Haemodynamics and wall remodelling of a growing cerebral aneurysm: a computational model

We have developed a computational simulation model for investigating an often postulated hypothesis connected with aneurysm growth. This hypothesis involves a combination of two parallel and interconnected mechanisms: according to the first mechanism, an endothelium-originating and wall shear stress-driven apoptotic behavior of smooth muscle cells, leading to loss of vascular tone is believed to be important to the aneurysm behavior. Vascular tone refers to the degree of constriction experienced by a blood vessel relative to its maximally dilated state. All resistance and capacitance vessels under basal conditions exhibit some degree of smooth muscle contraction that determines the diameter, and hence tone, of the vessel. The second mechanism is connected to the arterial wall remodeling. Remodeling of the arterial wall under constant tension is a biomechanical process of rupture, degradation and reconstruction of the medial elastin and collagen fibers. In order to investigate these two mechanisms within a computationally tractable framework, we devise mechanical analogues that involve three-dimensional haemodynamics, yielding estimates of the wall shear stress and pressure fields and a quasi-steady approach for the apoptosis and remodeling of the wall. These analogues are guided by experimental information for the connection of stimuli to responses at a cellular level, properly averaged over volumes or surfaces. The model predicts aneurysm growth and can attribute specific roles to the two mechanisms involved: the smooth muscle cell-related loss of tone is important to the initiation of aneurysm growth, but cannot account alone for the formation of fully grown sacks; the fiber-related remodeling is pivotal for the latter.     

Vascular smooth muscle cell stress as a determinant of cerebral artery myogenic tone

Although the level of myogenic tone (MT) varies considerably from vessel to vessel, the regulatory mechanisms through which the actual diameter set point is determined are not known. We hypothesized that a unifying principle may be the equalization of active force at the contractile filament level, which would be reflected in a normalization of wall stress or, more specifically, media stress. Branched segments of rat cerebral arteries ranging from <50 microm to >200 microm in diameter were cannulated and held at 60 mmHg with the objectives of: 1) evaluating the relationship between arterial diameter and the extent of myogenic tone, 2) determining whether differences in MT correlate with changes in cytosolic calcium ([Ca(2+)](i)), and 3) testing the hypothesis that a normalization of wall or media stress occurs during the process of tone development. The level of MT increased significantly as vessel size decreased. At 60 mmHg, vascular smooth muscle [Ca(2+)](i) concentrations were similar in all vessels studied (averaging 230 +/- 9.2 nM) and not correlated with vessel size or the extent of tone. Wall tension increased with increasing arterial size, but wall stress and media stress were similar in large versus small arteries. Media stress, in particular, was quite uniform in all vessels studied. Both morphological and calcium data support the concept of equalization of media stress (and, hence, vascular smooth muscle cell stress and force) as an underlying mechanism in determining the level of tone present in any particular vessel. The equalization of active (vascular smooth muscle cell) stress may thus explain differences in MT observed in the different-sized vessels constituting the arterial network and provide a link between arterial structure and function, in both short- and long-term (hypertension) pressure adaptation.     

Aortic stiffness is associated with vascular calcification and remodeling in a chronic kidney disease rat model

Increased aortic pulse-wave velocity (PWV) reflects increased arterial stiffness and is a strong predictor of cardiovascular risk in chronic kidney disease (CKD). We examined functional and structural correlations among PWV, aortic calcification, and vascular remodeling in a rodent model of CKD, the Lewis polycystic kidney (LPK) rat. Hemodynamic parameters and beat-to-beat aortic PWV were recorded in urethane-anesthetized animals [12-wk-old hypertensive female LPK rats (n = 5)] before the onset of end-stage renal disease and their age- and sex-matched normotensive controls (Lewis, n = 6). Animals were euthanized, and the aorta was collected to measure calcium content by atomic absorption spectrophotometry. A separate cohort of animals (n = 5/group) were anesthetized with pentobarbitone sodium and pressure perfused with formalin, and the aorta was collected for histomorphometry, which allowed calculation of aortic wall thickness, medial cross-sectional area (MCSA), elastic modulus (EM), and wall stress (WS), size and density of smooth muscle nuclei, and relative content of lamellae, interlamellae elastin, and collagen. Mean arterial pressure (MAP) and PWV were significantly greater in the LPK compared with Lewis (72 and 33%, respectively) animals. The LPK group had 6.8-fold greater aortic calcification, 38% greater aortic MCSA, 56% greater EM/WS, 13% greater aortic wall thickness, 21% smaller smooth muscle cell area, and 20% less elastin density with no difference in collagen fiber density. These findings demonstrate vascular remodeling and increased calcification with a functional increase in PWV and therefore aortic stiffness in hypertensive LPK rats.     

A constitutive formulation of arterial mechanics including vascular smooth muscle tone

A pseudo-strain energy function (pseudo-SEF) describing the biomechanical properties of large conduit arteries under the influence of vascular smooth muscle (VSM) tone is proposed. In contrast to previous models that include the effects of smooth muscle contraction through generation of an active stress, in this study we consider the vascular muscle as a structural element whose contribution to load bearing is modulated by the contraction. This novel pseudo-SEF models not only arterial mechanics at maximal VSM contraction but also the myogenic contraction of the VSM in response to local increases in stretch. The proposed pseudo-SEF was verified with experimentally obtained pressure-radius curves and zero-stress state configurations from rat carotid arteries displaying distinct differences in VSM tone: arteries from normotensive rats displaying minimal VSM tone and arteries from hypertensive rats exhibiting significant VSM tone. The pressure-radius curves were measured in three different VSM states: fully relaxed, maximally contracted, and normal VSM tone. The model fitted the experimental data very well (r2 > 0.99) in both the normo- and hypertensive groups for all three states of VSM activation. The pseudo-SEF was used to illustrate the localized reduction of circumferential stress in the arterial wall due to normal VSM tone, suggesting that the proposed pseudo-SEF can be of general utility for describing stress distribution not only under passive VSM conditions, as most SEFs proposed so far, but also under physiological and pathological conditions with varying levels of VSM tone.     

Organoid culture of cannulated rat resistance arteries: effect of serum factors on vasoactivity and remodeling

We developed an organoid culture technique to study the mechanisms involved in arterial remodeling. Resistance arteries were isolated from rat cremaster muscle and mounted in a pressure myograph at 75 mmHg. Vessels were studied during a 4-day culture period in DMEM with either 2% albumin, 10% heat-inactivated FCS (HI-FCS) or 10% dialyzed HI-FCS (12 kDa cut off) added to the perfusate. The albumin group showed a gradual loss of endothelial function and integrity, whereas smooth muscle agonist and myogenic responses were retained. No remodeling was observed. Vessels cultured in the presence of serum showed a progressive constriction. Smooth muscle responses and substance P-induced endothelium-dependent dilation were maintained. An inward remodeling of 17 +/- 4% in the HI-FCS group and 26 +/- 3% in the dialyzed HI-FCS group was found, while media cross-sectional areas were unchanged. These data show that pressurized resistance arteries can be maintained in culture for several days and undergo eutrophic remodeling in vitro in the presence of high molecular weight serum factors.     

PI3-kinase/Akt modulates vascular smooth muscle tone via cAMP signaling pathways.

Phosphatidylinositol 3-kinase (PI3-kinase) activates protein kinase B (also known as Akt), which phosphorylates and activates a cyclic nucleotide phosphodiesterase 3B. Increases in cyclic nucleotide concentrations inhibit agonist-induced contraction of vascular smooth muscle. Thus we hypothesized that the PI3-kinase/Akt pathway may regulate vascular smooth muscle tone. In unstimulated, intact bovine carotid artery smooth muscle, the basal phosphorylation of Akt was higher than that in cultured smooth muscle cells. The phosphorylation of Akt decreases in a time-dependent manner when incubated with the PI3-kinase inhibitor, LY-294002. Agonist (serotonin)-, phorbol ester (phorbol 12,13-dibutyrate; PDBu)-, and depolarization (KCl)-induced contractions of vascular smooth muscles were all inhibited in a dose-dependent fashion by LY-294002. However, LY-294002 did not inhibit serotonin- or PDBu-induced increases in myosin light chain phosphorylation or total O(2) consumption, suggesting that inhibition of contraction was not mediated by reversal or inhibition of the pathways that lead to smooth muscle activation and contraction. Treatment of vascular smooth muscle with LY-294002 increased the activity of cAMP-dependent protein kinase and increased the phosphorylation of the cAMP-dependent protein kinase substrate heat shock protein 20 (HSP20). These data suggest that activation of the PI3-kinase/Akt pathway in unstimulated smooth muscle may modulate vascular smooth muscle tone (allow agonist-induced contraction) through inhibition of the cyclic nucleotide/HSP20 pathway and suggest that cyclic nucleotide-dependent inhibition of contraction is dissociated from the myosin light chain contractile regulatory pathways.     

A logistic-type curve fits pressure-diameter relationship for relaxed and contracted dog renal arteries

In order to describe a possible effect of smooth muscle cell (SMC) activation on arterial wall distensibility, the present study derived a mathematical equation applicable to relaxed and contracted arterial walls. Pressure(P)-diameter(D) relationship of dog renal arteries was investigated in vitro under a cyclic loading and unloading process in the pressure range of 5-180 mmHg. Smooth muscle cells were activated by 10(-5)M norepinephrine. On the basis of the P-D curves obtained with fully contracted arteries, the vessel wall compliance dD/dP was assumed to be given by a second order polynomial of D, (formula; see text) The equation, including three parameters, Dmin, Dmax, and E, is integrated to yield the solution similar to the logistic curve as follows (formula; see text) where M(O) = (Dmax - D(O]/(D(O) - Dmin), and D(O) is the diameter at the point P = O. The constant, E, has the same dimension as the modulus of elasticity. The calculated P-D relationships coincided well with the experimental data for contracted and relaxed arteries. The most significant change due to wall contraction took place in the magnitude of M. This result, therefore, suggests that the parameter M is a good index of the degree of SMC contraction.     

Adaptation of active tone in the mouse descending thoracic aorta under acute changes in loading

Arteries can adapt to sustained changes in blood pressure and flow, and it is thought that these adaptive processes often begin with an altered smooth muscle cell activity that precedes any detectable changes in the passive wall components. Yet, due to the intrinsic coupling between the active and passive properties of the arterial wall, it has been difficult to delineate the adaptive contributions of active smooth muscle. To address this need, we used a novel experimental–computational approach to quantify adaptive functions of active smooth muscle in arterial rings excised from the proximal descending thoracic aorta of mice and subjected to short-term sustained circumferential stretches while stimulated with various agonists. A new mathematical model of the adaptive processes was derived and fit to data to describe and predict the effects of active tone adaptation. It was found that active tone was maintained when the artery was adapted close to the optimal stretch for maximal active force production, but it was reduced when adapted below the optimal stretch; there was no significant change in passive behavior in either case. Such active adaptations occurred only upon smooth muscle stimulation with phenylephrine, however, not stimulation with KCl or angiotensin II. Numerical simulations using the proposed model suggested further that active tone adaptation in vascular smooth muscle could play a stabilizing role for wall stress in large elastic arteries.     

Insulin-like growth factor I stimulates elastin synthesis by bovine pulmonary arterial smooth muscle cells

Insulin-like growth factor I stimulates mitogenesis in smooth muscle cells, and upregulates elastin synthesis in embryonic aortic tissue. Increased smooth muscle elastin synthesis may play an important role in vascular remodeling in chronic pulmonary hypertension. Therefore, we studied the effect of IGF-I on elastin and total protein synthesis by pulmonary arterial smooth muscle cells in vitro. Tropoelastin synthesis was measured by enzyme immunoassay, and total protein synthesis was measured by [3H]-leucine incorporation. In addition, the steady-state levels of tropoelastin mRNA were determined by slot blot hybridization. Incubation of confluent cultures with various concentrations of IGF-I resulted in a dose-dependent stimulation of elastin synthesis, with a 2.4-fold increase over control levels at 1000 ng/ml of IGF. The increase in elastin synthesis was reflected by a stimulation of the steady-state levels of tropoelastin mRNA. We conclude that IGF-I has potent elastogenic effects on vascular smooth muscle cells, and speculate that it may contribute to vascular wall remodeling in chronic hypertension.     

Sphingomyelinase and ceramide analogs induce contraction and rises in [Ca(2+)](i) in canine cerebral vascular muscle

Studies were designed to investigate effects of neutral sphingomyelinase (N-SMase) and ceramide analogs as well as phosphorylcholine on vascular tone and Ca(2+) mobilization in isolated canine cerebral arterial smooth muscle. N-SMase (0.001-0.1 U/ml) provoked a gradual but sustained vasoconstriction of arterial rings in a concentration-related manner that was endothelium independent. Incubation of denuded arterial rings in Ca(2+)-free medium or pretreatment with verapamil in extracellular Ca(2+) resulted in a reduction of the N-SMase-evoked constriction. Exposure of arterial rings to 1,2-bis(2-aminophenoxy)ethane-N,N,N', N'-tetraacetic acid (BAPTA)-AM did not, however, result in a reduction of N-SMase-induced constriction. Both staurosporine and bisindolymaleimide I attenuated N-SMase-induced contractions to 66% and 72% of control, respectively. N-SMase caused gradual and sustained rises in intracellular Ca(2+) concentration ([Ca(2+)](i)) in primary cultured cerebral vascular smooth muscle cells. Pretreatment of these cultured cells with nimodipine and verapamil caused a steady decline in N-SMase-induced rises in [Ca(2+)](i). Exposure of the cells to Ca(2+)-free solution reversed the [Ca(2+)](i)-induced rise triggered by N-SMase to the resting baseline. Both C(8) and C(16) ceramide (10(-9)-10(-6) M), but not phosphorylcholine, constricted denuded canine arterial rings in a concentration-related manner and elevated [Ca(2+)](i). Our results suggest that the sphingomyelin-signaling pathway, via a probable release of ceramide molecules, may play an important role in regulation of cerebral arterial wall tone.     

Elastic tissue and smooth muscle volume in elastic and muscular type arteries in the dog

1. Relative elastic tissue and smooth muscle volumes were determined by a stereological point-counting method in arteries with a progressively diminishing diameter, from the aorta towards the periphery. 2. The volume relationship between the smooth muscle cell and its nucleus was determined by the same method. Mean nuclear volume amounted to 6.9% of total smooth muscle cell volume. 3. Relative elastic tissue volume fell from the aorta towards the peripheral arteries, from 22.6% in the ascending aorta to 4--6% in the smallest arteries examined. 4. Relative smooth muscle volume was practically the same and differences between the individual values in the vast majority of arteries examined were non-significant. Total smooth muscle volume, calculated from the volume of the smooth muscle cell nuclei, varied mostly from 45 to 55%. 5. It can be concluded from these results that the ability of small and medium muscular type arteries to change their diameter actively by muscular contraction (as against elastic type arteries, in which this ability is less expressed) is facilitated not only by the organization of the structural components of the arterial wall, but also by the lower elastic tissue volume, which is compensated by the volume of the other passive components of the vascular wall, while relative smooth muscle volume remains the same.     

Changes of opening angle in hypertensive and hypotensive arteries in 3-day organ culture

To study the effect of pressure changes on the opening angle of arteries in organ culture, tubular segments of porcine common carotid arteries were cultured with pulsatile flow perfusion under hypertensive (150+/-20 mmHg), normotensive (100+/-20 mmHg), or hypotensive (30+/-10 mmHg) pressure while maintaining the arteris at a physiological wall shear stress of approximately 15 dyn/cm(2) for up to 3 days. Arteries were then cut into short ring segments by sections perpendicular to the axis and then cut open radially to observe the opening angle in aerated phosphate buffered saline solution (37 degrees C). Norepinephrine (NE, 10 microM), carbacol (CCh, 100 microM), and sodium nitroprusside (SNP, 10 microM) were added after the radial cut at 30, 20, and 30 min intervals, the opening angles were measured, respectively. Results show that hypertensive arteries developed a significantly larger opening angle than normotensive and hypotensive arteries, associated with a significant increase in cell proliferation. In addition, with smooth muscle contraction activated by NE, the opening angle decreases significantly in hypertensive arteries but has little change in hypotensive and normotensive arteries, indicating an enhancement of smooth muscle contraction on the lumen side of the hypertensive arterial wall. In comparison, hypotensive pressure has little effect on arterial opening angle and cell proliferation.     

Effects of longitudinal stretch on VSM tone and distensibility of muscular conduit arteries

With progressing age, large arteries diminish their longitudinal stretch, which in extreme cases results in tortuosity. Increased age is also associated with loss of vessel distensibility. We measured pressure-diameter curves from muscular porcine carotid arteries ex vivo at different longitudinal stretch ratios (lambda(z) = 1.4 and 1.8) and under different vascular smooth muscle (VSM) conditions (fully relaxed, normal VSM tone, and maximally contracted). Distensibility was found to be halved by decreasing longitudinal stretch from lambda(z) = 1.8 to 1.4 at physiological pressures. This counterintuitive observation is possible because highly nonlinear elastic modulus of the artery and anisotropic properties. Furthermore, a significantly larger basal VSM contraction was observed at lambda(z) = 1.8 than 1.4, although this was clearly not related to a myogenic response during inflation. This dependence of VSM tone to longitudinal stretch may have possible implications on the functional characteristics of the arterial wall.     

Biomechanical response of arterial wall to DOCA-salt hypertension in growing and middle-aged rats

To study arterial remodeling in response to hypertension, Deoxycortico-sterone acetate (DOCA)-salt hypertension was induced in immature (aged 16 weeks) and middle-aged (48 weeks) rats, and biomechanical properties and wall dimensions of common carotid arteries were determined. Arterial segments were excised at 10 or 16 weeks postoperatively from the immature rats and at 16 weeks from the middle-aged ones. In vitro pressure-diameter tests were performed under normal (in Krebs-Ringer solution), active (norepinephrine), and passive (papaverine) conditions. Non-treated, age-matched rats (26, 32, and 64 weeks) were used to obtain control data. Wall thickness at in vivo blood pressure level was increased by hypertension at all ages; however, there were no significant changes in inner diameter. In hypertensive rats, arterial outer diameter was smaller under normal condition than under passive condition, indicating the increase of smooth muscle tone by hypertension. Diameter reduction developed by norepinephrine was increased by hypertension, which was significant above 100 mmHg; however, there were no significant differences between hypertensive and normotensive arteries, if compared at respective in vivo blood pressures. No significant differences were observed in wall stiffness at in vivo pressure. Wall hoop stress at in vivo blood pressure had a significant positive correlation with the pressure in 26-week old arteries. However, there were no differences in the stress between hypertension and normotension in 32- and 64-week old arteries. These results were essentially similar to previous ones observed in Goldblatt hypertension and in younger animals. Age-related differences in arterial wall remodeling were not clearly observed.     

Myogenic tone,reactivity, and forced dilatation: a three-phase model of in vitro arterial myogenic behavior

Myogenic behavior, prevalent in resistance arteries and arterioles, involves arterial constriction in response to intravascular pressure. This process is often studied in vitro by using cannulated, pressurized arterial segments from different regional circulations. We propose a comprehensive model for myogenicity that consists of three interrelated but dissociable phases: 1) the initial development of myogenic tone (MT), 2) myogenic reactivity to subsequent changes in pressure (MR), and 3) forced dilatation at high transmural pressures (FD). The three phases span the physiological range of transmural pressures (e.g., MT, 40-60 mmHg; MR, 60-140 mmHg; FD, >140 mmHg in cerebral arteries) and are characterized by distinct changes in cytosolic calcium ([Ca(2+)](i)), which do not parallel arterial diameter or wall tension, and therefore suggest the existence of additional regulatory mechanisms. Specifically, the development of MT is accompanied by a substantial (200%) elevation in [Ca(2+)](i) and a reduction in lumen diameter and wall tension, whereas MR is associated with relatively small [Ca(2+)](i) increments (<20% over the entire pressure range) despite considerable increases in wall tension and force production but little or no change in diameter. FD is characterized by a significant additional elevation in [Ca(2+)](i) (>50%), complete loss of force production, and a rapid increase in wall tension. The utility of this model is that it provides a framework for comparing myogenic behavior of vessels of different size and anatomic origin and for investigating the underlying cellular mechanisms that govern vascular smooth muscle mechanotransduction and contribute to the regulation of peripheral resistance.     

Altered pulmonary vasoreactivity in the chronically hypoxic lung

Prolonged exposure to alveolar hypoxia induces physiological changes in the pulmonary vasculature that result in the development of pulmonary hypertension. A hallmark of hypoxic pulmonary hypertension is an increase in vasomotor tone. In vivo, pulmonary arterial smooth muscle cell contraction is influenced by vasoconstrictor and vasodilator factors secreted from the endothelium, lung parenchyma and in the circulation. During chronic hypoxia, production of vasoconstrictors such as endothelin-1 and angiotensin II is enhanced locally in the lung, while synthesis of vasodilators may be reduced. Altered reactivity to these vasoactive agonists is another physiological consequence of chronic exposure to hypoxia. Enhanced contraction in response to endothelin-1 and angiotensin II, as well as depressed vasodilation in response to endothelium-derived vasodilators, has been documented in models of hypoxic pulmonary hypertension. Chronic hypoxia may also have direct effects on pulmonary vascular smooth muscle cells, modulating receptor population, ion channel activity or signal transduction pathways. Following prolonged hypoxic exposure, pulmonary vascular smooth muscle exhibits alterations in K+ current, membrane depolarization, elevation in resting cytosolic calcium and changes in signal transduction pathways. These changes in the electrophysiological parameters of pulmonary vascular smooth muscle cells are likely associated with an increase in basal tone. Thus, hypoxia-induced modifications in pulmonary arterial myocyte function, changes in synthesis of vasoactive factors and altered vasoresponsiveness to these agents may shift the environment in the lung to one of contraction instead of relaxation, resulting in increased pulmonary vascular resistance and elevated pulmonary arterial pressure.     

Decreased blood pressure and vascular smooth muscle tone in mice lacking basolateral Na(+)-K(+)-2Cl(-) cotransporter

The basolateral Na(+)-K(+)-2Cl(-) cotransporter (NKCC1) functions in the maintenance of cellular electrolyte and volume homeostasis. NKCC1-deficient (Nkcc1(-/-)) mice were used to examine its role in cardiac function and in the maintenance of blood pressure and vascular tone. Tail-cuff measurements demonstrated that awake Nkcc1(-/-) mice had significantly lower systolic blood pressure than wild-type (Nkcc1(+/+)) mice (114.5 +/- 2.2 and 131.8 +/- 2.5 mmHg, respectively). Serum aldosterone levels were normal, indicating that extracellular fluid-volume homeostasis was not impaired. Studies using pressure transducers in the femoral artery and left ventricle showed that anesthetized Nkcc1(-/-) mice have decreased mean arterial pressure and left ventricular pressure, whereas myocardial contraction parameters were not significantly different from those of Nkcc1(+/+) mice. When stimulated with phenylephrine, aortic smooth muscle from Nkcc1(+/+) and Nkcc1(-/-) mice exhibited no significant differences in maximum contractility and only moderate dose-response shifts. In phasic portal vein smooth muscle from Nkcc1(-/-) mice, however, a sharp reduction in mechanical force was noted. These results indicate that NKCC1 can be important for the maintenance of normal blood pressure and vascular tone.     

Effect of acute ischaemia on active and passive large deformation mechanics of canine carotid arteries

Large deformation mechanical properties of dog carotid arteries excised following 1 hour of ischaemia and 1 hour of reperfusion were compared to those of contralaterial normal arteries in vitro. Vascular smooth muscle was invariably activated by 0.5 microgram/ml noradrenaline. Relative reduction in the diameter of postischaemia arteries following noradrenaline administration was twice as large (max.: 13.2 +/- 2.0%) as that of normal controls (max.: 5.7 +/- 1.5%) in the pressure range of 0--220 mmHg. If the smooth muscle was totally relaxed there were no differences between the geometrical (wall-thickness, radius) and mechanical properties (stress, incremental elastic modulus, incremental distensibility, strain-energy density) of the arteries in the two series. It is concluded that the increased reactivity of postischaemic arteries is not caused by changes in geometric or mechanical properties of their passive wall elements.     

Role of physical properties of resistance vessel wall in regulating peripheral blood flow--II. Structural and mechanical behavior

In order to examine the structural and mechanical properties of the vessel wall resistance when subjected to autoregulatory flow control, a mechanical model for the vascular wall was derived from a mathematical model. The mechanical model was an analogue model which connected in series the Maxwell model (elastic modulus: K3) with the parallel elements of Hill's model (elastic modules: K2) and Hooke's elastic model (elastic modulus: K1); it was also mathematically equivalent to the Spring model (see part I). The structural and mechanical properties of the resistance vessel wall were characterized by the three elastic moduli (K1, alpha K2 and K3) [mmHg]. The parameter alpha was a modification factor of the elastic modulus K2 given by the myogenic mechanism. After a numerical analysis of the experimental data given by the mechanical model, we confirmed that the arterial pressure range for autoregulatory flow controls shifted to the upper region with an increase of the elastic modulus K1 and the flow regulation was reduced.