Comparison of 4D phase-contrast MRI flow measurements to computational fluid dynamics simulations of cerebrospinal fluid motion in the cervical spine

Abstract

Cerebrospinal fluid (CSF) dynamics in the cervical spinal subarachnoid space (SSS) have been thought to be important to help diagnose and assess craniospinal disorders such as Chiari I malformation (CM). In this study we obtained time-resolved three directional velocity encoded phase-contrast MRI (4D PC MRI) in three healthy volunteers and four CM patients and compared the 4D PC MRI measurements to subject-specific 3D computational fluid dynamics (CFD) simulations. The CFD simulations considered the geometry to be rigid-walled and did not include small anatomical structures such as nerve roots, denticulate ligaments and arachnoid trabeculae. Results were compared at nine axial planes along the cervical SSS in terms of peak CSF velocities in both the cranial and caudal direction and visual interpretation of thru-plane velocity profiles. 4D PC MRI peak CSF velocities were consistently greater than the CFD peak velocities and these differences were more pronounced in CM patients than in healthy subjects. In the upper cervical SSS of CM patients the 4D PC MRI quantified stronger fluid jets than the CFD. Visual interpretation of the 4D PC MRI thru-plane velocity profiles showed greater pulsatile movement of CSF in the anterior SSS in comparison to the posterior and reduction in local CSF velocities near nerve roots. CFD velocity profiles were relatively uniform around the spinal cord for all subjects. This study represents the first comparison of 4D PC MRI measurements to CFD of CSF flow in the cervical SSS. The results highlight the utility of 4D PC MRI for evaluation of complex CSF dynamics and the need for improvement of CFD methodology. Future studies are needed to investigate whether integration of fine anatomical structures and gross motion of the brain and/or spinal cord into the computational model will lead to a better agreement between the two techniques.

Figure 1. Varying levels of anatomical assumptions in the literature when simulating CSF in the cervical spine.

(Decreasing level of anatomical complexity from left to right, respectively). a) A subject-specific rigid wall geometry with CSF moving within a SSS of anisotropic porosity . b) An idealized 2D SSS geometry including spinal cord nerve roots, arachnoid trabeculae and denticulate ligaments in a symmetric arrangement around the spinal cord . c) A subject-specific 3D SSS geometry without small anatomical structures and geometric smoothing . d) An idealized 3D geometry of a healthy subject . e) The first simulation of CSF in the cervical SSS idealized as two concentric ellipses . f) A 2D axisymmetric spinal cord and dura model with moving walls . g) A 2D axisymmetric model of wave propagation in the spine based on an analytical solution of concentric elastic tubes . Refer to Table 1 for details in each simulation.

Figure 2. 3D reconstruction of the cervical SSS based on manual segmentation.

Segmentation of the healthy subjects (left) and CM patients (right). The 3D reconstruction depicts the SSS where the CSF pulsates (between the dura and spinal cord tissue). Note the SSS constriction near the FM in the four CM patients in comparison to the healthy subjects.

Figure 3. Workflow for 4D PC MRI (top row) and CFD (bottom) methodology in a healthy volunteer.

a) 4D PC MRI velocity vectors superimposed on the coarse 2D anatomy scan. b) Placement of axial planes along the cervical SSS and c) 2D velocity profile visualization of the axial planes. d) Velocity profile example at the FM where ROI image truncation was required due to low velocities and noise in the MRI signal (see Methods for details). e) Velocity profile in the lower cervical SSS where the ROI required less image truncation. f) High resolution anatomical MRI scan used to define the geometry for the CFD simulation. g) 3D rendering of the cervical SSS segmentation before end truncation and geometric smoothing. h) 3D rendering of the smoothed cervical SSS geometry and axial planes where the CFD velocity profiles were observed. i) 2D velocity profile plots for each axial location. j) Velocity profile at the FM showing a larger cross-section than the FM in the 4D PC MRI (compare to d). k) Velocity profile in the lower cervical SSS that compares more favorably in terms of ROI size and shape to that observed in the 4D PC MRI (e).

Figure 4. Comparison of the mean thru-plane peak CSF velocities between 4D PC MRI and CFD.

Peak systolic and diastolic velocities were measured by the 4D PC MRI and simulated by CFD in the cervical spine (FM-C7, FM is near the head and C7 is towards the feet) in healthy volunteers (Healthy a, b and c) and CM patients (CM 1, 2, 3, and 4). Values are given as mean ± SD (cm/s) for the three healthy subjects (top) and four CM patients (bottom). Positive (diastolic) and negative (systolic) velocities reflect head and foot directed flow, respectively.

Figure 5. Thru-plane peak CSF velocity profiles (foot direction) at each axial location along the cervical spine.

The left and right image for each subject corresponds to the CFD simulation and 4D PC MRI measurements along the cervical spine (FM-C7 level), respectively. CSF velocities were elevated in the anterior SSS in comparison to the posterior space in all of the 4D PC MRI velocity profiles (healthy and patients). The posterior versus anterior flow differences were not present in the CFD results; which maintained a fairly uniform velocity profile around the spinal cord in all simulations except CM 1 and CM 2 near the FM. Note, velocity scales are different for each image (shown at bottom of each image set) so as to highlight the difference in velocity profiles.

Figure 6. Peak-systolic thru-plane CSF velocity profiles for a healthy subject and a CM patient.

Comparison of the peak systolic thru-plane CSF velocity profiles between the 4D PC MRI and CFD for HVa (left) and CM1 (right). Note the different velocity scales for each plot (optimized for visualization of flow profiles in each case). Colors indicate the magnitude of thru-plane velocities. ↑ symbols highlight the elevated anterior CSF velocities in comparison to the posterior that were observed in all of the 4D PC MRI velocity profiles (healthy and patients). The posterior versus anterior flow differences were not present in the CFD simulations (see Figure 5). +symbols indicate locations where the nerve roots appear to local CSF velocities.

Figure 7. Motion analysis of the MRI images for healthy subject c (Hty c) and CM patients.

Pixels in the image that are not masked in blue indicate tissue regions of the brain/spinal cord that move during the cardiac cycle. The larger the region, the greater the tissue motion; e.g. CM1, CM2 and CM4 appear to have the greater level of tissue motion in comparison to CM3. Unsteady CSF flow measured at the C1 and C2M is shown in the center row for each patient. CSF stroke volume (SV) at each axial location along the SSS (FM – C7) is shown in the bottom row for each subject.

Figure 8. Velocity-w at axial locations through the spinal cord for three grids of different density.

Plots of peak systolic velocity in the z direction (velocity w) along vectors through the cervical spinal cord for three different axial locations as calculated with three grids (a) Velocity-w along the vector at the cross-section of axial plane FM, (b) Velocity-w along the vector at the cross-section of axial plane C3 (c) Velocity-w along the vector at the cross-section of axial plane C7.