Clearance of Subarachnoid Hemorrhage from the Cerebrospinal Fluid in Computational and In Vitro Models

Abstract

Subarachnoid hemorrhage (SAH) mostly occurs following the rupture of cerebral aneurysm causing blood to leak into the cranial subarachnoid space (SAS). Hemorrhage volume has been linked to the development of secondary vasospasm. Therefore, eliminating blood contaminants from the cerebrospinal fluid (CSF) space after the initial hemorrhage could improve patient outcomes and prevent the development of vasospasm. A number of clinical trials demonstrate that lumbar drainage effectively clears hemorrhagic debris from the cranial compartment. The benefits of optimal lumbar drainage rate and patient orientation are difficult to determine by trial-and-error in live patients, because of the invasive nature, limited subject availability and ethical considerations. Therefore, there is a lack of consensus about clinical guidelines for the use of continuous lumbar drainage following the ictus of SAH. A realistic bench-top model which reproduces the anatomy and CSF dynamics of the human central nervous system (CNS) was built to experimentally study contaminant clearance scenarios under lumbar drainage. To mimic a hemorrhagic event, porcine blood was injected at the basal cistern level of the bench-top model and the efficacy of lumbar drains was assessed experimentally for different drainage rates and patient orientations. In addition, the efficacy of blood clearance was predicted with a computational fluid dynamics (CFD) model. Bench-top experiments and CFD simulations identify body position and drainage rates as key parameters for effective blood clearance. The study findings suggest the importance of treatment in upright position to maximize contaminant diversion from the cranial CSF compartment. The bench-top CNS model together with the validated CFD predictions of lumbar drainage systems can serve to optimize subject-specific treatment options for SAH patients.

Appendix: Methods

In vitro Model Test with Artificial CSF and Water

The in vitro model is tested with both normal water and artificial CSF to determine any impact the bulk fluid properties will have on blood distribution following subarachnoid hemorrhage.

Artificial CSF is produced using electrolytes, Na, K, Mg, Ca, Cl, HCO₃, P, Glucose, and albumin protein; concentrations presented in Appendix Table 3. We made 200 mL of aCSF for each run.

Table 3 Species concentrations for artificial CSF.42

Density as a Function of Temperature for In Vitro Model

The in vitro experiments were performed at the normal laboratory setting of 19^oC. We did not create a thermostatic environment due to size limitations. Additionally, the density ratio between CSF and blood was found to be temperature invariant. At 19° laboratory temperature and at body temperature of 37° CSF to blood density ratio is 0.937. The density for water, blood, and CSF at 19° and 37° is compiled in Appendix Table 4.

Table 4 Calculated Reynolds number and Womersley number in the computational model at five key axial planes in the spinal subarachnoid space for three patient orientations, vertical, incline (30°), and supine.35,54

Womersley numbers (α) were calculated with revision Eq. (4) to characterize the flow conditions due to a pulsatile pressure gradient.³⁸ Here ρ is the density (998.2 kg m⁻³), T is the period (s), D _h is the hydraulic diameter (m), and µ is the viscosity (0.001 kg s⁻¹m⁻¹).

$$ a^{2} = \frac{{\rho \cdot \left( {\frac{2\pi }{T}} \right) \cdot \left( {\frac{{D_{\text{h}} }}{2}} \right)^{2} }}{\mu } $$

(4)

Reynolds number is calculated by:

$$ Re = \frac{{\rho \cdot \nu \cdot D_{\text{h}} }}{\mu } $$

(5)

where ρ is the density (998.2 kg m⁻³), ν is the peak velocity at the location (m s⁻¹), D _h is the hydraulic diameter of that plane (m), and μ is the viscosity (0.001 kg s⁻¹ m⁻¹).