Zhang Jun
Department of Psychology, University of Michigan, Ann Arbor 48109-1109, USA.
J Opt Soc Am A Opt Image Sci Vis. 2005 Oct;22(10):2246-56. doi: 10.1364/josaa.22.002246.
When an oriented bar or grating is drifted across the receptive field of a cortical neuron at various orientations, the tuning function reflects both, and thus confounds the orientation (ORI) and the direction-of-motion (DIR) selectivity of the cell. Since ORI (or DIR), by definition, has a period of 180(or 360) deg/cycle, a popular method for separating these two components, due to Wörgötter and Eysel [Biol. Cybern. 57, 349 (1987)], is to Fourier decompose the neuron's response along the angular direction and then identify the first and the second harmonic with DIR and ORI, respectively (the SDO method). Zhang [Biol. Cybern. 63, 135 (1990)] pointed out that this interpretation is misconceived--all odd harmonics (not just the first harmonic) reflect the DIR component, whereas all even harmonics (including the second harmonic) contain contributions from both DIR and ORI. Here, a simplified procedure is proposed to accomplish the goal of unconfounding ORI and DIR. We first construct the sum of all odd harmonics of the overall tuning curve, denoted ODDSUM, by calculating the difference in the neuronal response to opposite drifting directions. Then we construct ODDSUM+/ODDSUM/ and identify it with DIR (here . denotes the absolute value). Subtracting DIR, that is ODDSUM+ /ODDSUM/, from the overall tuning curve gives ORI. Our method ensures that (i) the reconstructed DIR contains only one, positive peak at the preferred direction and can have power in all harmonics, and (ii) the reconstructed ORI has two peaks separated by 180 degrees and has zero power for all odd harmonics. Using this procedure, we have unconfounded orientation and direction components for a considerable sample of macaque striate cortical cells, and compared the results with those obtained using Wörgötter and Eysel's SDO method. We found that whereas the estimate of the peak angle of ORI remains largely unaffected, Wörgötter and Eysel's method considerably overestimated the relative strength of ORI. To conclude, a simple method is provided for appropriately separating the orientation and directional tuning in a neuron's response that is confounded as a result of the use of drifting oriented stimuli.
当一个有方向的条形或光栅以不同方向在皮层神经元的感受野上移动时，调谐函数会反映这两者，从而混淆了细胞的方向（ORI）和运动方向（DIR）选择性。根据定义，由于ORI（或DIR）的周期为180（或360）度/周期，一种由Wörgötter和Eysel [《生物控制论》57, 349 (1987)]提出的分离这两个成分的常用方法是对神经元沿角度方向的响应进行傅里叶分解，然后分别将一次谐波和二次谐波与DIR和ORI对应起来（SDO方法）。Zhang [《生物控制论》63, 135 (1990)]指出这种解释是错误的——所有奇次谐波（不仅仅是一次谐波）反映DIR成分，而所有偶次谐波（包括二次谐波）都包含DIR和ORI两者的贡献。在此，我们提出一种简化程序来实现区分ORI和DIR的目标。我们首先通过计算神经元对相反移动方向的响应差异来构建总体调谐曲线所有奇次谐波的总和，记为ODDSUM。然后我们构建ODDSUM+/ODDSUM/并将其与DIR对应起来（这里.表示绝对值）。从总体调谐曲线中减去DIR，即ODDSUM+/ODDSUM/，就得到ORI。我们的方法确保：（i）重建的DIR在偏好方向上仅包含一个正峰值，并且可以在所有谐波中具有功率；（ii）重建的ORI有两个相隔180度的峰值，并且对于所有奇次谐波功率为零。使用这个程序，我们已经区分了相当数量的猕猴纹状皮层细胞样本的方向和方向成分，并将结果与使用Wörgötter和Eysel的SDO方法获得的结果进行了比较。我们发现，虽然ORI峰值角度的估计基本不受影响，但Wörgötter和Eysel的方法大大高估了ORI的相对强度。总之，我们提供了一种简单的方法来适当地分离由于使用移动的有方向刺激而混淆的神经元响应中的方向和方向调谐。
