Effect of tonsillar herniation on cyclic CSF flow studied with computational flow analysis

A computational fluid dynamics study to assess the impact of coughing on cerebrospinal fluid dynamics in Chiari type 1 malformation

Chiari type 1 malformation is a neurological disorder characterized by an obstruction of the cerebrospinal fluid (CSF) circulation between the brain (intracranial) and spinal cord (spinal) compartments. Actions such as coughing might evoke spinal cord complications in patients with Chiari type 1 malformation, but the underlying mechanisms are not well understood. More insight into the impact of the obstruction on local and overall CSF dynamics can help reveal these mechanisms. Therefore, our previously developed computational fluid dynamics framework was used to establish a subject-specific model of the intracranial and upper spinal CSF space of a healthy control. In this model, we emulated a single cough and introduced porous zones to model a posterior (OBS-1), mild (OBS-2), and severe posterior-anterior (OBS-3) obstruction. OBS-1 and OBS-2 induced minor changes to the overall CSF pressures, while OBS-3 caused significantly larger changes with a decoupling between the intracranial and spinal compartment. Coughing led to a peak in overall CSF pressure. During this peak, pressure differences between the lateral ventricles and the spinal compartment were locally amplified for all degrees of obstruction. These results emphasize the effects of coughing and indicate that severe levels of obstruction lead to distinct changes in intracranial pressure.

Correlation of a new hydrodynamic index with other effective indexes in Chiari I malformation patients with different associations

This study aimed to find a new CSF hydrodynamic index to assess Chiari type I malformation (CM-I) patients’ conditions and examine the relationship of this new index with morphometric and volumetric changes in these patients and their clinical symptoms. To this end, 58 CM-I patients in four groups and 20 healthy subjects underwent PC-MRI. Ten morphometric and three volumetric parameters were calculated. The CSF hydrodynamic parameters were also analyzed through computational fluid dynamic (CFD) simulation. The maximum CSF pressure was identified as a new hydrodynamic parameter to assess the CM-I patients’ conditions. This parameter was similar in patients with the same symptoms regardless of the group to which they belonged. The result showed a weak correlation between the maximum CSF pressure and the morphometric parameters in the patients. Among the volumetric parameters, PCF volume had the highest correlation with the maximum CSF pressure, which its value being higher in patients with CM-I/SM/scoliosis (R² = 65.6%, P = 0.0022) than in the other patients. PCF volume was the more relevant volumetric parameter to assess the patients’ symptoms. The values of PCF volume were greater in patients that headache symptom was more obvious than other symptoms, as compared to the other patients.

Nonreflecting Boundary Conditions for a CSF Model of Fourth Ventricle: Spinal SAS Dynamics

In this paper, we introduce a one-dimensional model for analyzing the cerebrospinal fluid dynamics within the fourth ventricle and the spinal subarachnoid space (SSAS). The model has been derived starting from an original model of Linninger et al. and from the detailed mathematical analysis of two different reformulations. We show the steps of the modelization and the rigorous analysis of the first-order nonlinear hyperbolic system of equations which rules the new CSF model, whose conservative-law form and characteristic form are required for the boundary conditions treatment. By assuming sub-critical flows, for the particular dynamics we are dealing with, the most desirable option is to employ the nonreflecting boundary conditions, that allow the simple wave associated with the outgoing characteristic to exit the computational domain with no reflections. Finally, we carry out some numerical simulations related to different cerebral physiological conditions.

Non-invasive MRI quantification of cerebrospinal fluid dynamics in amyotrophic lateral sclerosis patients

Background

Developing novel therapeutic agents to treat amyotrophic lateral sclerosis (ALS) has been difficult due to multifactorial pathophysiologic processes at work. Intrathecal drug administration shows promise due to close proximity of cerebrospinal fluid (CSF) to affected tissues. Development of effective intrathecal pharmaceuticals will rely on accurate models of how drugs are dispersed in the CSF. Therefore, a method to quantify these dynamics and a characterization of differences across disease states is needed.

Methods

Complete intrathecal 3D CSF geometry and CSF flow velocities at six axial locations in the spinal canal were collected by T2-weighted and phase-contrast MRI, respectively. Scans were completed for eight people with ALS and ten healthy controls. Manual segmentation of the spinal subarachnoid space was performed and coupled with an interpolated model of CSF flow within the spinal canal. Geometric and hydrodynamic parameters were then generated at 1 mm slice intervals along the entire spine. Temporal analysis of the waveform spectral content and feature points was also completed.

Results

Comparison of ALS and control groups revealed a reduction in CSF flow magnitude and increased flow propagation velocities in the ALS cohort. Other differences in spectral harmonic content and geometric comparisons may support an overall decrease in intrathecal compliance in the ALS group. Notably, there was a high degree of variability between cases, with one ALS patient displaying nearly zero CSF flow along the entire spinal canal.

Conclusion

While our sample size limits statistical confidence about the differences observed in this study, it was possible to measure and quantify inter-individual and cohort variability in a non-invasive manner. Our study also shows the potential for MRI based measurements of CSF geometry and flow to provide information about  the hydrodynamic environment of the spinal subarachnoid space. These dynamics may be studied further to understand the behavior of CSF solute transport in healthy and diseased states.

Anthropomorphic Model of Intrathecal Cerebrospinal Fluid Dynamics Within the Spinal Subarachnoid Space: Spinal Cord Nerve Roots Increase Steady-Streaming

Cerebrospinal fluid (CSF) dynamics are thought to play a vital role in central nervous system (CNS) physiology. The objective of this study was to investigate the impact of spinal cord (SC) nerve roots (NR) on CSF dynamics. A subject-specific computational fluid dynamics (CFD) model of the complete spinal subarachnoid space (SSS) with and without anatomically realistic NR and nonuniform moving dura wall deformation was constructed. This CFD model allowed detailed investigation of the impact of NR on CSF velocities that is not possible in vivo using magnetic resonance imaging (MRI) or other noninvasive imaging methods. Results showed that NR altered CSF dynamics in terms of velocity field, steady-streaming, and vortical structures. Vortices occurred in the cervical spine around NR during CSF flow reversal. The magnitude of steady-streaming CSF flow increased with NR, in particular within the cervical spine. This increase was located axially upstream and downstream of NR due to the interface of adjacent vortices that formed around NR.

Minimally invasive posterior fossa decompression with duraplasty in Chiari malformation type I with and without syringomyelia

Background:

Posterior fossa decompression (PFD), with and without duraplasty, represents a valid treatment in Chiari malformation Type I (CM-I) with and without syringomyelia. Despite a large amount of series reported in literature, several controversies exist regarding the optimal surgical approach yet. In this study, we report our experience in the treatment of CM-I, with and without syringomyelia, highlighting how the application of some technical refinements could lead to a good outcome and a lesser rate of complications.

Methods:

Twenty-six patients with CM-I, with and without syringomyelia, underwent PFD through a 3 cm × 3 cm craniectomy with the removal of the most median third of the posterior arch of C1 and duraplasty. Signs and symptoms included sensory deficits, motor deficits, neck pain, paresthesias, headache, dizziness, lower cranial nerve deficits, and urinary incontinence. Postoperative magnetic resonance (MR) was performed in all patients.

Results:

Signs and symptoms improved in 76.9% of cases. Postoperative MR revealed a repositioning of cerebellar tonsils and the restoration of cerebrospinal fluid circulation. In our experience, the rate of complication was 23% (fistula, worsening of symptoms, and respiratory impairment).

Conclusion:

PFD through a 3 cm × 3 cm craniectomy and the removal of the most median third of posterior arch of C1 with duraplasty represents a feasible and valid surgical alternative to treat patients with CM-I, with and without syringomyelia, achieving a good outcome and a low rate of complications.

Relationship of Morphologic Changes in the Brain and Spinal Cord and Disease Symptoms with Cerebrospinal Fluid Hydrodynamic Changes in Patients with Chiari Malformation Type I

BACKGROUND

Morphometric analysis or examination of symptoms in patients with Chiari malformation type I (CM-I) with various associations does not suffice for evaluation of surgical outcome of these patients. We assessed the relationship of morphologic changes in brain and spinal cord and disease symptoms with changes in cerebrospinal fluid (CSF) hydrodynamic parameters in patients with CM-I.

METHODS

The study included 41 patients in 3 groups of CM-I, CM-I/occipitoatlantoaxial joint instability, and CM-I/tethered cord syndrome and 18 normal subjects. Phase-contrast magnetic resonance imaging and computational fluid dynamics analysis were done for all samples.

RESULTS

Maximum CSF velocities and pressures in patients had an increase of 17.1%-23.2% and 41.5%-56.8%, respectively, compared with normal subjects. The data dispersion of maximum CSF velocity was >3.1 times that of the maximum pressure. Results showed that maximum CSF pressure is a more appropriate hydrodynamic parameter than maximum CSF velocity for assessing the condition of patients. Results also showed that CSF and PCF volumes had declined 57% and 11.3%, respectively, in CM-I. These declines were greater in CM-I than in the other 2 groups.

CONCLUSIONS

Maximum CSF pressure regardless of the group the patients belonged to was similar in patients with symptoms of similar intensity. The correlation between maximum CSF pressure with CSF and PCF volumes decreased secondary to the disease. PCF volume was more favorable than CSF volume for assessing intensity of disease symptoms. Furthermore, in a constant pressure change, sensitivity of PCF volume in CM-I/occipitoatlantoaxial joint instability and CM-I/tethered cord syndrome groups was more than in the CM-I group.

The association between the pulse pressure gradient at the cranio-cervical junction derived from phase-contrast magnetic resonance imaging and invasively measured pulsatile intracranial pressure in symptomatic patients with Chiari malformation type 1

BACKGROUND

In symptomatic Chiari malformation type 1 (CMI), impaired intracranial compliance (ICC) is associated with an increased cranio-spinal pulsatile pressure gradient. Phase-contrast magnetic resonance imaging (MRI) represents a non-invasive modality for the assessment of the pulse pressure gradient at the cranio-cervical junction (CCJ). We wished to explore how the MRI-derived pulse pressure gradient (MRI-dP) compares with invasively measured pulsatile intracranial pressure (ICP) in CMI, and with healthy controls.

METHODS

From phase-contrast MRI of CMI patients and healthy controls, we computed cerebrospinal fluid (CSF) flow velocities and MRI-dP at the CCJ. We assessed bidirectional flow and compared the flow between the anterior and the posterior subarachnoid space at the CCJ. We computed total intracranial volume (ICV), ventricular CSF volume (VV), and posterior cranial fossa volume (PCFV). We analyzed the static and pulsatile ICP scores from overnight monitoring in CMI patients.

RESULTS

Five CMI patients and four healthy subjects were included. The CMI group had a significantly larger extent of tonsillar ectopia, smaller PCFV, and a smaller area of CSF in the FM. The pulsatile ICP (mean ICP wave amplitude, MWA) was abnormally increased in 4/5 CMI patients and correlated positively with MRI-dP. However, the MRI-dP as well as the CSF flow velocities did not differ significantly between CMI and healthy subjects. Moreover, bidirectional flow was observed in both CMI as well as healthy subjects, with no significant difference.

CONCLUSIONS

In symptomatic CMI patients, we found a significant association between the pulse pressure gradient at the CCJ derived from phase-contrast MRI and the pulsatile ICP (MWA) measured invasively. However, the MRI-dP was close to identical in CMI patients and healthy subjects. Moreover, the CSF flow velocities at the CCJ and the occurrence of bidirectional flow were not different in CMI patients and healthy individuals. Further studies are required to determine the diagnostic role of phase-contrast MRI in CMI patients.

Computational Investigation of Cerebrospinal Fluid Dynamics in the Posterior Cranial Fossa and Cervical Subarachnoid Space in Patients with Chiari I Malformation

Purpose

Previous computational fluid dynamics (CFD) studies have demonstrated that the Chiari malformation is associated with abnormal cerebrospinal fluid (CSF) flow in the cervical part of the subarachnoid space (SAS), but the flow in the SAS of the posterior cranial fossa has received little attention. This study extends previous modelling efforts by including the cerebellomedullary cistern, pontine cistern, and 4th ventricle in addition to the cervical subarachnoid space.

Methods

The study included one healthy control, Con1, and two patients with Chiari I malformation, P1 and P2. Meshes were constructed by segmenting images obtained from T2-weighted turbo spin-echo sequences. CFD simulations were performed with a previously verified and validated code. Patient-specific flow conditions in the aqueduct and the cervical SAS were used. Two patients with the Chiari malformation and one control were modelled.

Results

The results demonstrated increased maximal flow velocities in the Chiari patients, ranging from factor 5 in P1 to 14.8 in P2, when compared to Con1 at the level of Foramen Magnum (FM). Maximal velocities in the cervical SAS varied by a factor 2.3, while the maximal flow in the aqueduct varied by a factor 3.5. The pressure drop from the pontine cistern to the cervical SAS was similar in Con1 and P1, but a factor two higher in P2. The pressure drop between the aqueduct and the cervical SAS varied by a factor 9.4 where P1 was the one with the lowest pressure jump and P2 and Con1 differed only by a factor 1.6.

Conclusion

This pilot study demonstrates that including the posterior cranial fossa is feasible and suggests that previously found flow differences between Chiari I patients and healthy individuals in the cervical SAS may be present also in the SAS of the posterior cranial fossa.

Inter-operator Reliability of Magnetic Resonance Image-Based Computational Fluid Dynamics Prediction of Cerebrospinal Fluid Motion in the Cervical Spine

For the first time, inter-operator dependence of MRI based computational fluid dynamics (CFD) modeling of cerebrospinal fluid (CSF) in the cervical spinal subarachnoid space (SSS) is evaluated. In vivo MRI flow measurements and anatomy MRI images were obtained at the cervico-medullary junction of a healthy subject and a Chiari I malformation patient. 3D anatomies of the SSS were reconstructed by manual segmentation by four independent operators for both cases. CFD results were compared at nine axial locations along the SSS in terms of hydrodynamic and geometric parameters. Intraclass correlation (ICC) assessed the inter-operator agreement for each parameter over the axial locations and coefficient of variance (CV) compared the percentage of variance for each parameter between the operators. Greater operator dependence was found for the patient (0.19 < ICC < 0.99) near the craniovertebral junction compared to the healthy subject (ICC > 0.78). For the healthy subject, hydraulic diameter and Womersley number had the least variance (CV = ~2%). For the patient, peak diastolic velocity and Reynolds number had the smallest variance (CV = ~3%). These results show a high degree of inter-operator reliability for MRI-based CFD simulations of CSF flow in the cervical spine for healthy subjects and a lower degree of reliability for patients with Type I Chiari malformation.

Poro-elastic modeling of Syringomyelia - a systematic study of the effects of pia mater, central canal, median fissure, white and gray matter on pressure wave propagation and fluid movement within the cervical spinal cord

Syringomyelia, fluid-filled cavities within the spinal cord, occurs frequently in association with a Chiari I malformation and produces some of its most severe neurological symptoms. The exact mechanism causing syringomyelia remains unknown. Since syringomyelia occurs frequently in association with obstructed cerebrospinal fluid (CSF) flow, it has been hypothesized that syrinx formation is mechanically driven. In this study we model the spinal cord tissue either as a poro-elastic medium or as a solid linear elastic medium, and simulate the propagation of pressure waves through an anatomically plausible 3D geometry, with boundary conditions based on in vivo CSF pressure measurements. Then various anatomic and tissue properties are modified, resulting in a total of 11 variations of the model that are compared. The results show that an open segment of the central canal and a stiff pia (relative to the cord) both increase the radial pressure gradients and enhance interstitial fluid flow in the central canal. The anterior median fissure, anisotropic permeability of the white matter, and Poisson ratio play minor roles.

Characterization of the discrepancies between four-dimensional phase-contrast magnetic resonance imaging and in-silico simulations of cerebrospinal fluid dynamics

The purpose of the present study was to compare subject-specific magnetic resonance imaging (MRI)-based computational fluid dynamics (CFD) simulations with time-resolved three-directional (3D) velocity-encoded phase-contrast MRI (4D PCMRI) measurements of the cerebrospinal fluid (CSF) velocity field in the cervical spinal subarachnoid space (SSS). Three-dimensional models of the cervical SSS were constructed based on MRI image segmentation and anatomical measurements for a healthy subject and patient with Chiari I malformation. CFD was used to simulate the CSF motion and compared to the 4D PCMRI measurements. Four-dimensional PCMRI measurements had much greater CSF velocities compared to CFD simulations (1.4 to 5.6× greater). Four-dimensional PCMRI and CFD both showed anterior and anterolateral dominance of CSF velocities, although this flow feature was more pronounced in 4D PCMRI measurements compared to CFD. CSF flow jets were present near the nerve rootlets and denticulate ligaments (NRDL) in the CFD simulation. Flow jets were visible in the 4D PCMRI measurements, although they were not clearly attributable to nerve rootlets. Inclusion of spinal cord NRDL in the cervical SSS does not fully explain the differences between velocities obtained from 4D PCMRI measurements and CFD simulations.

Effect of craniovertebral decompression on CSF dynamics in Chiari malformation type I studied with computational fluid dynamics: Laboratory investigation

OBJECT

The effect of craniovertebral decompression surgery on CSF flow dynamics in patients with Chiari malformation Type I (CM-I) has been incompletely characterized. The authors used computational fluid dynamics to calculate the effect of decompression surgery on CSF flow dynamics in the posterior fossa and upper cervical spinal canal.

METHODS

Oscillatory flow was simulated in idealized 3D models of the normal adult and the CM-I subarachnoid spaces (both previously described) and in 3 models of CM-I post-craniovertebral decompressions. The 3 postoperative models were created from the CM model by virtually modifying the CM model subarachnoid space to simulate surgical decompressions of different magnitudes. Velocities and pressures were computed with the Navier-Stokes equations in Star-CD for multiple cycles of CSF flow oscillating at 80 cycles/min. Pressure gradients and velocities were compared for 8 levels extending from the posterior fossa to the C3-4 level. Relative pressures and peak velocities were plotted by level from the posterior fossa to C3-4. The heterogeneity of flow velocity distribution around the spinal cord was compared between models.

RESULTS

Peak systolic velocities were generally lower in the postoperative models than in the preoperative CM model. With the 2 larger surgical defects, peak systolic velocities were brought closer to normal model velocities (equal values at C-3 and C-4) than with the smallest surgical defect. For the smallest defect, peak velocities were decreased, but not to levels in the normal model. In the postoperative models, heterogeneity in flow velocity distribution around the spinal cord increased from normal model levels as the degree of decompression increased. Pressures in the 5 models differed in magnitude and in pattern. Pressure gradients along the spinal canal in the normal and CM models were nonlinear, with steeper gradients below C3-4 than above. The CM model had a steeper pressure gradient than the normal model above C3-4 and the same gradient below. The postoperative models had lower pressure gradients than the CM model above C2-3. The most conservative decompression had lower pressure gradients than the normal model above C2-3. The two larger decompression defects had CSF pressure gradients below those in the normal model above C2-3. These 2 models had a less steep gradient above C-3 and a steeper gradient below.

CONCLUSIONS

In computer simulations, craniovertebral surgical defects generally diminished CSF velocities and CSF pressures.

Spinal fluid biomechanics and imaging: an update for neuroradiologists

Flow imaging with cardiac-gated phase-contrast MR has applications in the management of neurologic disorders. Together with computational fluid dynamics, phase-contrast MR has advanced our understanding of spinal CSF flow. Phase-contrast MR is used to evaluate patients with Chiari I malformation who are candidates for surgical treatment. In theory, abnormal CSF flow resulting from the abnormal tonsil position causes syringomyelia and other neurologic signs and symptoms in patients with Chiari I. CSF flow imaging also has research applications in syringomyelia and spinal stenosis. To optimize MR acquisition and interpretation, neuroradiologists must have familiarity with healthy and pathologic patterns of CSF flow. The purpose of this review is to update concepts of CSF flow that are important for the practice of flow imaging in the spine.

The impact of spinal cord nerve roots and denticulate ligaments on cerebrospinal fluid dynamics in the cervical spine

Cerebrospinal fluid (CSF) dynamics in the spinal subarachnoid space (SSS) have been thought to play an important pathophysiological role in syringomyelia, Chiari I malformation (CM), and a role in intrathecal drug delivery. Yet, the impact that fine anatomical structures, including nerve roots and denticulate ligaments (NRDL), have on SSS CSF dynamics is not clear. In the present study we assessed the impact of NRDL on CSF dynamics in the cervical SSS. The 3D geometry of the cervical SSS was reconstructed based on manual segmentation of MRI images of a healthy volunteer and a patient with CM. Idealized NRDL were designed and added to each of the geometries based on in vivo measurments in the literature and confirmation by a neuroanatomist. CFD simulations were performed for the healthy and patient case with and without NRDL included. Our results showed that the NRDL had an important impact on CSF dynamics in terms of velocity field and flow patterns. However, pressure distribution was not altered greatly although the NRDL cases required a larger pressure gradient to maintain the same flow. Also, the NRDL did not alter CSF dynamics to a great degree in the SSS from the foramen magnum to the C1 level for the healthy subject and CM patient with mild tonsillar herniation (∼6 mm). Overall, the NRDL increased fluid mixing phenomena and resulted in a more complex flow field. Comparison of the streamlines of CSF flow revealed that the presence of NRDL lead to the formation of vortical structures and remarkably increased the local mixing of the CSF throughout the SSS.

Effect of the central canal in the spinal cord on fluid movement within the cord

Computational studies are used to demonstrate the effect of oscillating CSF flow on pressures within the spinal cord. We tested the hypothesis that the central canal in the spinal cord affects spinal cord pressure gradients resulting from oscillatory CSF flow. Two computational models of the spinal cord were created with the same dimensions. Model 1 had a homogeneous porous structure. Model 2 had the same structure with the addition of a central fluid filled space, representing the central canal of the cord. We simulated oscillatory flow in the fluid space using standard computational fluid dynamics tools. For all phases of the CSF flow cycle and for specific projections through the model we calculated pressure gradients and fluid movement in the cord models. Pressures in the models varied through the flow cycle. Model 1 had linearly varying pressure along its long axis that varied with the cycle and had no pressure gradients across the cord. Model 2 had nonlinear varying pressure along its long axis varying with the time in the cycle and had transient centrifugal and centripetal pressure gradients with a central fluid space. The radial pressures varied linearly with distance from the fluid space. Centrifugal and centripetal pressure gradients resulted in radially directed fluid flow in the cord. The central canal within the spinal cord alters the pressure fields occurring during oscillatory CSF flow and creates centrifugal and centripetal fluid flux in the cord.

Hydrodynamic and longitudinal impedance analysis of cerebrospinal fluid dynamics at the craniovertebral junction in type I Chiari malformation

Elevated or reduced velocity of cerebrospinal fluid (CSF) at the craniovertebral junction (CVJ) has been associated with type I Chiari malformation (CMI). Thus, quantification of hydrodynamic parameters that describe the CSF dynamics could help assess disease severity and surgical outcome. In this study, we describe the methodology to quantify CSF hydrodynamic parameters near the CVJ and upper cervical spine utilizing subject-specific computational fluid dynamics (CFD) simulations based on in vivo MRI measurements of flow and geometry. Hydrodynamic parameters were computed for a healthy subject and two CMI patients both pre- and post-decompression surgery to determine the differences between cases. For the first time, we present the methods to quantify longitudinal impedance (LI) to CSF motion, a subject-specific hydrodynamic parameter that may have value to help quantify the CSF flow blockage severity in CMI. In addition, the following hydrodynamic parameters were quantified for each case: maximum velocity in systole and diastole, Reynolds and Womersley number, and peak pressure drop during the CSF cardiac flow cycle. The following geometric parameters were quantified: cross-sectional area and hydraulic diameter of the spinal subarachnoid space (SAS). The mean values of the geometric parameters increased post-surgically for the CMI models, but remained smaller than the healthy volunteer. All hydrodynamic parameters, except pressure drop, decreased post-surgically for the CMI patients, but remained greater than in the healthy case. Peak pressure drop alterations were mixed. To our knowledge this study represents the first subject-specific CFD simulation of CMI decompression surgery and quantification of LI in the CSF space. Further study in a larger patient and control group is needed to determine if the presented geometric and/or hydrodynamic parameters are helpful for surgical planning.

Computational fluid dynamics modelling of cerebrospinal fluid pressure in Chiari malformation and syringomyelia

The pathogenesis of syringomyelia in association with Chiari malformation (CM) is unclear. Studies of patients with CM have shown alterations in the CSF velocity profile and these could contribute to syrinx development or enlargement. Few studies have considered the fluid mechanics of CM patients with and without syringomyelia separately. Three subject-specific CFD models were developed for a normal participant, a CM patient with syringomyelia and a CM patient without syringomyelia. Model geometries, CSF flow rate data and CSF velocity validation data were collected from MRI scans of the 3 subjects. The predicted peak CSF pressure was compared for the 3 models. An extension of the study performed geometry and flow substitution to investigate the relative effects of anatomy and CSF flow profile on resulting spinal CSF pressure. Based on 50 monitoring locations for each of the models, the CM models had significantly higher magnitude (p<0.01) peak CSF pressure compared with normal. When using the same CSF input flow waveform, changing the upper spinal geometry changed the magnitude of the CSF pressure gradient, and when using the same upper spinal geometry, changing the input flow waveform changed the timing of the peak pressure. This study may assist in understanding syringomyelia mechanisms and relative effects of CSF velocity profile and spinal geometry on CSF pressure.

CSF pressure and velocity in obstructions of the subarachnoid spaces

According to some theories, obstruction of CSF flow produces a pressure drop in the subarachnoid space in accordance with the Bernoulli theorem that explains the development of syringomyelia below the obstruction. However, Bernoulli's principle applies to inviscid stationary flow unlike CSF flow. Therefore, we performed a series of computational experiments to investigate the relationship between pressure drop, flow velocities, and obstructions under physiologic conditions. We created geometric models with dimensions approximating the spinal subarachnoid space with varying degrees of obstruction. Pressures and velocities for constant and oscillatory flow of a viscid fluid were calculated with the Navier-Stokes equations. Pressure and velocity along the length of the models were also calculated by the Bernoulli equation and compared with the results from the Navier-Stokes equations. In the models, fluid velocities and pressure gradients were approximately inversely proportional to the percentage of the channel that remained open. Pressure gradients increased minimally with 35% obstruction and with factors 1.4, 2.2 and 5.0 respectively with 60, 75 and 85% obstruction. Bernoulli's law underestimated pressure changes by at least a factor 2 and predicted a pressure increase downstream of the obstruction, which does not occur. For oscillatory flow the phase difference between pressure maxima and velocity maxima changed with the degree of obstruction. Inertia and viscosity which are not factored into the Bernoulli equation affect CSF flow. Obstruction of CSF flow in the cervical spinal canal increases pressure gradients and velocities and decreases the phase lag between pressure and velocity.

Simulating CSF flow dynamics in the normal and the Chiari I subarachnoid space during rest and exertion

BACKGROUND AND PURPOSE

CSF fluid dynamics in healthy subjects and patients with Chiari I have been characterized during rest with phase-contrast MR imaging and CFD. CSF flow velocities and pressures in the nonresting state have not been adequately characterized. We used computer simulations to study CSF dynamics during increased heart rates in the normal and Chiari I subarachnoid space.

MATERIALS AND METHODS

Cyclic CSF flow was simulated for multiple cycles in idealized 3D models of the subarachnoid space for normal and Chiari I malformation subarachnoid spaces, with flow cycles corresponding to 80 or 120 heart beats per minute. Flow velocities and pressures were computed by the Navier-Stokes equations. Synchronous bidirectional flow and flow patterns were displayed in Star-CD and inspected visually. Peak velocities and pressure differences in the 2 models were compared for the 2-cycle frequencies.

RESULTS

Elevating the cycle rate from 80 to 120 cpm increased peak superior-inferior pressure gradients (top-bottom) by just 0.01% in the normal model and 2% in the Chiari model. Corresponding average pressure gradients increased by 92% and 100%, respectively. In addition, in both models, the range of synchronous bidirectional flow velocities increased. Systolic velocities had smaller increases with faster cycling. For each cycle rate, peak and average pressure gradients in the Chiari model were greater than in the normal model by 11%-16%.

CONCLUSIONS

Raising the cycle rate from 80 to 120 cpm increased superior-inferior average pressure gradients and the range of synchronous bidirectional flow velocities in the normal and Chiari I models.

Patient-specific 3D simulation of cyclic CSF flow at the craniocervical region

BACKGROUND AND PURPOSE

Flow simulations in patient-specific models of the subarachnoid space characterize CSF flow in more detail than MR flow imaging. We extended previous simulation studies by including cyclic CSF flow and patient-specific models in multiple patients with Chiari I. We compared simulation results with MR flow measurements.

MATERIALS AND METHODS

Volumetric high resolution image sets acquired in 7 patients with Chiari I, 3 patients who had previous craniovertebral decompression, and 3 controls were segmented and converted to mathematical models of the subarachnoid space. CSF flow velocities and pressures were calculated with high spatial and temporal resolution during simulated oscillatory flow in each model with the Navier-Stokes equations. Pressures, velocities, and bidirectional flow were compared in the groups (with Student t test). Peak velocities in the simulations were compared with peak velocities measured in vivo with PCMR.

RESULTS

Flow visualization for patients and volunteers demonstrated nonuniform reversing patterns resembling those observed with PCMR. Velocities in the 13 subjects were greater between C2 and C5 than in the foramen magnum. Chiari patients had significantly greater peak systolic and diastolic velocities, synchronous bidirectional flow, and pressure gradients than controls. Peak velocities measured in PCMR correlated significantly (P = .003; regression analysis) despite differences between them.

CONCLUSIONS

In simulations of CSF, patients with Chiari I had significantly greater peak systolic and diastolic velocities, synchronous bidirectional flow, and pressure gradients than controls.