This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. We are interested in developing quantitative computational models for absolute determination of cerebral blood flow and metabolism in-vivo, providing new metrics for the study of acute and chronic brain injury, and functional cortical activation. In collaboration with both the Virtual Tissue Simulator (VTS) and Wide-field Functional Imaging (WiFI) projects (VP and MTT cores, respectively), we propose to develop and characterize models of temporal correlation diffusion in the spatial frequency domain. These models will provide a unified mathematical framework for WiFI's proposed combination of two LAMMP technologies: 1) modulated imaging (MI), a spatial-frequency-domain imaging method based on structured illumination, and 2) laser speckle imaging (LSI). In addition, they will provide additional forward kernels for the VTS system, allowing researchers to better predict and design wide-field LSI measurements. As described in the WiFI project, MI has demonstrated the capability of non-invasively mapping the absorption and scattering optical properties of biological tissues over a wide field-of-view. Optical absorption measurement at two or more wavelengths further allows local sampling of local in-vivo concentrations of oxy- and deoxy-hemoglobin, providing a direct assessment of blood volume and oxygen saturation at the tissue level. LSI mapping of speckle contrast[1] has traditionally provided a relative measure of local blood flow. However, with simultaneous, co-registered maps of local optical properties, blood volume and speckle contrast, absolute blood flow and local cerebral oxygen metabolism can be quantified. Moreover, spatial light modulation of laser speckle provides a new contrast mechanism for depth-resolving the tissue blood flow. Our hypothesis is that these quantitative models will provide new insight into brain function, allowing objective, longitudinal study of a wide variety of cerebrovascular applications, including stroke, trauma, epilepsy, and neuroprotective agent studies, as well as functional imaging paradigms such as cortical activation.