The Population Receptive Field (pRF) model is widely used to predict the location (retinotopy) and size of receptive fields on the visual space. Doing so allows for the creation of a mapping from locations in the visual field to the associated groups of neurons in the cortical region (within the visual cortex of the brain). However, using the pRF model is very time consuming. Past research has focused on the creation of Convolutional Neural Networks (CNN) to mimic the pRF model in a fraction of the time, and they have worked well under highly controlled conditions. However, these models have not been thoroughly tested on real human data. This thesis focused on adapting one of these CNNs to accurately predict the retinotopy of a real human subject using a dataset from the Human Connectome Project. The results show promise towards creating a fully functioning CNN, but they also expose new challenges that must be overcome before the model could be used to predict the retinotopy of new human subjects.

Functional magnetic resonance imaging (fMRI) has been widely used to measure the retinotopic organization of early visual cortex in the human brain. Previous studies have identified multiple visual field maps (VFMs) based on statistical analysis of fMRI signals, but the resulting geometry has not been fully characterized with mathematical models. This thesis explores using concepts from computational conformal geometry to create a custom software framework for examining and generating quantitative mathematical models for characterizing the geometry of early visual areas in the human brain. The software framework includes a graphical user interface built on top of a selected core conformal flattening algorithm and various software tools compiled specifically for processing and examining retinotopic data. Three conformal flattening algorithms were implemented and evaluated for speed and how well they preserve the conformal metric. All three algorithms performed well in preserving the conformal metric but the speed and stability of the algorithms varied. The software framework performed correctly on actual retinotopic data collected using the standard travelling-wave experiment. Preliminary analysis of the Beltrami coefficient for the early data set shows that selected regions of V1 that contain reasonably smooth eccentricity and polar angle gradients do show significant local conformality, warranting further investigation of this approach for analysis of early and higher visual cortex.