Reducing ground reaction forces in gymnastics’ landings may increase internal loading

The aim of this study was to use a subject-specific seven-link wobbling mass model of a gymnast, and a multi-layer model of a landing mat, to determine landing strategies that minimise ground reaction forces (GRF) and internal forces. Subject-specific strength parameters were determined that defined the maximum voluntary torque/angle/angular velocity relationship at each joint. These relationships were used to produce subject-specific ‘lumped’ linear muscle models for each joint. Muscle activation histories were optimised using a Simplex algorithm to minimise GRF or bone bending moments for forward and backward rotating vault landings. Optimising the landing strategy to minimise each of the GRF reduced the peak vertical and horizontal GRF by 9% for the backward rotating vault and by 8% and 48% for the forward rotating vault, compared to a matching simulation. However, most internal loading measures (bone bending moments, joint reaction forces and muscle forces) increased compared to the matching simulation. Optimising the landing strategy to minimise the peak bone bending moments resulted in reduced internal loading measures, and in most cases reduced GRF. Bone bending moments were reduced by 27% during the forward rotating vault and by 2% during the backward rotating vault landings when compared to the matching simulations. It is possible for a gymnast to modify their landing strategy in order to minimise internal forces and lower GRF. However, using a reduction in GRF, due to a change in landing strategy, as a basis for a reduction in injury potential in vaulting movements may not be appropriate since internal loading can increase.     

The influence of muscle model complexity in musculoskeletal motion modeling

A comparative study of four different muscle models in a musculoskeletal motion problem is made. The models vary in complexity from the simple input-output model to the more complex model of Hatze [1]. These models are used to solve a minimum time kicking problem using an optimal control algorithm. The results demonstrate the strong influence of the model choice on the various predicted kinematic and kinetic parameters in the problem. The study illustrates some of the advantages and disadvantages involved in trade-offs between model complexity and practicability in musculoskeletal motion studies. The results also illustrate the importance of appropriate detailed parameter estimation studies in the mathematical modeling of the musculoskeletal system.     

Computer simulation of the effects of shoe cushioning on internal and external loading during running impacts

Biomechanical aspects of running injuries are often inferred from external loading measurements. However, previous research has suggested that relationships between external loading and potential injury-inducing internal loads can be complex and nonintuitive. Further, the loading response to training interventions can vary widely between subjects. In this study, we use a subject-specific computer simulation approach to estimate internal and external loading of the distal tibia during the impact phase for two runners when running in shoes with different midsole cushioning parameters. The results suggest that: (1) changes in tibial loading induced by footwear are not reflected by changes in ground reaction force (GRF) magnitudes; (2) the GRF loading rate is a better surrogate measure of tibial loading and stress fracture risk than the GRF magnitude; and (3) averaging results across groups may potentially mask differential responses to training interventions between individuals.     

Making sense of parameter estimation and model simulation in bioprocesses

Most articles that report fitted parameters for kinetic models do not include meaningful statistical information. This study demonstrates the importance of reporting a complete statistical analysis and shows a methodology to perform it, using functionalities implemented in computational tools. As an example, alginate production is studied in a batch stirred-tank fermenter and modeled using the kinetic model proposed by Klimek and Ollis (1980). The model parameters and their 95% confidence intervals are estimated by nonlinear regression. The significance of the parameters value is checked using a hypothesis test. The uncertainty of the parameters is propagated to the output model variables through prediction intervals, showing that the kinetic model of Klimek and Ollis (1980) can simulate with high certainty the dynamic of the alginate production process. Finally, the results obtained in other studies are compared to show how the lack of statistical analysis can hold back a deeper understanding about bioprocesses.     

Numerical simulation of hemodynamics in stented internal carotid aneurysm based on patient-specific model

There is still a considerable lack of quantitative information concerning the effects of stent structures on blood flow in an aneurismal cavity. In this paper, five virtual stents with different structures and wire cross-sections were designed for incorporation into the same patient-specific aneurysm model. Computational fluid dynamics simulations were performed so as to study how these five types of stents modified hemodynamic parameters. Numerical results demonstrated that the mean flow rate in the aneurismal cavity decreased the most in the model that used a stent with a rectangular wire cross-section, and that the wall shear stresses at the dome and neck of the aneurysm decreased more in models that used a stent with a circular wire cross-section or a spiral stent with a rectangular wire cross-section compared to other models. In addition, the wall pressure on the aneurysm increased slightly after implantation of the stent in all five models. This result differs from that previously published, and may help guide the design and assist clinicians in selecting an appropriate stent for treating cerebral aneurysms.     

The internal mechanics of the intervertebral disc under cyclic loading

The mechanics of the intervertebral disc (IVD) under cyclic loading are investigated via a one-dimensional poroelastic model and experiment. The poroelastic model, based on that of Biot (J. Appl. Phys. 12 (1941) 155; J. Appl. Mech. 23 (1956) 91), includes a power-law relation between porosity and permeability, and a linear relation between the osmotic potential and solidity. The model was fitted to experimental data of the unconfined IVD undergoing 5 cyclic loads of 20 min compression by an applied stress of 1MPa, followed by 40 min expansion. To obtain a good agreement between experiment and theory, the initial elastic deformation of the IVD, possibly associated with the bulging of the IVD into the vertebral bodies or laterally, was removed from the experimental data. Many combinations of the permeability-porosity relationship with the initial osmotic potential (pi(i)) were investigated, and the best-fit parameters for the aggregate modulus (H(A)) and initial permeability (k(i)) were determined. The values of H(A) and k(i) were compared to literature values, and agreed well especially in the context of the adopted high-stress testing regime, and the strain related permeability in the model.     

The time delays influence on the dynamical complexity of algal blooms in the presence of bacteria

Bacteria associated with oceanic algal blooms are acknowledged to play important roles in carbon, nitrogen, and sulfur cycling. They influence the climate, mediate primary production, participate in biogeochemical cycles, and maintain ecological balance. A greater insight on the control of the interactions between microalgae and other microorganisms, particularly bacteria, would be helpful in exploring the role of bacteria on algal blooms in lakes. The present study is to investigate the effects of bacteria on the occurrence of algal blooms in lakes. We propose a nonlinear mathematical model by taking into account interactions among nutrients, algae, detritus and bacteria in a lake. We assume that bacteria enhance the growth of algal biomass through remineralization only. Equilibria are analyzed for feasibility and stability, substantiated via numerical simulations. Increase in uptake rate of nutrients by algae and bacteria death rate generates transcritical bifurcations. We perform a global sensitivity analysis to identify the important parameters of the model having a significant impact on the densities of algae and bacteria in the lake. Our findings show that massive algal production might occur in the presence of bacteria, and microalgae-bacteria interactions can be beneficial to the massive production of microalgae. Further, the effect of time delays involved in the bacterial decomposition conversion of detritus into nutrients is studied. Chaotic oscillations may arise via equilibrium destabilization on increasing the values of the time lag. To support chaos occurrence, the Poincaré map is drawn and the Lyapunov exponents are also computed. The findings, critically important for lake restoration, indicate that hypoxia in the lake can be prevented if detritus removal is performed on a regular basis, at time intervals smaller than the critical threshold in the delay with which detritus is decomposed into nutrients.     

The influence of concentric and eccentric loading on the finger pulley system

In this study we investigated the influence of the loading condition (concentric vs. eccentric loading) on the pulley system of the finger. For this purpose 39 cadaver finger (14 hands, 10 donors) were fixed into an isokinetic loading device. The forces in the flexor tendons and at the fingertip were recorded. In the concentric loading condition A2 and A4 ruptures as well as alternative events such as fracture of a phalanx or avulsion of the flexor tendons were almost equally distributed, whereas the A2 pulley rupture was the most common event (59%) in the eccentric loading condition and alternative events were rare (23.5%). The forces in the deep flexor tendon, the fingertip and in the pulleys were significantly lower in the eccentric loading condition. As the ruptures occurred at lower loads in the eccentric than in the concentric loading condition it can be concluded that friction may be an advantage for climbers, supporting the holding force of their flexor muscles but may also increase the susceptibility to injury.     

The effect of muscle loading on the simulation of bone remodelling in the proximal femur

A large number of finite element analyses of the proximal femur rely on a simplified set of muscle and joint contact loads to represent the boundary conditions of the model. In the context of bone remodelling analysis around hip implants, muscle loading affects directly the spatial distribution of the remodelling signal. In the present study we performed a sensitivity analysis on the effect of different muscle loading configurations on the outcome of the bone remodelling simulation. An anatomical model of the femur with the implanted stem in place was constructed using the CT data of the Visible Human Project dataset of the National Institute of Health. The model was loaded with three muscle force configurations with increasing level of complexity. A strain adaptive remodelling rule was employed to simulate the post-operative bone changes around the implant stem and the results of the simulation were assessed quantitatively in terms of the bone mineral content changes in 18 periprosthetic regions of interest. The results showed considerable differences in the amount of bone loss predicted between the three cases. The simplified models generally predicted more pronounced bone loss. Although the overall remodelling patterns observed were similar, the bone conserving effect of additional muscle forces in the vicinity of their areas of attachment was clear. The results of this study suggest that the loading configuration of the FE model does play an important role in the outcome of the remodelling simulation.     

Bone morphology allows estimation of loading history in a murine model of bone adaptation

Bone adapts its morphology (density/micro- architecture) in response to the local loading conditions in such a way that a uniform tissue loading is achieved (‘Wolff’s law’). This paradigm has been used as a basis for bone remodeling simulations to predict the formation and adaptation of trabecular bone. However, in order to predict bone architectural changes in patients, the physiological external loading conditions, to which the bone was adapted, need to be determined. In the present study, we developed a novel bone loading estimation method to predict such external loading conditions by calculating the loading history that produces the most uniform bone tissue loading. We applied this method to murine caudal vertebrae of two groups that were in vivo loaded by either 0 or 8 N, respectively. Plausible load cases were sequentially applied to micro-finite element models of the mice vertebrae, and scaling factors were calculated for each load case to derive the most uniform tissue strain-energy density when all scaled load cases are applied simultaneously. The bone loading estimation method was able to predict the difference in loading history of the two groups and the correct load magnitude for the loaded group. This result suggests that the bone loading history can be estimated from its morphology and that such a method could be useful for predicting the loading history for bone remodeling studies or at sites where measurements are difficult, as in bone in vivo or fossil bones.     

The influence of model parameters on model validation

The study examined the sensitivity of two musculoskeletal models to the parameters describing each model. Two different models were examined: a phenomenological model of human jumping with parameters based on live subject data, and the second a model of the First Dorsal Interosseous with parameters based on cadaveric measurements. Both models were sensitive to the model parameters, with the use of mean group data not producing model outputs reflective of either the performance of any group member or the mean group performance. These results highlight the value of subject specific model parameters, and the problems associated with model validation.     

The influence of mechanical loading on isolated chondrocytes seeded in agarose constructs

Articular cartilage is subjected to dynamic compressive loading during normal activity which influences chondrocyte metabolism through various mechanotransduction pathways. A well characterised and reproducible model system, involving chondrocytes embedded in agarose gel, has been used to investigate the effects of mechanical compression on chondrocytes, isolated from full depth cartilage or separately from the superficial and deep zone tissue. The role of nitric oxide as a mediator of mechanical-induced effects has also been studied. Chondrocytes were isolated, separately, from full depth, superficial and deep zone cartilage and seeded in 3% agarose constructs. Dynamic compressive strain was applied to the constructs using a range of frequencies (0.3, 1 and 3 Hz). Glycosaminoglycan synthesis, cell proliferation and nitrite production were assessed. In further experiments, constructs were compressed in the presence of 1 mM L-NAME or 10 microM dexamethasone. Glycosaminoglycan synthesis by full depth chondrocytes was affected by compressive strain in a frequency dependent manner. Dynamic strain at all frequencies induced an increase in [3H]-thymidine incorporation. Glycosaminoglycan synthesis by deep zone cells was affected by the strain regimes in a similar fashion to full depth cells, while superficial cells exhibited a similar proliferative response to full depth cells. Dynamic compression inhibited nitrite production, the effect being reversed by L-NAME. Compression induced stimulation of [3H]-TdR incorporation was reversed by L-NAME. These studies demonstrate that glycosaminoglycan synthesis and proliferation are influenced by the dynamic strain regimes in a distinct manner. Indeed the data suggest that these processes occur in different chondrocyte sub-populations. It may be speculated that nitric oxide acts as a mediator of mechanotransduction processes affecting proliferation primarily in the superficial cell sub-population.     

The influence of soft tissue movement on ground reaction forces, joint torques and joint reaction forces in drop landings

The aim of this study was to determine the effects that soft tissue motion has on ground reaction forces, joint torques and joint reaction forces in drop landings. To this end a four body-segment wobbling mass model was developed to reproduce the vertical ground reaction force curve for the first 100 ms of landing. Particular attention was paid to the passive impact phase, while selecting most model parameters a priori, thus permitting examination of the rigid body assumption on system kinetics. A two-dimensional wobbling mass model was developed in DADS (version 9.00, CADSI) to simulate landing from a drop of 43 cm. Subject-specific inertia parameters were calculated for both the rigid links and the wobbling masses. The magnitude and frequency response of the soft tissue of the subject to impulsive loading was measured and used as a criterion for assessing the wobbling mass motion. The model successfully reproduced the vertical ground reaction force for the first 100 ms of the landing with a peak vertical ground reaction force error of 1.2% and root mean square errors of 5% for the first 15 ms and 12% for the first 40 ms. The resultant joint forces and torques were lower for the wobbling mass model compared with a rigid body model, up to nearly 50% lower, indicating the important contribution of the wobbling masses on reducing system loading.     

Influence of internal loading on phosphorus concentration in shallow lakes before and after reduction of the external loading

An analysis of data from 49 shallow lakes showed, that the parameters of empirical models between phosphorus loading and concentration in the lake (e.g. Vollenweider type of relations) differ significantly for lakes without or with a reduced external loading. For lakes without a reduction of the external loading the summer phosphorus concentration is determined by the external phosphorus loading and the hydraulic loading. For these lakes the classical models suffice; deviations between calculations and measurements are partly due to errors made in the determination of the loading.In contrast, for lakes where the external loading was reduced, the measured internal loading explains most of the variation in the summer lake concentration. The external loading is of minor importance and the classical models cannot be applied. The internal loading measured before reduction of the external loading is not useful in predicting the concentration afterwards. Instead of the internal loading, the sediment composition can be used. The advantage of using sediment composition is that these variables are easier to determine and vary less in time. The most promising variable is the ratio between total P and total Fe in the sediment.Abbreviations: Q_s hydraulic loading (m y^-1) - hydraulic retention time (y) - L_ext external phosphorus loading (gP m^-2 y^-1) - L_int internal phosphorus loading (gP m^-2 y^-1) - P_lake phosphorus concentration in the lake (gP m^-3) - P_inlet phosphorus concentration in the inlet water (gP m^-3) - P_sed phosphorus content on the sediment (gP kg^-1 d.w.) - Fe_sed iron content of the sediment (gFe kg^-1 d.w.) - Y dependent variable multiple regression calculations - X1, X2 independent variables multiple regressions calculations - a, a1 constants - a2, b constants     

The influence of acceleration loading curve characteristics on traumatic brain injury

To prevent brain trauma, understanding the mechanism of injury is essential. Once the mechanism of brain injury has been identified, prevention technologies could then be developed to aid in their prevention. The incidence of brain injury is linked to how the kinematics of a brain injury event affects the internal structures of the brain. As a result it is essential that an attempt be made to describe how the characteristics of the linear and rotational acceleration influence specific traumatic brain injury lesions. As a result, the purpose of this study was to examine the influence of the characteristics of linear and rotational acceleration pulses and how they account for the variance in predicting the outcome of TBI lesions, namely contusion, subdural hematoma (SDH), subarachnoid hemorrhage (SAH), and epidural hematoma (EDH) using a principal components analysis (PCA). Monorail impacts were conducted which simulated falls which caused the TBI lesions. From these reconstructions, the characteristics of the linear and rotational acceleration were determined and used for a PCA analysis. The results indicated that peak resultant acceleration variables did not account for any of the variance in predicting TBI lesions. The majority of the variance was accounted for by duration of the resultant and component linear and rotational acceleration. In addition, the components of linear and rotational acceleration characteristics on the x, y, and z axes accounted for the majority of the remainder of the variance after duration.     

The influence of mechanical loading on osseointegration: an animal study

Osseointegration of implant provides a stable support for the prosthesis under functional loads. The timing of loading is a critical parameter that can govern the success of the osseointegration of implant. However, it is not clear whether the early loading can affect the success of osseointegration, or whether the no-loading healing period can be shortened. This paper presents an animal study conducted to investigate how external loads influence the osseointegration at the initial stage of healing. Titanium implants were inserted into the goat tibia laterally, and different axial loadings were applied to the implants in 4 weeks after surgery. After the 2 weeks period of early loading, animals were sacrificed and the tibia bones with the implants were cut off from the bodies. Then mechanical test was employed to find out the differences in the pull-out force, and shear strength at the bone-implant interface between the non-loaded and the loaded implants. The implant-bone interfaces were analyzed by histomorphometric method, SEM (scanning electron micrograph) and EDS (energy density spectrum). The results indicated that the bone-implant interface did not well integrate 4 weeks after surgery, and the fibrous tissue could be found at the interfaces of the specimens without loadings. While the results of loaded specimens with 10 N axial force showed that that parts of the interface were well integrated, indicating that the early mild loading may play a positive role in the process of the osseointegration. The results support that a certain range of external loading would influence the process of osseointegration, and appropriate mechanical loading can be applied to shorten the osseointegration period after surgery. Supported by the National Natural Science Foundation of China (Grant Nos. 30370376, 10529202 and 10672015).