Scaffolds with a Tunable Nonlinear Elastic Region Using a Corrugated Design

Elastin is the main component of arteries and is responsible for their high‐elastic high‐strain capacity. The biomechanics of biological tissues typically display a stress–strain curve characterized by a sigmoidal shape that has an initial region with low stress and high strain. Studies aimed at mimicking such biomechanical behavior focus on improving the synthesis of elastin or replicating elastin behavior, which proves to be a continuous challenge. Alternatively, scaffolds' architecture can potentially mimic the sigmoidal stress–strain curve of tissues. Hence, the aim of this study was to replicate the stress–strain curve of a carotid artery using a tailorable corrugated design. Results showed that the corrugated design unfolded during extension without generating significant stress and displayed a sigmoidal stress–strain curve that could be controlled depending on the corrugation features. Editing the amount of fibers resulted in a different Young's modulus, while the amplitude of the fibers and the amount of repeating units influenced the initial nonlinear region of the stress–strain curve. Scaffolds made of poly(ε‐caprolactone) (PCL) and poly(ethylene oxide terephthalate)/poly(butylene terephthalate (PEOT/PBT) were compared to determine the applicability of the design principles to different biodegradable polymers that normally do not have the same biomechanical behavior of soft tissues like arteries. The optimized designs had a similar stress–strain curve within the physiological range as porcine arteries. The corrugated design can serve as a biomimicry approach for vascular grafts or an alternative to vascular stents.


Introduction
Materials such as metals [1] and polymers, [2] with a high elastic strain, are of interest in many studies focusing on stent design and vascular tissue engineering.High elastic strain can also naturally occur in certain proteins, such as elastin and resilin. [3,4]hese elastic materials often show a stress-strain curve that is characterized by a sigmoidal shape, which has an initial region with a low stress and high strain. [5]specially in blood vessels, elasticity is important, as it improves the pumping efficiency of the heart. [6]The overall wall thickness of each vessel varies throughout the body in order to facilitate the fluctuations in blood pressure.Each type corresponds to a unique structural composition of cell types, elastin and collagen, that cumulatively define the unique stress/strain behavior of a vessel. [7]Together, this complex microenvironment is capable of withstanding physiological compliance ranging between 3% and 12%/100 mmHg with minimal energy loss. [8]Specifically, elastin has a pivotal role in elasticity in vivo, [9] whereas too little elastin content can result in arterial stiffening. [10]Mechanical mismatch in vascular grafts is a key indicator for graft patency and is a known clinical problem. [11,12]The amount of elastin dictates the shape of the stress-strain curve.In general, arteries or veins that have less elastin content have flattened stress-strain curves and a higher Young's modulus. [13,14]he initial part of the stress-strain curve within arteries is mainly elastin dominated and allows for a significant strain to occur on the artery whilst subjecting the tissue to minimal amounts of stress.This region is consistent with the loading mechanics of elastin fibers and mainly serves to support physiological pressures. [7,15]Whereas the elastin region has a low Young's moduli in the 0.2-0.6MPa range, this range increases tenfold as the upturning region is reached and stress becomes collagen dominated (2-6 MPa). [15]Hence, mimicking the sigmoidal stressstrain curve with synthetic scaffolds proves to be a formidable challenge.
There are mainly two ways to obtain a sigmoidal shaped stress-strain curve.First, this is usually achieved with the inherent material properties, for example, a dynamic hydrogel network with reversible crosslinks. [16]Another example is from elastin itself that disentangles when stretched. [17]Even though this macromolecular disentanglement behavior is found in vivo, mimicking the complex assembly of elastin into elastic fibers proves to be challenging as it requires 30 different proteins to form a complex elastic fiber. [18]It is known that the types of cells and scaffold affect elastin production [19] and attempts have been made to force de novo synthesis of elastin through mRNA transfection. [20]Scaffolds made out of alpha-elastin and tropoelastin have been made through electrospinning [21] and crosslinking, [22] respectively.Another way to obtain a sigmoidal stress-strain curve is through design of the pore architecture of a scaffold, even with materials that inherently do not have any elastic behavior. [23,24]A method to mimic the elastin behavior can be achieved, for example, through a mesh of small-diameter fibers that can disentangle before the individual fibers are stretched. [25,26]A different method for larger diameter fibers can be seen in many stent designs that can extend through fiber bending. [27]Many of these stents show some degree of flexibility, yet they are made of alloys such as cobalt-chrome or nickeltitanium. [28]The bulk properties of these materials display no sigmoidal stress-strain curve and an ultimate tensile strength in the Giga Pascal range, far too stiff for vascular grafts. [29,30]olymeric stents on the other hand use materials that have improved bulk properties. [31,32]Additional benefits are that these can be made out of biodegradable polymers [33] and can be functionalized with anticoagulants to reduce thrombosis and lower the risk of graft rejection. [34,35]Certain polymeric stent designs are also able to compress and extend in radius, allowing them to be deployed using balloon catheters. [36,37]Finally, the difficulty of manufacturing polymeric stents has decreased in recent years. [38]dditive manufacturing can be used to fabricate these complicated designs with high precision. [39]Specifically, manufacturing techniques that have a cylindrical collecting surface such as fused deposition modeling [31] and melt electrowriting [40] are of great interest to produce tubular structures.The combination of these techniques and a design that is minimalistic could result in a scaffold that offers tunable elastic-like features.This in turn could potentially mimic the characteristic nonlinear mechanical behavior of a major artery. [41]Methodologies based on fused deposition modeling (FDM) also show high potential in ondemand printing of vascular grafts through the large range of usable materials and freedom in design orientation. [42]lthough effective and highly customizable, the complex tubular design of the vasculature is often difficult to print and may therefore fall short in mechanical rigidity. [31,43]ence, the aim of this study is to develop a new method to create corrugated tubular scaffolds and investigate the influence of the scaffolds' architecture on the mechanical properties.This design could potentially be used for vascular tissue engineering.The correct replication of many of the mechanical properties such as compliance, diameter range, graft size, and Young's modulus can have highly beneficial effects on the long-term patency of synthetic grafts.Finally, the mechanical behaviors of the designs were compared to carotid arteries.

Scaffold Fabrication
A four-axis extrusion-based system was used, as previously described, to fabricate the scaffolds. [31]Briefly, polymer pellets were loaded in a cartridge and heated until the polymer melted.Afterwards, the polymer melt was extruded through a 260 μmdiameter nozzle (25G encapsulation needle, DL technology) using pressure and deposited on a 4 mm-diameter stainless steel mandrel.The deposition of materials along the mandrel was controlled by the displacement in a certain axis; at the same time the axis of the mandrel rotated, which allowed control of the filament deposition and the final obtained scaffold design.Two materials were chosen, poly(ε-caprolactone) (PCL, Mn = 45 000 g mol À1 , Sigma-Aldrich) as a stiffer material with a smaller elastic domain and poly(ethylene oxide terephthalate)/poly(butylene terephthalate (PEOT/PBT), comprising 1000 g mol À1 average molecular weight PEO and a PEOT:PBT weight ratio of 70:30, as a more elastic material.For PCL, the temperature was set at 110 °C and extruded at a pressure of 4 bar.PEOT/PBT was heated until 175 °C and extruded at a pressure of 5 bar.

Scaffold Design
A script was written in Python 3.7 (64-bit) to create the corrugated pattern with both adjustable and fixed parameters.The fixed parameters used throughout the study were the length of each segment (5 mm) to observe an unfolding effect of the corrugated design, the printing speed of 1.5 mm s À1 , and the total amount of segments per scaffold (set at 4).The adjustable parameters consisted of changes in the amplitude, strut fiber quantity, and the frequency of repeating units within one segment (Figure 1A).Each segment was closed with a ring at both ends.The scaffolds were labeled according to the maximum amplitude of the fiber in degrees (AM), the amount of units per fiber (U), and the amount of fibers per segment (F).For instance, AM100U2F7 had a maximum amplitude of 100°, with two units per fiber and seven fibers per segment.The amplitude of the scaffold ranged from 0°to a maximum of what was possible without fusion of the fibers at 200°.The amount of repeating units ranged from 2 to a maximum of 5; this was the limit as more units would prevent the scaffold from unfolding.The fiber quantity was fixed at 7 as this would still provide coverage around the lumen without restricting space for the corrugated design.Scaffold designs were visualized in 3D models using the Rhinoceros 6.0 modeling software and a custom-written grasshopper graphical plugin.To visualize the damage upon stretching during the luminal fiber recovery test, a complementary microfiber lumen was created on the inner side of the corrugated scaffolds following previously established methodologies. [44]Briefly, the lumen was fabricated through melt spinning using an external DC motor with a fixed rotational speed of ≈1100 RPM.Fiber extrusion was set at similar parameters of the skeletal support structure while moving over the longitudinal (X ) axis at 1 mm s À1 , hereby forming a tubular lumen on which the remainder of the scaffold was printed.

Scaffold Characterization
A stereomicroscope (SMZ25, Nikon instruments) with a darkfield illuminator (Nikon instruments) was used to visualize the scaffold structure.The diameter of the filaments, the angle of the fibers, and the distance between each fiber were measured with the stereomicroscope.Visualization of the microfiber structures was performed through scanning electron microscopy (JOEL JSM-IT SEM).Samples were fixed using JOEL-adhesive carbon tape and sputter coated in gold (SC7620, Quorum), followed by SEM imaging with an SED accelerating voltage of 10-20 kV (WD.12-14 mm, Mag.25x-30x).The microfiber resilience to uniaxial strain was quantified using the FIJI open-source imaging software by measuring pore volume expressed in percentage of the deformed luminal surface (%) on the varying degrees of uniaxial scaffold strain.

Mechanical Testing
Mechanical characterization was performed on a mechanical tester (ElectroForce, TA instruments) with a 45 Newton load cell ) 4.5 kg cm À2 , Electroforce).Tensile tests were performed in the longitudinal direction.A 4 mm-diameter stainless steel rod was partially inserted on both sides of the scaffold so that one segment on each end was covered.After mounting the stainless steel rods, parafilm (Heathrow Scientific) was wrapped around the segment to prevent slippage during the tensile test.The samples were uniaxially stretched at a rate of 1% strain per second up to a total displacement of 400% or until break.The loading and unloading cycles were performed until 110% strain with a strain rate of 10% per second for 10 cycles.Both tensile and load and unloading tests were captured with a camera (DMC-G3, Panasonic) with a macrolens (Panagor 90 mm f2.8, Komine).Images and videos were analyzed using ImageJ (Version 1.52p, NIH) and Adobe Premiere Pro (Version 12.0, Premiere Pro CC 2018).
The obtained force-displacement values from the mechanical tester were converted to stress and strain.The yield strength was obtained as the maximum force value before rupture.The Young's modulus was calculated as the slope in the linear part of the stress-strain curve before plastic deformation.The yield strain was calculated as the point when the plastic deformation started.The toughness was calculated as the area under the stress-strain curve until plastic deformation.The toe region of the samples was calculated using three different methods.A schematic representation is shown in Figure 1B.The first one was described by Freed et al. and defined as the initial linear part of the curve. [45]This was immediately followed up by a heel region, which was the nonlinear transition zone between the toe region and the linear elastic region.The second method was described by Vegas et al. as the nonlinear high-compliance region of the stress-strain curve that ended right before the start of the linear elastic region. [46]This method did not include a heel region.Finally Chandrashekar et al. calculated the toe region by approximating both the toe and linear regions as straight lines and calculated the intersection point between these two straight lines. [47]The luminal fiber recovery test under physiological strain was performed using similar settings as the tensile test.The testing limits were set at 10% strain, which represented values within physiological strain or 100% strain, which represented a definite strain.The samples were carefully removed and snap frozen in liquid nitrogen.An untested sample (0% strain) was used as control.

Finite-Element Modeling
COMSOL multiphysics (Version 6.0, Comsol B.V.) was used to simulate the tensile test of the scaffolds.A 3D computer-assisted design (CAD) model of the scaffolds was made using a customwritten plug-in for Rhino Grasshopper (Rhino 6, Version 6.24, Robert McNeel & Associates) that converts the programmed X-Y-Z and axial movements into a 3D model.During the tensile simulation, one of the ends was fixed, while the other end at a 5 mm displacement, the equivalent to 100% strain, was simulated in steps of 0.5 mm.

Carotid Artery Preparation
Both porcine and caprine arteries were kindly donated from the Central Animal Testing Facility (CPV) in Maastricht, right after animal sacrifice of other animal studies where arteries were not involved.Leftover carotid arteries were excised from the animals and kept in PBS.The arteries were prepared for tensile analyses by cutting them in pieces of ≈15 mm in length.Caprine (n = 2) and porcine (n = 6) arteries were obtained and further divided in 6 and 16 pieces for tensile testing, respectively.The inner diameter and thickness of the wall was measured using a caliper.Comparable to the developed scaffolds, the arterial samples were fixed around stainless steel rods (2.5 mm initial axial displacement) and put under a controlled strain until tissue rupture occurred.

Incremental Fatigue Analysis
The in vivo patency of a scaffold can be determined by its resilience to fatigue under physiological conditions and was tested by subjecting the sample to continuous cycles of natural strain.In this study, the cyclic resilience was quantified using mechanical loading of scaffolds at continuously increasing levels of strain.To induce incremental fatigue, software commands were set up to induce a sinusoidal waveform displacement (maximum displacement À5/5 mm), administering a 10% uniaxial strain.Each sample was subjected to a total of 100 cycles at a speed of 1 Hz (60 cycles/minute) representative of a physiological heartbeat in resting state following previously conducted research by Chapman et al. [48] After successive exposure to 100 cycles, the waveform strain was raised by 10% for a further 100 cycles, which was repeated until sample failure or a total displacement of 100% was reached.Fatigue test data was processed in material stress (σ, N mm À2 ) over fatigue cycles (cycles/time).

Statistical Analyses
Statistical analyses were performed with GraphPad Prism 8.1.2.Datasets were grouped according to sample design from which the population mean (μ) and standard deviations (SD) were calculated.Significant differences were tested using a student's t-test and were considered significant when p < 0.05.Statistical analyses for grouped datasets were assessed using two-way analysis of variance with multiple comparison (mixed model), followed by either Tukey honestly significant difference or Šidák correction posthoc analysis to confirm significance between variables.

Results
The nomenclature used to classify the scaffolds developed herein is shown in Figure 1.Briefly, scaffolds were fabricated with a four-axis extrusion-based system in a corrugated pattern.In this study, various parameters in the pattern were changed to investigate the influence on the mechanical properties.

The Effect of Amplitude Variation on the Mechanical Properties
Various PCL scaffolds with different amplitudes were fabricated.The amount of repeating units per segment and fibers was kept constant at 2 and 7, respectively (U2F7).Table 1 shows the fiber size and angle between the samples.There was a minor variation observed in fiber size between the samples ranging from 434 μm up to 508 μm in the AM0 and AM150, respectively.In addition, the angle of the fiber between the units decreased with the increase in amplitude.Figure 2A depicts an overview of the samples.
Analyses of the stress-strain curves revealed that the increase in amplitude caused an extension in the nonlinear region (Figure 2B).The Young's modulus decreased significantly with the introduction of the corrugated pattern from 1043.0 AE 42.1 to 100.7 AE 13.8 KPa in the AM0 and AM150 samples, respectively.However, with the corrugated pattern, the Young's modulus remained similar (Figure 2C).In addition, the yield strength of the scaffold decreased significantly from 13.2 AE 0.8 to 8.0 AE 1.3 N in the AM0 and AM200 samples, respectively (Figure 2D).The yield strain increased significantly from 20.7% AE 2.2% to 225.2% AE 19.8% strain in the AM0 and AM200 samples, respectively (Figure 2E).The toughness seemed to increase from 189.3 AE 30.4 to 556.2 AE 95.9 N mm À2 in the AM0 and AM200 samples, respectively (Figure 2F).
Comparing the three different methods for calculating the toe region revealed that method 1 gave the smallest toe region, method 3 an intermediate, and method 2 the largest toe region.In all three methods, the toe region increased with the increasing amplitude.Interesting to note was that the samples in the first part of the nonlinear region twisted to the inside and constricted the lumen of the scaffold, while it widened again in the second part of the nonlinear region (Figure S1 and Video S1, Supporting Information).This constricting effect was more evident with an increase in amplitude.Finite-element modeling showed this similar effect (Figure 3).The corrugated pattern caused a better stress distribution when stretched compared to a scaffold with straight fibers.In addition, it was noted that in the corrugated pattern, the stress builds up at the edges of the fiber rather than the middle of the fiber.The results also showed that it was impossible to increase the strain up to 100% in the AM0 samples without breaking the samples.

The Effect of Multiple Repeating Units on the Mechanical Properties
Various PCL scaffolds with different amount of repeating units were printed, as shown in Figure 4A.The amplitude was reduced with increasing amount of repeating units to keep the nonlinear part similar between designs.The amount of fibers per segment was kept constant at seven (F7).Table 2 shows an overview of the tested parameters.The fiber sizes between designs were similar with the smallest fiber diameter in the AM133U3 samples and the largest fiber in the AM80U5 samples at 471 and 499 μm, respectively.The fiber angle also remained similar even though the amplitude in every fiber of each sample was different.The representative stress-strain curves showed that there was an additional inflection point observed with the increasing amount of repeating units (Figure 4B).This overall resulted in a flattening of the stress-strain curve.After a closer inspection on the video data, it was observed that this initial inflection points corresponded to the corners of the fibers in the units tearing up while extending (Figure S2, Supporting Information).After 40% strain, AM80U5 kept stretching until the fibers broke at around 210% strain.Figure 4C shows that Young's modulus decreased with the increasing amount of units repeating per segment from 128.1 to 54.9 KPa at 2 and 5 units per fiber, respectively.Other values such as the yield strength, yield strain, and the toughness remained similar between the designs, assuming that the yield point was reached right before the scaffold broke.The calculation for the toe region using method 1 showed that the toe region increased with the amount of units per fibers from 74.6% to 83.8%.However, the second method showed an opposite trend with the largest toe region at 180.8% in AM200U2 samples and the smallest at 161.7% in the AM133U3 samples.The toe region for both the AM100U4 and AM80U5 samples could not be calculated, since the stress-strain curve was no longer sigmoidal shaped.To validate whether the scaffolds were operating in the elastic region, multiple loading and unloading cycles were performed until 110% strain.Figure 5A shows full recovery of AM200U2 while the AM80U5 samples did not recover, while the corners showed signs of tearing upon extension until 110% strain (Figure 5B).This resulted in the scaffold buckling after the unloading cycle at 0%.
Finite-element modeling showed that by increasing the amount of units per fiber, the amount of stress buildup also increased, specifically at the edges of the fibers (Figure 6).The model also showed that lumen constriction was less with the increasing amount of units per fiber, which was also observed in the mechanical test (Figure S3 and Video S2, Supporting Information).
Figure 3. Finite-element model of a tensile test with the AM0U2F7 and the AM200U2F7 design compared to the mechanical test.One end was fixated while the other end was displaced 5 mm (100% strain).A) AM0U2F7 model, in the left side, the unstimulated scaffold.The middle and right side show the scaffold after 100% strain was displayed as displacement and von Mises stress, respectively.B) AM200U2F7 model, in the left side, the unstimulated scaffold.The middle and right side show the scaffold after 100% strain was displayed as displacement and von Mises stress, respectively.C) Tensile test of the AM0U2F7 and AM200U2F7 samples until break or until 100% displacement, respectively.Scale bar represents 4 mm.

The Effect of Material Choice and the Mechanical Properties
Scaffolds of the same design as previously discussed with the changing amplitude and constant unit and fiber amount of 2 and 7, respectively, were fabricated with PEOT/PBT.These conditions had the best sigmoidal shaped stress-strain curve.Both materials have different bulk properties with PCL being stiffer compared to PEOT/PBT (86.1 AE 7.4 MPa and 16.9 AE 0.4 MPa respectively).This is reflected in the stress-strain curves as in all the tested conditions the PCL scaffolds have a higher Young's modulus, yield strength, and toughness.However, the shape of the stress-strain curve remained similar regardless of the material.The stress-strain curve did not contain any initial nonlinear region in the AM0 designs.The corrugated pattern did contain an extended nonlinear region that increased with the increase in amplitude.The calculations of the toe region revealed that there was a notable difference between the PEOT/PBT and PCL samples using method 1.The toe region in the AM100 design was 14.4% and 29.9%; in the AM200 design, 40.1%  Toe region is calculated after the initial inflection point.and 69.1% for PCL and PEOT/PBT, respectively.The differences between the other methods were less notable.The yield strain seemed mainly influenced by the design of the scaffold rather than the material, with both materials having similar yield strains throughout all the different designs (Figure 7 and Table 3).

Microfiber Lumen
An intraluminal microfiber layer was added to three PCL and PEOT/PBT scaffold types: AM0U0 (control), AM100U4, and AM200U2 (N = 5 per condition).The intraluminal microfibers have been added with a dual purpose.First, the layer is there to visualize any damage caused by overstretching the scaffold.
Second, it may help potential cellular integration into the scaffold.All scaffold types were exposed to a uniaxial strain of either 0% (control), 10% (within physiological strain), or 100% (definite strain) after which they were snap frozen, sectioned, and visualized using SEM.The luminal fibers were measured at an average width of 43 AE 5 μm for all scaffolds.Visually, both PCL and PEOT/PBT scaffolds displayed no major distortion at 10% strain compared to their respective controls (Figure 8A).In contrast, while PCL scaffolds exposed to 100% strain showed significant plastic deformation of both luminal fibers and the skeletal support structure, PEOT/PBT scaffolds displayed only minor dilation of the intraluminal space without major dysregulation of the structure or inherent damage to the individual fibers.Figure 8B,C shows the luminal deformation per uniaxial deformation of PCL and PEOT/PBT scaffolds.
The intraluminal deformation within the PCL scaffolds was 4.6% AE 1.8% at 0% strain and 5.8% AE 1.1% at 10% strain, showing a limited overall increase compared to 15.8% AE 0.9% deformation when subjected to 100% strain.The increase in strain was expected to result in an increase in the total area of deformation.The exact amount of deformation, however, does not necessarily follow a linear trend, since the design of the scaffold is capable of elastic recovery at lower strain values.This was indicated by the negligible difference in deformation between the control and 10% strain (4.6% AE 1.8% and 5.8% AE 1.1%, respectively).When comparing the deformation of PCL to PEOT/PBT (Figure 8C), interesting differences were found specifically in the designs subjected to 100% strain.Although significant differences were found between 0-10% and 100% strain deformation, no structural damage of the microfiber lumen was observed in the SEM visualization of PEOT/PBT scaffolds, which did occur in PCL-based scaffolds at 100% deformation (Figure 8A).The quantified luminal deformation area at 100% also decreased in PEOT/PBT compared to PCL in all design conditions.
Comparing the variation between design structures, clear differences were found between the overall deformed area of the control (AM0) and the two optimized corrugated scaffold designs (AM100, AM200).Larger deformation was noticed in all strain areas of the control (AM0) compared to AM100 and AM200, although it must be noted that this may have occurred due to the skeletal structure being quantified as the filled area in the threshold analysis.

Comparison of the Corrugated Design and Primary Animal Tissue
The designs with the largest amplitude (AM200U2) from both PCL and PEOT/PBT were compared to porcine and caprine carotid arteries.Table 4 shows an overview of the carotid arteries tested.The inner diameter between goat and pig carotid arteries was 2.8 AE 0.4 and 2.3 AE 0.4 mm, respectively.The wall thickness in the porcine samples was thicker compared to the caprine samples (1.0 AE 0.1 and 0.4 AE 0.1 mm, respectively).The tested scaffolds had a comparable wall thickness as the caprine samples.The tensile test revealed that both the caprine and porcine carotid artery had an initial linear region followed by an increase in slope at higher strain that extended beyond any of the tested designs (Figure 9B) However, when focusing on the initial 20% of the stress-strain curve, all the samples overlapped except for the AM200 design made of PCL.The Young's modulus of the PCL samples was significantly different compared to both the caprine and porcine arteries (128.1 AE 13.0, 35.3 AE 14.0, and 23.1 AE 6.7 KPa, respectively).

Cyclic Fatigue Analysis
To evaluate the resistance to continuous, fluctuating stresses, the scaffolds were exposed to an incremental fatigue model, where a continuous increase in strain was applied to assess the resilience to fatigue.The cyclic stress-strain response for most of the fatigue life can be satisfactorily described by the cyclic stressstrain (CSS) curve of the material under physiological conditions. [49]Under natural conditions, the inflation-extension rate of the carotid artery determines the physiological axial strain and typically has a natural strain rate of ≈10% in human carotid arteries, whilst for porcine carotids this was estimated around 50%. [50] Figure 10A shows a single block of 100 cycles at 10% strain deformation where, for the first number of cycles, scaffolds displayed stress saturation and further stabilization over the remaining cycles.Figure 10B displays the incremental fatigue cycle as the induced stress (σ, MPa) over the number of waveform cycles as a factor of time.Each loading block is indicated by a 10% increase in strain (ε þ 10%) causing a subsequent increase in the peak stress.Neither the PCL nor PEOT/PBT control designs (AM0U0) were able to withstand a cyclic strain rate of over 10% (100 cycles, ε = 10%).The PCL samples displayed a sharp decline in stress, indicating continuous plastic deformation of the sample and eventual material failure at 45 and 85 cycles.Interestingly, PEOT/PBT AM0U0 scaffolds were able to recover in the first waveform block (ε = 10%, T = 100), but showed a gradual decrease in stress over the four following blocks, eventually failing at 444 cycles (ε = 50%, T = 444).All tested corrugated designs were able to stabilize in stress values up to the maximally tested strain rate of ε = 100%.PCL AM100U4 scaffolds did display an overall higher stress compared to AM200U2 and all PEOT/PBT corrugated scaffolds (PCL AM100U4: 2.5 AE 0.2 MPa compared to PCL AM200U2: 1.1 AE 0.3 MPa; PEOT/PBT AM100U4: 0.6 AE 0.2 MPa and PEOT/PBT AM200U2: 0.2 AE 0.1 MPa, respectively).
As a follow up, stress/strain values that have showed stabilization in stress during each block were plotted in a CSS curve  (Figure 10C). [51]Permanent plastic deformation of a sample was confirmed through either full failure of the samples (PCL AM0U0, PEOT/PBT AM0U0) or by a decrease in overall stress while increasing stretch (PCL AM100U4).All other samples showed proper recovery up to the maximally tested rate of ε = 100%.Furthermore, the physiological stretch ranges of both human and porcine carotid arteries (Human ε = 20%, Porcine ε = 50%) were compared to the fatigue values and displayed in green (Figure 10C).All design models except for PCL AM0U0 were able to meet or exceed the maximal human passive strain rate (ε > 10%).Additionally, both PCL and PEOT/PBT designs with corrugated patterns exceeded the porcine models with regard to strain rate (ε > 50%).

Discussion
This study highlighted the use of a corrugated pattern and the influence of different design parameters on the mechanical properties of tubular scaffolds.The effect of the corrugated pattern was shown in the stress-strain curves where the nonlinear region was significantly extended by the introduction of the pattern.This also introduced a sigmoidal behavior represented by the J-shaped stress/strain relationship as observed in natural vessels. [52]By varying the length of the amplitude, it was shown that the nonlinear region and the yield strain could be controlled.An additional step can be taken to change the mechanical properties by introducing multiple units per segment of the corrugated pattern.This led to a decreased Young's modulus while the other parameters such as the yield strength, yield strain, and the toughness remained similar.The corrugated pattern was fabricated out of different materials to explore the effect of material properties.
It was shown that changing the material did not affect the yield strain and the length of the nonlinear region.However, other properties such as the Young's modulus, toughness, and yield strength were affected.Finally, the design with the longest nonlinear region was compared to pig and goat carotid arteries.
While the nonlinear region in the native carotid arteries was larger compared to the tested designs, the initial part of the stress-strain curve was similar, thus demonstrating that the corrugated pattern could have potential for flexible and extendable tubular tissues such as arteries.The stress-strain curves in the corrugated samples were considerably different compared to the AM0 samples that had a straight fiber arrangement.The Young's modulus of the straight fiber samples was significantly higher, while the differences between the other samples remained similar.This is also confirmed by modeling, where the von Mises stress was tenfold higher compared to the samples with the longest amplitude.In addition, the yield strain of the designs was increased with the corrugated pattern.While the yield strain of a straight PCL fiber was 21%, this was increased tenfold up to 225% strain in the samples with the largest amplitude.Fleischer et al. showed in a similar study that curled spring-like electrospun PCL fibers also showed a decreased Young's modulus and increased yield strain compared to straight fibers. [53]The only difference is that the corrugated design extended the nonlinear region while the curled spring-like fibers did not show an extended nonlinear region.A different study performed by Hochleitner et al. showed that sinusoidal-shaped melt electrowritten poly(L-lactide-co-ecaprolactone-co-acryloyl carbonate) fibers had a decreased Young's modulus and a sigmoidal stress-strain curve, [54] which was explained as the unfolding of the sinusoidal meanders, giving rise to a nonlinear behavior.This was also shown in this study with the corrugated pattern that can unfold to become a straight fiber before the plastic deformation starts.However, not all spring-like structures show this initial nonlinear region.Chen et al. revealed that a wave pattern can be created after electrospinning PEOT/PBT on a polylactic acid thermoshrinkable film. [55]The introduced wave patterns did only have an initial nonlinear region of 1% strain.The yield strain in the wave patterns, however, was 100% or greater in all of the tested conditions.Finally, a study on various stent designs showed that a corrugated design, with the corrugations in the circumferential direction, had an improved mechanical compatibility score but was more susceptible to pinching. [56]urther increasing the amplitude in the corrugated pattern would result in the fusion of the fibers due to the limited space between the fibers.To avoid this, the amount of repeating units was increased while correcting for the amplitude.Increasing the amount of repeating units resulted in more space between the fibers, allowing to potentially further increase the amplitude.Another benefit of increasing the amount of units was that there was less constriction of the lumen, as shown by the mechanical tests (Figure S2, Supporting Information).This was also confirmed by the finite-element model, where less constriction was observed when increasing the amount of units.Specifically, scaffolds with only two repeating units showed almost a full constriction at 100% strain, while the other scaffolds showed barely any constriction at the same amount of strain.The constriction in the lumen is undesirable especially for vascular applications where it could cause hypertension. [57]Yet, the constriction in the samples was noticeable at strain values higher than 20% strain, which is still beyond what is physiologically relevant. [50]This constrictive behavior, however, can be found in other tubular organs such as sphincters. [58,59]An interesting approach could be to combine this structural scaffold design approach with a technique that covers the lumen of the scaffold to investigate the constrictive behavior, [44] as the corrugated pattern was too porous to withhold liquid.One drawback of the corrugated design, as well as other metamaterial designs, is that they require space for unfolding. [60]When implanted, the surrounding tissue may impede this unfolding process, something that should be further investigated in the future.
Another mechanical consideration to note was that increasing the amount of units caused an additional inflection point in the Figure 10.Representative incremental fatigue plots of various corrugated designs (N = 5).A) Single-waveform fatigue cycle displaying stress stabilization of the scaffolds.Data is plotted as the peak stress (MPa) over each cycle (1 Hz, 60 cycles/minute).B) Total incremental fatigue graph.The peak stress of each cycle was plotted.Scaffolds were exposed to a total of 1000 cycles with a 10% increase in strain per 100 cycles.Fatigue propagation occurs whenever a sample is not able to recover from an increase in strain.C) CSS curve of the incremental fatigue model.Physiological strain ranges of both human and porcine carotid arteries are displayed in green.
stress-strain curve.Most likely this was caused by the corners of the fibers that acted as a hinge and started to tear, resulting in a buckling effect after the unloading cycle.These hinges in the scaffold correlate with the areas where the von Mises stresses were the highest.The results from the finite-element model also revealed that the stress increased with the amount of units per segment.Specifically, the samples with the largest amount of units per segment were torn as they unfolded.Once the hinges were torn, the slope of the stress-strain curve decreased, indicating that the biggest contributor of stress was the resistance caused by the unfolding of the hinges.After this additional inflection point, the main contributor of stress was the fibers that were pulled during the tensile test until the scaffold broke completely.Another reason why the samples with the longest amplitude and the smallest amount of units did not show this initial inflection point is that these require more force to bend the shorter fibers with an equivalent fiber diameter. [61]The obtained stress-strain curve showed two different yield points, the first one that represents the hinges tearing, but fibers in the scaffold still remain connected.The second yield point is where the fibers of the scaffolds start to tear and rupture of the scaffold soon follows after.Future studies could investigate if this tearing effect could be avoided using a sinusoidal pattern instead of a corrugated pattern.The generated fibers from the sinusoidal pattern should not have sharp corners that could act as a hinge.Other studies have conducted similar investigations using sinusoidal patterns and did not observe tearing at the corners of the scaffolds; however, mechanical testing was performed radially instead of longitudinally. [36,62]he different methods of calculating the toe region were compared here.The Freed method ends after the initial linear region and includes a heel region. [45]Compared to the other two methods described herein, this method consistently exhibits the smallest toe region.The reason being that the heel region, which is still considered a toe region by both the Vegas and Chandrashekar methods, is included in this.The endpoint of this heel region is the endpoint of the toe region used in the Vegas method.This method ends at the start of the linear elastic region. [46]f all the methods described here, the Vegas method has consistently the largest toe region and from a practical point of view it is also a simpler method that could still be used to calculate samples with a very small toe region.The Chandrashekar method uses the tangents of the two trend lines. [47]This method gave a toe region that was between the Freed and Vegas method; however it can be challenging to calculate the toe region if the region is small and if the initial part of the stress-strain curve is not linear (Figure S4, Supporting Information).It is important to consider that these methods have originally been developed to assess material properties and not structural properties of scaffolds.Specifically, scaffolds that have complicated designs make calculating mechanical properties more complex. [63,64]herefore, it is recommended to supplement the mechanical tests with additional observations, such as videos during the tensile test, to better understand the complex mechanical behavior of the scaffolds.
Fabricating the scaffolds with different materials resulted in stress-strain curves that followed a similar trend.The mechanical properties of the scaffolds are based on a combination of material properties and structural design. [31,65]Scaffolds were fabricated with different materials to differentiate between design and material properties.The stress-strain curves of both the PCL and PEOT/PBT scaffolds followed a similar trend.For example, the Young's modulus, toughness, and yield strength were more influenced by the mechanical properties rather than the design, with these parameters having at least a fivefold difference between the PCL and PEOT/PBT scaffolds throughout the tested designs.Interestingly, the difference in yield strain was nearly the same in both PCL and PEOT/PBT samples except at larger amplitudes, indicating that the corrugated design had a greater influence on the yield strain than the material properties.The method applied in this study could serve as a blueprint to investigate other designs, which have a major influence on mechanical properties.This result could give tissue engineers a wider range of materials to choose from, without the bulk properties of the chosen material having a mechanical mismatch to the intended tissue application.
[68] Additionally, results from our previous study on these melt-spun microfiber scaffolds revealed a successful circumferential alignment of smooth muscle cells within the lumen when cocultured with vascular endothelial cells. [44,69]ithin this study, the mechanical extent of luminal resilience under strain was further quantified, where no major structural deformation was found at passive physiological strain.Furthermore, the source material also appears to affect the total deformation at higher levels of strain, where a clear significant difference was found in total deformation of PCL scaffolds, whilst this was less apparent in PEOT/PBT scaffolds.These observations propose that the flexibility of PEOT/PBT serves as a major contributing factor in upholding fiber arrangement and preventing luminal collapse.The results support the hypothesis that the formation of a microfiber lumen is sufficiently resilient to the natural 20% strain of the human vasculature, only displaying deformation when high levels of strain (ε >= 100%) is exerted upon the scaffolds.
The carotid arteries from both pigs and goats had a long toe region of up to 200% strain.The main differences between the corrugated design and the carotid arteries were that there was almost no stress generated with the increasing strain before the linear region.However, the corrugated design did generate stress even with a more flexible material such as PEOT/PBT.In the corrugated design, there was a sharp drop when the scaffolds ruptured while the arteries had a more gradual decline in stress.This could be the result of the artery consisting of multiple components such as collagen and elastin, each with their own yield points. [70]Comparing the toe region between the corrugated design and the arteries revealed that the toe region was smaller in the corrugated design.The applied strain that is required to reach that toe region is, however, far beyond the physiological level of around 10%. [50] Focusing on the initial 20% strain, it was noted that the corrugated PEOT/PBT samples with the largest amplitude have a similar stress-strain curve to that of both a pig and goat carotid artery, indicating that they could be used as a biomimicking artificial graft alternative for vascular tissue engineering.
Exposure to continuous homeostatic strain can positively affect the shape and orientation of vascular cell types, increase proliferation rate, migration behavior, and synthesis of contractile and regulatory proteins. [71]The proper reproduction of natural mechanical behavior in scaffolds is therefore not only critical for proper tissue arrangement, but may also contribute to the formation and proper alignment of extracellular protein sheets, such as the internal elastic lamina or the adventitial type I and III collagen bundles. [72]For this reason, all optimized corrugated scaffolds were assessed for their compliance to continuous incremental strain for their resilience to continuous exposure to mechanical stressors representative of the passive forces occurring in a live host.
All designs exceeded the maximum human passive strain (ε = 20%).The radial strain rates in healthy humans often falls even lower than this benchmark, where the strain per pulse was found to average out around 2.81 AE 0.91%. [73]Additionally, the passive carotid strain of the used porcine arteries was higher at ε = 50%, which is also easily matched by all optimized corrugated scaffolds. [50,74]Interestingly, none of the control samples (AM0U0) were able to meet these passive strain values, with PCL failing at a 10% strain rate and PEOT/PBT at 20%, indicating that the corrugated design of the scaffold has a significant influence on the overall resilience to continuous strain.Having a mechanical mismatch with the host artery could cause graft failure. [11]Therefore using the design such as the one described in this study could help to reduce or eliminate the mechanical mismatch.Three out of the four optimized vascular scaffolds also showed proper recovery up to the maximally tested rate of 100% (PCL AM200U2, PEOT/PBT AM200U2, PEOT/ PBT AM100U4), with only PCL AM100U4 showing permanent plastic deformation in the CSS curve at 90% (Figure 10C).Studies on the average stress on the intact human carotid wall established the average stress in a range between 0.16 AE 0.04 and 0.9 AE 0.25 MPa, which also corresponds with the ranges of the previously mentioned corrugated designs. [75]lastin is the key component for elastic behavior in the human body.It is found in many organs such as the lungs, [76] skin, [77] tendons, [78] and vasculature. [79]Together with as many as 30 other proteins, it forms a complex elastic fiber. [9]The presence of these elastic fibers allows these tissues to expand or stretch without too much force required at low strain.Similarly, the corrugated pattern presented here also requires little force to stretch.However, the way it stretches is different compared to elastin.Whereas elastin forms a network of elastic fibers that can extend and recoil and the stretch is uniform throughout the tissue, [80] the corrugated pattern extends only locally at the bending points as shown in the models.Nonetheless, it is known that elastin synthesis only occurs at the embryonic development with no de novo elastin production in adults. [81,82]In combination with the complex structure of elastic fibers, this makes the corrugated pattern an easier off-the-shelf approach for potential vascular tissue engineering or the design of bioresorbable stents.In future studies, the corrugated design could be further investigated to assess a wider array of materials besides PCL and PEOT/ PBT.In addition, the production capacity of the corrugated design could be further improved and the compatibility of the proposed methodology with other fabrication techniques explored.

Conclusion
We demonstrated a corrugated pattern with a tunable nonlinear elastic region.Varying the amplitude of the corrugated pattern led to an increase in yield strain up to 200% compared to 15% without the pattern.The shape of the stress-strain curve became sigmoidal with the introduction of the corrugated pattern mimicking major arteries.Increasing the amount of repeating units led to an additional inflection point in the stress-strain curves generating two different yield points.In addition, mechanical data showed the corrugated pattern had a bigger influence on the yield strain than the material properties.Finally, the corrugated pattern was compared to different carotid arteries and revealed that the stress-strain curves were similar and had similar mechanical properties.These results highlight how the corrugated patterns studied here could be used as a biomechanical biomimicry approach in the fabrication of a vascular grafts.

Figure 1 .
Figure 1.Corrugated scaffold pattern.A) Nomenclature of the corrugated pattern with the AM100U2F7 as example.B) Example of the stress-strain curve with the different methods to calculate the toe region.

Figure 2 .
Figure 2. Overview and mechanical analyses of the corrugated pattern with varying amplitude.A) Stereomicroscopy images of the tested scaffolds.B) Representative stress-strain curve of the tested designs.C) Young's modulus, D) Yield strength, E) Yield strain, and F) toughness of the tested designs.Each condition contained n = 5.Scale bar represents 5 mm.****p < 0.0001.

Figure 4 .
Figure 4. Overview and mechanical analyses of the corrugated pattern with varying amounts of units and amplitude.A) Stereomicroscopy images of the tested scaffolds.B) Representative stress-strain curve, C) Young's modulus, D) yield strength, E) yield strain, and F) toughness of the tested designs.Each condition contained n = 5.Scale bar represents 5 mm.**p < 0.01, ****p < 0.0001.

Figure 5 .
Figure 5. Loading and unloading cycles of the A) AM200U2 and B) AM80U5 designs.The top panel depicts the scaffolds at various strains during the first loading cycle.The bottom panel shows the stress-strain curve during the cycle in black the first cycle and in red the second loading and unloading cycle.

Figure 6 .
Figure 6.Finite-element model of a tensile test on the corrugated designs with varying units and amplitude.One end was fixated while the other end was displaced by 5 mm (100% strain).Upper panel shows the unstimulated samples.Middle panel shows the samples after stimulation shown in displacement.Lower panel shows the samples after stimulation with von Mises stress.

Figure 9 .
Figure 9.Comparison between the corrugated pattern and carotid arteries from porcine and caprine.A) Young's modulus and B) representative stress-strain curve; the physiological strain range is highlighted and the inset in the top-right corner represents the physiological range.Each condition contained n = 5 for the polymer samples, n = 6 for the caprine samples, and n = 16 for the porcine samples.****p < 0.0001.

Table 1 .
Overview of the tested corrugated patterns with varying amplitude.

Table 2 .
Overview of the tested corrugated patterns with varying units and amplitude.

Table 3 .
Overview of the tested PCL and PEOT/PBT corrugated patterns with varying amplitude.

Table 4 .
Overview of the tested carotid arteries.
Animal source Inner diameter [mm] Wall thickness [mm] Amount of arteries