Multiscale Architecture Governs Stability in Suction-Actuated Variable Stiffness Catheters

Abstract

Endovascular procedures require devices with widely varying mechanical properties: flexibility for navigating tortuous vessels, and rigidity for stable therapeutic delivery. Suction-actuated variable stiffness sheaths attempt to address this challenge by incorporating axial wire string arrays that couple mechanically under suction to increase flexural rigidity. However, prototype devices achieve stiffening ratios well below theoretical predictions, suggesting that string array positioning and interlayer mechanics require investigation. We therefore investigated whether interweaving expanded polytetrafluoroethylene (PTFE) tape within the string array can enhance flexural rigidity modulation and improve bending uniformity along the catheter length. Prototypes with varying PTFE wrap configurations were fabricated and evaluated using three complementary approaches. First, flexural testing revealed that flexural rigidity in the actuated and unactuated states was largely unaffected by wrapping for small deformations. Second, curvature stability testing revealed that deformation through acute simulated vascular bends was higher than expected due to two failure mechanisms: slip, in which string arrays migrate after overcoming wrap-imposed friction, and buckling, in which arrays become locally pinned and deflect against the outer lumen. Finally, a mathematical model characterized stability limits as functions of the wrapping architecture and device mechanical properties, revealing criteria for which device performance improved. Results suggest design principles for intra-catheter wrapping that can narrow the gap between theoretical and achieved flexural rigidity ratios, potentially contributing to the development of endovascular devices capable of single-sheath navigation and intervention.

1. Introduction

Endovascular technologies enable minimally invasive treatment of vascular diseases by enabling interventionalists to navigate tools through the body’s vascular system and deliver therapy at distal target sites [1–3]. These techniques have become standard of care across a broad spectrum of conditions, including peripheral arterial disease [4,10,11], cerebral vascular disease [5–7,9], and treatment of acute ischemic stroke [1,8,17]. Operating through millimeter-scale punctures at the wrist or groin, interventionalists guide flexible catheters and wires under real-time fluoroscope imaging to reach distal vessels that were once accessible only through invasive open surgery [1–3]. Continued expansion of endovascular techniques has driven demand for devices with dramatically different mechanical properties: flexible devices capable of navigating tortuous anatomy without causing vessel trauma, and stable devices capable of providing platforms for therapeutic delivery [12–14,20,28]. This irreconcilable trade-off represents a core biomechanical challenge in endovascular surgery.

The conventional solution to this challenge relies on sequential exchanges of multiple catheters and sheaths of increasing stiffness, or combining multiple catheters and sheaths in a telescoping, coaxial fashion [15,16]. A flexible diagnostic catheter first navigates to the target anatomy, then is exchanged for progressively stiffer devices capable of supporting intervention. Each exchange, however, introduces risk of complications including vessel wall injury, thromboembolic events, and loss of vascular access [15,16,18]. Additionally, use of multiple catheters introduces increased cost and time into the procedure. Herniation, a mechanical instability in which stored elastic energy causes the catheter or sheath to suddenly deviate from its intended arterial pathway (Figure 1a), is a complication that often necessitates complete withdrawal and restart of the procedure [19,21,31]. This can pose potentially consequential risk in time-critical interventions such as stroke treatment, where every minute of delay increases the likelihood of poor clinical outcomes [17]. Similar challenges arise across both peripheral vascular and neurovascular procedures, highlighting a critical need for improved devices [18,19].

Figure 1. Variable stiffness catheters for neurovascular intervention.

(a) Schematic of transradial neurovascular catheter navigation illustrating successful advancement through tortuous vasculature (left) and a herniation event where the catheter buckles and fails to advance (right). (b) Exploded CAD rendering of a variable stiffness catheter showing the PTFE wrap construction. Scale bar, 1 mm. (c) Representative variable stiffness catheter (left, scale bar = 3 cm) and close-up photographs of the six PTFE wrapping patterns (Patterns 1–6) used in this study. Scale bar, 3 mm.

Several technologies have been developed to achieve variable stiffness in endovascular devices. These include magnetic manipulation of catheter tips [22–25], heating of shape memory polymers to induce flexural rigidity transitions [22–25], melting of low-temperature metals embedded within the catheter wall [26], and fiber jamming and friction-based mechanisms [27–28], and suction-actuated variable stiffness sheaths [32]. The latter are particularly promising as they achieve uniform flexural rigidity control along the device length and use simple activation mechanisms [28].

A suction-activated sheath design incorporates axially aligned metal string arrays positioned between inner and outer lumens that, in the unactuated state, can slide and rearrange along the inner catheter (Figure 1b). Upon application of suction through a syringe, the outer lumen contracts around the string arrays, pressing them against the inner catheter. This mechanical coupling transforms the loose strings into a unified composite beam structure with substantially increased flexural rigidity [32]. Composite beam theory applied to this architecture predicts stiffening ratios in the range of 150–880% [32]. Although prototypes have demonstrated clinically meaningful performance, transitioning from the flexibility of diagnostic catheters to the rigidity of support sheaths [32], the stiffening ratio falls substantially short of the theoretical range. Potential contributing factors include displacement of string arrays during bending, slip between layers under load, and non-uniform positioning of strings along the catheter length. Closing this gap in performance requires a deeper understanding of string array mechanics under clinically relevant loading conditions.

To explore this, we studied the structural mechanics of the string arrays, focusing on the weaving of polytetrafluoroethylene (PTFE) tape through the string array (Figure 1c), used to maintain spacing and prevent axial displacement during device manipulation [32]. We hypothesized that this wrapping is a determinant of device mechanical performance, including resistance to slip and buckling under bending loads, and uniformity of flexural rigidity changes along the catheter length. Prototype devices with varied wrap configurations were fabricated and evaluated using three complementary experimental and computational approaches. Flexural testing quantified flexural rigidity profiles along the catheter length in both actuated and unactuated states. Curvature stability testing subjected catheters to bending conditions mimicking passage through acute vascular turns, exposing two critical deformation mechanisms: slip, in which string arrays migrate after overcoming friction imposed by the PTFE wrap, and buckling, in which arrays become locally pinned between wraps and deflect against the outer lumen. A two-dimensional (2D) model was developed to interpret these deformation regimes and explore how wrap-dependent constraints may promote transitions from near-uniform bending to localized bulging and sliding. Together, these approaches establish design principles for intra-catheter wrapping that can advance the development of variable stiffness endovascular devices toward their theoretical mechanical potential.

2. Methods

2.1. Study overview

Studies were designed to test our hypothesis and provide a mechanistic understanding of catheter deformation mechanisms to guide wrap design in suction-actuated variable stiffness catheters. Six prototype catheters with varied PTFE wrap spacing were fabricated to isolate the effect of wrap configuration on device performance. Each prototype was evaluated using three-point bend testing to quantify flexural rigidity profiles and flexural rigidity change upon actuation; curvature stability testing to reveal slip and buckling mechanisms under clinically relevant bending. A mathematical model was developed to predict stability limits and interpret the transitions between deformation regimes.

2.2. Prototype design and construction

All prototypes shared a common multi-layer architecture derived from the suction-actuated variable stiffness sheath design described previously [32]. Three prototypes (Patterns 1–3) were manufactured by a medical device contract manufacturer (Resonetics, Nashua, NH), and the remaining three prototypes were manufactured in-house (Patterns 4–6). Note that due to material sourcing differences, the Resonetics and in-house prototypes differ slightly in dimension as described below.

In the Resonetics prototypes, the innermost layer consisted of a steel coil-reinforced thermoplastic elastomer catheter (Pebax 40D; inner diameter 1.9 mm, outer diameter 2.4 mm; Resonetics, Nashua, NH) that provided kink resistance, elastic recovery following deformation, and a working lumen for guidewire passage. Surrounding this inner catheter, stainless steel flat wires (304V SS, 76 μm × 305 μm cross-section; Resonetics, Nashua, NH) were arranged longitudinally and equally spaced around the circumference to form the string arrays. Each wire was soldered to a metal ring positioned at the proximal end, securing the array while permitting axial load transfer during actuation.

The in-house prototypes were constructed from a slightly larger inner catheter (Pebax 40D; inner diameter 2.0 mm, outer diameter 2.4 mm; Duke Empirical, Morgan Hill, CA) surrounded by stainless steel flat wires (304V SS, 76 μm × 305 μm cross-section; Ulbrich Specialty Wire Products, North Haven, CT). Rather than a soldered ring, the in-house catheters instead utilized a resin-based termination.

For all prototypes PTFE wrapping was applied with the PTFE interwoven between the longitudinal string arrays and around the inner lumen in an alternating over, under pattern, as described in [32]. The PTFE wrap was applied with a range of different patterns (Table 1, Figure 1c). Patterns 1–2 used a wider PTFE wrapping (2.0 mm) with helical configurations of 45° and 45° with decreased wrap spacing respectively. Pattern 3 utilized a 1.0 mm PTFE wrap with a 60° helical configuration. For Patterns 4–6 three wrapping configurations were evaluated: 60° with 2.0 mm PTFE wrap, 45° with a 1.0 mm PTFE wrap, and a 45° cross wrap with 2.0 mm PTFE, the latter consisting of two separate PTFE strands woven in opposite helical directions. Because the PTFE tape was applied manually, local variations in wrap width, tension, and contact area were present across all prototypes (visible in Figure 1c). Such non-uniformity can arise from stretching or deformation of the tape during wrapping and may produce spatial variations in frictional constraint along the catheter.

Table 1.

Prototype geometric and wrap parameters.

	Pattern 1	Pattern 2	Pattern 3	Pattern 4	Pattern 5	Pattern 6
Nominal wrap spacing	8 mm	6 mm	10 mm	15 mm	6 mm	12 mm
Nominal wrap width	2 mm	2 mm	1 mm	2 mm	1 mm	2 mm
Nominal wrap angle	45°	45°	60°	60°	45°	45° cross
Catheter length	44.5 cm	45.0 cm	45.0 cm	44.5 cm	44.5 cm	44.5 cm
Inner lumen, inner diameter	1.9 mm	1.9 mm	1.9 mm	2.0 mm	2.0 mm	2.0 mm
Outer lumen, inner diameter	3.1 mm	3.1 mm	3.1 mm	2.84 mm	2.84 mm	2.84 mm
Outer lumen, outer diameter	3.15 mm, 9.5 Fr	3.15 mm, 9.5 Fr	3.15 mm, 9.5 Fr	3 mm, 9 Fr	3 mm, 9 Fr	3 mm, 9 Fr
String array count	19	19	19	19	19	19
Manufacturer	Resonetics	Resonetics	Resonetics	In-house	In-house	In-house

The outermost layer consisted of a thin thermoplastic polyurethane lumen (Resonetics: TPU 80A; inner diameter 3.10 mm, outer diameter 3.15 mm; Resonetics, Nashua; in-house: Pellethane 2363 80A; inner diameter 2.84 mm, outer diameter 2.97 mm; Duke Empirical, Morgan Hill, CA) that enclosed the entire assembly and provided the compliant membrane necessary for suction-induced mechanical coupling.

At the proximal end, a T-connector (polycarbonate, two female Luer lock ports, one male slip; Merit Medical, South Jordan, UT) provided separate access to the inner catheter lumen and the annular space between inner and outer lumens. The outer lumen was fitted over the slip portion of the connector and sealed with UV-cured resin (Kisrel RG-2110), creating an airtight chamber. One Luer lock port provided access to the working lumen for guidewire insertion, while the other served as the actuation port for vacuum application. At the distal end, the outer lumen, string arrays, and inner catheter were sealed together with UV resin to complete the closed system. Application of suction to the actuation port via syringe caused the outer membrane to contract radially, conforming tightly around the string arrays and pressing them against the inner catheter to achieve mechanical coupling and increased flexural rigidity.

2.3. Three-point bending experiments

Flexural rigidity was quantified along the length of each prototype catheter using a custom three-point bend testing apparatus (Figure 2), following the methodology described in detail by Qiu et al. [28]. Briefly, the apparatus consisted of a modified 3-axis computer numerical control (CNC) router (Genmitsu 3018-PROVer) with the spindle motor replaced by a custom load cell fixture. A 4.90 N load cell (TAL221; Sparkfun, Niwot, CO) connected to an amplifier (HX711; Sparkfun) and Arduino Uno microcontroller provided continuous force measurement during testing. The test fixture incorporated two support pins separated by 30 mm, inner edge-to-edge, with additional roller supports above the specimen and aluminum channel rails on either side to maintain alignment of long devices during testing. Test locations were marked at 5 cm increments along the catheter length, starting from the distal tip. At each test point, the specimen was centered beneath the loading pin, which descended at a constant rate of 0.5 mm/s to a maximum displacement of 2 mm. The pin was held at maximum displacement for 5 seconds before retraction, during which force was recorded continuously. This loading profile was selected to remain within the linear elastic regime while providing sufficient signal for reliable measurement [28]. Because repeated bend cycles can mechanically condition or damage the string array, the set of 5 cm test stations evaluated differed between prototypes. Stations were selected by the operator based on usable catheter length and sample condition prior to the first test; additional stations were not added retrospectively to avoid confounding from accumulated mechanical conditioning. As a result, the Resonetics prototypes (Patterns 1–3), which had longer usable lengths, were evaluated at more axial stations than the in-house prototypes (Patterns 4–6) (Figure 3).

Figure 2. Three-point flexural testing of variable stiffness catheters.

(a) Schematic of the three-point bending apparatus with detail showing catheter loading configuration. (b) Photograph of the testing setup showing the supports, loading pin, and roller guides used for automated catheter advancement. The photograph shows the catheter near peak displacement (2 mm); flexural rigidity was calculated from the initial linear portion of the force-displacement curve at substantially smaller deflections (see Section 2.3). Scale bar, 10 mm. Right image in panel b reproduced with permission from reference [32].

Figure 3. Flexural rigidity measurements for Patterns 1–6.

(a-f) Individual data points, 95% confidence intervals, and mean values are shown for each catheter in both the unactuated and actuated states (n = 3 tests per catheter at each tested position in both the actuated and unactuated states; error bars represent standard deviation). Tested positions were sampled along the catheter length at 5 cm increments. The number of positions evaluated varied across prototypes: Patterns 1–3 (Resonetics) had longer usable lengths and thus more test stations than Patterns 4–6 (in-house). Positions were selected prior to the first test cycle for each prototype. Data from panel d-f reproduced with permission from reference [32].

Each prototype was tested in both the unactuated state (ambient pressure) and the actuated state (vacuum applied). For actuated measurements, suction was applied using a 30 mL syringe connected to the actuation port, and vacuum was maintained throughout the testing sequence. The time between actuation and the first measurement was standardized at 30 seconds to ensure consistent mechanical coupling. All measurements were performed at room temperature (22 ± 2°C). Each test point was measured three times per actuation state to assess repeatability. Flexural rigidity was calculated from the force-displacement data using Euler-Bernoulli beam theory [28]. Although the loading pin descended to a maximum displacement of 2 mm, the flexural rigidity was extracted exclusively from the initial linear portion of the force-displacement curve by linear regression, excluding both the initial contact nonlinearity and viscoelastic relaxation at peak displacement. Within this linear regime (typically $\delta <0.5\text{mm}$, corresponding to a deflection-to-span ratio $\delta /L\approx 0.017$ and a maximum beam slope below 3°), the small-deflection and linear geometry assumptions underlying Euler-Bernoulli theory are well satisfied. The full 2 mm displacement was applied to ensure that the linear region was clearly identifiable and to provide sufficient signal-to-noise ratio for reliable regression. Data processing was performed using custom scripts in MATLAB (MathWorks, Natick, MA).

2.4. Curvature stability experiments

2.4.1. Test apparatus

To evaluate catheter mechanical behavior under clinically relevant bending conditions, a custom curvature stability testing apparatus was designed and fabricated (Figure 4). The apparatus consisted of a U-shaped channel that imposed a fixed curved pathway on the catheter, simulating the geometry encountered when navigating acute vascular turns such as the aortic arch or infrarenal abdominal aortic bifurcation.

Figure 4. Catheter stability testing and angular deflection response.

The stability testing apparatus, and sequential stages of guidewire advancement: (a) after catheter activation but before guidewire advancement, (b) during guidewire advancement, (c) at completion of guidewire advancement showing peak angular deflection, and (d) after guidewire withdrawal showing residual plastic angular deflection, the permanent deformation remaining after unloading. Scale bar, 5 cm.

The U-shaped fixture was manufactured using a 3D printer (Original Prusa i3 MK3S+, Prusa Research a.s., Prague, Czech Republic) with polylactic acid (PLA) filament (Prusament PLA, 1.75 ± 0.02 mm diameter, Prusa Polymers a.s., Prague, Czech Republic). The channel had a centerline radius of curvature of 53.3 mm, a channel width of 5 mm (sized to accommodate the catheter outer diameter with minimal clearance), and a channel depth of 5 mm. Rigid barriers were incorporated at the inlet and outlet of the curved section to constrain catheter position while permitting controlled deformation. The outlet barrier, located on the right side of the apparatus, defined the zone of maximum curvature change where angular deflection measurements were obtained. The fixture was mounted to a rigid base plate to ensure consistent positioning during testing.

2.4.2. Test protocol

Testing proceeded through a standardized sequence designed to characterize catheter response to internal loading from guidewires of increasing flexural rigidity. First, each prototype catheter was manually conformed to the U-shaped channel while in its flexible (unactuated) state. With the catheter seated in the channel, suction was applied via a 30 mL syringe connected to the actuation port, transitioning the device to its rigid state while maintaining the curved configuration. This actuated, curved state served as the initial reference condition for subsequent measurements.

A series of five 0.035” guidewires spanning a range of flexural rigidities were then sequentially passed through the catheter lumen (Table 2). Wires were inserted from the proximal end and advanced until the distal tip extended 10 cm beyond the catheter tip. After each wire insertion, the system was allowed to equilibrate for 20 seconds before image capture. The wire was then fully withdrawn before inserting the next stiffer wire. This sequence was repeated for each prototype catheter.

Table 2.

Guidewires used in curvature stability testing, listed in order of increasing flexural rigidity (mean ± standard deviation).

Guidewire	Manufacturer	Proximal flexural rigidity, N cm2
0.035” Standard	Terumo	1.9 ± 0.017
0.035” Bentson	Boston Scientific	4.9 ± 0.096
0.035” Stiff Glidewire	Terumo	7.4 ± 0.32
0.035” Storq	Cordis	10 ± 0.67
0.035” Amplatz Extra Stiff	Cook Medical	16 ± 2.6

The rationale for this protocol was that stiffer guidewires would exert greater straightening forces on the curved catheter, progressively challenging the ability of the string array and PTFE wraps to maintain position. By incrementally increasing wire flexural rigidity, we aimed to probe how wrap architecture influences catheter response and to qualitatively observe when slip and buckling behaviors emerge. We note that the present protocol was designed to identify the occurrence of these mechanisms across patterns, not to quantify slip magnitude or determine precise load thresholds for slip initiation. Flexural rigidity for the guidewires was quantified using the method described in [20].

2.4.3. Image acquisition and analysis

Digital images were captured before wire insertion (reference state) and after insertion of each guidewire. A digital camera (iPhone SE, Apple, Cupertino, CA) was positioned 58 cm above the apparatus, oriented perpendicular to the plane of the U-shaped channel to minimize parallax error. A calibration scale bar of known length (10 mm) was included in the field of view to enable dimensional measurements. Images were captured at a resolution of 3264×2448 pixels.

Angular deflection was quantified using ImageJ (version 1.54; National Institutes of Health, Bethesda, MD). For each image, a reference axis was established by drawing a line along the tangent to the catheter centerline at a fixed anatomical landmark on the apparatus (the outlet barrier edge). A second line was drawn along the catheter centerline in the deflection zone, defined as the region extending 80 mm from the barrier outlet where maximum curvature change was observed. The angle between these two lines was measured, with the reference (actuated, no wire) state defined as zero deflection. Each measurement was repeated three times by a single operator, and the mean value was used for analysis.

Images were visually inspected to identify slip and buckling events within the string arrays. Slip was defined as observable migration of the string arrays relative to the PTFE wrap positions, typically manifested as a change in the spacing between adjacent wraps or visible displacement of individual wires along the catheter axis. Buckling was defined as localized out-of-plane deflection of string arrays, appearing as a visible bulge where wires pressed outward against the inner surface of the outer lumen (Figure 6)

Figure 6. Mechanisms of catheter deformation during guidewire advancement.

(a) Representative images illustrating slip (axial migration of string arrays relative to wrap positions) and buckling, including localized buckling with a single bulge (left), distributed buckling with multiple bulges (center), and permanent deformation after guidewire removal, with the catheter failing to return to the semicircular guide (right). Arrows denote bulges. In both modes, slip of the string array (axial migration relative to the PTFE wraps) preceded the onset of out-of-plane buckling and is visible as changes in wrap spacing in the image sequences. Scale bars: 3 mm. (b) Representative deformation sequence for a relatively poor-performing wrap pattern (Pattern 1) showing early guidewire insertion, initiation of a single kink, growth of the bulge, and peak angular deflection. Scale bars: 1 cm and 5 mm. (c) Representative deformation sequence for a well-performing wrap pattern (Pattern 2) showing initial bulging, multiple bulge initiation points, and progression to multiple well-developed bulges at peak deflection. Scale bars: 1 cm and 5 mm. (d) Permanent catheter deformation after guidewire removal, which increased with increasing guidewire stiffness. Panels (b) and (c) show representative deformation sequences for the two buckling modes observed in this study: localized (Pattern 1) and distributed (Pattern 2). These patterns were selected because they exhibited the most visually distinct examples of each mode. All remaining patterns exhibited one of these same two modes.

2.5. Idealized model

We studied a combined guidewire and catheter that was bent by a moment into a 180° arc of radius ${\rho }_0$, so that the length of catheter was $L={\rho }_o\pi$. Upon actuation of the catheter, the unstressed reference configuration changes to this curved configuration, but the unstressed reference configuration of the guidewire remains set as a straight configuration. As a result, the catheter-guidewire combination relaxes into a new configuration, a circular arc with radius ${\rho }_1$. In this configuration, the strain energy per unit length in the wire was approximated by Euler-Bernoulli beam theory as $\frac{1}{2}{B}_w\frac{1}{{\rho }^2}$, where $B_w$ is the flexural rigidity of the guidewire, so that the strain energy stored in the guidewire could be written:

$$U_w=\frac{1}{2}{\int }_0^L{B}_w\frac{1}{{\rho }^2\left(s\right)}\mathit{\text{ds}}\approx \frac{1}{2}{B}_w\frac{L}{{\rho }_1^2}$$ (1)

where s is path length. The strain energy in the catheter string array could be written similarly, but accounting for the curvature relative to the bent reference configuration:

$$U_c=\frac{1}{2}{\int }_0^L{B}_c{\left(\frac{1}{\rho (s)}-\frac{1}{{\rho }_o}\right)}^{2}ds=\frac{1}{2}{B}_c{\left(\frac{1}{{\rho }_1}-\frac{1}{{\rho }_o}\right)}^{2}L$$ (2)

where $B_c$ is the flexural rigidity of the catheter.

The equilibrium shape was found by minimizing the total strain energy with respect to ${\rho }_1$:

$$\frac{d}{d{\rho }_1}\left(U_w+U_c\right)=0$$ (3)

Substituting, defining $\alpha =B_w/B_c$, and rearranging:

$$\frac{d}{d{\rho }_1}\left(\frac{1}{{\rho }_1^2}+\frac{1}{\alpha }{\left(\frac{1}{{\rho }_1}-\frac{1}{{\rho }_o}\right)}^2\right)=-\frac{2}{{\rho }_1^3}+\frac{1}{2\alpha }\left(\frac{1}{{\rho }_1}-\frac{1}{{\rho }_o}\right)\left(-\frac{1}{{\rho }_1^2}\right)=0$$ (4)

or

$$\frac{{\rho }_1}{{\rho }_0}=1+\alpha$$ (5)

To calculate the relaxed angle, note that the length of the catheter arc does not change, so that $L=\pi {\rho }_0=\left(\pi -\phi \right){\rho }_1$, where the $(\pi -\phi )$ is the central angle of the arc, and $\phi$ is the angle that the free end of the catheter rotates during relaxation (Figure 4a). Solving for $\phi$:

$${\phi }_{\mathit{\text{uniform}}}=\pi \left(1-\frac{{\rho }_o}{{\rho }_1}\right)=\pi \left(\frac{\alpha }{1+\alpha }\right)$$ (6)

This model was used as a bounding comparison case for the experimentally measured deflection angles (Figure 5).

Figure 5. Peak angular deflection.

(a) Deflection graphed as a function of guidewire flexural rigidity for each catheter pattern (n = 3 tests per pattern; error bars: standard deviation). Dashed line shows the idealized model (Equation 6) evaluated at the maximum mean actuated catheter flexural rigidity among all patterns tested. Guidewire flexural rigidity was varied using different guidewires as specified in Table 2. (b) Peak angular deflection versus normalized stiffness ratio $\alpha =B_w/B_c$, with horizontal error bars reflecting uncertainty in catheter flexural rigidity. $B_c$ was measured by three-point bending prior to curvature stability testing; accordingly, $B_w/B_c$ represents a baseline normalization and does not account for changes in effective catheter stiffness that may occur following slip or buckling during the test sequence. The dashed line represents the model for the idealized case (Equation 6), revealing that all patterns outperform this model. Lower deflection for a given normalized stiffness indicates improved curvature stability. Normalization separates the data and reveals Pattern 2 as the top-performing design, exhibiting the lowest angular deflection and greatest deviation (downward) from the idealized model. Patterns 4–6, which plot closest to the idealized curve, exhibited the smallest performance gains relative to the theoretical baseline.

2.5. Model of buckling, bulging, and sliding

Experiments showed that the bulges emerged in discrete spaces between the $N$ Teflon wraps. The flexural rigidity of such regions changes from $B_c$ to $\beta B_c$ as a length of string $\gamma L/N$ is recruited from non-bulged regions. Both of these change the energetics. For $N$ such spacings, with bulges in $n$ of them, the energy stored in the wire could be written:

$$U_w=\frac{1}{2}{\int }_0^L{B}_w\frac{1}{{\rho }^2\left(s\right)}\mathit{\text{ds}}\approx \frac{1}{2}{B}_{w}L\left(\left(1-(1+\gamma )\eta \right)\frac{1}{{\rho }_1^2}+\eta \left(\frac{1}{{\rho }_2^2}\right)\right)$$ (7)

where ${\rho }_1$ is the final radius of curvature of the non-bulged regions, ${\rho }_2$ is that of the bulged regions, and $\eta =n/N$. Note that the region of distal guidewire formerly abutting the string array no longer stores strain energy following bulging in this model. The strain energy in the catheter string array could be written similarly, but accounting for the curvature relative to the bent reference configuration:

$$U_c=\frac{1}{2}{\int }_0^L{B}_c(s){\left(\frac{1}{\rho \left(s\right)}-\frac{1}{{\rho }_o\left(s\right)}\right)}^{2}ds\approx \frac{1}{2}{B}_{c}L\left(\left(1-(1+\gamma )\eta \right){\left(\frac{1}{{\rho }_1}-\frac{1}{{\rho }_o}\right)}^2+\beta \eta {\left(\frac{1}{{\rho }_2}-\frac{1}{{\rho }_p}\right)}^2\right)$$ (8)

where ${\rho }_p$ is the unloaded reference curvature of the bulged regions. Approximations of the lowest energy configurations can be found by minimizing energy:

$$\frac{\partial }{\partial {\rho }_1}\left(U_w+U_c\right)=0=-\left(1-\left(1+\gamma \right)\eta \right)\frac{2}{{\rho }_1^3}+\frac{1}{\alpha }\left(1-\left(1+\gamma \right)\eta \right)\left(-\frac{2}{{\rho }_1^2}\right)\left(\frac{1}{{\rho }_1}-\frac{1}{{\rho }_o}\right)$$ (9)

which again yields Equation (5). Repeating for ${\rho }_2$:

$$\frac{\partial }{\partial {\rho }_2}\left(U_w+U_c\right)=0=-2\frac{\eta }{{\rho }_2^3}+\frac{\beta \eta }{\alpha }\left(-\frac{2}{{\rho }_2^2}\right)\left(\frac{1}{{\rho }_2}-\frac{1}{{\rho }_p}\right)$$ (10)

or:

$$\frac{{\rho }_2}{{\rho }_p}=\frac{\alpha +\beta }{\beta }$$ (11)

Repeating the procedure with respect to $\eta$ and $\gamma$ reveals no achievable minimum.

To calculate the relaxed angle, note that the length of the non-bulged section of the catheter changes by $\gamma \eta L$, so that $L_1=\pi {\rho }_0(1-\eta )(1-\gamma \eta )=\left({\theta }_1\right){\rho }_1$, where the ${\theta }_1$ is the central angle of an arc formed by collocating all of the non-bulged region:

$${\theta }_1=\pi \frac{{\rho }_0}{{\rho }_1}(1-\eta )(1-\gamma \eta )=\frac{\pi }{1+\alpha }(1-\eta )(1-\gamma \eta )$$ (12)

The bulged region encompasses a region of arc length ${\theta }_2$:

$${\theta }_2=\frac{\eta \pi {\rho }_0}{{\rho }_2}=\pi \eta \frac{{\rho }_0}{{\rho }_p}\left(\frac{\beta }{\alpha +\beta }\right)$$ (13)

The tangent angle between the vertical axis and the catheter tip is then:

$${\varphi }_{\mathit{\text{distorted}}}=\pi -\left({\theta }_1+{\theta }_2\right)=\pi \left(1-\frac{1}{1+\alpha }\left(1-\eta \right)\left(1-\gamma \eta \right)-\eta \frac{{\rho }_0}{{\rho }_p}\left(\frac{\beta }{\alpha +\beta }\right)\right)$$ (14)

2.6. Statistical analysis

All statistical analyses were performed using MATLAB (version R2023a; MathWorks, Natick, MA). Data are presented as mean ± standard deviation unless otherwise noted. For three-point bending experiments, flexural rigidity values at each test location were compared between actuated and unactuated states using paired t-tests. Comparisons across the 6 prototype configurations were performed using one-way analysis of variance (ANOVA), with Tukey’s post-hoc test applied when the omnibus test indicated significant differences. The stiffening ratio (actuated/unactuated flexural rigidity) was similarly compared across prototypes using one-way ANOVA. For curvature stability experiments, angular deflection values were compared across prototypes at each guidewire flexural rigidity level using one-way ANOVA with Tukey’s post-hoc correction. Slip and buckling were assessed qualitatively from images and are presented as representative deformation sequences corresponding to wire flexural rigidity thresholds (Figure 6); no statistical comparisons of slip/buckling onset were performed.

For all analyses, statistical significance was defined as p < 0.05. Where multiple comparisons were performed, family-wise error rate was controlled using the Tukey HSD method. Sample sizes for each comparison are reported in the corresponding results sections.

3. Results

3.1. Three-point bending: flexural rigidity profiles

Three-point bending tests characterized the flexural rigidity of each catheter pattern along its length in both actuated and unactuated states (Figure 3). In the actuated state, flexural rigidity values ranged from 5.20 to 9.61 N cm² across the six patterns, with Patterns 4–6 (in-house prototypes) exhibiting higher flexural rigidity than Patterns 1–3 (Resonetics prototypes). Pattern 4 demonstrated the highest mean flexural rigidity (9.61 ± 0.29 N cm²), while Pattern 3 exhibited the lowest (5.20 ± 0.62 N cm²). Variability in flexural rigidity along the catheter length was modest for most patterns, with standard deviations ranging from 0.29 to 0.76 N cm² across test locations. These measurements established baseline flexural rigidity values for subsequent curvature stability testing and model validation. The number of test locations per catheter varied across prototypes due to operator selection and sample condition, and additional locations were not tested after repeated bend cycles to avoid conditioning artifacts.

3.2. Curvature stability testing and angular deflection responses

Curvature stability testing revealed the relationship between guidewire flexural rigidity and catheter angular deflection under clinically relevant bending conditions (Figure 4). In the absence of a guidewire, all catheter patterns maintained the imposed semicircular geometry with minimal deviation. Upon guidewire insertion, the catheter-guidewire system relaxed toward a straighter configuration, with the magnitude of angular deflection ${\varphi }_{max}$ increasing monotonically with guidewire flexural rigidity.

When plotted against absolute guidewire flexural rigidity (Figure 5a), all six patterns exhibited qualitatively similar behavior, with deflection angles ranging from approximately 5° to 120° across the tested guidewire range (1.9–16.4 N cm²). The idealized model (Equation 6), evaluated at the maximum actuated catheter flexural rigidity among all patterns tested, provided an upper bound for the expected deflection response.

Normalization of guidewire flexural rigidity by catheter flexural rigidity collapsed the data and revealed clear performance differences among wrap patterns (Figure 5b). The catheter flexural rigidity $B_c$ used for this normalization was measured by three-point bending prior to curvature testing, before any slip or buckling had occurred. Because slip and buckling can alter the effective flexural rigidity during curvature testing, $B_w/B_c$ should be interpreted as the ratio of guidewire stiffness to the intact baseline catheter stiffness, not as an instantaneous in situ stiffness ratio. This baseline normalization ensures a consistent comparison across patterns, because post-instability stiffness would depend on the test sequence rather than on wrap architecture alone, and is not a factor that a surgeon could reliably use in procedural design.

Pattern 2 consistently exhibited the lowest angular deflection across the tested range, indicating the greatest improvement relative to the idealized model. In contrast, Patterns 4–6 plotted closest to the idealized curve among all patterns tested, indicating that their wrap architectures provided the smallest improvement over the idealized (no-wrap-effect) baseline.

3.3. Deformation mechanisms

Visual inspection during curvature stability testing revealed two distinct deformation mechanisms in the string arrays: slip, defined as observable axial migration of strings relative to the PTFE wraps (Section 2.4.3), was evident in all patterns, particularly during advancement of the more compliant guidewires, and preceded the onset of visible buckling. Two distinct buckling modes were subsequently observed: localized buckling characterized by a single dominant bulge, and distributed buckling characterized by multiple bulges along the catheter length (Figure 6a). These two modes, localized and distributed buckling, were the only qualitatively distinct deformation morphologies observed across all six patterns. Patterns 1 and 2 are presented as representative examples of each mode because they exhibited the most clearly distinguishable localized and distributed behavior, respectively.

Following guidewire removal, permanent plastic deformation was observed in all patterns, with the catheter failing to return to the semicircular guide geometry, consistent with irreversible slip-driven rearrangement of the string array.

The relationship between buckling mode and catheter performance was evident when comparing individual patterns. Pattern 1, which exhibited relatively poor performance in curvature stability testing, demonstrated localized buckling behavior (Figure 6b). During guidewire advancement, a single kink initiated at one location and progressively grew into a dominant bulge, concentrating deformation in a narrow region. This localization resulted in large angular deflections and visible permanent deformation. Prior to the onset of visible buckling, axial slip of the string array was apparent as a change in wrap-to-wrap spacing in the region that subsequently kinked.

In contrast, Pattern 2, which performed well in curvature stability testing, exhibited distributed buckling (Figure 6c). Initial guidewire advancement produced small bulges at multiple locations along the catheter, which subsequently developed into several well-defined bulges at peak deflection. Slip was also observed in Pattern 2 but was distributed more uniformly across wrap segments, consistent with the tighter wrap spacing constraining string migration at each individual site. This distributed deformation mode spread strain across multiple sites rather than concentrating it at a single location, resulting in lower overall angular deflection and improved stability.

The extent of permanent deformation following guidewire removal increased with increasing guidewire flexural rigidity across all patterns (Figure 6d), consistent with progressive sliding of the string arrays and increased inelastic deformation under higher imposed loads.

3.4. Model predictions: parameter sensitivity analysis

The bulge-modified deflection model (Equation 14) was used to explore how variations in catheter and bulge properties influence angular deflection (Figure 7). Parameter sweeps were conducted around baseline values ($\eta =0.2$, $\gamma =0.2$, $\beta =1.1$, ${\rho }_0/{\rho }_p=1.20$) representative of the experimental observations.

Figure 7. Parameter sensitivity of the bulge-modified deflection model.

Model predictions for angular deflection as a function of normalized wire stiffness, with parameter sweeps around baseline values (0.2, 1.1, 1.20, 0.2). Dashed black line indicates the idealized uniform model (Equation 6) in all panels. (a) Effect of bulge fraction. (b) Effect of length recruitment factor. Both have relatively minor influence, with curves deviating minimally from the idealized model. (c) Effect of reference curvature ratio. Changes to the reference configuration have a pronounced effect, including nonphysical behavior at high values where a sliding instability would be required to initiate deformation. (d) Effect of stiffness ratio. Increasing has a modest effect, with stiffening in bulged regions being favorable for catheter stability.

The bulge fraction η and length recruitment factor γ had relatively minor influence on predicted deflection (Figure 7a–b). Across the tested ranges ($\eta :0-0.3$; $\gamma :0-0.5$), the model curves deviated only modestly from the idealized uniform model (Equation 6), suggesting that the extent of bulging and length redistribution are not primary drivers of performance differences among wrap patterns.

In contrast, the reference curvature ratio, ${\rho }_0/{\rho }_p$, exerted a pronounced effect on model predictions (Figure 7c). Values of ${\rho }_0/{\rho }_p$ substantially greater than one produced large deviations from the idealized model, including nonphysical behavior at high values where the model predicts that a sliding instability would be required to initiate deformation. This sensitivity suggests that the rest curvature adopted by bulged regions, determined by the interplay between wrap constraint, string array geometry, and plastic deformation, is a critical determinant of catheter stability.

The flexural rigidity ratio $\beta$ had a modest effect on predicted deflection (Figure 7d). Increasing $\beta$ (stiffer bulged regions relative to non-bulged regions) shifted curves toward lower deflection angles, indicating that stiffening due to bulge formation is favorable for catheter stability. This finding is mechanistically consistent with the observation that distributed buckling (multiple smaller bulges) outperformed localized buckling (single large bulge): distributed deformation may maintain higher effective flexural rigidity in bulged regions compared to severe local kinking.

Following bulging or slipping, the tangent angle is reduced according to Equation (14). The degree of reduction can be estimated by noting that:

$${\varphi }_{\mathit{\text{distorted}}}={\varphi }_{\mathit{\text{uniform}}}(1+\Delta )$$ (15)

where, for $\alpha >0$,

$$\Delta =\frac{\eta }{\alpha }\left(1+\gamma \left(1-\eta \right)-\beta \frac{{\rho }_0}{{\rho }_p}\left(\frac{1+\alpha }{\alpha +\beta }\right)\right)$$ (16)

The key question is whether bulging increases or reduces the ability of the catheter to retain its curved shape as a guidewire passes through it. For bulged regions of the catheter to adopt a tighter reference radius of curvature, ${\varphi }_{\mathit{\text{distorted}}}$ must be in the range of $0\le {\varphi }_{\mathit{\text{distorted}}}\le \pi$, so that:

$$\pi \left(1-\frac{1}{1+\alpha }\left(1-\eta \right)\left(1-\gamma \eta \right)-\eta \frac{{\rho }_0}{{\rho }_p}\left(\frac{\beta }{\alpha +\beta }\right)\right)\ge 0$$ (17)

Rearranging yields:

$$\frac{{\rho }_0}{{\rho }_p}\le \frac{1}{\eta }\left(1+\frac{\alpha }{\beta }\right)\left[1-\frac{1}{1+\alpha }\left(1-\eta \right)\left(1-\gamma \eta \right)\right]$$ (18)

For ${\rho }_0/{\rho }_p$ that does not satisfy Equation (18), no solution exists, indicating that insufficient energy is stored in the system to enable the change of reference configuration. In these cases, the response would be expected to parallel the relation for a non-bulged catheter until an instability is triggered, at which point the response would switch to the curves in Figure 7c. This behavior can be seen in each of the prototypes, especially Patterns 1 and 2 (Figure 5).

4. Discussion

This study demonstrates that PTFE wrap configuration is a key determinant of mechanical performance in suction-actuated variable stiffness catheters. Our combined experiments and models suggest that the observed gap between theoretical stiffening ratios (150–880%) and experimentally observed values is consistent with slip and buckling of the string array contributing to loss of effective mechanical coupling during bending, in addition to other practical factors such as manufacturing variability and geometric tolerances. Results provide mechanistic insight into device performance and suggest design principles for selecting wrap architecture.

4.1. Catheter deformation mechanisms

Curvature stability testing revealed sequential deformation mechanisms as internal loading from guidewire passage increases. First, slip, visible as axial migration of string arrays relative to the PTFE wrap positions (Section 3.3, Figure 6), was observed even with the most compliant guidewire tested. However, this reduction in mechanical coupling was outweighed by buckling that was evident, especially with stiffer guidewires. This is evident from the initial plateau in the angular deflection versus guidewire flexural rigidity curves (Figure 5a), where increasingly stiff guidewires produce diminishing additional catheter straightening. This can occur as one or more string array segments become locally pinned between adjacent PTFE wraps and deflects outward against the inner surface of the outer lumen. Visual inspection revealed two distinct buckling modes: localized buckling characterized by a single dominant bulge and distributed buckling characterized by multiple smaller bulges along the catheter length (Figure 6a). The selection of these modes appears to depend on wrap spacing, with tighter spacing promoting the distributed mode. Distributed buckling spreads strain across multiple sites rather than concentrating it at a single location, resulting in lower overall angular deflection and improved stability. Figures 6b–c show representative deformation sequences from the median-performing (Pattern 1) and best-performing (Pattern 2) patterns, selected to illustrate these two modes of behavior. Inelastic deformation increased with guidewire flexural rigidity across all patterns (Figure 6d); both slip and buckling involved rearrangement of the string array that is not reversed until the suction was removed.

4.2. Model-experiment integration and design implications

The idealized model, Eq. (6), captured the fundamental relationship between guidewire-to-catheter flexural rigidity ratio and angular deflection, establishing a theoretical baseline. All patterns tested outperformed this baseline, indicating that PTFE wrapping provides mechanical benefit beyond simple string positioning. The bulge-modified model, Eq. 14, suggested the mechanistic basis for this. Parameter sensitivity analysis revealed that the reference curvature ratio (${\rho }_0/{\rho }_p$) is the most important factor (Figure 7c), with localization of wires reducing the stored elastic energy of a curved configuration. The mathematical model predicted that a sliding instability is needed for this response mode to fully engage, suggesting that guidewires even more compliant than the most flexible one tested would lead to responses closer to those of the less-effective idealized model. This sensitivity to (${\rho }_0/{\rho }_p$) suggests that wrap design should aim to constrain bulged regions such that they adopt reference curvatures close to the imposed vessel curvature, thereby reducing the energetic driving force for further straightening.

In contrast, the fraction of regions along a catheter that buckled ($\eta$) and the length recruitment factor $\gamma$ had relatively minor influence on predicted deflection (Figure 7a,b). This implies that the total extent of bulging is less critical than the geometric configuration adopted by bulged regions: wrap architectures that permit distributed bulges may be preferable to those that resist bulging entirely but eventually fail with a single large bulge.

The flexural rigidity ratio $\beta$ had a modest but favorable effect, with higher values (stiffer bulged regions) shifting curves toward lower deflection angles (Figure 7d). This observation is consistent with the superior performance of distributed versus localized buckling: multiple smaller bulges may maintain higher effective flexural rigidity compared to severe local kinking. Designs that increase the bending resistance of bulged regions, such as tighter wrap spacing or stiffer wrap materials, may therefore improve stability.

Three design principles thus emerge: first, tighter wrap spacing generally improves stability by promoting distributed rather than localized buckling and bulging, although excessively tight spacing may compromise flexibility in the unactuated state, establishing a trade-off that must be balanced against application-specific requirements. Second, wrap angle influences the mode of string array constraint: the 45° wrap angle appeared to provide more uniform constraint than the 60° angle (Pattern 4) or cross-wrap configuration (Pattern 6). The cross-wrap architecture, despite its expected advantage of bidirectional constraint, did not demonstrate superior performance in curvature stability testing, suggesting that interactions between opposing wrap directions hinder the sliding underlying the mechanisms that enable the catheter to outperform the idealized model. Third, the annular gap between the inner and outer lumens differs between the two manufacturing routes (outer lumen inner diameter: 2.84 mm for Patterns 4–6 versus 3.10 mm for Patterns 1–3). The tighter fit in the in-house prototypes increases baseline frictional contact between the string array and outer lumen, contributing to higher measured flexural rigidity in both actuated and unactuated states. However, this same geometric constraint may impede the controlled axial sliding that precedes distributed buckling. This is consistent with the observation that Patterns 4–6, despite their higher absolute stiffness, plotted closer to the idealized curve in Figure 5b; the elevated $B_c$ does not translate into proportionally improved curvature stability because the tight annular gap inhibits the deformation mode (distributed buckling) associated with the best performance.

4.3. Comparison to alternative variable stiffness technologies

The suction-actuated mechanism studied here offers distinct advantages compared to alternative variable stiffness technologies. Unlike magnetically actuated catheters [22–25], which require external field generators and may be limited by the strength of achievable magnetic fields at depth, suction-actuated devices operate through simple mechanical actuation accessible via standard syringe. Unlike thermally actuated shape memory polymer systems [23,24], which require heating elements and face response time limitations due to thermal mass, suction-actuated devices can transition between states rapidly and reversibly. Unlike low-melting-point metal systems [26], which require careful temperature control to avoid tissue damage, suction-actuated devices operate at ambient temperature. Fiber jamming mechanisms [27,28] represent the closest functional analog, achieving variable stiffness through friction-based mechanical coupling. The present results suggest that string array-based designs may offer advantages in terms of non-uniformity along the device length, provided that wrap architecture is adequate. The mechanistic understanding developed here regarding trade-offs between slip resistance, buckling mode, and baseline flexural rigidity may inform the design of fiber jamming devices as well.

Results extend prior work on catheter navigation and stability [21,31] by demonstrating that internal device architecture drives mechanical responses during navigation. Herniation, in which stored elastic energy causes sudden deviation from the intended vascular pathway [19,21,31], remains a significant clinical concern; the present results suggest that careful wrap design might enable greater improvement over the theoretical limit of uniform deformation.

4.4. Limitations

Several limitations of this study warrant consideration. First, only six wrapping configurations were tested experimentally. Although the mathematical model partially addressed this limitation through parametric studies, experimental validation across a broader range of configurations is needed to confirm model predictions and identify potential nonlinear interactions between design variables.

Curvature stability testing was performed using a fixed U-shaped geometry that represents only one of many anatomical configurations encountered clinically. Performance may differ in tighter or more gradual curves, in 3D tortuous pathways, or under the combined loading of curvature and axial compression. The centerline radius of curvature used here approximates some clinical scenarios (e.g., the aortic arch) but may not capture the full range of relevant conditions.

The mathematical model employed a 2D simplification of the inherently three-dimensional catheter structure. While this captured the essential mechanics of bending-induced instability in the plane of imposed curvature, it could not represent circumferential variations in string array behavior, out-of-plane deformation modes, or torsional loading.

Curvature stability testing can alter the effective flexural rigidity and reference configuration of the catheter through slip and buckling. The catheter flexural rigidity used for normalization in Figure 5b was measured by three-point bending prior to curvature testing and represents an intact baseline value. Post-instability stiffness was not measured because three-point bending was not repeated after curvature testing. As a result, the $B_w/B_c$ ratios reported for stiffer guidewires, which were inserted after instability had already occurred in some patterns, may underestimate the true in situ stiffness ratio. Although these are the ratios that could be expected to be available to a surgeon planning a procedure, future studies incorporating post-test three-point bending would enable quantification of how the effective normalization evolves across the guidewire sequence.

All testing was quasi-static, but clinical use involves dynamic loading scenarios including pulsatile blood flow, operator manipulation during navigation, and forces associated with therapeutic device deployment. The effects of cyclic loading, strain rate, and viscoelastic relaxation on slip and buckling behavior remain to be characterized.

Patterns 1–3 (Resonetics-manufactured) and Patterns 4–6 (in-house) differed in manufacturing, outer lumen fit, and assembly method. These differences introduce confounding variables such as the annular gap between inner and outer lumens that affect both the measured flexural rigidity and the slip/buckling mechanics. While Section 4.2 offers a mechanistic interpretation of the observed performance difference, cross-group comparisons remain qualitative. A definitive separation of wrap-pattern effects from manufacturing-route effects would require a uniformly fabricated set of prototypes varying only in wrap architecture, which we identify as a priority for future experimental work.

Additionally, visible variation in PTFE wrap width and uniformity (Figure 1c), arising from manual application of compliant PTFE tape, may produce local differences in frictional constraint along the catheter. Such non-uniformity could influence where slip initiates and where buckles nucleate, contributing to the scatter observed in Figures 3 and 5. While the principal findings were reproducible across trials, including observations that wrap architecture governs buckling mode and that distributed buckling outperforms localized buckling, the quantitative agreement between model and experiment may improve with tighter process control or automated wrapping, which would reduce wrap-to-wrap variability within and between prototypes.

Finally, this study focused on short-term mechanical performance. Long-term durability, including the effects of repeated actuation cycles, potential fatigue of the string arrays or PTFE wraps, and performance following sterilization, was not assessed. Such testing will be essential for clinical translation and regulatory approval.

5. Conclusions

Results demonstrate that slip and buckling of the string array, rather than material properties or actuation efficiency, are the primary mechanisms underlying the performance gap between theoretical and achieved stiffening ratios in suction-actuated variable stiffness catheters. Through experimental and modeling approaches, we established that PTFE wrap configuration is a critical determinant of device mechanical performance and identified three principal design guidelines. First, tighter wrap spacing promotes distributed buckling over localized buckling, spreading strain across multiple sites and reducing overall angular deflection under load. This finding was exemplified by Pattern 2, which demonstrated superior curvature stability among the tested configurations. Second, the reference curvature adopted by bulged regions is the dominant factor governing stability limits, as revealed by model sensitivity analysis; wrap architectures should constrain bulged regions to adopt reference curvatures close to the imposed vessel curvature. Third, wrap angle influences the mode of string array constraint, with 45° configurations providing more uniform performance than steeper angles or cross-wrap architectures.

These findings provide a mechanistic foundation for enhancing wrap architecture in variable stiffness endovascular devices. By designing wraps that promote distributed deformation modes while maintaining favorable reference curvatures in bulged regions, it may be possible to narrow the gap between theoretical stiffening ratios and clinically achieved values. Quantitative characterization of slip magnitude, for example, through digital image correlation or high-resolution video tracking of individual string displacements, remains an important objective for future studies seeking to establish predictive relationships between slip, buckling, and angular deflection. Similarly, fabrication of a geometrically matched prototype set using a single manufacturing process would enable definitive isolation of wrap-architecture effects from confounding variables related to lumen dimensions and assembly tolerances. Such advances could contribute to the development of single-sheath devices capable of both flexible navigation through tortuous anatomy and rigid support for therapeutic delivery, potentially reducing procedural complications, cost, and time in endovascular interventions.