A holistic numerical model to predict strain hardening and damage of UHMWPE under multiple total knee replacement kinematics and experimental validation

Experimental wear testing is an essential step in the evaluation of total knee replacement (TKR) design. Unfortunately, experiments can be prohibitively expensive and time consuming, which has made computational wear simulation a more desirable alternative for screening designs. While previous attempts have demonstrated positive results, few models have fully incorporated the affect of strain hardening (or cross shear), or tested the model under more than one loading condition. The objective of this study was to develop and evaluate the performance of a new holistic TKR damage model, capable of predicting damage caused by wear, including the effects of strain hardening and creep. For the first time, a frictional work-based damage model was compared against multiple sets of experimental TKR wear testing data using different input kinematics. The wear model was tuned using experimental measurements and was then able to accurately predict the volumetric polyethylene wear volume during experiments with different kinematic inputs. The size and shape of the damage patch on the surface of the polyethylene inserts were also accurately predicted under multiple input kinematics. The ability of this model to predict implant damage under multiple loading profiles by accounting for strain hardening makes it ideal for screening new implant designs, since implant kinematics are largely a function of the shape of the components.     

Stair climbing results in more challenging patellofemoral contact mechanics and kinematics than walking at early knee flexion under physiological-like quadriceps loading

The mechanical environment during stair climbing has been associated with patellofemoral pain, but the contribution of loading to this condition is not clearly understood. It was hypothesized that the loading conditions during stair climbing induce higher patellofemoral pressures, a more lateral force distribution on the trochlea and a more lateral shift and tilt of the patella compared to walking at early knee flexion. Optical markers for kinematic measurements were attached to eight cadaveric knees, which were loaded with muscle forces at instances of walking and stair climbing cycles at 12° and 30° knee flexion. Contact mechanics were determined using a pressure sensitive film. At 12° knee flexion, stair climbing loads resulted in higher peak pressure (p=0.012) than walking, more lateral force distribution (p=0.012) and more lateral tilt (p=0.012), whilst mean pressure (p=0.069) and contact area (p=0.123) were not significantly different. At 30° knee flexion, although stair climbing compared to walking loads resulted in significantly higher patellofemoral mean (p=0.012) and peak pressures (p=0.012), contact area (p=0.025), as well as tilt (p=0.017), the medial–lateral force distribution (p=0.674) was not significantly different. No significant differences were observed in patellar shift between walking and stair climbing at either 12° (p=0.093) or 30° (p=0.575) knee flexion. Stair climbing thus leads to more challenging patellofemoral contact mechanics and kinematics than level walking at early knee flexion. The increase in patellofemoral pressure, lateral force distribution and lateral tilt during stair climbing provides a possible biomechanical explanation for the patellofemoral pain frequently experienced during this activity.     

A new approach to the human muscle model

Hill's (1938) two component muscle model is used as basis for digital computer simulation of human muscular contraction by means of an iterative process. The contractile (CC) and series elastic (SEC) components are lumped components of structures which produce and transmit torque to the external environment. The CC is described in angular terms along four dimensions as a series of non-planar torque-angle-angular velocity surfaces stacked on top of each other, each surface being appropriate to a given level of muscular activation. The SEC is described similarly along dimensions of torque, angular stretch, overall muscle angular displacement and activation. The iterative process introduces negligible error and allows the mechanical outcome of a variety of normal muscular contractions to be evaluated parsimoniously. The model allows analysis of many aspects of muscle behaviour as well as optimization studies. Definition of relevant relations should also allow reproduction and prediction of the outcome of contractions in individuals.     

A new in vivo technique for determination of femoro-tibial and femoro-patellar 3D kinematics in total knee arthroplasty

Aim was to develop an in vivo technique which allows determination of femoro-tibial and of femoro-patellar 3D-kinematics in TKA simultaneously. The knees of 20 healthy volunteers and of eight patients with TKA (PCR, rotating platform) were investigated. Kinematics analysis was performed in an open MR-system at different flexion angles with external loads being applied. The TKA components were identified using a 3D-fitting technique, which allows an automated 3D-3D-registration of the TKA. Femoro-patellar and femoro-tibial 3D-kinematics were analyzed by image postprocessing. The validity of the postprocessing technique demonstrated a coefficient of determination of 0.98 for translation and of 0.97 for rotation. The reproducibility yielded a coefficient of variation (CV%) for patella kinematics between 0.17% (patello-femoral angle) and 6.8% (patella tilt). The femoro-tibial displacement also showed a high reproducibility with CV% of 4.0% for translation and of 7.1% for rotation. While in the healthy knees the typical screw-home mechanism was observed, a paradoxical anterior translation of the femur relative to the tibia combined with an external rotation occurred after TKA. Fifty percent of the TKA's experienced a condylar lift-off of >1mm predominately on the medial side. Regarding patellar kinematics significant changes were found in both planes in TKA with an increased patella height in the sagittal plane and patella tilt and shift in the transversal plane. The results demonstrate that the presented 3D MR-open based method is highly reproducible and valid for image acquisition and postprocessing and provides--for the first time--in vivo data of 3D-kinematics of the tibio-femoral and simultaneously of the patello-femoral joint during knee flexion.     

Developing simulations to reproduce in vivo fluoroscopy kinematics in total knee replacement patients

For clinically predictive testing and design-phase evaluation of prospective total knee replacement (TKR) implants, devices should ideally be evaluated under physiological loading conditions which incorporate population-level variability. A challenge exists for experimental and computational researchers in determining appropriate loading conditions for wear and kinematic knee simulators which reflect in vivo joint loading conditions. There is a great deal of kinematic data available from fluoroscopy studies. The purpose of this work was to develop computational methods to derive anterior–posterior (A–P) and internal–external (I–E) tibiofemoral (TF) joint loading conditions from in vivo kinematic data. Two computational models were developed, a simple TF model, and a more complex lower limb model. These models were driven through external loads applied to the tibia and femur in the TF model, and applied to the hip, ankle and muscles in the lower limb model. A custom feedback controller was integrated with the finite element environment and used to determine the external loads required to reproduce target kinematics at the TF joint. The computational platform was evaluated using in vivo kinematic data from four fluoroscopy patients, and reproduced in vivo A–P and I–E motions and compressive force with a root-mean-square (RMS) accuracy of less than 1 mm, 0.1°, and 40 N in the TF model and in vivo A–P and I–E motions, TF flexion, and compressive loads with a RMS accuracy of less than 1 mm, 0.1°, 1.4°, and 48 N in the lower limb model. The external loading conditions derived from these models can ultimately be used to establish population variability in loading conditions, for eventual use in computational as well as experimental activity simulations.     

An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo

This paper examined if an electromyography (EMG) driven musculoskeletal model of the human knee could be used to predict knee moments, calculated using inverse dynamics, across a varied range of dynamic contractile conditions. Muscle-tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three-dimensional anatomical model of the lower limb. Muscle activation was determined using a second-order discrete non-linear model using rectified and low-pass filtered EMG as input. A modified Hill-type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs. The model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion/extension (FE) muscle moment with those measured by inverse dynamics. The model was calibrated for each subject using 5 different tasks, including passive and active FE in an isokinetic dynamometer, running, and cutting manoeuvres recorded using three-dimensional motion analysis. Once calibrated, the model was used to predict the FE moments, estimated via inverse dynamics, from over 200 isokinetic dynamometer, running and sidestepping tasks. The inverse dynamics joint moments were predicted with an average R(2) of 0.91 and mean residual error of approximately 12 Nm. A re-calibration of only the EMG-to-activation parameters revealed FE moments prediction across weeks of similar accuracy. Changing the muscle model to one that is more physiologically correct produced better predictions. The modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks.     

A three-dimensional study of the kinematics of the human knee

This paper represents a three-dimensional study of the human knee-joint and studies kinematic effects of the cruciate ligaments. Two methods were used for our studies, one method was preferred. This method used a time lapse photograph and strobe light to give us a plot of reference points to carry out our analysis using the method of Rouleaux applied to three dimensions. Five cadaver joints were used, each of which was used for three series of experiments, including the joint with capsule intact, with one of the ligaments cut and with the remaining ligament cut. Both lateral and medial studies were conducted to provide data for a three-dimensional study.

It was found that the cruciate ligaments had little effect on the kinematics of the knee, and that the knee motion remained unchanged after cutting one or both of the cruciate ligaments. It was concluded that the motion of the knee was due to the geometry of the bones and perhaps the collateral ligaments, and that the joint could be replaced with a prosthesis having a three dimensional axis of rotation with a fixed center.     

Apparatus to obtain rotational flexibility of the human knee under moment loads in vivo

The contributions of this paper are twofold. One is the design and performance evaluation of new equipment to determine the rotational flexibility of the human knee in vivo. Since determining knee flexibility requires the application of external loads and the measurement of knee rotations, the new equipment consists of a load application stand and a triaxial goniometer. The triaxial goniometer noninvasively mounts to the leg and directly measures the relative three degrees-of-freedom rotations of the knee sequentially and independently. The goniometer incorporates several unique design features which enhance measurement accuracy. The load stand applies pure varus/valgus and external/internal axial moments either individually or in combination through the use of motors controlled by the test subject. Unique to this design are features which enable the application of moments to the knee which minimise shear forces. Other unique design features permit the stand to control hip and knee flexion angles, muscle contraction, and axial loading. To assess the accuracy with which rotations are measured during experiments, three tests were conducted with the equipment. One test evaluated the inherent accuracy of the goniometer, a second test assessed the potential for goniometer slippage during loading, and a third explored the effect of goniometer mounting on the repeatability of results. A special verification apparatus facilitated evaluation of goniometer inherent accuracy. A second contribution of the paper is an investigation of the effect of foot constraints (i.e. boundary conditions) on flexibility results. To make this investigation, three subjects were tested with the knee at 15 degrees of flexion. Results revealed large differences in flexibility between constraining the foot in both external/internal and varus/valgus rotations and permitting the foot to rotate freely in the direction not being loaded. Further, constraint moments as high as 23 Nm were also recorded. These results emphasise that in order to obtain accurate flexibility results for isolated loads, the foot must be unconstrained by the loading apparatus.     

A new method to investigate in vivo knee behavior using a finite element model of the lower limb

Several finite element models have been developed for estimating the mechanical response of joint internal structures, where direct or indirect in vivo measurement is difficult or impossible. The quality of the predictions made by those models is largely dependent on the quality of the experimental data (e.g. load/displacement) used to drive them. Also numerical problems have been described in the literature when using implicit finite element techniques to simulate problems that involve contacts and large displacements. In this study, a unique strategy was developed combining high accuracy in vivo three-dimensional kinematics and a lower limb finite element model based on explicit finite element techniques. The method presents an analytical technique applied to a dynamic loading condition (impact during hopping on one leg). The validation of the lower limb model focused on the response of the whole model and the knee joint in particular to the imposed 3D femoral in vivo kinematics and ground reaction forces. The approach outlined in this study introduces a generic tool for the study of in vivo knee joint behavior.     

A micromechanical model to predict damage and failure in biological tissues. Application to the ligament-to-bone attachment in the human knee joint

Computational models are developed in injury biomechanics to assess lesions in biological tissues based on mechanical measurements. The linear mechanics of fracture theory (LMFT) is a common approach to establish injuries based on thresholds (such as force or strain thresholds) which are straightforward to implement and computationally efficient. However, LMFT does not apply to non-linear heterogeneous materials and does not have the ability to predict failure onset. This paper proposes the cohesive zone model theory (CZMT) as an alternative. CZMT focuses on the development of behaviour laws for crack initiation and propagation at an interface that apply within a fibrous material or at the interface between materials. With the view of evaluating CZMT for biological tissues, the model developed by Raous et al. [1999. A consistent model coupling adhesion, friction and unilateral contact. Comput. Methods Appl. Mech. Eng., 177, 383–399] was applied to the ligament-to-bone interface in the human knee joint. This model accounts for adhesion, friction and damage at the interface and provides a smooth transition from total adhesion to complete failure through the intensity of adhesion variable. A 2D finite element model was developed to mimic previous experiments, and the model parameters were determined using a dichotomy method. The model showed good results by its ability to predict damage. The extension to a 3D geometry, with an inverse problem approach, is, however, required to better estimate the model parameters values. Although it is computationally costly, CZMT supplements the improvements achieved in microimaging techniques to support the development of micro/macro approaches in biomechanical modelling.     

A point cluster method for in vivo motion analysis: applied to a study of knee kinematics.

A new method for deriving limb segment motion from markers placed on the skin is described. The method provides a basis for determining the artifact associated with nonrigid body movement of points placed on the skin. The method is based on a cluster of points uniformly distributed on the limb segment. Each point is assigned an arbitrary mass. The center of mass and the inertia tensor of this cluster of points are calculated. The eigenvalues and eigenvectors of the inertia tensor are used to define a coordinate system in the cluster as well as to provide a basis for evaluating non-rigid body movement. The eigenvalues of the inertia tensor remain invariant if the segment is behaving as a rigid body, thereby providing a basis for determining variations for nonrigid body movement. The method was tested in a simulation model where systematic and random errors were introduced into a fixed cluster of points. The simulation demonstrated that the error due to nonrigid body movement could be substantially reduced. The method was also evaluated in a group of ten normal subjects during walking. The results for knee rotation and translation obtained from the point cluster method compared favorably to results previously obtained from normal subjects with intra-cortical pins placed into the femur and tibia. The resulting methodology described in this paper provides a unique approach to the measurement of in vivo motion using skin-based marker systems.     

Insulin activation of phosphatidylinositol 3-kinase in human skeletal muscle in vivo

Hickey, Matthew S., Charles J. Tanner, D. Sean O'Neill,Lydia J. Morgan, G. Lynis Dohm, and Joseph A. Houmard. Insulin activation of phosphatidylinositol 3-kinase in human skeletal muscle invivo. J. Appl. Physiol. 83(3):718-722, 1997.The purpose of this investigation was to determinewhether insulin-stimulated phosphatidylinositol 3-kinase (PI3-kinase)activity is detectable in needle biopsies of human skeletal muscle.Sixteen healthy nonobese males matched for age, percent fat, fastinginsulin, and fasting glucose participated in one of two experimentalprotocols. During an intravenous glucose tolerance test (IVGTT)protocol, insulin-stimulated PI3-kinase activity was determined frompercutaneous needle biopsies at 2, 5, and 15 min post-insulinadministration (0.025 U/kg). In the second group, a 2-h, 100 mU · m² · min¹euglycemic hyperinsulinemic clamp was performed, and biopsies wereobtained at 15, 60, and 120 min after insulin infusion was begun.Insulin stimulated PI3-kinase activity by 1.6 ± 0.2-, 2.2 ± 0.3-, and 2.2 ± 0.4-fold at 2, 5, and 15 min, respectively, duringthe IVGTT. During the clamp protocol, PI3-kinase was elevated by 5.3 ± 1.3-, 8.0 ± 2.6-, and 2.7 ± 1.4-fold abovebasal at 15, 60, and 120 min, respectively. Insulin-stimulatedPI3-kinase activity at 15 min post-insulin administration wassignificantly greater during the clamp protocol vs. the IVGTT(P < 0.05). These observations suggest that insulin-stimulated PI3-kinase activity is detectable inneedle biopsies of human skeletal muscle, and furthermore, that theeuglycemic, hyperinsulinemic clamp protocol may be a useful tool toassess insulin signaling in vivo.

     

Computational wear prediction of a total knee replacement from in vivo kinematics

Wear of ultra-high molecular weight polyethylene bearings in total knee replacements remains a major limitation to the longevity of these clinically successful devices. Few design tools are currently available to predict mild wear in implants based on varying kinematics, loads, and material properties. This paper reports the implementation of a computer modeling approach that uses fluoroscopically measured motions as inputs and predicts patient-specific implant damage using computationally efficient dynamic contact and tribological analyses. Multibody dynamic simulations of two activities (gait and stair) with two loading conditions (70-30 and 50-50 medial-lateral load splits) were generated from fluoroscopic data to predict contact pressure and slip velocity time histories for individual elements on the tibial insert surface. These time histories were used in a computational wear analysis to predict the depth of damage due to wear and creep experienced by each element. Predicted damage areas, volumes, and maximum depths were evaluated against a tibial insert retrieved from the same patient who provided the in vivo motions. Overall, the predicted damage was in close agreement with damage observed on the retrieval. The gait and stair simulations separately predicted the correct location of maximum damage on the lateral side, whereas a combination of gait and stair was required to predict the correct location on the medial side. Predicted maximum damage depths were consistent with the retrieval as well. Total computation time for each damage prediction was less than 30 min. Continuing refinement of this approach will provide a robust tool for accurately predicting clinically relevant wear in total knee replacements.     

A new method for measuring passive length-tension properties of human gastrocnemius muscle in vivo

The study of muscle growth and muscle length adaptations requires measurement of passive length-tension properties of individual muscles, but until now such measurements have only been made in animal muscles. We describe a new method for measuring passive length-tension properties of human gastrocnemius muscles in vivo. Passive ankle torque and ankle angle data were obtained as the ankle was rotated through its full range with the knee in a range of positions. To extract gastrocnemius passive length-tension curves from passive torque-angle data it was assumed that passive ankle torque was the sum of torque due to structures which crossed only the ankle joint (this torque was a 6-parameter function of ankle joint angle) and a torque due to the gastrocnemius muscle (a 3-parameter function of knee and ankle angle). Parameter values were estimated with non-linear regression and used to reconstruct passive length-tension curves of the gastrocnemius. The reliability of the method was examined in 11 subjects by comparing three sets of measurements: two on the same day and the other at least a week later. Length-tension curves were reproducible: the average root mean square error was 5.1+/-1.1 N for pairs of measurements taken within a day and 7.3+/-1.2 N for pairs of measurements taken at least a week apart (about 3% and 6% of maximal passive tension, respectively). Length-tension curves were sensitive to mis-specification of moment arms, but changes in length-tension curves were not. The new method enables reliable measurement of passive length-tension properties of human gastrocnemius in vivo, and is likely to be useful for investigation of changes in length-tension curves over time.     

A model for steady isometric muscle activation

The present model of the motoneuronal (MN) pool – muscle complex (MNPMC) is deterministic and designed for steady isometric muscle activation. Time-dependent quantities are treated as time-averages. The character of the model is continuous in the sense that the motor unit (MU) population is described by a continuous density function. In contrast to most already published models, the wiring (synaptic weight) between the input fibers to the MNPMC and the MNs (about which no detailed data are known) is deduced, whereas the input–force relation is given. As suggested by experimental data, this relation is assumed to be linear during MU recruitment, but the model allows other, nonlinear relations. The input to the MN pool is defined as the number of action potentials per second in all input fibers, and the excitatory postsynaptic potential (EPSP) conductance in MNs evoked by the input is assumed to be proportional to the input. A single compartment model with a homogeneous membrane is used for a MN. The MNs start firing after passing a constant voltage threshold. The synaptic current–frequency relation is described by a linear function and the frequency–force transformation of a MU by an exponential function. The sum of the MU contraction forces is the muscle force, and the activation of the MUs obeys the size principle. The model parameters were determined a priori, i.e., the model was not used for their estimation. The analysis of the model reveals special features of the activation curve which we define as the relation between the input normalized by the threshold input of the MN pool and the force normalized by the maximal muscle force. This curve for any muscle turned out to be completely determined by the activation factor, the slope of the linear part of the activation curve (during MU recruitment). This factor determines quantitatively the relation between MU recruitment and rate modulation. This property of the model (the only known model with this property) allows a quantification of the recruitment gain (Kernell and Hultborn 1990). The interest of the activation factor is illustrated using two human muscles, namely the first dorsal interosseus muscle, a small muscle with a relatively small force at the end of recruitment, and the medial gastrocnemius muscle, a strong muscle with a relatively large force at the end of recruitment. It is concluded that the present model allows us to reproduce the main features of muscle activation in the steady state. Its analytical character facilitates a deeper understanding of these features. Received: 24 November 1997 / Accepted in revised form: 30 November 1998     

Individual muscle contributions to knee joint impedance following a sudden perturbation: An in vivo inverted pendulum model

Previous research has suggested that muscle forces, generated by reflexes, contribute to joint stability prior to the more coordinated voluntary muscle forces. The purpose of the current study was to quantify the behaviour of the leg muscles, through the calculation of individual muscle contributions to joint rotational impedance (MJRI), with a specific interest in the neuromuscular contribution in the period following shortly after a sudden knee extension perturbation. The knee was selected as an in vivo system to represent an inverted pendulum model. Kinematic and sEMG data were collected while subjects were in a prone position and exposed to sudden knee extension perturbations. A biomechanical model was used to estimate muscle forces and moments about the knee and these data were then used to calculate instantaneous MJRI. Data indicated that pre-voluntary muscle forces do contribute significantly to MJRI following a sudden knee extension perturbation as there was a 40% increase in total MJRI in the flexion/extension and valgus/varus axes immediately following the perturbation, suggesting their importance in stabilizing the joint immediately after a disturbance. Additionally, knowledge of perturbation timing was shown to increase anticipatory MJRI levels, pre-perturbation (p < 0.05), indicating that it is advantageous for the neuromuscular system to prepare for a sudden disturbance. In conclusion, the data show that the neuromuscular feedback system significantly contributes to MJRI and it is believed that this behaviour enhances joint impedance following a sudden knee extension perturbation.     

A validated model of passive skeletal muscle to predict force and intramuscular pressure

The passive properties of skeletal muscle are often overlooked in muscle studies, yet they play a key role in tissue function in vivo. Studies analyzing and modeling muscle passive properties, while not uncommon, have never investigated the role of fluid content within the tissue. Additionally, intramuscular pressure (IMP) has been shown to correlate with muscle force in vivo and could be used to predict muscle force in the clinic. In this study, a novel model of skeletal muscle was developed and validated to predict both muscle stress and IMP under passive conditions for the New Zealand White Rabbit tibialis anterior. This model is the first to include fluid content within the tissue and uses whole muscle geometry. A nonlinear optimization scheme was highly effective at fitting model stress output to experimental stress data (normalized mean square error or NMSE fit value of 0.993) and validation showed very good agreement to experimental data (NMSE fit values of 0.955 and 0.860 for IMP and stress, respectively). While future work to include muscle activation would broaden the physiological application of this model, the passive implementation could be used to guide surgeries where passive muscle is stretched.     

A three-dimensional whole-body model to predict human walking on level ground

Predictive simulation of human walking has great potential in clinical motion analysis and rehabilitation engineering assessment, but large computational cost and reliance on measurement data to provide initial guess have limited its wide use. We developed a computationally efficient model combining optimization and inverse dynamics to predict three-dimensional whole-body motions and forces during human walking without relying on measurement data. Using the model, we explored two different optimization objectives, mechanical energy expenditure and the time integral of normalized joint torque. Of the two criteria, the sum of the time integrals of the normalized joint torques produced a more realistic walking gait. The reason for this difference is that most of the mechanical energy expenditure is in the sagittal plane (based on measurement data) and this leads to difficulty in prediction in the other two planes. We conclude that mechanical energy may only account for part of the complex performance criteria driving human walking in three dimensions.

     

Approximation of the functional kinematics of posterior stabilised total knee replacements using a two-dimensional sagittal plane patello-femoral model: comparing model approximation to in vivo measurement

Previous in vivo studies have observed that current designs of posterior stabilised (PS) total knee replacements (TKRs) may be ineffective in restoring normal kinematics in Late flexion. Computer-based models can prove a useful tool in improving PS knee replacement designs. This study investigates the accuracy of a two-dimensional (2D) sagittal plane model capable of predicting the functional sagittal plane kinematics of PS TKR implanted knees against direct in vivo measurement. Implant constraints are often used as determinants of anterior–posterior tibio-femoral positioning. This allowed the use of a patello-femoral modelling approach to determine the effect of implant constraints. The model was executed using motion simulation software which uses the constraint force algorithm to achieve a solution. A group of 10 patients implanted with Scorpio PS implants were recruited and underwent fluoroscopic imaging of their knees. The fluoroscopic images were used to determine relative implant orientation using a three-dimensional reconstruction method. The determined relative tibio-femoral orientations were then input to the model. The model calculated the patella tendon angles (PTAs) which were then compared with those measured from the in vivo fluoroscopic images. There were no significant differences between the measured and calculated PTAs. The average root mean square error between measured and modelled ranged from 1.17° to 2.10° over the flexion range. A sagittal plane patello-femoral model could conceivably be used to predict the functional 2D kinematics of an implanted knee joint. This may prove particularly useful in optimising PS designs.