A sigmoid function is the best fit for the ascending limb of the Hoffmann reflex recruitment curve
A sigmoid function is the best fit for the ascending limb of the Hoffmann reflex recruitment curve
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DOI：
10.1007/s00221-007-1207-6
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发表时间：
2008-03-01
影响因子：
2
通讯作者：
Zehr, E. Paul
中科院分区：
文献类型：
--
作者：
Klimstra, Marc;Zehr, E. Paul
霍夫曼（H）反射作为脊髓兴奋性的量度已被广泛研究。通常，研究人员将实验条件下的H反射与从募集曲线（RC）确定的值进行比较。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-峰幅度，实验获得RC。取自RC的值可以提供关于反射兴奋性变化的不同信息。因此，获取多个RC参数进行比较非常重要。RC可以通过测量电流（HCRC）或不测量电流（HMRC）来获得。然后用数学分析技术拟合RC的上升支，以确定感兴趣的参数，例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，一个标准化的分析技术可以用来确定RC上的重要点，无论数据呈现方法（HCRC或HMRC）。对于使用40个随机递送的刺激产生的HCRC和HMRC，使用拟合优度统计（r方，RMSE）比较六种不同的数学分析方法[线性回归、多项式、平滑样条、具有自定义逻辑（S形）方程的一般最小二乘模型、功率和对数]。在各种应用中，包括从已发表的数据中产生的运动和体感调节过程中产生的RC，对所选曲线拟合的行为和稳健性进行了检查。结果表明，S形函数是HCRC和HMRC的H反射募集曲线上升支的最可靠估计。此外，感兴趣的参数相对于呈现方法和分析技术而不同地改变。总之，S形函数是一种可靠的分析技术，它模拟了募集曲线上升支的输入/输出关系的生理预测。因此，对于参考刺激电流或M波振幅获得的H反射募集曲线，应将S形函数视为可接受且优选的分析工具。
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.