Function of Circle of Willis

Nearly 400 years ago, Thomas Willis gave the most detailed anatomic description of the arterial anastomosis at the base of the brain, surrounded by cerebrospinal fluid. The arterial anastomotic ring that connects the left internal carotid artery (ICA), right ICA, and vertebrobasilar circulation by communicating arteries is called the circle of Willis (CW) (Figure 1). This arterial circle was well known before Thomas Willis, but it is said that with his detailed description he also recognized its function.¹ In his work,¹ Thomas Willis states that CW functions as a compensatory mechanism in the case of occlusion or stenosis of ICA or vertebral artery.^{2, 3}

The compensatory function stated by Thomas Willis is still considered valid. When Thomas Willis introduced his theory, he did not consider the function of CW from the evolutionary point of view. After the introduction of the theory of evolution, that came 200 years later, a lot has changed in the scientific view of Life. Since ‘nothing in biology makes sense except in the light of evolution’,⁴ Thomas Willis could not have made a proper biologic analysis of the function of CW. Therefore, we hypothesize that the primary function of CW is not the redistribution of blood flow in the case of occlusion event.

When studying the specific design of an organism, or its part, one has to take into account; (1) structural, (2) functional, and (3) environmental point of view, along with (4) the change in time. The structural shape of a specific part or entire organism dictates function. The environment in which structure appears and develops has to be accounted. Proper evolutionary analysis can be done only when dimension of time is considered too.⁵ After all four aspects have been accounted for, conclusions about an organism or its specific part can be made. Thus, conclusions about function can be wrong, if the environment and the time are not considered.

According to compensatory theory, CW maintains cerebral blood flow in the case of ICA or basilar artery occlusion or stenosis.^{6, 7, 8, 9} It is important to stress that in case of slowly progressing stenosis of large cerebral artery anatomically complete communicating arteries will have time to adapt and enlarge to maintain perfusion. After observation of enlarged communicating arteries during the study of a few pathologic processes, it was accepted that ensuring collateral blood flow is the function of CW, implying that CW has no function under physiologic conditions. It is unlikely that pathologic process, such as vascular occlusion, could steer evolutionary process. Evolution produces organisms with structural specificities that are adaptations to specific environments. Evolution results in a specific anatomic structure that in turn will result in specific pathologies, and not the other way around. Therefore, pathologic process would not force species to adapt; rather it would lead to its extinction. It is more likely that physical constraints and physical loads act as a selective pressure in a specific circumstance (i.e., running distance limitation in cheetahs due to overheating). The current theory of function of CW does not make sense due to several considerations.

First, an explanation of the function of CW is drawn from very specific environment. Cardiovascular events are leading cause of death today, since several epidemiologic transitions have allowed humans to live longer. Before the rise of modern medicine in the last two centuries, it was very unlikely that people would succumb to cerebrovascular disease. Global human life span at the beginning of the 19th century was 28.5 years,¹⁰ and at this age, cardiovascular disease is extremely rare. The occlusion event is more likely to occur in the older population of the higher social status, which represents extremely small portion of the entire human population that ever lived. If CW has a compensatory function, then hypoplastic or missing communicating arteries would be undesirable trait, but evident probably after a carrier was more than a decade sexually mature and probably have had propagated his/her genes. Since the majority of human beings that ever lived died before the age when a stenosis is expected to develop, such pathologic process cannot act as a selective force (i.e., trait not under evolutionary pressure, similar to Huntington's disease). Even today, the prevalence of carotid artery stenosis in the general population is around 1% or less,¹¹ and carotid arteries deliver ∼80% of the blood to the brain.^{12, 13} Therefore, the diseases of older age that became prevalent with Western civilization cannot explain the existence and the function of CW. The current interpretation of the function of CW has even less sense if the other species are taken into account, since it is unlikely for an animal to experience the cerebrovascular disease.

Second, the current view of the function of CW is anthropocentric, as it ignores other species' CW and analog structures. Circle of Willis-like structures are found in a large number of animals that vary in brain size, body size, and type of circulation (i.e., contribution of carotid and vertebrobasilar flow to overall blood supply).^{14, 15} Birds and mammals have structures similar to CW, although their common ancestor lived in the Permian period.¹⁶ Birds have a well-developed arterial communication between ICAs (cerebral intercarotid anastomosis; ‘H’, ‘X’, or ‘I’ type).^{14, 15} The commonness of CW and analog structures indicates that its function is not compensatory in the case of occlusion event, since the majority of birds and other animals do not die from cerebrovascular events. It is more likely that CW is a convergent evolutionary structure that has a function under physiologic conditions. The colonization of the land and the air coincides with the development of complex circulatory systems with high arterial pressures, which expose brain enclosed in the cranial cavity to high pulsatile stress. The development of CW is probably a forced move, the evolutionary selected solution in the constraints of previous evolutionary moves in Life's adjustment to the environment outside the water.

Third, the compensatory theory of CW implies that evolution has a foresight. Evolution has no foresight; it is a process, a force that acts in the present time in the constraints of previously made evolutionary steps and physical abilities. New structures appear and are evolutionary preserved if they increase survival, i.e., give an evolutionary advantage to the carrier. Some structures may be preadaptive; might serve some purpose in the future, but such occurrence is a result of randomness, not of foresight.

Fourth, the most common location for the arterial stenosis or occlusion (thrombotic or embolic) is proximal part of the ICA and the distal part of middle cerebral artery (MCA).¹⁷ It was observed that the compensatory function is only possible in the vicinity of CW.⁶ If CW has a compensatory function then it is odd that the redundancy is only partially effective for distal parts of the MCA, thus leaving a large part of each hemisphere unprotected. (Pial arterial anastomoses between the terminal arteries of anterior and posterior cerebral artery with the MCA terminal distribution arteries provide enough collateral blood flow into the edge of the MCA distribution region.)

Fifth, it was shown that under physiologic conditions blood does not cross the midline of the brain.¹⁸ The absence of effective contralateral blood flow was observed even within anatomically and functionally complete CW.^{6, 18} Anatomic and physiologic textbooks^{6, 18} state that communicating arteries are too small for effective blood flow, since their radius is too small. According to the Poisseuille law, flow of the viscous fluid through the vessel is dependent of the fourth exponent of radius (Equation 1); V—volume, t—time, R—radius, P—pressure, η—viscosity of the blood, and L—length of vessel segment.

Sixth, it was found that 50% of the population had a CW with at least one communicating artery missing, very small or incompletely developed and complete CW is present in only 21% of persons.¹⁹ Anatomically complete CW is present in most individuals, although functional completeness was identified in less than a half of the population, since one of the communicating arteries is usually too narrow (diameter <0.3 mm) to enable effective blood flow.²⁰ The most common variation is hypoplastic posterior communicating artery, while other structural variations include duplicated or missing communicating arteries.⁶ Studies investigating the anatomy of CW in random populations found the presence of at least one communicating artery and considerable anatomic variations in the number and diameter of the arteries of CW (Table 1).^{19, 21, 22, 23, 24, 25, 26, 27} In all studied individuals, ICA was always connected through at least one communicating artery to other parts of CW. Previous studies suggest that ‘a diameter range in which a communicating artery may be either functional or not […] spread from 0.5 mm to 1.0 mm’.²⁸ If CW has a compensatory function then hypoplastic or missing communicating arteries would not be frequent in the population; one would expect to find relatively larger communicating arteries that would allow an effective blood flow. Since anatomically complete CW is present in the large proportion of the population, the development of arterial stenosis near CW in an individual would allow gradual widening of the communicant arteries to maintain cerebral perfusion. Incomplete CW is more common in patients with classic migraine (migraine with aura),²⁹ while the absence of all three communicant arteries was described in a single case report of a 33-year-old woman, whose brain perfusion was preserved, but had severe headache attacks.³⁰ It was suggested that a headache in this case might be caused by hemodynamic stress.³⁰

Everything in the skull pulsates in synchrony with heartbeat.^{31, 32} With every heartbeat, energy in the form of blood flow (flow pulsation) and a traveling pulse wave (pressure pulsation) is inserted into the arterial system. The cardiovascular system is considered to be in a steady-state oscillation; characterized by a periodic rise and fall of the arterial pressure under physiologic conditions. It has been proposed that every heart beat should be considered as an isolated event.³³ Because the aorta is compliant, the vessel wall expands as blood is ejected into the aorta. That expansion of the vessel wall is essential for the accommodation to the increased volume of blood, since already present blood is inert and cannot be instantly moved distally. Thus, blood inflow to the aorta is higher than the blood outflow during systole (Equation 2); Q—flow.

The aorta has the highest compliance among all arteries, but its branches also add to overall compliance of the arterial system. If it was not for the compliance, all new blood would have to go through the peripheral vessels between systoles and no blood flow would occur during diastole.³⁴ Aortic pressure rises as new blood accumulates in the aorta, (Equation 3); P—arterial pressure, C—arterial compliance, and t—time.

Pressure rise depends on the ability of the arterial wall to expand. At one point pressure overcomes inertia and starts to propagate through the arterial system in the form of pressure pulse—this is called transmission of the pressure pulse. This pressure pulse is a traveling wave of pressure or simple, pulse wave that equals the difference between systolic and diastolic arterial pressure. Every heart beat creates a separate pulse wave; with its speed c. Pulse wave is a wavefront that represents the change in specific property (pressure) during the observed time.³³ Newly introduced perturbations in arterial system will propagate as a wave; in forward with the speed U+c, and in the backward direction with the speed U—c; U—velocity of the blood, c—wave speed dependent on elastic properties of arteries.³³ Traveling pulse wave expands arteries, which, in turn compress the surrounding tissue. This arterial expansion under the skin can be observed as a pulse. Strong pressure pulse under physiologic conditions is found during physical exercise and pregnancy, reaching up to 100 mm Hg in contrast to resting 40 mm Hg. Also, it can be found under some pathologic conditions, such as aortic insufficiency, anemia, fever, and beriberi disease.¹⁸ Pressure pulse can be extremely strong and cause hearable sounds or even head nodding in synchrony with the heart beat.¹⁸ Pulse wave propagates mostly independent of blood flow; pulse wave travels 4 m/s in aorta and speeds up to 30 m/s in distal arteries, while blood flows 10 to 15 times slower.¹⁸ Although velocity of the blood flow is mostly independent of the velocity of the pulse wave, peak systolic velocity of the blood flow increases 0.0021 m/s for every 1 mm Hg increase in pressure pulse.³⁵

Pulse wave represents traveling energy that can be described with wave intensity. The wave intensity (I) is defined as a change in pressure (P) times the change in speed (V), during the period of time (t) (Equation 4). The wave intensity represents a newly arrived energy per unit area; and has unit W/m².

Because of the arterial damping, dissipation of the energy of the pulse wave equals to resistance (R) times compliance (C) (Equation 5).

The compliance of elastic arteries, mainly aorta and its branches (also called conducting arteries), has an important function of dampening of the pulsatile output of the heart, thereby reducing the intensity of the pulse wave.³⁴ Therefore, elastic reservoir of the arterial system dissipates newly entered energy and evens out the blood flow at the capillary level. If it was not for the compliance, arteries would behave similar to rigid tubes; blood would flow only during the systole. Elastic properties of the large arteries are essential for their compliance. These properties are in part due to their relatively greater proportion of elastin fibers to smooth muscle and collagen fibers. Together, elastin fibers and vascular smooth muscle cells provide flexibility and resilience to the elastic arteries. Hence, reduced compliance will result in a higher intensity of the pulse wave (Equation 5).³⁴

As the pulse wave travels forward through a conductive medium (blood), its energy decreases toward the periphery, due to the elastic properties of arterial reservoir. When forward traveling pulse wave reaches the distal end of the arterial system (physically described as the discontinuity of conditions) it is transmitted and reflected.³³ The magnitudes of transmitted and reflected pulse waves are dependent on the reflection coefficient; reflecting wave arises because boundary conditions have to be satisfied.³³ Arterial bifurcations give rise to small but constant amount of the reflecting pulse waves, while the peripheral arterioles contribution varies depending on arteriole constriction.³⁶ Increased peripheral resistance will result with the reflected pulse wave of high intensity.³⁶ Wave intensity at a given point is a sum of forward and backward traveling pulse wave intensities (Equation 6); I—wave intensity.

Arterial compliance enables blood flow through the entire cardiac cycle and it also creates reservoir pressure. Traveling pulse wave causes an increase in pressure in observed arterial segment. Thus, intraarterial pressure is a sum of pulse wave pressure (P_wave) and reservoir pressure (P_reservoir) (Equation 7).^{37, 38}

If reservoir pressure is ignored (as in the system that lacks compliance), forward pulse wave accounts for 70% and backward pulse wave for 30% of the total pressure.³⁸ When reservoir pressure is accounted for, it contributes to total arterial pressure with ∼50%, forward pulse wave with 44% and backward pulse wave with 6%.³⁸

Arterial flow in cerebral arteries changes during exercise;³⁹ systolic velocity increases while diastolic velocity is unchanged—similar to the behavior of the fluid in a conducting system with low compliance, indicating that pulse wave pressure (forward and backward) might be the major contributor to the total cerebral arterial pressure. If it was not for dampening and gradual dissipation of energy of the pulse wave, a sudden transfer of energy at the end of arterial system would cause structural damage.³¹ Such sudden transfer of energy can be compared with an effect of closing a downstream valve in the rigid tube system that, in turn, will cause a loud bang produced by a sudden stop of incompressible fluid and subsequent transfer of energy to the system of tubes. A sharp increase in pressure caused by the stop of fluid in a system of tubes is called hydraulic shock, or water hammer, and in the arterial system it is described by an equation (8); P—pressure, ρ—density of the blood, c—pulse wave velocity, U—blood flow velocity,±—negative sign denotes backward, and positive forward traveling wave.

Since the brain is exposed to high pulsatile stress⁴⁰ and due to several specificities of cerebral circulation (when compared with the systemic circulation), avoidance of hemodynamic stress in the brain is of great importance.

Cerebral blood flow is constant when arterial pressure is between 70 and 140 mm Hg.¹⁸ Cerebral autoregulation is controlled by myogenic, metabolic, and neurogenic mechanisms,^{13, 41, 42, 43} which ensure perfusion and protect the blood–brain barrier (BBB) and fragile neural tissue from sudden changes in arterial pressure.⁴⁴ Stable flow is maintained with adjustment of vascular resistance, since the BBB can be easily disrupted with a sudden marked increase in blood pressure.¹⁸ The response time for cerebral autoregulation is ∼3 to 5 seconds, therefore blood velocity fluctuates in large cerebral arteries,⁴⁵ indicating that cerebral arteries are exposed to high physical stress.

The cerebral arterial circulation consists of cerebral macrocirculation and microcirculation, connected with penetrating arterioles. Cerebral macrocirculation consists of the four delivering arteries, its large branches and small pial that continue into penetrating arteries, found in the Virchow–Robinson space in the brain parenchyma. Microcirculation is composed of small arterioles, capillaries, and venules.

Previous studies indicate that cerebral arteries (especially lenticular arteries) are prone to structural damage (bursting), compared with other systemic arteries in humans.⁴⁶ The cerebral arteries of different animal models have 3 to 4 times larger diameter for a given arterial pressure than arteries of other systems,⁴⁷ and according to the law of Laplace for cylindrical structures, arterial wall tension for a given amount of arterial pressure is larger in cerebral arteries. Cerebral arteries structurally differ from the other systemic arteries; have scarce elastin fibers in medial layer and thin adventitia, lack external elastic lamina (between medial layer and adventitia), and have well-developed internal elastic lamina instead (between intimal and medial layer).⁴⁸ Smooth muscle fibers of the cerebral arteries are arranged circularly, perpendicularly oriented to the blood flow, while other systemic arteries have smooth muscle fibers arranged spirally around the long axis of the vessel.⁴³ Perpendicular orientation of smooth muscles may be an adaptation to the high wall tension present in cerebral arteries, where such structural property might have a preventive role against the arterial wall bursting.

Bifurcations of cerebral arteries, in comparison with other systemic arteries of similar size, tend to be more perpendicular than parallel, while penetrating arteries have right angle bifurcations with pial arteries.⁴³ Such bifurcations ensure a significant decrease in blood velocity, larger transfer of kinetic energy and larger increase in hydrostatic pressure (through mechanisms called hydraulic shock). Another anatomic specificity of cerebral arteries is that they branch more progressively into smaller arteries and arterioles than other peripheral arteries.⁴³ Therefore, as the contact surface between blood and vessels increases, resistance in the arterial system rises sharply. To protect the microcirculation from the sharp pressure rise, large cerebral arteries receive a large portion of pressure burden.

It was previously reported that cerebrovascular resistance under resting conditions lies downstream of MCA, at the arteriolar level, and with the increase in systolic pressure (i.e., during exercise) resistance shifts toward large cerebral arteries,^{44, 49} toward CW. Anatomically, energy dissipation is shifted toward CW when the input of the energy into the cerebral circulation (in the form of higher pulse wave intensity and velocity) is increased.

After a craniotomy in anesthetized patients, moderate changes in diameter occurred in distal cerebral arteries in response to changes in arterial pressure and CO₂, whereas changes in diameter of the major cerebral arteries were <4%.⁵⁰ Early studies of proximal MCA diameter without craniotomy also could not detect significant changes with CO₂ alterations or lower body negative pressure.^{51, 52} However, more recent work does indicate a small but significant inverse correlation of the extracranial ICA diameter with arterial pressure and concordant differences in the slope of the relationship of ICA volumetric flow versus ICA velocity with pharmacologically induced changes in arterial pressure.⁵³ Because the percent changes in MCA velocity matched the percent changes in ICA velocity, MCA diameter may also have an inverse relationship with arterial pressure and thereby contribute to autoregulation. Thus, some uncertainty remains about the magnitude of diameter changes that occur in the proximal MCA. Recently, Koller and Toth⁵⁴ reported that an increase in the intraluminal pressure and blood flow may cause an increase in vascular tone of large cerebral arteries. Nevertheless, the relatively small magnitude of diameter changes in the proximal MCA suggests a relatively small reservoir pressure component in large cerebral arteries.

In different physiologic and pathophysiologic circumstances, arterial blood pressure rises well above the resting values.¹⁸ During heavy exercise in healthy subjects, with heart rate around 150 per minute, pressure pulse increases up to 100 mm Hg and mean arterial pressure up to 100 mm Hg.³⁹ The same study established that the mean blood velocity through MCA increased from 0.61 m/s to 0.71 m/s, more specifically, systolic blood velocity and mean blood velocity increased while diastolic blood velocity decreased.³⁹ Ogoh et al³⁹ also showed that the arterial blood pressure in MCA reaches 180 to 190 mm Hg during heavy exercise, while maximal systolic blood velocity in MCA reaches 1.9 m/s (resting value was up to 0.9 m/s). Strenuous physical exercise causes an increase in intraabdominal and intrathoracic pressures, with subsequent obstruction of cerebral blood outflow via the internal jugular vein, thus leading to the increase in intracranial pressure.^{55, 56} Therefore, physical exercise, as well as other physiologic and pathophysiologic conditions (coughing, defecating, emesis, and obesity⁵⁷), increases intracranial pressure. As intracranial pressure increases, intracranial compliance decreases.³¹ (Intracranial compliance is ‘comprised of four main components: actual brain tissue compliance (which is small), arterial compliance, venous compliance (veins have highly compliant walls), and compliance of the spinal thecal sac (which communicates with the brain via the cerebrospinal fluid spaces) which is made out of four components.³¹) Intracranial pressure and volume have an exponential relationship; increased pressure will cause the system to become more rigid (less compliant) and prone to a large increase in pulsatility after a minor increase in volume.³¹ Therefore, physical exercise represents a challenge to cerebral autoregulation; a large and sharp increase in pressure pulse and systolic blood velocity has to be surmounted to ensure protection of the sensitive BBB and neural tissue.

Cerebral blood flow is maintained constant under physiologic conditions. The cerebral circulation consists of cerebral macrocirculation and microcirculation, connected with penetrating arterioles. As cerebral arteries branch progressively, contact surface increases sharply, causing a sharp increase in resistance. This marked increase in resistance protects microcirculation and the BBB from high systolic pressure. The basal cerebral vessel tone is set by intraluminal pressure and flow, and can be modulated by metabolism, neural signals, and astrocyte–glia interactions.⁵⁴

Cerebral circulation is exposed to cardiac-generated pulsatility: arterial pressure pulsation and flow pulsation. These circulation components input energy into the skull which has to be dissipated to protect microcirculation and BBB from damage. It was reported that cerebrovascular resistance lies downstream from large cerebral arteries, but with the increase in systolic pressure, resistance (energy dissipation) shifts toward larger arteries, toward CW. Relative small magnitude of diameter changes observed in large cerebral arteries indicates that these arteries might be less compliant and less capable in dampening pulse wave intensity (through compliance-based dampening mechanism).

In extracranial tissues, tissue compliance dissipates pulse energy. Due to structural and physical constraints, cranial tissues have complex cranial compliance composed of four different components (brain parenchyma compliance, arterial compliance, venous and spinal thecal sac compliance) that should dampen the arterial pulsations and ensure protection of the sensitive BBB and neural tissue, but not entirely, since some pulsation is essential for proper function of microcirculation.

Intracranial compliance decreases with increased intracranial pressure. Intracranial pressure and volume have an exponential relationship; increased pressure will cause a system to become less compliant and prone to a large increase in pulsatility after a minor increase in volume.

According to system analysis, flow and pressure energy (input signals) that is being inputted into the cranium (system) has to be converted (absorbed) to an acceptable level (output signal) that will not damage the intracranial structures. Modulation of absorption of energy inputted into the system is complex and dependent on cardiac frequency.^{31, 58, 59}

We hypothesize that CW functions as a pressure absorber mechanism that prevents damage of the cranial microvasculature and BBB.

Hydraulic shock is a transitory pressure increase, occurring due to a sudden change in a direction or velocity of the fluid. Sudden deceleration of the fluid in closed tubes causes pressure build up and transfer of energy to the walls, resulting in the propagating shock wave. If the shock wave would not be controlled, wall damage would occur, because incompressible fluid and wall cannot absorb the shock. Similarly, a sudden change in blood flow direction and velocity causes the pressure rise. Every waveform of the blood velocity has a specific momentum per unit of volume flow.⁶⁰ The waveform of blood velocity converts its energy to pressure when it decelerates or stops, and that occurs near bifurcations from which communicating arteries branch-out.⁶⁰ Momentum is converted into pressure that is transmitted to the arterial wall and surrounding structures. Pulsatile impulse (I) is a change in the momentum (p) with respect to time t (Equation 9). During physical exercise, when the time t between the systolic flows is decreased, increased blood velocity will cause transmission of the higher force to the arterial wall and surrounding tissue (Equation 10); F—force, t—time, and p—pressure. Thus, total pressure exerted to the arterial wall is a sum of the impulse energy and pulse wave intensities.⁶⁰

When the pressure exerted to the arterial wall exceeds vessel ‘strength’, an artery can burst or become aneurysmally dilated, hence aneurismal dilatations of the arterial wall are most often found in CW, with exception of the aorta.⁶¹ Cerebral aneurysms are berry-shaped arterial wall dilatations caused by weakening of the vessel wall. It is considered that they appear due to changes in intrinsic factors of the arterial wall and possibly due to exposure to hydraulic stress.⁶¹ It has been shown that the location of the berry aneurisms does not correspond to structural defects in cerebral arteries, but rather to the anatomic location, where a significant amount of blood momentum is preserved.⁶⁰ Aneurisms are mostly located at the communicating arteries; in anterior cerebral artery (around anterior communicating artery), in proximal MCA (around posterior communicating artery), and in distal MCA.⁶² Berry aneurysms are often found in patients with aortic coarctation.⁶¹ Coarctation is a localized narrowing of the aorta and it is most often seen in the proximal portion of the aorta, near left subclavian artery. Aortic coarctation causes high arterial pressures in cerebral circulation and exposes CW to high hemodynamic stress. Thus, high hemodynamic stress is associated with higher risk of developing berry aneurisms in the vicinity of CW.

Four different pulse waves from the four large arteries that supply the brain arrive at different times to CW. The asynchronous arrival of pulse waves is a result of the anatomic configuration of the arterial system. First aortal branch is brachiocephalic trunk that branches into the right subclavian artery and right common carotid artery, the latter terminating with ICA and external carotid artery. The second branch is left common carotid artery that has the same branches as the right-sided artery. Third artery that arises from the arch of the aorta is the left subclavian artery. The branching is similar in both subclavian arteries, and the first major branch is vertebral artery. Such anatomic configuration results with longer left-side cerebral arteries (distance from the heart to CW). Due to left-right asymmetry of the arterial system, pulse waves and blood flow reach CW at different times.⁶³ A small increase in volume can lead to a significant pressure rise in the low compliance system, such as cranial cavity can be, indicating that asymmetry of the cerebral arterial tree might be important for the physiology of the cerebral circulation. Moreover, the asynchronous arrival of forward pulse waves leads to asynchrony of backward pulse waves too. It was observed in arterial circulation models that the symmetry of the arterial tree ‘resulted in simultaneous reflections from each of the legs which resulted in unwanted interactions between reflected waves’.⁶³

Due to a progressive branching of cerebral arteries after CW, peripheral resistance sharply increases. As blood slows down, its kinetic energy is transferred to arterial walls, locally increasing the hydrostatic pressure. Perpendicular bifurcations of the large cerebral arteries ensure transfer of a significant amount of the kinetic energy to the arterial wall, causing the large increase in hydrostatic pressure.

As the pulse wave travels independently of blood to the end of the arterial system in the brain, it speeds up due to the low compliance. When forward traveling pulse wave reaches small, resistant arteries and arterioles, it reflects and goes backwards, as backward traveling pulse wave. Forward and backward traveling pulse waves may pass through the arterial segment at the same time, further increasing local hydrostatic pressure. Positive interference of forward and backward traveling pulse waves is a stochastic event, but it can occur, and when it occurs, it is necessary that the sum of the pressures is lower than what cerebral artery can withstand.

As previously shown, diameter of large cerebral arteries is constant, or of small magnitude of diameter change under various physiologic conditions, indicating diminished reservoir pressures (compliance). The properties of large cerebral arteries found in vivo are similar to conducting system with low compliance and reduced energy dissipation ability. Structural specificities of cerebral arteries might compensate for decreased compliance (i.e., perpendicularly oriented smooth muscle fibers exert more force compared with oblique oriented smooth muscle fibers). Since large cerebral arteries have diminished active energy dissipation system (compliance), we infer that communicating arteries function as a passive energy dissipation system. As the blood flow through communicating arteries is almost nonexistent under physiologic conditions, we infer that the blood in the communicating arteries acts as an analog of rubber diaphragm found in the rigid tube system. Rubber diaphragm absorbs the energy of moving fluid and pressure rise at the high pressure end by stretching into the low pressure area, thus transferring the pressure to low pressure end. Blood already present in the communicating arteries serves as a medium in which elastic wave (pressure) propagates and allows dissipation of the pressure to the low pressure end, namely, the arterial tree of other artery that comprises CW, without a significant blood flow. Pressure dissipation is possible because pulse waves and blood flow through main conducting arteries to the cranial cavity arrive asynchronously. Therefore, lack of communicating arteries (or other arterial components of CW that resemble communicating arteries, depending on CW variations) would expose cerebral microcirculation to high stress that might cause arterial wall and BBB damage, especially during strenuous physical activity. In this context, a rare anatomic variation, such as embryological remnants (persistent primitive trigeminal artery, carotid–basilar anastomosis that is associated with numerous vascular abnormalities^{64, 65}), would represent a valuable hemodynamic model for testing the function of the communicating arteries.

From the evolutionary point of view, the compensatory function of the CW is incorrect, since pathologic conditions of the older age are unlikely to steer evolution. Moreover, the communicating arteries are too small or hypoplastic in majority of the population, hence ineffective for blood transfer. The communicating arteries of CW probably serve as a passive energy (pressure) dissipating system: they transfer pressure without considerable blood flow from the high pressure end to the low pressure end, the latter being other arterial components of CW, where pulse wave and blood flow arrive asynchronously.

The authors would like to acknowledge the anonymous reviewers and Professor Sven Kurbel whose suggestions were helpful in preparing this manuscript.