The stretched exponential function has many applications in modeling numerous types of experimental relaxation data. However, problems arise when using standard algorithms to fit this function: we have observed that different initializations result in distinct fitted parameters. To avoid this problem, we developed a novel algorithm for fitting the stretched exponential model to relaxation data. This method is advantageous both because it requires only a single adjustable parameter and because it does not require initialization in the solution space. We tested this method on simulated data and experimental stress-relaxation data from bone and cartilage and found favorable results compared to a commonly-used Quasi-Newton method. For the simulated data, strong correlations were found between the simulated and fitted parameters suggesting that this method can accurately determine stretched exponential parameters. When this method was tested on experimental data, high quality fits were observed for both bone and cartilage stress-relaxation data that were significantly better than those determined with the Quasi-Newton algorithm.

Measurements of neuronal activity across brain areas are important for understanding the neural correlates of cognitive and motor processes such as attention, decision-making and action selection. However, techniques that allow cellular resolution measurements are expensive and require a high degree of technical expertise, which limits their broad use. Wide-field imaging of genetically encoded indicators is a high-throughput, cost-effective and flexible approach to measure activity of specific cell populations with high temporal resolution and a cortex-wide field of view. Here we outline our protocol for assembling a wide-field macroscope setup, performing surgery to prepare the intact skull and imaging neural activity chronically in behaving, transgenic mice. Further, we highlight a processing pipeline that leverages novel, cloud-based methods to analyze large-scale imaging datasets. The protocol targets laboratories that are seeking to build macroscopes, optimize surgical procedures for long-term chronic imaging and/or analyze cortex-wide neuronal recordings. The entire protocol, including steps for assembly and calibration of the macroscope, surgical preparation, imaging and data analysis, requires a total of 8 h. It is designed to be accessible to laboratories with limited expertise in imaging methods or interest in high-throughput imaging during behavior.