Strain-rate sensitivity of the lateral collateral ligament of the knee
Timothy J Bonner1,2, Nicolas Newell2, Angelo Karunaratne2, Andy D Pullen3, Andrew A Amis4,5, AnthonyMJBull2, SpyrosDMasouros2
1The Academic Department of Military Surgery and Trauma, The Royal Centre for Defence Medicine, Birmingham, B15 2SQ
2Department of Bioengineering, Imperial College London, London SW7 2AZ, UK
3Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
4Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
5Department of Musculoskeletal Surgery, Imperial College London, London W6 8RF, UK
Corresponding author:
Dr Spyros Masouros
Lecturer in Trauma Biomechanics
Department of Bioengineering,
Imperial College London,
London SW7 2BP,
United Kingdom
Tel:+44 20 75942645
Fax: +44 20 75949817
E-mail:
Abstract
The material properties of ligaments are not well characterized at rates of deformation that occur during high-speed injuries. The aim of this study was to measure the material properties of lateral collateral ligament of the porcine stifle joint in a uniaxial tension model through strain rates in the range from 0.01-100/s. Failure strain, tensile modulus and failure stress were calculated. Across the range of strain rates, tensile modulus increased from 288 to 905MPa and failure stress increased from 39.9 to 77.3MPa. The strain-rate sensitivity of the material properties decreased as deformation rates increased, and reached a limit at approximately 1/s, beyond which there was no further significant change. In addition, time resolved microfocus small angle X-ray scattering was used to measure the effective fibril modulus (stress/fibril strain) and fibril to tissue strain ratio. The nano scale data suggest that the contribution of the collagen fibrils towards the observed tissue-level deformation of ligaments diminishes as the loading rate increases. These findings help to predict the patterns of limb injuries that occur at different speeds and improve computational models used to assess and develop mitigation technology.
Keywords.Ligament, stress, modulus, strain rate, injury
1.Introduction
Human ligament injuries are common and can cause significant morbidity and long-term disablement[1]. The EUROCOST reference group estimate the incidence of knee ligament injuries at 0.04% population/year with associated treatment costs alone at an average of €1,727 per injury [2]. The types of joint injuries that occur may vary according to health, age, sex, anatomy, mechanism of trauma and rate of loading [3]. Prevention of significant joint injuries requires us to understand why different patterns of injury may occur with different traumatic mechanisms and rates of loading. Computational modelling of joint injuries is one method that may be useful to help predict different patterns of injury and assess mitigation technologies. However, reliable biomechanical measurements of the connective tissues of joints are required if the models are to be accurate and useful.
Ligaments are viscoelastic materials made of collagen fibres, which change in strength and stiffness relative to their rate of loading[4,5]. Tensile modulus and failure stress are useful measurements to compare the material properties of different ligaments. These material properties are important input parameters to computational models of human joint injuries. Previous laboratory studies have found that the tensile modulus and failure stress of ligaments both increase as the rate of loading increases [6-9]. However, many of the previous studies have focused on the failure characteristics at quasi-static loading rates or assessed only a few different loading rates [6,10-12].
This strain-rate dependent material behaviour of ligament tissue cannot be understood without considering the hierarchical nature of the structure. Small angle X-ray diffraction(SAXD) has been performed previously on collagenous tissues such as tendons, bones and cartilage in an attempt to quantify the viscoelastic properties of the tissues at a fibrillar level and utilize them to explain their typical macroscopic behaviour [27-29]. Fratzlet al. proposed a simple model explaining why the ratio of fibril-to-tissue strain increases with strain rate in the quasi-static range. They suggest that the proteoglycan-rich matrix becomes stiffer due to an increase of the viscous component as strain rate increases. Unfortunately, the maximum strain rate at which they tested was 0.001/s and so their observations are not adequate to demonstrate or explain potential changes in strength and modulus at strain rates experienced at injury.
Whilst work at slow rates is useful to understand behaviour in normal joint function and to choose replacement grafts, the application of these results to high-speed injury modelling may not be valid;significant error may occur if lowstrain-rate material properties are applied to simulations of traumatic injury. The limitations of previous work are likely to be caused by the technical difficulties of measuring stress and strain at rates that simulate high-speed injuries, such as motor vehicle collisions or battlefield injuries due to blast [15,16].
The aim of this study was to investigate the material properties of ligaments in a uniaxial tension model at strainrates in the range from 0.01-100/s. A porcine stifle joint ligament experimental model was designed to simulate the strain rates that may occur during a full range of different human knee ligament loading. The hypothesis was formulated that the strain-rate sensitive material properties of a ligament would diminish as strain rate increased.Studying ligament properties over a large order of magnitude of strainrates also provides an insight into the different structural explanations for their viscoelasticity. Furthermore,time resolved synchrotron small angle X-ray scattering on human ligaments was used to investigate the deformation mechanisms at the nanoscalein order an attempt to explain the strain-rate dependent behaviour of ligaments.
2.Methods
2.1.Specimen preparation
Ligaments of the porcine stifle joint wereselected because of their similarity in morphology, size, structure, material properties and physiological loading to the human knee joint [18]. Sixty porcine hind limbs were delivered to the laboratory on the day of slaughter from a local abattoir. Excess muscle bulk was removed from the limbs, which were then stored at -20°C. All limbs were utilized within one month of slaughter to minimize any potential deterioration in their mechanical properties [17].All limbs were from healthy female large-white pigs, aged between 9 and 12 months. The demographics of the pigs were controlled to limit the physiological variation in material properties, which is known to occur between sexes, age groups, pig breeds and in unhealthy subjects[19,20].
Each hind limb was thawed at room temperature on the day of testing. The lateral collateral ligament (LCL) of the porcine stifle joint was isolated by removing skin, muscle, other joint ligaments and tibia, thus leaving the femur, LCL and fibula intact. A hand saw was used to cut a 15 × 15 × 25 mm bone block around the femoral attachment of the LCL. A similar bone block was created with the fibula by removing its rounded proximal margin and dividing it transversely at 40 mm in length. A thin longitudinal round segment of ligament was isolated along the posterior margin of each LCL, such that each ligament’s fascicles were easily aligned, similar in length and would reliably fail in its mid-substance. The unwanted anterior segment was removed by separating the ligament via blunt dissection in line with the fascicles, and divided transversely both proximally and distally when the fascicles could no longer be easily separated; thus ensuring no structural damage. Thiscreated a test specimen with a long thin middle section of a relatively constant cross-sectional area, with a broad anchor at either end made of the bone blocks and fibrocartilage transition zone (Figure 1).
Cross-sectional area was measured using a previously validated technique for use in soft tissues [21].Each specimenwas held under 1N of tension and the mid-substance of the ligamentwas cast in a quick-setting, stiff alginate paste (Blueprint®cremix, DentsplyDeTrey, Germany). The solid alginate paste was cut perpendicular to the long axis of the construct after removal of the ligament. Digital photographs were taken of the cut sections of alginate paste at three different sites. Each photograph was converted into binary code, based on whether or not each pixel contained an image of the ligament cast. The number of pixels in each photograph was counted using a custom computer code (MatLAB, MathWorks Inc., Natick, MA, USA). The cross-sectional area was calculated by comparing the mean of the three pixel counts against a calibration photograph of a shape with a known cross section.
The bone blocks were placed into cylindrical aluminium potsand secured byalignment screws.Positioning of the ligament samplewas carefully adjusted such that it was coaxial with the uniaxial tension test. The bone blocks were then set in polymethyl-methacrylate (PMMA) bone cement. Petroleum jelly and saline soaked gauze were used to keep the ligament hydrated and particularly to protect its attachments from the heat generated during cement polymerization. Multiple small black dots were made across both ends of the ligament with permanent black ink (Staedtler Ltd., UK) during set up on the tensile testing machines. The samples were then sprayed with water to ensure they did not dry out before testing.The length of each ligament sample was measured once with digital callipers before testing to provide an estimate of the deformation rates needed to achieve the required strain rates. All tests were performed at room temperature.
2.2.Tensile testing
Tests were carried out to achieve target strain rates of 0.01, 0.1, 1,10, and 100/s.
Quasi-static tensile tests
A screw-driven electro-mechanical (5866; Instron, Canton, MA, USA) and a servo-hydraulic (8872; Instron, Canton, MA, USA) materials testing machines were used for tensile tests at 0.01-0.1/s and 1/s, respectively. Pre-conditioning of the ligaments was performed for the quasi-static tests with cyclic loading between 1 and 10N at 10mm/min, and repeated five times, then held at 0N for 10 seconds [17]. The specimens were loaded to failure at extension rates of 0.47, 4.7 and 47mm/s to achieve strainrates in the region of 0.01,0.1, and 1/s, respectively. Two specimens were extended at 0.39mm/s and 0.55mm/s because the ligaments were shorter and longer, respectively, than the rest. Force-extension data was measured simultaneously using the built in load cell and extensometer at a sampling rate of 50Hz, then recordedwith the machine’s accompanying materials testing software (Bluehill® v2.11, Instron, High Wycombe, UK)
Impact tensile tests
Tensile tests atstrain rates in the region of 10 and 100/s were performed using an InstronDynatup 9250-HV spring-assisted drop-weight rig (Instron, High Wycombe, UK). A custom-made impact tensile adaptor (ITA) was manufactured for the experiment (Figure 2). The upper aluminium pot was attached by a spherical rod-end connector to a fixed steel crossbeam. The lower pot was attached to an aluminium rectangular fixture, free to move vertically in the axis of the tensile test, which was rapidly accelerated by a 7.45kg impactor with a 50mm diameter head for each test. The velocity of the impactor could be altered by changing its drop height, or with the addition of accelerator springs. A pair of diametrically-opposedbi-axial strain gauge rosettes(FCA-6;Techni Measure, Warwickshire, UK) were bonded tothe upper aluminium pot in a Wheatstone full-bridge configuration in order to measure load. The strain gauge output was calibrated in a series of preliminary tests against known loads.A PXIe data acquisition system in conjunction with a custom-written LabVIEW® software program (NI instruments, Austin, TX, USA) was used to record strain gauge output with a sampling rate of 16 kHz– 2MHz.Strainrates in the region of 10 and 100/s were achieved with an impactor velocity at impact of 1 m/s and 8-12m/s,respectively. The impactor velocity for the 100/s tests was increased from 8 to 12m/s after six tests because the average strainrate was less thanthe target rate.
2.3.Data Analysis
Strain was measured directly from the mid-substance of each ligament using high-speed photography (Phantom V12.1, frame rate 27 - 47000 fps). Two points were selected at either end of the ligament and were tracked across frames using digital tracking software (Phantom Camera Control Application 1.3, Vision Research, NJ, USA) by noting their pixel position at every frame. For each frame, strain was calculated as the change in pixelseparation of the pair of points, divided by the pixelseparationof the two points in a reference frame. This procedure was repeated for an additional 2 pairs of points, and ligament strain was taken as the mean value of the 3 pairs.
Strain rate was calculated as the gradient of the linear part of the strain-time curve for each test. Stress was calculated as the recorded force over the calculated original area. Stress-strain curves were created and used to calculate the tensile modulus, and stress and strain at failure for each sample. Pearson’s correlation coefficient was calculated to establish thelinear relationship between time and strain before failure.Changes across the range of strain rates of strain at failure, stress at failure and tensile modulus were examined using one-way analysis of variance (ANOVA) with post-hoc Bonferonni testing; p<0.05 was taken to indicate a significant change.
2.4.Nano-scale experiments
In an attempt to understand the strain-rate sensitivity at a fibrillar level we conducted mechanical testing utilizing synchrotron SAXD on human LCLs. Ethical approval had been secured prior to testing from the local research ethics committee. We used the same experimental protocol to previous studies[27,28,30,31]to measure fibrillar deformation at 0.001, 0.005, 0.01, and 0.05/s. Twenty human LCL samples were prepared (5 per strain rate) and gripped in a micro-tensile tester [30] that was mounted on a 2 axis motorised stage beam-line I22 at Diamond Light Source, UK. A synchrotron X-ray beam (wavelength 0.886Å, beam cross section 1012µm) was used to measure the SAXD patterns, which were collected by a Pilatus detector system. The sample-to-detector distance was 1m. Foreach strain rate a SAXD pattern with 1sexposure time was collected at every 1% applied external (grip-to-grip) strain up to failure. The fibril strain was measured as described elsewhere [27,28,29] by tracking the change in the D-periodicity (~67nm) of the meridional banding patterns in the collagen fibrils arising from the intrafibrillartropocollagen packing (Figure 3).
3.Results
The data-sets resulting from 41 ligament tests were available for analysis; the remaining data-sets were not used due to either trigger failure during testing, inadequate image capture, early sample failure around the bone block, or use in preliminary testing. One further sample was excluded during the analysis because the sample was a gross outlier and is likely to have failed in an atypical way.
The time to failure of the ligaments ranged from less than 1ms at the higher strain rates, to greater than 20s at the lower strain rates. The cross-sectional areas of the samples was 3.6(SD=1.1) mm2. The relationship between strain and time was linear for all tests (mean R2=0.99 (SD=0.02), p0.001); hence constant strain rate was achieved across all experimental setups.Figure 4apresents typical stress-strain curves for each strain rate. A non-linear – often called‘toe’ – region was pronounced at lower strain rates, requiring up to 3-4% strain before a linear gradient was observed. A ‘yield’ point could be observed with some samples at the two lowest strainrates, but complete structural failure occurred shortly afterwards with minimal further deformation. Toe region and ‘yield’ point were not observed at the two fastest strainrates. There was a general trend towards a negative relationship between the failure strain and strainrate (Table 1). Figure 4b presents the mean curves at the five target strain rates of the study. Failure stress was found to increase at the three slowest strain rates, but further change was insignificant after approximately 1/s. This was supported by ANOVA tests, which showed that there were statistically significant increases in tensile modulus and stress at failure between each consecutive strain-rate group up to0.94/s (p<0.05), but not beyond. This suggests that a strain-rate sensitivity limit occurs at approximately 1/s.
Tensile modulus and failure stress as a function of strain rate are shown inFigure 5. Tensile modulus and failure stress of the ligament increased by an average of approximately 3- and 2-fold respectively over the strain rates tested, but the change occurred almost entirely over the three slowest strain rates.The relationship between tensile modulus and failure stress with strain rate was fitted with logarithmic and bilinear curves. The bilinear relationship was found to fit the data with a smaller error than the logarithmic. Specifically:
Tensile modulus, in MPa (R2 = 0.76).