A new lumped-parameter model of cerebrospinal hydrodynamics during the cardiac cycle in healthy volunteers

Relationship between the shape of intracranial pressure pulse waveform and computed tomography characteristics in patients after traumatic brain injury

BACKGROUND

Midline shift and mass lesions may occur with traumatic brain injury (TBI) and are associated with higher mortality and morbidity. The shape of intracranial pressure (ICP) pulse waveform reflects the state of cerebrospinal pressure-volume compensation which may be disturbed by brain injury. We aimed to investigate the link between ICP pulse shape and pathological computed tomography (CT) features.

METHODS

ICP recordings and CT scans from 130 TBI patients from the CENTER-TBI high-resolution sub-study were analyzed retrospectively. Midline shift, lesion volume, Marshall and Rotterdam scores were assessed in the first CT scan after admission and compared with indices derived from the first 24 h of ICP recording: mean ICP, pulse amplitude of ICP (AmpICP) and pulse shape index (PSI). A neural network model was applied to automatically group ICP pulses into four classes ranging from 1 (normal) to 4 (pathological), with PSI calculated as the weighted sum of class numbers. The relationship between each metric and CT measures was assessed using Mann-Whitney U test (groups with midline shift > 5 mm or lesions > 25 cm3 present/absent) and the Spearman correlation coefficient. Performance of ICP-derived metrics in identifying patients with pathological CT findings was assessed using the area under the receiver operating characteristic curve (AUC).

RESULTS

PSI was significantly higher in patients with mass lesions (with lesions: 2.4 [1.9-3.1] vs. 1.8 [1.1-2.3] in those without; p << 0.001) and those with midline shift (2.5 [1.9-3.4] vs. 1.8 [1.2-2.4]; p < 0.001), whereas mean ICP and AmpICP were comparable. PSI was significantly correlated with the extent of midline shift, total lesion volume and the Marshall and Rotterdam scores. PSI showed AUCs > 0.7 in classification of patients as presenting pathological CT features compared to AUCs ≤ 0.6 for mean ICP and AmpICP.

CONCLUSIONS

ICP pulse shape reflects the reduction in cerebrospinal compensatory reserve related to space-occupying lesions despite comparable mean ICP and AmpICP levels. Future validation of PSI is necessary to explore its association with volume imbalance in the intracranial space and a potential complementary role to the existing monitoring strategies.

Analysis of intracranial pressure pulse waveform in studies on cerebrospinal compliance: a narrative review

Continuous monitoring of mean intracranial pressure (ICP) has been an essential part of neurocritical care for more than half a century. Cerebrospinal pressure-volume compensation, i.e. the ability of the cerebrospinal system to buffer changes in volume without substantial increases in ICP, is considered an important factor in preventing adverse effects on the patient's condition that are associated with ICP elevation. However, existing assessment methods are poorly suited to the management of brain injured patients as they require external manipulation of intracranial volume. In the 1980s, studies suggested that spontaneous short-term variations in the ICP signal over a single cardiac cycle, called the ICP pulse waveform, may provide information on cerebrospinal compensatory reserve. In this review we discuss the approaches that have been proposed so far to derive this information, from pulse amplitude estimation and spectral techniques to most recent advances in morphological analysis based on artificial intelligence solutions. Each method is presented with focus on its clinical significance and the potential for application in standard clinical practice. Finally, we highlight the missing links that need to be addressed in future studies in order for ICP pulse waveform analysis to achieve widespread use in the neurocritical care setting.

Impact of continuous-flow mechanical circulatory support on cerebrospinal fluid motility

BACKGROUND

Mechanical circulatory support (MCS), including ventricular assist devices (VADs), have emerged as promising therapeutic alternatives for end-stage congestive heart failure (CHF). The latest generation of these devices are continuous flow (CF) blood pumps. While there have been demonstrated benefits to patient outcomes due to CF-MCS, there continue to be significant clinical challenges. Research to-date has concentrated on mitigating thromboembolic risk (stroke), while the downstream impact of CF-MCS on the cerebrospinal fluid (CSF) flow has not been well investigated. Disturbances in the CSF pressure and flow patterns are known to be associated with neurologic impairment and diseased states. Thus, here we seek to develop an understanding of the pathophysiologic consequences of CF-MCS on CSF dynamics.

METHODS

We built and validated a computational framework using lumped parameter modeling of cardiovascular, cerebrovascular physics, CSF dynamics, and autoregulation. A sensitivity analysis was performed to confirm robustness of the modeling framework. Then, we characterized the impact of CF-MCS on the CSF and investigated cardiovascular conditions of healthy and end-stage heart failure.

RESULTS

Modeling results demonstrated appropriate hemodynamics and indicated that CSF pressure depends on blood flow pulsatility more than CSF flow. An acute equilibrium between CSF production and absorption was observed in the CF-MCS case, characterized by CSF pressure remaining elevated, and CSF flow rates remaining below healthy, but higher than CHF states.

CONCLUSION

This research has advanced our understanding of the impact of CF-MCS on CSF dynamics and cerebral hemodynamics.

Compliance of the cerebrospinal space: comparison of three methods

BACKGROUND

Cerebrospinal compliance describes the ability of the cerebrospinal space to buffer changes in volume. Diminished compliance is associated with increased risk of potentially threatening increases in intracranial pressure (ICP) when changes in cerebrospinal volume occur. However, despite various methods of estimation proposed so far, compliance is seldom used in clinical practice. This study aimed to compare three measures of cerebrospinal compliance.

METHODS

ICP recordings from 36 normal-pressure hydrocephalus patients who underwent infusion tests with parallel recording of transcranial Doppler blood flow velocity were retrospectively analysed. Three methods were used to calculate compliance estimates during changes in the mean ICP induced by infusion of fluid into the cerebrospinal fluid space: (a) based on Marmarou's model of cerebrospinal fluid dynamics (C_CSF), (b) based on the evaluation of changes in cerebral arterial blood volume (C_CaBV), and (c) based on the amplitudes of peaks P1 and P2 of ICP pulse waveform (C_P1/P2).

RESULTS

Increase in ICP caused a significant decrease in all compliance estimates (p < 0.0001). Time courses of compliance estimators were strongly positively correlated with each other (group-averaged Spearman correlation coefficients: 0.94 [0.88-0.97] for C_CSF vs. C_CaBV, 0.77 [0.63-0.91] for C_CSF vs. C_P1/P2, and 0.68 [0.48-0.91] for C_CaBV vs. C_P1/P2).

CONCLUSIONS

Indirect methods, C_CaBV and C_P1/P2, allow for the assessment of relative changes in cerebrospinal compliance and produce results exhibiting good correlation with the direct method of volumetric manipulation. This opens the possibility of monitoring relative changes in compliance continuously.

Measuring intracranial pressure by invasive, less invasive or non-invasive means: limitations and avenues for improvement

Sixty years have passed since neurosurgeon Nils Lundberg presented his thesis about intracranial pressure (ICP) monitoring, which represents a milestone for its clinical introduction. Monitoring of ICP has since become a clinical routine worldwide, and today represents a cornerstone in surveillance of patients with acute brain injury or disease, and a diagnostic of individuals with chronic neurological disease. There is, however, controversy regarding indications, clinical usefulness and the clinical role of the various ICP scores. In this paper, we critically review limitations and weaknesses with the current ICP measurement approaches for invasive, less invasive and non-invasive ICP monitoring. While risk related to the invasiveness of ICP monitoring is extensively covered in the literature, we highlight other limitations in current ICP measurement technologies, including limited ICP source signal quality control, shifts and drifts in zero pressure reference level, affecting mean ICP scores and mean ICP-derived indices. Control of the quality of the ICP source signal is particularly important for non-invasive and less invasive ICP measurements. We conclude that we need more focus on mitigation of the current limitations of today's ICP modalities if we are to improve the clinical utility of ICP monitoring.

Validating faster DENSE measurements of cardiac-induced brain tissue expansion as a potential tool for investigating cerebral microvascular pulsations

Displacement Encoding with Stimulated Echoes (DENSE) has recently shown potential for measuring cardiac-induced cerebral volumetric strain in the human brain. As such, it may provide a powerful tool for investigating the cerebral small vessels. However, further development and validation are necessary. This study aims, first, to validate a retrospectively-gated implementation of the DENSE method for assessing brain tissue pulsations as a physiological marker, and second, to use the acquired measurements to explore intracranial volume dynamics. We acquired repeated measurements of cerebral volumetric strain in 8 healthy subjects, and internally validated these measurements by comparing them to spinal CSF stroke volumes obtained in the same scan session. Peak volumetric strain was found to be highly repeatable between scan sessions. First/second measured peak volumetric strains were: (6.4 ​± ​1.7)x10^-4/(6.7 ​± ​1.6)x10^-4 for whole brain, (9.5 ​± ​2.5)x10^-4/(9.6 ​± ​2.4)x10^-4 for grey matter, and (4.4 ​± ​1.7)x10^-4/(4.1 ​± ​0.8)x10^-4 for white matter. Grey matter showed significantly higher peak strain (p ​< ​0.001) and earlier time-to-peak strain (p ​< ​0.02) than white matter. An approximately linear relationship was found between CSF and brain tissue volume pulsations over the cardiac cycle (mean slope and R² of 0.88 ​± ​0.23 and 0.89 ​± ​0.07, respectively). The close similarity between CSF and brain tissue volume pulsations implies limited contributions from large intracranial vessel pulsations, providing further evidence for venous compression as an additional mechanism for maintaining stable intracranial pressures over the cardiac cycle. Cerebral pulsatility showed consistent inter-subject peak values in healthy subjects, and was strongly correlated to CSF stroke volumes. These results strengthen the potential of brain tissue volumetric strain as a means for investigating the intracranial dynamics of the ageing brain in normal or diseased states.

Validation of a mathematical model for understanding intracranial pressure curve morphology

The physiology underlying the intracranial pressure (ICP) curve morphology is not fully understood. Recent research has suggested that the morphology could be dependent on arterial cerebral inflow and the physiological and pathophysiological properties of the intracranial cavity. If understood, the ICP curve could provide information about the patient’s cerebrovascular state important in individualizing treatment in neuro intensive care patients. A mathematical model based on known physiological properties of the intracranial compartment was created. Clinical measurements from ten neuro intensive care patients in whom intracranial arterial blood inflow, venous blood outflow and cerebrospinal fluid flow over the foramen magnum had been measured with phase contrast MRI, concomitant with ICP measurements were used to validate the model. In nine patients the mathematical model was able to create an ICP curve mimicking the measured by using arterial intracranial inflow and adjusting physiological parameters of the model. The venous outflow and cerebrospinal fluid (CSF) flow over the foramen magnum predicted by the model were within physiologically reasonable limits and in most cases followed the MRI measured values in close adjunct. The presented model could produce an ICP curve in close resemblance of the in vivo measured curves. This strengthens the hypothesis that the ICP curve is shaped by the arterial intracranial inflow and the physiological properties of the intracranial cavity.

Predicting the Aqueductal Cerebrospinal Fluid Pulse: A Statistical Approach

The cerebrospinal fluid (CSF) pulse in the Aqueduct of Sylvius (aCSF pulse) is often used to evaluate structural changes in the brain. Here we present a novel application of the general linear model (GLM) to predict the motion of the aCSF pulse. MR venography was performed on 13 healthy adults (9 female and 4 males—mean age = 33.2 years). Flow data was acquired from the arterial, venous and CSF vessels in the neck (C2/C3 level) and from the AoS. Regression analysis was undertaken to predict the motion of the aCSF pulse using the cervical flow rates as predictor variables. The relative contribution of these variables to predicting aCSF flow rate was assessed using a relative weights method, coupled with an ANOVA. Analysis revealed that the aCSF pulse could be accurately predicted (mean (SD) adjusted r2 = 0.794 (0.184)) using the GLM (p < 0.01). Venous flow rate in the neck was the strongest predictor of aCSF pulse (p = 0.001). In healthy individuals, the motion of the aCSF pulse can be predicted using the GLM. This indicates that the intracranial fluidic system has broadly linear characteristics. Venous flow in the neck is the strongest predictor of the aCSF pulse.

Cerebral blood flow augmentation using a cardiac-gated intracranial pulsating balloon pump in a swine model of elevated ICP

OBJECTIVE

Augmenting brain perfusion or reducing intracranial pressure (ICP) dose is the end target of many therapies in the neuro-critical care unit. Many present therapies rely on aggressive systemic interventions that may lead to untoward effects. Previous studies have used a cardiac-gated intracranial balloon pump (ICBP) to model hydrocephalus or to flatten the ICP waveform. The authors sought to sought to optimize ICBP activation parameters to improve cerebral physiological parameters in a swine model of raised ICP.

METHODS

The authors developed a cardiac-gated ICBP in which the volume, timing, and duty cycle (time relative to a single cardiac cycle) of balloon inflation could be altered. They studied the ICBP in a swine model of elevated ICP attained by continuous intracranial fluid infusion with continuous monitoring of systemic and cerebral physiological parameters, and defined two specific protocols of ICBP activation.

RESULTS

Eleven swine were studied, 3 of which were studied to define the optimal timing, volume, and duty cycle of balloon inflation. Eight swine were studied with two defined protocols at baseline and with ICP gradually raised to a mean of 30.5 mm Hg. ICBP activation caused a consistent modification of the ICP waveform. Two ICBP activation protocols were used. Balloon activation protocol A led to a consistent elevation in cerebral blood flow (8%-25% above baseline, p < 0.00001). Protocol B resulted in a modest reduction of ICP over time (8%-11%, p < 0.0001) at all ICP levels. Neither protocol significantly affected systemic physiological parameters.

CONCLUSIONS

The preliminary results indicate that optimized protocols of ICBP activation may have beneficial effects on cerebral physiological parameters, with minimal effect on systemic parameters. Further studies are warranted to explore whether ICBP protocols may be of clinical benefit in patients with brain injuries with increased ICP.

Slow sinusoidal tilt movements demonstrate the contribution to orthostatic tolerance of cerebrospinal fluid movement to and from the spinal dural space

Standing up elicits a host of cardiovascular changes which all affect the cerebral circulation. Lowered mean arterial blood pressure (ABP) at brain level, change in the cerebral venous outflow path, lowered end-tidal PCO2 (PET CO2 ), and intracranial pressure (ICP) modify cerebral blood flow (CBF). The question we undertook to answer is whether gravity-induced blood pressure (BP) changes are compensated in CBF with the same dynamics as are spontaneous or induced ABP changes in a stable position. Twenty-two healthy subjects (18/4 m/f, 40 ± 8 years) were subjected to 30° and 70° head-up tilt (HUT) and sinusoidal tilts (SinTilt, 0°↨60° around 30° at 2.5-10 tilts/min). Additionally, at those three tilt levels, they performed paced breathing at 6-15 breaths/min to induce larger than spontaneous cardiovascular oscillations. We measured continuous finger BP and cerebral blood flow velocity (CBFv) in the middle cerebral artery by transcranial Doppler to compute transfer functions (TFs) from ABP- to CBFv oscillations. SinTilt induces the largest ABP oscillations at brain level with CBFv gains strikingly lower than for paced breathing or spontaneous variations. This would imply better autoregulation for dynamic gravitational changes. We demonstrate in a mathematical model that this difference is explained by ICP changes due to movement of cerebrospinal fluid (CSF) into and out of the spinal dural sack. Dynamic cerebrovascular autoregulation seems insensitive to how BP oscillations originate if the effect of ICP is factored in. CSF-movement in-and-out of the spinal dural space contributes importantly to orthostatic tolerance by its effect on cerebral perfusion pressure.

Cerebral venous collaterals: A new fort for fighting ischemic stroke?

Stroke therapy has entered a new era highlighted by the use of endovascular therapy in addition to intravenous thrombolysis. However, the efficacy of current therapeutic regimens might be reduced by their associated adverse events. For example, over-reperfusion and futile recanalization may lead to large infarct, brain swelling, hemorrhagic complication and neurological deterioration. The traditional pathophysiological understanding on ischemic stroke can hardly address these occurrences. Accumulating evidence suggests that a functional cerebral venous drainage, the major blood reservoir and drainage system in brain, may be as critical as arterial infusion for stroke evolution and clinical sequelae. Further exploration of the multi-faceted function of cerebral venous system may add new implications for stroke outcome prediction and future therapeutic decision-making. In this review, we emphasize the anatomical and functional characteristics of the cerebral venous system and illustrate its necessity in facilitating the arterial infusion and maintaining the cerebral perfusion in the pathological stroke content. We then summarize the recent critical clinical studies that underscore the associations between cerebral venous collateral and outcome of ischemic stroke with advanced imaging techniques. A novel three-level venous system classification is proposed to demonstrate the distinct characteristics of venous collaterals in the setting of ischemic stroke. Finally, we discuss the current directions for assessment of cerebral venous collaterals and provide future challenges and opportunities for therapeutic strategies in the light of these new concepts.

An anatomy-based lumped parameter model of cerebrospinal venous circulation: can an extracranial anatomical change impact intracranial hemodynamics?

BACKGROUND

The relationship between extracranial venous system abnormalities and central nervous system disorders has been recently theorized. In this paper we delve into this hypothesis by modeling the venous drainage in brain and spinal column areas and simulating the intracranial flow changes due to extracranial morphological stenoses.

METHODS

A lumped parameter model of the cerebro-spinal venous drainage was created based on anatomical knowledge and vessels diameters and lengths taken from literature. Each vein was modeled as a hydraulic resistance, calculated through Poiseuille's law. The inputs of the model were arterial flow rates of the intracranial, vertebral and lumbar districts. The effects of the obstruction of the main venous outflows were simulated. A database comprising 112 Multiple Sclerosis patients (Male/Female = 42/70; median age ± standard deviation = 43.7 ± 10.5 years) was retrospectively analyzed.

RESULTS

The flow rate of the main veins estimated with the model was similar to the measures of 21 healthy controls (Male/Female = 10/11; mean age ± standard deviation = 31 ± 11 years), obtained with a 1.5 T Magnetic Resonance scanner. The intracranial reflux topography predicted with the model in cases of internal jugular vein diameter reduction was similar to those observed in the patients with internal jugular vein obstacles.

CONCLUSIONS

The proposed model can predict physiological and pathological behaviors with good fidelity. Despite the simplifications introduced in cerebrospinal venous circulation modeling, the key anatomical feature of the lumped parameter model allowed for a detailed analysis of the consequences of extracranial venous impairments on intracranial pressure and hemodynamics.

Venous hemodynamics in neurological disorders: an analytical review with hydrodynamic analysis

Venous abnormalities contribute to the pathophysiology of several neurological conditions. This paper reviews the literature regarding venous abnormalities in multiple sclerosis (MS), leukoaraiosis, and normal-pressure hydrocephalus (NPH). The review is supplemented with hydrodynamic analysis to assess the effects on cerebrospinal fluid (CSF) dynamics and cerebral blood flow (CBF) of venous hypertension in general, and chronic cerebrospinal venous insufficiency (CCSVI) in particular.CCSVI-like venous anomalies seem unlikely to account for reduced CBF in patients with MS, thus other mechanisms must be at work, which increase the hydraulic resistance of the cerebral vascular bed in MS. Similarly, hydrodynamic changes appear to be responsible for reduced CBF in leukoaraiosis. The hydrodynamic properties of the periventricular veins make these vessels particularly vulnerable to ischemia and plaque formation.Venous hypertension in the dural sinuses can alter intracranial compliance. Consequently, venous hypertension may change the CSF dynamics, affecting the intracranial windkessel mechanism. MS and NPH appear to share some similar characteristics, with both conditions exhibiting increased CSF pulsatility in the aqueduct of Sylvius.CCSVI appears to be a real phenomenon associated with MS, which causes venous hypertension in the dural sinuses. However, the role of CCSVI in the pathophysiology of MS remains unclear.

Cerebral venous outflow resistance and interpretation of cervical plethysmography data with respect to the diagnosis of chronic cerebrospinal venous insufficiency

OBJECTIVE

While chronic cerebrospinal venous insufficiency (CCSVI) can be characterized using cervical plethysmography, much remains unknown about the haemodynamics associated with this procedure. The aim of the study was therefore to gain a deeper understanding of the observed haemodynamics.

METHOD

Forty healthy controls and 44 CCSVI patients underwent cervical plethysmography, which involved placing a strain-gauge collar around their necks and tipping them from the upright (90(o)) to supine position (0(o)) in a chair. Once stabilized, they were returned to the upright position, allowing blood to drain from the neck. A mathematical model was used to calculate the hydraulic resistance of the extracranial venous system for each subject in the study.

RESULTS

The mean hydraulic resistance of the extracranial venous system was 10.28 (standard deviation [SD] 5.14) mmHg.s/mL in the healthy controls and 16.81 (SD 9.22) in the CCSVI patients (P < 0.001).

CONCLUSIONS

The haemodynamics of the extracranial venous system are greatly altered in CCSVI patients.

Dynamics of hydrocephalus: a physical approach

As brain ventricles lose their ability to regulate the cerebrospinal fluid (CSF) pressure, serious brain conditions collectively named hydrocephalus can appear. By modelling ventricular dynamics with the laws of physics, dynamical instabilities are evidenced, caused by either CSF transport dysregulations or abnormal properties of the elasticity of the ependyma. We show that these instabilities would lead, in most cases, to dilation of the ventricles, establishing a close connection to hydrocephalus, or in some other cases to a ventricular contraction as observed in the slit ventricle syndrome. Signs seem to indicate the possibility of phase transitions occurring as a result of these instabilities, which might have important clinical consequences, such as the inability to recover a healthy state. Even so, our dynamical approach could allow the development of a unified view of these complex intracranial conditions along with a classification that might be clinically relevant.

A one-dimensional model of the spinal cerebrospinal-fluid compartment

Modeling of the cerebrospinal fluid (CSF) system in the spine is strongly motivated by the need to understand the origins of pathological conditions such as the emergence and growth of fluid-filled cysts in the spinal cord. In this study, a one-dimensional (1D) approximation for the flow in elastic conduits was used to formulate a model of the spinal CSF compartment. The modeling was based around a coaxial geometry in which the inner elastic cylinder represented the spinal cord, middle elastic tube represented the dura, and the outermost tube represented the vertebral column. The fluid-filled annuli between the cord and dura, and the dura and vertebral column, represented the subarachnoid and epidural spaces, respectively. The system of governing equations was constructed by applying a 1D form of mass and momentum conservation to all segments of the model. The developed 1D model was used to simulate CSF pulse excited by pressure disturbances in the subarachnoid and epidural spaces. The results were compared to those obtained from an equivalent two-dimensional finite element (FE) model which was implemented using a commercial software package. The analysis of linearized governing equations revealed the existence of three types of waves, of which the two slower waves can be clearly related to the wave modes identified in previous similar studies. The third, much faster, wave emanates directly from the vertebral column and has little effect on the deformation of the spinal cord. The results obtained from the 1D model and its FE counterpart were found to be in good general agreement even when sharp spatial gradients of the spinal cord stiffness were included; both models predicted large radial displacements of the cord at the location of an initial cyst. This study suggests that 1D modeling, which is computationally inexpensive and amenable to coupling with the models of the cranial CSF system, should be a useful approach for the analysis of some aspects of the CSF dynamics in the spine. The simulation of the CSF pulse excited by a pressure disturbance in the epidural space, points to the possibility that regions of the spinal cord with abnormally low stiffness may be prone to experiencing large strains due to coughing and sneezing.

Changes of circulatory-metabolic indices and skull biomechanics with brain activity during aging

The cerebral blood flow values used in experimental and clinical investigations as the informative criteria for brain blood supply are often misleading. The correlation between the cerebral blood supply and brain function is not proven in all cases. An increase of brain activity is known to be accompanied by a rise of blood flow in activated regions, while a decreased activity results in a decreased blood flow. This demonstrates the close correlation between the brain blood supply and its activity. Such a correlation had not been noted in the age-dependent decrease of cerebral blood flow, suggesting the existence of special age-related mechanisms that develop with age to maintain brain metabolism. The biomechanical properties are of special significance as predicted in the early 20th century. Only recently were they validated by the simultaneous recording of Transcranial Dopplerogram and Rheoencephalogram with in-depth analysis focused on single cardiac cycles. Functioning of the intracranial blood and cerebrospinal fluid dynamics was integrated with a special physiological test "Prognosis-2" to measure brain cognitive function. Correlation was demonstrated with the circulatory-metabolic state of brain activity, especially in people with changing cognitive function. The data supports a conceptual model of adequate circulatory-metabolic supply of brain activity, showing the functional unity, which follows from integration of the mentioned systems.

Cerebral hydrodynamics are at a most a third order system

The human body employs a sophisticated windkessel mechanism to dampen the arterial pulse entering the brain, thus ensuring the smooth flow of blood through the cerebral capillary bed. The energy from the arterial pulse is transferred to the cerebrospinal fluid (CSF), which pulses backwards and forwards across the foramen magnum. The dynamics associated with this system are complex and poorly understood. In an attempt to better understand the physiology, a number of researchers have constructed electrical analogue circuits to simulate the hydrodynamic behaviour of the brain. These generally consist of several low-pass filters. While such models have great potential, to date, they have met with only limited success. We suspect that this is in part due to a failure to identify the order of the model required to successfully capture the hydrodynamics of the brain. Here, we advance the hypothesis that the cerebral hydrodynamic system is at most a third order system, using evidence collected from the spectral eigen-system of the arterial, venous and CSF flows. Using singular spectrum analysis we computed the singular vectors for the measured arterial, venous and CSF flows from an individual. This revealed that the first singular vector contributes 67% of the observed variance; the first plus the second singular vectors contribute 96% of the variance; and sum of the first three singular vectors contribute more than 99.5% of the observed variance.

A lumped-parameter model of the cerebrospinal system for investigating arterial-driven flow in posttraumatic syringomyelia

Fluid transport in syringomyelia has remained enigmatic ever since the disease was first identified some three centuries ago. However, accumulating evidence in the last decade from animal studies implicates arterial pulsations in syrinx formation. In particular, it has been suggested that a phase difference between the pressure pulse in the spinal subarachnoid space and the perivascular spaces, due to a pathologically disturbed cerebrospinal fluid (CSF) or blood supply, could result in a net influx of CSF into the spinal cord (SC). A lumped-parameter model is developed of the cerebrospinal system to investigate this conjecture. It is found that although this phase-lag mechanism may operate, it requires the SC to have an intrinsic storage capacity due to the collapsibility of the contained venous reservoir. This net flux is associated with a higher mean pressure in the SC than the SSS which is maintained in the periodic steady state. According to our simulations the mechanical perturbations of arachnoiditis exacerbate the phase-lag effect, which may be partially alleviated by the presence of a posttraumatic syrinx and more completely by a syringo-subarachnoid shunt.

Noninvasive intracranial compliance from MRI-based measurements of transcranial blood and CSF flows: indirect versus direct approach

Intracranial compliance (ICC) determines the ability of the intracranial compartment to accommodate an increase in volume without a large increase in intracranial pressure (ICP). The clinical utilization of ICC is limited by the invasiveness of current measurement. Several investigators attempted to estimate ICC noninvasively, from magnetic resonance imaging (MRI) measurements of cerebral blood and cerebral spinal fluid flows, either using indirect measures of ICC or directly by measuring the ratio of the changes in intracranial volume and pressure during the cardiac cycle. The indirect measures include the phase lag between the cerebrospinal fluid (CSF) and its driving force, either arterial inflow or net transcranial blood flow. This study compares the sensitivity of phase-based and amplitude-based measures of ICC to changes in ICC. In vivo volumetric blood and CSF flows measured by MRI phase contrast from healthy volunteers and from patients with elevated ICP were used for the comparison. An RLC circuit model of the craniospinal system was utilized to simulate the effect of a change in ICC on the CSF flow waveform. The simulations demonstrated that amplitude-based measures of ICC are considerably more sensitive than phase-based measures, and among the amplitude-based measures, the ICC index provides the most reliable estimate of ICC.