Summary

用统计学方法分析了不同地形对选取的步态参数、步态参数的variability以及代谢耗能的影响

• 影响是否有统计学意义；正相关/负相关；一点点直观的原因解释
• 步态参数的相关性

步态参数及其variability与代谢耗能的相关性（线性回归、统计分析）

步态参数预估代谢耗能 （principal components regression (PCR) ； partial least squares regression (PLSR)和单因素回归）

Research question

how foot paths change with terrain, and how they relate to the energetic cost of walking.

foot path refers to the foot’s translation in three dimensions during a single swing phase, starting from the previous stance phase and including the ending stance phase, when the foot is stationary.

Introduction

Effects of ground terrain: the elevation change over a step, average stride length and width, mid-swing(higher on the uneven terrain), foot placement for stabilizing adjustments $\Rightarrow$ energy expenditure

Methods

实验

Fig 1. Measurement of foot paths and energy expenditure on outdoor terrain. Subjects walked on different terrains while wearing a portable respirometry system, a global positioning system (GPS) device, and one inertial measurement unit (IMU) per foot. Sample data from one subject show traces for walking speed and elevation from GPS, rates of oxygen consumption and carbon dioxide production, and angular velocity and translational acceleration vs. time. Terrains included Sidewalk, Gravel, Grass, Woodchip, and Dirt, along with transitions between them (gray lines, not analyzed). Walking speed was loosely regulated via GPS (average speeds listed); terrain segments were selected to avoid large net changes in elevation during trials.

数据处理

• last 3min / 8min的steady-state数据；为了reduce the amount of data只用左脚的数据
• 对IMU数据积分两次得到foot path（inertial drift reduced by correcting the velocities during stance to zero）
• normalization: body mass $M$, standing leg length $L$ (defined as floor to greater trochanter), and gravitational acceleration $g$ as base units. stride distances were normalized by $L$, and net metabolic power [28] by $Mg^{1.5}L^{0.5}$ (average 0.90 m, 1893 W across subjects
• repeated-measures ANOVA tests $\Rightarrow$ terrain conditions affected energy expenditure and gait parameters
• linear regression for each variable individually. The latter included a separate offset constant for each individual, included in the fit, with overall goodness of fit therefore evaluated with an adjusted $R^2 \Rightarrow$ correlation between energy expenditure and the gait parameter
• principal components analysis (PCA) and linear discriminant analysis (LDA) $\Rightarrow$ reduction ofdimensionality within the data
• principal components regression (PCR) and partial least squares regression (PLSR) $\Rightarrow$ using stride measures to predict metabolic rate

Results

各个参数差异不大但是有统计学意义

While the average gait pattern changed little, variability in most of the gait measures examined showed high dependence on terrain.

The most notable sensitivities were for variability in stride height, stride width, virtual clearance, and lateral swing motion. Variability could result directly from the unevenness of ground, or from controlled adjustments made to stabilize balance, which is thought to be passively unstable in the lateral direction [22,23]. Active stabilization is achieved in part through lateral foot placement [23,31–34]. Uneven ground appears to disrupt gait to a substantial degree, and would be expected to require substantial active stabilization. Aggregating these various contributions, the overall effect is that uneven ground leads to uneven foot motion and uneven steps.

the preferred stride length vs. speed relationship remained fairly intact across different terrains.

more challenging terrain caused increases in virtual ground clearance and in the variability of most measures

considerable interdependency among measures, as revealed by dimensionality reduction techniques

Limits/Further Work

Our foot path estimation relies on the foot being nearly stationary at some point during stance, which may not occur for every stride on softer terrains such as Woodchips. This

Thoughts/Comments

• variability的差异也成了分析的因素，这点之前没想到

  但是不知道这个RMS是怎么算的，其中的均值是所有subject在这个地形的mean还是这个subject的？此处这个RMS的定义和传统的均方根（平方和除以加和样本数再开方）不太一样We report average and root-mean-square (RMS, equivalent to standard deviation) variability

  而且这样是不是基本也只能分析用了？或者走几步统计？不知道能不能在线

• 对inter-subject differences的处理

  做代谢线性回归的时候每个人有不同的offset

  那这样$\text{Ind } R^2$是怎么算的？A：见$R^2$的定义，offset变了就是$f_i$变了，正常算就行

• PCA怎么计算这个成分包含的all data variability？就是特征值除以特征值的和吗？A：是

补充知识

• Coefficient of determination $R^2$

  • ${\displaystyle SS_{\text{res}}=\sum _{i}(y_{i}-f_{i})^{2}=\sum _{i}e_{i}^{2},}$
  • ${\displaystyle SS_{\text{tot}}=\sum _{i}(y_{i}-{\bar {y}})^{2}}$
  • ${\displaystyle R^{2}=1-{SS_{\rm {res}} \over SS_{\rm {tot}}},}$

• Adjusted $R^2$ (one common notation is ${\displaystyle {\bar {R}}^{2}}$, pronounced “R bar squared”; another is ${\displaystyle R_{\text{adj}}^{2}}$)

  ${\displaystyle {\bar {R}}^{2}=1-(1-R^{2}){n-1 \over n-p-1}}$, where $p$ is the total number of explanatory variables in the model (not including the constant term), and $n$ is the sample size.