27 Moreover, since the volume fraction sarcoplasmic reticulum into the cytosol.* Such release
of mitochondria (17-37%) is considerably larger in will diminish the amount of sarcoplasmic reticulum
cardiac*031 than in skeletal muscle cells (2%), peak calcium available for release in the ensuing beat(s) or,
cardiac stress, normalized for myofibrillar cross-sec- perhaps, partially inactivate the subsequent calcium-
tional area, will be in the vicinity of 25-30 g/mm. induced calcium release of calcium.
These tensions are comparable to those observed by From these considerations, we conclude that in-
Gordon et al in the intact frog skeletal musclefiberand creases in [Ca2+]0 alone can increase developed tension
are very close to the 35 g/mm measured by Ramsey to near maximal levels achievable by ferret papillary
and Street" in the intact single fibers of frog semiten- muscles. We also conclude that peak cardiac stress per
dinosus. The overall agreement between the peak unit cross-sectional area of myofibrils at the point of
stresses of intact length-clamped papillary muscles and saturation of twitch force is around 30 g/mm2 and that
intact single skeletal fibers is probably as good as can this peak force is reliably achieved in one twitch with
be reasonably expected from such measurements and the RPP maneuver. Because peak forces evoked by
calculations, especially considering that the multicel- RPP are virtually indistinguishable from maximal
lular preparation with its complex cell-to-cell attach- calcium-activated force of a single skeletal fiber1428
ments and branchings" cannot achieve the structural and because these tensions were usually much larger
arrangement of the more uniform longitudinal striation than the maximal calcium-activated forces of skinned
of the single skeletal fiber. Thus, we suspect that cardiac cells6 or tetanized papillary muscles,1213 we
cardiac and skeletal contractile proteins are capable of also suspect that peak segment-controlled RPP ten-
generating about the same amount of peak force as
previously suggested by Brady. Effect of Clungti In l«nfth on Ampbtud*
of TtUnic Ptatuu Forct
In rat ventricular trabeculae in which central segment
sarcomere shortening was prevented17 and in rabbit
papillary muscles in which the sarcolemma was ren-
dered hyperpermeable with EDTA,3 the peak tensions
wereremarkablysimilar to those observed in our study.
In contrast, the maximal calcium-activated forces of
chemically skinned single rabbit and rat ventricular
cells were considerably smaller.6 In a preparation
similar to ours but without length control, the maxi-
mum plateau forces evoked by ryanodine-induced
tetanization1213 averaged only half of the peak tensions
elicited by the RPP maneuver. Uncontrolled internal 800
shortening at the expense of stretch of the damaged Timt «i
ends17"-54-33 is a likely reason for prominent inhibitory FIGURE 7. At Lma, increases in [Ca2*]. beyond 5 mM did not
effects. further increase amplitude of tetanic plateau. However, changes
The findings of this study further illustrate that in length from 90 to 98% ofL^ clearly increased amplitude of
similar maximum twitch tensions can be achieved using tetanic force (see text for details).
Downloaded from http://circres.ahajournals.org/ by guest on March 6, 2015Urthaler et al Maximal Force of Intact Cardiac Muscle 71
Comparison between RPP and Tetanus
Evoked Force Central Segment Lengths Relationships
A RPP FIGURE 8. Comparison between RPP- and tetanus-
• Tetanus
evokedforce-length relations. Panel A: Forces expressed
in g/mnr. Panel B: Forces normalized and expressed in
12 % offorce at SL^. Dotted line in Panel B represents a
reference steady-state twitch tension-length curve ob-
1.0 J
tained in 10 muscles exposed to 1.25 mM [Ca2*]..
Calculated slope of this reference curve is 5.3 (T - 0.99),
and percent increase of force between lowest and highest
length is 45%. •, Force-length curve obtained in 12
caffeine-pretreated tetanized muscles; normalized slope
(Panel B) is 3.1 (r = 0.95). A, Force-length curve from
C«'+]72 Circulation Research Vol 62, No 1, January 1988
not altogether clear whether the brief initial positive influx through the voltage-dependent slow channels as
inotropic response should be ascribed to an immediate well as the calcium entry via the membrane potential-
transient release of calcium from an internal store4* or dependent Na-Ca exchange.
to an increase in sensitivity of the myofilaments to 2) It is assumed that with each beat, the SR and the
calcium.43 On the other hand, it appears that the SL compete for reuptake of calcium. In our model, the
prolonged decrease in contractility can be largely disposal of calcium by the SL includes the calcium
attributed to a reduction of calcium release into the extrusion via both the Na-Ca exchanger and an ATPase-
cytoplasm from the sarcoplasmic reticulum.42-43 operated pump. It is further assumed that under given
Recently, it has also been shown that in papillary experimental conditions, reuptake of calcium by the SR
muscles varying [Ca 2+ ] 0 caused marked changes in the will be a constant fraction, x, of the total activator
level of tetanic force.1213 Our study is in accord with calcium.
these observations since increases in [Ca 2+ ] o from 2.5 3) It is assumed that the SR always releases the same
to 5.0 mM consistently raised the level of the tetanus amount of calcium that it took up on the previous beat.
plateau tensions. However, while further increases in 4) It is assumed that the amount of calcium entering
[Ca 2+ ] 0 beyond 5 mM caused no further increments in through the SL is a constant amount, A, at least for the
tetanic force, presumably because of maximal activa- 6-8 beats following the RPP maneuver, implying that
tion, the amplitudes of the tetanic plateau tension still the RPP maneuver per se does not alter the fractional
varied appreciably with changes in length. In other amount of transsarcolemmal flux of calcium during
words, at any length between 0.90 and 0.98 L^,, the these 6-8 beats. It can be some other constant (and
amplitude of the tetanus plateau was no greater at 8 or should be) under different conditions.
10 mM [Ca 2+ ] 0 than at 5 mM [Ca 2+ ] 0 , although
increments in length caused the same amount of Mathematical Derivation
increase in tetanic force at all three [Ca 2+ ] 0 . 5) Let the amount of calcium for the potentiated beat
In the region of optimal myofilament overlap, the be denoted by Co (C for calcium, 0 for reference beat).
normalized tetanus force-length curves exhibited For the first beat after the maximal potentiated beat, the
slopes that were considerably steeper than those amount of calcium from the SR is xC0 (assumptions 2
obtained with the RPP maneuver. Because the tetanus and 3), and the amount of calcium entering through the
slopes were identical at 5, 8, and 10 mM [Ca 2+ ] 0 , it sarcolemma is A (assumption 4). The total activator
is unlikely that caffeine reduced sarcolemmal trans- calcium for this beat, C,, is the sum of these (assump-
location of calcium so as to precisely offset the tion 1):
increments of the transsarcolemmal calcium gradient
that occurred when [Ca 2+ ] 0 increased. Taken together,
these observations raise the important question of why C, = xC0 + A
the slopes of the force-length curves are steeper with For beat 2,
tetanus than with RPP. This difference in slope cannot
be ascribed to physical factors since it is consistently C2 = xC, + A
demonstrable when the same muscles are examined where C2 is the total amount of activator calcium,
with RPP and tetanus. Furthermore, if one accepts xC, of which comes from the SR and A through the SL.
that muscles exposed to 5 mM caffeine and 5 mM In general, for beat (n+ 1),
[Ca 2+ ] 0 are subjected to maximal activation, then
changes in length should not be associated with Cn+l=xC, + A (1)
changes in force resulting from altered myofilament Eventually, a new steady state will be reached in
sensitivity to calcium. The observation that further which the amount of activator calcium is essentially
increases in [ C a ] 0 to 8 and even 10 mM had no effect the same for every beat. This amount of calcium is
of their own on the slope of the tetanus force-length denoted by Ca. Equation 1 must still be satisfied, so
curves strongly supports this assertion. Thus, other
mechanism(s) must be invoked to explain the steeper = xCL + A (2)
length-dependent maximal activation of force induced To eliminate A from Equation 1, Equation 2 is
by tetanization with caffeine. By exclusion, we solved for A:
arrived at the suggestion that caffeine may well exert
significant downstream inhibitory effect(s), i.e., that A = C. - xC.
caffeine could, in fact, diminish the response of the Equation 1 now becomes
contractile proteins to a given level of occupancy of
the calcium binding sites on troponin C.
= x(Cn - C J + C.
(3)
Appendix
Excitation-Contraction Coupling Model • = X
1) It is assumed that activator calcium (C) comes c —c
from the sarcoplasmic reticulum (SR) and through the Final Assumption
sarcolemma (SL), which refers to all sources of 6) A final assumption is that to a reasonable ap-
transsarcolemmal calcium entry such as the calcium proximation, the force developed in a beat is propor-
Downloaded from http://circres.ahajournals.org/ by guest on March 6, 2015Urthaler et al Maximal Force of Intact Cardiac Muscle 73
tional to the activator calcium, at least in the range seen of single skinned cardiac cells. J Physiol (Lond) 1975;
249:469-495
in our experiments. If k is the constant of proportional- 11. Fabiato A: Calcium release in skinned cardiac cells: Variation
ity, then with species, tissues and development. Fed Proc 1982;41:
C = JtF 2238-2244
12. Yue DT, Marban E, Wier WG: Relationship between force and
*-•„= krn intracellular [Ca2+] in tetanized mammalian heart muscle. J
Gen Physiol 1986;87:223-242
13. Marban E, Kusuoka H, Yue DT, Weisfeldt ML, Wier WG:
where F n + , is developed force in (n+ l)st beat, F, is Maximal Ca:+-activated force elicited by tetanization of ferret
developed force in the immediately preceding beat, papillary muscle and whole heart: Mechanism and character-
and F» is developed force in the steady-state beat. istics of steady contractile activation in intact myocardium.
Circ Res 1986;59:262-269
Substitute these into Equation 3:
14. Gordon AM, Huxley AF, Julian FJ: The variation in isometric
—C JtF — JtF F —F AF tension with sarcomere length in vertebrate muscle fibers. J
X = Physiol (Lond) 1966; 184:170-192
F -F. AF. 15. Ramsey RW, Street SF: The isometric length-tension diagram
c.-c. of isolated skeletal muscle fibers of the frog. J Cell Comp
AF n+1 Physiol 1940;15:ll-34
X = (4) 16. Pollack GH, Krueger JW: Sarcomere dynamics in intact cardiac
AF muscle. Eur J Cardiol 1976;4(suppl):53-65
17. Ter Keurs HEDJ, Rijnsburger WH, Van Henningen R, Nagel-
This means that one can determine x simply by smith MJ: Tension development and sarcomere length in rat
forming the ratio shown. For any two successive beats, cardiac trabeculae. Evidence of length-dependent activation.
the steady-state force is subtracted and then the ratio of Circ Res 1980;46:703-714
the differences is calculated. 18. Gordon AM, Pollack GH: Effect of calcium on the sarco-
mere length-tension relation in rat cardiac muscle. Implica-
It can also be shown37 that x, as defined above and tions for the Frank-Starling mechanism. Circ Res 1980;47:
using the previous assumption, is related to K (Figure 610-619
6), the beat constant for decay, by the equation: 19. Donald TC, Reeves DNS, Reeves RC, Walker AA, Hefner LL:
Effect of damaged ends in papillary muscle preparations. Am
J Physiol 1980;238:H14-H23
20. Urthaler F, Walker AA, James TN: Changing negative ino-
For each decay, with a mathematical approach, sev- tropic effect of acetylcholine in maturing canine cardiac
eral values of x can be directly calculated and thus, by muscle. Am J Physiol 198O;238:H1-H7
averaging, a reliable estimate of x can be obtained. In 21. Urthaler F, Walker AA: Indirect stimulatory action of the
contrast, with the graphic approach, only one value of calcium channel blockers AQA-39. J Pharmacol Exp Ther
1984;230:336-340
K (1/e) can be obtained; hence, only one value of x can 22. Forman R, Ford LE, Sonnenblick EH: Effect of muscle length
be obtained. on the force-velocity relationship of tetanized cardiac muscle.
Circ Res 1972;31:195-206
23. Ford LE, Forman R: Tetanized cardiac muscle, in Ciba
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modified postextrasystolic potentiation.
F Urthaler, A A Walker, D N Reeves and L L Hefner
Circ Res. 1988;62:65-74
doi: 10.1161/01.RES.62.1.65
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