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.

Numerical simulations of the pulsating flow of cerebrospinal fluid flow in the cervical spinal canal of a Chiari patient.

The flow of cerebrospinal fluid (CSF) in a patient-specific model of the subarachnoid space in a Chiari I patient was investigated using numerical simulations. The pulsating CSF flow was modeled using a time-varying velocity pulse based on peak velocity measurements (diastole and systole) derived from a selection of patients with Chiari I malformation. The present study introduces the general definition of the Reynolds number to provide a measure of CSF flow instability to give an estimate of the possibility of turbulence occurring in CSF flow. This was motivated by the fact that the combination of pulsating flow and the geometric complexity of the spinal canal may result in local Reynolds numbers that are significantly higher than the commonly used global measure such that flow instabilities may develop into turbulent flow in these regions. The local Reynolds number was used in combination with derived statistics to characterize the flow. The results revealed the existence of both local unstable regions and local regions with velocity fluctuations similar in magnitude to what is observed in fully turbulent flows. The results also indicated that the fluctuations were not self-sustained turbulence, but rather flow instabilities that may develop into turbulence. The case considered was therefore believed to represent a CSF flow close to transition.

Visualization of vorticity and vortices in wall-bounded turbulent flows.

This study was initiated by the scientifically interesting prospect of applying advanced visualization techniques to gain further insight into various spatio-temporal characteristics of turbulent flows. The ability to study complex kinematical and dynamical features of turbulence provides means of extracting the underlying physics of turbulent fluid motion. The objective is to analyze the use of a vorticity field line approach to study numerically generated incompressible turbulent flows. In order to study the vorticity field, we present a field line animation technique which uses a specialized particle advection and seeding strategy. Efficient analysis is achieved by decoupling the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. Multifield visualizations are obtained using a flexible volume rendering framework which is presented in this paper. Vorticity field lines have been employed as indicators to provide a means to identify "ejection" and "sweep" regions; two particularly important spatio-temporal events in wall-bounded turbulent flows. Their relation to the rate of turbulent kinetic energy production and viscous dissipation, respectively, have been identified.

High-quality and interactive animations of 3D time-varying vector fields.

In this paper, we present an interactive texture-based method for visualizing three-dimensional unsteady vector fields. The visualization method uses a sparse and global representation of the flow, such that it does not suffer from the same perceptual issues as is the case for visualizing dense representations. The animation is made by injecting a collection of particles evenly distributed throughout the physical domain. These particles are then tracked along their path lines. At each time step, these particles are used as seed points to generate field lines using any vector field such as the velocity field or vorticity field. In this way, the animation shows the advection of particles while each frame in the animation shows the instantaneous vector field. In order to maintain a coherent particle density and to avoid clustering as time passes, we have developed a novel particle advection strategy which produces approximately evenly-spaced field lines at each time step. To improve rendering performance, we decouple the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. The final display is rendered using texture-based direct volume rendering.

Visualization of vector fields using seed LIC and volume rendering.

Line Integral Convolution (LIC) is a powerful texture-based technique for visualizing vector fields. Due to the high computational expense of generating the 3D textures and the difficulties of effectively displaying the result, LIC has most commonly been used to depict vector fields in 2D or over a surface in 3D. Here, we propose new methods for more effective volume visualization of three-dimensional vector fields using LIC: 1) We present a fast method for computing volume LIC textures that exploits the sparsity of the input texture. 2) We propose the use of a shading technique, called limb darkening, to reveal the depth relations among the field lines. The shading effect is obtained simply by using appropriate transfer functions and, therefore, avoids using expensive shading techniques. 3) We demonstrate how two-field visualization techniques can be used to enhance the visual information describing a vector field. The volume LIC textures are rendered using texture-based rendering techniques, which allows interactive exploration of a vector field.