Open access publication rates have been steadily increasing over time. In spite of this growth, academics in low income settings struggle to gain access to the full canon of research literature. While the vast majority of open access repositories and funding organizations with open access policies are based in high income countries, the geographic patterns of open access publication itself are not well characterized. In this study, we developed a computational approach to better understand the topical and geographical landscape of open access publications in the biomedical research literature. Surprisingly, we found a strong negative correlation between country per capita income and the percentage of open access publication. Open access publication rates were particularly high in sub-Saharan Africa, but vastly lower in the Middle East and North Africa, South Asia, and East Asia and the Pacific. These effects persisted when considering papers only bearing authors from within each region and income group. However, papers resulting from international collaborations did have a higher percentage of OA than single-country papers, and inter-regional collaboration increased OA publication for all world regions. There was no clear relationship between the number of open access policies in a region and the percentage of open access publications in that region. To understand the distribution of open access across topics of biomedical research, we examined keywords that were most enriched and depleted in open access papers. Keywords related to genomics, computational biology, animal models, and infectious disease were enriched in open access publications, while keywords related to the environment, nursing, and surgery were depleted in open access publications. This work identifies geographic regions and fields of research that could be priority areas for open access advocacy. The finding that open access publication rates are highest in sub-Saharan Africa and low income countries suggests that factors other than open access policy strongly influence authors' decisions to make their work openly accessible. The high proportion of OA resulting from international collaborations indicates yet another benefit of collaborative research. Certain applied fields of medical research, notably nursing, surgery, and environmental fields, appear to have a greater proportion of fee-for-access publications, which presumably creates barriers that prevent researchers and practitioners in low income settings from accessing the literature in those fields.