Time Series Analysis of Particle Tracking Data for Molecular Motion on the Cell Membrane

Biophysicists use single particle tracking (SPT) methods to probe the dynamic behavior of individual proteins and lipids in cell membranes. The mean squared displacement (MSD) has proven to be a powerful tool for analyzing the data and drawing conclusions about membrane organization, including features like lipid rafts, protein islands, and confinement zones defined by cytoskeletal barriers. Here, we implement time series analysis as a new analytic tool to analyze further the motion of membrane proteins. The experimental data track the motion of 40 nm gold particles bound to Class I major histocompatibility complex (MHCI) molecules on the membranes of mouse hepatoma cells. Our first novel result is that the tracks are significantly autocorrelated. Because of this, we developed linear autoregressive models to elucidate the autocorrelations. Estimates of the signal to noise ratio for the models show that the autocorrelated part of the motion is significant. Next, we fit the probability distributions of jump sizes with four different models. The first model is a general Weibull distribution that shows that the motion is characterized by an excess of short jumps as compared to a normal random walk. We also fit the data with a chi distribution which provides a natural estimate of the dimension d of the space in which a random walk is occurring. For the biological data, the estimates satisfy 1<d<2, implying that particle motion is not confined to a line, but also does not occur freely in the plane. The dimension gives a quantitative estimate of the amount of nanometer scale obstruction met by a diffusing molecule. We introduce a new distribution and use the generalized extreme value distribution to show that the biological data also have an excess of long jumps as compared to normal diffusion. These fits provide novel estimates of the microscopic diffusion constant.     

MRI development and validation of two new predictive methods of glenohumeral joint centre location identification and comparison with established techniques

Identification of the centre of the glenohumeral joint (GHJ) is essential for three-dimensional (3D) upper limb motion analysis. A number of convenient, yet un-validated methods are routinely used to estimate the GHJ location in preference to the International Society of Biomechanics (ISB) recommended methods. The current study developed a new regression model, and simple 3D offset method for GHJ location estimation, employing easy to administer measures, and compared the estimates with the known GHJ location measured with magnetic resonance imaging (MRI). The accuracy and reliability of the new regression and simple 3D offset techniques were compared with six established predictive methods. Twenty subjects wore a 3D motion analysis marker set that was also visible in MRI. Immediately following imaging, they underwent 3D motion analysis acquisition. The GHJ and anatomical landmark positions of 15 participants were used to determine the new regression and simple 3D generic offset methods. These were compared for accuracy with six established methods using 10 subject's data. A cross validation on 5 participants not used for regression model development was also performed. Finally, 10 participants underwent a further two MRI's and subsequent 3D motion analysis analyses for inter-tester and intra-tester reliability quantification. When compared with any of the other established methods, our newly developed regression model found an average GHJ location closer to the actual MRI location, having an GHJ location error of 13±2 mm, and had significantly lower inter-tester reliability error, 6±4 mm (p<0.01).     

Effect of arm motion on standing lateral jumps

The role of arm swing in jumping has been examined in numerous studies of standing jumps for height and forward distance, but no prior studies have explored its effect on lateral jumping. The purpose of the present study was to investigate the effect of arm motion on standing lateral jump performance and to examine the biomechanical mechanisms that may explain differences in jump distance. Six participants executed a series of jumps for maximum lateral distance from two in-ground force platforms for two jump cases (free and restricted arms) while an eight-camera, passive-reflector, motion capture system collected 3D position data throughout the movements. Inverse kinematics and dynamics analyses were performed for all jumps using three-dimensional (3D) link models to calculate segment angular velocities, joint moments, joint powers, and joint work. Free arm motion improved standing lateral jump performance by 29% on average. This improvement was due to increased takeoff velocity and improved lateral and vertical positions of the center of gravity (CG) at takeoff and touchdown. Improved velocity and position of the CG at takeoff resulted from a 33% increase in the work done by the body. This increase in work in free arm jumps compared to restricted arm jumps was found in both upper and lower body joints with the largest improvements (>30 J) occurring at the lower back, right hip, and right shoulder.     

Recalage 2D-3D dans le domaine fréquentiel pour l’étude du mouvement en condition quasi-statique : étude pilote sur l’articulation du genou

ObjectivesIn order to make kinematics studies, an estimation of the bones motions is necessary. In this paper, we develop a new method to make 2D-3D registration in order to estimate the bones motion of the knee (femur and tibia). Our registration is made in the frequency domain using different pairs of radiographs and 3D reconstruction of the bone in the initial position.Material and methodWe use the knee bones radiographs of two healthy persons. These acquisitions are made by a new low dose radiographic system called EOS. Acquisitions are made in full extension, in 30° and 60° of knee flexion. A 3D reconstruction of the bones is made in the extension position and a new 2D-3D registration method based on the frequency domain is applied to make the motion estimation for the flexion positions.ResultsOur registration method is made in the frequency domain and does not need to make radiograph simulations as it is commonly made in 2D-3D registration methods. We compare our results to a manual registration of the data. The precision we get is similar to the previous works precision.DiscussionFor acquisitions, we use a low dose radiographic system which limits the X-ray irradiation for the patients.     

A Deep Neural Network-based method for estimation of 3D lifting motions

The aim of this study is developing and validating a Deep Neural Network (DNN) based method for 3D pose estimation during lifting. The proposed DNN based method addresses problems associated with marker-based motion capture systems like excessive preparation time, movement obstruction, and controlled environment requirement. Twelve healthy adults participated in a protocol and performed nine lifting tasks with different vertical heights and asymmetry angles. They lifted a crate and placed it on a shelf while being filmed by two camcorders and a synchronized motion capture system, which directly measured their body movement. A DNN with two-stage cascaded structure was designed to estimate subjects’ 3D body pose from images captured by camcorders. Our DNN augmented Hourglass network for monocular 2D pose estimation with a novel 3D pose generator subnetwork, which synthesized information from all available views to predict accurate 3D pose. We validated the results against the marker-based motion capture system as a reference and examined the method performance under different lifting conditions. The average Euclidean distance between the estimated 3D pose and reference (3D pose error) on the whole dataset was 14.72 ± 2.96 mm. Repeated measures ANOVAs showed lifting conditions can affect the method performance e.g. 60° asymmetry angle and shoulder height lifting showed higher 3D pose error compare to other lifting conditions. The results demonstrated the capability of the proposed method for 3D pose estimation with high accuracy and without limitations of marker-based motion capture systems. The proposed method may be utilized as an on-site biomechanical analysis tool.     

Effect of segmentation errors on 3D-to-2D registration of implant models in X-ray images

In many biomedical applications, it is desirable to estimate the three-dimensional (3D) position and orientation (pose) of a metallic rigid object (such as a knee or hip implant) from its projection in a two-dimensional (2D) X-ray image. If the geometry of the object is known, as well as the details of the image formation process, then the pose of the object with respect to the sensor can be determined. A common method for 3D-to-2D registration is to first segment the silhouette contour from the X-ray image; that is, identify all points in the image that belong to the 2D silhouette and not to the background. This segmentation step is then followed by a search for the 3D pose that will best match the observed contour with a predicted contour. Although the silhouette of a metallic object is often clearly visible in an X-ray image, adjacent tissue and occlusions can make the exact location of the silhouette contour difficult to determine in places. Occlusion can occur when another object (such as another implant component) partially blocks the view of the object of interest. In this paper, we argue that common methods for segmentation can produce errors in the location of the 2D contour, and hence errors in the resulting 3D estimate of the pose. We show, on a typical fluoroscopy image of a knee implant component, that interactive and automatic methods for segmentation result in segmented contours that vary significantly. We show how the variability in the 2D contours (quantified by two different metrics) corresponds to variability in the 3D poses. Finally, we illustrate how traditional segmentation methods can fail completely in the (not uncommon) cases of images with occlusion.     

Analysis of forearm rotational motion using biplane fluoroscopic intensity-based 2D–3D matching

Measuring three-dimensional (3D) forearm rotational motion is difficult. We aimed to develop and validate a new method for analyzing 3D forearm rotational motion. We proposed biplane fluoroscopic intensity-based 2D–3D matching, which employs automatic registration processing using the evolutionary optimization strategy. Biplane fluoroscopy was conducted for forearm rotation at 12.5 frames per second along with computed tomography (CT) at one static position. An arm phantom was embedded with eight stainless steel spheres (diameter, 1.5 mm), and forearm rotational motion measurements using the proposed method were compared with those using radiostereometric analysis, which is considered the ground truth. As for the time resolution analysis, we measured radiohumeral joint motion in a patient with posterolateral rotatory instability and compared the 2D–3D matching method with the simulated multiple CT method, which uses CTs at multiple positions and interpolates between the positions. Rotation errors of the radius and ulna between these two methods were 0.31 ± 0.35° and 0.32 ± 0.33°, respectively, translation errors were 0.43 ± 0.35 mm and 0.29 ± 0.25 mm, respectively. Although the 2D–3D method could detect joint dislocation, the multiple CT method could not detect quick motion during joint dislocation. The proposed method enabled high temporal- and spatial-resolution motion analyses with low radiation exposure. Moreover, it enabled the detection of a sudden motion, such as joint dislocation, and may contribute to 3D motion analysis, including joint dislocation, which currently cannot be analyzed using conventional methods.     

滇西北森林郁闭度估测模型——基于全球生态系统动力学调查多波束激光雷达数据

探究全球生态系统动力学调查(GEDI)多波束激光雷达数据估测区域森林郁闭度(FCC)的潜力,对于评估森林生态系统状态和林分环境具有重要作用。选取滇西北典型生态脆弱区香格里拉为研究区,以GEDI波形数据为信息源,提取46245个有林地光斑参数,使用经验贝叶斯克里金法(EBK)获取光斑参数在研究区未知空间的连续分布,结合54块实测样地数据,采用支持向量机的递归特征消除法(SVM-RFE)、随机森林(RF)和Pearson分析分别优选特征变量,基于贝叶斯优化(BO)随机森林回归模型(BO-RFR)、贝叶斯优化梯度回归模型(BO-GBRT)和偏最小二乘法(PLSR)研建森林郁闭度最佳估测模型。结果表明:(1)EBK法预测精度高,估测结果可靠,R²:0.20-0.92,RMSE:0.004-2812.912,MAE:0.003-1996.258,MRE:0.007-4.423;(2)基于不同特征优选方法筛选的特征变量和数量略有差异,SVM-RFE 法优选出6个参数(cover、pai、sensitivity、rv_a1、rv_a4、rg_a4)的平均交叉验证精度达0.84,RF法以贡献度5%为阈值筛选出5个参数(cover、pai、pgap_theta_error、modis_treecover、modis_nonvegetated),Pearson法以相关性大于0.3且在0.01水平显著优选出5个参数(cover、pai、rv_a5、rg_a5、pgap_theta_error);(3)不同特征变量优选方法筛选的建模参数研建估测模型精度差异性较大,以SVM-RFE和RF方法优选参数构建估测模型的精度更佳,SVM-RFE方法优选参数研建估测模型精度变化相对稳定,以 RF方法中的BO-GBRT模型为最佳FCC估测模型(R²=0.85、RMSE=0.069,P=86.5%);(4)采用BO-GBRT模型估测研究区森林郁闭度和空间制图,与GEDI pai参数预测的FCC具有较高空间相关性达0.53,FCC均值分别为0.58、0.61,主要分布在0.4-0.7,分别占比65.45%、51.79%。研究区森林郁闭度主要处于中度郁闭,北部区域主要为高度郁闭区,与研究区植被覆盖度的空间分布具有一致性,说明使用GEDI数据估测森林郁闭度的方法具有可行性、结果具有可靠性。研究为使用GEDI数据高效、及时、低成本估测大空间尺度的森林水平结构参数的相关研究奠定了基础。     

Human Mammary Epithelial Cells Exhibit a Bimodal Correlated Random Walk Pattern

Background

Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW).

Methodology/Principal Findings

Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation).

Conclusions/Significance

Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.     

Comparative assessment of bone pose estimation using Point Cluster Technique and OpenSim

Estimating the position of the bones from optical motion capture data is a challenge associated with human movement analysis. Bone pose estimation techniques such as the Point Cluster Technique (PCT) and simulations of movement through software packages such as OpenSim are used to minimize soft tissue artifact and estimate skeletal position; however, using different methods for analysis may produce differing kinematic results which could lead to differences in clinical interpretation such as a misclassification of normal or pathological gait. This study evaluated the differences present in knee joint kinematics as a result of calculating joint angles using various techniques. We calculated knee joint kinematics from experimental gait data using the standard PCT, the least squares approach in OpenSim applied to experimental marker data, and the least squares approach in OpenSim applied to the results of the PCT algorithm. Maximum and resultant RMS differences in knee angles were calculated between all techniques. We observed differences in flexion/extension, varus/valgus, and internal/external rotation angles between all approaches. The largest differences were between the PCT results and all results calculated using OpenSim. The RMS differences averaged nearly 5° for flexion/extension angles with maximum differences exceeding 15°. Average RMS differences were relatively small (< 1.08°) between results calculated within OpenSim, suggesting that the choice of marker weighting is not critical to the results of the least squares inverse kinematics calculations. The largest difference between techniques appeared to be a constant offset between the PCT and all OpenSim results, which may be due to differences in the definition of anatomical reference frames, scaling of musculoskeletal models, and/or placement of virtual markers within OpenSim. Different methods for data analysis can produce largely different kinematic results, which could lead to the misclassification of normal or pathological gait. Improved techniques to allow non-uniform scaling of generic models to more accurately reflect subject-specific bone geometries and anatomical reference frames may reduce differences between bone pose estimation techniques and allow for comparison across gait analysis platforms.     

Estimating Mean First Passage Time of Biased Random Walks with Short Relaxation Time on Complex Networks

Biased random walk has been studied extensively over the past decade especially in the transport and communication networks communities. The mean first passage time (MFPT) of a biased random walk is an important performance indicator in those domains. While the fundamental matrix approach gives precise solution to MFPT, the computation is expensive and the solution lacks interpretability. Other approaches based on the Mean Field Theory relate MFPT to the node degree alone. However, nodes with the same degree may have very different local weight distribution, which may result in vastly different MFPT. We derive an approximate bound to the MFPT of biased random walk with short relaxation time on complex network where the biases are controlled by arbitrarily assigned node weights. We show that the MFPT of a node in this general case is closely related to not only its node degree, but also its local weight distribution. The MFPTs obtained from computer simulations also agree with the new theoretical analysis. Our result enables fast estimation of MFPT, which is useful especially to differentiate between nodes that have very different local node weight distribution even though they share the same node degrees.     

Turn designation, sampling rate and the misidentification of power laws in movement path data using maximum likelihood estimates

Many authors have claimed to observe animal movement paths that appear to be Lévy walks, i.e. a random walk where the distribution of move lengths follows an inverse power law. A Lévy walk is known to be the optimal search strategy of a particular class of random walks in certain environments; hence, it is important to distinguish correctly between Lévy walks and other types of random walks in observed animal movement paths. Evidence of a power law distribution in the step length distribution of observed animal movement paths is often used to classify a particular movement path as a Lévy walk. However, there is some doubt about the accuracy of early studies that apparently found Lévy walk behaviour. A recently accepted method to determine whether a movement path truly exhibits Lévy walk behaviour is based on an analysis of move lengths with a maximum likelihood estimate using Akaike weights. Here, we show that simulated (non-Lévy) random walks representing different types of animal movement behaviour (a composite correlated random walk; pooled data from a set of random walks with different levels of correlation and three-dimensional correlated random walks projected into one dimension) can all show apparent power law behaviour typical of Lévy walks when using the maximum likelihood estimation method. The probability of the movement path being identified as having a power law step distribution is related to both the sampling rate used by the observer and the way that ‘turns’ or ‘reorientations’ in the movement path are designated. However, identification is also dependent on the nature and properties of the simulated path, and there is currently no standard method of observation and analysis that is robust for all cases. Our results indicate that even apparently robust maximum likelihood methods can lead to a mismatch between pattern and process, as paths arising from non-Lévy walks exhibit Lévy-like patterns.     

Fully Automatic Localization and Segmentation of 3D Vertebral Bodies from CT/MR Images via a Learning-Based Method

In this paper, we address the problems of fully automatic localization and segmentation of 3D vertebral bodies from CT/MR images. We propose a learning-based, unified random forest regression and classification framework to tackle these two problems. More specifically, in the first stage, the localization of 3D vertebral bodies is solved with random forest regression where we aggregate the votes from a set of randomly sampled image patches to get a probability map of the center of a target vertebral body in a given image. The resultant probability map is then further regularized by Hidden Markov Model (HMM) to eliminate potential ambiguity caused by the neighboring vertebral bodies. The output from the first stage allows us to define a region of interest (ROI) for the segmentation step, where we use random forest classification to estimate the likelihood of a voxel in the ROI being foreground or background. The estimated likelihood is combined with the prior probability, which is learned from a set of training data, to get the posterior probability of the voxel. The segmentation of the target vertebral body is then done by a binary thresholding of the estimated probability. We evaluated the present approach on two openly available datasets: 1) 3D T2-weighted spine MR images from 23 patients and 2) 3D spine CT images from 10 patients. Taking manual segmentation as the ground truth (each MR image contains at least 7 vertebral bodies from T11 to L5 and each CT image contains 5 vertebral bodies from L1 to L5), we evaluated the present approach with leave-one-out experiments. Specifically, for the T2-weighted MR images, we achieved for localization a mean error of 1.6 mm, and for segmentation a mean Dice metric of 88.7% and a mean surface distance of 1.5 mm, respectively. For the CT images we achieved for localization a mean error of 1.9 mm, and for segmentation a mean Dice metric of 91.0% and a mean surface distance of 0.9 mm, respectively.     

Restricted BLUP for Mixed Linear Models

A new estimation procedure for mixed regression models is introduced. It is a development of Henderson's best linear unbiased prediction procedure which uses the joint distribution of the observed dependent random variables and the unknown realisations of the random components of the model. It is proposed to replace the likelihood of the observations given the random components by the asymptotic likelihood of the maximum likelihood estimators and the prior distribution of the random components by a restricted prior distribution which is consistent with the usual restrictions placed on the random components when they are considered conditionally fixed.     

基于GF-2的油松人工林地上生物量反演

油松是黄土高原地区重要的造林树种.快速准确地估测其地上生物量,对开展该地区森林资源动态监测等具有重要作用.本研究选取陕西省黄龙山林区石堡林场的油松人工林为对象,结合国产卫星高分二号(GF-2)的多光谱遥感影像与野外同时段实测样地数据,对其地上生物量进行了估算.提取了5种植被指数和8种纹理信息,基于普通回归、逐步回归、岭回归、拉索回归与主成分回归5种方法在4种纹理窗口(3×3、5×5、7×7和9×9)下建模,使用留一法交叉验证测试了每个模型的估算精度.结果表明: 提取的遥感因子之间存在着较为严重的多重共线性关系,大部分遥感因子与油松人工林地上生物量有较为显著的相关性;GF-2数据在石堡林场油松人工林地上生物量的反演中可以实现较高精度,其中估算效果最好的是使用了9×9纹理窗口的主成分回归模型,估算效果最差的是使用了3×3纹理窗口的普通回归模型.利用国产高分辨率卫星影像对油松人工林地上生物量进行反演研究,可以为西北地区林业部门进行森林生物量监测、资源管理与可持续经营提供科学依据.     

Feasibility of estimating isokinetic knee torque using a neural network model

Many studies have investigated the relationships between electromyography (EMG) and torque production. A few investigators have used adjusted learning algorithms and feed-forward artificial neural networks (ANNs) to estimate joint torque in the elbow. This study sought to estimate net isokinetic knee torque using ANN models. Isokinetic knee extensor and flexor torque data were measured simultaneously with agonist and antagonist EMG during concentric and eccentric contractions at joint velocities of 30 degrees /s and 60 degrees /s. Age, gender, height, body mass, agonist EMG, antagonist EMG, joint position and joint velocity were entered as predictive variables of net torque. A three-layer ANN model was developed and trained using an adjusted back-propagation algorithm. Accuracy results were compared against those of forward stepwise regression models. Stepwise regression models included body mass, body height and joint position as the most influential predictors, followed by agonist EMG for concentric and eccentric contractions. Estimation of eccentric torque included antagonist EMG following the agonist activation. ANN models resulted in more accurate torque estimation (R=0.96), compared to the stepwise regression models (R=0.71). ANN model accuracy increased greatly when the number of hidden units increased from 5 to 10, continuing to increase gradually with additional hidden units. The average number of training epochs necessary for solution convergence and the relative accuracy of the model indicate a strong ability for the ANN model to generalize these estimations to a broader sample. The ANN model appears to be a feasible technique for estimating joint torque in the knee.     

cameratrapR: An R package for estimating animal density using camera trapping data

• 1.Camera trapping plays an important role in wildlife surveys, and provides valuable information for estimation of population density. While mark-recapture techniques can estimate population density for species that can be individually recognized or marked, there are no robust methods to estimate density of species that cannot be individually identified.
• 2.We developed a new approach to estimate population density based on the simulation of individual movement within the camera grid. Simulated animals followed a correlated random walk with the movement parameters of segment length, angular deflection, movement distance and home-range size derived from empirical movement paths. Movement was simulated under a series of population densities. We used the Random Forest algorithm to determine the population density with the highest likelihood of matching the camera trap data. We developed an R package, cameratrapR, to conduct simulations and estimate population density.
• 3.Compared with line transect surveys and the random encounter model, cameratrapR provides more reliable estimates of wildlife density with narrower confidence intervals. Functions are provided to visualize movement paths, derive movement parameters, and plot camera trapping results.
• 4.The package allows researchers to estimate population sizes/densities of animals that cannot be individually identified and cameras are deployed in a grid pattern.

     

Theoretical study of sequence-dependent nanopore unzipping of DNA

We theoretically investigate the unzipping of DNA electrically driven through a nanometer-size pore. Taking the DNA base sequence explicitly into account, the unpairing and translocation process is described by a biased random walk in a one-dimensional energy landscape determined by the sequential basepair opening. Distributions of translocation times are numerically calculated as a function of applied voltage and temperature. We show that varying these two parameters changes the dynamics from a predominantly diffusive behavior to a dynamics governed by jumps over local energy barriers. The work suggests experimentally studying sequence effects, by comparing the average value and standard deviation of the statistical distribution of translocation times.     

Hip joint centre localisation with an unscented Kalman filter

The accurate estimation of the hip joint centre (HJC) in gait analysis and in computer assisted orthopaedic procedures is a basic requirement. Functional methods, based on rigid body localisation, assessing the kinematics of the femur during circumduction movements (pivoting) have been used for estimating the HJC. Localising the femoral segment only, as it is usually done in total knee replacement procedure, can give rise to estimation errors, since the pelvis, during the passive pivoting manoeuvre, might undergo spatial displacements. This paper presents the design and test of an unscented Kalman filter that allows the estimation of the HJC by observing the pose of the femur and the 3D coordinates of a single marker attached to the pelvis. This new approach was validated using a hip joint mechanical simulator, mimicking both hard and soft tissues. The algorithm performances were compared with the literature standards and proved to have better performances in case of pelvis translation greater than 8 mm, thus satisfying the clinical requirements of the application.     

Joint model selection of marginal mean regression and correlation structure for longitudinal data with missing outcome and covariates

This work develops a joint model selection criterion for simultaneously selecting the marginal mean regression and the correlation/covariance structure in longitudinal data analysis where both the outcome and the covariate variables may be subject to general intermittent patterns of missingness under the missing at random mechanism. The new proposal, termed “joint longitudinal information criterion” (JLIC), is based on the expected quadratic error for assessing model adequacy, and the second‐order weighted generalized estimating equation (WGEE) estimation for mean and covariance models. Simulation results reveal that JLIC outperforms existing methods performing model selection for the mean regression and the correlation structure in a two stage and hence separate manner. We apply the proposal to a longitudinal study to identify factors associated with life satisfaction in the elderly of Taiwan.