## 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

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.

## 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 Mg^{2+}, 1.2 Ca^{2+}, 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.

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 Ca^{2+}, 2.1 Mg^{2+}, 1.54 H_{2}PO
, 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% O_{2}-5% CO_{2} 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 (F_{x}, F_{y}), and distance between the stainless beads in both directions (*d _{x}
*,

*d*), 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(ν), Q(ν), and Th(ν) respectively, in which ν is the frequency in Herz.

_{y}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(ν)_{measured}] was then corrected for the pressure drop using Q(ν) and the perfusion system impedance to obtain the septal perfusion pressure P(ν).

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)
Equation 1
Equation 2
*G*
_{q} and α_{1}-α_{4}are parameters to be determined, *G*
_{ThV} is the conversion factor for expressing volume in terms of thickness, and ω is frequency in radians per second. The two equations were simultaneously fitted to the experimental data by minimizing the following cost function
Equation 3The factors*e*
_{1i}-*e*
_{4i}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 ω is in radians per second and ω = 2πν, and ν 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
Equation 4where ΔV is the variation in V around the working value V_{0}. *K* is the sensitivity of resistance for volume in the working point (V_{0},*R*
_{0}). 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 (V_{1}) influences*R*
_{1} and a portion of *R*
_{m}, therefore we have two sensitivity values for these resistances,*K*
_{1} and *K*
_{m1}. Similarly, the volume in the second compartment (V_{2}) influences*R*
_{2} and the other part of*R*
_{m} by the sensitivity values*K*
_{2} and *K*
_{m2}, respectively.

Because *R*
_{m} depends on both the volumes in the first and the second compartment, a factor *X* was introduced to define which fraction of *R*
_{m} was sensitive to the volume in the proximal compartment. Hence, the fraction of*R*
_{m} sensitive to the distal compartment equals (1 − *X*) · *R*
_{m}.

Our earlier study demonstrated how the fitting parameters (*G*
_{q} and α_{1}–α_{4}) depend on the physical parameters of the model (*R*
_{1}, *R*
_{m},*R*
_{2}, *X*, *C*
_{1},*C*
_{2}, V_{1}, V_{2},*K*
_{1}, *K*
_{m1},*K*
_{m2}, and *K*
_{2}). 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
Equation 5
*2*) According to the law of Poiseuille and assuming constant length *R* = A/V^{2}, therefore
Equation 6
*3*) Total vascular volume (V_{tot}) should be >5 and <15 ml/100 g, *4*) V_{1} should be >5 and <35% of V_{tot}, 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 *R*
_{m} (*R*
_{m,average}) and the average of the maximal and the minimal possible value of*X* at *R*
_{m,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 2
*A* shows the forces in the circumferential and base-to-apex directions for the different stretch conditions. Figure 2
*B* 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 (*S*
_{xy}) in the table included with the figure. Stiffness is calculated as the ratio of the root mean square of the sum of the forces (F_{i}) to the root mean square of the sum of the strains (ε_{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.

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 Table1, the total static coronary resistance and the pressure after an occlusion of 50 s of zero flow pressure (P_{ZF}) 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.

For both the UN and stretched conditions, the admittance modulus (Fig.3
*A*) 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.3
*C*) has a maximum at ∼2 Hz, which is lower in the UN than the stretched condition. Both the modulus (Fig. 3
*B*) and phase (Fig. 3
*D*) 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*R*
_{1}, *R*
_{2},*C*
_{1}, *C*
_{2}, V_{1}, and V_{2} on *R*
_{m} at different values of*X* is shown for one experiment (*experiment 4*,*P* = 50 mmHg). In Fig. 5, the dependence of *K*
_{1},*K*
_{m1}, *K*
_{m2}, and*K*
_{2} on *R*
_{m} 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*R*
_{m} under stretch is about twice its UN value in this case.

The error bars in Fig. 6 give the ranges of possible values for the parameters *R*
_{1},*R*
_{m}, *R*
_{2},*C*
_{1}, *C*
_{2}, V_{1}, and V_{2} 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. *R*
_{1} 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*R*
_{m} and *X*.

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 *R*
_{m},*R*
_{2}, V_{1}, V_{2},*K*
_{1}, *K*
_{m2}, and*K*
_{2} are significantly different for the UN and stretched conditions. The ranges for *R*
_{m} for the UN and stretched conditions do not overlap, except for *experiment 2*, where the ranges of *R*
_{m} overlap for 30% at *P* = 30 mmHg and for 10% at *P* = 50 mmHg. For *R*
_{m} to remain unaltered or decrease during stretch, maximal 30% for *P* = 30 mmHg and 10% at *P* = 50 mmHg, V_{1} has to increase with stretch. In reality, it is highly unlikely that V_{1}increases with stretch. *R*
_{1}, being unaffected by uncertainty if the model remains constant in our estimations during stretch, implies that either V_{1} remains constant or even decreases as a result of reduced vascular diameters.

Averaged *R*
_{m} for overall pressures in the UN state was 17 ± 10 mmHg · ml^{−1} · s · 100 g (means ± SD; UN) and increases to 50 ± 46 mmHg · ml^{−1} · s · 100 g in the stretched state (means ± SD; BI), *P* < 0.05.

In contrast, *R*
_{1} is not affected by stretch, being 9.6 ± 4.8 mmHg · ml^{−1} · s · 100 g (means ± SD, UN) and *R*
_{1} = 10 ± 3.8 mmHg · ml^{−1} · s · 100 g (means ± SD, BI). The representative values of*C*
_{1} are also not significantly affected by stretch, being 0.014 ± 0.001 ml · mmHg^{−1} · 100 g^{−1}(means ± SD, UN) in the UN state, and 0.011 ± 0.0004 ml · mmHg^{−1} · 100 g^{−1}(means ± SD, BI) under stretch.

The ranges of the values for *R*
_{2},*C*
_{2}, V_{1}, and V_{2} 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.

## 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 *R*
_{m} 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 P_{ZF}s (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 P_{ZF}s 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*C*
_{2} would be the minimum of the*R*
_{m} versus *C*
_{2} curve and this additional assumption allowed us to estimate absolute values of V_{1} and V_{2}. 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*R*
_{1} and *C*
_{1}, and*R*
_{m} came also out to be stretch dependent, similarly to the dependence presented above. The conclusions, with respect to *R*
_{m}, were considered to be of physiological significance but could be biased by the assumption of minimal *C*
_{2}. Therefore, we changed our strategy of parameter estimation from minimum *C*
_{2} 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 *R*
_{m} on V_{1} and V_{2}. As presented above,*R*
_{m} remained convincingly dependent on stretch. However, the possibility of estimating absolute volumes disappeared.

According to the parameter estimation, the proximal resistance*R*
_{1} and capacitance *C*
_{1} are unaffected by stretch. Because these are the most proximal components in the model, it is understandable that, following the parameter estimation, *R*
_{m} is affected by stretch. We found that by taking the middle of the possible ranges of*R*
_{m} 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 *R*
_{m} in the UN state and the minimal values of *R*
_{m} in the stretched state would be the true values. However, these extreme values of*R*
_{m} 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 V_{1} 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 P_{ZF} values are quite low compared with in vivo coronary circulation (5). The variations in resistance and P_{ZF}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 (*R*
_{1} +*R*
_{m}). 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 *R*
_{m} because tissue pressure will be higher at higher perfusion pressures, and the stretch effects on*R*
_{m} 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 P_{1} and pressure over capacitance (P_{C1}) by affecting proximal vessels (*R*
_{1}, *C*
_{1}, and*R*
_{m}). Even if stretch had no effect on the phase difference between distal volume and P_{C1}, the local maximum in the capacitance plots would be visible because these plots relate dominantly distal volume with P_{1}, which has a phase shift relative to P_{C1}. 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., *R*
_{m}.

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*R*
_{m} 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.

## Acknowledgments

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).

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- Copyright © 2001 the American Physiological Society