A parametric approach to numerical modeling of TKR contact forces

In vivo knee contact forces are difficult to determine using numerical methods because there are more unknown forces than equilibrium equations available. We developed parametric methods for computing contact forces across the knee joint during the stance phase of level walking. Three-dimensional contact forces were calculated at two points of contact between the tibia and the femur, one on the lateral aspect of the tibial plateau, and one on the medial side. Muscle activations were parametrically varied over their physiologic range resulting in a solution space of contact forces. The obtained solution space was reasonably small and the resulting force pattern compared well to a previous model from the literature for kinematics and external kinetics from the same patient. Peak forces of the parametric model and the previous model were similar for the first half of the stance phase, but differed for the second half. The previous model did not take into account the transverse external moment about the knee and could not calculate muscle activation levels. Ultimately, the parametric model will result in more accurate contact force inputs for total knee simulators, as current inputs are not generally based on kinematics and kinetics inputs from TKR patients.     

Subject-specific hip geometry affects predicted hip joint contact forces during gait

Hip loading affects bone remodeling and implant fixation. In this study, we have analyzed the effect of subject-specific modeling of hip geometry on muscle activation patterns and hip contact forces during gait, using musculoskeletal modeling, inverse dynamic analysis and static optimization. We first used sensitivity analysis to analyze the effect of isolated changes in femoral neck-length (NL) and neck-shaft angle (NSA) on calculated muscle activations and hip contact force during the stance phase of gait. A deformable generic musculoskeletal model was adjusted incrementally to adopt a physiological range of NL and NSA. In a second similar analysis, we adjusted hip geometry to the measurements from digitized radiographs of 20 subjects with primary hip osteoarthrosis. Finally, we studied the effect of hip abductor weakness on muscle activation patterns and hip contact force. This analysis showed that differences in NL (41-74 mm) and NSA (113-140 degrees ) affect the muscle activation of the hip abductors during stance phase and hence hip contact force by up to three times body weight. In conclusion, the results from both the sensitivity and subject-specific analysis showed that at the moment of peak contact force, altered NSA has only a minor effect on the loading configuration of the hip. Increased NL, however, results in an increase of the three hip contact-force components and a reduced vertical loading. The results of these analyses are essential to understand modified hip joint loading, and for planning hip surgery for patients with osteoarthrosis.     

Subject-specific hip geometry and hip joint centre location affects calculated contact forces at the hip during gait

Hip loading affects the development of hip osteoarthritis, bone remodelling and osseointegration of implants. In this study, we analyzed the effect of subject-specific modelling of hip geometry and hip joint centre (HJC) location on the quantification of hip joint moments, muscle moments and hip contact forces during gait, using musculoskeletal modelling, inverse dynamic analysis and static optimization. For 10 subjects, hip joint moments, muscle moments and hip loading in terms of magnitude and orientation were quantified using three different model types, each including a different amount of subject-specific detail: (1) a generic scaled musculoskeletal model, (2) a generic scaled musculoskeletal model with subject-specific hip geometry (femoral anteversion, neck-length and neck-shaft angle) and (3) a generic scaled musculoskeletal model with subject-specific hip geometry including HJC location. Subject-specific geometry and HJC location were derived from CT. Significant differences were found between the three model types in HJC location, hip flexion–extension moment and inclination angle of the total contact force in the frontal plane. No model agreement was found between the three model types for the calculation of contact forces in terms of magnitude and orientations, and muscle moments. Therefore, we suggest that personalized models with individualized hip joint geometry and HJC location should be used for the quantification of hip loading. For biomechanical analyses aiming to understand modified hip joint loading, and planning hip surgery in patients with osteoarthritis, the amount of subject-specific detail, related to bone geometry and joint centre location in the musculoskeletal models used, needs to be considered.     

Influence of altered gait patterns on the hip joint contact forces

Children who exhibit gait deviations often present a range of bone deformities, particularly at the proximal femur. Altered gait may affect bone growth and lead to deformities by exerting abnormal stresses on the developing bones. The objective of this study was to calculate variations in the hip joint contact forces with different gait patterns. Muscle and hip joint contact forces of four children with different walking characteristics were calculated using an inverse dynamic analysis and a static optimisation algorithm. Kinematic and kinetic analyses were based on a generic musculoskeletal model scaled down to accommodate the dimensions of each child. Results showed that for all the children with altered gaits both the orientation and magnitude of the hip joint contact force deviated from normal. The child with the most severe gait deviations had hip joint contact forces 30% greater than normal, most likely due to the increase in muscle forces required to sustain his crouched stance. Determining how altered gait affects joint loading may help in planning treatment strategies to preserve correct loading on the bone from a young age.     

A novel gait platform to measure isolated plantar metatarsal forces during walking

A new gait platform described in this report allows an isolated measurement of the vertical and shear forces under an individual metatarsal head during barefoot walking. The apparatus incorporated a customized tactile force sensor and a high-speed camera system, which enabled easy identification of a single anatomical landmark at the forefoot’s plantar surface that is in contact with the sensor throughout stance. After calibration, the measured peak forces under the 2nd MTH showed variability of 3.7%, 9.2%, and 8.9% in vertical, anterior–posterior, and medial–lateral directions, respectively. The device therefore provides information about the magnitude and timing of such local metatarsal forces, and has been shown to be of significant research and clinical interest. Its ability to achieve this with a high degree of accuracy ensures its potential as a valuable research tool.     

Stability-normalised walking speed: A new approach for human gait perturbation research

In gait stability research, neither self-selected walking speeds, nor the same prescribed walking speed for all participants, guarantee equivalent gait stability among participants. Furthermore, these options may differentially affect the response to different gait perturbations, which is problematic when comparing groups with different capacities. We present a method for decreasing inter-individual differences in gait stability by adjusting walking speed to equivalent margins of stability (MoS). Eighteen healthy adults walked on a split-belt treadmill for two-minute bouts at 0.4 m/s up to 1.8 m/s in 0.2 m/s intervals. The stability-normalised walking speed (MoS = 0.05 m) was calculated using the mean MoS at touchdown of the final 10 steps of each speed. Participants then walked for three minutes at this speed and were subsequently exposed to a treadmill belt acceleration perturbation. A further 12 healthy adults were exposed to the same perturbation while walking at 1.3 m/s: the average of the previous group. Large ranges in MoS were observed during the prescribed speeds (6–10 cm across speeds) and walking speed significantly (P < 0.001) affected MoS. The stability-normalised walking speeds resulted in MoS equal or very close to the desired 0.05 m and reduced between-participant variability in MoS. The second group of participants walking at 1.3 m/s had greater inter-individual variation in MoS during both unperturbed and perturbed walking compared to 12 sex, height and leg length-matched participants from the stability-normalised walking speed group. The current method decreases inter-individual differences in gait stability which may benefit gait perturbation and stability research, in particular studies on populations with different locomotor capacities. [Preprint: https://doi.org/10.1101/314757]     

A parametric method for cumulative incidence modeling with a new four-parameter log-logistic distribution

Background

The invasion of a new species into an established ecosystem can be directly compared to the steps involved in cancer metastasis. Cancer must grow in a primary site, extravasate and survive in the circulation to then intravasate into target organ (invasive species survival in transport). Cancer cells often lay dormant at their metastatic site for a long period of time (lag period for invasive species) before proliferating (invasive spread). Proliferation in the new site has an impact on the target organ microenvironment (ecological impact) and eventually the human host (biosphere impact).

Results

Tilman has described mathematical equations for the competition between invasive species in a structured habitat. These equations were adapted to study the invasion of cancer cells into the bone marrow microenvironment as a structured habitat. A large proportion of solid tumor metastases are bone metastases, known to usurp hematopoietic stem cells (HSC) homing pathways to establish footholds in the bone marrow. This required accounting for the fact that this is the natural home of hematopoietic stem cells and that they already occupy this structured space. The adapted Tilman model of invasion dynamics is especially valuable for modeling the lag period or dormancy of cancer cells.

Conclusions

The Tilman equations for modeling the invasion of two species into a defined space have been modified to study the invasion of cancer cells into the bone marrow microenvironment. These modified equations allow a more flexible way to model the space competition between the two cell species. The ability to model initial density, metastatic seeding into the bone marrow and growth once the cells are present, and movement of cells out of the bone marrow niche and apoptosis of cells are all aspects of the adapted equations. These equations are currently being applied to clinical data sets for verification and further refinement of the models.     

Ground reaction forces during termination of human gait.

This is the first published report of the ground reaction forces during gait termination. Two mechanisms appear to be used to stop walking: increased braking forces and decreased push-off force. There appears to be a short interval of time during the gait cycle in which a decision to take an additional step is to be made.     

Influence of weak hip abductor muscles on joint contact forces during normal walking: probabilistic modeling analysis

The weakness of hip abductor muscles is related to lower-limb joint osteoarthritis, and joint overloading may increase the risk for disease progression. The relationship between muscle strength, structural joint deterioration and joint loading makes the latter an important parameter in the study of onset and follow-up of the disease. Since the relationship between hip abductor weakness and joint loading still remains an open question, the purpose of this study was to adopt a probabilistic modeling approach to give insights into how the weakness of hip abductor muscles, in the extent to which normal gait could be unaltered, affects ipsilateral joint contact forces. A generic musculoskeletal model was scaled to each healthy subject included in the study, and the maximum force-generating capacity of each hip abductor muscle in the model was perturbed to evaluate how all physiologically possible configurations of hip abductor weakness affected the joint contact forces during walking. In general, the muscular system was able to compensate for abductor weakness. The reduced force-generating capacity of the abductor muscles affected joint contact forces to a mild extent, with 50th percentile mean differences up to 0.5 BW (maximum 1.7 BW). There were greater increases in the peak knee joint loads than in loads at the hip or ankle. Gluteus medius, particularly the anterior compartment, was the abductor muscle with the most influence on hip and knee loads. Further studies should assess if these increases in joint loading may affect initiation and progression of osteoarthritis.     

Musculoskeletal model choice influences hip joint load estimations during gait

The prevalence of musculoskeletal modeling studies investigating hip contact forces and the number of models used to conduct such investigations has increased in recent years. However, the consistency between models remain unknown and differences in model predicted hip contact forces between studies are difficult to distinguish from natural inter-individual differences. The purpose of this study was therefore to evaluate differences in hip joint contact forces during gait between four OpenSim models. These models included the generic models gait2392 and the Arnold Lower Limb Model, as well as the hip specific models hip2372 and London Lower Limb Model. Data from four individuals who have had a total hip replacement with instrumented hip implants performing slow, normal, and fast walking trials were taken from the HIP98 database to evaluate the various models effectiveness at estimating hip loads. Muscle forces were estimated using static optimization and hip contact forces were calculated using the JointReaction analysis in OpenSim. Results indicated that, for gait, the hip specific London Lower Limb Model consistently predicted peak push-off hip joint contact forces with lower magnitude and timing errors compared to the other models. Likewise, root mean square error values were lowest and correlation coefficients were highest for the London Lower Limb Model. These results suggest that the London Lower Limb Model is the most appropriate model for investigations focused on hip joint loading.     

Mathematical modelling of stress in the hip during gait.

A mathematical model is developed for calculating the contact stress distribution in the hip for a known resultant hip force and characteristic geometrical parameters. Using a relatively simple single nonlinear algebraic equation, the model can be readily applied in clinical practice to estimate the stress distribution in the most frequent body positions of everyday activities. This is demonstrated by analyzing the data on the resultant hip force obtained from laboratory observations where a stance period of gait is considered.     

A new approach to modeling daily probabilities of conception

Standard conception probabilities models assume that different acts of intercourse make independent contributions to the probability of conception in viable cycles. We propose an alternative, approximate model based on the assumption that the act of intercourse closest to the time of maximum fertility is the one most likely to have caused conception. We describe an adaptive algorithm [the most fertile intercourse day (MFID) algorithm] that estimates the most fertile intercourse day in each cycle. The approach is easily extended to include covariates and random between-couple differences in fecundability that affect the probability of conception in a given cycle. Reanalyses of two data sets reported in the literature are presented. Estimates of the probability of conception during the most fertile period of the cycle and of the effects of covariates are similar to estimates found using standard models.     

Internal forces and moments in the femur of the rat during gait

The rat is of increasing importance for experimental studies on fracture healing. The healing outcome of long bone fractures is strongly influenced by mechanical factors, such as the interfragmentary movement. This movement depends on the stability of the fracture fixation and the musculoskeletal loads. However, little is known about these loads in rats.The musculoskeletal loads during gait were estimated using an inverse-dynamic musculoskeletal model of the right hindlimb of the rat. This model was based on a micro-CT scan of the lower extremities and an anatomical study using 15 rat cadavers. Kinematics were reconstructed from X-ray movies, taken simultaneously from two perpendicular directions during a gait cycle. The ground reaction forces were taken from the literature. The muscle forces were calculated using an optimization procedure.The internal forces and moments varied over the gait cycle and along the femoral axis. The greatest internal force (up to 7 times bodyweight) acted in the longitudinal direction. The greatest internal moment (up to 13.8 bodyweight times millimeter) acted in the sagittal plane of the femur. The validity of the model was corroborated by comparing the estimated strains caused by the calculated loads on the surface of the femoral mid-shaft with those from the literature.Knowledge of the internal loads in the femur of the rat allows adjustment of the biomechanical properties of fixation devices in fracture healing studies to the desired interfragmentary movement.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.     

A mechanical device for leg disturbance during gait

A method of applying a mometary mechanical stimulus to a human leg at any selected time during treadmill locomotion is described. The stimulus is produced by the breaking of a loop of fine copper wire by means of a motor and clutch device. An electrical signal at the time of stimulus is provided and the apparatus has no detrimental effect on normal walking.     

In vivo hip joint loads and pedal forces during ergometer cycling

The rising prevalence of osteoarthritis and an increase in total hip replacements calls for attention to potential therapeutic activities. Cycling is considered as a low impact exercise for the hip joint and hence recommended. However, there are limited data about hip joint loading to support this claim. The aim of this study was to measure synchronously the in vivo hip joint loads and pedal forces during cycling. The in vivo hip joint loads were measured in 5 patients with instrumented hip implants. Data were collected at several combinations of power and cadence, at two saddle heights.Joint loads and pedal forces showed strong linear correlation with power. So the relationship between the external pedal forces and internal joint forces was shown. While cycling at different cadences the minimum joint loads were acquired at 60 RPM. The lower saddle height configuration results in an approximately 15% increase compared to normal saddle height.The results offered new insights into the actual effects of cycling on the hip joint and can serve as useful tools while developing an optimum cycling regimen for individuals with coxarthrosis or following total hip arthroplasty. Due to the relatively low contact forces, cycling at a moderate power level of 90 W at a normal saddle height is suitable for patients.     

A dynamic optimization technique for predicting muscle forces in the swing phase of gait

The muscle force sharing problem was solved for the swing phase of gait using a dynamic optimization algorithm. For comparison purposes the problem was also solved using a typical static optimization algorithm. The objective function for the dynamic optimization algorithm was a combination of the tracking error and the metabolic energy consumption. The latter quantity was taken to be the sum of the total work done by the muscles and the enthalpy change during the contraction. The objective function for the static optimization problem was the sum of the cubes of the muscle stresses. To solve the problem using the static approach, the inverse dynamics problem was first solved in order to determine the resultant joint torques required to generate the given hip, knee and ankle trajectories. To this effect the angular velocities and accelerations were obtained by numerical differentiation using a low-pass digital filter. The dynamic optimization problem was solved using the Fletcher-Reeves conjugate gradient algorithm, and the static optimization problem was solved using the Gradient-restoration algorithm. The results show influence of internal muscle dynamics on muscle control histories vis a vis muscle forces. They also illustrate the strong sensitivity of the results to the differentiation procedure used in the static optimization approach.     

A multiphysics approach for modeling early atherosclerosis

This work is devoted to the development of a mathematical model of the early stages of atherosclerosis incorporating processes of all time scales of the disease and to show their interactions. The cardiovascular mechanics is modeled by a fluid–structure interaction approach coupling a non-Newtonian fluid to a hyperelastic solid undergoing anisotropic growth and a change of its constitutive equation. Additionally, the transport of low-density lipoproteins and its penetration through the endothelium is considered by a coupled set of advection–diffusion-reaction equations. Thereby, the permeability of the endothelium is wall-shear stress modulated resulting in a locally varying accumulation of foam cells triggering a novel growth and remodeling formulation. The model is calibrated and applied to an murine-specific case study, and a qualitative validation of the computational results is performed. The model is utilized to further investigate the influence of the pulsatile blood flow and the compliance of the artery wall to the atherosclerotic process. The computational results imply that the pulsatile blood flow is crucial, whereas the compliance of the aorta has only a minor influence on atherosclerosis. Further, it is shown that the novel model is capable to produce a narrowing of the vessel lumen inducing an adaption of the endothelial permeability pattern.     

A system for modelling forces on the hip joint in one-legged stance

We describe a method of testing hip prostheses. The prosthesis is implanted in a proximal section of femur, which is loaded to model the forces applied through the acetabulum via the greater trochanter.     

A finite element model of the lower limb during stance phase of gait cycle including the muscle forces

Background

Results of finite element (FE) analyses can give insight into musculoskeletal diseases if physiological boundary conditions, which include the muscle forces during specific activities of daily life, are considered in the FE modelling. So far, many simplifications of the boundary conditions are currently made. This study presents an approach for FE modelling of the lower limb for which muscle forces were included.

Methods

The stance phase of normal gait was simulated. Muscle forces were calculated using a musculoskeletal rigid body (RB) model of the human body, and were subsequently applied to a FE model of the lower limb. It was shown that the inertial forces are negligible during the stance phase of normal gait. The contact surfaces between the parts within the knee were modelled as bonded. Weak springs were attached to the distal tibia for numerical reasons.

Results

Hip joint reaction forces from the RB model and those from the FE model were similar in magnitude with relative differences less than 16%. The forces of the weak spring were negligible compared to the applied muscle forces. The maximal strain was 0.23% in the proximal region of the femoral diaphysis and 1.7% in the contact zone between the tibia and the fibula.

Conclusions

The presented approach based on FE modelling by including muscle forces from inverse dynamic analysis of musculoskeletal RB model can be used to perform analyses of the lower limb with very realistic boundary conditions. In the present form, this model can be used to better understand the loading, stresses and strains of bones in the knee area and hence to analyse osteotomy fixation devices.