Alterations of musculoskeletal models for a more accurate estimation of lower limb joint contact forces during normal gait: A systematic review

Musculoskeletal modelling is a methodology used to investigate joint contact forces during a movement. High accuracy in the estimation of the hip or knee joint contact forces can be obtained with subject-specific models. However, construction of subject-specific models remains time consuming and expensive. The purpose of this systematic review of the literature was to identify what alterations can be made on generic (i.e. literature-based, without any subject-specific measurement other than body size and weight) musculoskeletal models to obtain a better estimation of the joint contact forces. The impact of these alterations on the accuracy of the estimated joint contact forces were appraised.The systematic search yielded to 141 articles and 24 papers were included in the review. Different strategies of alterations were found: skeletal and joint model (e.g. number of degrees of freedom, knee alignment), muscle model (e.g. Hill-type muscle parameters, level of muscular redundancy), and optimisation problem (e.g. objective function, design variables, constraints). All these alterations had an impact on joint contact force accuracy, so demonstrating the potential for improving the model predictions without necessarily involving costly and time consuming medical images. However, due to discrepancies in the reported evidence about this impact and despite a high quality of the reviewed studies, it was not possible to highlight any trend defining which alteration had the largest impact.     

Ultrasound-based subject-specific parameters improve fascicle behaviour estimation in Hill-type muscle model

The estimation of muscle fascicle behaviour is decisive in a Hill-type model as they are related to muscle force by the force–length–velocity relationship and the tendon force–strain relationship. This study was aimed at investigating the influence of subject-specific tendon force–strain relationship and initial fascicle geometry (IFG) on the estimation of muscle forces and fascicle behaviour during isometric contractions. Ultrasonography was used to estimate the in vivo muscle fascicle behaviour and compare the muscle fascicle length and pennation angle estimated from the Hill-type model. The calibration–prediction process of the electromyography-driven model was performed using generic or subject-specific tendon definition with or without IFG as constraint. The combination of subject-specific tendon definition and IFG led to muscle fascicle behaviour closer to ultrasound data and significant lower forces of the ankle dorsiflexor and plantarflexor muscles compared to the other conditions. Thus, subject-specific ultrasound measurements improve the accuracy of Hill-type models on muscle fascicle behaviour.     

A new approach for assigning bone material properties from CT images into finite element models

Generation of subject-specific finite element (FE) models from computed tomography (CT) datasets is of significance for application of the FE analysis to bone structures. A great challenge that remains is the automatic assignment of bone material properties from CT Hounsfield Units into finite element models. This paper proposes a new assignment approach, in which material properties are directly assigned to each integration point. Instead of modifying the dataset of FE models, the proposed approach divides the assignment procedure into two steps: generating the data file of the image intensity of a bone in a MATLAB program and reading the file into ABAQUS via user subroutines. Its accuracy has been validated by assigning the density of a bone phantom into a FE model. The proposed approach has been applied to the FE model of a sheep tibia and its applicability tested on a variety of element types. The proposed assignment approach is simple and illustrative. It can be easily modified to fit users’ situations.     

The estimation of root length in samples and sub-samples

Summary Methods for estimating the root length in a sample using the line intersect principle were compared. One method involved visual techniques and used simple equipment. Another method introduced a new machine designed to estimate root length automatically. Either method had a high degree of accuracy, comparable with or better than other reported methods. Furthermore, the methods were tested over a wide range of root lengths up to 50 m. Even larger samples could be estimated using a reliable sub-sampling technique. The development of the root machine enabled the estimation of root length to become a simple laboratory routine.     

Subject-specific tendon-aponeurosis definition in hill-type model predicts higher muscle forces in dynamic tasks

Neuromusculoskeletal models are a common method to estimate muscle forces. Developing accurate neuromusculoskeletal models is a challenging task due to the complexity of the system and large inter-subject variability. The estimation of muscles force is based on the mechanical properties of tendon-aponeurosis complex. Most neuromusculoskeletal models use a generic definition of the tendon-aponeurosis complex based on in vitro test, perhaps limiting their validity. Ultrasonography allows subject-specific estimates of the tendon-aponeurosis complex's mechanical properties. The aim of this study was to investigate the influence of subject-specific mechanical properties of the tendon-aponeurosis complex on a neuromusculoskeletal model of the ankle joint. Seven subjects performed isometric contractions from which the tendon-aponeurosis force-strain relationship was estimated. Hopping and running tasks were performed and muscle forces were estimated using subject-specific tendon-aponeurosis and generic tendon properties. Two ultrasound probes positioned over the muscle-tendon junction and the mid-belly were combined with motion capture to estimate the in vivo tendon and aponeurosis strain of the medial head of gastrocnemius muscle. The tendon-aponeurosis force-strain relationship was scaled for the other ankle muscles based on tendon and aponeurosis length of each muscle measured by ultrasonography. The EMG-driven model was calibrated twice - using the generic tendon definition and a subject-specific tendon-aponeurosis force-strain definition. The use of subject-specific tendon-aponeurosis definition leads to a higher muscle force estimate for the soleus muscle and the plantar-flexor group, and to a better model prediction of the ankle joint moment compared to the model estimate which used a generic definition. Furthermore, the subject-specific tendon-aponeurosis definition leads to a decoupling behaviour between the muscle fibre and muscle-tendon unit in agreement with previous experiments using ultrasonography. These results indicate the use of subject-specific tendon-aponeurosis definitions in a neuromusculoskeletal model produce better agreement with measured external loads and more physiological model behaviour.     

Accuracy of space-for-time substitution for vegetation state prediction following shrub restoration

Aims Space-for-time substitution (SFT) is often used for vegetation status estimation during the recovery process of deserts. However, the evaluated accuracy of SFT remains uncertain. An eight-year located observation was used to assess the validity of SFT for vegetation state prediction.Methods This study analyzed a chronosequence of Caragana microphylla Lam. plantings using the located observation method to test the accuracy of SFT for vegetation state prediction in the mobile sand dunes of the Horqin Sandy Land in northeastern China from July 2005 to June 2013.Important findings According to SFT, simple vegetation parameters (density, coverage and biomass) were found to be unstable, while sophisticated vegetation parameters (species diversity and evenness) were relatively stable across the experimental treatments during the study period. Conversely, both the simple and sophisticated parameters were found to be relatively stable when tested using the located observation method. Furthermore, most simple vegetation parameters slightly increased, while sophisticated parameters slightly decreased after eight years of field observations. Thus, long-term restoration management facilitated improvements in the simple parameters, but may have adversely impacted the sophisticated parameters in the post-restoration community. Our results suggest that sophisticated vegetation parameter states can be predicted by SFT, while simple vegetation parameter states are not well predicted by SFT. In conclusion, located observations or other effective evaluation methods must be employed to offset the deficiency of the SFT method for the prediction of vegetation parameters.     

Trunk density profile estimates from dual X-ray absorptiometry

Accurate body segment parameters are necessary to estimate joint loads when using biomechanical models. Geometric methods can provide individualized data for these models but the accuracy of the geometric methods depends on accurate segment density estimates. The trunk, which is important in many biomechanical models, has the largest variability in density along its length. Therefore, the objectives of this study were to: (1) develop a new method for modeling trunk density profiles based on dual X-ray absorptiometry (DXA) and (2) develop a trunk density function for college-aged females and males that can be used in geometric methods. To this end, the density profiles of 25 females and 24 males were determined by combining the measurements from a photogrammetric method and DXA readings. A discrete Fourier transformation was then used to develop the density functions for each sex. The individual density and average density profiles compare well with the literature. There were distinct differences between the profiles of two of participants (one female and one male), and the average for their sex. It is believed that the variations in these two participants' density profiles were a result of the amount and distribution of fat they possessed. Further studies are needed to support this possibility. The new density functions eliminate the uniform density assumption associated with some geometric models thus providing more accurate trunk segment parameter estimates. In turn, more accurate moments and forces can be estimated for the kinetic analyses of certain human movements.     

Subject-specific mechanical properties of vertebral cancellous bone assessed using a low-dose X-ray device

ObjectivesAccording to the inter-individual variability of bone mechanical properties, subject-specific evaluation of the cancellous bone Young's modulus is needed to build finite-element models predicting vertebral strength with accuracy. Relationships based on the density assessed by quantitative computed tomography were proposed. However, quantitative computed tomography is not always suited for the analysis of the whole spine for patients’ follow-up because of the high radiation dose. Hence, this study aims at evaluating the mechanical properties of the vertebral cancellous bone using a low-dose X-ray device.Material and methodsNineteen vertebrae were considered. Biplanar radiographs were made using the low-dose EOS^® system with a dual-energy modality to evaluate antero-posterior and lateral areal bone mineral densities. A cylindrical sample was extracted from each vertebral body and tested until failure to assess the Young's modulus and the ultimate stress of the vertebral cancellous bone.Results and discussionMechanical properties were significantly related to the EOS^® areal densities. On one hand, the relationships remained less predictive than those based on quantitative computed tomography, but on the other hand, they better predict mechanical properties than previous studies using dual X-ray absorptiometry (clinical gold standard system for density assessment).ConclusionThe study shows the feasibility to predict the Young's modulus of the vertebral cancellous bone from the whole vertebral areal bone mineral density (BMD). It gives promising prospects to build finite-element models, including both subject-specific geometry and subject-specific mechanical properties by using a low-dose X-ray device for regions where high radiation doses would limit tomography assessment possibilities.     

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.     

Hazard ratio estimation for biomarker-calibrated dietary exposures

Uncertainty concerning the measurement error properties of self-reported diet has important implications for the reliability of nutritional epidemiology reports. Biomarkers based on the urinary recovery of expended nutrients can provide an objective measure of short-term nutrient consumption for certain nutrients and, when applied to a subset of a study cohort, can be used to calibrate corresponding self-report nutrient consumption assessments. A nonstandard measurement error model that makes provision for systematic error and subject-specific error, along with the usual independent random error, is needed for the self-report data. Three estimation procedures for hazard ratio (Cox model) parameters are extended for application to this more complex measurement error structure. These procedures are risk set regression calibration, conditional score, and nonparametric corrected score. An estimator for the cumulative baseline hazard function is also provided. The performance of each method is assessed in a simulation study. The methods are then applied to an example from the Women's Health Initiative Dietary Modification Trial.     

基于数字土壤制图技术的土壤有机碳储量估算

精准的土壤属性空间分布信息有助于提升土壤有机碳储量估算的精度.本研究以河南省济源市南山林场为研究区,以地形因子为预测因子,利用模糊C均值(FCM)聚类方法对土壤有机碳含量、土壤容重、土壤厚度和土壤砾石含量进行数字土壤预测制图,基于数字制图结果实现土壤有机碳密度预测制图和土壤有机碳储量估算.结果表明:基于数字土壤制图方法...     

An accurate estimation of bone density improves the accuracy of subject-specific finite element models

An experimental-numerical study was performed to investigate the relationships between computed tomography (CT)-density and ash density, and between ash density and apparent density for bone tissue, to evaluate their influence on the accuracy of subject-specific FE models of human bones. Sixty cylindrical bone specimens were examined. CT-densities were computed from CT images while apparent and ash densities were measured experimentally. The CT/ash-density and ash/apparent-density relationships were calculated. Finite element models of eight human femurs were generated considering these relationships to assess their effect on strain prediction accuracy. CT and ash density were linearly correlated (R(2)=0.997) over the whole density range but not equivalent (intercep t <0, slope >1). A constant ash/apparent-density ratio (0.598+/-0.004) was found for cortical bone. A lower ratio, with a larger dispersion, was found for trabecular bone (0.459+/-0.100), but it became less dispersed, and equal to that of cortical tissue, when testing smaller trabecular specimens (0.598+/-0.036). This suggests that an experimental error occurred in apparent-density measurements for large trabecular specimens and a constant ratio can be assumed valid for the whole density range. Introducing the obtained relationships in the FE modelling procedure improved strain prediction accuracy (R(2)=0.95, RMSE=7%). The results suggest that: (i) a correction of the densitometric calibration should be used when evaluating bone ash-density from clinical CT scans, to avoid ash-density underestimation and overestimation for low- and high-density bone tissue, respectively; (ii) the ash/apparent-density ratio can be assumed constant in human femurs and (iii) the correction improves significantly the model accuracy and should be considered in subject-specific bone modelling.     

A Bayesian approach for subgroup analysis

Several penalization approaches have been developed to identify homogeneous subgroups based on a regression model with subject-specific intercepts in subgroup analysis. These methods often apply concave penalty functions to pairwise comparisons of the intercepts, such that the subjects with similar intercept values are assigned to the same group, which is very similar to the procedure of the penalization approaches for variable selection. Since the Bayesian methods are commonly used in variable selection, it is worth considering the corresponding approaches to subgroup analysis in the Bayesian framework. In this paper, a Bayesian hierarchical model with appropriate prior structures is developed for the pairwise differences of intercepts based on a regression model with subject-specific intercepts, which can automatically detect and identify homogeneous subgroups. A Gibbs sampling algorithm is also provided to select the hyperparameter and estimate the intercepts and coefficients of the covariates simultaneously, which is computationally efficient for pairwise comparisons compared to the time-consuming procedures for parameter estimation of the penalization methods (e.g., alternating direction method of multiplier) in the case of large sample sizes. The effectiveness and usefulness of the proposed Bayesian method are evaluated through simulation studies and analysis of a Cleveland Heart Disease Dataset.     

Improved nonparametric estimation of the optimal diagnostic cut‐off point associated with the Youden index under different sampling schemes

A diagnostic cut‐off point of a biomarker measurement is needed for classifying a random subject to be either diseased or healthy. However, the cut‐off point is usually unknown and needs to be estimated by some optimization criteria. One important criterion is the Youden index, which has been widely adopted in practice. The Youden index, which is defined as the maximum of (sensitivity + specificity ?1), directly measures the largest total diagnostic accuracy a biomarker can achieve. Therefore, it is desirable to estimate the optimal cut‐off point associated with the Youden index. Sometimes, taking the actual measurements of a biomarker is very difficult and expensive, while ranking them without the actual measurement can be relatively easy. In such cases, ranked set sampling can give more precise estimation than simple random sampling, as ranked set samples are more likely to span the full range of the population. In this study, kernel density estimation is utilized to numerically solve for an estimate of the optimal cut‐off point. The asymptotic distributions of the kernel estimators based on two sampling schemes are derived analytically and we prove that the estimators based on ranked set sampling are relatively more efficient than that of simple random sampling and both estimators are asymptotically unbiased. Furthermore, the asymptotic confidence intervals are derived. Intensive simulations are carried out to compare the proposed method using ranked set sampling with simple random sampling, with the proposed method outperforming simple random sampling in all cases. A real data set is analyzed for illustrating the proposed method.     

Subject-specific finite element models of long bones: An in vitro evaluation of the overall accuracy

The determination of the mechanical stresses induced in human bones is of great importance in both research and clinical practice. Since the stresses in bones cannot be measured non-invasively in vivo, the only way to estimate them is through subject-specific finite element modelling. Several methods exist for the automatic generation of these models from CT data, but before bringing them in the clinical practice it is necessary to assess their accuracy in the predictions of the bone stresses. Particular attention should be paid to those regions, like the epiphyseal and metaphyseal parts of long bones, where the automatic methods are typically less accurate. Aim of the present study was to implement a general procedure to automatically generate subject-specific finite element models of bones from CT data and estimate the accuracy of this general procedure by applying it to one real femur. This femur was tested in vitro under five different loading scenarios and the results of these tests were used to verify how the adoption of a simplified two-material homogeneous model would change the accuracy with respect to the density-based inhomogeneous one, with special attention paid to the epiphyseal and metaphyseal proximal regions of the bone. The results showed that the density-based inhomogeneous model predicts with a very good accuracy the measured stresses (R(2)=0.91, RMSE=8.6%, peak error=27%), while the two-material model was less accurate (R(2)=0.89, RMSE=9.6%, peak error=35%). The results showed that it is possible to automatically generate accurate finite element models of bones from CT data and that the strategy of material properties mapping has a significant influence on its accuracy.     

Estimating animal population density using passive acoustics

Reliable estimation of the size or density of wild animal populations is very important for effective wildlife management, conservation and ecology. Currently, the most widely used methods for obtaining such estimates involve either sighting animals from transect lines or some form of capture‐recapture on marked or uniquely identifiable individuals. However, many species are difficult to sight, and cannot be easily marked or recaptured. Some of these species produce readily identifiable sounds, providing an opportunity to use passive acoustic data to estimate animal density. In addition, even for species for which other visually based methods are feasible, passive acoustic methods offer the potential for greater detection ranges in some environments (e.g. underwater or in dense forest), and hence potentially better precision. Automated data collection means that surveys can take place at times and in places where it would be too expensive or dangerous to send human observers. Here, we present an overview of animal density estimation using passive acoustic data, a relatively new and fast‐developing field. We review the types of data and methodological approaches currently available to researchers and we provide a framework for acoustics‐based density estimation, illustrated with examples from real‐world case studies. We mention moving sensor platforms (e.g. towed acoustics), but then focus on methods involving sensors at fixed locations, particularly hydrophones to survey marine mammals, as acoustic‐based density estimation research to date has been concentrated in this area. Primary among these are methods based on distance sampling and spatially explicit capture‐recapture. The methods are also applicable to other aquatic and terrestrial sound‐producing taxa. We conclude that, despite being in its infancy, density estimation based on passive acoustic data likely will become an important method for surveying a number of diverse taxa, such as sea mammals, fish, birds, amphibians, and insects, especially in situations where inferences are required over long periods of time. There is considerable work ahead, with several potentially fruitful research areas, including the development of (i) hardware and software for data acquisition, (ii) efficient, calibrated, automated detection and classification systems, and (iii) statistical approaches optimized for this application. Further, survey design will need to be developed, and research is needed on the acoustic behaviour of target species. Fundamental research on vocalization rates and group sizes, and the relation between these and other factors such as season or behaviour state, is critical. Evaluation of the methods under known density scenarios will be important for empirically validating the approaches presented here.     

Two-stage functional mixed models for evaluating the effect of longitudinal covariate profiles on a scalar outcome

The Daily Hormone Study, a substudy of the Study of Women's Health Across the Nation (SWAN) consisting of more than 600 pre- and perimenopausal women, includes a scalar measure of total hip bone mineral density (BMD) together with repeated measures of creatinine-adjusted follicle stimulating hormone (FSH) assayed from daily urine samples collected over one menstrual cycle. It is of scientific interest to investigate the effect of the FSH time profile during a menstrual cycle on total hip BMD, adjusting for age and body mass index. The statistical analysis is challenged by several features of the data: (1) the covariate FSH is measured longitudinally and its effect on the scalar outcome BMD may be complex; (2) due to varying menstrual cycle lengths, subjects have unbalanced longitudinal measures of FSH; and (3) the longitudinal measures of FSH are subject to considerable among- and within-subject variations and measurement errors. We propose a measurement error partial functional linear model, where repeated measures of FSH are modeled using a functional mixed effects model and the effect of the FSH time profile on BMD is modeled using a partial functional linear model by treating the unobserved true subject-specific FSH time profile as a functional covariate. We develop a two-stage nonparametric regression calibration method using period smoothing splines. Using the connection between smoothing splines and mixed models, we show that a key feature of our approach is that estimation at both stages can be conveniently cast into a unified mixed model framework. A simple testing procedure for constant functional covariate effect is also proposed. The proposed methods are evaluated using simulation studies and applied to the SWAN data.     

Phylogeny reconstruction: increasing the accuracy of pairwise distance estimation using Bayesian inference of evolutionary rates

Distance-based methods for phylogeny reconstruction are the fastest and easiest to use, and their popularity is accordingly high. They are also the only known methods that can cope with huge datasets of thousands of sequences. These methods rely on evolutionary distance estimation and are sensitive to errors in such estimations. In this study, a novel Bayesian method for estimation of evolutionary distances is developed. The proposed method enables the use of a sophisticated evolutionary model that better accounts for among-site rate variation (ASRV), thereby improving the accuracy of distance estimation. Rate variations are estimated within a Bayesian framework by extracting information from the entire dataset of sequences, unlike standard methods that can only use one pair of sequences at a time. We compare the accuracy of a cascade of distance estimation methods, starting from commonly used methods and moving towards the more sophisticated novel method. Simulation studies show significant improvements in the accuracy of distance estimation by the novel method over the commonly used ones. We demonstrate the effect of the improved accuracy on tree reconstruction using both real and simulated protein sequence alignments. An implementation of this method is available as part of the SEMPHY package.     

A penalized spline approach to functional mixed effects model analysis

In this article, we propose penalized spline (P-spline)-based methods for functional mixed effects models with varying coefficients. We decompose longitudinal outcomes as a sum of several terms: a population mean function, covariates with time-varying coefficients, functional subject-specific random effects, and residual measurement error processes. Using P-splines, we propose nonparametric estimation of the population mean function, varying coefficient, random subject-specific curves, and the associated covariance function that represents between-subject variation and the variance function of the residual measurement errors which represents within-subject variation. Proposed methods offer flexible estimation of both the population- and subject-level curves. In addition, decomposing variability of the outcomes as a between- and within-subject source is useful in identifying the dominant variance component therefore optimally model a covariance function. We use a likelihood-based method to select multiple smoothing parameters. Furthermore, we study the asymptotics of the baseline P-spline estimator with longitudinal data. We conduct simulation studies to investigate performance of the proposed methods. The benefit of the between- and within-subject covariance decomposition is illustrated through an analysis of Berkeley growth data, where we identified clearly distinct patterns of the between- and within-subject covariance functions of children's heights. We also apply the proposed methods to estimate the effect of antihypertensive treatment from the Framingham Heart Study data.     

Estimation of time of divergence from phylogenetic studies.

Recent studies with comparative data on base sequences of homologous DNA's or amino acid sequences of homologous proteins indicate that simultaneous estimation of phylogenetic structure and time of divergence is often cumbersome and time consuming. On the other hand, when the topology of an evolutionary tree is known, it is shown in this paper that the least squares theory may be applied to obtain simple estimates of the relative time lengths for each segment of the tree under the assumption of uniform random substitutions in each segment. The method is illustrated with amino acid sequence data on various globin molecules and cytochrome c. The evolutionary significance of some of the estimates is also discussed.