24 Surgeons routinely perform incremental releases on overly tight ligaments d uring total knee 25 arthroplasty (TKA) to reduce ligament tension and achieve their desired implant alignment. 26 However, current methods to assess whether the surgeon achieved their desired reduction in the 27 tension of a released ligament are subjective and/or do not provide a quantitative metric of 28 tension in an individual ligament. Accordingly, the purpose of this study was to determine 29 whether shear wave tensiometry, a novel method to assess tension in individual ligaments based 30 on the speed of shear wave pro pagation, can detect changes in ligament tension following 31 incremental releases. In seven medial and eight lateral collateral porcine ligaments (MCL and 32 LCL, respectively), we measured shear wave speeds and ligament tension before and after 33 incremental rel eases consisting of punctures with an 18 -gauge needle. We found that shear wave 34 speed squared decreased linearly with decreasing tension in both the MCL (r2avg = 0.76) and LCL 35 (r2avg = 0.94). We determined that errors in predicting tension following increm ental releases 36 were 24.5 N and 12.2 N in the MCL and LCL, respectively, using specimen -specific calibrations. 37 These results suggest shear wave tensiometry is a promising method to objectively measure the 38 tension reduction in released structures. Clinical Significance : Direct, objective measurements 39 of the tension changes in individual ligaments following release could enhance surgical precision 40 during soft tissue balancing in TKA. Thus, shear wave tensiometry could help surgeons reduce 41 the risk of poor out comes associated with overly tight ligaments, including residual knee pain 42 and stiffness. 43 44 Keywords 45 Total knee arthroplasty, ligament tensiometry, soft tissue balancing, intraoperative sensor, 46 ligament release 47 48 Introduction 49 During total knee arthroplasty ( TKA), surgeons routinely have to address overly tight 50 ligaments. The traditional alignment targets in TKA (i.e., mechanical alignment with equal and 51 rectangular gaps) often cause the surgeon to alter the patient’s native alignment and gaps, 52 creating overly tight ligaments.1-4 Additionally, prior studies suggest that ligaments in the 53 diseased compartment (e.g., the medial collateral ligament in a knee with osteoarthritis in the 54 medial compartment) contract and/or become stiffer.5,6 Thus, to achieve their des ired implant 55 alignment and soft tissue balance,2,7 surgeons commonly reduce ligament tension using a 56 3 ligament release technique called “pie crusting”. Pie crusting, or the “inside -out” technique, 57 involves iteratively puncturing the overly tight ligament wi th a needle or scalpel to reduce the 58 tension in that ligament.8,9 Previous ex vivo10-14 and in vivo8,15 studies have shown that pie 59 crusting does reduce the tension in ligaments, but tracking these reductions in tension remain 60 challenging. Indeed, improper ligament tensioning is one of the primary factors associated with 61 knee stiffness and pain,16,17 which are two common reasons patients report not being satisfied 62 following TKA.18 With up to 19% of patients reporting that they are not satisfied following 63 TKA,16,17,19,20 a method to track ligament tension reductions during iterative release procedures is 64 needed to mitigate the risk of improper ligament tension post -operatively. 65 Current methods to assess reductions in ligament tension during these releases are 66 subjective and/or not capable of directly measuring the tension in an individual ligament. Laxity 67 assessments,21,22 gap tensioners,23,24 and spacer blocks25 are most commonly used to assess 68 ligament tension during TKA. However, many ligaments work in parallel to determine joint 69 laxity, and clinical assessments of laxity are often qualitative. A recent stu dy showed that 70 assessing ligament tension based on joint gaps alone, one common measure of joint laxity, 71 resulted in average tibiofemoral contact forces up to 350 N,26 which are about three -times greater 72 than those in the native knee.27 An alternative to l axity and gap assessments are instrumented 73 trials that measure the tibiofemoral contact forces;18,28 however, these trials provide quantitative 74 guidance about the tensions of all the ligaments in a compartment rather than the tension in a 75 particular ligame nt. Thus, a direct and objective method to track changes in tension in the 76 released ligament would enhance the surgeon’s ability to determine when they have achieved a 77 desired reduction in tension during iterative releases. 78 4 One promising method to measure the tension in individual ligaments during TKA 79 directly and objectively is shear wave tensiometry.29,30 Prior studies have shown that shear wave 80 speed squared is proportional to the axial stress in tendons29 and ligaments.30 This relationship 81 between shea r wave speed squared and axial stress is consistent with the analytical relationship 82 predicted by a tensioned beam model.29 However, it is unknown whether reductions in tension 83 due to releases alter shear wave propagation speed differently than reductions in tension due to 84 changes in the axial stretch of an intact ligament. Thus, a pre -requisite step to translating shear 85 wave tensiometry into the operating room to monitor ligament tension during soft tissue 86 balancing is to determine whether shear wave speed s track ligament tension changes following 87 iterative releases. 88 Accordingly, we had two objectives for this study. Our first objective was to characterize 89 the relationship between shear wave speed and tension in medial and lateral collateral ligaments 90 (MCL and LCL, respectively) following incremental releases. We chose to study the MCL and 91 LCL because collateral ligament tension is a common focus of soft tissue balancing during TKA. 92 Our second objective was to determine the errors in predicting tension using shear wave speeds 93 during incremental releases in the MCL and LCL. 94 95 METHODS 96 Specimen preparation 97 We procured eight MCLs and eight LCLs from a crossbreed of large white, landrace, and 98 red duroc pigs for this study (weight = 139.0 ± 6.8 kg, age = 6 months). One MCL failed during 99 testing and was excluded. We used porcine collateral ligaments for this study because MCLs 100 5 from pigs of this siz e have been previously shown to have similar structural (e.g., stiffness, 101 failure deformation) and material (e.g., modulus, failure strain) properties to those of human 102 MCLs.31 103 Specimen preparation consisted of the following steps. We first exposed each li gament 104 by removing all superficial tissue, and then flexed each knee (i.e., stifle joint) to the angle where 105 the fibers across the ligament appeared to be most uniformly taught; this angle was typically 106 around 80° of flexion.31 Next, we cut bone blocks con taining the ligament attachments from the 107 distal femoral condyle and proximal tibia/fibula using an oscillating saw. We then secured each 108 bone block in an aluminum cup using a potting material (Bondo Fiberglass Resin, 3M, St. Paul, 109 MN). Finally, we dissect ed away excess tissue superficial and deep to the outer surface of the 110 ligament prior to experimentation. 111 Experimental procedure 112 Following dissection, we mounted each specimen for experimentation using the 113 following steps. First, we secured the potting cu ps in the grips of an electrodynamic testing 114 system (Acumen 3, MTS, Eden Prairie, MN) with the specimen aligned visually with the loading 115 axis. We fine -tuned the orientation of the potting cups to achieve the most -uniform tension 116 across the width of the li gament. Next, we mounted the three components of the shear wave 117 tensiometer, which housed the piezoelectric tapping device and two accelerometers, in a 3D - 118 printed structure that pressed each component against the outer surface of the ligament with a 119 contro lled force of 1.4 ± 0.2 N (Figure 1). The level of this controlled force was set to minimally 120 influence the shear wave speeds.32 We measured the controlled force of each component using a 121 load cell (LC101, Omegadyne Inc., with reported linearity = 0.25 N). The piezoelectric tapping 122 device (PK4JQP1, Thorlabs Inc, Newton, NJ) induced shear waves in each specimen by 123 6 delivering 20 -μm impulsive taps across the width of the ligament at a tap rate of 10 Hz. The pair 124 of single -axis accelerometers (Model 352C23, PCB Piezotronics), spaced 6.5 mm apart, tracked 125 the shear wave propagation.29 Further details on the tapping device and the accelerometer arms 126 are described in the Supplemental materials (Supplement A, Figures S -1, S-2, and S -3). We 127 completed two repeatabilit y studies using this apparatus to mimic (1) setting the apparatus up on 128 different days and (2) reapplying contact of the tapper and accelerometer arms on the ligament 129 between experimental trials (Supplement B, Figures S -4 and S -5). We determined the 130 repeat ability limits33 for the first scenario to be 6.70 m/s for the MCL and 4.58 m/s for the LCL, 131 and those for the second scenario to be 1.49 m /s for the MCL and 2.70 m/s for the LCL. 132 Before testing, we preconditioned each ligament with the following procedure. First, we 133 axially loaded each ligament with 50 cycles from 25 to 250 N at 1 Hz followed by a static hold at 134 250 N for 30 minutes to minimize viscoelastic effects.30 We limited the maximum load to 250 N 135 based on pilot studies that showed failures at the bony attachments of some porcine ligaments 136 when applied loads exceeded 250 N. We recorded the maximum stretch during the 30 -minute 137 static hold at 250 N, referred to subsequently a s δ250. 138 Following preconditioning, we measured shear wave speeds before and after sets of 139 incremental releases. First, we cycled each ligament 10 times between its slack length and δ 250 at 140 1 Hz, and then we measured the shear wave speeds with the intact l igament held to a stretch of 141 δ250. We then repeated three steps (i.e., release, cycle, and measure) to characterize changes in 142 shear wave speed following incremental releases (Figure 2). In the release step, we stretched the 143 ligament to δ 250 and performed a set of incremental releases. Each set of releases consisted of a 144 minimum of five punctures across the ligament width using an 18 -gauge needle. We performed 145 more than five punctures for some trials to ensure that the tension in the ligament stretch to δ 250 146 7 dropped by at least 10 N in each set of releases. We performed subsequent release sets about 2 147 mm above the previous row of punctures. In the cycle step, we cycled the ligament 10 times 148 between its slack length and δ 250 at 1 Hz to simulate the surgeon in traoperatively flexing and 149 extending the knee following release (i.e., pie crusting). In the measure step, we held the 150 ligament at a stretch of δ 250 and placed the tapper and accelerometer arms on the surface of the 151 ligament as described previously. We hel d the ligament at a stretch of δ 250 for 10 seconds while 152 measuring both the shear wave speed and applied axial tension. We repeated this release -cycle - 153 measure procedure until the tension in the ligament when stretched to δ 250 was below 50 N. 154 Throughout tes ting, we kept the ligaments moist by regularly spraying them with 0.9% saline. 155 Post-processing 156 We post -processed the recorded accelerometer signals to obtain the data used in later 157 analyses. We computed the shear wave speeds following each tap by measurin g the time delay 158 between the arrivals of the shear waves at the two accelerometers. We filtered waveforms using a 159 second -order Butterworth bandpass filter (MATLAB R20 20b) with lower and upper cutoff 160 frequencies of 150 and 2500 Hz, respectively. To determine the time delay in shear wave arrival 161 between accelerometers, we computed the normalized cross -correlation between the first 162 accelerometer waveform (i.e., the template signal was the first 0.8 ms of the transient response 163 after tap onset) with the second accelerometer waveform (i.e., a search region that extended to 164 1.0 ms after tap onset).29 The time shift that maximized the normalized cross -correlation was 165 determined. We performed a sub -sample interpolation using a local 3 -point cosine fit of the 166 normalized cross -correlation values.34 We computed the shear wave speeds by dividing the 167 spacing between the accelerometers (6.5 mm) by the time delay in wave arrival. The tension was 168 8 ascertained by averaging the data from the MTS load cell (661.18E -02, M TS, reported 169 hysteresis/non -linearity = 0.08% full scale) across the 10 -second measurement. 170 Statistical analysis 171 To characterize the relationship between shear wave speed and tension, we performed simple 172 linear regressions for each ligament type with shear wave speed squared as the independent 173 variable and tension as the dependent variable. Although the analytic relationship is between 174 shear wave speed squared and axial stress, we chose to use tension in the present study because 175 (1) tension is a more under standable quantity for clinicians, and (2) our ligaments all had similar 176 cross -sectional areas so using tension instead of axial stress only scaled the slope of our fits. The 177 level of significance, α, was set to 0.05. With at least seven ligaments of each type, strong 178 relationships between shear wave speed squared and tension (i.e., r2 = 0.64) could be detected 179 with α = 0.05 and power, 1 -β, set to 0.8 .35 180 To determine the errors in measuring tension after releases, we evaluated three different 181 cases. The fir st case was predicting the tension in a ligament using shear wave speed data from 182 both MCLs and LCLs. For this first case, we performed a leave -one-out analysis in which we 183 performed a linear regression between shear wave speed squared and tension from 14 ligaments 184 and then used this regression equation to predict the tension in the 15th ligament. We repeated 185 this procedure for all combinations of 15 ligaments , and characterized the resulting errors in 186 tension by the mean (bias), standard deviation (precision), and root -mean -square error (RMSE) 187 (ISO 5725 -1, ASTM E177 -13).33,36 The second case was predicting tension in a ligament using 188 data from the same ligam ent type (e.g., LCL tension predicted only from LCL data). For this 189 second case, we also performed a leave -one-out analysis as described above, but we performed 190 the linear regression using data from all but one MCL or LCL and then predicted tension in the 191 9 MCL or LCL not included in the linear regression, respectively. The third case was predicting 192 tension using data from that same ligament. For this third case, we determined the bias, 193 precision, and RMSE of the residual errors from the linear regression of each ligament. 194 195 RESULTS 196 The shear wave speed squared of both the MCL and the LCL decreased linearly with 197 decreasing tension (Figure 3). The mean ± standard deviation of the coefficients of determination 198 (r2) of the individual MCLs and LCLs were 0.76 ± 0.18 and 0.94 ± 0.07, respectively (individual 199 data shown in Supplement C, Figures S -6 and S -7). Within each ligament type, the r2 values for 200 fits to the pooled data of each ligament decreased to 0.58 and 0.73 for the MCL and LCL, 201 respectively. 202 The error analysis showed that the errors in the predicted tension using shear wave speed 203 were smallest when using ligament -specific data compared to using data from other ligaments 204 (Tables 1 and 2). For the MCL, the average RMSEs of predicted tension were 40.3 N (1 6.1% of 205 250-N max) when predicting based on data from all other MCLs and LCLs, 40.9 N (16.4% of 206 250-N max) when predicting based on data from all other MCLs, and 24.5 N (9.8% of 250 -N 207 max) when predicting based on data from the specific MCL (Table 1). For the LCL, the average 208 RMSEs of predicted tension were 41.5 N (16.6% of 250 -N max) when predicting based on the 209 data from all other MCLs and LCLs, 43.4 N (17.4% of 250 -N max) when predicting based on 210 data from all other LCLs, and 12.2 N (4.9% of 250 -N max) w hen predicting based on data from 211 the specific LCL (Table 2). 212 213 10 DISCUSSION 214 The objectives of the study were to (1) characterize the relationship between shear wave 215 speed squared and tension in porcine collateral ligaments following incremental releases and (2) 216 determine the errors in predicting tension from shear wave speeds duri ng incremental releases of 217 porcine collateral ligaments. The first key finding was that there were strong, linear relationships 218 between shear wave speed squared and tension in both the MCL and the LCL following 219 incremental releases. The second key finding was that ligament tension could be predicted from 220 the measured shear wave speeds to within 24.5 N for the MCL and 12.2 N for the LCL . 221 Regarding the first key finding, we demonstrated that the tensioned beam model,29 shown 222 previously to hold in intact ligam ents,30 also applies to ligaments damaged by iterative releases. 223 Our extension of shear wave tensiometry to ligaments damaged by needle punctures suggests 224 that our technique could also work in ligaments damaged by other means (e.g., ligament sprain ). 225 The i ndividual r2-values for the LCL (0.94 ± 0.07) are consistent with previous studies using 226 shear wave tensiometry to measure intact MCLs and LCLs (r2 = 0.94 and 0.98 . respectively) and 227 porcine digital flexor tendons (mean r2 = 0.96 -0.98).29,30,37 However, while the individual r2- 228 values for the MCL are still moderately strong (0.76 ± 0.18), the values are lower than the LCL 229 and previous studies on intact ligaments. One possible explanation for these lower r2-values in 230 the MCL compared to those in t he LCL is that the fibers in the MCL might engage more non - 231 uniformly than fibers in the LCL. We are not aware of any studies that have characterized 232 ligament fiber engagement in porcine collateral ligaments , but assuming that the engagement 233 patterns are si milar to those in human collateral ligaments, the fibers of the MCL will engage 234 less uniform ly across the width of ligament compared to those in the LCL .38 This non -uniform 235 engagement of fibers in the MCL could increase the variability of the measured she ar wave 236 11 speeds after releases because each puncture could have a different impact on shear wave 237 propagation depending on whether the needle severed a tighter or looser fiber. Investigating 238 these regional differences is beyond the scope of the present study , but regional differences are a 239 topic of ongoing research in our lab. 240 The range of shear wave speeds in the present study were lower than that in a previous 241 study with intact porcine ligaments.30 In the present study, the shear wave speeds ranged from 242 14.3 to 46.5 m/s, whereas Blank et al. measured shear wave speeds in intact ligaments to be 32.5 243 to 160.3 m/s for the same load range.30 The primary difference between the two studies is the 244 sensors used to track shear wave propagation. Blank et al. tracked s hear wave propagation with 245 laser Doppler vibrometers,30 a non -contact measurement technique. We tracked shear wave 246 propagation with accelerometers, a contact measurement technique. The contacting 247 accelerometers likely increase inertia and damping present i n the system. The tensioned beam 248 model suggests that the effective material density is the constant of proportionality between 249 shear wave speed squared and stress.29 Effective material density includes both the material 250 density and inertia of the surroundings. For example, a previous study showed that shear wave 251 speeds in porcine digital flexor tendons immersed in a saline were 22% less than those measured 252 in air.37 In the present study, we expect the added mass of the tensiometer components (Figure 1) 253 to be greater than that of saline surrounding the tissue, which likely explains why the range of 254 our shear wave speeds are on average 75% lower than those measured with laser Doppler 255 vibrometers in air.30 Inherent damping due to the contact tensiometer may also alter the 256 frequency content of the vibration measured at the two sensors, and thereby alter the wave speed 257 as ascertained from the transient vibrations. The potent ial added -mass and damping effect 258 indicates that the shear wave speeds measured are dependent on the tensiometer design, and care 259 12 must be taken to consider such effects when interpreting wave speed measures in tensioned 260 tissues. 261 Regarding the second key f inding , our errors in predicting tension in a released ligament 262 (12.2 to 43.4 N) are comparable to the current gold standard intraoperative measurements of 263 tibiofemoral contact force (VERASENSE, OrthoSensor, Inc ).39 A recent study showed that the 264 best-case RMSE for contact force of the femur on the tibia within a compartment measured by 265 the VERASENSE was 13.8 N.40 During passive flexion, the tensions in the ligaments largely 266 determine the contact forces of femur on the tibia. Thus, with comparable errors in predicting 267 load and the advantage of being able to measuring the tension in individual ligaments, shear 268 wave tensiometry is a promising approach to intraoperative monitoring of ligament tension 269 during release. 270 Three limitations should be considered when interpreting our findings. First, we 271 performed these measurements in porcine ligaments rather than human ligaments. The human 272 MCL, in particular, has a greater aspect ratio (average human = 15.341 and average porcine MCL 273 = 3.0; Supplement D , Table s S-1 and S-2), which may lead to a greater non -uniformity of fiber 274 engagement. Further investigation is needed to ascertain whether the larger aspect ratio results in 275 more variable effects of a needle puncture. The similar mechanical behavior between human and 276 porcine MCLs31 suggests that human ligaments would also demonstrate a predictable reduction 277 in shear wave speed with ligament releases, but that the absolute changes in shear wave speed 278 may differ from those determined in the present study. Second, we studied isolated ligaments in 279 the present study. Thus, the effects of surrounding structures were not included in this initial 280 study because we wanted to focus on the changes in the ligament without potential confounding 281 effects. As described above,29,37 the surrounding tissues/implants in vivo might further decrease 282 13 the range of shear wave speeds. Now that we have shown that the relationship between shear 283 wave speed and tension holds following release, we can explore whether this relationship 284 changes in situ in future studies. Third, achieving the minimum errors reported requires a 285 ligament -specific calibration. Because shear wave tensiometry has been shown to track tension 286 using shear wave speed squared in both intact30 and released ligaments, one possible option to 287 calibrate shear wave speeds in a particular ligament that is to be released is to calibrate the shear 288 wave speed -tension relationship during a laxity assessment before release. The tension in the 289 ligament pre -release could be estimated based on the applied load and the patient’s anatomy .42 290 The shear wave speed -tension relationship pre -release could then be determined using a 291 regression between squared shear wave speed and the estimated tension , and this pre -release 292 relationship could then be used to determine reductions in tension following iterative releases . 293 In conclusion, this study showed that shear wave tensiometry can track reductions in 294 tension due incremental releases of the MCL and LCL within 24.5 N and 12.2 N, respectively 295 (9.8 to 4.9% of the initial 250 -N tension). The strength of the relationship between shear wave 296 speed and tension was similar following release to that seen previously in intact ligaments.30 297 Thus, using shear wave tensiometry to measure tension is a promising approach to guide 298 incremental ligament releases to achieve a desired reduction in an overly tight ligament. 299 300 ACKNOWLEDGMENTS 301 This work was supported by the National Institute of Biomedical Imaging and 302 Bioengineering (NIBIB) of the National Institutes of Health u nder award number R21EB024957. 303 Two of the authors ( JDR and DGT) are co -inventors on a pending patent application for 304 technology relating to the methods described herein. 305 14