INTRODUCTION

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THE STUDY OF ARTERIAL SYSTEM DYNAMICS involves the analysis of its components: the wall of the arteries, the blood, and the interrelation between them, which can be related to complex processes that could be the origin of arterial diseases (6, 7, 15, 21, 22).

The use of an arterial wall mathematical modelization should be carried out through models involving coefficients with accurate physical meanings. For such a goal, these models should allow a clinical approach that might be useful in the evaluation of aging, hypertension, atherosclerosis, and other arterial disorders (1).

Blood viscosity and its determinants were largely evaluated showing that most of these blood constituents were related to several well-established cardiovascular risk factors (7, 21, 23). Moreover, different studies (12, 17) have demonstrated that plasma viscosity was related to the incidence of cardiovascular events.

Experimental and clinical assessment of arterial wall mechanics has been carried out in health and disease states by our research group during the last years (1, 2, 16). As far as we are concerned, the relationship between arterial wall-tone elastic behavior and endothelium-mediated blood shear force has not been established accurately in experimental research.

The aim of this study was to characterize the arterial wall elastic behavior in intact and deendothelized (DE) ovine segments of brachiocephalic trunks submitted to different levels of blood viscosity and maintaining constant levels of flow-induced shear rate during the time course of the experimental session.

	METHODS

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Surgical procedure. Seven healthy male Corriedale sheep, weighing 25-35 kg and aged between 30 and 48 mo, were prepared for the present study. During the 2 wk before surgery, the sheep were given adequate food and water and assessed for adequate clinical status. All of the sheep were operated on while under general anesthesia induced by thiopental sodium (20 mg/kg iv) and, after intubation, maintained with 2.5% enfluorane in pure oxygen (4 l/min) through a Bain tube connected to a Mark VIII respirator (Bird). The animals were positioned in left lateral decubitus, and a sterile thoracotomy was performed at the left third intercostal space. The brachiocephalic artery was then instrumented with a pressure microtransducer and a pair of ultrasonic dimension gauges.

In vitro measurements. All experiments were performed on segments of ovine arteries perfused with four different levels of hematocrit within a range of 12-35% and were obtained by separating the whole ovine blood through sedimentation and combination of plasma and red blood cells. Thus we obtained different levels of blood viscosity by adding red blood cell concentrate, obtained by centrifugation of blood in each animal, to the plasma. Viscosity of lamb blood samples (2 ml), anticoagulated with EDTA (1.5 mg/ml), was measured by using a rotational viscometer (LVDT-II+ Digital Viscometer, Brookfield; Stoughton, MA) at a shear-rate range of 0.6-200 s¹.

View larger version (29K): [in this window] [in a new window]   Fig. 1.   Mock circulation loop used to test arterial segments. The perfusion line was powered by a pneumatic pump (P). Adjustments were made with the windkessel chamber size (W), the resistances modulator (R), and the Utah heart driver. Hematocrit changes were made in the reservoir with blood containing oxygen bubbles at 37°C. Each artery segment was mounted in the perfusion line and immersed in a thermally regulated Tyrode's solution (T). Statham P23 transducer (PS) was used to calibrate the pressure microtransducer (PK). Pressure and diameter (D, sonomicrometer) signals were displayed on a monitor (M), registered (CR, chart recorder), and digitized with a personal computer (PC).

View larger version (28K): [in this window] [in a new window]   Fig. 2.   In vitro (A) and in vivo (B) pressure (left measurement units) and diameter (right measurement units) waves obtained in the same artery sample.

Calculations. Arterial wall thickness (h) was calculated as the difference between the external artery radius (R_e), obtained by ultrasonic measurements, and the internal radius (R_i), estimated according to the following equation
where V is the artery volume, calculated by using the weight of the artery segment and assuming a tissue density of 1.066 g/ml, and L is the length of the artery segment (1).

Histological studies. Histological studies using hematoxilin-eosin stain, Gomori stain, and orcein stain for elastic fiber technique were performed to confirm successful endothelial removing in the analyzed segments of ovine arteries. Particular attention was directed to detect alterations in the media and adventitia layers structure.

Statistical analysis. All measurements and calculated values were expressed as means ± SD. Values of P < 0.05 were considered statistically significant. Regression analysis was performed by the least-squares method. Results were subjected to one-way analysis of variance for repeated measurements with a Bonferroni post hoc test.

	RESULTS

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Histological studies, which were performed to confirm endothelial removal, revealed the integrity of the media and adventitia layers. No technical mistakes were observed during each experimental session.

Increases in blood hematocrit always resulted in increases of blood viscosity. Increases in viscosity levels induced increases in mean arterial diameter (in absolute values). Essentially, in our experiments, changes in mean arterial diameter induced by raising blood viscosity were more remarkable in intact arteries (Fig. 3). Statistical differences (P < 0.05) in arterial diameters between endothelized and DE arteries were found >2.50 mPa · s viscosity value.

View larger version (18K): [in this window] [in a new window]   Fig. 3.   Absolute values of mean diameter changes in intact arteries and after deendothelization (DE) at different blood viscosity (BV) levels. *P < 0.05.

To summarize in only one variable the opposite pulsatile diameter changes, experimented by intact arteries and after DE, we defined a new variable (PD) equal to
where PDIA_a is the actual pulse diameter value at each different viscosity level and PDIA₀ is the initial diameter value, both in intact arteries. PDDE_a is the actual pulse diameter value at each different viscosity level and PDDE₀ is the initial diameter value, both after DE. Statistical differences in PD were found beyond blood viscosity levels of 2.50 mPa · s (P < 0.05) (see Fig. 4).

View larger version (12K): [in this window] [in a new window]   Fig. 4.   Mean pulse diameter changes (PD) at different BV levels. *P < 0.05.

As shown in Fig. 5, an inverse relationship between E_inc and blood viscosity values was found in an intact artery under study (Fig. 5, closed circles). This behavior was fitted with the use of an exponential regression analysis (Fig. 5, solid trace). This procedure allowed an exponential regression analysis in each intact artery and a logarithmic regression analysis in each DE artery of the entire population under study. In both cases, the following strong regression coefficient was observed: r = 0.87 ± 0.12 and r = 0.90 ± 0.09, respectively. From the exponential and logarithmic curves, we selected the E_inc values corresponding to each blood viscosity level.

View larger version (11K): [in this window] [in a new window]   Fig. 5.   Exponential regression analysis (solid trace) of incremental elastic modulus (Einc)-BV data () measured in an intact artery.

E_inc values were not statistically different in the presence or absence of endothelium (3.11 vs. 3.16 × 10⁷ dyn/cm²) at a blood viscosity of 2.00 mPa · s (see Table 1). Increases in blood viscosity levels (i.e., 2.50, 3.00, 3.50, and 4.00 mPa · s) always resulted in decreases of E_inc before DE (P < 0.05); inversely, similar increases in blood viscosity resulted in positive increments of E_inc after DE (P < 0.05). These values of E_inc before DE were always significantly lower (P < 0.05) than those obtained after DE for identical levels of blood viscosity (see Table 1).

For the same blood viscosity incremented levels, E_inc before and after DE was significantly different (P < 0.05) (see Fig. 6).

View larger version (15K): [in this window] [in a new window]   Fig. 6.   Einc values for each level of BV before and after DE were significantly different (P < 0.05). Einc values were always statistically significant (P < 0.05) compared with basal value (Einc = 0).

	DISCUSSION

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The aim of this work was to investigate changes in arterial wall compliance, through incremental elastic modulus, due to viscosity-induced changes in shear stress in a circulation loop maintaining constant blood flow. The major finding was that increases in blood viscosity determined decreases in the incremental elastic modulus in normal intact arteries, whereas similar increases in blood viscosity determined increases in the incremental elastic modulus in DE arteries. It was also observed that increases in blood viscosity levels induced changes in arterial diameters.

Changes in arterial diameter values, due to shear force increments induced by blood viscosity, showed similar trends as those reported previously (18, 19, 24). The lack of statistical significance before achieving 2.5 mPa · s in blood viscosity might be due either to the small sample of arteries explored or to the fact that the increase in viscosity was not enough to induce significant changes in diameter. Another explanation would be that diameter measurements were performed using the ultrasonic technique and slight arterial diameter changes (<2.3%) might be due to the fact of assuming constant the velocity of sound through different levels of hematocrit. This spurious effect could induce mistakes in the absolute diameter measurement in the order of 3%, according to specifications of the Sonomicrometer operator manual (Triton Technologies; San Diego, CA).

Changes in mean arterial diameter induced by raising blood viscosity were remarkable in intact arteries. This behavior is similar to previous in vivo and in vitro study reports, where vasodilatation was found in intact arteries and no changes were observed after DE (19).

Elastic changes are shown in Fig. 7, in which three blood viscosity levels determined different pressure-diameter schematic relationships before and after DE in the same artery. It is important to point out that in intact arteries, as blood viscosity was raised, arterial compliance increases resulted in an augmentation in pulse diameter. On the other hand, after DE, as blood viscosity was raised, arterial compliance decreases resulted in a decrease in pulse diameter. This trend was observed previously in conscious dog aortic wall studies involving smooth muscle tone changes mediated by phenylephrine infusion (1, 2).

View larger version (24K): [in this window] [in a new window]   Fig. 7.   Schematic diagram of arterial purely elastic pressure-diameter (P-D) relationship in three different BV levels in an artery before and after deendothelization (DE). , Mean diameters. P1 and P2 pressure values of aortic pressure correspond to pulse diameter values (PD1-PD3) at different levels of BV.

Because the effect of an increase in blood viscosity could be compared with the variations found under smooth muscle tone modifications, it could be observed that raises in smooth muscle tone (increases in blood viscosity after DE) tended to increase E_inc and to decrease mean and pulsatile diameter. A decrease in smooth muscle tone (raises in blood viscosity in intact arteries) tended to decrease E_inc and to increase mean and pulsatile diameter. The conjunction of these conditions was a decrease in E_inc and a trend to vasodilatation and pulsatile diameter increase.

In the light of these findings, the endothelium existence could allow an increase in compliance even more sharply than the one attributed to endothelium-derived relaxation factor release. In fact, arterial wall tone elasticity was modulated by blood viscosity-induced-shear stress in this study. Certainly, the response of incremental modulus seemed to be mediated by endothelium factors when blood viscosity increases. The elevation of E_inc after DE contrasted sharply with the behavior of the intact artery; this is consistent with previous reports (9). This physiological effect might protect the integrity of ventricular-arterial coupling and could suggest that in endothelial dysfunction, increases in blood viscosity would involve changes in vascular tone and arterial stiffness, which would impair the performance of left ventricular pump function.

The in vitro model of mock circulation loop used in this study allowed to perform experimental sessions with arteries submitted to physiological ranges of pressure, stretching rate, and blood flow at different hematocrit values. This is an important issue, because smooth muscle tone mediated by endothelium factors are reported to be dependent of the beating activity of the heart (4, 10, 11, 13). Besides, the mechanical response of a viscoelastic material (as the arterial wall) depends both on the force applied and on the time it acts (3). Also, smooth muscle tone depends on blood viscosity, blood flow, and hematocrit values (15, 19, 20).

We had a special interest in mimicking in vivo pressure and diameter time waveforms. The in vivo curves obtained in the present study allowed to reach the physiological condition of the artery and to assess directly the diastolic phase, i.e., the pure elastic relationship.

Calculation of E_inc was performed by using a method that was developed previously in our laboratory, through the purely elastic stress-strain relationship, which could be used with either intact or DE arteries (1, 2). On the basis of the arterial wall is an orthotropic, nonhomogeneous, and nonlinear material subjected to large strain variations; its dynamic behavior was characterized previously by our group (1), with the use of a second-order mechanic model with linear inertial and viscous moduli and nonlinear elasticity. However, in the present study, we focused our attention on the effect of blood shear force on the elastic behavior of the arterial wall. Therefore, we analyzed only the diastolic phase of the stress-strain loop, because its lower harmonic content coincides with the pure elastic stress-strain relationship. Our assumption allowed E_inc calculation based on a linear elastic theory, as described previously (1). In fact, the use of the pure elastic stress-strain relationship allows the study of the elastic component of the total dynamic behavior of the arterial wall (5). Also, the elastic modulus calculation could be used in the characterizaton of a nonlinear elastic material. In the special case of the arterial wall, this E_inc modulus, evaluated at mean pressure level, characterized the elastic response of the elastin fibers modulated by smooth muscle vasomotor tone (1, 5). Moreover, values of E_inc obtained in our in vitro experiments were similar to those reported (3, 5, 14) in the same conditions.

The viscosity values used for the viscosity-E_inc relationship calculation were those corresponding to a shear-rate value of 200 s¹. This value was chosen because shear-rate values >96 s¹ cause a minimal decrease in blood viscosity, so it can be considered as a Newtonian fluid; e.g., the viscosity values are independent of shear-rate values.

The arterial denudation method used in this study had been tested previously (20). We considered that the integrity of the arterial wall was preserved because no structural wall alteration in the media and adventitia layers were detected in histological studies. However, the endothelium removal could alter the wall thickness and might influence the calculation of E_inc.

In conclusion, our results showed that arterial wall elasticity assessed through E_inc was strongly influenced by blood viscosity (i.e., shear stress), probably due to either the presence or absence of endothelium relaxing factors, or direct shear smooth muscle activation when endothelial cells are removed.