Characterization of Cyclic CSF Flow in the Foramen Magnum and Upper Cervical Spinal Canal with MR Flow Imaging and Computational Fluid Dynamics

Sketches illustrating an idealized model of the SAS for CFD. A, A 3D hollow funnel-shaped structure is used to represent the surfaces of the SAS in the lower cranial vault and in the cervical spine. The internal surface of the SAS is created by the idealized model of the brain and spinal cord inserted into a nearly funnel-shaped structure. The transverse line in A represents the location of the craniovertebral junction in the model. B, A sagittal section of the structure shows the SAS as white and tissues external and internal to it as gray. C, An oblique axial section at the craniovertebral junction shows the SAS as white. Reprinted with permission from Linge et al.²²

Line graphs demonstrating different time courses for CSF flow that can be used as input functions in CFD simulations. The y-axis shows the magnitude of flow in positive and negative directions; the x-axis shows time as a decimal fraction of the cardiac cycle. One time course (green line) illustrates CSF flowing in a sinusoidal manner, similar to that observed in some PC MR studies.¹¹ The other (blue line) illustrates CSF flowing in a less symmetric manner as observed in other PC MR studies.⁷ The 3 red points illustrate first the maximal velocity in a positive direction (systolic flow) and then the change in direction from a positive to a negative flow and then maximal negative (diastolic) flow. Systolic flow lasts a shorter time and has a greater magnitude than diastolic flow in the second plot. Net flow during the cardiac cycle is zero in both plots.

Examples of CSF velocity simulations for maximal systolic flow for a single axial section in an idealized model of the SAS with different cord shapes or sizes. The asymmetric CSF flow pattern from Fig 3 is assumed for this simulation. The upper image shows velocities for a SAS containing a cord assumed to have a cylindric shape. The next image shows systolic flow when the cord is modeled with an elliptic rather than a circular cross-section. The boundary conditions are otherwise the same as those for the upper image. Note that changing the shape of the spinal cord changes the flow pattern during systole. The bottom image illustrates velocities in a model with a larger cylindric spinal cord and a smaller SAS. Note the marked increase in velocities due to a smaller SAS.

Effect of different temporal patterns of CSF flow on the homogeneity and magnitude of CSF velocities. In the first model used in Fig 4, CSF velocities at peak systolic flow (left column), at the transition to diastolic flow (middle column), and at peak diastolic flow (right column) are shown for an asymmetric temporal flow pattern (top row) and a symmetric sinusoidal flow pattern (lower row). For the asymmetric flow pattern, systolic velocities are greater than those for the symmetric flow pattern. Simultaneous cephalad (negative) and caudad flow (positive) at the transition is more obvious for the asymmetric flow pattern. During peak diastolic flow (right column), both positive and negative flow velocities are noted for the asymmetric flow patterns.

CSF flow velocities and pressures simulated in patient-specific models of the SAS for a healthy subject (left) and a patients with Chiari I (right). A, Pressure distribution at the inlet and along the outer spinal canal surface for the normal (left) and Chiari I (right) models during peak systole. B, Axial sections at the foramen magnum (upper images) and 4 cm lower in the spinal canal (lower images) are shown. The magnitude of flow through the axial section is indicated in centimeters per second by a color scale (reader's far right). The magnitude and direction of secondary (in section) flow are indicated by arrows. Flow is more inhomogeneous and faster in the patient with Chiari than in the healthy subject. Velocities are greater in both subjects at the foramen magnum than at the selected lower section. Courtesy of Alejandro Roldan.

Idealized models (above) of the brain, spinal cord, and SAS for simulating CSF flow in a healthy subject (left) and in a patient with Chiari (right). The red lines indicate the volume for which flow was calculated, and the yellow lines, the location of the axial section (below). In the axial sections, the flow patterns are heterogeneous in both the healthy subject (left in A and B) and the patient with Chiari (right in A and B). Peak velocities reach 2.27 cm/s in the healthy volunteer and 5.24 cm/s in the patient with Chiari (color scales to the right of the images).