Vol. 281, Issue 6, H2687-H2696, December 2001
Evidence for stretch-induced resistance increase of proximal
coronary microcirculation
Annemiek J. M.
Cornelissen1,2,
Jos A. E.
Spaan2,
Jenny
Dankelman1,
Charles C.
Chan3, and
Frank C. P.
Yin3
1 Man Machine Systems and Control Group, Faculty of Design,
Engineering and Production, Department of Biomedical Engineering and
Mechanics, Delft University of Technology, 2628 CD Delft;
2 Department of Medical Physics, Cardiovascular Research
Institute Amsterdam, Academic Medical Center, University of Amsterdam,
1100 DE Amsterdam, The Netherlands; 3 Department of Biomedical
Engineering, Washington University, St. Louis, Missouri 63130-4899
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ABSTRACT |
We investigated the influence of stretch on
regional hemodynamic parameters of the septal circulation. We used a
similar experimental setup and mathematical model, as described
previously (14). Five ventricular septa were isolated from
anesthetized dogs, sutured to a biaxial stretching apparatus, and
perfused with an oxygenated perfluorochemical emulsion at maximal
vasodilation. Under unloaded and biaxially stretched conditions, flow
and septal thickness (to index vascular volume) were measured
continuously. Pressure was varied sinusoidally at 30, 50, and 70 mmHg
with amplitude of 7.5 mmHg over frequencies ranging between 0.015 and 7 Hz. Admittance (flow/pressure) and capacitance (thickness/pressure)
transfer functions were calculated and interpreted in terms of a
two-compartmental model with volume-dependent resistances. Parameter
estimation showed that the proximal resistance and compliance were
unaffected, whereas the resistance of the proximal part of the
microcirculation, including the small arterioles, increased with
stretch. The effect of stretch on the distal resistance and
capacitance, however, could not be determined unequivocally.
coronary resistance distribution; admittance; intramyocardial
compliance; model; pressure-dependent resistance
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INTRODUCTION |
STRETCH OF THE
MYOCARDIUM results in an increase in total coronary resistance.
For example, under full vasodilation, pressure-flow relations shifted
to higher pressures as left ventricular diastolic pressure was
increased (thereby stretching the heart) both in normal
(2) and in hypertrophic hearts (6). In the
isolated septum preparation, where stretch could be imposed independent of ventricular pressure, stretch-induced increase in coronary resistance (10) was coupled to a decrease of intramural
vascular volume (8).
There is no information, however, on the anatomic location of the
stretch-induced increase in coronary resistance. Stretch certainly will
affect the geometry and thereby resistance of arteries and arterioles.
Moreover, because resistance is nonlinearly dependent on pressure,
being more sensitive at low pressures, the resistance in the
low-pressure capillary and venous portions of the coronary circulation
is also likely to be affected by stretch.
It has been shown (3, 14) that resistance of the arteries
and arterioles are important determinants of the frequency response of
input admittance of the coronary circulation. Using the isolated septal
preparation and a two-compartment model of the coronary circulation, we
(14) previously showed that the frequency and pressure
dependence of admittance and capacitance provided considerable insight
into the distribution of resistance between the proximal and distal
portions of the coronary bed. This same approach will be extended here
to estimate the site of stretch-induced vascular resistance increase in
the septum under conditions of full vasodilation.
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METHODS |
Specimen preparation.
We used the canine isolated, perfused, and septal preparation as
previously described (10). The animal experiments were performed at the Cardiology Division, Johns Hopkins University School
of Medicine (Baltimore, MD), from September 1994 to June 1995 (under
the supervision of Dr. F. C. P. Yin). Briefly, five mongrel
dogs of either sex weighing 18-22 kg were anesthetized with
intravenous pentobarbital sodium (35 mg/kg). The animals were intubated
and ventilated, and the heart was exposed via a midline sternotomy.
Heparin sodium (5,000 U) was infused to minimize thrombi formation.
Each dog was systemically cooled to 28°C, at which time the heart was
arrested by rapid injection into the ascending aorta of cold (4°C)
cardioplegic solution composed of (in mM) 120 Na+, 16.0 K+, 16 Mg2+, 1.2 Ca2+, 160.4 Cl
, 10 HCO
, and 1.0 adenosine. The
heart, which usually fibrillated and then became asystolic within
1-2 min, was removed. A cannula was inserted directly into the
septal artery, connected to a reservoir, and continuously perfused with cold cardioplegic solution until the specimen was mounted in the test
apparatus. The perfusion pressure was kept <30 mmHg throughout the
preparatory time to minimize tissue edema.
To prevent shunting to the collateral vessels, the left anterior
descending, left circumflex, and right coronary arteries were
individually cannulated and filled (by injection via a syringe) with
dental rubber to which a few drops of catalyst had been added. Once the
dental rubber filled the smallest visible arteries on the surface of
the heart wall, the left and right ventricles were cut away within the
perfusion boundary of these embolized arteries. It has been verified
(10) that this methodology results in an isolated perfused
septal bed with no leaks or shunts.
The isolated septum, with its right ventricular surface facing upward,
was then mounted to a biaxial (BI) mechanical stretching apparatus as
described previously (7). Four edges of the septum, roughly defining a rectangle, were connected by a series of threads in
a trampoline-like arrangement to the carriages of the stretching apparatus (10) so that the septum could be stretched in
the base-to-apex and circumferential directions [see Fig.
1 in Resar et al. (10)].
The forces in each direction were measured by force transducers (model
sf-10; Interface) mounted on the carriages.
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Fig. 1.
Two-compartmental model for the septal circulation. Both
compartments consist of a resistance-capacitance-resistance network
with the model interpretation of resistance (Rm)
being divided between the two compartments. The first compartment
reflects predominantly the larger arteries and larger resistance
vessels, whereas the second compartment reflects predominantly the
microcirculation and the venules. Q1, Qm, and
Q2 are defined as flow through R1,
Rm, and R2, which are the
resistances in the model. C1 and
C2 are the capacitances in the model.
Pin and P0 are the inlet and outlet pressures,
respectively. PC1 and PC2 reflect the pressures
over the capacitances, and QC1 and QC2 the flow
to and from the capacitances, respectively. R1,
Rm, and R2 are assumed to
vary with volume of the capacitances.
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The deformations in both directions in the central region were measured
by a video system imaging four stainless steel beads glued to the
central septal surface forming a rectangular shape. Septal thickness
was measured with a pair of sonomicrometer crystals (Triton Technology;
La Jolla, CA) glued onto the left and right ventricular surfaces of the
septum. The crystals were placed in the area demarcated by the four
stainless steel beads. Two platinum wires were sewn on the outer edges
of the specimen and connected to a stimulator (model S88, Grass
Instruments; Quincy, MA).
The septum was mounted to the stretching apparatus and the cannula was
connected with stiff tubing to a pressurized reservoir. The air
pressure in the reservoir was controlled by an electrically controlled
pneumatic needle valve connected to a signal generator. Flow at the
entrance of the septum was measured with a 1-mm-inner diameter
cannulating electromagnetic flow probe (model 774-100-2.0-1.0, Skalar
Medical; Delft, The Netherlands) connected to a flowmeter (model 1401, Skalar Medical). The inlet pressure at the proximal end of the cannula
was measured via a plastic T piece with a micromanometer (model PC-450,
Millar Instruments; Houston, TX).
The cold cardioplegic perfusate was changed to a room-temperature
perfluorochemical emulsion (FC-43, Green Cross; Osaka, Japan) with the
following composition (in mM) 137 Na+, 5.2 K+,
2.6 Ca2+, 2.1 Mg2+, 1.54 H2PO
, 119 Cl, 25.8 HCO, and 11.5 glucose, along with 2 mg/100 ml
adenosine and 5.8 g/100 ml albumin. Adenosine was sufficient to fully
dilate the vascular bed. The perfusate was gently bubbled with 95%
O2-5% CO2 to maintain pH between 7.4 and 7.5 and to keep oxygen tension >600 mmHg. After a few minutes, the
specimen could be electrically stimulated to beat. The pressure was
then increased sufficiently to produce diastolic flows of ~25 ml/min.
The specimen was paced at a rate of 0.4 Hz for ~30-45 min to
allow recovery and stabilization from the cardioplegia. Sufficient
lidocaine was added to the perfusate to prevent spontaneous contractions when the specimen was not electrically stimulated. All
measurements were performed in noncontracting conditions. At the end of
the experiment, Evans blue dye was injected into the cannula to
delineate the perfusion area, which was cut out of the septum and weighed.
Stretching protocols.
The septum was examined in an unloaded (UN) condition and a BI
stretched condition. Stretch was quantified in terms of the strain in
both circumferential and base-to-apex directions. Strain was defined as
the difference between reference, UN length, and the length after
stretching the septum, divided by the reference length. We aimed to
apply equal strain in both directions of ~20%. However, we did not
want to apply excessively high forces, so we kept the forces within a
range of 500-2,000 g.
Coronary dynamics protocol.
The dynamic responses of flow and thickness, i.e., vascular volume
(14), to 15-mmHg peak-to-peak sinusoidal pressure
perturbations at frequencies ranging from ~0.015 to 10 Hz under UN
and BI-stretched conditions were examined. The perturbations were
performed at mean pressures of 30, 50, and 70 mmHg. We have previously
shown that this amplitude of the pressure oscillations provides
sufficient resolution for the thickness signal, whereas the variation
in pressure is still linearly related to variations in flow and
thickness. After each change in frequency, mean pressure, and stretch
condition, the specimen was allowed to equilibrate for a few minutes.
The UN condition and then the BI-stretched condition were examined. The
order of the mean pressures, however, was chosen arbitrarily. In the
lower-frequency range (0.015-0.5 Hz), the data were digitized at a
sampling rate of 10 Hz and at higher frequencies at 100 Hz.
Data analysis.
A set of data, composed of pressure (P), flow (Q), thickness (Th),
forces in both directions (Fx,
Fy), and distance between the stainless beads in
both directions (dx, dy), was analyzed with custom software. First, any baseline drift was removed from the entire data set. The data at each discrete frequency were then centered about the mean. At least two complete periods during
steady-state condition were extracted and further analyzed. Flow was
normalized to 100 g of perfused tissue weight. The amplitude and
phase angle of pressure, flow, and thickness were obtained by spectral
analyses using the MATLAB fast Fourier Transform algorithm and
expressed as complex numbers, namely P(
), Q(), and Th() respectively, in which is the frequency in Herz.
To correct for the pressure drop from the reservoir to the tip of the
cannula, we first measured the system impedance with the cannula open
to air. The measured P(v) [P()measured] was then corrected for the pressure drop using Q() and the perfusion system impedance to obtain the septal perfusion pressure P().
The dynamic responses are reported in terms of transfer functions in a
standard Bode plot format. The pressure-flow (i.e., admittance)
transfer function consists of plots of the ratio of flow to pressure
modulus versus frequency and the difference between flow and pressure
phase angle versus frequency. Similarly, the pressure-volume (i.e.,
capacitance) transfer function consists of the ratio of volume to
pressure modulus and the difference between volume and pressure phase
angle. Volume was calculated from thickness applying a correction
factor derived from the fitting procedure explained below.
Fitting of Bode plots by second-order transfer functions.
The fitting procedure and the physical interpretation of the fitting
parameters are described in detail in Spaan et al. (14). The following is a brief overview.
The Bode plots were fitted using second-order transfer functions,
corresponding to the structure of the model outlined in the next
paragraph (see Fig. 1)
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(1)
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(2)
|
Gq and 
1-4
are parameters to be determined, GThV is the
conversion factor for expressing volume in terms of thickness, and 
is frequency in radians per second. The two equations were simultaneously fitted to the experimental data by minimizing the following cost function
|
(3)
|
The factors
e1i-e4i
are relative differences between the theoretical and experimental
values of modulus and phase of the admittance and capacitance at the
different frequencies; n is the number of frequencies and
i is the index (14). Note that is in
radians per second and = 2
, and is frequency in Hz.
The value of "cost" was minimized by varying the parameters of the
admittance and capacitance functions with the use of the procedure of
simulated annealing (1, 14). The contributions to the cost
function for frequencies <1 Hz were 1.5 times the contributions for
higher frequencies.
Two-compartment model of the septal circulation.
The two-compartment model with volume-dependent resistances, as
described in Spaan et al. (14), was used to interpret the data. Briefly, the model consists of a network of resistances and
capacitances, as shown in Fig. 1. The compartments reflect the proximal
and the distal part of the vascular bed, i.e., the arteries and
arterioles and the capillaries and venules, respectively. To account
for the volume dependencies of the resistances during the sinusoidal
changes of pressure around a mean, the resistances were assumed to
depend piecewise linearly on volume around nominal working values
according to
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(4)
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where 
V is the variation in V around the working value
V0. K is the sensitivity of resistance for
volume in the working point (V0,
R0). Because the law of Poiseuille gives a
nonlinear relation between volume and resistance, this approximation is only valid for limited variations in volume. The variations in capacitance during the sinusoidal pressure variations were neglected (14).
The volume in the first compartment (V1) influences
R1 and a portion of Rm,
therefore we have two sensitivity values for these resistances,
K1 and Km1. Similarly,
the volume in the second compartment (V2) influences
R2 and the other part of
Rm by the sensitivity values
K2 and Km2, respectively.
Because Rm depends on both the volumes in the
first and the second compartment, a factor X was introduced
to define which fraction of Rm was sensitive to
the volume in the proximal compartment. Hence, the fraction of
Rm sensitive to the distal compartment equals
(1 
X) · Rm.
Our earlier study demonstrated how the fitting parameters
(Gq and 1-4)
depend on the physical parameters of the model
(R1, Rm,
R2, X, C1,
C2, V1, V2,
K1, Km1,
Km2, and K2). The
resulting set of equations is overparameterized. That is, because our
model has two parameters in excess of the number of equations, we had to make additional assumptions to arrive at possible values of parameters. We choose the following physiological additional constraints.
1) Steady-state resistance should equal the sum of the
resistances
|
(5)
|
2) According to the law of Poiseuille and assuming
constant length R = A/V2, therefore
|
(6)
|
3) Total vascular volume (Vtot) should
be >5 and <15 ml/100 g, 4) V1 should be >5
and <35% of Vtot, and 5) X should
be >0 and <1.
These constraints allow us to analyze the ranges of possible values of
the parameters within physiological realistic boundary conditions.
Statistical analysis.
To evaluate the effect of stretch on the various parameters,
representative values within the range of possible values were determined by taking the average of the maximal and minimal possible value of Rm (Rm,average)
and the average of the maximal and the minimal possible value of
X at Rm,average. The representative values of the remaining parameters follow from the relations between the fitting parameters and the physical parameters of the model and the
constraints 1 and 2. These uniquely defined
representative values were subjected to the statistical tests.
We tested whether the level of mean pressure influenced the effect of
stretch and vice versa on each parameter. One-way repeated-measures analysis of variance was applied to analyze whether there was a
difference between the representative values of the UN and stretched group. Pairwise comparisons for effects of stretch were made using the
Student-Newman-Keuls test. Statistical significance was defined to be
at the P = 0.05 level.
When the possible ranges for a parameter for the UN and stretched
situation do not overlap and the representative values were significantly different, the parameter was qualified as affected by
stretch. In all other situations, we could not unequivocally determine
the effect of stretch on the subjected parameter.
| |
RESULTS |
In Fig. 2, the stretch conditions
for the five different septa are shown. Figure 2A shows the
forces in the circumferential and base-to-apex directions for the
different stretch conditions. Figure 2B shows the
corresponding strains. In each panel, the UN and BI stretch conditions
at the different mean pressures for the five septa are given. The
different symbols with error bars reflect the means ± SE of the
average force and strain at a certain mean pressure and stretch
condition. The small or even 0 SE (no error bars drawn) indicates the
small variations for each specimen during a certain protocol. However,
the mechanical properties of each of the septa were quite different.
This is shown by the stiffness (Sxy) in the
table included with the figure. Stiffness is calculated as the ratio of
the root mean square of the sum of the forces (Fi) to the
root mean square of the sum of the strains (
i)
The strain for the stiff septa (experiment 1, open
square, and experiment 3, open inverted triangle) was
limited to ~12% because we did not want to apply a force >2,000
g. In contrast, the compliant septum (experiment
4, open diamond) had to be stretched ~30% to achieve the
desired lower limit of 500 g force.
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Fig. 2.
Stretch conditions for the 5 different septa. A:
unloaded (UN) forces in the x- and y-directions
and during biaxial (BI) stretch. B: strain in x-
and y-direction during UN and BI stretch. The different
symbols denote the 5 septa. The symbols and error bars reflect the
means ± SE of the average force and strain of the different
tracings. The small or even 0 SE (no error bars drawn) indicate the
small variations in stretch conditions. The table in the figure shows
the average stiffness of each septum (Sxy). For
more detailed information, see RESULTS.
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Not all conditions could be tested in each experiment. In
experiment 2, the pressure could not be increased to 70 mmHg, because of the pump limitations and the low-septal vascular
resistance. In experiments 1 and 3, BI stretch at
P = 30 mmHg resulted in too low a flow to allow
accurate measurements of flow variation. In Table
1, the total static coronary resistance
and the pressure after an occlusion of 50 s of zero flow pressure
(PZF) are shown.
Typical results for the admittance (Fig.
3, A and C) and
capacitance (Fig. 3, B and D) transfer functions
in one specimen under control and stretch conditions at
P = 50 mmHg are shown in Fig. 3.
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Fig. 3.
The effect of stretch on admittance and capacitance at a mean
pressure of 50 mmHg. The admittance modulus (A) increases
with increasing frequency, i.e., with constant pressure amplitude the
flow amplitude increases. At low frequencies, the admittance modulus
was the largest in the UN state; with stretching of the septum, the
admittance modulus decreases. At higher frequencies, the difference is
less clear. The admittance phase (C) has a maximum at ~2
Hz, which is the smallest in the UN state and increases with stretching
the septum. The capacitance modulus (B) decreases with
increasing frequency. The capacitance phase (D) decreases
with increasing frequency. At ~2 Hz, a slight bump can be seen in the
capacitance phase. There is only a small dependence of capacitance on
stretch. The curves in the panels are the best fits with the admittance
and phase equations.
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For both the UN and stretched conditions, the admittance modulus (Fig.
3A) increases with increasing frequency. Stretch has a
prominent effect on the admittance modulus at low frequencies, whereas
its effect is less at higher frequencies. The admittance phase (Fig.
3C) has a maximum at ~2 Hz, which is lower in the UN than
the stretched condition. Both the modulus (Fig. 3B) and phase (Fig. 3D) of the capacitance decrease with increasing
frequency at lower frequency. There is, however, only a small
dependence of capacitance on stretch. Results comparable to those in
Fig. 3 were observed at other mean pressures as well as for each of the
other experiments.
The curves shown in Fig. 3 are those with the lowest cost criterion
obtained by running the fitting procedure 10 times, each with a
different starting condition. The variation in these 10 estimates for
the coefficients of the transfer functions was small, indicating that
the estimates for each parameter were robust. The variation between the
experiments and between the different stretch conditions was larger.
The parameters obtained with the curve of the optimal fit were used for
further analyses. We ignored the outlying data in the UN condition for
experiment 5 at P = 70 mmHg, because as was
shown in our previous study, the estimate of total volume exceeds
tissue volume.
Possible values of the parameters fulfilling our relations between the
fitting parameters and the physical parameters of the model and
constraints 1 and 2, for both the UN and BI
stretch condition, are demonstrated in Figs. 4 and 5, by the thin black lines. In Fig. 4, the dependence of
R1, R2,
C1, C2, V1,
and V2 on Rm at different values of
X is shown for one experiment (experiment 4,
P = 50 mmHg). In Fig. 5,
the dependence of K1,
Km1, Km2, and K2 on Rm at different
values of X is shown for the same experiment. The ranges of
realistic parameter values can be inferred by applying the
constraints 3-5. The thick solid and dotted lines
denote the boundary conditions, and the symbols denote the minimal and
maximal values that fulfill these constraints. The uncertainty in the values of the parameters notwithstanding, it is clear that the value of
Rm under stretch is about twice its UN value in
this case.
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Fig. 4.
Sensitivity analysis of resistance, compliance, and volume
parameters on choice of Rm and X. For
experiment 4 at a mean pressure of 50 mmHg, the estimated
relationships between Rm vs.
R1, R2,
C1, C2, V1,
and V2 for different values of X, for the UN and
stretched (BI) conditions are shown that fulfill the relationships
between the fitting parameters and the physical parameters of the model
and constraints 1 and 2. For X = 0, Rm is only sensitive to distal volume. For
X = 1, Rm is only sensitive to
proximal volume. R1 is independent of both
X and Rm. R2
is linearly related to Rm. The thick solid lines
indicate ranges of parameter values and the symbols indicate the
minimum and maximum parameter values, fulfilling the physiological
constraints 1-5.
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Fig. 5.
Sensitivity analysis of the sensitivity parameters on choice of
Rm and X. For experiment 4 at a mean pressure of 50 mmHg, the estimated relationships between
Rm vs. K1,
Km1, Km2, and
K2 for different values of X, for the
UN and BI conditions are shown. Thick solid lines indicate ranges of
parameter values and the symbols indicate the minimum and maximum
parameter values, fulfilling the physiological constraints
1-5.
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The error bars in Fig. 6 give the ranges
of possible values for the parameters R1,
Rm, R2,
C1, C2, V1,
and V2 applying the relations between the fitting
parameters and the physical parameters (14) and the
constraints 1-5 to the five experiments for
the UN and stretched conditions. R1 is
explicitly determined by the relationship between the fitting
parameters and the physical parameters. All of the other physical
parameters are dependent on the additional constraints. The symbols in
Fig. 6 represent the representative values obtained by calculating the
average of the maximal and minimal possible values of
Rm and X.
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Fig. 6.
The error bars show the ranges of realistic parameter values
obtained from the relations and constraints shown in Fig. 4, for UN and
BI conditions. Symbols are the representative values calculated using
the average of the minimal and maximal possible values for
Rm and X. *P < 0.05, the parameter of which the representative values are influenced by
stretch. In general, the ranges of Rm do not
overlap and the values increase with stretch. The ranges of values for
the other parameters for the UN condition overlap with those for the
stretch condition. For further details, see RESULTS.
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For the representative values of the parameters, the level of mean
perfusion pressure did not influence the effect of stretch or vice
versa. The representative values of Rm,
R2, V1, V2,
K1, Km2, and
K2 are significantly different for the UN and
stretched conditions. The ranges for Rm for the
UN and stretched conditions do not overlap, except for experiment
2, where the ranges of Rm overlap for 30%
at P = 30 mmHg and for 10% at P = 50 mmHg. For Rm to remain unaltered or decrease
during stretch, maximal 30% for P = 30 mmHg and 10%
at P = 50 mmHg, V1 has to increase with stretch. In reality, it is highly unlikely that V1
increases with stretch. R1, being unaffected by
uncertainty if the model remains constant in our estimations during
stretch, implies that either V1 remains constant or even
decreases as a result of reduced vascular diameters.
Averaged Rm for overall pressures in the UN
state was 17 ± 10 mmHg · ml1 · s · 100 g
(means ± SD; UN) and increases to 50 ± 46 mmHg · ml1 · s · 100 g in the
stretched state (means ± SD; BI), P < 0.05.
In contrast, R1 is not affected by stretch,
being 9.6 ± 4.8 mmHg · ml1 · s · 100 g
(means ± SD, UN) and R1 = 10 ± 3.8 mmHg · ml1 · s · 100 g
(means ± SD, BI). The representative values of
C1 are also not significantly affected by
stretch, being 0.014 ± 0.001 ml · mmHg1 · 100 g1
(means ± SD, UN) in the UN state, and 0.011 ± 0.0004 ml · mmHg1 · 100 g1
(means ± SD, BI) under stretch.
The ranges of the values for R2,
C2, V1, and V2 for the
UN and loaded condition overlap, implying that for these parameters the
effect of stretch could not be unequivocally determined. The ranges of
the K values for the UN and loaded condition, not shown in
Fig. 6, overlap as well.
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DISCUSSION |
The present results show that stretching the myocardium
significantly influences coronary vascular frequency responses in a
fully dilated bed. The model interpretations suggest that stretch increases the resistance Rm between the two
compartments, which likely represents the resistance of the
microvessels, including the arterioles and the capillaries. The
proximal resistance and capacitance are unaffected. The effect of
stretch on the distal resistance and compliance is ambiguous because
these parameters are largely dependent on the model assumptions. Before
discussing the implications of our results, we first briefly critique
our methods.
Critique of experimental method and data analyses.
The experimental method and the parameter estimation method used in
this paper have been critically evaluated in the previous study
(14). Those points that are specifically related to
stretching will be further discussed here.
The amount of stretch applied to the five septa was not the same
because the septa had different stress-strain properties. The two
stiffest septa (experiment 1 and 3, Fig. 2) also
had higher coronary resistances and PZFs (Table 1) than the
other specimens. A consequence of the high stiffness in these septa was
that, with BI stretch, the flow was too low for the dynamic
interventions at 30 mmHg and no data were acquired at this pressure.
The higher PZFs could indicate the presence of edema in
these two septa. We did not specifically recognize any problems during
the specimen preparation period that could have resulted in edema in
these two septa; however, we cannot rule out this possibility.
The spectral analysis method assumes linear responses of flow and
thickness to the pressure variations. For the stretched condition, we
checked this by comparing the magnitude of the Fourier transform of the
flow and thickness signal with the magnitude of the Fourier transform
of the pressure signal. The harmonics of flow and thickness could all
be explained by harmonics in the pressure signal. Thus, for the
stretched condition, like the UN condition, the linearity criteria for
cause-effect relations were fulfilled. These linear relationships are
possible in the presence of pressure or volume-dependent resistances,
as we discussed before (14).
It was inevitable to perform these experiments under vasodilated
conditions alone. With tone intact, application of sinusoidal perfusion
pressure variations would stimulate tone variations, and because of the
time constants of inducible tone changes, there would be frequency
dependence not distinguishable from the stretch-induced variations in
resistance (4).
Imposed average perfusion pressures were low, <70 mmHg, compared with
physiological levels of normal systemic pressure in the presence of
tone. This threshold was chosen because of practical reasons. Higher
levels of pressure would have increased microvascular pressure too much
and induced edema. In fact, pressure at the capillary level will have
been quite normal in our study, compared with the normal physiological
case where this pressure is limited by the higher levels of resistance
in the proximal arterioles and small arteries.
In our earlier study (14), we assumed that
C2 would be the minimum of the
Rm versus C2 curve and
this additional assumption allowed us to estimate absolute values of
V1 and V2. The sum of the two was in
reasonable agreement with absolute intramural blood volumes
determined in alternative manners. The assumption of
minimal compliance also resulted in a stretch-independent
R1 and C1, and Rm came also out to be stretch dependent,
similarly to the dependence presented above. The conclusions, with
respect to Rm, were considered to be of
physiological significance but could be biased by the assumption of
minimal C2. Therefore, we changed our strategy
of parameter estimation from minimum C2 to
defining physiologically acceptable boundaries for intramural volume
and volume distribution. The parameter X was allowed to vary
between 0 and 1, which implies that no restriction was given to the
distribution of the dependence of Rm on
V1 and V2. As presented above,
Rm remained convincingly dependent on stretch.
However, the possibility of estimating absolute volumes disappeared.
According to the parameter estimation, the proximal resistance
R1 and capacitance C1 are
unaffected by stretch. Because these are the most proximal components
in the model, it is understandable that, following the parameter
estimation, Rm is affected by stretch. We found
that by taking the middle of the possible ranges of
Rm as the true value, that this resistance could
increase by a factor of 2. Obviously, the difference could be smaller
when the maximal value of Rm in the UN state and
the minimal values of Rm in the stretched state
would be the true values. However, these extreme values of
Rm within their respective ranges are unlikely
because other boundary conditions would have demonstrated unrealistic dependence on stretch as well. For example, one has to assume that
V1 would increase with stretch and most likely the opposite is the case.
The five septa studied demonstrated under UN conditions a variability
in overall resistance not abnormal for coronary perfusion studies in
animals and humans (5, 9, 16). The PZF values are quite low compared with in vivo coronary circulation
(5). The variations in resistance and PZF
become more apparent under the influence of stretch. This may well be
the result of a loading situation of the septum that is different from
the natural one. However, comparing the variation in resistance between
P = 50 and P = 70 for the same set of
experiments (excluding septum 2), the variation at P = 50 equals 72%, whereas at 70 mmHg this is reduced to 50% of the mean.
It is likely that at the higher perfusion pressure the intramural
circulation becomes less determined by the deformations and
compressions as the result of external loading. Notwithstanding these
variations in average results, it should be noted that the conclusion
of the stretch effect on the microvasular resistance is the result of a
paired test of results within septa. The conclusion of increased
resistance is the result of 12 paired experiments (stretch vs. UN),
whereas in only 2 cases of the 12, there was a small overlap of
possible values.
Comparison with other experiments.
Volume changes as a consequence of cyclic BI loading from 300 to 900 g at different perfusion pressures were reported by Yin et
al. (17). The authors used the same isolated perfused
septum preparation as ours; however, they used digital subtraction
angiography to more directly estimate intravascular volume. They found
that the fluctuations in vascular volume due to stretch fluctuations increased with perfusion pressure. Interpolating their results to 50 mmHg results in volume estimates of 13.0 ml/100 g in the stretched
condition and 15.3 ml/100 g in the UN condition. This decrease in
intramural blood volume is consistent with an increase of proximal
resistance (R1 + Rm). In case the stretch would only increase
outflow resistance, capillary and arteriolar pressure would have
increased, which would have resulted in an increase of intramural
volume
Resar et al. (10) demonstrated that circumferential
stretch increased coronary resistance more than base-to-apex stretch. Moreover, Sipkema et al. (12) demonstrated that a single
vessel is more sensitive to stretch of the surrounded tissue in the
axial than in the radial direction. However, the present study focused on determining the distribution of vascular volume and resistance changes due to stretch rather than on the effects of stretch direction.
Interpretation of results.
The coronary admittance frequency response is clearly affected by
stretch. As has been discussed earlier (3, 14, 15), these
responses are more sensitive to physical parameters of the proximal bed
than to the distal bed. Stretch, therefore, affects the proximal bed
and the model provides a means to interpret these results.
Coronary vessels are embedded in tissue and stretching tissue will
stretch vessels of all types, thereby reducing their diameter and
increasing resistance (11-13). However, tissue
pressure has also been suggested as a factor that could explain the
stretch effect on resistance. Such a tissue pressure would affect the more distal vessels more because of their lower intravascular pressure.
However, it is unlikely that tissue pressure is the cause of the
increased Rm because tissue pressure will be
higher at higher perfusion pressures, and the stretch effects on
Rm were not higher at a higher perfusion pressure.
Stretch had also an effect on the capacitance curve and especially on
the frequency phase relationship by accentuating a local maximum at
higher frequencies. One has to be careful to relate this local maximum
to a stretch effect on the distal compartment. Stretch induces a phase
shift between P1 and pressure over capacitance (PC1) by affecting proximal vessels
(R1, C1, and
Rm). Even if stretch had no effect on the phase
difference between distal volume and PC1, the local maximum
in the capacitance plots would be visible because these plots relate
dominantly distal volume with P1, which has a phase shift
relative to PC1. Hence, rather than reflecting the effect
of stretch on distal volume, the bump in the capacitance phase plot
reflects the phase changes induced by stretch on the first compartment,
i.e., Rm.
In our earlier study, we needed to analyze only the effect of pressure
on the interdependencies between estimated parameters, whereas in the
present study, we have to include the additional effect of stretch.
Most likely, stretch will have an effect on the distensibility of
intramural blood vessels and consequently on interdependence of
compliance and sensitivity of resistance on vascular volume. However,
as indicated by Figs. 4 and 5, only the "possible ranges" for
Rm discriminate sufficiently between the loaded
and UN states, but the possible ranges for other parameters do overlap
strongly. This conclusion is further confirmed by Fig. 6, which
demonstrates the overlap for the parameters of the distal compartment for the other septa and pressures. Although the present study furthers our understanding of the effect of stretch on
microvascular resistance proximal to capillaries, only additional
measurements of signals from the microcirculation can provide for
unique solutions of the other parameters and consequently clarify
relationships further distal within the coronary tree.
The stretched-induced increase of resistance of the vessels proximal to
the capillaries makes sense in relation to maintenance of
intracapillary pressure. If stretch had an effect on only the outflow
part of the coronary system, capillary pressure would increase with
stretch. This, undoubtedly, would result in edema of tissue and reduced
capacity of the heart to contract. As such, the stretch increase of
proximal resistance functions as a passive protective mechanism of
tissue water balance in case of increased end-diastolic ventricular volume.
The absence of tone might seem to limit the impact of the present
results. However, understanding of the hemodynamics of the coronary
circulation in the presence of tone requires knowledge of this system
in the absence of tone. Moreover, the condition of vasodilatation is
used to evaluate clinically the physiological significance of a
coronary stenosis (9). Therefore, it is important that the
effect of stretch, e.g., as induced by end-diastolic ventricular
pressure, is understood.
It is clear that the conclusion on the effect of stretch on proximal
resistance cannot be obtained from steady-state measurements of
pressure versus flow. The dynamic measurements in combination with a
distributed model allow us to draw conclusions on the stretch effect on
more proximal vessels. The overparameterization limits the
quantification of the distributed effect of stretch, and additional measurements, like microvascular pressure, will be needed to provide more detailed information.
In conclusion, it was found that stretched-induced increase in vascular
resistance during maximal vasodilation is pronounced in the proximal
portion of the microvascular bed, i.e., the arterioles. Such an effect
contributes to the maintenance of capillary pressure and stabilizing
interstitial pressure at higher end-diastolic volumes.
| |
ACKNOWLEDGEMENTS |
This work was supported in part by The Netherlands Heart Foundation
Grant 43.016 (to J. A. E. Spaan), The Netherlands Heart Foundation Grant D94.011 (to A. J. M. Cornelissen), The
Netherlands Heart Foundation Grant 95.020 (to J. Dankelman) and
National Heart, Lung, and Blood Institute Grant HL-44399 (to F. C. P. Yin).
| |
FOOTNOTES |
Address for reprint requests and other correspondence: J. A. E. Spaan, Dept. of Medical Physics, Cardiovascular Research
Institute Amsterdam, Academic Medical Center, Univ. of Amsterdam, PO
Box 22700, 1100 DE Amsterdam, The Netherlands (E-mail:
j.a.spaan{at}amc.uva.nl).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 21 July 2000; accepted in final form 20 August 2001.
| |
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ABSTRACT
INTRODUCTION
