15 Soft tissues such as tendon and ligament undergo a combina tion of shear and tensile loading in 16 vivo due to their boundary conditions at muscle and /or bone. Current experimental protocols are limited 17 to either pure tensile loading , biaxial loading, or simple shear, and thus may not fully characterize the 18 mechanics of these tissues under physiological load ing scenarios . Our objective was to create an 19 experimental protocol to determin e the shear modulus of fibrous tissues at different tensile loads . We 20 assembled a four-actuator experimental system that facilitated shear deformation to be superimposed on 21 a tissue subjected to an axial preload. We measured shear modulus in axially loaded electrospun 22 nanofiber scaffolds with either randomly -oriented or aligned fiber s. We found that shear modulus in the 23 nanofiber phantoms was shear -strain stiffening and dependent on both the axial load (p < 0.001) and 24 fiber alignment (p < 0.001) of the scaffold . The proposed system can enhance our understanding of 25 microstructure and functional mechanics in soft tissues, while also provid ing a platform to investigate 26 the behavior of electrospun scaffolds for tissue regeneration . Our experimental protocol for determining 27 loaded shear modulus would be further useful as a method to gauge tissue mechanics under loading 28 conditions that are more representative of physiological loads applied to tendon and ligament. 29 2 1. Introduction 30 Tendon s and ligament s are musculoskeletal soft tissues that connect muscle to bone and bone to 31 bone, respectively. Tendons transmit forces generated by individual and/or groups of muscles to enable 32 joint motion . Ligaments serve to passively guide joint motion across a broad range of relative bone 33 rotation s and translations to fulfill their anatomical function (Wilson, Feikes, and O’Connor 1998) . Due 34 to these unique boundary conditions, the physiological loading of these tissues is highly complex, 35 resulting in nonuniform deformations due to both axial and shear loads (Gardiner and Weiss 2003; 36 Willinger et al. 2020) . The microstructure of these tissues directly affect s how they respond to complex 37 physiological loading (Lake et al. 2010; Blank et al. 2021; Blank, Thelen, and Roth 2023) , where 38 tendons have highly aligned fibers, and ligament s exhibit a more distributed fiber alignment (Amis 39 1998; Provenzano and Vanderby 2006) . The health state of the tissue also can substantially alter 40 microstructure and mechanics, such as in tendinopathy (Arya and Kulig 2010) and following injury or 41 repair (Freedman et al. 2016) . Thus, understanding the micro structure -function relationships of 42 musculoskeletal soft tissues like tendons and ligaments require s mechanical tests that induce complex 43 loading and consider fiber alignment as a feature that may alter their mechanics . 44 Despite the complex loading in vivo, b enchtop methods for assessing the mechanics of 45 musculoskeletal tissues have been mostly limited to tensile testing, and in some cases shear or biaxial 46 testing (Claeson and Barocas 2017; Tan et al. 2016) of tissue sections or representative scaffolds (Weiss, 47 Gardiner, and Bonifasi -Lista 2002; Gardiner and Weiss 2001; Driscoll et al. 2011) . These techniques 48 have enable d a better understanding of the capacity for healthy tissues to transmit load and their 49 mechanics within the se simple loading paradigm s. Other studies have characterized the combined 50 mechanics within a tissue during either tension or shear, such as interfibrillar shear strain (Szczesny and 51 Elliott 2014; Muench, Thelen, and Henak 2020) and stress (Szczesny et al. 2015) within a tendon 52 3 fascicle during tension, or the distribution of stress and tensile forces within a tissue during shear. 53 However, the mechanics resulting from combine d shear -tensile loading remains unelucidated . 54 Accordingly, t he objective s of this study were to (1) develop a novel loading paradigm for 55 determining the axially preloaded shear modulus of fibrous soft tissues, and (2) characterize differences 56 in shear behavior in isotropic and anisotropic fibrous tissues using this loading paradigm . We 57 hypothesized that shear modulus in the isotropic scaffold would be higher than the anisotropic scaffold 58 due to unaligned fibers resisting shear (Blank et al. 2021) . To accomplish these objectives, we 59 constructed a fixture capable of applying combined shear -tensile loading. We fabricated isotropic and 60 anisotropic tissue scaffolds , which we expected would have different shear response s, and characterized 61 their tangential shear modulus in the axially preloaded state. 62 63 2. Methods 64 2.1 Shear -Tensile Loading Paradigm 65 To compute the loaded shear modulus, we consider a sample undergoing deformation at four 66 different locations (Fig. 1). The two top grips attached to the sample are translated to load the sample in 67 axial tension . Next, the two grips from one side are translated to load the middle of the sample in shear 68 while maintaining the initial axial tension . We consider the sample to be symmetric in its force balance 69 about the centerline of the structure, and th us, can resolve the shear force acting on the longitudinal 70 cross -section along the centerline from the force balance of one side (Fig. 1 c). The average shear stress 71 can be resolved as the shear force over the cross -sectional area of the section . The shear strain applied 72 can be computed using the width of the shear region between the left and right grips . The se two 73 measures represent the effective average shear stress and the maximum shear strain applied to the center 74 region of the sample . 75 4 76 77 Figure 1: (a) A tissue section subject to a combination of (b) tension (in the z-direction , where Fc = -FA) 78 and (c) shear (in the xz-plane) . The shear force can be resolved as Fshear = F c - FA. 79 80 5 2.2. Fixture Design 81 We designed an experimental system that is capable of loading a tissue section according to the 82 paradigm outlined in Section 2.1. Our fixture consisted of four motor -driven linear actuators 83 (Kollmorgen EN60034, < 20 µm backlash, 2 top, 2 bottom ) that were each instrumented with a 84 submersible load cell (Futek LSB210). Each load cell was attached to a 3D -printed grip lined with 85 sandpaper to minimize the chance that the specimen slip s within the grip. The entire instrumented grip 86 system was placed in an acrylic bath with a window for backlit optical measures of strain (Raghupathy 87 et al. 2011) or fiber alignment (York et al. 2014) . 88 89 90 6 Figure 2: (i) We designed and fabricated a fixture capable of loading a soft tissue sample in combined 91 shear and tension. The fixture featured four actuators (A-D), a bath, and a transparent imaging window 92 through which backlit videos could be recorded. (ii) Specimens seen in polarized light images were 93 loaded first in tension and then in shear. (iii-iv) The plots show that the four actuators moved 94 independently to load the soft tissue to an axial strain of 0 -9% and a shear strain of 0 -40%. (v) Plot 95 shows that the shear force was computed on both sides of the specimen and found to be equal, indicating 96 force balance across the tissue width. (vi) Plot shows how w e computed the shear modulus in the linear 97 region of the shear stress -shear strain curve. 98 99 2.3. Implementation in Fibrous Tissues 100 2.3.1. Specimen preparation 101 We prepared poly-ε-caprolactone (PCL) scaffolds via electrospinning (Li et al. 2002) . We 102 dissolved PCL in a 7:1 mixture of chloroform (TCM) and N,N-dimethylformamyde (DMF) to achieve a 103 0.12 g/mL PCL solution. We chose TCM as a solvent because it was capable of producing fibers that 104 were a similar diameter as observed in tendon and ligament (1 -20 um) and added DMF to increase the 105 dielectric potential of our mixture. The polymer solution was driven through an 18 -gauge needle at 1.2 106 mL/hr with a 16kV potential through a distance of 10 cm. A rotating, circular drum with a diameter of 107 11.75 cm was placed in the polymer jet path (Fig. S1) . We controlled rotation speed to generate 108 anisotropic fiber scaffolds with fiber alignments that spanned a near -isotropic alignment (linear velocity 109 = 0.2 m/s) to highly aligned fibers (linear velocity = 14 m/s) (Li et al. 2007; Barber et al. 2013) (Fig. 110 S1). 111 112 7 113 Figure 3: (a-b) We created two electrospun scaffolds, one with isotropic fibers (bottom electron 114 microscope and polarized light images) and one with anisotropic fibers (top electron microscope and 115 polarized light images) . Scale bars represent 100 µm. (c) We characterized the fiber angle of the scaffold 116 when loaded into the grips of the testing fixture based on the polarized light images (b) . The isotropic 117 fiber scaffold had a near -uniform distribution of fibers (top histogram) , while the anisotropic scaffold 118 had a high concentration of fibers oriented along the loading direction (bottom histogram) . 119 120 2.3.2. Imaging 121 We imaged all electrospun scaffolds to verify fiber alignment. Representative sections from each 122 scaffold were sputter -coated with gold and mounted in a scanning electron microscope (SEM) (Zeiss 123 Gemini 300). Three images of the surface of each scaffold were recorded at 200x (1024 x 768 pixels). 124 8 To determine fiber alignment, we applied a 5x5 Prewitt operator (Kekre and Gharge 2010) to the 125 greyscale intensity values of each SEM image . We then determined the orientation of each pixel group . 126 Angle values were then binned and centered at 0° to confirm the isotropy of the scaffold . The fiber 127 alignment was assumed to be constant across all specimens from a single scaffold. 128 129 2.3.3. Mechanical testing 130 We mounted n=5 specimens per fiber alignment level between sandpaper grips on a custom axial - 131 shear dynamic testing fixture (Fig. 2) . The four motor -driven linear actuators (<20 µm backlash) load ed 132 the specimen both in axial tension and shear (Fig. 2) . These actuators were controlled using a 133 commercially available software in LabVIEW (simVITRO , Cleveland Clinic ). Prior to testing, we 134 recorded the thickness of each specimen using three repeated caliper measurements along the length of 135 the structure. The width was computed as the average of these measurements. We preloaded each 136 specimen to between 0.05 and 0.1 N tension on either side. After preloading, we loaded each specimen in 137 shear with a sawtooth displacement profile from 0 -40% shear strain at a rate of 10%/s for 10 cycles. We 138 then loaded specimens to axial strains of 3, 6, and 9% at a rate of 1%/s . At each axial strain , we applied 139 the same sawtooth shear displacement profile. 140 141 2.3.4. Shear modulus computation 142 We measured shear modulus during the last cycle to minimize viscoelastic effects. If 143 viscoelasticity (i.e., stress relaxation following the axial prestrain) was still present, t he stress -relaxation 144 component of the axial loading was fit using a first -order exponential and subtracted from the overall 145 axial -shear load to obtain an approximation of the elastic response (Fig. S2) . We determined the linear 146 9 region of the shear stress response using an exponential -linear optimization function (Tanaka et al. 2011) . 147 The shear modulus was then computed as the slope of a linear fit to the linear region. 148 149 2.4. Statistical Analys es 150 We assessed the shear modulus ( μ) at each axial prestrain level (ε). We compared the shear 151 modul i of the isotropic and anisotropic scaffolds at each level of axial prestrain using a two-factor 152 analysis of variance (ANOVAs) with post -hoc Tukey tests . The first factor was fiber alignment ( 2 153 levels: isotropic and anisotropic), and the second factor was axial prestrain (4 levels: 0%, 3%, 6%, 9%). 154 Because our data violated the sphericity assumption (ε shpericity = 0.37), we used Greenhouse -Geisser 155 corrections to conservative ly estimate significance of differences across axial prestrain and fiber 156 alignment . For all analyses , we set significance at α = 0.05. 157 158 3. Results 159 The shear modul i of both the isotropic and anisotropic scaffolds increase d monotonically with 160 increasing axial prestrain ( Table 1 ). We measured an unloaded shear modulus of 1148 ± 174 kPa in the 161 isotropic scaffold , which was higher than the unloaded shear modulus of 289 ± 97 kPa in the anisotropic 162 scaffold (p < 0.001 ). The shear modulus of the isotropic scaffold was higher than the anisotropic 163 scaffold at all other levels of axial prestrain (p < 0.001). 164 165 Table 1: Shear modulus (in kPa) measured at each axial prestrain level for n = 5 isotropic and n = 5 166 anisotropic electrospun scaffolds. The right column indicate s the p -value of the post -hoc Tukey tests . 167 Shear modulus [kPa] Prestrain Isotropic Anisotropic p-value 0% 1148 ± 174 289 ± 97 < 0.001 3% 1269 ± 225 366 ± 122 < 0.001 10 6% 1397 ± 265 441 ± 152 < 0.001 9% 1547 ± 2710 498 ± 150 < 0.001 168 The shear modulus of the isotropic scaffold was consistently greater than the shear modulus of 169 the anisotropic scaffold (Fig. 4) . For both scaffold types, shear modulus was dependent on the axial 170 prestrain (p < 0.001 ). We also detected a significant interaction between the degree of anisotropy of the 171 scaffolds and axial prestrain on tangential shear modulus (p = 0.016) . 172 173 174 Figure 4: Increase in shear modulus across axial prestrain levels in the isotropic and anisotropic 175 electrospun scaffolds relative to the unloaded shear modul i. Tangential shear modulus in both scaffolds 176 increased monotonically with increasing axial prestrain. Points represent the mean increase s, and e rror 177 bars represent the standard deviation of the increase s. 178 179 4. Discussion 180 The objectives of this study were to (1) develop a novel loading paradigm for determining the 181 axially preloaded shear modulus of fibrous soft tissues, and (2) characterize differences in shear 182 behavior in isotropic and anisotropic fibrous tissue scaffolds using this loading paradigm. Our first key 183 contribution was that w e successfully constructed a benchtop testing system capable of producing 184 11 combined shear -tensile loading in a tissue sample . Using this loading paradigm, we presented a method 185 to compute the tangential shear modulus of the tissue in the axially preloaded state. Our second key 186 contribution was to demonstrate that this method was sufficiently sensitive to detect changes in the 187 tangential shear modulus across both axial prestrain levels and in tissue surrogates with different fiber 188 alignments. 189 Concerning our first objective, we constructed a fixture capable of resolving the shear modulus 190 of a soft tissue section under an axial prestrain (Fig s. 1 and 2). Previously, shear testing in 191 musculoskeletal soft tissues was limited to either simple (Bonifasi -Lista et al. 2005; Weiss, Gardiner, 192 and Bonifasi -Lista 2002; Gardiner and Weiss 2001) or interfibrillar (Szczesny et al. 2015; Szczesny and 193 Elliott 2014; Muench, Thelen, and Henak 2020) shear. Thus, t o our knowledge, this is the first 194 implementation of a benchtop technique to determine the pretensioned shear modulus of a fibrous soft 195 tissue sectio n. This system is adaptable to test a range of tissue scales from thin sections required when 196 performing simultaneous polarized light imaging to complete ligaments/tendons. Only the capacity of 197 the load cells would need to change between these tissue scales. Additionally, the linear actuators we 198 selected are capable of much greater loads than necessary for most applications of ligament -tendon 199 testing. Thus, if building a system from scratch with this particular loading paradigm in mind, then 200 different actuators could be used following the design and loading paradigm developed in this study . 201 Concerning o ur second objective , we found that our fixture was capable of resolving the axially 202 prestrained shear modulus and was sensitive enough to detect changes in shear modulus due to both 203 fiber alignment ( p < 0.001 ) and axial prestrain (p < 0.001 ) (Table 1 and Fig. 4). This finding has 204 important implications to both our fundamental understanding of the structure -function relationship of 205 musculoskeletal soft tissues and our understanding about how to design electrospun nanofiber scaffolds 206 to best replicate the mechanical environment of biological tissues. Regarding the first implication, these 207 12 findings demonstrate how tissues with more anisotropic fiber alignments (e.g., ligaments) become stiffer 208 in shear as the tissue is axially strained, which likely enhances load transfer across a wide range of joint 209 configurations (Provenzano and Vanderby 2006; Lake et al. 2010) . We also found that more highly 210 aligned scaffolds had a smaller increase in shear modulus across axial prestrain levels. This finding may 211 be informative for the function of tendon s, which have relatively more highly aligned fibers than 212 ligaments due to transmitting primarily axial loads . However, tendons also feature a bony insertion, 213 areas of compression, and an interface with an in -series muscle that may contribute to anisotropic 214 material properties relevant to both tension and shear (Thomopoulos et al. 2003; Wheatley et al. 2023; 215 Shan et al. 2021; Lake et al. 2010) . Regarding the s econd implication , we characterized shear mechanics 216 in electrospun scaffolds, which are required to undergo unique loading paradigms to replicate the 217 musculoskeletal loading environment when used for tissue engineering/regeneration (Brennan et al. 218 2018) . To this point, scaffolds are often designed to replicate the alignment, and thus mechanics of 219 tissues (Nerurkar, Elliott, and Mauck 2007; Li et al. 2007) . Scaffolds can also be used to model different 220 tissues or different tissue regions (Xie et al. 2010) . Because shear mechanics , in particular , are sensitive 221 to alignment or orientation of fibers (Driscoll et al. 2011) , the pretensioned shear modulus may be a 222 consideration for these scaffolds to better replicate the native loading environment of their target tissue. 223 Our mechanical testing procedure has a few limitations to consider when interpreting results. 224 First, it is likely that the current protocol is sensitive to viscoelastic effects despite preconditioning 225 specimens both axially and in shear. At sequential axial prestrains, it is likely that the tissue is stress 226 relaxing and stretching over time . Thus, the axially prestrained shear moduli may be underestimated due 227 to a lower overall axial tension over time. The axial prestrain order should thus be randomized in future 228 tests to further eliminate the influence of viscoelastic effects in test results and to reduce the effect of 229 systematic effects. A force or hybrid -controlled implementation may also better mitigate viscoelastic 230 13 effects due to stress relaxation. Second, our results are likely sensitive to the horizontal spacing of the 231 four grips ( x-direction, Fig. 1). We used preliminary finite element models to choose t he horizontal 232 spacing of our grips (3 mm) based on comparisons to controlled single -element predictions of loaded 233 shear, but it is possible that a wider spacing may better reflect the physiological mechanics of different 234 tissue types, and thus grip spacing should be considered for each application of this technique. Third , 235 while not a limitation of the technique overall, we chose to examine scaffolds with two different fiber 236 alignments that roughly represent a range of alignments encountered in musculoskeletal tissues. More 237 studies are required to determine the sensitivity of this technique to more subtle variations in fiber 238 alignment. 239 In conclusion, we presented a novel technique for resolving the axially preloaded shear modulus . 240 This technique should be considered to enhance ongoing analysis of structure, function, and mechanics 241 in musculoskeletal soft tissues or electrospun scaffolds for tissue regeneration. 242 243 Acknowledgments 244 We gratefully acknowledge Dr. Darryl Thelen for his technical insight into devising a combined 245 shear -tensile loading paradigm. We thank Dr. Wan -Ju Li for his assistance in fabricating nanofiber 246 scaffolds. We thank Dr. Julie Morasch and the University of Wisconsin -Madison Nanoscale Imaging 247 and Analysis Center (NIAC) for their assistance in obtaining scanning electron microscope images. The 248 authors would also like to acknowledge the simVITRO team for their support with software 249 implementation of our loading paradigm. 250 251 Funding 252 14 This material is based upon work supported by the National Science Foundation Graduate 253 Research Fellowship Program under Grant No. DGE -1747503. Any opinions, findings, and conclusions 254 or recommendations expressed in this material are those of the author(s) and do not necessarily reflect 255 the views of the National Science Foundation. 256 Funding for materials in this project came from Dr. Roth’s start -up funds through the UW - 257 Madison Department of Orthopedics and Rehabilitation. 258 259