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.

Supplementary Figure S2: (a) 3D geometry of model and (b) computational mesh with refinement in the cerebral aqueduct.
In Supplementary Figure S1, the % changes of these two parameters for each mesh compared to the finest mesh were evaluated showing a difference of less than 3% for the mesh with 1.14 million elements.The mesh is visualized in Supplementary Figure S2.In Supplementary Table T1 the mesh properties of the selected mesh are presented.
Supplementary Table T1: Properties corresponding to the selected mesh.

Global mesh size
Global element seed size: max element 3 Min size limit 0.5

Elements in gap 1
Refinement 5

Growth law exponential
Height ratio 2

B. Schematic windkessel boundary conditions
Supplementary Figure S3: Schematic of the intracranial and spinal compartment with the four different outlets represented as physical components.The windkessel outlets include an absorption path and buffering compartment whereas the resistive outlets have only an absorption path.

C. Validation study: approximating tonsil herniation obstruction using a porous zone approach
In the model presented in the main text, two porous zones were introduced to model the obstruction created by the herniation of cerebellar tonsils in patients with Chiari type 1 malformation.The question here remains whether such a porous zone is a good approximation of the herniation of the cerebellar tonsils to predict the pressure difference over the obstruction, and to what level of area obstruction the porous zones are expected to correspond.Therefore, an additional study was performed whereby the effects of the porous zones were compared with those of blockages based on the physiological shape of the herniated tonsils.

C.1 Materials and methods
This additional study was performed on a cropped model containing the lower part of the CSF model presented in the main text to limit the necessary computational cost.

Geometry
The cropped model was created from the 3D model geometry where only the CSF space around the cranio-cervical junction was maintained (= base).Then, cone-shaped volumes were added using Mimics 24.0 (Materialize, Leuven, Belgium) to enlarge the cerebellum and in that way occupy a larger part of the CSF space.This finally resulted in a model without obstruction (control) and four models with area stenosis of 29% (herniation 1), 70% (herniation 2), 92% (herniation 3), and 99% (herniation 4) as depicted in Supplementary Figure S4.
Supplementary 2017, who modelled the spinal cord as a poroelastic medium and suggested that the permeability (a) of 1E-14 m² was most realistic 1 .The viscous resistance can be described as 1/a, indicating that a value of 1E14 1/m² would be adequate for neurological tissue and thus the obstruction.To make the final selection for the viscous resistance values of the anterior porous zone (OBS-2 and OBS-3), we evaluated the pressure in the fourth ventricle for viscous resistances varying from 1E6 until 1E10 1/m².The results corresponding to the selected porous zone obstructions (OBS-1, OBS-2, and OBS-3) and the physical obstructions were evaluated to verify whether porous zones adequately capture the impact of herniated tonsils on CSF flow.

Selecting the viscous resistance of the anterior zone
We found that a viscous resistance of 1E8 1/m² displayed the first significant increase in pressure compared to OBS-1 as depicted in Supplementary Figure S6, and was therefore selected as OBS-2.
Finally, a viscous resistance of 1E10 1/m² induced as lowest value a peak pressure in the fourth ventricle lager than the mean intracranial pressure of 10 mmHg considered in this work, and therefore was judged suitable as most severe case (OBS-3).
Figure S4: Control model and four different degrees of obstruction (herniation 1, 2, 3 and 4) with visualization of a cross-section (location z = -0.055m)with corresponding % obstruction.The transient inlet velocity profile was calculated from the smoothed in vivo flow measurements obtained at the level of the cerebral aqueduct ( ) and in the spinal SAS ( ).different degrees of obstruction (OBS-1, OBS-2, OBS-3) were realized using a porous zone approach by adapting the viscous resistance of the porous zones as discussed in main text.The viscous resistance of the posterior zone was based on the permeability values used by Bertram et al.