Estimation of In Vivo ACL Force Changes in Response to Increased Weightbearing

Transcription

1 Ali Hosseini Department of Orthopaedic Surgery, Bioengineering Laboratory, Massachusetts General Hospital/Harvard Medical School, Boston, MA 02114; Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA Thomas J. Gill Samuel K. Van de Velde Guoan Li 1 gli1@partners.org Department of Orthopaedic Surgery, Bioengineering Laboratory, Massachusetts General Hospital/Harvard Medical School, Boston, MA Estimation of In Vivo ACL Force Changes in Response to Increased Weightbearing Accurate knowledge of in vivo anterior cruciate ligament (ACL) forces is instrumental for understanding normal ACL function and improving surgical ACL reconstruction techniques. The objective of this study was to estimate the change in ACL forces under in vivo loading conditions using a noninvasive technique. A combination of magnetic resonance and dual fluoroscopic imaging system was used to determine ACL in vivo elongation during controlled weightbearing at discrete flexion angles, and a robotic testing system was utilized to determine the ACL force-elongation data in vitro. The in vivo ACL elongation data were mapped to the in vitro ACL force-elongation curve to estimate the change in in vivo ACL forces in response to full body weightbearing using a weighted mean statistical method. The data demonstrated that by assuming that there was no tension in the ACL under zero weightbearing, the changes in in vivo ACL force caused by full body weightbearing were N at 15 deg, N at 30 deg, and N at 45 deg of flexion. However, when the assumed tension in the ACL under zero weightbearing was over 20 N, the change in the estimated ACL force in response to the full body weightbearing approached an asymptotic value. With an assumed ACL tension of 40 N under zero weightbearing, the full body weight caused an ACL force increase in N at 15 deg, N at 30 deg, and N at 45 deg of flexion. The in vivo ACL forces were dependent on the flexion angle with higher force changes at low flexion angles. Under full body weightbearing, the ACL may experience less than 250 N. These data may provide a valuable insight into the biomechanical behavior of the ACL under in vivo loading conditions. DOI: / Keywords: anterior cruciate ligament (ACL), in vivo ACL force changes, knee 1 Introduction Accurate knowledge of anterior cruciate ligament ACL forces under functional loading conditions is instrumental for understanding normal ACL function and improving the surgical treatment of ACL injuries. Numerous studies have investigated the in vitro function of the ACL 1 5. Different measurement techniques such as buckle transducers 6 8, implantable pressure transducers 3,9, and robotic techniques have been used to measure the ACL forces in vitro. Most of these studies measured the ACL forces by applying anterior tibial loads 10,14,15, simulated muscle loads 9,13,16, or rotational moments to the knee joint However, the ACL might carry much higher forces during in vivo activities than the forces measured in in vitro experiments 20 because in vivo loads can be much larger than those applied in in vitro experiments to simulate physiological loading conditions 15. In addition, in vitro studies rarely include the contribution of the other important structures such as the muscles, which mainly determine the loading in the knee. Computational studies have also shown that the in-vivo loads are commonly much higher than those applied in vitro 21,22. The estimation of in vivo ACL forces among nondiseased knees during functional joint loading conditions could be used to provide norms for optimal tensioning of the graft during ACL reconstruction. The assessment of ACL forces under in vivo physiological loading conditions remains challenging. The in vivo biomechanics of the ACL has been investigated by measuring the anteromedial 1 Corresponding author. Contributed by the Bioengineering Division of ASME for publication in the JOUR- NAL OF BIOMECHANICAL ENGINEERING. Manuscript received May 25, 2010; final manuscript received March 2, 2011; accepted manuscript posted March 9, 2011; published online April 11, Assoc. Editor: Richard E. Debski. AM surface strains of the ACL using a differential variable reluctance transducer 4,23,24 and by measuring ACL elongation using a combined magnetic resonance MR and dual fluoroscopic imaging system DFIS 25,26. Also, computational methods have been used to determine the role of the ACL in the knee joint 21,27,28. The findings from validated computational methods have been helpful in understanding the knee joint mechanics and the force and stress distribution within the ACL. However, computational modeling has intrinsic limitations such as the assumption of the ACL as an isotropic, homogeneous material, the muscle input that is often apportioned according to the muscle size, and the exclusion of the meniscus-cartilage interface in the knee model. While these studies have improved our knowledge of the in vivo ACL biomechanics considerably, the knowledge of the in vivo forces within the ACL under functional loading is limited. Roberts et al. 29 measured the forces in the human ACL in vivo by using arthroscopic implantable force transducer AIFT during passive knee flexion/extension. However, these data on ACL forces were obtained through an invasive arthroscopic procedure on injured subjects who required surgery for knee pathology. The objective of this study was to determine noninvasively the changes in in vivo ACL forces in response to a controlled weightbearing activity. The ACL force-elongation data were obtained from experimental testing of cadaver knees and were mapped to previously published in vivo knee joint kinematics data in response to controlled weightbearing at discrete flexion angles 30 to determine changes in in vivo ACL forces in healthy subjects. 2 Methods 2.1 Measurement of In Vivo Elongation of the ACL in Response to Increased Weightbearing. The in vivo ACL elongation data in response to increased weightbearing have been published Journal of Biomechanical Engineering Copyright 2011 by ASME MAY 2011, Vol. 133 /

2 Table 1 Clinical data on the subjects tested Subject No. Sex Leg Age yr Height cm Weight N BWI kg/m 2 1 M R M R F L F R M R F L M L F R F L Mean SD before 30. In short, nine healthy subjects Table 1 were recruited under the approval of the Institutional Review Board, and consent forms were collected. One knee of each subject randomly chosen right or left was scanned in full extension position using a 3.0 T MR scanner MAGNETOM Trio, Siemens, Malvern, PA in both sagittal and coronal planes. The MR images size: mm 2 ; resolution: pixels were imported into a solid modeling software RHINOCEROS, Robert McNeel & Associates, Seattle, WA for the construction of 3D models of the knee, including the tibia, femur, and insertion sites of the ACL on the tibia and femur 26. The insertions of the ACL were outlined on the MR images in both sagittal and coronal planes, and the femoral and tibial insertion sites were created on the 3D bone models. This method has been extensively used in the literature 26,30,31. The same knee was then imaged using a DFIS during a singleleg lunge activity in a series of static positions at 15 deg, 30 deg, and 45 deg of knee flexion Fig. 1. This system consists of two fluoroscopes BV Pulsera, Philips, Bothell, WA, with image intensifiers positioned orthogonally to each other fluoroscopy mode, exposure time of 0.44 s, beam current of 1 ma, beam energy of 50 kvp, source to intensifier distance of 950 mm, and interbeam angle of 90 deg. A force plate constructed using a six degree of freedom DOF force-moment sensor JR3, San Francisco, CA was integrated into the dual fluoroscopic system. The two fluoroscope units were hardwired together such that a single button initiated the data collection sequence from the fluoroscopy units, but this hardwiring did not synchronize the actual timing of the radiation exposure firing from the fluoroscope sources. The force plate was synched with the fluoroscopes using a graphical programming software NI LABVIEW, Austin, TX. During the experiment, the subject positioned the tested leg on the force plate with the tibia perpendicular to the ground, and the ground reaction forces were displayed on a monitor in front of the subject Fig. 1. The platform was equipped with handles to help the subject balance him/herself and create the target external loading at each flexion angle, while the other leg was in contact with the ground. Simultaneous fluoroscopic images of the knee were taken at each target flexion angle under two in vivo weightbearing conditions: zero load 10 N and 1.0 times body weight BW. To represent the zero load condition at each flexion angle, the subject was requested to place the testing leg on the force plate, while the force plate measured a minimum vertical ground reaction force 10 N. Full body weight loading condition was defined when the force plate measured a vertical ground reaction force equal to the full body weight of the subject. At each loading position, the subject was asked to pause for 2 s while the fluoroscopic images were captured. The flexion angles were controlled using a goniometer. The force plate was directly connected to LABVIEW as well as the fluoroscopes. LABVIEW recorded the time as well as the signals from the force plate and each fluoroscope every 1 ms. When the desired weight was applied to the force plate, by pushing one button, the fluoroscopes generated the radiation and LAB- VIEW recorded the signals. The amount of radiation to which the subject was exposed during the entire experiment was 6 mrem. A virtual dual fluoroscopic system based on the geometry of the actual experimental system was created in the 3D modeling software 32 Fig. 2. An adapted polynomial Gronenschild 33,34 global surface mapping technique was employed to remove the distortion of the fluoroscopic images caused by perturbations of the X-ray beam from the environment and from the slightly curved surface of the image intensifier 35. The technique was implemented by mapping a set of polynomial expressions between the actual geometry of a plexi-plate grid and the acquired distorted image. A correction of the images was accomplished by using spatial mapping to distort the image pixels to their correct location based on the mapped polynomial expressions by interpolating the Fig. 1 Schematic of the dual fluoroscopic imaging system Fig. 2 Virtual dual fluoroscopic system created based on the geometry of the actual experimental system from Hosseiniet al. 30, with permission / Vol. 133, MAY 2011 Transactions of the ASME

3 Table 2 History of the cadaver donors Donor No. Sex Leg Age yr 1 M R 57 2 M L 57 3 M R 44 4 M L 44 5 F R 36 6 F L 36 Mean SD image s intensity values. All image pairs acquired by the DFIS are corrected in this manner before further imaging processing. Then, the actual relative locations of the two fluoroscopes intensifiers and X-ray sources were determined based on calibration shots. The pair of fluoroscopic images of the knee captured at each position as well as the bony models were imported into the software, and the in vivo knee positions were reproduced by manually matching the projections of the 3D knee model to the images of the knee captured by the fluoroscopes 32. The relative positions of the ACL insertion sites could be determined by using the series of matched knee models under different loading conditions and at different flexion angles. The length of the ACL was measured as the distance between the centroids of the ACL insertion site on the tibia and femur. At each flexion angle, the length of the ACL under zero weightbearing was used as a reference for measuring the ACL elongation under full body weight. In order to determine the ACL elongation at exact 15 deg, 30 deg, and 45 deg of knee flexion, the true flexion angles were obtained from the final matched positions, and the corresponding measured in vivo elongations were interpolated for the target flexion angles. In general, the difference of true measured flexion angles and the target angles were less than 5 deg. The reliability of the manual matching process was reported less than 0.15 mm In Vitro Force-Elongation Relations of the ACL. Forceelongation curves of the ACL were determined using six human cadaveric knee specimens fresh frozen, Table 2 in a uniaxial tensile test performed on a robotic testing system Fig. 3 a at the same target flexion angles as used for the living subjects. The testing system is composed of a 6DOF manipulator Kawasaki UZ150, Kawasaki Heavy Industry, Japan; load capacity of 1500 N and repeatability of 0.3 mm at maximum load when the manipulator s arm is fully extended, a 6DOF force-moment sensor JR3, San Francisco, CA, and custom-made fixture and pedestal, which can operate in both displacement and force control modes 10. The knees were thawed 24 h before testing. The femur and tibia were cut approximately 20 cm from the joint line, and bone ends were stripped of musculature, potted in bone cement, and secured in thick-walled aluminum cylinders using metal screws Fig. 3 a. The passive flexion path of each intact knee was defined as a set of flexion angles at which the forces and moments at the knee joint were minimal 5 N and 0.5 N m and determined by the robot in the force control mode 10. This was done in 1 deg increments from full extension to 45 deg of knee flexion. Then, all the soft tissues of the knee were dissected away, except for the ACL. The tibial and femoral insertion sites of the ACL were digitized using a 3D digitizer MicroScribe G2LX, Amherst, VA. The long axis of the ACL was defined as the line connecting the centroids of the digitized insertion sites. The robotic testing system was programed to stretch the ACL along this longitudinal axis. All the forces were transformed from the load cell coordinate system attached to the end effector of the robot s arm to the knee joint coordinate system using the corresponding Euler angles. At each target flexion angle 15 deg, 30 deg, and 45 deg, the knee was prestretched five times along the long axis of the ACL at a rate of 12 mm/s until a 400 N load was reached preconditioning of the soft tissue. Then, the ACL was stretched along the same path at the same rate up to 400 N, and the in vitro force-elongation data were recorded Fig. 3 b. After prestretching as well as stretching at each flexion angle, the specimen was allowed to recover for 10 min in the relaxed slack condition before testing at the next flexion angle the force-elongation curves were repeatable after 10 min of relaxation time. The specimen was constantly sprayed with saline solution to prevent dehydration. The ACL was completely relaxed at the start point on the neutral path of the knee joint. By stretching the ligament along its long axis, the ACL force was increased with a delay compared with the displacement, which confirmed that the ACL was slack. In order to capture the natural force-elongation characteristics of the ACL, no other measurement instruments were attached to the fibers of the ACL during our in vitro experiments. In addition, it was not practically possible to check all the ACL fibers to make sure whether all of them are taut during the in vitro elongation test. The force-elongation curves of the ACL were determined for each specimen in the same way and the averaged force-elongation curves of the six specimens were calculated at each flexion angle. 2.3 Estimation of the In Vivo ACL Force Changes. The change in the in vivo force of the ACL in response to full body weightbearing was determined by using a weighted mean statistical method 37. At each target flexion angle, the in vivo ACL elongation data of each subject under full body weight were Fig. 3 a Robotic testing system with installed knee specimen before removing soft tissues. b Stretching the ACL along its long axis using the robot arm. Journal of Biomechanical Engineering MAY 2011, Vol. 133 /

4 Fig. 4 Schematic diagram showing the methodology used for determination of in vivo ACL tension. a Weightbearing elongation of the ACL from in vivo weightbearing. b Force elongation of the ACL from in vitro robotic test. c Estimation of in vivo ACL tension for each individual as a function of weightbearing. d Average in vivo ACL force-weightbearing data of all living knees using weighted mean statistical method. These figures are only conceptual and do not present experimental results. BW: body weight. matched to the in vitro elongation data on the average forceelongation curves shown schematically in Figs. 4 a and 4 b. By mapping the in vivo elongation data of each subject to the elongation data on the in vitro force-elongation curve from the in vitro tensile test at each flexion angle, the in vivo ACL force of each subject under the full body weight was determined by a mean value F i and a standard deviation i plotted schematically in Fig. 4 c. Thus, in vivo ACL force of all living knees can be represented by their mean values and standard deviations F i i, i=1,2,...,9 at each target flexion angle. It should be noted that since the in vivo ACL elongation was measured using its length at zero loading as a reference, the ACL force determined using this elongation actually represented the ACL force change or increase when the weightbearing increased from zero to full body weight. To estimate the average in vivo ACL force increase of all living knees, a weighted mean statistical method was used 37. This method weighs each living knee force in proportion to its error or standard deviation. If the ACL force of the ith subject is expressed as F i i, the weighted mean of in vivo ACL force and its corresponding standard error, denoted as F, can be calculated using the following equations 37 : 2 1 = N 2 1/ i i=1 F = N 2 F i / i i=1 N 2 1/ i i=1 and N: total number of the living subjects This method has been widely used in both engineering and physics when processing experimental data. The above procedure determined the mean in vivo ACL force increase caused by full body weight at all target flexion angles schematic in Fig. 4 d. 2.4 Effect of Assumed Tension in the ACL Under Zero Weightbearing on In Vivo ACL Force Estimation. The above procedure for the estimation of in vivo ACL forces assumed that the ACL forces were zero when the weightbearing load was zero. The determined ACL forces represent the ACL force change when the weightbearing increased from zero to full body weight. If the ACL was initially tensioned under the zero weightbearing condition, matching of the in vivo ACL elongation should be initiated from the corresponding force level on the in vitro forceelongation curves. Due to the nonlinearity of the ACL forceelongation curve at low force levels, a change in the initial point of matching affects the evaluation of the increase in the ACL force. Therefore, we evaluated the effect of different values of assumed tension in the ACL under zero weightbearing every 10 Nupto50N on the evaluation of in vivo ACL force changes caused when a full body weight was applied to the tibia. By elevating the assumed ACL tension under zero weightbearing and entering the linear part of the force-elongation curve, the initial ACL tension will not have any effect on the estimated ACL force increase. The in vivo ACL forces at each assumed ACL tension under zero weightbearing was estimated as the summation of that assumed ACL tension under zero weightbearing and the increase in the ACL force due to full body weight. If the ACL was slack at the zero weightbearing, the actual ACL force would be lower than the values obtained in this study by assuming no ACL tension under zero weightbearing. 2.5 Sensitivity Study. The accurate identification of the centroid of the ACL insertions on the femur and tibia is critical as a shift in the location of the centroid could have an impact on the estimated ACL forces. A previous study showed that the effect of the position of the centroid of the ACL insertions on the elongation of the ACL was maximally 0.34 mm 30. Depending on different flexion angles and the assumed tension in the ACL, this can cause variations in the estimated changes in the ACL force. A sensitivity study was performed to determine the effect of the position of the ACL insertion centroid on the estimated ACL force in different flexion angles. The variations in the estimated changes / Vol. 133, MAY 2011 Transactions of the ASME

5 Table 3 Elongation of the ACL when the subjects applied full body weight on the force plate results from previous study 30 Flexion angle Subject No. 15 deg 30 deg 45 deg Mean SD in the ACL force, caused by a maximum ACL elongation error of 0.34 mm during the mapping process, were determined. 2.6 Statistical Analysis. In this study, the in vivo ACL force increase was estimated as a function of assumed ACL tension under zero weightbearing and knee flexion angle. A two-way repeated measures analysis of variance ANOVA and a post hoc Student Newman Keuls test were used to determine the statistically significant differences in the force increase among different flexion angles as a function of assumed ACL tension under zero weightbearing Statistica StatSoft, Inc., Tulsa, OK. The independent variables were the flexion angle and the assumed ACL tension under zero weightbearing. The dependent variable was increase in the ACL force due to full body weightbearing. The level of significance was set at Results 3.1 In Vivo ACL Elongation Due to Full Body Weight. The values of the in vivo ACL elongation of the individual living subjects at tested flexion angles are presented in Table 3. Also, the mean values of the in vivo elongation are shown in Fig. 5 a. The data demonstrated that the ACL elongated when subjects applied full body weight to the force plate. The elongations of the ACL were mm, mm, and mm at 15 deg, 30 deg, and 45 deg of flexion, respectively. 3.2 In Vitro Force-Elongation Behavior of the ACL. The averaged in vitro force-elongation behavior of the ACL at different flexion angles is presented in Fig. 5 b. The in vitro data Fig. 6 The increase in the in vivo ACL force when the subject placed full body weight on the force plate plotted with increasing assumed initial tension in the ACL showed that the structural properties of the ACL under loading were dependent on the flexion angle. The amount of the forces experienced by the ACL due to a fixed amount of elongation was greater at 15 deg and 30 deg of flexion compared with 45 deg of flexion. The stiffness values of the ACL in the region up to 400 N of the force-elongation curves were N/mm at 15 deg of flexion, N/mm at 30 deg, and finally N/mm at 45 deg of flexion. The change in the stiffness from 15 deg to 30 deg of flexion was not statistically significant P 0.1 ; however, the stiffness at 45 deg of flexion was significantly less than that at 15 deg and 30 deg of flexion P In Vivo ACL Force Increase Due to Full Body Weight. In vivo ACL force increases due to full body weight were calculated by assuming various assumed ACL tensions under zero weightbearing Fig. 6. The patterns of the forces showed that the estimated in vivo ACL force increase approached an asymptote at each flexion angle when the assumed ACL tension under zero weightbearing increased over 20 N. When the assumed ACL tension under zero weightbearing was beyond 20 N, the variations in force increase in the ACL due to the applied load were not significant in all tested knee flexion angles P Therefore, the asymptotic value might represent an upper bound of the increase in ACL force as the weightbearing increased from zero to full body weight. The percentage of change in the ACL force increase under full body weight due to a 10 N increase in an assumed ACL tension under zero weightbearing is shown in Table 4. At an as- Fig. 5 a In vivo weightbearing-elongation behavior of the ACL at 15 deg, 30 deg, and 45 deg of flexion results from previous study 30. b In vitro force-elongation curves of the ACL at 15 deg, 30 deg, and 45 deg of flexion standard deviation bars for 30 deg are not shown for the purpose of figure clarity. Journal of Biomechanical Engineering MAY 2011, Vol. 133 /

6 Table 4 Percentage of change in the ACL force increase under full body weight due to 10 N increase in the ACL tension under zero body weight ACL tension under zero weightbearing N sumed ACL tension of 40 N under zero weightbearing, the increase in the ACL force changed by less than 5% when an assumed ACL tension of 50 N was used under zero weightbearing. This percentage of change in the ACL force increase would approach zero by entering the linear region of the ACL forceelongation curves Fig. 5 b. We have chosen this 5% criterion to define an approximation of the upper bound of the changes in the ACL forces. Assuming that the ACL tension was 0 N under zero weightbearing, the increases in in vivo ACL forces caused by full body weight were N at 15 deg, N at 30 deg, and N at 45 deg of flexion Fig. 6. The increases in the in vivo ACL forces due to full body weight were N, N, and N, respectively, at 15 deg, 30 deg, and 45 deg of flexion with an assumed ACL tension of 40 N under zero weightbearing Fig. 6. In general, the ACL force increases at 15 deg and 30 deg of knee flexion were significantly greater than those at 45 deg of flexion P However, the ACL force increases at 15 deg and 30 deg of flexion were not significantly different P Estimation of In Vivo ACL Force. At each assumed ACL tension under zero weightbearing, the in vivo ACL forces were estimated as the summation of the assumed ACL tension and the increase in the ACL force caused by full body weight, which was estimated at the assumed ACL tension. With an ACL tension of 0 N at zero weightbearing, the in vivo ACL force would be the same as the increase in the ACL force. When the ACL tension under zero weightbearing was 40 N, the estimated ACL forces under full weightbearing were N at 15 deg, N at 30 deg, and N at 45 deg of flexion. At 15 deg and 30 deg, the ACL forces were not significantly different. These forces were significantly less in 45 deg than those in 15 deg and 30 deg of flexion. 3.5 Sensitivity Study. Depending on different flexion angles and the assumed ACL tension under zero weightbearing, a maximum ACL elongation error of 0.34 mm 30 caused variations in the estimated changes in the ACL force. At 15 deg of flexion, the variation in the position of the centroid of the ACL insertions caused a maximum force variation of 37.7 N at 0NofACL tension under zero weightbearing 42.4 N at 40 N of ACL tension under zero weightbearing. At 45 deg of flexion, this force variation was maximally 22.3 N at 0NofACLtension under zero weightbearing 34.4 N at 40 N of ACL tension under zero weightbearing. 4 Discussion Flexion angle 15 deg 30 deg 45 deg This study estimated the changes in the in vivo forces of the ACL at three discrete flexion angles with zero and full body weights applied by the subject on a force plate. A combined MR and dual fluoroscopic imaging system was used to obtain the in vivo ACL elongation data, 30 and a robotic testing system 38 was employed to measure the in vitro force-elongation data of the ACL at the different flexion angles. Finally, a weighted mean statistical method was used to estimate the in vivo ACL force increases. The results showed that when subjects applied full body weight to the force plate, the ACL was subjected to a mild force increase below 250 N when compared with the ACL failure tension of about 1500 N that has been measured in middle-aged cadaver knees 5. The ACL force increase was significantly higher at 15 deg and 30 deg than at 45 deg of flexion. Numerous studies have reported on in situ forces in the ACL using in vitro experimental setups, and ACL forces have been reported to be higher at low flexion angles 10,17,39. For example, the in vitro force in the ACL was found to peak between 15 deg and 30 deg of flexion in response to various simulated muscle loads 10. The values of ACL force under a 400 N quadriceps loading were reported to be N and N at full extension and 30 deg of knee flexion, respectively 10. Also, the ACL experienced a maximum force of 131 N at 30 deg flexion under an anterior tibial load of 130 N 40. However, it has always been challenging to determine the ACL forces in vivo. Fleming et al. 17,39 studied the ACL strain on the anterior part of the ACL surface of living subjects using a differential variable reluctance transducer. They similarly reported that the ACL strain decreased with flexion beyond 15 deg. Under isometric quadriceps contraction 30 N m of extension torque, the peak strain was reported to be % at 15 deg of flexion 39. Previous in vivo studies showed that the ACL has a larger elongation at low flexion angles 25,26 Fig. 5 a. A direct comparison between these studies is difficult though since the loading conditions among these studies were not the same. However, all these reports were consistent in that the ACL was found to carry higher forces at lower flexion angles. In general, the increases in in vivo ACL forces in response to controlled weightbearing were greater in all tested flexion angles compared to those in the ACL forces reported in previous in vitro studies. e.g., 131 N under the anterior tibial load 40, N under the quadriceps load 10 in in vitro studies, and N under in vivo increased weightbearing with 40 N of assumed ACL tension under zero weightbearing, all at 30 deg of knee flexion. This observation supports the hypothesis that the ACL forces during in vivo activities are more substantial than those measured in in vitro studies. Furthermore, our conclusions are in agreement with previous computational studies that have predicted higher ACL forces during functional activities 21,41. Shelburne et al. 21 reported a peak ACL force of 303 N at the beginning of the gait cycle at contralateral toe off. In this study, the in vitro force elongation of the ACL was determined using a tensile test at different knee flexion angles. The ACL tensile behavior at different flexion angles has been extensively studied by Woo et al. 5. In their study, anteriorposterior displacement tests with the intact knee at 30 deg and 90 deg of flexion revealed a significant effect of the knee flexion angle 5. Our data described a similar dependence of the ACL tensile behavior on the flexion angle. This might be due to the varying contribution of the AM and posterolateral PL bundles of the ACL at different flexion angles. The role of each bundle under various external loadings and at different flexion angles has been investigated in great detail 13,15,42. In the present study, the potential varying role of individual bundles was indirectly considered by extracting the in vitro force elongation of the ACL at different flexion angles. When determining in vivo ACL forces, it is always difficult to determine an initial reference length of the ACL In the present study, we used the ACL length measured at the zero weightbearing condition at each flexion angle as a reference. Consequently, the estimated forces in our study before adding the assumed ACL tension under zero weightbearing represented the ACL force increases when weightbearing increased from zero to full body weight. Since the in vivo ACL tension under zero weightbearing could not be determined, we evaluated the effect of different values of ACL tensions under zero weightbearing on the estimated in / Vol. 133, MAY 2011 Transactions of the ASME

7 creases in ACL force when the weightbearing increased from zero to full body weight. The data indicated that when the assumed ACL tension under zero weightbearing was over 20 N, the change in the estimated ACL force approached an asymptotic value. This may be due to the decrease in the nonlinearity of the forceelongation curve as the force level increased Fig. 5 b. Therefore, the asymptotic value might represent an upper bound of the increase in ACL force as the weightbearing increased from zero to full body weight. This upper bound corresponds to the constant slope of the force-elongation curve in its linear region. At an assumed ACL tension of 40 N under zero weightbearing, the increase in the ACL force changed by less than 5% when an assumed ACL tension of 50 N was used under zero weightbearing Table 4. This percentage would approach zero by completely entering the linear region of the ACL force-elongation curves. In this study, an assumed 40 N of ACL tension under zero weightbearing corresponding to a criterion of 5% change in the ACL force increase was used to estimate the ACL force changes. Using a uniaxial tensile test to obtain the in vitro forceelongation data and stretching the ACL along its longitudinal axis can recruit a higher number of fibers under tension, whereas in the in vivo study, the ACL elongation data were obtained from the 6DOF knee motion, which may or may not use all the fibers of the ACL 30. Mapping such in vivo ACL elongation to the uniaxial force-elongation curve may have overestimated the in vivo ACL force changes. Furthermore, if the ACL was slack when subjects were applying zero weightbearing to the force plate, the actual ACL force would be lower than the values obtained in this study by assuming no ACL tension under zero weightbearing. The current technique for estimating the in vivo ACL forces has several limitations. First, due to the difficulty in obtaining knee specimens from healthy younger donors, the in vitro forceelongation data were determined using six relatively older cadaveric knee specimens, inhibiting age matching. Furthermore, ACL elongation data were only obtained at 15 deg, 30 deg, and 45 deg of flexion as the ACL was found to carry higher forces at lower flexion angles. A complete understanding of ACL forces under in vivo loading conditions requires an examination of a full spectrum of functional activities, such as gait and stair climbing. The in vivo ACL force increase was indirectly estimated using in vitro ACL force-elongation data and in vivo ACL elongation data. A direct measurement of the in vivo ACL force is not possible at present. Since the tension of the ACL was not known when the subject placed zero weight on the force plate, the estimated force only represented the ACL force change when the subjects increased the weight on the force plate from zero to full body weight. The estimation of the overall in vivo ACL force depends on the value of ACL tension under zero weightbearing, which could not be determined at present. Therefore, we estimated the ACL force by using different ACL tensions under zero weightbearing. Finally, the loading rates in in vitro and in vivo studies were not the same even though effort has been made to control the in vitro loading in a similar time range as the in vivo loading. Despite these technical challenges, the data revealed that the ACL force only changed by less than 250 N when the subjects applied a weight on the force plate from zero to full body weight, which accounts for less than 20% of the ultimate strength of the ACL 5. The present in vivo ACL force values were estimated during only weightbearing and were evaluated at 15 deg, 30 deg, and 45 deg of flexion. Therefore, caution is advised when extrapolating the data to functional activities. Nevertheless, we believe that the clinical implication of this study is considerable. This study presents a noninvasive estimation of in vivo forces transmitted by the ACL data critical for the optimal restoration of the ligament s mechanical function. In future studies, the same methodology could be applied to compare the in vivo ACL/graft forces before and after various reconstruction techniques. In conclusion, the previously described combined MR and dual fluoroscopic imaging system and a robotic testing system were utilized to investigate noninvasively the in vivo ACL force increases in response to a change in weightbearing from zero to full body weight. The data demonstrated that the increase in the ACL force was dependent on the flexion angle, with a larger increase in ACL force at low flexions. The estimated in vivo ACL force increase was assumed to be an overestimated value, which indicated that under full body weight, the ACL might experience less than 250 N of tensile force. This study presents an insight into the biomechanical behavior of the ACL under a functional in vivo loading condition. Acknowledgment The authors would like to gratefully acknowledge the financial support of the National Institutes of Health Grant Nos. R21 AR and R01 AR and the Department of Orthopaedic Surgery at the Massachusetts General Hospital. The technical assistance of Michal Kozanek is greatly appreciated. Appendix: Validation of the In Vivo ACL Force Estimation Method In this validation study, a robotic testing system was used to apply an external load on a cadaveric knee specimen and to measure the corresponding ACL force as the gold standard. These force values were compared with those estimated by the method introduced in this study. The magnitude and direction of the forces measured by the robotic testing system have been validated before 43,44. One fresh-frozen cadaveric knee specimen left knee, 48 year old man was used. MR images of the knee were acquired, while all soft tissues of the knee were intact. The 3D surface model of the knee, including tibia, femur, and insertion sites of the ACL on each bone, was created using the protocol described in Sec. 2. Then, the knee specimen was installed in the robotic testing system, and its passive flexion path was determined in 1 deg increments in the same way descried in Sec. 2. Next, the dual fluoroscopic testing system was set up orthogonally in such a way that the installed knee specimen was in the field of view of both intensifiers Fig. 7 a. Following the setting up of both robotic and fluoroscopic systems, the intact knee was tested under a 130 N anterior tibial load at 15 deg, 30 deg, and 45 deg of knee flexions on the passive path by using a published protocol 10 a force applied anteriorly toward the front of the body to the proximal tibia. First, at each target flexion angle, the knee was imaged by the fluoroscopes on the passive path. Then, the anterior tibial load was applied to the knee specimen by the robot arm, and the forces transmitted through the joint as well as the corresponding kinematics response of the knee to the applied load were recorded. Simultaneously, a pair of fluoroscopic images of the knee joint was captured. After recording data at all aimed flexion angles, the ACL was resected via a small arthrotomy with the knee in 30 deg of flexion. Then, the arthrotomy and skin were closed in layers. At each flexion angle, the recorded kinematics of the intact knee under anterior tibial load was replayed by the robot and the force transmitted through the joint was measured. Using the principle of superposition, the difference between the forces measured in the ACL deficient knee and the intact ACL knee represents the in vitro ACL force under the anterior tibial load 13. At the next step, the 3D knee models were matched to the corresponding pair of fluoroscopic images in a virtual dual fluoroscopic imaging system using the protocol explained in Sec. 2. Then, the elongation of the ACL at each flexion angle was measured. The length of the ACL with the knee under no load passive path was chosen as the reference length. ACL tensions under zero load bearing were considered from 0Nto50Nin10Nincre- ments. At each target flexion angle, by mapping the elongation of the ACL under anterior tibial load to the in vitro force-elongation data obtained from six specimens, the ACL force increases for different assumed ACL tensions at zero load bearing were esti- Journal of Biomechanical Engineering MAY 2011, Vol. 133 /

8 Fig. 7 a A knee specimen installed on the robotic testing system with the fluoroscopes to image the knee joint during applying load validation study. b The in vitro ACL forces due to 130 N anterior tibial load measured by robot hatched bars and the corresponding estimation of the ACL forces with different ACL tensions under zero weightbearing at 15 deg, 30 deg, and 45 deg of knee flexion solid bars. mated. Finally, the absolute values of the ACL force were calculated by adding the ACL tension under zero load bearing to the estimated force increase in the ACL. The estimated absolute values of the ACL force at different ACL tensions at zero load bearing were compared with the in vitro ACL force measured by the robotic testing system Fig. 7 b. The in vitro ACL forces, measured by the robot, were N, N, and N at 15 deg, 30 deg, and 45 deg of flexion, respectively. Using the method introduced in this study for the estimation of in vivo ACL forces, the estimated ACL forces force increase and ACL tension under zero load bearing with 40 N of ACL tension at zero load bearing were N, N, and N at 15 deg, 30 deg, and 45 deg of flexion, respectively. At all three different flexion angles, the actual ACL forces were less than the estimated ACL force with an ACL tension of 40 N under zero load bearing by 23.7% at 15 deg, 3.3% at 30 deg, and 5.5% at 45 deg. In other words, the estimated ACL forces by using 40 N of ACL tension under zero loading were a reasonable overestimation of the real ACL force at all flexions. Variable ACL tension at zero load bearing condition might be the reason for a greater difference percentage at 15 deg of flexion. Because of the lack of knowledge about the ACL tension at zero loading, we cannot predict the exact ACL force. References 1 Butler, D. L., Guan, Y., Kay, M. D., Cummings, J. F., Feder, S. M., and Levy, M. S., 1992, Location-Dependent Variations in the Material Properties of the Anterior Cruciate Ligament, J. Biomech., 25 5, pp Chandrashekar, N., Mansouri, H., Slauterbeck, J., and Hashemi, J., 2006, Sex-Based Differences in the Tensile Properties of the Human Anterior Cruciate Ligament, J. Biomech., 39 16, pp Henning, C. E., Lynch, M. A., and Glick, K. R., Jr., 1985, An In-Vivo Strain Gage Study of Elongation of the Anterior Cruciate Ligament, Am. J. Sports Med., 13 1, pp Fleming, B. C., Beynnon, B. D., Tohyama, H., Johnson, R. J., Nichols, C. E., Renstöm, P., and Pope, M. H., 1994, Determination of a Zero Strain Reference for the Anteromedial Band of the Anterior Cruciate Ligament, J. Orthop. Res., 12, pp Woo, S. L., Hollis, J. M., Adams, D. J., Lyon, R. M., and Takai, S., 1991, Tensile Properties of the Human Femur-Anterior Cruciate Ligament-Tibia Complex. The Effects of Specimen Age and Orientation, Am. J. Sports Med., 19 3, pp Ahmed, A. M., Burke, D. L., Duncan, N. A., and Chan, K. H., 1992, Ligament Tension Pattern in the Flexed Knee in Combined Passive Anterior Translation and Axial Rotation, J. Orthop. Res., 10, pp Jasty, M., Lew, W. D., and Lewis, J. L., 1982, In-Vitro Ligament Forces in the Normal Knee Using Buckle Transducers, Trans. Annu. Meet. - Orthop. Res. Soc., 7, pp Lewis, J. L., Lew, W. D., and Schmidt, J., 1982, A Note on the Application and Evaluation of the Buckle Transducer for Knee Ligament Force Measurement, ASME J. Biomech. Eng., 104, pp Claes, L. E., Dürselen, L., and Kiefer, H., 1986, Influence of Load, Flexion and Muscle-Forces on the Stress and Strain of Knee Ligaments, Trans. Annu. Meet. - Orthop. Res. Soc., 11, pp Li, G., Zayontz, S., Most, E., Defrate, L. E., Suggs, J. F., and Rubash, H. E., 2004, In Situ Forces of the Anterior and Posterior Cruciate Ligaments in High Knee Flexion: An In Vitro Investigation, J. Orthop. Res., 22 2, pp Rudy, T. W., Livesay, G. A., Woo, S. L., and Fu, F. H., 1996, A Combined Robotic/Universal Force Sensor Approach to Determine In Situ Forces of Knee Ligaments, J. Biomech., 29 10, pp Woo, S. L., Wu, C., Dede, O., Vercillo, F., and Noorani, S., 2006, Biomechanics and Anterior Cruciate Ligament Reconstruction, J Orthop. Surg. and Res., 1, pp Li, G., Rudy, T. W., Sakane, M., Kanamori, A., Ma, C. B., and Woo, S. L., 1999, The Importance of Quadriceps and Hamstring Muscle Loading on Knee Kinematics and In-Situ Forces in the ACL, J. Biomech., 32 4, pp Fleming, B. C., Beynnon, B. D., Nichols, C. E., Johnson, R. J., and Pope, M. H., 1993, An In Vivo Comparison of Anterior Tibial Translation and Strain in the Anteromedial Band of the Anterior Cruciate Ligament, J. Biomech., 26, pp Sakane, M., Fox, R. J., Woo, S. L., Livesay, G. A., Li, G., and Fu, F. H., 1997, In Situ Forces in the Anterior Cruciate Ligament and Its Bundles in Response to Anterior Tibial Loads, J. Orthop. Res., 15 2, pp Wu, J. L., Seon, J. K., Gadikota, H. R., Hosseini, A., Sutton, K. M., Gill, T. J., and Li, G., 2010, In Situ Forces in the Anteromedial and Posterolateral Bundles of the Anterior Cruciate Ligament under Simulated Functional Loading Conditions, Am. J. Sports Med., 30, pp Fleming, B. C., Renstrom, P. A., Beynnon, B. D., Engstrom, B., Peura, G. D., Badger, G. J., and Johnson, R. J., 2001, The Effect of Weightbearing and External Loading on Anterior Cruciate Ligament Strain, J. Biomech., 34 2, pp Fukubayashi, T., Torzilli, P. A., Sherman, M. F., and Warren, R. F., 1982, An In-Vitro Biomechanical Evaluation of Anterior-Posterior Motion of the Knee, J. Bone Jt. Surg., Am. Vol., 64A 2, pp Kanamori, A., Zeminski, J., Rudy, T. W., Li, G., Fu, F. H., and Woo, S. L., 2002, The Effect of Axial Tibial Torque on the Function of the Anterior Cruciate Ligament: A Biomechanical Study of a Simulated Pivot Shift Test, Arthroscopy, 18 4, pp Nagura, T., Dyrby, C., Alexander, E., and Andriacchi, T., 2002, Mechanical Loads at the Knee Joint During Deep Flexion, J. Orthop. Res., 20, pp Shelburne, K. B., Torry, M. R., and Pandy, M. G., 2005, Muscle, Ligament, and Joint-Contact Forces at the Knee During Walking, Med. Sci. Sports Exercise, 37 11, pp Shelburne, K. B., Pandy, M. G., Anderson, F. C., and Torry, M. R., 2004, Pattern of Anterior Cruciate Ligament Force in Normal Walking, J. Biomech., 37 6, pp Beynnon, B. D., Fleming, B. C., Johnson, R. J., Nichols, C. E., Renström, P. A., and Pope, M. H., 1995, Anterior Cruciate Ligament Strain Behavior During Rehabilitation Exercises In Vivo, Am. J. Sports Med., 23 1, pp Beynnon, B. D., Johnson, R. J., Fleming, B. C., Renström, P. A., Nichols, C. E., Pope, M. H., and Haugh, L. D., 1994, The Measurement of Elongation of Anterior Cruciate-Ligament Grafts In-Vivo, J. Bone Jt. Surg., Am. Vol., 76 4, pp Li, G., Defrate, L. E., Rubash, H. E., and Gill, T. J., 2005, In Vivo Kinematics of the ACL During Weight-Bearing Knee Flexion, J. Orthop. Res., 23 2, pp Jordan, S. S., Defrate, L. E., Nha, K. W., Papannagari, R., Gill, T. J., and Li, / Vol. 133, MAY 2011 Transactions of the ASME

9 G., 2007, The In Vivo Kinematics of the Anteromedial and Posterolateral Bundles of the Anterior Cruciate Ligament During Weightbearing Knee Flexion, Am. J. Sports Med., 35 4, pp Li, G., Suggs, J., and Gill, T., 2002, The Effect of Anterior Cruciate Ligament Injury on Knee Joint Function Under a Simulated Muscle Load: A Three- Dimensional Computational Simulation, Ann. Biomed. Eng., 30 5, pp Song, Y., Debski, R. E., Musahl, V., Thomas, M., and Woo, S. L., 2004, A Three-Dimensional Finite Element Model of the Human Anterior Cruciate Ligament: A Computational Analysis With Experimental Validation, J. Biomech., 37 3, pp Roberts, C. S., Cumming, J. F., Grood, E. S., and Noyes, F. R., 1994, In Vivo Measurement of Human Anterior Cruciate Ligament Forces During Knee Extension Exercises, Trans. Annu. Meet. - Orthop. Res. Soc., 19, pp Hosseini, A., Gill, T. J., and Li, G., 2009, In Vivo Anterior Cruciate Ligament Elongation in Response to Axial Tibial Loads, J. Orthop. Sci., 14 3, pp Wu, J. L., Hosseini, A., Kozanek, M., Gadikota, H. R., Gill, T. J. T., and Li, G., 2010, Kinematics of the Anterior Cruciate Ligament During Gait, Am. J. Sports Med., 38 7, pp Li, G., Wuerz, T. H., and DeFrate, L. E., 2004, Feasibility of Using Orthogonal Fluoroscopic Images to Measure In Vivo Joint Kinematics, ASME J. Biomech. Eng., 126 2, pp Gronenschild, E., 1997, The Accuracy and Reproducibility of a Global Method to Correct for Geometric Image Distortion in the X-Ray Imaging Chain, Med. Phys., 24 12, pp Gronenschild, E., 1999, Correction for Geometric Image Distortion in the X-Ray Imaging Chain: Local Technique Versus Global Technique, Med. Phys., 26 12, pp Bingham, J., and Li, G., 2006, An Optimized Image Matching Method for Determining In-Vivo TKA Kinematics With a Dual-Orthogonal Fluoroscopic Imaging System, ASME J. Biomech. Eng., 128 4, pp Li, G., Van De Velde, S. K., and Bingham, J. T., 2008, Validation of a Non-Invasive Fluoroscopic Imaging Technique for the Measurement of Dynamic Knee Joint Motion, J. Biomech., 41 7, pp Leo, W. R., 1992, Techniques for Nuclear and Particle Physics Experiments, Springer-Verlag, London. 38 Most, E., Li, G., Schule, S., Sultan, P., Park, S. E., Zayontz, S., and Rubash, H. E., 2003, The Kinematics of Fixed- and Mobile-Bearing Total Knee Arthroplasty, Clin. Orthop. Relat. Res., 416, pp Fleming, B. C., Beynnon, B. D., Renstrom, P. A., Johnson, R. J., Nichols, C. E., Peura, G. D., and Uh, B. S., 1999, The Strain Behavior of the Anterior Cruciate Ligament During Stair Climbing: An In Vivo Study, Arthroscopy, 15 2, pp Li, G., Papannagari, R., Defrate, L. E., Yoo, J. D., Park, S. E., and Gill, T. J., 2006, Comparison of the ACL and ACL Graft Forces Before and After ACL Reconstruction: An In-Vitro Robotic Investigation, Acta Orthop., 77 2, pp Harrington, I. J., 1976, A Bioengineering Analysis of Force Actions at the Knee in Normal and Pathological Gait, Biomed. Eng., 11 5, pp Gabriel, M. T., Wong, E. K., Woo, S. L., Yagi, M., and Debski, R. E., 2004, Distribution of In Situ Forces in the Anterior Cruciate Ligament in Response to Rotatory Loads, J. Orthop. Res., 22 1, pp Fujie, H., Livesay, G. A., Woo, S. L., Kashiwaguchi, S., and Blomstrom, G., 1995, The Use of a Universal Force-Moment Sensor to Determine In-Situ Forces in Ligaments: A New Methodology, ASME J. Biomech. Eng., 117 1, pp Most, E., 2000, Development of a 6-DOF Robotic Test System for Studying the Biomechanics of Total Knee Replacement, MS thesis, Massachusetts Institute of Technology, Cambridge, MA. Journal of Biomechanical Engineering MAY 2011, Vol. 133 /