Research articlesEnhanced wall shear stress prevents obstruction by astrocytes in ventricular catheters
Abstract
The treatment of hydrocephalus often involves the placement of a shunt catheter into the cerebrospinal ventricular space, though such ventricular catheters often fail by tissue obstruction. While diverse cell types contribute to the obstruction, astrocytes are believed to contribute to late catheter failure that can occur months after shunt insertion. Using in vitro microfluidic cultures of astrocytes, we show that applied fluid shear stress leads to a decrease of cell confluency and the loss of their typical stellate cell morphology. Furthermore, we show that astrocytes exposed to moderate shear stress for an extended period of time are detached more easily upon suddenly imposed high fluid shear stress. In light of these findings and examining the range of values of wall shear stress in a typical ventricular catheter through computational fluid dynamics (CFD) simulation, we find that the typical geometry of ventricular catheters has low wall shear stress zones that can favour the growth and adhesion of astrocytes, thus promoting obstruction. Using high-precision direct flow visualization and CFD simulations, we discover that the catheter flow can be formulated as a network of Poiseuille flows. Based on this observation, we leverage a Poiseuille network model to optimize ventricular catheter design such that the distribution of wall shear stress is above a critical threshold to minimize astrocyte adhesion and growth. Using this approach, we also suggest a novel design principle that not only optimizes the wall shear stress distribution but also eliminates a stagnation zone with low wall shear stress, which is common to current ventricular catheters.
1. Introduction
Hydrocephalus is a disease of the cerebrospinal fluid (CSF) circulation that often manifests with enlarged cerebral ventricles due to excess CSF in the cerebral ventricular system [1]. The shunt (figure 1a), a catheter-based CSF drainage system, has been widely employed to treat this condition. A typical shunt is made of a proximal (ventricular) catheter (figure 1b), a shunt valve and a distal catheter. The ventricular catheter is placed in the cerebral ventricles, and the distal catheter is placed elsewhere in the body for drainage. When the ventricular CSF pressure, also known as intracranial pressure (ICP), rises and the pressure differential across the valve becomes larger than a prescribed threshold, the valve opens and drains CSF from the ventricles, most often into the abdominal cavity or the right atrium [2].
Figure 1. (a) Illustration of shunt system. (b) Example of three-dimensional model of ventricular catheter, reconstructed from measurement of a Codman EDS 3 Clear Ventricular CSF Catheter [16].
In pediatric patients, the shunt system has a low lifespan, particularly due to obstruction occurring at the ventricular catheter by brain tissue [3]. A recent prospective study reported that 60% of pediatric shunts fail within 2 years, and the obstruction of the ventricular catheter is the most frequent cause, accounting for 27% of such failures [4]. Obstruction causes acute symptoms to patients, such as headaches, nausea, vomiting, irritability, cranial nerve palsies, blindness and even death. Thus, shunt obstructions require urgent shunt revision surgery, which carries the risk of infection and damage to brain tissue [5–8]. Although there is a variety of ventricular catheter designs commercially available, none have been shown in clinical trials to be superior in preventing obstruction [8].
Recent studies based on immunostaining of explanted ventricular catheters found that glial tissue ingrowth, mainly by astrocytes and microglia, is the most frequent culprit of obstructions [9,10]. Astrocytes and microglia are involved in the immune response of the central nervous system, forming dense glial tissue around foreign bodies such as neural electrodes [11] and ventricular catheters [9,10]. It has been reported that microglia first migrate to the catheter after shunt insertion and astrocytes gradually become the dominant cell type forming fibrous tissue in the catheter [9,10]. Given that astrocyte-dominant tissue typically becomes prevalent on the catheter surface in the late stage of cellular response to a catheter (greater than two months) [10], improving the shunt lifespan by years necessitates hindering astrocytic tissue formation.
Astrocytes on the inner walls of an implanted ventricular catheter encounter CSF flow (figure 2). This CSF flow touching the inner walls induces a shear stress to the walls (i.e. wall shear stress). As the size of astrocytes (approx. 10 μm) is much smaller than the characteristic length scale of a ventricular catheter hole (approx. 500 μm), we can assume that the fluid shear stress imposed by the CSF on the astrocytes is given by the wall shear stress. Since astrocytes are exposed to the shear stress imposed by the CSF flow and given the significant finding of astrocyte aggregation in shunt catheters, this study focuses on understanding astrocyte behaviour in response to fluid shear stress, which is one possible fluid-dynamic design parameter to help suppress astrocytic tissue formation.
Figure 2. Wall shear stress, τi, formed at the inner surfaces of holes and lumina due to CSF flow. The wall shear stress is assumed to be the fluid shear stress imposed on the astrocytes (shown in green) coating the walls. Holes that face each other have the same wall shear stress due to geometric symmetry. The subscript denotes the index of a segment that is counted from the catheter tip. The superscripts and represent hole and lumen, respectively. Wall shear stress defined here is the spatially averaged value.
The behaviour of astrocytes under long-term fluid shear stress is poorly understood, particularly in the context of ventricular catheter obstruction. Cornelison et al. [12] reported that when cocultured astrocytes and microglia are exposed to in vitro fluid shear stress for 1 h, they exhibit increased S1P3 expression which is upregulated in pro-inflammatory conditions [13]. Given that astrocytes in the inflammatory state can proliferate [14], the implication from this study is that fluid shear stress may enhance astrocyte proliferation. However, experimental results from Harris et al. [15] suggest that astrocytes are vulnerable to fluid shear stress particularly on longer timescales (approx. 10 h). The authors performed bioreactor studies in which astrocytes were allowed to migrate from an artificial brain parenchyma tissue mimic surrounding a ventricular catheter. They found that a flow culture of 18 h perfusion resulted in a lower number of astrocytes on ventricular catheters when compared with a static culture. We hypothesize that the lower number of astrocytes in the flow culture is either due to forced cell detachment by the shear stress or hindered cell proliferation.
To explore this hypothesis and to understand the behaviour of astrocytes under long-term fluid shear stress, we performed in vitro microfluidic experiments that imposed fluid shear stress on astrocytes for 48 h. We find that the long-term fluid shear decreases astrocyte confluency, which is the area percentage covered by cells and is an estimate of cellular growth rate. Additionally, we find a loss of the stellate cellular morphology, typical of healthy astrocytes (§2.2). Instead, the cells appear to form aggregates. Moreover, we find that astrocytes exposed to long-term fluid shear are detached more easily upon sudden transition to high fluid shear stress (§2.3). In light of the findings that astrocytes are vulnerable to long-term fluid shear stress, we show that the typical geometry of current ventricular catheters may promote astrocyte obstruction due to the inherent presence of regions with comparatively low wall shear stress. Using computational fluid dynamic (CFD) simulations of the flow in a typical ventricular catheter, and using a Poiseuille network model (PNM) proposed in this study, we conducted dimensional analyses of a typical ventricular catheter and derived a general design principle to optimize the wall shear stress distribution (§4). We also identify and discuss another weak point of typical ventricular catheters, which is the formation of a stagnation zone with low wall shear stress. Finally, we propose a novel ventricular catheter geometric design principle that both optimizes the wall shear stress distribution and eliminates the stagnation zone (§4.5).
2. Astrocytes vulnerable to long-term fluid shear stress
2.1. Microfluidic experiment set-up
We cultured a mouse astrocyte cell line (C8D1A, ATCC) in a commercial transparent microfluidic channel (μ-Slide I Luer, ibidi GmbH) to investigate the response of astrocytes under fluid shear stress (figure 3). Two cases were studied with the channel: (1) a static culture with zero fluid shear stress and (2) a flow culture with fluid shear stress of 3 mPa. The culture medium was Dulbecco’s Modified Eagle’s Medium (D6429, Sigma), supplemented with 10% fetal bovine serum (FBS001, Neuromics), 1% penicillin–streptomycin (#15140122, Gibco) and 2.5 U ml−1 nystatin (N6261, Sigma). Using a high-precision rotational rheometer (HR-1, TA Instruments), the viscosity of the medium was measured to be 1 mPa s at 37°C. Both cultures were maintained at 37°C in a humidified atmosphere of 10% CO2. Astrocytes were first cultured in flasks until their confluency reached 80–90% and then seeded into the channel with a seeding density of 2.0 × 104 cells cm−2. Seeded astrocytes were pre-cultured for 24 h in the channel to ensure cell adhesion. In this study, T = 0 h is defined as the time immediately after pre-culture. Passage numbers 8–11 upon delivery from ATCC were used in all experiments, where the passage number refers to the number of times a cell culture was subcultured.
Figure 3. (a) Transparent microfluidic channel used in this study (left) [18] and illustration of channel cross-section (right), with a bottom plate that is gas-permeable so that pH remains controlled with sufficient gas exchange. The bottom surface is chemically treated for adherence of cells. (b) Schematic of microfluidic experiment set-up embedded in controlled CO2 environmental chamber.
For the static culture, the medium was changed every 24 h to ensure sufficient nutrient supply. For mammalian cell cultures in flasks, it is usually recommended to use a medium supply rate of 0.07–1 ml cm−2 d−1 [17]. In our case, the medium supply rate was 0.09 ml cm−2 d−1, within the recommended range. We also confirmed that a medium supply rate of 0.18 ml cm−2 d−1 did not result in a statistical difference in confluency evolution. For the flow culture, as illustrated in figure 3b, the equilibrated medium with pH 7.4 was injected into the microfludic channel by a syringe pump with constant flow rate of 6 μl min−1 to achieve 3 mPa of uniform wall shear stress across the channel’s bottom surface. This wall shear stress was less than one-tenth of the wall shear stress that induced instant forced detachment of the cells. We monitored the pH of both cultures using pH strips and observed that a pH of 7.1–7.4 was maintained in both cultures. The cultures were maintained until T = 48 h. Phase-contrast microscopy (Ti-U, Nikon) was performed every 24 h to monitor changes in cell confluency and morphology.
2.2. Decrease of confluency and change in cell morphology upon long-term fluid shear stress
Astrocytes in static culture exhibited a gradual increase of confluency and maintained their star-shaped/stellate morphology that is the typical shape of physiological astrocytes; this stellate shape is commonly observed in both nonreactive and reactive astrocytes [19]. By contrast, astrocytes under prolonged fluid shear stress showed a decrease in confluency within the first 24 h, a loss of their characteristic star-like morphology, and the formation of cell aggregates (figures 4 and 5). Confluency was estimated across a region where fluid shear stress was homogeneous (electronic supplementary material, S3) and measured using a segmentation method proposed by Jaccard et al. [20] (electronic supplementary material, S4). The loss of characteristic projections under applied fluid shear stress may suggest cytotoxicity of long-term fluid shear stress to astrocytes as such loss is frequently observed in astrocytes with pathological conditions [21–24]. Also, cellular aggregates found on explanted ventricular catheters showed an extensive mesh of astrocytes with characteristic cellular projections emanating from the cell bodies [10], characteristic of healthy astrocytes, which we found in our static cell culture but not in the flow culture.
Figure 4. Phase-contrast imaging of static (a) and flow (b) cultures, showing clear difference in confluency of cells over time (up to 48 h here). Scale bar is 200 μm. Figure 5. Quantification of change of cell confluency over time in static (0 mPa shear stress) and flow (3 mPa shear stress) cultures, such as those shown in figure 4. Error bars reflect the standard deviation over n number of independent experiments performed.
2.3. Long-term fluid shear stress facilitates forced detachment by high fluid shear stress
We further observed that astrocytes exposed to long-term moderate fluid shear stress were more easily detached from the surface upon sudden imposition of high fluid shear stress. At T = 72 h, both static and flow cultures were subjected to a sudden high fluid shear stress of 30 mPa. Here, the ramping time from 0 to 100% of flow rate was about 17 ± 3 s (SD with n = 3), indeed a much shorter ramping time than the 163 ± 24 s (SD with n = 3) used for imposition of continuous flow rate conditions in other experiments. The channels were exposed to the high fluid shear stress for 1 min and were imaged via phase-contrast microscopy to subsequently digitally quantify the resultant change in confluency. We performed this procedure three times for each channel, with a 3-min total exposure time to high shear stress. This high fluid shear stress corresponds to a level that can be found in typical ventricular catheters with flow rates of Q = 1 ml min−1, a reported upper bound on shunt flow rate [25,26]. We observed that after 3 min, astrocytes cultured under continuous moderate shear stress showed a decrease in relative confluency (defined as confluency normalized by the initial confluency) due to both detachment and cell retraction. In contrast, static cultured astrocytes exhibited a decrease, but solely due to cell retraction (figures 6 and 7). The videos provided in electronic supplementary material, movie S1, show that the detachment upon high shear stress only occurs to astrocytes cultured under continuous moderate shear stress, in contrast to astrocytes statically cultured, which appear more robustly attached and instead only show a change in morphology in response to the suddenly imposed high shear stress condition.
Figure 6. Phase contrast imaging of the response of astrocytes to short high fluid shear stress of 30 mPa at T = 72 h. Here (above each column), t is the duration for which the high fluid shear stress is imposed. Astrocytes cultured under continuous long-term moderate fluid shear stress (b) exhibit more detachment, while those from static culture (a) only show change in cell morphology, with noticeable regions of cell retraction. Scale bar is 200 μm. The videos are provided in electronic supplementary material, movie S1. Figure 7. (a) Changes of confluency of astrocytes from the static and flow cultures when subjected to 30 mPa fluid shear stress computed from images such as those shown in figure 6. (b) Changes of relative confluency corresponding to (a), normalized by confluency value at t = 0 min. The difference in relative confluency between the static and flow cultures increases over time. At t = 3 min, the difference between the groups is 22%, a statistically significant difference (p < 0.05 of a two-sided Mann–Whitney U test). Error bars give the standard deviation across independent experiments (n).
Although little information is available on the temporal change of shunt flow rates, we can expect that the flow rate fluctuates with changes in ICP, which can be caused by posture change or respiratory variation in ICP that cause intermittent opening of the shunt valve [25,27]. According to a bench test with actual catheters, with mathematical models of ICP, the flow rate can attain maximum values close to 1 ml min−1 [25]. We performed a CFD simulation with 1 ml min−1 of the flow rate in the catheter given in figure 1b and observed that the wall shear stress at the most downstream lumen was larger than 50 mPa. This implies that astrocytes in an actual ventricular catheter can be exposed to fluid shear stress that induces forced detachment—as shown in our experiment—and which can be enhanced by long-term fluid shear stress whose fluctuating timescale and amplitude in patients were observed to be of the order of O(1 h) and O(0.1 ml min−1), respectively [28].
Ultimately, the experimental results shown in this section provide a key insight for a new approach to the design of ventricular catheters: How can wall shear stress distribution on the inner wall surfaces be optimized to hinder obstructive astrocytic glial tissue formation?
3. Formation of low wall shear stress zone in typical ventricular catheter
3.1. Computational fluid dynamics simulation set-up
In the light of our discovery of the vulnerability of astrocytes to long-term fluid shear stress, we performed CFD simulations (Fluent 2019 R1) to investigate the wall shear stress distribution in typical ventricular catheters. In this study, we considered a case where the cerebral ventricles are so enlarged that frictional loss from the ventricular wall is negligible. We ensured this condition in the simulation by enclosing the ventricular catheter into a box domain whose walls are sufficiently distant from the catheter (figure 8), which also meets the distance condition suggested by Weisenberg et al. [29]. We imposed a constant normal velocity condition on the surface of the domain that faces the tip of the catheter and zero-pressure condition on the outlet of the catheter. A no-slip boundary condition is applied to the other walls.
Figure 8. Example of three-dimensional models used in our CFD simulations. The size of the domain is set to be sufficiently large, to ensure negligible wall effects, including frictional loss. The inlet and outlet have constant-velocity and zero-pressure conditions, respectively. No-slip boundary conditions are imposed on the other walls.
Flows in ventricular catheter have low Reynolds numbers (Re); thus, a laminar model that solves the incompressible Navier–Stokes equations was used in all simulations. Re is defined as
3.2. Quasi-exponential decay of wall shear stress across typical ventricular catheters
Figure 9 shows the design of a typical ventricular catheter. Here, a typical ventricular catheter represents a catheter whose holes have the same diameter, depth, spacing interval, and number of holes per segment. From CFD simulations, we found that the typical ventricular catheter features a quasi-exponential decay of MWSS over decreasing index of holes or lumina (figure 10). This exponential decay leaves many holes with low WSS, which can be favourable to the adhesion and growth of astrocytes. In the simulation, we set the flow rate Q to 0.03 ml min−1 which is 10% of the typical CSF production rate in the cerebral ventricular system [32]. This flow rate represents a physiological lower bound of the shunt flow rate, which we consider to be a worst-case scenario in terms low WSS values insufficient to alter astrocyte dynamics and adhesion.
Figure 9. Schematic of a typical ventricular catheter and its geometric parameters. Every hole has the same diameter d, depth l, wall thickness η, and spacing interval L. Each hole segment (dashed box) has m holes, and the total number of hole segments is n. Figure 10. Results of CFD simulations discussed in §3.2 on a typical ventricular catheter with total flow rate of 0.03 ml min−1, which is 10% of a typical CSF production rate. (a) Wall shear stress contour inside the catheter. Scale bar is 1 mm. (b) Spatially averaged mean wall shear stress at each catheter section shown in schematic (a).
We observed from the astrocyte experiments (§2) that fluid shear stress of approximately O(1 mPa) prevents astrocytes from increasing confluency and from maintaining their healthy morphology. When applying 1 mPa as a cut-off WSS to the simulation in figure 10, we conclude that all holes and lumina except H8 and L8 have WSS that are lower than the ideal threshold condition that could prevent obstruction. This implies that a typical ventricular catheter may not have sufficient WSS across all inner surfaces if it is designed without particular consideration for the optimization of WSS distribution. We thus turn towards a more systematic approach to optimize the ventricular catheter design to ensure WSS values hindering astrocyte attachment and potential for obstruction.
4. Optimization of typical ventricular catheter using dimensional analysis
4.1. Poiseuille flow in ventricular catheters
Building on the key combined insights that (1) astrocytes are vulnerable to fluid shear stress and (2) they can play a major role in catheter obstruction, maximizing the WSS inside a ventricular catheter is a valuable strategy to reduce obstruction. This requires understanding the characteristics of the flow within typical catheters. To develop this understanding, we performed direct flow visualization on an actual catheter (Codman EDS 3 Clear Ventricular Catheter, Codman & Shurtleff), using direct fluorescent particle tracking performed by high-speed fluorescent microscopy (Ti-U, Nikon). Given the curvature of catheter tubing, accurate measurements required optical correction of the curvature-induced image distortions. We did this with refractive index matching between the chosen working liquid and the material of the catheter. The details of the experimental methodology, including the calculation enabling us to determine the optimal choice of refractive index matching are in Lee [33] and Saksena et al. [34].
From the visualization experiments, we first found that the flow entering a hole does not have a uniform velocity profile (figure 11b). The entrance length l at which a laminar flow becomes fully developed classically follows l/d = 0.06Re, where d is the hole diameter [35]. Assuming that the flow enters a catheter hole with a uniform velocity profile, the entrance length l would be ∼O(0.1d) for a hole with local Reynolds number Re ∼ O(1). In fact, our measurements (e.g. electronic supplementary material, movie S2) show that the flow profile is pre-developed from the outside of the hole, inducing an entrance length that is shorter than that expected from classical estimates. Indeed, Sparrow & Anderson [36] performed numerical simulations of a two-dimensional flow that is drawn from a large reservoir to a channel, finding that the entrance length for Re = 25—which is the highest Re in a catheter system—to be around 35% of the channel height. Note that the classical entrance length estimation gives 150% of the height [35], four times larger than the value for a flow from the large reservoir to a small channel. This implies that the flow at the catheter hole would become a fully developed Poiseuille flow shortly upon hole entrance. Given the lack of prior quantitative flow measurements in such catheter systems [37], we had to directly measure the actual velocity profiles at the catheter holes to confirm the nature of the flow profiles.
Figure 11. Flow visualization at a hole closest to the valve, using fluorescent particle tracking by high-speed microscopy. (a) Dashed and solid boxes indicate the region of interest in (b) and (c), respectively. Scale bar is 1 mm. (b,c) Pathlines of fluorescent particles illustrate the entry of a flow, followed by the confluence of flows in the lumen. In both (b,c), the Reynolds number, (3.1), is 0.5. The plane of focus of the microscope objective was located to the middle plane of the catheter. Scale bar in (c) is 200 μm and also applies to (b). The videos of (b) and (c) are given in electronic supplementary material, movie S2.
Figure 12a,b shows an example of direct experimental measurements of velocity profile at a catheter hole. First, this measured—reconstructed from particle tracking—profile matches well the associated flow rate-matched theoretical fully developed Poiseulle flow profile, with a 5% error, showing excellent agreement with the Poiseuille fully developed flow hypothesis (figure 12c). In this comparison, the flow rate was computed from integration of the experimentally measured flow profile. Second, we also compare the CFD predicted flow profile against the measured profile—again, reconstructed from particle tracking—and find 12% error, showing that the CFD prediction is also reasonable (figure 12d). Here, the error is defined as ||V − Vexp||2/||Vexp||2, where V is a vector, the predicted velocity at all grid nodes, and Vexp is the corresponding vector from the experimentally measured velocity profile. The step size of the grid is 1% of the diameter of the cross-section.
Figure 12. Measurement of three-dimensional velocity profile. (a) Velocity profile at a catheter hole closest to the valve was measured by direct particle tracking with high-speed imaging coupled to fluorescent microscopy. Using vertical layering of images, or z-stacking, we directly measured the three-dimensional velocity profile at the middle plane of holes. (b) Directly measured velocity profiles. Two-dimensional velocity profiles at different z-locations are given in electronic supplementary material, S1 with more details including error bars. (c) Poiseuille flow profile matches very well the measured profile. (d) The profile calculated by CFD analysis shows also a reasonable agreement with the directly measured profiles. Here, the Reynolds number, (3.1), is 1, and d and V are the diameter of the cross-sectional area and the mean y-directional velocity over the area, respectively.
Additionally, we also performed CFD simulations for a flow with higher inertia (Re = 25) confirming that the flows in holes and the lumen remain well approximated by a Poiseuille profile (electronic supplementary material, S1).
4.2. Poiseuille network model and identification of dimensionless numbers
Having validated that the flow is indeed of Poiseuille type in most of the relevant regions of a typical catheter (figure 12), we discuss here a PNM we developed to describe a typical ventricular catheter as a multi-pipe system where Poiseuille flow applies at every section. From the model, we identified dimensionless numbers that determine the wall shear stress distribution inside a catheter. Using CFD simulations, we validated this approach, showing that the matched dimensionless numbers across different structural models lead to the same wall shear stress distribution as that of the PNM developed and discussed in detail in electronic supplementary material, S2.
The PNM consists of the following. Consider a typical ventricular catheter with lumen diameter D, hole diameter d and depth l, hole spacing interval L, wall thickness η, m number of holes per segment and n number of segments (figure 9). Here, we assume that the hole depth, l, is approximately the wall thickness η. Using the PNM, we predict the spatially averaged MWSS at the inner surface of a hole or lumen as
From (4.1) to (4.3), four dimensionless numbers associated with a typical ventricular catheter can be identified
Figure 13. Non-dimensional MWSS distributions in three different scenarios, obtained from CFD simulations. All scenarios share the same m = 2, n = 8, and .
Figure 14. Three different ventricular catheters that share the same dimensionless numbers of m = 2, n = 8, and . The dimensional geometric parameters of the catheters are given in table 1. Scale bar is 1 mm.
| l (mm) | L (mm) | d (mm) | D (mm) | Q (ml min−1) | μ (mPa s) | Re | |
|---|---|---|---|---|---|---|---|
| scenario 1 | 0.60 | 1.0 | 1.00 | 1.3 | 0.03 | 0.8 | 1 |
| scenario 2 | 0.72 | 1.2 | 1.08 | 1.4 | 0.30 | 0.8 | 6 |
| scenario 3 | 0.84 | 1.4 | 1.15 | 1.5 | 1.00 | 0.8 | 18 |
4.3. Manipulation of dimensionless numbers to enhance wall shear stress
Here, using CFD and dimensional analysis, we studied how the MWSS levels at holes and lumina can be optimized by adjusting the dimensionless numbers. As we are now interested in the dimensional MWSS values, we re-express (4.1)–(4.3) in their dimensional form:
Using CFD, we show that the MWSS monotonically increases at every section when m, n or decreases or increases (figure 15). Unlike these straightforward trends, increasing enhanced the value of MWSS of every lumen considered here, but not of every hole. Starting from a geometric model that is not optimized, we optimized the MWSS distribution by controlling a single dimensionless number at a time. During the optimization, we also keep the geometric parameters in a design range that is relevant and consistent with current commercial catheters [2,26]. The geometric parameters of the starting geometry are
Figure 15. Improving wall shear stress distribution by manipulating a single dimensionless number at a time. All results were obtained from CFD simulations. The total flow rate and CSF viscosity were 0.03 ml min−1 and 0.8 mPa s, respectively.
As can be seen in figure 15, we first tested the effect of by increasing its value from 0.3 to 0.6, from the circle to square symbols, while keeping the other dimensionless numbers fixed. Increasing helped optimize the MWSS distribution inside the catheter. Indeed, increasing increased the minimum MWSS of both holes and lumina, i.e. the MWSS increased at H1 and L1. The PNM provides the rationale for such changes. Substituting (4.4) into (4.8) solves for the MWSS at the first hole which is the minimum MWSS across all holes:
Now, from (4.4) to (4.13), we obtain
When it comes to the lumen regions (L1–L8), the increased enhanced the MWSS levels in all lumina except for L8 whose MWSS remains unchanged. Plugging (4.14) into equation (4.9) gives
As a next step, we changed from 0.77 to 0.46 (from square to triangle symbols in figure 15), keeping the other dimensionless numbers fixed. Decreasing significantly enhanced the MWSS levels at all sections. This implies and , which are proved in electronic supplementary material, S5.3 and 5.5. Changing has a greater effect on the MWSS distribution, compared with changing other dimensionless numbers. This can be attributed to the high-order nonlinear effect that can be identified in the PNM system (equations (4.7)–(4.9)).
Increasing raised the MWSS of all sections (from triangle to right-pointing triangle symbols). As τd is the non-dimensionalizing factor in the PNM (equations (4.1)–(4.3)), MWSS levels at all sections are simply proportional to . Since designs with different n do not allow the one-to-one comparison across sections, we now compare the minimum MWSS of holes or lumina. and are the minimum MWSS across holes and lumina, respectively, according to (4.4) and (4.14). As can be seen in figure 15, decreasing n increases both and (from right-point to left-point triangles), since when n1 > n2 in (4.13).
In sum, in this section, using the CFD and our proposed PNM, we elucidated how dimensionless numbers controlling catheter design should be manipulated to optimize the WSS distribution inside a catheter. The final MWSS distribution, shown with diamond markers in figure 15, has MWSS levels larger than 1 mPa in all sections, meeting optimal threshold condition of minimal adhesion and ease of removal of astrocytes, thus expected minimal flow obstruction potential.
4.4. Formation of stagnation zone at the catheter’s tip
Although we showed that the MWSS distribution can be optimized by manipulating the dimensionless numbers, there is still a region which the approach cannot optimize. Indeed, the analysis of §4.3 does not predict the WSS distribution at the surfaces of the region that is shown boxed in figure 16. This region features a stagnation zone, where CSF stagnates and recirculates, inducing very low shear stress on the wall. Based on our results above (§2), this region would be favourable for astrocyte accumulation, allowing for robust adhesion in the region and proliferation that could propagate downstream over time. To avoid this particular stagnation region, in the next section, we propose a new design principle that suppresses such stagnation zone inherent to current ventricular catheter designs.
Figure 16. Formation of stagnation zone, revealed by CFD calculations to be near the tip of a typical ventricular catheter, here shown for total system flow rate of Q = 0.03 ml min−1 and viscosity μ = 0.8 mPa s. The catheter and wall shear stress contour shown here corresponds to the left-pointing triangle markers in figure 15. The stagnation zone has very low wall shear stress, three orders of magnitude lower than 1 mPa, which is the cut-off wall shear stress. Scale bar is 1 mm.
4.5. A ventricular catheter with open tip-end and its optimization
We suggest a new geometry whose tip has an aperture with a depth of Le (figure 17a). The newly formed aperture is now called L0. Using a similar argument given in the derivation of the PNM for typical ventricular catheters, we can introduce another PNM to take the new aperture into account:
Figure 17. (a) Geometric parameters involved in designing a novel catheter with open tip end discussed in §4.4. (b) WSS heat-map of the catheter with such open end optimized for all MWSS values to be larger than 1 mPa, i.e. meeting the threshold condition of low proliferation and adhesion of astrocytes. Scale bar is 1 mm.
Figure 18. MWSS value distribution formed in an optimized catheter with open tip end (§4.4), all maintained above the 1 mPa threshold above which low proliferation and adhesion of astrocytes are expected. An error between the MWSS level from the CFD and PNM at a section is less than 16%, where the error is quantified by |MWSSPNM − MWSSCFD|/MWSSCFD.
As can be seen in the computational (CFD) results of figure 17b, for Q = 0.03 ml min−1, the optimal solution shows MWSS values larger than 1 mPa for every inner surface, with no stagnation zone. The PNM calculation also shows a good agreement with that from the CFD analysis (figure 18), confirming again that the PNM can be used instead of CFD to design optimized ventricular catheters while ensuring not only fast computation but also accuracy.
5. Discussion
Hydrocephalus involves enlarged cerebral ventricles due to excess CSF in the cerebral ventricular system. Ventricular catheters have had great success in alleviating this condition. However, they have a low lifespan due to obstruction, with 60% failure rate within 2 years. The obstruction is caused in large part by glial tissue ingrowth, consisting mainly of astrocytes and microglia. These two cell types populate the catheter at different timescales, with early migration by microglia and later dominance by astrocytes. Improving the shunt lifespan by years particularly requires prevention of the astrocyte-dominant tissue formation since astrocytes are most frequently found in catheters explanted for late shunt failures (greater than two months). We focused this study on elucidating the long-term fluid shear stress effect on astrocytes in the context of the obstruction of ventricular catheters and used our findings to propose a systematic and efficient method of optimization of ventricular catheter designs that can alleviate the adhesion and proliferation of these cells, thus potentially addressing one family of obstructions. To do so, we conducted in vitro cultures of astrocytes in microfluidic channels, mimicking glial tissue formation in ventricular catheters. We discovered that long-term fluid shear stress decreases confluency and increases loss of their star-like morphology. Furthermore, the long-term fluid shear stress facilitated the forced detachment by suddenly imposed high fluid shear stress that could be encountered during regular changes of position of patients, coughs, that result in shunt-valve opening. Our results offer fundamental insights into an approach for geometric optimization of the design of ventricular catheter intended to minimize astrocyte-induced obstructions.
The underlying mechanism governing the observed behaviour of astrocytes upon long-term shear fluid stress remains to be confirmed. The literature suggests that it may be governed by mechano-sensitive calcium channels on the cell membrane. Indeed, Charles et al. [40] found that mechanical poking to rat glial cells results in increased measured calcium levels in the poked glial cell and also generates calcium waves from the poked cell to neighbouring cells. More recently, Maneshi et al. [41] identified the type of calcium channels that causes calcium entry into rat astrocytes upon fluid shear stress shock. Given this mechano-sensitive calcium channel of astrocytes, it is also known that calcium overload in glial cells can trigger their death [42–44]. These prior results coupled with our results suggest that long-term fluid shear stress may induce prolonged opening of astrocyte calcium channels, leading to a disturbed homeostasis of their cytosolic calcium level, ultimately causing decrease in their confluency and loss of their typical star-like morphology. Note that our results on cytotoxicity of fluid shear stress to astrocytes were derived using culture of a single cell type.
From detailed analyses of explanted catheters, it is known that microglia first migrate to the catheter and astrocytes form glial tissue thereafter [9,10]. Given that microglia have been found to support the function of astrocytes in multiple immunological contexts [45,46], investigating the response of a co-culture system of astrocytes and microglia under shear flow would be a valuable next objective to more precisely understand the obstruction by astrocytic glial tissue. Also, studying the activity of glial cells under long-term shear flow, such as identifying associated gene expression profiles, would enable us to further characterize the biological state of glial cells in response to persistent shear flow. The results presented in this study are a baseline for future studies considering additional complexity and factors from co-culturing with microglia to preconditioning astrocytes to a biochemical state that relates to a specific pathological condition.
Lin et al. [37] first reported that typical ventricular catheter designs exceedingly concentrate flow at the most downstream set of holes. The authors hypothesized that the elevated flow through these holes can elevate the probability of blockages at these holes and that their obstruction may extend to the luminal part of the catheter and thereby disable the entire catheter at once. In support of their hypothesis, the authors state that obstructing tissue is found most frequently around the most downstream set of holes in explanted catheters, yet clear evidence for this claim is currently lacking. However, based on this hypothesis, multiple studies have attempted to homogenize the flow rate distribution across catheter holes by changing the catheter hole geometry [29,37,47] in an effort to decrease the probability of aspirating bulk tissue and cells at a given hole. By contrast, based on the response of astrocytes to long-term shear flow, we set the design objective for ventricular catheters to maximizing wall shear stress across the inner surfaces of a catheter. This objective is fundamentally different from the objective of the prior studies on catheter design optimization that focused on homogenizing flow rate distribution across holes. Indeed, we established another goal for designing ventricular catheters, particularly related to the obstruction by astrocytes: enhancing the wall shear stress inside a ventricular catheter. It is important to note that this goal is not necessarily attained by homogenizing the flow rate distribution. According to the PNM, is scaled by , where and di are the flow rate and diameter of the ith hole, respectively. This scaling implies that a geometry that has equally distributed flow rates can fail to achieve the minimal value of wall shear stress across a hole that hinders astrocyte obstruction, due to hole diameters that are chosen to be too large. Our PNM for ventricular catheters can also be used for the exploration of a range of viable design principles that seek to achieve multiple design objectives regarding the catheter flow. For example, one may be interested in wall shear stress maximization and also flow rate homogenization across holes. Such a solution can be obtained, as illustrated in electronic supplementary material, S7, by coupling the PNM with a multi-objective genetic algorithm [48]. Moreover, the lumped-element approach of the PNM enables exploration of designs whose hole depths, hole spacing, and hole diameters are not constant, allowing us to explore flow optimization in a large parameter space [49].
This study tackles how astrocytes attached on the catheter surface respond to long-term fluid shear stress. It does not address the mechanism of initial migration of astrocytes to the catheter. Harris & McAllister [50] conducted bioreactor experiments that exposed different catheter models to an astrocyte suspension. The authors sought to address the effect of hole size on the adhesion of astrocytes from the liquid suspension. Their study shows that the smaller the catheter hole (and the higher the computed wall shear stress), the higher the number of astrocytes that adhere to the hole surface. Our work here appears to contradict the results obtained by Harris & McAllister [50]. However, CFD simulations of their catheter designs, including the effect of taper of the catheter holes that are evident from fig. 5 in Harris & McAllister [50], demonstrate that their calculated wall shear stress for the smaller catheter holes when ignoring the taper is an overestimate of the average wall shear stress across holes when taking the taper into account. When accounting for the taper, the catheters with the smaller holes have smaller wall shear stress values compared to those with larger holes. Detailed simulations of the shunt flow through holes of different size and taper might be required to understand further how wall shear stress is affected by various design parameters.
Lastly, we suggest that the introduction of bulk tissue, such as choroid plexus, to a hole can form low wall shear stress zones at the hole surface. Our preliminary CFD results given in electronic supplementary material, S8, show that a partially blocked hole results in local regions where wall shear stress is lower than that of the unblocked control case. This result implies that astrocytes may grow in the regions of low wall shear stress, filling the spatial gap between the blocking tissue and the hole surface. This hypothesis aligns with the observations by Hanak et al. [10] that astrocytes are found between the catheter surface and bulk tissue.
In sum, using a microfluidic culture system, we showed that astrocytes are vulnerable to long-term fluid shear stress. Based on this insight, and having experimentally confirmed Poiseulle-type flow in the catheter, we developed a physics-based PNM to guide optimization of the geometric parameters to enhance wall shear stress inside typical ventricular catheters in addition to a design principle that suppresses a potentially nefarious flow stagnation zone which is commonly formed in current typical ventricular catheters. The design principles [49] provided in this study are expected to extend the lifespan of ventricular catheters and enhance the quality of life of hydrocephalus patients.
Data accessibility
The key experimental and numerical data are all given in the article and electronic supplementary material.
Authors' contributions
S.L. carried out the laboratory work, data collection and analysis, clinical sample analysis, the theoretical and numerical computations, participated in the design of the study and drafted and revised the manuscript; N.K. carried out initial explorations of the microscopy and CFD simulations; J.H. supervised clinical data collection and critically revised the manuscript; T.H. and L.B. conceived of the study, designed the study, supervised the study, coordinated the study and helped draft and revise the manuscript. All authors gave final approval for publication and agree to be held accountable for the work performed therein.
Competing interests
We declare we have no competing interests.
Funding
We thank the Edgerton Fund and the MIT Research Committee Funds (Reed, Ferry and Westaway) for partially supporting this work. S.L. thanks the Kwanjeong Educational Foundation Scholarship for partial financial support.
Acknowledgements
S.L. thanks Raj Dandekar at Bourouiba Group and Tak Ko at Picower Institute for valuable discussions. The authors wish to thank Leewon Seo for help with illustrating the shunt system and Dr Michael D. Perloff, Brandon Finn, Helena Lau, and Dr Sherida Padilla at Boston Medical Center for help with obtaining the CSF samples.
