Arterial Pulsation-driven Cerebrospinal Fluid Flow in the Perivascular Space: A Computational Model

This study was conducted to determine whether local arterial pulsations are sufficient to cause cerebrospinal fluid (CSF) flow along perivascular spaces (PVS) within the spinal cord. A theoretical model of the perivascular space surrounding a "typical" small artery was analysed using computational fluid dynamics. Systolic pulsations were modelled as travelling waves on the arterial wall. The effects of wave geometry and variable pressure conditions on fluid flow were investigated. Arterial pulsations induce fluid movement in the PVS in the direction of arterial wave travel. Perivascular flow continues even in the presence of adverse pressure gradients of a few kilopascals. Flow rates are greater with increasing pulse wave velocities and arterial deformation, as both an absolute amplitude and as a proportion of the PVS. The model suggests that arterial pulsations are sufficient to cause fluid flow in the perivascular space even against modest adverse pressure gradients. Local increases in flow in this perivascular pumping mechanism or reduction in outflow may be important in the etiology of syringomyelia.     

Sustained high-pressure in the spinal subarachnoid space while arterial expansion is low may be linked to syrinx development

Syringomyelia (a spinal cord cyst) usually develops as a result of conditions that cause cerebrospinal fluid (CSF) obstruction. The mechanism of syrinx formation and enlargement remains unclear, though previous studies suggest that the fluid enters via the perivascular spaces (PVS) of the penetrating arteries of the spinal cord, and that alterations in the CSF pulse timing and pressure could contribute to enhanced PVS inflow. This study uses an idealised computational model of the PVS to investigate the factors that influence peri-arterial fluid flow. First, we used three sample patient-specific models to explore whether changes in subarachnoid space (SAS) pressures in individuals with and without syringomyelia could influence PVS inflow. Second we conducted a parametric study to determine how features of the CSF pulse altered perivascular fluid, including alterations to timing and magnitude of the peak SAS pressure, the timing of reversal from high to low pressure (diastolic phase), and the area under the pressure–time curve. The model for the patient with syringomyelia had higher net CSF inflow to the PVS than the two subjects without syringomyelia. In the parametric study, only increasing the area under the high pressure region of the SAS pulse substantially increased PVS inflow, when coupled with a temporal shift in arterial and SAS pulses. This suggests that a period of sustained high SAS pressure while arterial diameter is low may increase net CSF pumping into the PVS.     

A coupled hydrodynamic model of the cardiovascular and cerebrospinal fluid system

Coupling of the cardiovascular and cerebrospinal fluid (CSF) system is considered to be important to understand the pathophysiology of cerebrovascular and craniospinal disease and intrathecal drug delivery. A coupled cardiovascular and CSF system model was designed to examine the relation of spinal cord (SC) blood flow (SCBF) and CSF pulsations along the spinal subarachnoid space (SSS). A one-dimensional (1-D) cardiovascular tree model was constructed including a simplified SC arterial network. Connection between the cardiovascular and CSF system was accomplished by a transfer function based on in vivo measurements of CSF and cerebral blood flow. A 1-D tube model of the SSS was constructed based on in vivo measurements in the literature. Pressure and flow throughout the cardiovascular and CSF system were determined for different values of craniospinal compliance. SCBF results indicated that the cervical, thoracic, and lumbar SC each had a signature waveform shape. The cerebral blood flow to CSF transfer function reproduced an in vivo-like CSF flow waveform. The 1-D tube model of the SSS resulted in a distribution of CSF pressure and flow and a wave speed that were similar to those in vivo. The SCBF to CSF pulse delay was found to vary a great degree along the spine depending on craniospinal compliance and vascular anatomy. The properties and anatomy of the SC arterial network and SSS were found to have an important impact on pressure and flow and perivascular fluid movement to the SC. Overall, the coupled model provides predictions about the flow and pressure environment in the SC and SSS. More detailed measurements are needed to fully validate the model.     

The effects of variation in the arterial pulse waveform on perivascular flow

Cerebrospinal fluid (CSF) enters nervous tissues through perivascular spaces. Flow through these pathways is important for solute transport and to prevent fluid accumulation. Syringomyelia is commonly associated with subarachnoid space obstructions such as Chiari I malformation. However, the mechanism of development of these fluid-filled cavities is unclear. Studies have suggested that changes in the arterial and CSF pressures could alter normal perivascular flow. This study uses an idealised model of the perivascular space to investigate how variation in the arterial pulse influences fluid flow. The model used simulated subarachnoid pressures from healthy controls (N = 9), Chiari patients with (N = 7) and without (N = 8) syringomyelia. A parametric analysis was conducted to determine how features of the arterial pulse altered flow. The features of interest included: the timing and magnitude of the peak displacement, and the area under the curve in the phases of uptake and decline. A secondary aim was to determine if the previously observed differences between subject groups were sensitive to variation in the arterial pulse wave. The study demonstrated that the Chiari patients without a syrinx maintained a significantly higher level of perivascular inflow over a physiologically likely range of pulse wave shapes. The analysis also suggested that age-related changes in the arterial pulse (i.e. increased late systolic pulse amplitude and faster diastolic decay), could increase resistance to perivascular inflow affecting solute transport.     

Syrinx fluid transport: modeling pressure-wave-induced flux across the spinal pial membrane

Syrinxes are fluid-filled cavities of the spinal cord that characterize syringomyelia, a disease involving neurological damage. Their formation and expansion is poorly understood, which has hindered successful treatment. Syrinx cavities are hydraulically connected with the spinal subarachnoid space (SSS) enveloping the spinal cord via the cord interstitium and the network of perivascular spaces (PVSs), which surround blood vessels penetrating the pial membrane that is adherent to the cord surface. Since the spinal canal supports pressure wave propagation, it has been hypothesized that wave-induced fluid exchange across the pial membrane may play a role in syrinx filling. To investigate this conjecture a pair of one-dimensional (1-d) analytical models were developed from classical elastic tube theory coupled with Darcy's law for either perivascular or interstitial flow. The results show that transpial flux serves as a mechanism for damping pressure waves by alleviating hoop stress in the pial membrane. The timescale ratio over which viscous and inertial forces compete was explicitly determined, which predicts that dilated PVS, SSS flow obstructions, and a stiffer and thicker pial membrane-all associated with syringomyelia-will increase transpial flux and retard wave travel. It was also revealed that the propagation of a pressure wave is aided by a less-permeable pial membrane and, in contrast, by a more-permeable spinal cord. This is the first modeling of the spinal canal to include both pressure-wave propagation along the spinal axis and a pathway for fluid to enter and leave the cord, which provides an analytical foundation from which to approach the full poroelastic problem.     

On the transmission of external pressure fluctuations to the cerebrospinal fluid

A theory has been formulated to explain the manner in which external pressure fluctuations are transmitted to the cerebrospinal fluid (CSF). The theory is based upon a three-compartment model which consists of the cerebral ventricles, the basal cisterns and spinal subarachnoid space, and the cortical subarachnoid space. The external pressure disturbance is represented by a Fourier series summed over the frequency ω. The mathematical analysis leads to a time constant τ which depends upon the compliances of the spinal region and sources of external pressure fluctuations, the rate of CSF absorption and the rate of fluid transfer between compartments. For arterial pulsations where ωτ ? 1, the theory is in accord with the experimental observations that (i) the arterial and CSF pulse waves are nearly identical in shape, and (ii) the amplitude of the CSF pulse wave increases with intracranial pressure. Moreover, it predicts that the amplitude of the wave will be larger in the spinal region than in the ventricles. The theory also accounts for the observation of one per minute pulse waves observed in hydrocephalic patients with decreased absorption rates.     

Mechanisms to explain the reverse perivascular transport of solutes out of the brain

Experimental studies and observations in the human brain indicate that interstitial fluid and solutes, such as amyloid-beta (Abeta), are eliminated from grey matter of the brain along pericapillary and periarterial pathways. It is unclear, however, what constitutes the motive force for such transport within blood vessel walls, which is in the opposite direction to blood flow. In this paper the potential for global pressure differences to achieve such transport are considered. A mathematical model is constructed in order to test the hypothesis that perivascular drainage of interstitial fluid and solutes out of brain tissue is driven by pulsations of the blood vessel walls. Here it is assumed that drainage occurs through a thin layer between astrocytes and endothelial cells or between smooth muscle cells. The model suggests that, during each pulse cycle, there are periods when fluid and solutes are driven along perivascular spaces in the reverse direction to the flow of blood. It is shown that successful drainage may depend upon some attachment of solutes to the lining of the perivascular space, in order to produce a valve-like effect, although an alternative without this requirement is also postulated. Reduction in pulse amplitude, as in ageing cerebral vessels, would prolong the attachment time, encourage precipitation of Abeta peptides in vessel walls, and impair elimination of Abeta from the brain. These factors may play a role in the pathogenesis of cerebral amyloid angiopathy and in the accumulation of Abeta in the brain in Alzheimer's disease.     

Widespread enlarged perivascular spaces associated with dementia and focal brain dysfunction: case report

Background

Enlarged perivascular spaces (PVS) are common magnetic resonance imaging (MRI) findings, whereas widespread enlarged PVS are extremely rare. Although most patients with widespread enlarged PVS remain asymptomatic, some develop neurological dysfunctions; however, it remains unclear whether these are the consequence of widespread enlarged PVS.

Case presentation

A 64-year-old female patient developed consciousness disturbance, cognitive dysfunctions, fluent aphasia, agraphia, acalculia, and left-right disorientation after suffering from bronchopneumonia. Brain MRI revealed unusually widespread enlarged PVS predominantly in the left cerebral hemisphere. Following bronchopneumonia treatment, her cognitive dysfunction, fluent aphasia, agraphia, acalculia, and left-right disorientation persisted despite improvement of her general condition. Furthermore, the hypoperfusion area on single photon emission computed tomography and slow wave sites on electroencephalography were consistent with the location of enlarged PVS, indicating that severe enlarged PVS impaired focal brain functions.

Conclusions

This case suggested that widespread enlarged PVS could be a potential cause of neurological deficits. We propose that impaired perivascular circulation due to enlarged PVS might lead to focal brain dysfunction.

     

Modulation of human muscle spindle discharge by arterial pulsations--functional effects and consequences

Arterial pulsations are known to modulate muscle spindle firing; however, the physiological significance of such synchronised modulation has not been investigated. Unitary recordings were made from 75 human muscle spindle afferents innervating the pretibial muscles. The modulation of muscle spindle discharge by arterial pulsations was evaluated by R-wave triggered averaging and power spectral analysis. We describe various effects arterial pulsations may have on muscle spindle afferent discharge. Afferents could be "driven" by arterial pulsations, e.g., showing no other spontaneous activity than spikes generated with cardiac rhythmicity. Among afferents showing ongoing discharge that was not primarily related to cardiac rhythmicity we illustrate several mechanisms by which individual spikes may become phase-locked. However, in the majority of afferents the discharge rate was modulated by the pulse wave without spikes being phase locked. Then we assessed whether these influences changed in two physiological conditions in which a sustained increase in muscle sympathetic nerve activity was observed without activation of fusimotor neurones: a maximal inspiratory breath-hold, which causes a fall in systolic pressure, and acute muscle pain, which causes an increase in systolic pressure. The majority of primary muscle spindle afferents displayed pulse-wave modulation, but neither apnoea nor pain had any significant effect on the strength of this modulation, suggesting that the physiological noise injected by the arterial pulsations is robust and relatively insensitive to fluctuations in blood pressure. Within the afferent population there was a similar number of muscle spindles that were inhibited and that were excited by the arterial pulse wave, indicating that after signal integration at the population level, arterial pulsations of opposite polarity would cancel each other out. We speculate that with close-to-threshold stimuli the arterial pulsations may serve as an endogenous noise source that may synchronise the sporadic discharge within the afferent population and thus facilitate the detection of weak stimuli.     

RV instantaneous intraventricular diastolic pressure and velocity distributions in normal and volume overload awake dog disease models

Intraventricular diastolic right ventricular (RV) flow field dynamics were studied by functional imaging using three-dimensional (3D) real-time echocardiography with sonomicrometry and computational fluid dynamics in seven awake dogs at control with normal wall motion (NWM) and RV volume overload with diastolic paradoxical septal motion. Burgeoning flow cross section between inflow anulus and chamber walls induces a convective pressure rise, which represents a "convective deceleration load" (CDL). High spatiotemporal resolution dynamic pressure and velocity distributions of the intraventricular RV flow field revealed time-dependent, subtle interactions between intraventricular local acceleration and convective pressure gradients. During the E-wave upstroke, the total pressure gradient along intraventricular flow is the algebraic sum of a pressure decrease contributed by local acceleration and a pressure rise contributed by a convective deceleration that partially counterbalances the local acceleration gradient. This underlies the smallness of early diastolic intraventricular gradients. At peak volumetric inflow, local acceleration vanishes and the total adverse intraventricular gradient is convective. During the E-wave downstroke, the strongly adverse gradient embodies the streamwise pressure augmentations from both local and convective decelerations. It induces flow separation and large-scale vortical motions, stronger in NWM. Their dynamic corollaries on intraventricular pressure and velocity distributions were ascertained. In the NWM pattern, the strong ring-like vortex surrounding the central core encroaches on the area available for flow toward the apex. This results in higher linear velocities later in the downstroke of the E wave than at peak inflow rate. The augmentation of CDL by ventriculoannular disproportion may contribute to E wave and E-to-A ratio depression with chamber dilatation.     

Wave Propagation in a Viscous Fluid Contained in an Orthotropic Elastic Tube

The problem of pressure wave propagation through a viscous fluid contained in an orthotropic elastic tube is considered in connection with arterial blood flow. Solutions to the fluid flow and elasticity equations are obtained for the presence of a reflected wave. Numerical results are presented for both isotropic and orthotropic elastic tubes. In particular, the pressure pulse, flow rate, axial fluid velocity, and wall displacements are plotted vs. time at various stations along the ascending aorta of man. The results indicate an increase in the peak value of the pressure pulse and a decrease in the flow rate as the pulse propagates away from the heart. Finally, the velocity of wave propagation depends mainly on the tangential modulus of elasticity of the arterial wall, and anisotropy of the wall accounts in part for the reduction of longitudinal movements and an increase in the hydraulic resistance.     

A mathematical model of twin-twin transfusion syndrome with pulsatile arterial circulations

The twin-twin transfusion syndrome (TTTS) is a severe complication of monochorionic twin pregnancies caused by a net transfusion of blood from one twin (the donor) to the other (the recipient) through placental anastomoses. To examine the pathophysiology of TTTS evolving through clinical stages I to IV, we extended our mathematical model to include pulsating circulations propagating along the arterial tree as well as placental and cerebral vascular resistances, and arterial wall thickness and stiffness. The model demonstrates that abnormal umbilical arterial flow (TTTS stage III) in the donor twin results from increased placental resistance as well as reduced resistance in the cerebral arteries. In contrast, recipient twin abnormal umbilical arterial flow requires a significantly greater increase in placental resistance, resulting from the compressive effects of high amniotic fluid pressure. Thus simulated abnormalities of donor umbilical arterial pulsations occur in the donor more commonly and earlier than in the recipient. The "normal" staging sequence (I, II, III, IV) correlates with the presence of compensating placental anastomoses, constituting the majority of monochorionic twin placentas. However, TTTS stage III may occur before manifestations of stage II (lack of donor bladder filling), in our model correlating with severe TTTS from a single arteriovenous anastomosis, an infrequent occurring placental angioarchitecture. In conclusion, this mathematical model describes the onset and development of the four stages of TTTS, reproduces a variety of clinical manifestations, and may contribute to identifying the underlying pathophysiology of the staging sequence in TTTS.     

Assessment of Model Based (Input) Impedance,Pulse Wave Velocity,and Wave Reflection in the Asklepios Cohort

Objectives

Arterial stiffness and wave reflection parameters assessed from both invasive and non-invasive pressure and flow readings are used as surrogates for ventricular and vascular load. They have been reported to predict adverse cardiovascular events, but clinical assessment is laborious and may limit widespread use. This study aims to investigate measures of arterial stiffness and central hemodynamics provided by arterial tonometry alone and in combination with aortic root flows derived by echocardiography against surrogates derived by a mathematical pressure and flow model in a healthy middle-aged cohort.

Methods

Measurements of carotid artery tonometry and echocardiography were performed on 2226 ASKLEPIOS study participants and parameters of systemic hemodynamics, arterial stiffness and wave reflection based on pressure and flow were measured. In a second step, the analysis was repeated but echocardiography derived flows were substituted by flows provided by a novel mathematical model. This was followed by a quantitative method comparison.

Results

All investigated parameters showed a significant association between the methods. Overall agreement was acceptable for all parameters (mean differences: -0.0102 (0.033 SD) mmHg*s/ml for characteristic impedance, 0.36 (4.21 SD) mmHg for forward pressure amplitude, 2.26 (3.51 SD) mmHg for backward pressure amplitude and 0.717 (1.25 SD) m/s for pulse wave velocity).

Conclusion

The results indicate that the use of model-based surrogates in a healthy middle aged cohort is feasible and deserves further attention.     

Pressure and flow in the systemic arterial system

The dynamic characteristics of the proximal arterial system are studied by solving the nonlinear momentum and mass conservation equations for pressure and flow. The equations are solved for a model systemic arterial system that includes the aorta, common iliacs, and the internal and external iliac arteries. The model includes geometric and elastic taper of the aorta, nonlinearly elastic arteries, side flows, and a complex distal impedance. The model pressure wave shape, inlet and outlet impedance, wave travel, and apparent wave velocity compare favorably with the values measured on humans. Calculations indicate that: (i) reflections are the major factor determining the shape and distal amplification of the pressure wave in the arterial tree; (ii) although important in attenuating the proximal transmission of reflecting waves, geometric taper is not the major cause of the distal pressure wave amplification; (iii) the dicrotic wave is a result of peripheral reflection and is not due to the sudden change in flow at the end of systole; (iv) the elastic taper and nonlinearity of the wall elasticity are of minor significance in determining the flow and pressure profiles; and (v) in spite of numerous nonlinearities, the system behaves in a somewhat linear fashion for the lower frequency components.     

Fluid mechanics in the perivascular space

Perivascular space (PVS) within the brain is an important pathway for interstitial fluid (ISF) and solute transport. Fluid flowing in the PVS can affect these transport processes and has significant impacts on physiology. In this paper, we carry out a theoretical analysis to investigate the fluid mechanics in the PVS. With certain assumptions and approximations, we are able to find an analytical solution to the problem. We discuss the physical meanings of the solution and particularly examine the consequences of the induced fluid flow in the context of convection-enhanced delivery (CED). We conclude that peristaltic motions of the blood vessel walls can facilitate fluid and solute transport in the PVS.     

Epithelial water transport in a balanced gradient system.

The relationship between epithelial fluid transport, standing osmotic gradients, and standing hydrostatic pressure gradients has been investigated using a perturbation expansion of the governing equations. The assumptions used in the expansion are: (a) the volume of lateral intercellular space per unit volume of epithelium is small; (b) the membrane osmotic permeability is much larger than the solute permeability. We find that the rate of fluid reabsorption is set by the rate of active solute transport across lateral membranes. The fluid that crosses the lateral membranes and enters the intercellular cleft is driven longitudinally by small gradients in hydrostatic pressure. The small hydrostatic pressure in the intercellular space is capable of causing significant transmembrane fluid movement, however, the transmembrane effect is countered by the presence of a small standing osmotic gradient. Longitudinal hydrostatic and osmotic gradients balance such that their combined effect on transmembrane fluid flow is zero, whereas longitudinal flow is driven by the hydrostatic gradient. Because of this balance, standing gradients within intercellular clefts are effectively uncoupled from the rate of fluid reabsorption, which is driven by small, localized osmotic gradients within the cells. Water enters the cells across apical membranes and leaves across the lateral intercellular membranes. Fluid that enters the intercellular clefts can, in principle, exit either the basal end or be secreted from the apical end through tight junctions. Fluid flow through tight junctions is shown to depend on a dimensionless parameter, which scales the resistance to solute flow of the entire cleft relative to that of the junction. Estimates of the value of this parameter suggest that an electrically leaky epithelium may be effectively a tight epithelium in regard to fluid flow.     

The velocity of the arterial pulse wave: a viscous-fluid shock wave in an elastic tube

Background

The arterial pulse is a viscous-fluid shock wave that is initiated by blood ejected from the heart. This wave travels away from the heart at a speed termed the pulse wave velocity (PWV). The PWV increases during the course of a number of diseases, and this increase is often attributed to arterial stiffness. As the pulse wave approaches a point in an artery, the pressure rises as does the pressure gradient. This pressure gradient increases the rate of blood flow ahead of the wave. The rate of blood flow ahead of the wave decreases with distance because the pressure gradient also decreases with distance ahead of the wave. Consequently, the amount of blood per unit length in a segment of an artery increases ahead of the wave, and this increase stretches the wall of the artery. As a result, the tension in the wall increases, and this results in an increase in the pressure of blood in the artery.

Methods

An expression for the PWV is derived from an equation describing the flow-pressure coupling (FPC) for a pulse wave in an incompressible, viscous fluid in an elastic tube. The initial increase in force of the fluid in the tube is described by an increasing exponential function of time. The relationship between force gradient and fluid flow is approximated by an expression known to hold for a rigid tube.

Results

For large arteries, the PWV derived by this method agrees with the Korteweg-Moens equation for the PWV in a non-viscous fluid. For small arteries, the PWV is approximately proportional to the Korteweg-Moens velocity divided by the radius of the artery. The PWV in small arteries is also predicted to increase when the specific rate of increase in pressure as a function of time decreases. This rate decreases with increasing myocardial ischemia, suggesting an explanation for the observation that an increase in the PWV is a predictor of future myocardial infarction. The derivation of the equation for the PWV that has been used for more than fifty years is analyzed and shown to yield predictions that do not appear to be correct.

Conclusion

Contrary to the theory used for more than fifty years to predict the PWV, it speeds up as arteries become smaller and smaller. Furthermore, an increase in the PWV in some cases may be due to decreasing force of myocardial contraction rather than arterial stiffness.     

A thick walled viscoelastic model for the mechanics of arteries

A knowledge of the mechanics of arteries is of importance in the determination of vessel rheological properties and in the studies of blood flow and certain arterial diseases. Most existing arterial models treat only wave motions; however, other types of motion, in particular those associated with flow development and other end effects, occur in the vascular system. Thus, a model is needed which can be applied to a variety of possible types of motion.

An arterial model is described which includes the effects of thick walls, linear viscoelasticity, and wall tethering. The forms of the displacements and stresses are found independently of the exact form of the applied fluid stresses; thus, the results are applicable to a range of possible dynamical conditions. Displacements and stress states can then be found from experimental or theoretical knowledge of the blood pressure and flow. The results are applied to flow development and wave propagation regions in the arteries.     

Epinephrine induces tissue perfusion deficit in porcine endotoxin shock: evaluation by regional CO(2) content gradients and lactate-to-pyruvate ratios

Epinephrine is widely used as a vasoconstrictor or inotrope in shock, although it may typically induce or augment lactic acidosis. Ongoing debate addresses the question of whether hyperlactatemia per se is a sign of tissue perfusion deficit or aerobic glycolysis. We wanted to test the hypothesis that epinephrine has selective detrimental effects on visceral perfusion and metabolism. We performed rigorous regional venous blood gas analyses as well as intraperitoneal microdialysis. We used a mathematical model to calculate regional arteriovenous CO(2) content gradients and estimated the magnitude of the Haldane effect in a porcine model of prolonged hypotensive shock induced by endotoxin infusion (mean arterial blood pressure < 60 mmHg). Subsequently, vasopressors (epinephrine or norepinephrine) were administered and adjusted to maintain systemic mean arterial pressure > 70 mmHg for 4 h. Epinephrine caused systemic hyperlactatemia and acidosis. Importantly, both systemic and regional venous lactate-to-pyruvate ratios increased. Epinephrine was associated with decreasing portal blood flow despite apparently maintained total splanchnic blood flow. Epinephrine increased gastric venous-to-arterial Pco(2) gradients and CO(2) content gradients with decreasing magnitude of the Haldane effect, and the regional gastric respiratory quotient remained higher after epinephrine as opposed to norepinephrine infusion. In addition, epinephrine induced intraperitoneal lactate and glycerol release. We did not observe these adverse hemodynamic or metabolic changes related to norepinephrine with the same arterial pressure goal. We conclude that high CO(2) content gradients with decreasing magnitude of the Haldane effect pinpoint the most pronounced perfusion deficiency to the gastric wall when epinephrine, as opposed to norepinephrine, is used in experimental endotoxin shock.