# C3 VFC: A Method for Tracing and Quantification of Microglia in 3D Temporal Images
## 1 Introduction  
The recent realization that the central nervous system (CNS) and the immune system are not two isolated systems, but rather connected systems, implies the relationship and interaction between neurons and immune cells in the CNS [1, 2]. Researchers are attempting to understand the impact of microglia not only in development and homeostasis, but also their role in injury, diseases, and aging [3, 4, 5, 6]. The morphological changes of microglia are directly associated with functional roles in normal and pathological central nervous systems. Microglia have processes, or branches, that extend from the soma, or cell body. In a healthy brain, the processes dynamically extend and retract to respond to changes and to surveil the environment [7, 8, 9, 10, 11, 12]. However, in response to diseased settings, activated microglia transition from a highly ramified state to a less ramified, amoeboid state [13, 14]. These changes suggest that microglia may be related to the progression of neurodegenerative diseases, such as Parkinson's disease, multiple sclerosis, and Alzheimer's disease. However, little is known about how the decrease in the activity and motility of a microglia's processes affect the microglia's ability to perform surveillance functions in the brain. This work meets a major need of the immunology and neuroscience communities; namely, it provides a toolbox of image-based bioinformatics for glia. Quantifying morphological changes can lead to understanding the function and activation of microglia in different settings. The complex structure of the thin microglia processes and inhomogenous, noisy microscopy images make manual and automatic tracing challenging. Currently, most glia image analysis is done by hand, where scientists manually trace the processes. With high-throughput imaging, researchers may be able toreveal a quantitative model of morphological differences, but in such cases, manual analysis is infeasible. Existing studies have manually traced glial images or used heuristic image processing methods to measure process length, extension, and retraction over time [15; 16; 17; 18; 19]. However, manual tracing can be prone to human error and user-variability. Ramified microglia have fine processes that can intertwine which makes it difficult to distinguish between cells. Most tracings done for analysis was performed on 2D images where branches overlap or are occluded and lead to further loss of information and inaccurate analysis. Manual or semi-automated methods are time-consuming with high-throughput imaging and larger datasets. Common automatic image analysis approaches used for quantification depend on thresholding inhomogenous and noisy images which result in over-segmented reconstructions or an under-segmentation with missing branches. Some papers related to the reconstruction and analysis of microglia have provided significant contributions to the structural analysis of these cells, but they use thresholding techniques that are are not able to accurately capture the entire cell [19; 20]. Our goal is to create an automatic tracing method that achieves consistent reconstructions of 3D images over time to obtain an accurate analysis of the image and video data. An accurate tracing of tubular cells yields the medial axis, or centerline, of the structure. In [21; 22], the researchers developed an algorithm that automatically skeletonized and segmented 3D images of microglia. They were able to find the centerline of the processes using an active contour method and gradient vector field. However, the image was reconstructed one pixel or voxel at a time to counter the difficulties of open curve tracing. Other centerline tracing methods find and connect endpoints and critical points of an object [23]. Critical points indicate the key structural changes of an object and can be identified by analyzing the topology of vector fields.