Classic blood flow dynamics can be given by the Hagen-Poiseuille equation where volumetric blood flow, Φ, is given as:
is pressure loss (differences in inflow and outflow pressure), L
is the length of the vessel tube, η
is blood viscosity, and R
is the radius of the vessel [10
Under physiological conditions, L
can be treated as constant, and regional blood flow, Φr
, within the unit area can be given as:
In the systemic circulation, the autonomic nervous system is responsible for Φr
by controlling both ∆P
through neural and/or chemical control of contractile structures of cardiac and circulatory systems. In contrast, capillaries lack contractile structures and, therefore, capillary blood flow cannot be directly controlled by the autonomic nervous system. Although contractile function of pericytes and its neurotransmitter control has been proposed [11
], considering its common, wide spread functionality related to angiogenesis and stem cell like behavior [12
], it is difficult to accept that pericytes are the primary structural component for flow regulation. It is, therefore, highly plausible to consider that capillary flow dynamics are a passive phenomenon which are significantly affected by the architectural properties of the capillaries per se.
2.2. Common Capillaries and Tissue Perfusion
Common capillaries in the systemic circulation have a leaky endothelium. Water flow between intra-capillary and interstitial fluid is relatively free and follows the forces defined by the Starling equation:
is the trans endothelial fluid filtration volume per second, Pc
is the capillary hydrostatic pressure, Pi
is the interstitial hydrostatic pressure, πp
is the plasma protein oncotic pressure, πi
is the interstitial oncotic pressure, Lp
is the hydraulic conductivity of the membrane, S
is the surface area for filtration, and σ
is the Staverman’s reflection coefficient, respectively [13
The term in the Starling equation represents the net driving force for the trans endothelial fluid filtration volume per second, Jv. Under physiological conditions, and Pi will be virtually constant and, therefore, regional flow per second, Φr per second, and hence averaged ∆P per second, will directly translate into Jv, defining tissue perfusion. Simply stated, for systemic, leaky capillaries, R remains constant, Kr.
Accordingly, Φr is a function of ∆P.
Therefore, as far as tissues with common capillaries are concerned, the hydrostatic pressure field generated by the heart is by far the most important, if not sole, factor governing tissue perfusion. The systolic force of the heart effectively extrudes water out of the capillaries without much resistance into the interstitial fluid system as well as helps create significant interstitial fluid motion necessary for interstitial fluid circulation (see below).
In clear contrast, brain capillaries have significantly different water permeability characteristics due to the presence of the BBB. Therefore, the principles of regional blood flow and interstitial fluid circulation described for common capillaries are not applicable to regional cerebral blood flow (rCBF).
2.3. Cerebral Autoregulation
Cerebral autoregulation signifies an intrinsic ability of cerebral vasculature to maintain cerebral blood flow at a relatively constant rate of ca. 50 mL per 100 g brain tissue per minute in the face of blood pressure changes [14
]. Autoregulation generally functions between mean blood pressures of 60 and 150 mm Hg. It is preserved in animals that have undergone parasympathetic and/or sympathetic denervation [14
], and the system is independent from extrinsic neural control. Instead, intrinsic neural nitric oxide (NO) control [19
] and release of vasoactive substrates by the brain are believed to play essential roles in maintaining constant cerebral perfusion [16
]. Perfusion is held constant by means of cerebral vasculature smooth muscle constriction and dilation in response to elevated and decreased systemic pressure, respectively [14
In the context of the principles of the blood flow dynamics described above, cerebral autoregulation translates to rigorous maintenance of a constant ∆P (differences in inflow and outflow pressure), Kp.
If brain capillaries have structural properties similar to common capillaries, rCBF would be essentially constant.
This is indeed the primary functionality of cerebral autoregulation, which rigorously maintains a rather constant perfusion of the brain in the presence of significant fluctuation in systemic circulation associated with various physiological activities [14
2.4. Neurovascular Coupling
Increased rCBF associated with brain activation is a well-recognized phenomenon that is known as neurovascular coupling. It is relatively small increase in rCBF compared to steady rCBF, which is rigorously regulated by autoregulation [20
]. Nevertheless, the rCBF increase associated with neurovascular coupling seemingly contradicts the purpose of cerebral autoregulation and, therefore, neurovascular coupling should have a role essential to maintain brain functionality and closely related molecular phenomena associated with neural activities.
It was once thought that neurovascular coupling serves to ensure adequate neuronal nutrient supply. This intuitively appealing notion failed to account for the large quantitative discrepancy between supply and demand. The amount of essential nutrients delivered by the increased rCBF, such as oxygen and glucose, exceeds actual consumption by more than six times. Such a large discrepancy is virtually unknown in any other biological system, indicating that a factor other than nutrient supply underlies the observed disproportionate increase in rCBF [20
]. Subsequent studies indicate that increased rCBF associated with brain activation serves as a heat removal mechanism. Information processing by brain generates considerable heat and water flow is the primary means of heat removal. It is therefore evident that the apparent surfeit in rCBF increase serves as a quick removal system of the additional heat generated by neural activities [21
Neurovascular coupling is a micro, rather than macro environmental event occurring within an area limited to 250 µm around the site of neural activity [23
]. Therefore, the regulatory mechanism for neurovascular coupling should be within the capillaries, independent from cerebral autoregulation per se. Brain capillaries have a very tight endothelium which severely restricts water permeability. Therefore, hydrostatic pressure differences between intra-capillary fluid and interstitial fluid affects the capillary’s structure as in the case of a Starling resistor [24
]. This can provide the environment where small rCBF increase associated with neural activities, Φnvc
, under rigorous control of rCBF by autoregulation is a function of small changes in capillary diameter ∂R
2.5. Flow and Pressure in a Starling Resistor
The experimental device consisted of an elastic tube clamped between two rigid pipes, surrounded by an outer pressure chamber, known as a Starling resistor, and was used in an isolated-heart preparation by Ernest Henry Starling. Studies using the device eventually led to the Frank-Starling law of the heart [13
] (Figure 2
). The static pressure of the outer pressure chamber controls the degree of collapse of the tube, providing a variable resistor to simulate total peripheral resistance. As a rule, the device initially shows linear behavior, namely, linear changes in tube diameter that corresponds to the relationship between the pressure of the outer chamber and hydrodynamic pressure in the tube. It eventually shows non-linear behavior, leading to two non-linear phenomena known as the waterfall effect and self-excited oscillations, the biological equivalents of which represent expiratory flow limitation in chronic obstructive pulmonary disease (COPD) and snoring, respectively [25
Brain capillaries, owing to tight endothelium, have virtually identical physiological conditions as a Starling resistor. The brain capillary is a biological pliable tube clamped between two rigid tubes, namely, arteriole (artery) and venule (vein) as depicted in Figure 2
. Cerebral autoregulation rigorously maintains hydrodynamic pressure corresponding to Pup
. Similar to the elastic tube in a Sterling resistor, the diameter of which is controlled by the pressure of the outer pressure chamber, Pext,
in Figure 2
. The diameter of a given brain capillary, Rcap
, is a function of the static pressure of the surrounding interstitial fluid in the peri-capillary space (Virchow-Robin space), PVRS