Conclusions

The chapter has given a brief exposure to the popular mathematical tools used for modeling, mapping and extracting useful information from the brain. Every great leap in neuroscience has been preceded by the development of instrumentation or methodology. The rate of methodological progress has been steadily increasing, resulting in more comprehensive and useful maps of brain structure and function. There also has been an ever-closer relationship between neuroscience and those disciplines (especially mathematics and statistics) that can help accelerate the development of tools to map the brain.(Toga and Mazziotta, 2002)

Mathematical techniques used in structural and functional neuroimaging studies, like

• diffusion tensor imaging, • state-of-the-art algorithms for computational anatomy and algorithms

for meta-analysis of functional images,

• methods to relate imaging information to genetics, • cutting-edge methods for image registration and segmentation indis-

pensable steps in all brain image analysis,

• sophisticated modeling of cortical anatomy and function, • statistics of anatomical variation in development and disease, • creation of anatomical templates and atlases to represent popula-

tions, and

• automatic labeling of brain structures are discussed in the special issue of NeuroImage, entitled Mathematics in Brain Imaging (Thompson et al., 2009).