3.1 Design
In the development of our duckbill valve, we have adopted a design featuring flexible leaflets constructed from polydimethylsiloxane (PDMS) as shown in Fig. 2. As depicted in Fig. 2a, we have integrated a silicone tube with a 0.6 mm outer diameter between the leaflets to maintain the valve’s inlet side in an open position. A comprehensive illustration of the valve’s mechanism can be found in Fig. 6a. The dynamic operation of this valve relies on its response to pressure differences: when pressure differential exceeds cracking pressure (∆ P > PT), the leaflets deflect apart, facilitating fluid flow. Conversely, when pressure differential is lower than cracking pressure (∆ P < PT), it causes the leaflets to close, effectively preventing reverse flow. The valve’s behavior is influenced by a combination of factors, including the internal stresses within the PDMS material resulting from tube insertion and the specific geometric attributes of the leaflets. We have fine-tuned the cracking pressure and outflow resistance by adjusting leaflet parameters, such as the width of the fluid channel (W), bill length (L), and thickness (T). These adjustments allow us to tailor the valve’s performance to meet the requirements of specific applications. For reference, conventional shunts equipped with a differential pressure valve (DPV) are categorized based on their cracking pressure, typically classified as low (3.68 mmHg), medium (7.36 mmHg), or high (11.03 mmHg). [35–37] The fabricated valve presented here can be manipulated to fit within these specific ranges, providing versatility for individualized applications.
3.2 Valve behavior using benchtop setup
The characteristics of the PDMS duckbill valve were assessed using the benchtop setup depicted in Fig. 3. The temporal response for this valve’s geometry, characterized by a channel width of 0.8 mm, a bill length less than 0.5 mm, and a thickness of 0.1 mm, was studied with regard to its reaction to pressure and flow rate changes during pump operation, as demonstrated in Fig. 5a and Fig. 5b with rectangular-shaped waveforms applied via a programmed syringe pump. By analyzing the pressure and flow rate waveforms, we observed that during periods of negative pressure, the flow rate approached zero, indicating no detectable leakage. Upon switching the pump’s direction to forward, the pressure began to rise. Once the pressure reached the cracking pressure (as indicated by red dots), fluid release was initiated by the valve, resulting in an increased flow rate. The valve’s outflow resistance contributed to a continuous pressure increase. When the pump’s direction was reversed, the pressure decreased to negative values, and the flow rate returned to zero. The cracking pressure was defined as the pressure when the flow rate was in the range of 20–40 µL/min. Any flow rates below this range were attributed to environmental artifacts in the setup. These environmental artifacts refer to minor deviations in the flow rate measurements that can arise from various sources in the experimental setup, such as tubing compliance and the pump and sensor response time. [38] The relationship between pressure and flow rate, established through pressure vs. flow rate plotting, is presented in Fig. 5c. The valve exhibited highly directional behavior, demonstrating significant diodicity with averaging reverse flow leakage of -11 ± 0.0006 µL/min. However, this value did not represent the actual reverse flow rate of the valve, which might be considered as leakage. Instead, this can be considered as artifacts due to the environmental factors mentioned above. The measured cracking pressure was 2.22 ± 0.07 mmHg, falling within a low cracking pressure range of standard DPV shunts (3.68 mmHg). Despite the pump applying a flow of 1 mL/min, the valve’s resistance, combined with the experimental setup, resulted in a reduced flow rate. By analyzing the plot, we defined the valve’s outflow resistance (22.00 ± 0.70 mmHg/mL/min) as the average resistance across the pressure range of 2 – 18 mmHg, utilizing the linear fit function in Matlab.
As discussed in the Design section, the valve’s behavior can be controlled by adjusting parameters to achieve target cracking pressure ranges, which may vary on an individual basis for DPV shunts categorized as having high, medium, or low cracking pressure. In Fig. 6a, the thickness (T) of the PDMS layer was kept constant at ≈ 0.1 mm, while we focused on adjusting two key parameters: the width of the fluid channel (W) and the bill length (L). To modify the width, the deposition of PR on the PDMS surface was varied during the fabrication process, leading to alterations in the pattern derived from the photomask. For the adjustment of the bill length, precise trimming was performed under a microscope. The effect of parameter variation on valve behavior was analyzed by examining the relationship between pressure and flow rate, as illustrated in Fig. 6b. A total of six valves were tested for each parameter, showing an average reverse flow leakage of -8 ± 0.0048 µL/min. The cracking pressure associated with each parameter setting were presented in Fig. 6c and Table. 1. For a W of 0.6 mm, only bill lengths less than 0.5 mm showed cracking pressures within the medium target range for DPV shunts. In the case of a W of 0.8 mm, all bill lengths demonstrated cracking pressures within the target range, offering three pressure range options for DPV shunts: high, medium, or low.
In Fig. 6c and Table. 2, we calculated the outflow resistances for each parameter setting using the method of linear fit function in Matlab, as explained earlier. Notably, these outflow resistances are significantly higher than the values observed in DPV shunts, which are typically below 6 mmHg/mL/min. It is important to note that the increased resistances can be attributed, in part, to differences in materials and variations in the experimental setup. In the forthcoming Discussion section, we will explore potential solutions to mitigate and reduce these resistances.
Table 1: Cracking pressure of varying parameters. (n=6)
Width
Length
|
0.6 mm
|
0.8 mm
|
2 mm
|
25.36 ± 0.05 mmHg
|
10.62 ± 0.58 mmHg
|
1 mm
|
21.25 ± 0.92 mmHg
|
7.31 ± 0.09 mmHg
|
< 0.5 mm
|
4.58 ± 0.64 mmHg
|
2.22 ± 0.07 mmHg
|
Table 2: Outflow resistance of varying parameters. (n=6)
Width
Length
|
0.6 mm
|
0.8 mm
|
2 mm
|
50.39 ± 2.63 mmHg/ml/min
|
30.69 ± 1.35 mmHg/ml/min
|
1 mm
|
42.86 ± 2.74 mmHg/ml/min
|
28.57 ± 1.97 mmHg/ml/min
|
< 0.5 mm
|
32.77 ± 1.94 mmHg/ml/min
|
22.00 ± 0.70 mmHg/ml/min
|
To verify the reliability of the valve, we conducted long-term testing with 18,720 cycles (2 min / cycle) of repetitive forward / reverse sequences, controlled by a programmable pump. Three valves were tested, each with a W = 0.8 mm, a L < 0.5 mm, and a T = 0.04 mm. The results are presented in Table 3, which shows the average cracking pressure and average reverse leakage for each valve. While fluctuations in the cracking pressure were observed, these are attributed to unavoidable environmental artifacts related to the test setup. These fluctuations do not indicate degradation of the valve. We examined the valves after the long-term testing and did not observe any degradation. Additionally, during the long-term testing, unlike the short-term testing, we observed bubbles forming inside the tubes. Despite these constraints, the tested valves showed relatively constant cracking pressure and reverse leakage, demonstrating the valve’s reliability and robustness.
Table 3: Average values of cracking pressure and reverse flow leakage for 3 valves over 18,720 cycles.
Valve
|
Avg. Cracking Pressure [mmHg]
|
Avg. Reverse Leakage [µl/min]
|
1
|
1.365 ± 0.304
|
0.0117 ± 0.0041
|
2
|
1.167 ± 0.258
|
0.0017 ± 0.0123
|
3
|
1.529 ± 0.53
|
-0.00412 ± 0.0139
|
3.3 Animal study
The valve (W = 0.8 mm, L < 0.5 mm) was assessed through an infusion test conducted on a live rat to observe its behavior in vivo. Initially, our plan was to implant the valve’s outlet directly into the SSS. However, due to the small size of the rat’s SSS (≈ 1 mm), implanting the valve without additional support was challenging. Instead, we opted for an alternative location within the CM, which is the SAS situated between the medulla and cerebellum, as shown in Fig. 7a. To understand the CSF pathway, it is essential to note that CSF flows from the lateral ventricle to the CM, then proceeds to the SAS, and finally drains into the SSS through the AGs (Fig. 7a). The choice of the CM insertion offered the advantage of being able to observe the fluid flow through the valve since the valve’s outlet was exposed.
For the in vivo test, we used a total of seven rats. Four rats were successfully tested, as shown in Fig. 7b-d and Fig. S-1. In the other three rats, we encountered inlet blockage issues during the valve insertion into the CM. Despite several attempts to relocate the valve, the CM was damaged, necessitating the use of additional rats. As depicted in Fig. 7b-d, we conducted infusion tests on three individual rats and presented the results of these tests for each rat separately. The results of the infusion tests, summarized in Table 4, show significant differences in ICP changes between treated and untreated states across three cycles for three individual rats. In the treated state, the increases in ICP were consistently lower compared to the untreated state. Additionally, after injection stopped, ICP returned to the baseline within 2 min for treated state. The untreated state, the return to baseline was slower (in some cases, the clamp had to be released to facilitate the return to baseline). Fig. 7d presented pressure data with baseline shift, which made it difficult to measure the ICP differences accurately. Although this result did not show as considerable changes in pressure compared to the results in Fig. 7b and Fig. 7c, discernible differences between the treated and untreated states were still observable. The consistent reduction in ICP increases in the treated state across all rats indicates the effectiveness of the valve in mitigating the rise in ICP during the infusion tests.
Table 4: Summary of ICP Changes in treated and untreated states
Rat
|
cycle
|
Condition
|
Baseline ICP (mmHg)
|
ICP increase (mmHg)
|
1
|
1st
|
Treated
|
9.50
|
3.02
|
Untreated
|
10.04
|
26.87
|
2nd
|
Treated
|
10.90
|
3.52
|
Untreated
|
10.90
|
26.73
|
3rd
|
Treated
|
10.50
|
3.73
|
Untreated
|
11.16
|
26.75
|
2
|
1st
|
Treated
|
7.10
|
1.50
|
Untreated
|
5.70
|
23.10
|
2nd
|
Treated
|
6.90
|
2.27
|
Untreated
|
4.80
|
21.00
|
3rd
|
Treated
|
5.42
|
0.91
|
Untreated
|
3.80
|
15.95
|
3
|
1st
|
Treated
|
11.54
|
3.52
|
Untreated
|
10.82
|
9.77
|
2nd
|
Treated
|
9.20
|
1.78
|
Untreated
|
8.34
|
7.80
|
3rd
|
Treated
|
5.96
|
1.26
|
Untreated
|
3.57
|
4.34
|