Research on Predicting Trunk Isometric Strength with Core Stability Related Measurements
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摘要: 选择躯干等长力量（TIS）测试、躯干伸肌耐力（EE）测试、躯干屈伸活动范围（TFE）测试、优势侧单腿站立（DLS）测试和优势侧单腿跳远（DLH）测试共5类测试项目，分别反映核心稳定性（CS）的力量、耐力、柔韧性、平衡能力和功能性，对4项核心稳定性相关测试与TIS之间的关系进行了Pearson相关分析和多元线性回归分析。结果显示：TFE与A60、A90、A120和T120具有显著性负相关关系，DLH与A60、T60、A90、T90、A120、T120具有显著性相关关系。提示：TFE和DLH是预测TIS的有效指标，TFE、DLH与TIS的共享变异度具有环节位置特异性；核心力量训练时应特别关注运动环节间的位置关系，以提高训练效率。Abstract: Trunk isometric strength test (TIS), extensor endurance test (EE), trunk flexion and extension test (TFE), dominant leg standing test (DLS) and dominant leg hop test (DLH) were selected to represent the strength, flexibility, endurance, balance and coordinate ability of the core stability (CS). Pearson analysis and Multiple Linear Regression analysis were employed to analyze the correlation among CS related measurements (CSRM). The results find that TFE had significantly negative correlations with A60, while DLH correlated with A60 significantly. The conclusions are as follows:TFE and DLH were good predictors for TIS, and the correlation level was specific to the angle position of trunk. The position among body segments should be highly considered to promote the efficiency of core strength training.
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Keywords:
- core stability /
- core strength /
- trunk /
- isokinetic /
- physical training
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拉格朗日函数（Lagrange Function）是描述约束条件下优化问题的解析表达式，包含目标函数与约束条件，能有效应对约束最优化、强对偶性等问题。它在经济学理论领域的贡献是寻找多元函数在变量约束下的极值并提供最优解，在实践领域主要用于解决资源最优化问题。我国现有公共体育服务供给评价多采用指标体系构建方法，如层次分析法、熵值法、德尔菲法及模糊综合评价法等，缺乏引入经济模型进行评价的尝试。基于拉格朗日函数的特性与功能，将其应用于公共体育服务供给评价，可增加公共体育服务供给评价方法的选择范围，并提升决策部门优化公共体育服务供给方案的科学性。公共体育服务供给是一个复杂且不稳定的系统。基于双重属性的公共体育服务可细分为有形性公共体育服务与无形性公共体育服务。有形性公共体育服务主要针对基础设施的优化及资源配置效率的提升来补齐供给短板，如健身场地设施等；而无形性公共体育服务更强调公共体育服务的公益性，如公共体育服务政策等。为了实现帕累托最优，需要合理配置有形性公共体育服务和无形性公共体育服务的份额，使资源利用效率和投放效果达到最大化。因此，构建公共体育服务供给效用最大化的函数模型，需要先厘清公共体育服务供给结构，再建立带约束的拉格朗日函数，给出政府决策的最优条件，从而获取达到一般均衡的最佳比例。评价最优解要求有形性公共体育服务与无形性公共体育服务的边际替代率（MRS）相等，即有形性公共体育服务的边际效用（MU）要等于无形性公共体育服务的边际效用，此时公共体育服务的供给结构在理论上达到最佳状态。该函数模型的应用难点在于能否获得完整可靠的数据，从而保证有形性公共体育服务和无形性公共体育服务的量化标准统一。此外，拉格朗日函数解决的是带约束条件的最值问题，因此，不能用于衡量具体的公共体育服务供给水平与质量。
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表 1 CSRM的统计结果(n=20)
Table 1 Descriptive statistics for CSRM (n=20)
类别 Mean±SE TFE/cm 18.8±0.8 DLS/s 33.5±3.1 DLH/H 0.99±0.05 EE/s 75.5±6.2 A60/ (N·m·kg-1) 3.86±0.24** T60 /(N·m·kg-1) 1.70±0.10 A90/ (N·m·kg-1) 3.62±0.21** T90 / (N·m·kg-1) 2.04±0.10 A120/ (N·m·kg-1) 3.51±0.21** T120 / (N·m·kg-1) 1.96±0.12 注：A60、A90、A120分别表示等动训练仪在60°、90°、120°位置时，体质量标准化后的躯干后伸等长力矩峰值；T60、T90、T120分别表示等动训练仪在60°、90°、120°位置时，体质量标准化后的躯干前屈等长力矩峰值；**表示P＜0.01，即与相同速度或角度条件下的相反力矩方向进行对比具有显著性差异；DLH/H是指身高标准化后的DLH值 
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表 2 CSRM与TIS的Pearson相关分析结果(n=20)
Table 2 The Pearson analysis between CSRM and TIS (n=20)
类别 TFE DLS DLH/H EE A60 0.630** 0.313 0.570** 0.092 T60 -0.195 0.106 0.507* -0.410* A90 -0.591** 0.302 0.501* 0.152 T90 -0.342 0.052 0.654** -0.338 A120 -0.733** 0.279 0.445* 0.131 T120 -0.616** 0.286 0.793** -0.111 注：*表示P＜0.05，**表示P＜0.01
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表 3 采用多元线性回归法建立的躯干等长力量预测方程及相关参数
Table 3 Prediction equations of TIS set by multiple linear regression analysis and the related parameters
预测方程 相关系数 R2 P SE A60=7.41-0.19TFE 0.63 0.40 0.03 83.9 T60=0.66+1.05DLH/H 0.51 0.26 0.02 38.3 A90=6.59-0.16TFE 0.59 0.35 0.006 77.7 T90=0.72+1.33DLH/H 0.65 0.43 0.002 33.0 A120=7.22-0.20TFE 0.73 0.54 0.000 66.1 T120=1.32+1.63DLH/H-0.05TFE 0.85 0.73 0.024 29.0
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表 4 TIS实测值与预测值的Pearson相关分析结果(n=20)
Table 4 Pearson analysis on the relationship between measured values and predicted values of TIS (n=20)
类别 相关系数 P A60 0.63 0.003 T60 0.47 0.038 A90 0.59 0.006 T90 0.62 0.004 A120 0.73 0.000 T120 0.79 0.000
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