Klimstra Marc, Zehr E Paul
School of Exercise Science, Physical and Health Education, University of Victoria, Victoria, BC, Canada.
Exp Brain Res. 2008 Mar;186(1):93-105. doi: 10.1007/s00221-007-1207-6. Epub 2007 Nov 27.
The Hoffmann (H)-reflex has been studied extensively as a measure of spinal excitability. Often, researchers compare the H-reflex between experimental conditions with values determined from a recruitment curve (RC). An RC is obtained experimentally by varying the stimulus intensity to a nerve and recording the peak-to-peak amplitudes of the evoked H-reflex and direct motor (M)-wave. The values taken from an RC may provide different information with respect to a change in reflex excitability. Therefore, it is important to obtain a number of RC parameters for comparison. RCs can be obtained with a measure of current (HCRC) or without current (HMRC). The ascending limb of the RC is then fit with a mathematical analysis technique in order to determine parameters of interest such as the threshold of activation and the slope of the function. The purpose of this study was to determine an unbiased estimate of the specific parameters of interest in an RC through mathematical analysis. We hypothesized that a standardized analysis technique could be used to ascertain important points on an RC, regardless of data presentation methodology (HCRC or HMRC). For both HCRC and HMRC produced using 40 randomly delivered stimuli, six different methods of mathematical analysis [linear regression, polynomial, smoothing spline, general least squares model with custom logistic (sigmoid) equation, power, and logarithmic] were compared using goodness of fit statistics (r-square, RMSE). Behaviour and robustness of selected curve fits were examined in various applications including RCs generated during movement and somatosensory conditioning from published data. Results show that a sigmoid function is the most reliable estimate of the ascending limb of an H-reflex recruitment curve for both HCRC and HMRC. Further, the parameters of interest change differentially with respect to the presentation methodology and the analysis technique. In conclusion, the sigmoid function is a reliable analysis technique which mimics the physiologically based prediction of the input/output relation of the ascending limb of the recruitment curve. Therefore, the sigmoid function should be considered an acceptable and preferable analytical tool for H-reflex recruitment curves obtained with reference to stimulation current or M-wave amplitude.
霍夫曼（H）反射作为一种测量脊髓兴奋性的指标，已经得到了广泛研究。研究人员通常会将实验条件下的H反射与根据募集曲线（RC）确定的值进行比较。RC是通过改变对神经的刺激强度并记录诱发的H反射和直接运动（M）波的峰峰值振幅来实验获得的。从RC中获取的值可能会提供关于反射兴奋性变化的不同信息。因此，获取多个RC参数进行比较很重要。RC可以通过电流测量（HCRC）或无电流测量（HMRC）获得。然后，使用数学分析技术对RC的上升支进行拟合，以确定感兴趣的参数，如激活阈值和函数斜率。本研究的目的是通过数学分析确定RC中感兴趣的特定参数的无偏估计。我们假设可以使用标准化分析技术来确定RC上的重要点，而不管数据呈现方法（HCRC或HMRC）如何。对于使用40个随机发放刺激产生的HCRC和HMRC，使用拟合优度统计量（决定系数、均方根误差）比较了六种不同的数学分析方法[线性回归、多项式、平滑样条、带有定制逻辑（S形）方程的广义最小二乘模型、幂函数和对数函数]。在各种应用中检查了所选曲线拟合的行为和稳健性，包括从已发表数据中获取的运动期间生成的RC和体感调节。结果表明，对于HCRC和HMRC，S形函数是H反射募集曲线上升支最可靠的估计。此外，感兴趣的参数因呈现方法和分析技术而异。总之，S形函数是一种可靠的分析技术，它模仿了基于生理学的募集曲线上升支输入/输出关系的预测。因此，对于参照刺激电流或M波振幅获得的H反射募集曲线，S形函数应被视为一种可接受且更可取的分析工具。
