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Department of Cardiology, Thoraxcenter, Erasmus University Rotterdam, Cardiovascular Research Institute, 3000 DR Rotterdam, The Netherlands
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ABSTRACT |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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In anesthetized
pigs, we investigated whether asynchrony
(
T) and nonuniformity (regional
differences) in contractility (E) could describe the interaction between normal and stunned myocardium. Mechanical interaction was evaluated by regional postsystolic work
(PSW) before and after production of stunning by a 5-min occlusion of
the left circumflex coronary artery [LCX (LCX stunning)] and a subsequent 10-min occlusion of the left anterior descending coronary artery [LAD (LAD stunning)].
T and
E were intensified by intracoronary
(LAD) infusions of dobutamine. From regional end-systolic
pressure-segment length relationships, systolic segment shortening
(SS), end-systolic elastance (E),
external work (EW), and PSW were determined. LCX
stunning decreased SSLCX from 14 ± 2 (mean ± SE, n = 9) to 10 ± 2% and
ELCX from 103 ± 25 to 52 ± 7 mmHg/mm, whereas the LAD region was unaffected.
EWLCX decreased from 165 ± 16 to 138 ± 20 mmHg · mm, whereas
PSWLCX increased from 
4 ± 6 to 8 ± 3 mmHg · mm. Additional LAD
stunning reduced SSLAD from 16 ± 2 to 9 ± 3% and
ELAD from 79 ± 10 to 31 ± 6 mmHg/mm, without affecting
SSLCX and
ELCX. In the
normal myocardium, PSWLAD increased and PSWLCX decreased,
but, during local LAD dobutamine infusions after stunning, both
PSWLCX and
PSWLAD increased. In normal
myocardium, the changes in PSWLCX
could be described by T (65 ± 11%) and E
(37 ± 15%). After stunning of the LAD area, the contribution of
E increased to 55 ± 14% at the
expense of T (37 ± 15%).
Similar contributions of E (54 ± 13%) and T (57 ± 13%)
were found when both the LCX and LAD distribution areas were stunned.
In normal myocardium, both T and
E modulate mechanical interaction,
with the contribution of T
exceeding that of E. In stunned
myocardium, both factors contribute, but the contribution shifts in
favor of E.
myocardial interaction; inotropic intervention; end-systolic pressure-segment length relationship; pig
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INTRODUCTION |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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MECHANICAL INTERACTION between different myocardial regions has been studied extensively during regional ischemia, a condition in which regional myocardial function of the ischemic segment is decreased but that of the adjacent normal myocardium may be increased (2, 5, 7, 8, 12, 16-18, 20, 23). In these studies, regional myocardial function is usually assessed by load-dependent parameters such as systolic segment shortening or systolic wall thickening. However, several groups of authors have proposed that regional end-systolic elastance (E), a parameter derived from regional left ventricular (LV) pressure-segment length relationships, is less load dependent and may be a more appropriate index for regional myocardial contractility (3, 14, 15). This approach also has the advantage that the area inside the LV pressure-segment length loop provides an estimate of the external work (EW) (6, 19, 24, 27, 29). Most of the EW is performed during LV ejection, but a fraction can occur during isovolumic relaxation after the ejection period [postsystolic work (PSW)]. Because total LV volume remains constant during isovolumic relaxation and thus global PSW is zero, positive PSW in one region implies that PSW must be negative in another region. Hence, PSW may be used as an index for mechanical interaction.
In regionally stunned myocardium, EW is not only decreased but also a larger fraction is performed as PSW (1, 4, 14, 15). This PSW is believed to result from a slower contraction of the stunned myocardial region (asynchrony). It has been shown repeatedly that contractility is decreased in stunned myocardium (3, 14, 15), but whether PSW is also affected by the decrements in contractile force of the stunned region has not yet been investigated. In addition, it is not yet known how contractility changes of the adjacent nonstunned region modulate PSW of the stunned region. To clarify the contribution of contractility and asynchrony on mechanical interaction during stunning and to investigate whether factors other than loss of contractility and asynchrony are needed in stunned myocardium, selective intracoronary infusions of dobutamine were used before and after stunning that region.
Furthermore, because stunned myocardium retains its contractile reserve, it is often treated with intravenous administration of inotropic agents (13a, 14). Knowledge about mechanical interaction is important in these conditions, because the effect of these agents on regional inotropy could be modulated by the concomitant increase in contractility of the adjacent nonstunned myocardium.
The aim of the present study was therefore to evaluate in anesthetized
pigs the contribution of asynchrony of contraction (T) and regional nonuniformity in
contractile force (E) to
mechanical interaction in normal regions, in normal stunned regions,
and in stunned-stunned regional myocardium.
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MATERIALS AND METHODS |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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General
All experiments were performed in accordance with the "Guiding Principles in the Care and Use of Laboratory Animals" as approved by the Council of the American Physiological Society and under the regulations of the Animal Care Committee of the Erasmus University Rotterdam.Cross-bred Landrace × Yorkshire pigs (HVC, Hedel, The
Netherlands) of either sex (23-30 kg) were sedated with 20 mg/kg
ketamine im (AUV, Cuijk, The Netherlands) and anesthetized with 20 mg/kg pentobarbital sodium (Apharmo, Arnhem, The Netherlands) before intubation and connection to a ventilator for intermittent positive pressure ventilation with an
O2-N2
(1:2, vol/vol) mixture. Respiratory rate and tidal volume were
controlled to keep arterial blood gases within the normal range. An
8-Fr fluid-filled catheter was placed in the superior caval vein for
continuous infusion of 5-10
mg · kg
1 · h1
of pentobarbital sodium, and another 8-Fr catheter was placed in the
descending aorta for withdrawal of arterial blood samples and
measurement of central aortic blood pressure. A 7-Fr Sensodyn micromanometer-tipped catheter (B. Braun Medical, Uden, The
Netherlands) was inserted into the left carotid artery and advanced
into the LV cavity for measurement of LV pressure and its first
derivative (LV dP/dt). A 7-Fr
Fogarty balloon catheter was inserted into the right carotid artery and
advanced into the ascending aorta to vary afterload for the
determination of the LV end-systolic pressure-segment length
relationships (ESPSLR; see below).
After administration of 4 mg of pancuronium (Organon Teknika, Boxtel, The Netherlands), the thorax was opened via a midline sternotomy. The left mammary vessels were ligated, the second left rib was removed, and the heart was suspended in a pericardial cradle. An electromagnetic flow probe (Skalar, Delft, The Netherlands) was placed around the ascending aorta for measurement of blood flow cardiac output. Proximal parts of the left anterior descending coronary artery (LAD) and left circumflex coronary artery (LCX) were dissected free for later positioning of an atraumatic clamp, while the proximal LAD was cannulated for intracoronary infusion of dobutamine. Rectal temperature was maintained between 37 and 38°C using external heating pads and appropriate coverings for the animals.
Regional myocardial segment length changes were monitored by sonomicrometry (Triton Technology, San Diego, CA) by placing one pair of ultrasonic crystals (Sonotek, Del Mar, CA) in the distribution territory of the LAD and a second pair in the distribution area of the LCX. The crystals were placed in the midmyocardium in the direction of circumferential muscle fibers (25) at a distance of ~10 mm. Proper positioning of the crystals in the allocated distribution areas was verified by brief coronary artery occlusions.
Experimental Protocols
After a stabilization period of 30-45 min, baseline recordings were made of systemic hemodynamic variables and regional myocardial function. With the respirator switched off, ascending aortic blood pressure was increased over a 5- to 10-s period by gradual inflation of the balloon of the Fogarty catheter to determine the regional LV ESPSLR. LV pressure and regional segment-length signals were digitized (sample rate 400 Hz) with an eight-bit analog-to-digital converter and stored on disk for off-line analysis (14, 15).After baseline recordings were made, three sequential experimental
protocols were performed. In the first protocol
(n = 9), mechanical interaction in the
normal LV was studied by intracoronary LAD infusion of three doses
(0.01, 0.02, and 0.04 µg · kg1 · min1)
of dobutamine (Dobutrex, Eli Lilly Nederland, Nieuwegein, The Netherlands). The doses of intracoronary dobutamine were based on
previous studies from our laboratory using intravenous dobutamine (14,
15). Data were collected before infusion of dobutamine and after 3 min
of each infusion rate. In the second protocol (n = 8), the distribution territory of
the LAD was stunned by a 5-min occlusion and 10 min of reperfusion, and
the contribution of these parameters to the mechanical interaction
between regionally stunned and the adjacent nonstunned myocardium was
studied by repeating the intracoronary dobutamine (LAD) infusions. In
the third protocol (n = 6), mechanical
interaction between two stunned regions was studied. Hitherto, the
distribution area of the LAD was also stunned by a 10-min occlusion and
30 min of reperfusion before the local dobutamine infusions were
repeated. The shorter occlusion duration for the LCX region was
employed to avoid gross impairment of global LV pump function. Each
protocol was performed after a 30-min washout period, which was
sufficiently long to allow functional parameters to return to
predobutamine values.
Data Analysis and Statistics
Systolic segment shortening (SS) was calculated as the difference between the segment length at end diastole, defined as the instant that LV dP/dt increased to >250 mmHg/s, and that at end systole (determined at peakLV
dP/dt), expressed as a percentage of
end-diastolic length.
The ESPSLR was determined by fitting the LV end-systolic
pressure-segment length data points to a second-order polynomial, using
an interactive algorithm (14, 15). Each ESPSLR was characterized by the
slope (E; an expression of elastance)
at 120 mmHg and the intercept of the regression equation, or the length
at zero LV pressure
(L0) (14,
15). The area inside the LV pressure-segment length loop
was taken as a measure of regional EW, of which the fraction that occurred after closure of the aortic valve is PSW (22).
PSW was considered positive when minimal length
(Lmin) was less
than end-systolic length and negative when
Lmin was greater than end-systolic length (Fig. 1). The
duration of contraction in the LAD and LCX regions was defined as the
time intervals between LV end diastole and regional
Lmin
(TLAD and
TLCX,
respectively). Asynchrony of contraction between the
LAD and LCX regions was defined as
T = TLAD TLCX.
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A univariate regression analysis was performed with
PSWLCX as the dependent variable
and TLAD,
TLCX,
T,
ELAD,
ELCX, and
E as independent variables.
Significantly correlated independent variables were entered into a
multivariate regression analysis, which was performed for each of the
three protocols. Multicolinearity between the independent variables was
evaluated by the variance inflation factor (VIF) and the condition
index (CI), applying a standard statistical software package (SPSS,
Chicago, IL) (9). The relative contribution of each parameter in the
multivariate linear regression model was evaluated by standardizing the
parameter. Standardization involved subtracting its mean and dividing
by its SD (9). The multiregression analysis was repeated with these
standardized parameters. Statistical analyses of hemodynamic and
functional data were performed by repeated-measures analysis of
variance. When significance was reached
(P < 0.05), paired t-tests were applied with a Bonferroni
correction for multiple measurements. All data have been presented as
means ± SE.
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RESULTS |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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Systemic Hemodynamics
In each of the three protocols, the intracoronary dobutamine infusions produced dose-dependent increases in maximum LV dP/dt, without affecting any of the other system hemodynamic parameters (Table 1).
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Regional Segment Length and ESPSLRs
Normal LAD and LCX myocardium. SSLCX and ELCX did not change during the selective LAD infusions of dobutamine. In contrast, ELAD increased dose dependently from 65 ± 8 to 155 ± 24 mmHg/mm (P < 0.05), but SSLAD remained unchanged. EWLAD and EWLCX were also not affected by the dobutamine infusions, but PSWLAD and PSWLCX, which were not different from zero at baseline, became negative and positive, respectively (Table 2).
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Normal LAD and stunned LCX myocardium.
After stunning of the distribution area of the LAD,
SSLCX decreased from 14 ± 2 to
10 ± 2% (P < 0.05) and
ELCX decreased
from 103 ± 25 to 52 ± 7 mmHg/mm
(P < 0.05), whereas
SSLAD and
ELAD remained
unchanged. During the dobutamine infusions, neither
SSLAD nor
SSLCX was affected, whereas
ELAD increased
from 61 ± 7 to 229 ± 54 mmHg/min
(P < 0.05).
ELCX, which had
remained unchanged during the LAD dobutamine infusions before stunning,
now increased from 52 ± 7 to 113 ± 32 mmHg/min. Both
ELAD and
ELCX returned to
predobutamine values during the washout period. Stunning the LAD region
had no effect on EWLAD but
produced a decrease in EWLAD from
165 ± 16 to 138 ± 20 mmHg · mm
(P < 0.05). The subsequent dobutamine infusions did not affect
EWLAD or
EWLCX compared with stunning
levels. PSWLCX, which had
increased from 4 ± 6 mmHg · mm
at baseline to 8 ± 3 mmHg · mm following stunning
(P < 0.05), decreased dose
dependently to 10 ± 4 mmHg · mm
(P < 0.05) during the dobutamine
infusions. PSWLAD, which had
decreased after stunning of the LCX region, decreased further during
the dobutamine infusion (Fig. 2).
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Stunned LAD and LCX myocardium.
After additional stunning of the distribution area of the LAD,
SSLAD decreased from 16 ± 2 to
9 ± 3% and
ELAD from 79 ± 10 to 31 ± 6 mmHg/mm (both P < 0.05), whereas in the LCX region these variables remained
unchanged. During the dobutamine infusions, SSLAD increased to 12 ± 2%,
while ELAD
increased almost fourfold (both P < 0.05). The responses of SSLCX and
ELCX to
dobutamine were similar to the responses when only the distribution
area of the LCX was stunned. After the LAD distribution area was
stunned, EWLAD decreased from 187 ± 12 to 126 ± 24 mmHg · mm
(P < 0.05), whereas
EWLCX remained unaffected. The
dobutamine infusions did not affect
EWLAD or
EWLCX.
PSWLAD increased from 3 ± 3 to
31 ± 7 mmHg · mm
(P < 0.05) after LAD stunning but
decreased to 9 ± 9 mmHg · mm during the
highest dose of dobutamine. The response of
PSWLCX was not different from the
response when only the distribution area of the LCX was stunned (Fig.
3).
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Duration of Contraction
In the normal heart, TLAD decreased up to 26% (P < 0.05) during the dobutamine infusion, whereas TLCX remained unaffected (Table 3).
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After stunning of the LCX region, TLCX increased up to 23% (P < 0.05), indicating that contraction of the LCX region had become slower. During the subsequent dobutamine infusions, TLAD decreased dose dependently. Unlike the LCX region before stunning, TLCX now decreased during the dobutamine infusion (P < 0.05).
Stunning of the LAD region slowed the contraction in that region, as reflected by a significant decrease in TLAD (P < 0.05), which was restored by the infusion of dobutamine. A decrease of TLCX was again observed during the dobutamine infusion.
Contribution of T and
E to Mechanical Interaction
E and
T were statistically
significant predictors of PSWLCX
in all three protocols (Table 4, Fig.
4). Consequently, as the second step, the
multiregression model, PSWLCX = 
E + 
T + 
was applied to each of the three experimental protocols; was
introduced to evaluate whether an unknown factor might still contribute
significantly. Table 4 shows that the contribution of
E () increased after LCX
stunning, whereas the contribution of
T () decreased; was not
significantly different from zero in the first and second protocol but
achieved statistical significance in the third protocol.
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Additional analysis focused on the detection of multicolinearity
between E and
T. The VIF (1.2, 1.1, and 1.0 for
protocols 1, 2,
and 3, respectively) and CI (maximum
values of 2.2, 2.4, and 2.8 for
protocols
1, 2,
and 3, respectively) were small
compared with the values (8-10) considered significant for
colinearity (9).
Standardization of the parameters revealed that
T explained 65 ± 11% and
E explained 37 ± 15% of the
variation in PSWLCX in the normal
myocardium (Fig. 4). After LCX stunning,
T and E explained 37 ± 15 and 55 ± 14% (both P < 0.05),
respectively, of the variability in
PSWLCX. The contribution of
E remained at 54 ± 13%
(P < 0.05) after additional LAD
stunning, whereas the contribution of T increased to 57 ± 13%, which was similar to that during baseline conditions.
Model Simulations
To evaluate the independent effect ofT and
E on the shape of the
pressure-segment length loops, a mathematical model was developed based
on a two-spring model in series (see
APPENDIX). A
E of 50%, without
T, induced a backward leaning of
the simulated LV pressure-segment length loop (Fig.
5A).
T of 10% of the cardiac cycle,
without a change in contractility, induced asymmetric loops with a
backward leaning of the simulated pressure-length loop during
isovolumic relaxation (Fig. 5B). A
combination of a 50% E and 10%
T is compatible with the present
experimental findings. When differences in both contractility and
asynchrony were applied, the backward leaning of the loop was increased
above each individual effect (Fig.
5C). However, the backward leaning
of the simulated pressure-length loop was not found when the low
contractile muscle contracted earlier than the strong muscle (Fig.
5D). It is to be noted that backward
leaning implies a positive PSW and thereby signifies the changes found
during LAD and LCX stunning.
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DISCUSSION |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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The present study describes the mechanical interaction between normal
and stunned myocardial segments in the porcine LV and determined the
relative contributions of E and
T to mechanical interaction.
E was used to characterize the regional contractile state of the myocardium. Several studies have shown that E is a more appropriate parameter for regional contractility than SS or wall thickening (3, 14, 15). Consistent with earlier studies, we observed that, in both normal and stunned LAD myocardium, E was more sensitive than SS to local infusions of dobutamine and that TLAD decreased. The distribution territory of the LCX responded differently before and after stunning. Before stunning of the LCX region, the LAD dobutamine infusion did not affect ELCX and TLCX, but after stunning of the LCX region, ELCX increased while TLCX decreased.
Changes in the area enclosed by the LV pressure-segment length relationship reflect changes in regional EW (19, 22, 29). During regional ischemia and stunning, a significant fraction of EW is performed during the isovolumic relaxation phase (1, 4, 5, 14, 15, 22) and therefore does not directly contribute to pump function. We used this PSW as an index of myocardial interaction because it occurs during a phase in which global LV volume is constant and might therefore be interpreted as the work of a myocardial region to stretch (if positive) or to be stretched by (if negative) another nonstunned region (1, 4, 16, 22). Indeed, we observed an inverse relationship between PSWLCX and PSWLAD in normal myocardium during the dobutamine infusions, which is in agreement with previous studies (11, 23). However, after stunning of the LCX perfused region and also after additional stunning of the LAD region, dobutamine infusions induced parallel decreases of PSWLCX and PSWLAD. The mechanism underlying mechanical interaction has almost exclusively been studied during regional ischemia.
Underlying Mechanism
During ischemia, three independent factors have been identified to contribute to mechanical interaction: 1) changes in sympathetic tone, 2) the Frank-Starling mechanism, and 3) direct myocardial unloading (2, 7, 8, 10, 12, 16, 17, 20, 23, 28, 30). The proposed mechanism to explain mechanical interaction during ischemia is discussed for the present experimental conditions.In the present experiments, changes in aortic pressure were very small in response to both stunning and intracoronary dobutamine infusions. As a consequence, the contribution of baroreceptor stimulation is (probably) negligible in the present experiments. Furthermore, because there were no significant changes in end-diastolic pressure and regional end-diastolic length in any of the experimental conditions, the involvement of a regional Frank-Starling mechanism appears also not to be a major factor for the explanation of the changes in PSW observed in the present study.
This implies that direct regional unloading of the muscle fibers is the
most likely factor to explain the present findings. It has been
postulated that, during regional ischemia, either a difference in
contractility ("weak and strong muscles in series") or a
difference in timing ("asynchrony") between ischemic and nonischemic regions is responsible for the mechanical interaction (2,
16, 17, 20, 23, 28). In the present study, we confirmed a role for both
mechanisms in regionally stunned myocardium. At the same time, we could
exclude parameters that were related to absolute contractility or
timing of the nonstunned and stunned regions. Moreover, we found
evidence not only that both T and E contributed to mechanical
interaction in stunned myocardium but also that, compared with normal
myocardium, the relative contribution of
E to mechanical interaction
increased at the expense of T.
Model simulation helped to understand this finding as both
E and
T exerted an effect on the
simulated pressure-length loop. A mathematical model incorporating a
strong-weak muscle in series produced a backward leaning of the
simulated pressure-segment length loop in the region of the weak
muscle. An additional change in T
either increased or even prevented the leaning of the simulated pressure-segment length loop. With these two parameters, we could therefore qualitatively mimic some of the conditions studied during the
experiments. However, the model did not offer an explanation for the
increment in contractility of the stunned LCX region when the LAD
region was stimulated by local infusion of dobutamine. Furthermore, the
model could also not explain the large intercept of the regression
model after both the LAD and LCX regions were stunned. These latter two
observations imply that an additional factor, not included in the
model, has to be taken into account. A possible explanation might be a
third unobserved myocardial region contracting in asynchrony with
either or both of the other two regions.
Consequence of Myocardial Interaction in Stunning
Myocardial stunning represents viable tissue with a low contractile state but with normal contractile reserve (14, 32). Inotropic interventions are used to reverse stunning, and increases in SS and E produced by inotropic agents are considered to be a direct effect of these agents on the stunned region. The present study shows that increases of the contractile state of normal myocardium, as is achieved by intravenous infusions, may also affect the indexes used to quantify the contractile state of stunned myocardium, such as SS and E.Limitations of Method
Several confounding factors have to be excluded. First, overflow of dobutamine from the LAD into the LCX region could contribute to the explanation of the present findings. We believe this to be unlikely, because we could not detect Evans blue dye in the LCX region when this dye was injected into LAD at an infusion rate comparable to the highest dose of dobutamine.Second, recirculation of dobutamine might have occurred, which implies that dobutamine could have exerted its effect on the LCX region directly. This possibility was evaluated by intravenous infusion of the highest dose of dobutamine at the end of the protocol. Because no changes in hemodynamic or regional mechanical parameters were detected, this possibility could also be excluded as playing a significant role.
The local infusion of dobutamine sometimes produced complex shapes of the pressure-segment length loops. As a consequence, especially during the highest dose, the end-systolic pressure-segment relationship points could not be determined in a number of cases (which is the reason for the smaller number of observations with the highest infusion rate of dobutamine). The reported data are reliable, because E responded to dobutamine and stunning as expected and the measurements were reproducible, which can be deduced from the washout measurements.
We have analyzed E only at 120 mmHg, which is in the measurement range. Analyses at different end-systolic pressures have been presented before (14, 15). In those studies, it was shown that stunning produced similar responses at different end-systolic pressures before and after dobutamine (3, 14, 15). In addition, several in vitro studies have provided evidence that changes in E reliably reflect changes in myocardial contractility. On the basis of these studies (3, 14, 15, 21, 26), it may be concluded that elastance is relatively insensitive to changes in loading conditions. However, it has never been investigated in vivo, which warrants some caution for the use of E as an index of contractility in vivo. As a consequence, identifying E as an index for contractility of the muscle fiber should be done with caution.
Two assumptions of the multivariate model need to be addressed: first,
the assumption of absence of correlation between
E and
T, and, second, the absence of
interdependence of E and T. The former assumption is
important because synchrony and differences in contractility are
usually coupled parameters. We have evaluated this assumption by the
calculation of standard colinearity diagnostics (VIF, CI) (9). As those
diagnostics were low, the model is not redundant. The latter assumption
was also tested by introducing a cross term into the present model
(E · T).
The coefficients of the cross term were not statistically different
from zero in any of the three experimental protocols. Therefore, both
assumptions seem justified.
To compare different conditions and tissue properties, it is customary in mechanics to use a normalized length value (strain). In the present experiment, L0 could serve that purpose. Because we did not detect any systemic effects on L0, we have not adopted this approach and have presented the measurements without normalization.
The aim of the present study was to evaluate fiber contraction at the midmyocardium. It is known that different muscle layers exist with different fiber direction in the myocardium. Subendocardial muscle fibers are known to be more sensitive to ischemia than subepicardial fibers. We cannot exclude the possibility that part of the effects noticed in the present study are caused by changes in the different layers of muscle fibers, especially the subendocardial muscle fibers.
In conclusion, the present study provided evidence that mechanical
interaction was affected by regionally stunning the myocardium. The
underlying mechanism could be explained by at least two independent factors: E and
T between the region under study
and the adjacent myocardium. During baseline conditions,
T was the main factor, whereas,
after stunning of the LCX region, contractility increased its influence
on mechanical interaction at the expense of
T. Stunning of both the LCX- and
the LAD-perfused regions shifted the relative contribution of both
parameters such that both factors contributed equally to mechanical
interaction.
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APPENDIX |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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A mathematical model was developed in SIMULINK (Math Works), describing the behavior of two active springs in series. The two springs signify the two regions under study (LCX and LAD regions) and were put in series to simulate the circumferentially oriented muscle fibers. We started with the description of a single muscle based on a time-varying stiffness according to Suga and co-workers (21, 26) for the whole ventricle. Second, two time-varying active springs were put in series. As a consequence, we have the following four equations
![<IT>E</IT>(<IT>t</IT>) = <IT>E</IT><SUB>i</SUB>(<IT>t</IT>) ⋅ <IT>E</IT><SUB>2</SUB>(<IT>t</IT>)/[<IT>E</IT>(<IT>t</IT><SUB>1</SUB>) + <IT>E</IT><SUB>2</SUB>(<IT>t</IT>)]](/content/vol273/issue5/fulltext/H2146/img001.gif)
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![<IT>E</IT>(<IT>t</IT>)/<IT>E</IT><SUB>2</SUB>(<IT>t</IT>) = <IT>L</IT><SUB>2</SUB>(<IT>t</IT>)/[<IT>L</IT><SUB>1</SUB>(<IT>t</IT>) + <IT>L</IT><SUB>2</SUB>(<IT>t</IT>)]](/content/vol273/issue5/fulltext/H2146/img002.gif)
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![<IT>E</IT>(<IT>t</IT>)/<IT>E</IT><SUB>1</SUB>(<IT>t</IT>) = <IT>L</IT><SUB>1</SUB>(<IT>t</IT>)/[<IT>L</IT><SUB>1</SUB>(<IT>t</IT>) + <IT>L</IT><SUB>2</SUB>(<IT>t</IT>)]](/content/vol273/issue5/fulltext/H2146/img003.gif)
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The assumption underlying the model is that the myocardium may be
represented by a linear time-varying elastance, which may be subdivided
into two regions with different properties (21, 26). Furthermore,
coupling between these two regions is direct, without the assumption of
a border zone. The time shift (T)
between two regions is constant over the cardiac cycle.
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ACKNOWLEDGEMENTS |
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The technical assistance of R. H. van Bremen and secretarial assistance of D. de Bruyn are gratefully acknowledged.
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FOOTNOTES |
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This work was supported by Grant 92.308 from The Netherlands Heart Foundation.
The research of D. J. Duncker is supported by a fellowship of the Royal Netherlands Academy of Arts and Sciences.
Address for reprint requests: R. Krams, Experimental Cardiology, Thoraxcenter, Erasmus Univ. Rotterdam, PO Box 1738, 3000 DR Rotterdam, The Netherlands.
Received 24 October 1996; accepted in final form 11 July 1997.
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REFERENCES |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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), after stunning the distribution territory of left
circumflex coronary artery (LCX; 
), and after stunning the
distribution territories of both LCX
(A) and LAD
(B; 
). Data are presented as means ± SE. Notice that, in distribution territory of LAD, effect of
dobutamine on SS was negligible but that
ELAD consistently
increased. Responses in distribution territory of LCX were different
before and after stunning. PD, pre-dobutamine.
