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Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation
Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation Alexander R. Mait n, Adwait Mane, Jason L. Forman, John Paul Donlon, Bingbing Nie, Richard W. Kent Department of Mechanical and Aerospace Engineering University of Virginia, Center for Applied Biomechanics, 4040 Lewis and Clark Drive, Charlottesville, VA 22911, USA
art ic l e i nf o
a b s t r a c t
Article history: Accepted 3 January 2017
The purpose of this study was to determine the long-time and transient characteristics of the moment generated by external (ER) and internal (IR) rotation of the calcaneus with respect to the tibia. Two human cadaver legs were disarticulated at the knee joint while maintaining the connective tissue between the tibia and fibula. An axial rotation of 21° was applied to the proximal tibia to generate either ER or IR while the fibula was unconstrained and the calcaneus was permitted to translate in the transverse plane. These boundary conditions were intended to allow natural motion of the fibula and for the effective applied axis of rotation to move relative to the ankle and subtalar joints based on natural articular motions among the tibia, fibula, talus, and calcaneus. A load cell at the proximal tibia measured all components of force and moment. A quasi-linear model of the moment along the tibia axis was developed to determine the transient and long-time loads generated by this ER/IR. Initially neutral, everted, inverted, dorsiflexed, and plantarflexed foot orientations were tested. For the neutral position, the transient elastic moment was 16.5 N-m for one specimen and 30.3 N-m for the other in ER with 26.3 and 32.1 N-m in IR. The long-time moments were 5.5 and 13.2 N-m (ER) and 9.0 and 9.5 N-m (IR). These loads were found to be transient over time similar to previous studies on other biological structures where the moment relaxed as time progressed after the initial ramp in rotation. & 2017 Elsevier Ltd. All rights reserved.
Keywords: Ankle Kinetics Transient QLV Foot rotation
1. Introduction Excessive rotation of the foot injures the foot–ankle complex in the human leg, specifically the distal tibiofibular syndesmosis joint (Bloemers and Bakker, 2006; Funk, 2011; Wei et al., 2012). Previous experiments investigated the effects of foot rotation on leg kinetics and the syndesmosis joint (Markolf et al., 1989; Michelson et al., 1997; Wei et al., 2012; Xenos et al., 1995), but with limitations. Though Xenos et al. (1995) allowed the fibula to move freely, the leg was rigidly constrained in four locations. This created an unclear axis of rotation in the ankle by preventing the foot from translating naturally during foot rotation. Wei et al. (2012), Markolf et al. (1989), and Michelson et al. (1997) disarticulated the tibia and fibula mid-shaft, thus disrupting the proximal interosseous membrane (IOM) and tibiofibular joint. These studies rigidly fixed the tibia and fibula together, preventing the fibula from
n
Corresponding author. Fax: þ 1 434 297 8083. E-mail address: [email protected] (A.R. Mait).
moving freely during rotation, therefore altering ankle mechanics (Skraba and Greenwald, 1984). The transient behaviors of biological structures have been studied previously (Funk et al., 2000; Kent et al., 2009; Lucas et al., 2008), though, to the authors’ knowledge, not for kinetic responses to applied foot rotation. The current study aimed to determine the long-time and transient characteristics of the moment generated about the tibia during foot external rotation (ER) and internal rotation (IR). Imposing functionally relevant boundary conditions on the leg was also a goal of the study, such that a more realistic anatomic configuration is created where the fibula is unconstrained and foot translation is permitted. Transient and long-time relationships between cadaveric leg kinetics and foot rotation was hypothesized. With imposing boundary conditions designed to recreate a more realistic loading within the leg, reliable kinetic data responses to applied rotation will be used to inform future experiments aimed at describing ankle injury characteristics. Understanding the loads throughout the leg during more realistic motion also facilitates future injury-prediction model development on a current finite element (FE) model (Nie et al., 2015).
http://dx.doi.org/10.1016/j.jbiomech.2017.01.006 0021-9290/& 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Mait, A.R., et al., Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation. Journal of Biomechanics (2017), http://dx.doi.org/10.1016/j.jbiomech.2017.01.006i
A.R. Mait et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
Fig. 1. Potted tibia of a specimen with Bondo body filler covering the anterior, posterior, and medial sides of the proximal tibia and wood screws driven into the shank of the tibia at varying heights and angles along the potting cup. Soft tissue was left undisturbed around the fibula and lateral aspect of the tibia to preserve the IOM and proximal tibiofibular ligament connections. Placement of the tibia and calcaneus markers as well as the open-faced mount around the calcaneus with threaded rods driven from lateral to medial are shown. The lateral face of the calcaneus mount had several holes for threaded rods to pass through to accommodate different sizes of specimens, whereas the medial face was made of solid polyvinyl chloride for the threaded rods to anchor.
2. Methods 2.1. Specimen preparation Experiments were conducted on fresh-frozen left lower limbs from two male cadavers (Table 1). The specimens were acquired with the approval of and prepared in accordance with the policies and procedures of the UVA Center for Applied Biomechanics Oversight Committee (Ethics Approval #: CAB2014-07). The subjects were confirmed free of infectious diseases including HIV and Hepatitis B/C. Computed tomography (CT) scans of each specimen were taken prior to testing to confirm the absence of bony trauma. Limbs were stored at –15 °C and thawed to room temperature for 48 h before test preparation. The tibia and fibula were disarticulated at the knee while retaining an intact proximal IOM and tibiofibular joint ligaments. Soft tissue was cleared from the tibial plateau. The proximal tibia was rigidly attached to a potting cup using wood screws and Bondo body filler (part #261, 3 M Company, St. Paul, MN, USA) with the fibula left free (Fig. 1). A mount assembled with acetal homopolymer resin and polyvinyl chloride, reinforced with machine screws, was fixed to the calcaneus using threaded rods passing from lateral to medial directly tapping into the polyvinyl chloride (Fig. 1). 2.2. Testing procedure A custom rig was designed to rotate the specimen to a desired effective angle of foot rotation in the global X–Y–Z coordinate system, defined where the center of the tibial plateau was fixed to the center of the potting cup, and apply a constant compressive load down the Z-axis (Fig. 2A). The potting cup around the proximal tibia was attached to a rotary index table which was used to manually impart the desired quasi-static effective foot rotation about the Z-axis. A bi-directional linear rail system attached to the calcaneus mount allowed the foot to translate in the global X and Y directions, and linear bearing tracks permitted motion in the Z-axis (vertical direction), thus allowing the Z-axis of rotation to adjust to the natural axis of rotation in the leg (Fig. 2B). The foot was mounted to this rail system using two gimbals with orthogonal rotation axes, originally parallel to the global axes in a neutral foot position when specimens were placed into the test apparatus. The gimbals allowed the foot to be locked in this neutral orientation or in varying degrees of eversion, inversion, dorsiflexion, and plantarflexion. These foot orientations were defined grossly as rotations of the calcaneus relative to the tibia. The gimbals (fixed to the calcaneus mount) rotated the calcaneus into eversion, inversion, dorsiflexion, or plantarflexion within a nominal range of 10–20°, used since within physiological range of motion of the ankle joint (Nigg et al., 1990; Roaas and Andersson, 1982), at increments of 5°. A 6-axis load cell (Model #5024J, Robert A Denton, Inc., Rochester Hills, MI, USA) and rotary potentiometer (Model #SP22GS, ETI Systems, Carlsbad, CA, USA), aligned between the centers of the potting cup and index table, measured forces and moments acting at the proximal tibia and the imposed effective foot rotation (Fig. 2B). These functionally relevant boundary conditions (fibula not fixed to tibia and foot translation permitted) address deficiencies in previous studies (Markolf et al., 1989; Michelson et al., 1997; Wei et al., 2012; Xenos et al., 1995), so that the leg is not artificially constrained and more realistic interactions among ankle bones and ligaments are attained. Specimens were initially placed in a nominally neutral position, such that the distal end of the first phalanx, the approximate centroid of the calcaneus, and the long axis of the tibia formed a right angle in the sagittal plane (Fig. 2B).
Table 1 Specimen anthropometric data: gender, age at time of death, and whole-body height and weight of the two specimens used in this study. Specimen ID#
Gender
Age (yr)
Height (cm)
Weight (kg)
616L 743L
Male Male
46 31
177 188
113 100
Note: L indicates a left leg specimen. A compressive preload of approximately 110 N, chosen to not overly constrain the leg but still initiate ligaments and joint congruency, was applied via static weight to the calcaneus mount. Maximum effective foot rotation of 7 30° was determined to be non-injurious (Wei et al., 2012), yet greater than physiological range of motion (Nigg et al., 1990). In this neutral position, all specimens were preconditioned before testing by rotating the index table for 10 cycles from þ30 to 30°. The specimens were then either kept in neutral or placed into a desired configuration of eversion, inversion, dorsiflexion, or plantarflexion, and rotated to the predetermined degree of quasi-static effective foot rotation by the index table. This position was held while the orientation and position of the specimen's tibia was scanned with a three-dimensional laser scanner (ROMER Absolute Arm, Hexagon Metrology, Inc., RA-7330SI-2), throughout which kinetics were measured by the load cell. A marker was rigidly attached to the tibia using wood screws and to the calcaneus mount. Each bone's orientation and position was defined in a local x–y–z coordinate system based on the marker position as detailed by Shaw et al. (2009) (Fig. 2B). The difference between the initial and final position of these markers was used to determine the rotation of the tibia caused by the effective foot rotation input from the index table. In this test rig, there was a fixed boundary condition at both the proximal tibia and the calcaneus (Fig. 2A). After applying the index table effective foot rotation through the fixed proximal tibia, the true foot rotation, defined as ER and IR, was measured as the axial rotation of the fixed calcaneus about the tibia's z-axis. Post-test necropsies were performed to confirm the lack of ligament damage and bone fracture. The anterior and posterior tibiofibular ligaments, IOM, anterior and posterior talofibular ligaments, calcaneofibular ligament, tibiocalcaneal ligament, and tibionavicular ligament were inspected.
2.3. Kinetic analysis Force and moment vectors acting within the leg were measured over time at the proximal tibia to determine the leg's kinetic response to an input ER/IR. The moment about the tibial long axis (Mz), defined to be initially coincident with the Z-axis, was of particular interest. Previous studies (Funk et al., 2000; Kent et al., 2009; Lucas et al., 2008) have described the transient and long-time behaviors of biological structures with Fung's quasi-linear viscoelastic (QLV) theory (Fung, 1993). This theory was adapted in the current study to describe the relationship between Mz and rotation. A Supplementary Work section for this manuscript details the derivations for this QLV model. The transient elastic moment response (Mz0) was calculated from each test's QLV model (Supplementary Work, Equation 2) at all angles of ER/IR. These Mz0 values were utilized to calculate (Supplementary Work, Equation 4) the long-time moment response (Mz1) using the long-time relaxation parameter (G1).
Please cite this article as: Mait, A.R., et al., Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation. Journal of Biomechanics (2017), http://dx.doi.org/10.1016/j.jbiomech.2017.01.006i
A.R. Mait et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Fig. 2. (A) Schematic of the experimental boundary conditions with the locations of the input rotation and axial load. The global coordinate system (X–Y–Z) is defined at the proximal tibia (X-axis inserts at the origin of the Z and Y axes and is aligned parallel to the second metatarsal). (B) Experimental test rig photograph of a specimen (neutral foot rotated to its final position) detailing each component or device used during testing as well as placement of these components in the test rig. The global coordinate system (X–Y–Z) is defined at the proximal tibia connection to the potting cup and load cell. The local tibia coordinate system (x–y–z) is defined at the tibial plafond (x-axis inserts at the origin of the z and y axes and is aligned parallel to the second metatarsal) using the location of the tibia marker in CT scans and transformation processing similar to that of Shaw et al. (2009).
Fig. 3. Transient elastic (Mz0) and long-time (Mz1) moment responses from the QLV model for specimens 616 L and 743 L subjected to (A) ER and (B) IR of 21°. Initial foot positions of neutral, everted, inverted, dorsiflexed, and plantarflexed are reported.
A.R. Mait et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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3. Results At least 721° of ER/IR, based on the three-dimensional scans of the tibia marker, was applied to the z-axis in all tests and moment magnitudes at this peak rotation are reported to directly compare specimen results. Rotation-time histories (imparted by the index table about the Z-axis) used in the QLV model were scaled based on the minimum ER/IR (calcaneus axial rotation relative to tibia). Mz0 and Mz1 values were found for ER and IR tests in all initial foot positions throughout the entire rotation-time histories. Peak Mz0, calculated at 721° of ER/IR, ranged between 15 N-m and 30 N-m for the neutral initial foot position with varying trends across other initial foot positions (Fig. 3). Trends among Mz1
magnitudes, calculated from the peak Mz0, were similar to those seen in Mz0. To illustrate the ramp and hold input of foot rotation, Fig. 4 details the experimental moment-time histories of specimens 616L and 743L during ER and IR under all initial foot positions. Mz increases steeply and then relaxes over time in quasi-static ER/IR. Some tests on specimen 616L were ramped to lower magnitudes of ER/IR and subsequently held before ramping to maximum ER/IR to confirm that the Mz relaxation phenomenon holds for a range of steps in ER/IR. Peak experimental Mz for all tests was measured to range between 15 N-m and 35 N-m. No ligament tears, avulsions, or bone fractures were found on either specimen during the posttest necropsies.
Fig. 4. Experimental moment-time histories measured by the load cell for specimens 616L and 743L subjected to (A) ER and (B) IR. Initial foot positions of neutral, everted, inverted, dorsiflexed, and plantarflexed are reported.
Please cite this article as: Mait, A.R., et al., Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation. Journal of Biomechanics (2017), http://dx.doi.org/10.1016/j.jbiomech.2017.01.006i
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4. Discussion
Acknowledgements
This study sought to apply foot rotation while allowing the axis of rotation in the leg to move based on the natural bony motion of the foot–ankle complex. Previous studies have tended to use artificially restrictive boundary conditions when testing foot rotation effects (Markolf et al., 1989; Michelson et al., 1997; Wei et al., 2012, Xenos et al., 1995). While using functionally relevant boundary conditions of an unconstrained fibula and permitted foot translation, this study found transient and long-time relationships between Mz and applied ER/IR (Figs. 3 and 4). A QLV model adapted from previous studies conducted on other biological structures (Funk et al., 2000; Kent et al., 2009; Lucas et al., 2008) predicted the experimental Mz (Supplementary Work, Figs. 5 and 6) with high determination (R2 greater than 0.995 for all tests). Combined with the results for Mz0 and Mz1 (Fig. 3), this confirms the transient and long-time relationships between Mz and applied foot rotation in the cadaveric leg. To the authors’ knowledge, such a relationship has not been documented previously. This study was limited by testing a small number of specimens, however a baseline for future studies has been developed. The current study established an initial investigation of foot positioning effects on cadaveric leg mechanical responses, where moment magnitude responses are altered by initial foot position (Figs. 3 and 4), e.g. higher Mz0 magnitude for eversion than neutral or inversion under IR. Future studies utilizing similar realistic and functionally relevant boundary conditions from this study should be performed to investigate the effects of applied foot rotation on ankle kinematics and injury classifications. Transient and long-time kinetic responses in the leg vary from one initial foot position to another, which advances knowledge regarding leg mechanics. Linking this knowledge with future ankle kinematic and injury studies will facilitate injury-prediction FE model development. Ultimately, this study acts as a foundation for subsequent experimental and computational investigations of ankle injuries, which will inform clinical diagnoses and prevention techniques.
Funding for this study was provided by Biomechanics Consulting & Research, LLC (Biocore). The authors would like to thank the members of the Foot & Ankle Subcommittee of the National Football League (Grant number 144728-101-GI13822-31345) for funding, supporting, and providing valuable input to this study.
Conflict of interest statement One of the co-authors (Kent) has an ownership interest in one of the sponsors of the study (Biocore).
Appendix A. Suppementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech.2017.01.006.
REFERENCES Bloemers, F., Bakker, F., 2006. Acute ankle syndesmosis injury in athletes. Eur. J. Trauma 4, 350–356. Fung, Y., 1993. Biomechanics: Material Properties of Living Tissues. Springer, New York, pp. 242–320. Funk, J., 2011. Ankle Injury mechanisms: lessons learned from cadaveric studies. Clin. Anat. 24, 350–361. Funk, J., Hall, G., Crandall, J., Pilkey, W., 2000. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J. Biomech. Eng. 122, 15–22. Kent, R., Woods, W., Salzar, R., Damon, A., Bass, C., 2009. The transient relationship between pressure and volume in the pediatric pulmonary system. J. Biomech. 42, 1656–1663. Lucas, S., Bass, C., Salzar, R., Oyen, M., Planchak, C., Ziemba, A., Shender, B., Paskoff, G., 2008. Viscoelastic properties of the cervical spinal ligaments under fast strain-rate deformations. Acta Biomater. 4, 117–125. Markolf, K., Schmalzried, T., Ferkel, R., 1989. Torsional strength of the ankle in vitro: the supination-external-rotation injury. Clin. Orthop. Relat. Res. 246, 266–272. Michelson, J., Solocoff, D., Waldman, B., Kendell, K., Ahn, U., 1997. Ankle fractures: the Lauge-Hansen classification revisited. Clin. Orthop. Relat. Res. 345, 198–205. Nie, B., Panzer, M., Mane, A., Mait, A., Donlon, J.-P., Forman, J., Kent, R., 2015. A framework for parametric modeling of ankle ligaments to determine the in situ response under gross foot motion. Comput. Methods Biomech. Biomed. Eng., 1–12. Nigg, B., Skarvan, G., Frank, C., 1990. Elongation of forces of ankle ligaments in a physiological range of motion. Foot Ankle 11, 30–40. Roaas, A., Andersson, G., 1982. Normal range of motion of the hip, knee and ankle joints in male subjects, 30-40 years of age. Acta Orthop. Scand. 53, 205–208. Shaw, G., Parent, D., Purtsezov, S., Lessley, D., Crandall, J., Kent, R., Guillemot, H., Ridella, S., Takhounts, E., Martin, P., 2009. Impact response of restrained PMHS in frontal sled tests: skeletal deformation patterns under seat belt loading. Stapp Car Crash J. 53, 1–48. Skraba, J., Greenwald, A., 1984. The role of the interosseous membrane on tibiofibular weightbearing. Foot Ankle 4, 301–304. Wei, F., Post, J., Braman, J., Meyer, E., Powell, J., Haut, R., 2012. Eversion during external rotation of the human cadaver foot produces high ankle sprains. J. Orthop. Res. 30, 1423–1429. Xenos, J., Hopkinson, W., Mulligan, M., Olson, E., Popovic, N., 1995. The tibiofibular syndesmosis: evaluation of the ligamentous structures, methods of fixation, and radiographic assessment. J. Bone Jt. Surg. 77-A, 847–856.
Please cite this article as: Mait, A.R., et al., Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation. Journal of Biomechanics (2017), http://dx.doi.org/10.1016/j.jbiomech.2017.01.006i
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation Alexander R. Mait n, Adwait Mane, Jason L. Forman, John Paul Donlon, Bingbing Nie, Richard W. Kent Department of Mechanical and Aerospace Engineering University of Virginia, Center for Applied Biomechanics, 4040 Lewis and Clark Drive, Charlottesville, VA 22911, USA
art ic l e i nf o
a b s t r a c t
Article history: Accepted 3 January 2017
The purpose of this study was to determine the long-time and transient characteristics of the moment generated by external (ER) and internal (IR) rotation of the calcaneus with respect to the tibia. Two human cadaver legs were disarticulated at the knee joint while maintaining the connective tissue between the tibia and fibula. An axial rotation of 21° was applied to the proximal tibia to generate either ER or IR while the fibula was unconstrained and the calcaneus was permitted to translate in the transverse plane. These boundary conditions were intended to allow natural motion of the fibula and for the effective applied axis of rotation to move relative to the ankle and subtalar joints based on natural articular motions among the tibia, fibula, talus, and calcaneus. A load cell at the proximal tibia measured all components of force and moment. A quasi-linear model of the moment along the tibia axis was developed to determine the transient and long-time loads generated by this ER/IR. Initially neutral, everted, inverted, dorsiflexed, and plantarflexed foot orientations were tested. For the neutral position, the transient elastic moment was 16.5 N-m for one specimen and 30.3 N-m for the other in ER with 26.3 and 32.1 N-m in IR. The long-time moments were 5.5 and 13.2 N-m (ER) and 9.0 and 9.5 N-m (IR). These loads were found to be transient over time similar to previous studies on other biological structures where the moment relaxed as time progressed after the initial ramp in rotation. & 2017 Elsevier Ltd. All rights reserved.
Keywords: Ankle Kinetics Transient QLV Foot rotation
1. Introduction Excessive rotation of the foot injures the foot–ankle complex in the human leg, specifically the distal tibiofibular syndesmosis joint (Bloemers and Bakker, 2006; Funk, 2011; Wei et al., 2012). Previous experiments investigated the effects of foot rotation on leg kinetics and the syndesmosis joint (Markolf et al., 1989; Michelson et al., 1997; Wei et al., 2012; Xenos et al., 1995), but with limitations. Though Xenos et al. (1995) allowed the fibula to move freely, the leg was rigidly constrained in four locations. This created an unclear axis of rotation in the ankle by preventing the foot from translating naturally during foot rotation. Wei et al. (2012), Markolf et al. (1989), and Michelson et al. (1997) disarticulated the tibia and fibula mid-shaft, thus disrupting the proximal interosseous membrane (IOM) and tibiofibular joint. These studies rigidly fixed the tibia and fibula together, preventing the fibula from
n
Corresponding author. Fax: þ 1 434 297 8083. E-mail address: [email protected] (A.R. Mait).
moving freely during rotation, therefore altering ankle mechanics (Skraba and Greenwald, 1984). The transient behaviors of biological structures have been studied previously (Funk et al., 2000; Kent et al., 2009; Lucas et al., 2008), though, to the authors’ knowledge, not for kinetic responses to applied foot rotation. The current study aimed to determine the long-time and transient characteristics of the moment generated about the tibia during foot external rotation (ER) and internal rotation (IR). Imposing functionally relevant boundary conditions on the leg was also a goal of the study, such that a more realistic anatomic configuration is created where the fibula is unconstrained and foot translation is permitted. Transient and long-time relationships between cadaveric leg kinetics and foot rotation was hypothesized. With imposing boundary conditions designed to recreate a more realistic loading within the leg, reliable kinetic data responses to applied rotation will be used to inform future experiments aimed at describing ankle injury characteristics. Understanding the loads throughout the leg during more realistic motion also facilitates future injury-prediction model development on a current finite element (FE) model (Nie et al., 2015).
http://dx.doi.org/10.1016/j.jbiomech.2017.01.006 0021-9290/& 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Mait, A.R., et al., Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation. Journal of Biomechanics (2017), http://dx.doi.org/10.1016/j.jbiomech.2017.01.006i
A.R. Mait et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
Fig. 1. Potted tibia of a specimen with Bondo body filler covering the anterior, posterior, and medial sides of the proximal tibia and wood screws driven into the shank of the tibia at varying heights and angles along the potting cup. Soft tissue was left undisturbed around the fibula and lateral aspect of the tibia to preserve the IOM and proximal tibiofibular ligament connections. Placement of the tibia and calcaneus markers as well as the open-faced mount around the calcaneus with threaded rods driven from lateral to medial are shown. The lateral face of the calcaneus mount had several holes for threaded rods to pass through to accommodate different sizes of specimens, whereas the medial face was made of solid polyvinyl chloride for the threaded rods to anchor.
2. Methods 2.1. Specimen preparation Experiments were conducted on fresh-frozen left lower limbs from two male cadavers (Table 1). The specimens were acquired with the approval of and prepared in accordance with the policies and procedures of the UVA Center for Applied Biomechanics Oversight Committee (Ethics Approval #: CAB2014-07). The subjects were confirmed free of infectious diseases including HIV and Hepatitis B/C. Computed tomography (CT) scans of each specimen were taken prior to testing to confirm the absence of bony trauma. Limbs were stored at –15 °C and thawed to room temperature for 48 h before test preparation. The tibia and fibula were disarticulated at the knee while retaining an intact proximal IOM and tibiofibular joint ligaments. Soft tissue was cleared from the tibial plateau. The proximal tibia was rigidly attached to a potting cup using wood screws and Bondo body filler (part #261, 3 M Company, St. Paul, MN, USA) with the fibula left free (Fig. 1). A mount assembled with acetal homopolymer resin and polyvinyl chloride, reinforced with machine screws, was fixed to the calcaneus using threaded rods passing from lateral to medial directly tapping into the polyvinyl chloride (Fig. 1). 2.2. Testing procedure A custom rig was designed to rotate the specimen to a desired effective angle of foot rotation in the global X–Y–Z coordinate system, defined where the center of the tibial plateau was fixed to the center of the potting cup, and apply a constant compressive load down the Z-axis (Fig. 2A). The potting cup around the proximal tibia was attached to a rotary index table which was used to manually impart the desired quasi-static effective foot rotation about the Z-axis. A bi-directional linear rail system attached to the calcaneus mount allowed the foot to translate in the global X and Y directions, and linear bearing tracks permitted motion in the Z-axis (vertical direction), thus allowing the Z-axis of rotation to adjust to the natural axis of rotation in the leg (Fig. 2B). The foot was mounted to this rail system using two gimbals with orthogonal rotation axes, originally parallel to the global axes in a neutral foot position when specimens were placed into the test apparatus. The gimbals allowed the foot to be locked in this neutral orientation or in varying degrees of eversion, inversion, dorsiflexion, and plantarflexion. These foot orientations were defined grossly as rotations of the calcaneus relative to the tibia. The gimbals (fixed to the calcaneus mount) rotated the calcaneus into eversion, inversion, dorsiflexion, or plantarflexion within a nominal range of 10–20°, used since within physiological range of motion of the ankle joint (Nigg et al., 1990; Roaas and Andersson, 1982), at increments of 5°. A 6-axis load cell (Model #5024J, Robert A Denton, Inc., Rochester Hills, MI, USA) and rotary potentiometer (Model #SP22GS, ETI Systems, Carlsbad, CA, USA), aligned between the centers of the potting cup and index table, measured forces and moments acting at the proximal tibia and the imposed effective foot rotation (Fig. 2B). These functionally relevant boundary conditions (fibula not fixed to tibia and foot translation permitted) address deficiencies in previous studies (Markolf et al., 1989; Michelson et al., 1997; Wei et al., 2012; Xenos et al., 1995), so that the leg is not artificially constrained and more realistic interactions among ankle bones and ligaments are attained. Specimens were initially placed in a nominally neutral position, such that the distal end of the first phalanx, the approximate centroid of the calcaneus, and the long axis of the tibia formed a right angle in the sagittal plane (Fig. 2B).
Table 1 Specimen anthropometric data: gender, age at time of death, and whole-body height and weight of the two specimens used in this study. Specimen ID#
Gender
Age (yr)
Height (cm)
Weight (kg)
616L 743L
Male Male
46 31
177 188
113 100
Note: L indicates a left leg specimen. A compressive preload of approximately 110 N, chosen to not overly constrain the leg but still initiate ligaments and joint congruency, was applied via static weight to the calcaneus mount. Maximum effective foot rotation of 7 30° was determined to be non-injurious (Wei et al., 2012), yet greater than physiological range of motion (Nigg et al., 1990). In this neutral position, all specimens were preconditioned before testing by rotating the index table for 10 cycles from þ30 to 30°. The specimens were then either kept in neutral or placed into a desired configuration of eversion, inversion, dorsiflexion, or plantarflexion, and rotated to the predetermined degree of quasi-static effective foot rotation by the index table. This position was held while the orientation and position of the specimen's tibia was scanned with a three-dimensional laser scanner (ROMER Absolute Arm, Hexagon Metrology, Inc., RA-7330SI-2), throughout which kinetics were measured by the load cell. A marker was rigidly attached to the tibia using wood screws and to the calcaneus mount. Each bone's orientation and position was defined in a local x–y–z coordinate system based on the marker position as detailed by Shaw et al. (2009) (Fig. 2B). The difference between the initial and final position of these markers was used to determine the rotation of the tibia caused by the effective foot rotation input from the index table. In this test rig, there was a fixed boundary condition at both the proximal tibia and the calcaneus (Fig. 2A). After applying the index table effective foot rotation through the fixed proximal tibia, the true foot rotation, defined as ER and IR, was measured as the axial rotation of the fixed calcaneus about the tibia's z-axis. Post-test necropsies were performed to confirm the lack of ligament damage and bone fracture. The anterior and posterior tibiofibular ligaments, IOM, anterior and posterior talofibular ligaments, calcaneofibular ligament, tibiocalcaneal ligament, and tibionavicular ligament were inspected.
2.3. Kinetic analysis Force and moment vectors acting within the leg were measured over time at the proximal tibia to determine the leg's kinetic response to an input ER/IR. The moment about the tibial long axis (Mz), defined to be initially coincident with the Z-axis, was of particular interest. Previous studies (Funk et al., 2000; Kent et al., 2009; Lucas et al., 2008) have described the transient and long-time behaviors of biological structures with Fung's quasi-linear viscoelastic (QLV) theory (Fung, 1993). This theory was adapted in the current study to describe the relationship between Mz and rotation. A Supplementary Work section for this manuscript details the derivations for this QLV model. The transient elastic moment response (Mz0) was calculated from each test's QLV model (Supplementary Work, Equation 2) at all angles of ER/IR. These Mz0 values were utilized to calculate (Supplementary Work, Equation 4) the long-time moment response (Mz1) using the long-time relaxation parameter (G1).
Please cite this article as: Mait, A.R., et al., Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation. Journal of Biomechanics (2017), http://dx.doi.org/10.1016/j.jbiomech.2017.01.006i
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Fig. 2. (A) Schematic of the experimental boundary conditions with the locations of the input rotation and axial load. The global coordinate system (X–Y–Z) is defined at the proximal tibia (X-axis inserts at the origin of the Z and Y axes and is aligned parallel to the second metatarsal). (B) Experimental test rig photograph of a specimen (neutral foot rotated to its final position) detailing each component or device used during testing as well as placement of these components in the test rig. The global coordinate system (X–Y–Z) is defined at the proximal tibia connection to the potting cup and load cell. The local tibia coordinate system (x–y–z) is defined at the tibial plafond (x-axis inserts at the origin of the z and y axes and is aligned parallel to the second metatarsal) using the location of the tibia marker in CT scans and transformation processing similar to that of Shaw et al. (2009).
Fig. 3. Transient elastic (Mz0) and long-time (Mz1) moment responses from the QLV model for specimens 616 L and 743 L subjected to (A) ER and (B) IR of 21°. Initial foot positions of neutral, everted, inverted, dorsiflexed, and plantarflexed are reported.
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3. Results At least 721° of ER/IR, based on the three-dimensional scans of the tibia marker, was applied to the z-axis in all tests and moment magnitudes at this peak rotation are reported to directly compare specimen results. Rotation-time histories (imparted by the index table about the Z-axis) used in the QLV model were scaled based on the minimum ER/IR (calcaneus axial rotation relative to tibia). Mz0 and Mz1 values were found for ER and IR tests in all initial foot positions throughout the entire rotation-time histories. Peak Mz0, calculated at 721° of ER/IR, ranged between 15 N-m and 30 N-m for the neutral initial foot position with varying trends across other initial foot positions (Fig. 3). Trends among Mz1
magnitudes, calculated from the peak Mz0, were similar to those seen in Mz0. To illustrate the ramp and hold input of foot rotation, Fig. 4 details the experimental moment-time histories of specimens 616L and 743L during ER and IR under all initial foot positions. Mz increases steeply and then relaxes over time in quasi-static ER/IR. Some tests on specimen 616L were ramped to lower magnitudes of ER/IR and subsequently held before ramping to maximum ER/IR to confirm that the Mz relaxation phenomenon holds for a range of steps in ER/IR. Peak experimental Mz for all tests was measured to range between 15 N-m and 35 N-m. No ligament tears, avulsions, or bone fractures were found on either specimen during the posttest necropsies.
Fig. 4. Experimental moment-time histories measured by the load cell for specimens 616L and 743L subjected to (A) ER and (B) IR. Initial foot positions of neutral, everted, inverted, dorsiflexed, and plantarflexed are reported.
Please cite this article as: Mait, A.R., et al., Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation. Journal of Biomechanics (2017), http://dx.doi.org/10.1016/j.jbiomech.2017.01.006i
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4. Discussion
Acknowledgements
This study sought to apply foot rotation while allowing the axis of rotation in the leg to move based on the natural bony motion of the foot–ankle complex. Previous studies have tended to use artificially restrictive boundary conditions when testing foot rotation effects (Markolf et al., 1989; Michelson et al., 1997; Wei et al., 2012, Xenos et al., 1995). While using functionally relevant boundary conditions of an unconstrained fibula and permitted foot translation, this study found transient and long-time relationships between Mz and applied ER/IR (Figs. 3 and 4). A QLV model adapted from previous studies conducted on other biological structures (Funk et al., 2000; Kent et al., 2009; Lucas et al., 2008) predicted the experimental Mz (Supplementary Work, Figs. 5 and 6) with high determination (R2 greater than 0.995 for all tests). Combined with the results for Mz0 and Mz1 (Fig. 3), this confirms the transient and long-time relationships between Mz and applied foot rotation in the cadaveric leg. To the authors’ knowledge, such a relationship has not been documented previously. This study was limited by testing a small number of specimens, however a baseline for future studies has been developed. The current study established an initial investigation of foot positioning effects on cadaveric leg mechanical responses, where moment magnitude responses are altered by initial foot position (Figs. 3 and 4), e.g. higher Mz0 magnitude for eversion than neutral or inversion under IR. Future studies utilizing similar realistic and functionally relevant boundary conditions from this study should be performed to investigate the effects of applied foot rotation on ankle kinematics and injury classifications. Transient and long-time kinetic responses in the leg vary from one initial foot position to another, which advances knowledge regarding leg mechanics. Linking this knowledge with future ankle kinematic and injury studies will facilitate injury-prediction FE model development. Ultimately, this study acts as a foundation for subsequent experimental and computational investigations of ankle injuries, which will inform clinical diagnoses and prevention techniques.
Funding for this study was provided by Biomechanics Consulting & Research, LLC (Biocore). The authors would like to thank the members of the Foot & Ankle Subcommittee of the National Football League (Grant number 144728-101-GI13822-31345) for funding, supporting, and providing valuable input to this study.
Conflict of interest statement One of the co-authors (Kent) has an ownership interest in one of the sponsors of the study (Biocore).
Appendix A. Suppementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech.2017.01.006.
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Please cite this article as: Mait, A.R., et al., Transient and long-time kinetic responses of the cadaveric leg during internal and external foot rotation. Journal of Biomechanics (2017), http://dx.doi.org/10.1016/j.jbiomech.2017.01.006i