Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts, United States of America.
PLoS One. 2011;6(6):e20490. doi: 10.1371/journal.pone.0020490. Epub 2011 Jun 7.
Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.
双光子钙成像现在是生物系统体内成像的重要工具。通过实现亚细胞分辨率的神经元群体成像，这种模式为深入了解大脑解剖结构和生理学提供了一种方法。钙成像数据的正确分析需要去噪，即将信号与复杂的生理噪声分离。为了分析双光子脑成像数据，我们提出了一个信号加色噪声模型，其中信号表示为谐波回归，相关噪声表示为阶自回归过程。我们提供了一种有效的循环下降算法，通过将加权最小二乘程序与 Burg 算法相结合，计算近似最大似然参数估计。我们使用赤池信息量准则来指导谐波回归和自回归模型阶数的选择。我们灵活而简约的建模方法可靠地将刺激诱发的荧光响应与背景活动和噪声分离，评估拟合优度，并估计置信区间和信噪比。这种精细的分离导致个体细胞的图像对比度显著增强，包括亚细胞细节和网络活动的清晰描绘。我们的方法应用于雪貂初级视觉皮层的体内成像数据表明，我们的方法可以得到大大去噪的信号估计。我们还提供了一个一般的 Volterra 级数框架，用于推导这种和其他用于成像的信号加相关噪声模型。这种分析双光子钙成像数据的方法可以很容易地应用于其他应用相关噪声模型的计算生物学问题。
