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Women are at higher risk of Alzheimer’s and other neurological diseases after menopause, and yet research con- necting female brain health to sex hormone fluctuations is limited. We seek to investigate this connection by develop- ing tools that quantify 3D shape changes that occur in the brain during sex hormone fluctuations. Geodesic regression on the space of 3D discrete surfaces offers a principled way to characterize the evolution of a brain’s shape. However, in its current form, this approach is too computationally expensive for practical use. In this paper, we pro- pose approximation schemes that accelerate geodesic regression on shape spaces of 3D discrete surfaces. We also provide rules of thumb for when each approximation can be used. We test our approach on synthetic data to quantify the speed-accuracy trade-off of these approximations and show that practitioners can expect very significant speed-up while only sacrificing little accuracy. Finally, we apply the method to real brain shape data and produce the first characterization of how the female hippocampus changes shape during the menstrual cycle as a function of progesterone: a characterization made (practically) possible by our approximation schemes. Our work paves the way for comprehensive, practical shape analyses in the fields of bio-medicine and computer vision. Our implementation is publicly avail- able on GitHub. 

Long overlooked in neuroscience research, sex and gender are increasingly included as key variables potentially impacting all levels of neurobehavioral analysis. Still, many neuroscientists do not understand the difference between the terms “sex” and “gender,” the complexity and nuance of each, or how to best include them as variables in research designs. This TechSights article outlines rationales for considering the influence of sex and gender across taxa, and provides technical guidance for strengthening the rigor and reproducibility of such analyses. This guidance includes the use of appropriate statistical methods for comparing groups as well as controls for key covariates of sex (e.g., total intracranial volume) and gender (e.g., income, caregiver stress, bias). We also recommend approaches for interpreting and communicating sex- and gender-related findings about the brain, which have often been misconstrued by neuroscientists and the lay public alike.