The CFD and in vitro model provided a systematic comparison of lumbar drain to Neurapheresis therapy after SAH. These models allow detailed comparison of results without the confounding impact of many variables that would be difficult to control for in vivo animal models or SAH patients. Computer simulations provided the theoretical basis to interpret bench top in vitro results by better elucidating the complex tracer clearance patterns in pulsatile CSF after SAH.
In vitro verification of numerical results
Studies show that wide variability exists in CFD modeling techniques and the choice of numerical solvers and settings are complex and can yield disparate results for biofluids simulations (53). Thus, in vitro models play a critical role to help verify numerical results. Unfortunately, at present there is no known method to map exact spatial-temporal blood concentration within the CSF over time for SAH patients. Thus, a true model validation against in vivo measurements is not possible. The model results are presented as a prediction for how blood can potentially be removed from the CSF.
Comparison of spatial-temporal cross-sectional average tracer concentration profiles revealed similar clearance trends for both CFD and in vitro under Neurapheresis therapy and lumbar drain conditions (Fig 5). A strong linear correlation was found between CFD and in vitro results under Neurapheresis therapy (R2=0.89, Fig 7a1), and a moderate linear correlation for lumbar drain (R2 = 0.65, Fig 7b1). Lumbar drain correlation was lower likely due to the lower degree of tracer changes that were present in that experiment. It was noted that linear correlation of results was stronger within the central region of the models. We expect that results had improved agreement within the central region of the model because our optical imaging field of view was most accurately aligned to CFD results within that region of the model. Near the model ends, the camera viewing angle was not orthogonal to the model domain and therefore did not provide information in the exact axial z-orientation as CFD results. Even with these in vitro imaging limitations, CFD results showed 95% of the CFD tracer concentration results were within ~2% of the in vitro findings with a mean difference of ~0.1% in both cases (Fig 7a2 and b2). In combination, these results help verify the numerical modeling approach using a frozen flow field that excluded mass diffusion. While these results agree, they cannot be assumed to correctly represent in vivo as many model assumptions were made that may not exactly represent in vivo CSF mass transport (see limitations). These model predictions should be tested against in vivo measurements in animals and/or humans.
Our model results are difficult to directly compare with previous research as no study has been conducted previously with an anatomically realistic model and with Neurapheresis therapy applied with an exact catheter geometry. However, Tangen et al (37) used an anatomically idealized bench-top CSF model and corresponding CFD analysis to study CSF blood clearance following SAH under various body orientations and lumbar drain rates with an intraventricular catheter inserted for 3 hours. They found the fastest blood clearance was achieved in the vertical body position and that an increase in lumbar drainage flow rate accelerated blood clearance. Their results, using a lumbar drain and intraventricular catheter, showed that after 60 minutes of filtration, contamination concentration was 3.5% at the T6 vertebral level. After 60 minutes, tracer clearance was 1.5 % at T6 in our numerical model using Neurapheresis therapy (Fig 5a1). This difference is likely due to the 2X higher filtration rate applied in our study 2.0 mL/min versus 1.0 mL/min by Tangen et al. Also, for the lumbar drain case with 0.2 mL/min drainage rate, 12% clearance was observed in Tangen et al (37) versus 10% clearance in our simulation. Since drainage rate for lumbar drain is equal on both studies, the clearance rates are similar.
Comparison of Neurapheresis therapy and lumbar drain
After 24 hours, results from Neurapheresis therapy showed that 4.9% of tracer remained in the model (Fig 6a) while 6.5% tracer concentration remained after lumbar drainage (Fig 6b). Cranial tracer clearance was nearly identical in both the lumbar drain and Neurapheresis therapy (Fig 5a1 and 5b1). The mechanistic reason for increased tracer clearance under Neurapheresis therapy is that it applies a CSF flow loop that returns filtered CSF back to the upper thoracic spine. The CSF flow loop increases steady-streaming velocities within the flow loop region (Fig. 4), which allows more rapid removal of the tracer. While the clinical impact of greater blood clearance on SAH outcomes has not been proven, researchers have shown the potential that more quickly reducing the levels of blood and inflammatory cytokines in the CSF post SAH could improve outcomes (54, 55)
The Neurapheresis therapy flow rate applied in our study was 2.0 mL/min with a 1.8 mL/min return flow rate. A flow rate of 2.0 mL/min is not possible to apply using a lumbar drain because it would remove CSF more rapidly than it is being produced at the choroid plexus (~500 mL/day) (56). To help compare Neurapheresis and lumbar drain tracer clearance efficiency, we compared tracer clearance under a lumbar drain and Neurapheresis waste rate both set to 0.2 mL/min (288 mL in 24 hours). To the best of our knowledge, this flow rate represents an upper bound for what is possible to withdraw under lumbar drain. In clinical practice, the drainage rate settings for lumbar drains may be lower.
Importance of frozen field approach in the numerical model
Transient simulations of oscillating fluids are computationally intensive, in particular when conducted over long time periods with small time-step size. For example, in the present case representing CSF oscillations, computation of a single CSF flow cycle requires ~3.6 hours using 38 processors (Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz) and 126 (GB) Memory. Simultaneously solving the passive transport equation requires additional time. Neurapheresis therapy is conducted over a period of more than 24-hours. As such, we applied a two-part CFD method that neglected diffusion to obtain a computationally tractable solution over the 24-hour timeframe. First, a transient Navier-Stokes solution of 11 flow cycles was performed to obtain the steady-streaming velocity field. Steady-streaming is postulated to be responsible for the time-average bulk movement of CSF in the SAS that results from nonlinear cumulative effects of convective acceleration (57). Steady streaming is important in this context because it has been shown to be the primary mode of mass transport within the oscillatory CSF flow field (58). Second, the velocity field was applied as a “frozen flow field” as described by Kuttler et al.(40). The frozen field approach is valid for periodic flow when advection is the main mode of mass transport.
The numbers computed in our study, by using the effective diffusivity of the tracer, were 7.56 E-06 and 9.6 E-03 for the cortical and spinal SAS, respectively. It should be noted that the low Sherwood number based on does not necessarily convey that shear-augmented diffusion is important, in particular for the present case in which substantial mixing can be produced by the complex spinal cord nerve root geometry. Further study is needed to compare the effect of diffusion to steady-streaming based advection.
In this study, we did not include the potential impact of microscopic anatomy within the domain such as arachnoid trabeculae or blood vessels, nor hydrodynamic affects on finite-size particles (red blood cells, in particular). Other numerical studies have investigated the potential impact of microscopic structures (41) within the CSF and found they can have varying degrees of impact on solute transport (59-61) and pressure gradients (62). Thus, our numerical and in vitro predictions should be confirmed with in vivo experiments. Albeit, these experiments may not be possible at present as we do not have a non-invasive in vivo imaging modality that can quantify blood concentration throughout the CSF system over 24-hours.
In this study, blood dispersion was modeled by fluorescein tracer mixed in a single continuum CSF phase at room temperature. Physiologically, blood cells and debris create a suspension when mixed into CSF. The biochemistry of blood coagulation within the CSF was not reproduced. Additionally, once exposed to the SAS environment, blood cells can rupture releasing oxyhemoglobin which is further enzymatically converted to bilirubin (63, 64). While the electrolytes and enzymatic interactions between blood components and CSF have an impact, our fluid mechanical study did not take into account pharmacokinetics of blood proteins, blood cell lysis, and blood cell component metabolism. Accounting for red blood cell byproducts and reaction kinetics could provide a more realistic scenario for testing biochemical effects of SAH. However, the effective diffusivity is independent of molecular diffusivity since Rmax is large compared to unity. Therefore, the chosen tracer provides good similitude for blood. The in vitro experiments were performed at 19 ºC. We did not create a thermostatic environment due to size limitations, because the density ratio between CSF and fluorescein tracer is not different whether the experiment is conducted at 19 ºC or at body temperature of 37 ºC.
In the comparison between simulation and experiments, the highest deviations occurred in the cranial SAS. It is likely these differences were larger in the cranial SAS due to the 2D imaging technique that used a picture obtained for a single angle relative to the model, whereas, the CFD concentrations were precisely averaged across each 3 mm thick slice, including fluid located within the ventricles of the brain. Future work could potentially improve agreement of in vitro and numerical results by utilizing tomographic projection imaging (65) of the in vitro model or quantitative contrast enhanced MRI techniques (66).
The numerical simulations in this study were based on MRI measurements for a single subject-specific CSF system geometry and CSF flow waveform. These parameters should be investigated in a larger cohort to determine the potential impact of age, sex, and disease states on CSF solute transport. However, the consistency of CSF dynamics across humans in the healthy state and with ALS has been studied by our group and we found relatively small differences across subjects (67). Therefore, we expect our results would hold true for other human cases with slightly different CSF space geometry. Also, for future research, we may need to investigate the effect of filtration for a longer periods of 48, 72 or 120 hours for different neurological conditions (68).
Our modeling approach did not include flow oscillations within the ventricles (69, 70) or a respiratory component of CSF pulsations (71-73) because the MRI scanning time did not allow measurement of these parameters in addition to the other parameters used to formulate the model. Additionally, the presented model used a rigid material in which boundary motion of the dura was not prescribed (25). This model also did not account for permeability of the CNS tissue or dura matter (74). We chose a rigid model without permeability to allow verification of numerical results in a precisely known domain. Future studies should investigate the relevance of tissue permeability and motion.
Our model only had one single site of CSF production in the lateral ventricles because the focus of our study was on CSF solute transport within the subarachnoid space, external to the ventricles, we simplified CSF production to occur at a single site within the lateral ventricle. CSF production was assumed to flow out into the cisterna magna where mixing occurs with CSF in the subarachnoid space. Also, the in vitro system did not allow imaging of tracer concentration within the ventricles, and therefore we were not able to compare in vitro to computational results within the ventricles. Future studies should investigate the impact of CSF production location by adding the choroid plexus in the third and fourth ventricles.
No attempt was made in this study to optimize catheter design or positioning for Neurapheresis therapy. The effect of Neurapheresis therapy on CSF steady-streaming velocities in the spinal SAS were investigated in our previous study (21). The present study extended the previous model by including a complete CSF system, integration of a two-phase model, and developing a method for in vitro verification of results.