Table 1.
Summary of previous spinal CSF dynamics numerical studies with key information on the numerical method, anatomic/physiologic feature investigated and the feature impact on CSF dynamics
| Study | Numerical method | Three-dimensional (3D) | Subject-specific | Full spine | TM | NR | AT | Anatomic/physiologic feature investigated | Feature impact on CSF dynamics |
|---|---|---|---|---|---|---|---|---|---|
| Khani et al. (present study) | Finite volume | x | x | x | x | x | NR and nonuniform CSF flow | Steady-streaming flow and CSF vortices created during flow reversal | |
| Tangen et al. [22] | Finite volume | x | x | x | x | x | x | Impact of AT on CSF pressure and solute spread | AT increase pressure drop but have little impact on drug spread to cervical spine |
| Khani et al. [25] | Finite volume | x | x | x | x | Nonuniform CSF flow in a nonhuman primate | Laminar, inertial dominated CSF flow found throughout nonhuman primate spine | ||
| Hsu et al. [26,27] | Finite volume | x | x | x | x | Impact of CSF pulse freq. and mag. on drug spread | Increased CSF pulse frequency and magnitude increase drug spread | ||
| Cheng et al. [28] | Finite volume | x | x | x | x | FSI between CSF and SC | Caused up to 2 mm of SC displacement | ||
| Tangen et al. [29] | Finite volume | x | x | x | x | Infusion settings, drug chemistry and anatomy | Drug dispersion is impacted by infusion, chemistry and anatomy | ||
| Tangen et al. [23] | Finite volume | x | x | x | x | Lumbar CSF drainage after subarachnoid hemorrhage | Body position and CSF drainage rate impact blood removal from CSF | ||
| Kuttler et al. [30] | Finite volume | x | x | x | Impact of slow or fast bolus dose | Pulsation and breathing dominated long-term bolus spread (not bolus speed) | |||
| Pizzichelli et al. [31] | Finite element | x | x | x | Catheter position and angle and tissue permeability | Injection perpendicular to cord increased penetration to the cord tissue | |||
| Haga et al. [32] | Finite element | x | x | x | Catheter position, angle, and injection flow rates | Catheter position, angle and injection flow rates impact solute distribution | |||
| Heidari Pahlavian et al. [33,34] | Finite volume | x | x | x | Comparison of in vivo and in vitro MRI with CFD results | in vitro MRI compared well with CFD results, in vivo compared poorly with CFD | |||
| Heidari Pahlavian et al. [35] | Finite volume | x | x | x | Presence of NR and DL | Increased peak CSF velocities, mixing and bi-directional flow | |||
| Stockman [20] | Lattice Boltzmann | x | x | x | NR, DL, and AT | Increased nonstreamwise components of CSF velocity | |||
| Pahlavian et al. [9] | Finite volume | x | x | x | Pulsatile motion of cerebellar tonsils | Increased peak CSF velocities, mixing, and bidirectional flow | |||
| Bertram et al. [36] | Finite element | x | x | SC and dura compliance | Pressure wave propagation impacted by the elastic properties of tissue | ||||
| Bertram et al. [37] | Finite element | x | x | SC tethering due to arachnoiditis | Increased tensile radial stress and decreased pressure in the SC material | ||||
| Elliott et al. [38] | Finite difference | x | x | Posttraumatic syringomyelia | Stress induced by syrinx fluid sloshing diminishes as syrinx expands | ||||
| Elliott [39] | Analytic | x | x | Syrinx filling due to CSF wave mechanics | Syrinx filling impacted by CSF flow obstruction and tissue properties | ||||
| Jain et al. [40] | Lattice Boltzmann | x | x | Highly resolved direct numerical simulation | Onset of transitional CSF flow in Chiari patients | ||||
| Cheng et al. [41] | Finite volume | x | x | Arachnoiditis permeability | Increased bidirectional flow, peak CSF pressure timing shifted | ||||
| Rutkowska et al. [42] | Finite volume | x | x | Presence of tonsillar herniation | Increased peak CSF velocities, gradient, and bidirectional flow | ||||
| Yiallourou et al. [43] | Finite volume | x | x | Presence of tonsillar herniation | Increased peak systolic CSF velocities, flow jets near foramen magnum | ||||
| Clarke et al. [44] | Finite volume | x | x | Presence of tonsillar herniation | Increased magnitude of peak pressure | ||||
| Shaffer et al. [45] | Finite volume | x | x | Tonsillar descent | Increased longitudinal impedance to CSF flow and correlated with tonsillar descent | ||||
| Martin et al. [46] | Finite volume | x | x | Tonsillar descent | Increased peak CSF velocities, pressure gradient, and longitudinal impedance | ||||
| Roldan et al. [47] | Boundary element | x | x | Tonsillar descent | Increased peak CSF velocities near the CVJ and peak pressure gradient along SSS | ||||
| Linge et al. [48] | Finite volume | x | Tonsillar descent & surgery impact | Increase peak CSF velocities, velocity heterogeneity and CSF pressure gradient | |||||
| Linge et al. [49] | Finite volume | x | Presence of tonsillar herniation | Increased peak CSF velocities and pressure gradient near the tonsils | |||||
| Linge et al. [50] | Finite volume | x | Increase in cardiac rate | Increased pressure gradient, increased magnitude of bi-directional flow | |||||
| Bilston et al. [51] | Finite volume | Decreased arachnoiditis permeability | Increased pressure gradient along the SSS | ||||||
| Loth et al. [52] | Finite volume | x | x | Cross-sectional geometry and SC motion | Pressure gradient waveform dependent on CSF flow waveform and cross-sectional area |
Note: 3D—model constructed in three-dimensional, TM—tissue motion included in model, AT—arachnoid trabeculae included in model, NR—nerve roots included in model.