The Effect of Mechanical Loading on Sprouting Angiogenesis from Engineered Macro‐vessel Model

Abstract

The influence of mechanical signals on sprouting angiogenesis has been of interest in the field of tissue engineering and biomechanics. Here, a unique experimental methodology is developed to apply mechanical loading on an engineered macro‐vessel model to study the influence on angiogenic sprouting. The polydimethylsiloxane (PDMS) stretchable device contains an engineered macro‐vessel embedded within a collagen matrix. The model is loaded either parallel or perpendicular to the macro‐vessel (longitudinal or lateral, respectively). A finite element analysis is performed to characterize the strain maps of the PDMS‐collagen setup. The results indicate high uniform strain around the macro‐vessel perimeter under longitudinal loading, while lateral loading results in low strain in the horizontal direction and high strain along the vertical direction. Experimental results for lateral loading show increased sprouting events and capillary orientation in the stretch direction following the organization of matrix fibers, while longitudinal loading results in sprouting inhibition. These findings allow prediction of angiogenic sprouting under specified mechanical loading profiles and may serve as a tool to rationally design and control vascular network architecture by physical means. Finally, the presented approach can serve as a platform for studying cell behavior under mechanical loading for any physiological tubular duct or vessel model.

A stretchable macro‐vessel model embedded in collagen is subjected to distinct mechanical loading profiles to study sprouting angiogenesis. Finite element analysis maps strain distributions, revealing that lateral stretch enhances sprouting and alignment, while longitudinal stretch inhibits it. The study offers a predictive, controllable platform to guide vascular architecture using external mechanical cues.

1. Introduction

Sprouting angiogenesis is a key process driving the formation of a functional, hierarchical, and dynamic vasculature needed for the proper exchange of nutrients and gases.^{[ 1} , ^{2 ]} Hence, understanding underlying mechanisms that regulate this essential process can provide important insights for basic research in developmental biology, pathogenesis of cardiovascular disease, and for multiple applications in tissue engineering, seeking new tools to control vascularization.

In recent decades, the regulation of angiogenesis by paracrine factors was studied thoroughly, and the role of many pro‐angiogenic factors was revealed, including VEGF, FGF, PDGF, and others.^{[ 3} , ⁴ , ^{5 ]} The role of physical signals on sprouting angiogenesis has mainly focused on the role of both intraluminal and interstitial fluid flow‐mediated shear stress. Many such studies have relied on applying flow to 2D or 3D in‐vitro culture models, and have demonstrated an inhibitory effect by the application of high levels of shear stress ^{[ 6} , ⁷ , ^{8 ]} and a pro‐angiogenic effect by applying low flow rate alternately.^{[ 9 ]} Recent studies have shown that external tension forces applied to a tissue can control capillary vessel (<50 µm) network formation. While static loading led to capillary network organization with preferred orientation along the stretch axis, the application of cyclic loading led to orthogonal vessel arrangement.^{[ 10} , ¹¹ , ^{12 ]} Moreover, there is evidence that mechanical stimulation, like cyclic strain can represent a cue for angiogenic sprouts to develop larger lumens over cellular migration and subsequent sprout length.^{[ 13} , ^{14 ]} Although these studies indicate the importance of mechanical forces on microvasculature formation, the effects of stretch on larger‐scale and hierarchical vasculature have not been studied in great depth. Previous studies demonstrated the ability to create blood vessels in larger scales ranging between meso vessels like arterioles and venules (50–1000 µm) to arteries and veins like vessels (>1 mm).^{[ 15 ]} These studies focused mainly on the interactions between macro‐vessels and micro capillaries in one system,^{[ 16} , ¹⁷ , ^{18 ]} anastomosis,^{[ 19 ]} and in vivo integration.^{[ 6} , ^{20 ]} The studies of physical forces on larger vessels are mainly focused on the effect of flow‐induced shear stress on the macro‐vessel models, demonstrating facilitation of macro‐vessel integrity, endothelium maturation, and sprouting angiogenesis.^{[ 16} , ^{21 ]} Yet, the influence of external mechanical forces, like tension on the surrounding tissue on such macro‐vessel models remains largely unknown. To bridge this gap, we developed a new experimental assay that enables us to study the effect of mechanical loading on sprouting angiogenesis from engineered macro‐vessel model.

2. Results

2.1. Construction of 3D Macro Vessel Model for Studying Sprouting Angiogenesis under Mechanical Loading

A stretchable device was designed to allow the application of external forces on an engineered macro vessel model and measure the effect in real time using light microscopy. The device was made of PDMS and contains a rounded well in the middle (5 mm diameter, 2 mm high) for casting an ECM‐based hydrogel and leading channels for positioning a templating rod. The middle well also contains a PDMS net in the upper layer of the casting well to ensure mechanical support to the gel during stretching. An opposite mold was designed using CAD software and printed using butenediol vinyl alcohol co‐polymer (BVOH)sacrificial material. After PDMS casting and curing, the sacrificial material was washed with distilled water, and the elastic device was extracted (Figure  1A; Figure S1, Supporting Information). Next, a macro‐vessel model was built by inserting a templating rod that passes through the central well, and then is removed after hydrogel solidification, creating a macro channel (500 µm diameter) later lined with endothelial cells (ECs). After two days of incubation, the cells form a complete endothelium that lines the channel, forming an intact macro‐vessel. Proangiogenic factors are then added to the medium to stimulate the initiation of new sprouts from the engineered macro‐vessel (Figures 1B and 2).

Figure 1.

Construction of the stretch‐induced sprouting angiogenesis model. A) Schematic illustration of the fabrication process. (i) An opposite mold was printed with BVOH sacrificial material followed by (ii) PDMS casting and BVOH dissolving. (iii) A protective rod was placed in the middle well for fabricating a macro‐channel embedded within the hydrogel. (iv) EC lining of the channel led to inner lumen formation, (v) fixation frame was added for stretch application on the engineered macro vessel model. B) Illustration of various loading conditions, including unloaded condition, lateral stretch, and longitudinal stretch.

Figure 2.

Finite element simulations for the experimental assay under mechanical loading. (A) FEM results of the developed equivalent strain maps under longitudinal stretch (left) and lateral stretch (right) in a middle cross‐section. (B) Higher magnification of the strains evolves in the embedded macro‐channel under longitudinal stretch (left) and lateral stretch (right). (C) 2D presentation of the strain develops along the macro‐channel perimeter under longitudinal (left) and lateral (right) stretch, white and yellow triangles indicate high and low strain levels respectively.

2.2. Characterization of the Strain Maps within the 3D Macro Vessel Model under Various Mechanical Loading Conditions

To characterize the strains that develop for the different stretch conditions, we performed finite element analysis (FEA) of the combined PDMS‐hydrogel geometries and loading conditions using ANSYS software. The resulting equivalent strain maps indicated high uniform strain levels around the macro‐vessel perimeter under longitudinal loading (Figure 2Ai‐Ci). In comparison, lateral loading resulted in low strain levels in the macro‐vessel lateral direction (Figure 2Aii‐Cii, yellow triangles) and high strain values on top and bottom of the vessel perimeter (Figure 2Aii‐Cii, white triangles). When we examined the strain per angle in the center of the macro‐vessel, it was possible to see the uniform strain distribution received from longitudinal stretch compared to gradient strain profile in the lateral stretch condition (Figure 2). To empirically measure the developing displacement and strain maps under stretch, red fluorescent beads were embedded within the casted hydrogel (Figure S2A, Supporting Information). Using a commercial stretch bioreactor (Ebers T3), the elastic device was stepwise stretched by 0.1 mm intervals up to 10% stretch level. A representative image was captured for each step so the displacement of the beads could be followed. For the 10% stretch level, the displacement map was measured, and the equivalent strain map was calculated (Figure S2A,B, Supporting Information). The comparison between the experimentally measured strain and the calculated FEA strain values revealed similar strain levels (Figure S2C,D, Supporting Information). In addition, both the simulation and empirically measured results show uniform strain distribution along the axis perpendicular to the stretch (Figure S2D, Supporting Information).

Based on these strain maps, we hypothesized that the difference between the two loading conditions may lead to a distinct cellular response. The relatively high and uniform strain levels observed under longitudinal loading, compared to the more heterogeneous strain under lateral loading, might inhibit endothelial cell (EC) activity within the macro‐channel. Previous studies have demonstrated that high shear stress levels, induced by flow, can inhibit sprouting.^{[ 6} , ⁷ , ^{8 ]} Similarly, excessive mechanical loading in our system may suppress new sprout formation, while moderate loading could promote directional sprouting of newly formed vessels originating from the macro‐vessel model. To examine the stretch‐induced perimeter geometry change, the inner macro‐channel surface of the elastic device was coated with green, fluorescent beads. The displacements were measured, validating shortening in the horizontal and vertical direction under longitudinal stretch, and elongation at the horizontal direction under lateral stretch as predicted by the FEA simulation (Figure S3, Supporting Information).

2.3. The Effect of Longitudinal and Lateral Mechanical Loading on Sprouting Angiogenesis from Macro‐Vessel Model

After characterizing the strains computationally, we next examined experimentally the effect of external forces on sprouting angiogenesis. Uniaxial static stretch (10% strain) was applied on the device parallel (longitudinal stretch) or perpendicular (lateral stretch) to the macro‐vessel axis. In addition, unloaded devices served as a control. The sprouting characteristics were measured in the following 5 days using a confocal microscope (Figure 3). The results from the stretch experiments showed a significant difference in sprouting behavior under different loading conditions. Stretch in the lateral direction resulted in the highest values of sprouting events (8.69 ± 0.99 sprouts per 1 mm of macro‐vessel length), the highest value of total sprout length (2811.52 ± 67.1 µm) and sprouts orientation mainly in the lateral direction (72.19 ± 4% of the sprouts oriented in the range of 60°‐ 90° referring to the macro‐vessel axis) (Figure 3B,C). In contrast, stretch in the longitudinal direction resulted in a decreased number of sprouting events relative to unstretched controls (1.85 ± 0.21 sprouts per 1 mm of macro‐vessel length), decreased value of total sprout length (362.89 ± 58 µm), and sprout orientation mainly in the longitudinal direction (71.1 ± 3.6% of the sprouts oriented in the range of 0°–30° referring to the macro‐vessel axis). The control group without stretch results in 4.78 ± 0.78 sprouting events, 833.79 ± 259.1.3 µm total sprout length, and sprout orientation mainly in the 30°–60° direction with respect to the macro‐vessel axis (59.79 ± 3% of the sprouts) (Figure 3B,C).

Figure 3.

Sprouting angiogenesis from macro‐vessel under static stretch. (A) Confocal imaging after 2 and 5 days of sprouting angiogenesis from macro‐vessel without stretch, macro‐vessel under 10% lateral static stretch, and macro‐vessel under 10% longitudinal static stretch (Scale bar: 200µm). Quantification for sprouts orientation (B), sprouts number and length (C) for different loading conditions. Data are presented as means ± SEM. n=4 (*P < 0.05, **P < 0.01, ***P<0.001, ****P<0.0001).

2.4. Connectivity and Patency of the Stretch‐Induced Hierarchical Vasculature

To investigate the functionality of stretch‐induced multiscale vasculature, a 10 kDa dextran was injected into the engineered macro‐vessel. As can be observed in Figure 4A, the dextran perfused through the macro‐vessel without noticeable leakages, indicating the capability of the engineered macro‐vessel to serve as an endothelial barrier. In addition, higher magnification imaging reveals the entrance of dextran into the newly formed vessel sprouts, indicating connectivity and patency of the newly developed multiscale vasculature to the macro vessels (Figure 4A).

Figure 4.

Functionality of the stretch‐induced multi‐scale vasculature. A) Patency validation by Dextran (blue) entrance from the engineered macro‐vessel into the micro vessel sprouts. (Scale bar: 200 µm (left), 50 µm (right)). B) VE‐cadherin (red) and DAPI (blue) staining of a HAMEC ZSgreen (green) macro‐vessel endothelium. (Scale bar: 20 µm). C) VE‐cadherin (red) and DAPI (blue) staining of a HAMEC ZSgreen (green) under lateral stretch condition showing full integrity of new vessel sprouts. (Scale bar: 200 µm).

Moreover, VE‐Cadherin staining shows mature, tight endothelium of the engineered macro‐vessel lumen (Figure 4B) and integrity of the luminal structure for the micro‐vessel sprouts (Figure 4C).

2.5. Hydrogel Fiber Alignment under Mechanical Stretch

To better understand the effects of stretch on the hydrogel in our system, we used fluorescently labeled hydrogel to examine the gel fibers’ organization under static stretch. After the gel polymerized, the device was imaged in an unloaded condition as control and in a 10% stretch condition. While images of the unloaded condition revealed random heterogeneous fibers arrangement, Images of the stretch condition revealed fiber alignment in the stretch direction (90^°) and a decrease in the fibers arranged in other directions as compared to the unloaded control (Figure 5A; Figure S5, Supporting Information). Calculating the nematic order parameter (NOP index), which indicates the alignment level of the hydrogel fibers per degree, showed higher fiber alignment in the stretch direction (NOP = 1) for the loaded condition as compared to the control (Figure 5B). The ratio between stretch and control conditions also demonstrates a preferable fiber arrangement in the stretch direction (90°–60°) with significantly higher values as compared to other directions (Figure 5C).

Figure 5.

Hydrogel fiber alignment analysis. A) Representative images of stained hydrogel fibers under unloaded (i) and stretched (ii) conditions. Fibers aligned in 0 ^o − 30 ^o orientation are marked in green, and 30 ^o − 90 ^o orientation are marked in blue. (Scale bar – 100 µm (left), 50 µm (right)). B) Ratio between lateral stretch and control as a function of NOP index. C) Quantification of fiber alignment ratio per degree. D) Comparison of average fibers length (i) and percentage of elongated fibers (>20 µm) between stretch and control groups. n = 8 for each group (^** p < 0.01, ^**** p < 0.0001).

Additional analysis regarding fiber length revealed higher fiber length under stretch condition. The average fiber length at the stretch condition is 9.26[µm] while 7.16[µm] in the control group (Figure 5Di). Furthermore, the stretch condition contains a high percentage of elongated fibers longer than 20 microns as compared to short fiber fragments in the unloaded condition (Figure 5Dii; Figure S5, Supporting Information).

3. Discussion

Vascularization of engineered tissue is a major key for developing thick, viable, functional constructs in vitro, and for achieving rapid and robust graft integration in vivo.^{[ 22} , ^{23 ]} Previous research showed that external mechanical forces applied on engineered tissues may influence capillary network orientation, facilitate maturation, and improve vascular integration after implantation.^{[ 10} , ^{11 ]} In another study, we showed the superiority of multiscale vasculature over only micro‐scale capillary network for fabricating thick, viable dense tissue construct which promotes rapid and robust integration with the host vasculature in vivo.^{[ 8 ]} Taking a step beyond previous microscale capillary network systems, in this research, we aimed to study the influence of mechanical forces on sprouting angiogenesis in a macro‐vessel model with relevant large blood vessel scale for developing an optimal hierarchical vessel network with defined organization.

As aforementioned, we developed a new experimental assay with a PDMS stretchable device, which enables the application of mechanical stretch stimulation in various directions on a 3D engineered macro‐vessel model (Figure 1). The chosen stretch level (10%) is known to induce endothelial cell response, like vascular morphogenesis ^{[ 10 ]} and to rearrange matrix,^{[ 24 ]} while a lower stretch level (5%) induces a moderate effect and a higher stretch level (15%) results in a comparable effect on fiber alignment^{[ 24 ]} and the developing strain field (Figure S6, Supporting Information). Using finite element analysis, we predicted the developed strain maps under the application of mechanical stretch, indicating relatively high and uniform strain levels under longitudinal loading as compared to lateral loading (Figure 2). In addition, limited sprouting was observed under this condition indicating possible sprouting inhibition under excessive mechanical loading in correspondence to previous works indicating a similar effect under high shear stress levels induced by flow.^{[ 6} , ⁷ , ^{8 ]} In contrast, a moderate loading in the lateral direction led to an increase in sprouts number with oriented growth direction in parallel to the stretch axis while the unloaded control sprouted sporadically in a 30–60 degrees direction (Figure 3), with similar vessel orientation as reported in previous studies under unloaded conditions ^{[ 25} , ^{26 ]} These experimental results are in correspondence to the FEA simulations, which reveal a high number of long and oriented sprouts growing in the low‐strain horizontal direction under lateral loading, and significantly fewer sprouts in the high‐strain longitudinal loading condition. These results suggest that angiogenic sprouting can be regulated by external mechanical loading of the tissue.

For further examination of the stretch effect on the hydrogel in our system, we loaded the elastic device with labeled hydrogel. As a result, we observed that the gel fibers oriented and elongated in the stretch direction, creating uniaxial fiber alignment as compared to random, heterogeneous fiber arrangement in the unloaded control group (Figure 5; Figure S5, Supporting Information). In accordance with previous works that demonstrated cell arrangement according to ECM fiber alignment,^{[ 12} , ²⁴ , ²⁷ , ^{28 ]} the fiber organization indicates a possible spatial‐structural guidance of the endothelial cells to create new sprouts in the direction of the stretch. This observation highlights the ability to guide cell migration and vessel sprouting by using mechanical forces for regulating ECM fiber alignment. The precise molecular pathways involved in stretch‐regulated angiogenesis (e.g., YAP/TAZ, integrin signaling) remain to be elucidated. Altogether, the new experimental system validated the important role of axial tension on sprouting angiogenesis which can either lead to sprouting formation or inhibition by strain location and level dependence. This study provides new beneficial insights for rationally design and develop improved hierarchical vasculature in engineered tissues with defined vascular architectures, by inducing external mechanical loading, therefore potentially improving network organization and graft vascular integration. The presented results demonstrate the possibility of harnessing specific force profiles to either promote or inhibit vessel sprouting according to desired maturation phase including optimal conditions for vessel formation and vessel stabilization. Lastly, those insights from this in vitro model may be useful as a starting point to conduct following research for better understanding the role of mechanical forces on vasculature remodeling and stabilization in vivo under physiological conditions.

4. Experimental Section

PDMS Stretch Device Design and Fabrication

The elastic stretch device with the middle well (2‐mm‐thick and 5mm‐diameter) was designed using SOLIDWORKS 2017 CAD software, with precise leading channel designed for placing a templating rod (500 µm diameter in parallel orientation with 1 mm relative distance). Negative pattern molds were made of water‐soluble butenediol vinyl alcohol co‐polymer (BVOH) and printed with a PRUSA MK2.5 3D printer. The mold was cast with poly(dimethylsiloxane) (PDMS; 1:10; Sylgard 184; Dow‐Corning), cured for 4 h, at 60 °C, and washed with distilled water overnight to remove sacrificial material.

Simulation of Loading Profiles on 3D Macro‐Vessel Model

The elastic device and a hydrogel disc in the size of the inner well of the stretch device were modeled using SOLIDWORKS 2017 CAD software. Both models contain a centered 500 µm diameter channel in a parallel orientation, which represents the macro‐vessel. The two parts were defined as one part with a common face (the rim of the disc) and were defined in a continuous model. The material properties assigned to the stretch device were according to the Material Property Database for PDMS^{[ 29 ]} and previous in‐vitro characterization^{[ 30 ]} with a Young's modulus of 3.6 MPa. In addition, the material properties assigned to the hydrogel disc were as rat tail collagen type 1 according to Corning ^{[ 31 ]} with a Young's modulus of 198.6 Pa (for 3.5 mg mL⁻¹ final concentration) compatible with native tissue physiological stiffness. Both parts meshed together with element size of 0.5 mm. To ensure an optimal mesh for accurate solutions, a mesh convergence test was performed using an iterative process. Convergence was defined as achieving less than a 0.05% difference in the maximum equivalent stress between successive iterations. Using ANSYS Mechanic, uniaxial stretch on the joined parts was simulated such that one end of the stretch device was fixed, and the opposite end was displaced so the model was deformed to 10% from its initial length corresponding to the in vitro strain. The stretch applied in parallel and perpendicular direction to the inner channel like the in vitro conditions.

Cell Culture

Primary human endothelial cells derived from human adipose micro‐vascular endothelial cells lentivirally transduced with ZsGreen fluorescent protein (HAMECs, ScienceCell) were cultured in endothelial cell medium (ECM, ScienceCell, Cat. No. 1001). Cells were grown to passage 5–8 in T‐flasks incubated in 5% CO₂ and 37 °C.

Engineered Macro‐Vessel Seeding

Pre‐seeding preparation included fibronectin coating of the PDMS middle well (100 µg mL⁻¹, Sigma), for 1 h at 37 °C, in a tissue culture incubator. 50 µL collagen (3.5 mg mL⁻¹, rat tail collagen type 1, Corning), was prepared according to the manufacturer protocol, casted onto the middle well and allowed to solidify for 30 min at 37 °C, and 5% CO₂. Macro‐vessel fabrication included gentle removal of templating rods and injection of HAMEC (1 × 10⁷ cells/mL) into the macro channel. Uniform cell attachment to the lumen was achieved by flipping the construct every 10 min during 30 min incubation, at 37 °C. Detached cells were washed away with HAMEC medium and samples were then incubated in a HAMEC culture (5 mL per well). Endothelial cell medium was changed any other day and the macro‐vessel models were monitored for 5 days to follow sprouting angiogenesis dynamics in a relevant time period for HAMEC capillary formation as reported before.^{[ 6 ]}

Evaluation of Vasculature In Vitro Patency

To evaluate the patency of the vasculature in vitro, 10 mg mL⁻¹ cascade‐blue–dextran (average MW 10000, Sigma–Aldrich) was directly injected into the open ends of the engineered macro‐vessel. The fluorescent dye was then viewed and analyzed via confocal microscope imaging.

Histology and Immunofluorescence Staining

For whole‐mount immunofluorescence staining, constructs were fixed with 4% paraformaldehyde (PFA; Electron Microscopy Sciences) for 15 min, rinsed with phosphate‐buffered saline (PBS) (Gibco Life Technologies) for 5 min x3 times, and permeabilized with 0.3% Triton X‐100 (Bio Lab Ltd.) for 10 min at room temperature. Following PBS washes (5 min x3) and overnight incubation in blocking buffer (5% bovine serum albumin (Merck Millipore) in PBS) at 4 °C, constructs were incubated overnight, at 4 °C, with goat anti‐VE‐cadherin antibodies (Sigma‐ Aldrich) diluted 1:100 in blocking buffer. Following PBS washes, samples were incubated with secondary antibodies (1:400 donkey anti‐mouse Alexa Fluor647 or 1:100 donkey anti‐goat Alexa Fluor647; Jackson ImmunoResearch) and 1:1000 4′,6‐diamidino‐2‐phenylindole (DAPI, Sigma‐Aldrich), for 2 h, with gentle shaking, followed by PBS washes (5 min, x3). Constructs were imaged with a confocal microscope, using the Zen software. Image processing and further analysis were performed using FIJI software.

Hydrogel Fiber Alignment Analysis

Alexa Fluor 546 stained thrombin (12 UI) was received from Lesman lab and mixed with fibrinogen 20 mg mL⁻¹ solution (evicell) in a 1:1 ratio. The solution was cast into the middle well of the bio‐reactor and allowed to solidify for 30 min at 37 °C, and 5% CO₂. When gel polymerization was achieved, the device was placed on a fixation frame, holding the device at a 10% strain. The whole complex was captured using a confocal microscope LSM 700 (Zeiss) before (control) and after inserting the frame (stretch). The images obtained from the LSM were converted to black and white masks using ImageJ (NIH) for further analysis via OrientationJ, an ImageJ plugin. The OrientationJ analysis gives the amount of fibers aligned in each degree. In each sample, every count for each degree was normalized by dividing it in all the counts received from all the degrees in the specific sample. In addition, each degree was converted into a NOP index (Equation 1) which indicates the level of alignment of the fibers. In this equation, index “1” indicates alignment in the stretching direction, index “0” indicates anisotropic alignment and index ‘‐1′ indicates alignment perpendicular to the stretching direction. The ratio between the stretch and the control was calculated by dividing the average count in stretch samples by the average counts of the control for every NOP index.

$$NOP=2COS{\left(\theta \right)}^2-1;\theta =\frac{\pi }{2}-\alpha$$ (1)

Fiber Length Analysis

The length and area of fibrin fibers in the stretch direction were quantified using AngioTool. First, using OrientationJ, the mask images were split into three channels representing 3 groups of angles (0^° − 30^°,30 − 60^°,60^° − 90^°). The 0^° − 30^° images were used for further analysis. Afterward, the directional masks were analyzed with and without thresholding of removing small particles with an area below 4440 square micrometers to receive only fibers with a length above 20 microns (Figure S4, Supporting Information). Average fiber length was received from running AngioTool on images without the thresholding. The percentage of fibers above 20 µm calculated by dividing the data received from the threshold analysis to the data received from the analysis without thresholding.

In Vitro Displacement and Strain Analysis

For measuring the strain maps in vitro, red fluorescent polystyrene beads (7.76 diameter PS‐FluoRed, microParticles GmbH, Germany) were imbedded in fibrin 20 mg mL⁻¹ solution (evicell) in a 1:400 ratio. The solution was cast into the middle well of the elastic device and allowed to solidify for 30 min at 37 °C, and 5% CO₂. After polymerization, the device was stretched using an EBERs TC‐3 bioreactor and captured after every 0.1 mm stretch. After achieving a 10% strain, the images were merged into a stack using ImageJ. A vector‐based map representing the displacement of the beads across multiple time frames was generated using the TrackMate ^{[ 32 ]} plugin of ImageJ. The resulting table, which contained data for over 1000 tracks divided into 14 time frames, was processed by a Python algorithm. For each track, the algorithm calculated the displacement as the Euclidean distance between its initial and final positions based on the provided X and Y coordinates. To ensure accuracy, exaggerated measurements and small noises caused by tracking misreadings were filtered out. The resulting filtered data was then used to render the final displacement map. A scale of 0.7 and a width of 0.004 were chosen in order to facilitate visualization. In addition, manual strain displacements were measured using Equation (2).

$$\epsilon =\frac{l_f-l_0}{l_0}$$ (2)

where l ₀ is the length between two horizontal dots in first frame and l_f is the length between the same dots in the last frame. Both lengths were measured using ImageJ.

The strain measurement was compared to the strain achieved by simulation using ANSYS model of the system as described previously.

Statistical Analysis

Data are presented as mean ± SEM, while group differences were determined using the unpaired, two‐tailed Student's t‐test. A two‐way analysis of variation (ANOVA) was performed to examine the influence of two independent categorical variables, followed by Bonferroni's multiple comparison. Prior to applying parametric tests data were assessed for normality using the Shapiro–Wilk test. p < 0.05 was taken to indicate a statistically significant difference between groups. Sample size (n) for each condition is noted in figure legends. The statistical analyses were performed using Prism (GraphPad) Software.

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

L.D and O.K. contributed equally to this work. L.D., O.K., C.S.C, and S.L. designed research. L.D. and O.K. performed research. L.D., O.K., A.S., and T.F. analyzed the data. L.D., O.K., C.S.C., and S.L. wrote the paper. S.L. supervised the research.

Supporting information

Supporting Information

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.