The neuroanatomical organization of the hypothalamus is driven by spatial and topological efficiency

Abstract

The hypothalamus in the mammalian brain is responsible for regulating functions associated with survival and reproduction representing a complex set of highly interconnected, yet anatomically and functionally distinct, sub-regions. It remains unclear what factors drive the spatial organization of sub-regions within the hypothalamus. One potential factor may be structural connectivity of the network that promotes efficient function with well-connected sub-regions placed closer together geometrically, i.e., the strongest axonal signal transferred through the shortest geometrical distance. To empirically test for such efficiency, we use hypothalamic data derived from the Allen Mouse Brain Connectivity Atlas, which provides a structural connectivity map of mouse brain regions derived from a series of viral tracing experiments. Using both cost function minimization and comparison with a weighted, sphere-packing ensemble, we demonstrate that the sum of the distances between hypothalamic sub-regions are not close to the minimum possible distance, consistent with prior whole brain studies. However, if such distances are weighted by the inverse of the magnitude of the connectivity, their sum is among the lowest possible values. Specifically, the hypothalamus appears within the top 94th percentile of neural efficiencies of randomly packed configurations and within one standard deviation of the median efficiency when packings are optimized for maximal neural efficiency. Our results, therefore, indicate that a combination of geometrical and topological constraints help govern the structure of the hypothalamus.

Keywords: Allen Brain Atlas; Monte - Carlo simulation; computational biology; connectivity; connectome; efficiency; graph theory - graph algorithms; hypothalamus.

Figure 1

(A) The spatial structure of the 26 sub-regions of hypothalamus derived from the Allen Brain Atlas. The outlier regions, PVH, ADP, and SBPV, are removed. (B) The spherical model of the sub-regions of the hypothalamus. For a list of sub-region abbreviations, see Appendix A. (C) Graphical representation of the hypothalamic network. Each node represents a brain region and each arrow an axonal projection. The width of the arrows represents the axonal volume. (D) 3D projection of the spatial structure of the hypothalamus. See Appendix A for a list of abbreviations.

Figure 2

A visual summary of the random packing algorithm used to generate theoretical hypothalamic configurations to compare to the true configuration of the hypothalamus.

Figure 3

The wiring cost, defined in Eq. (2), is minimized for 10⁴ different starting points in the $26\times 3$ dimensional phase-space. The histogram shows the optimal wiring costs. The vertical red line represents the wiring cost of true hypothalamus.

Figure 4

(A) A histogram of maximized efficiencies as defined in Eq. (1) for 10,000 random initial guesses. The vertical red line represents the efficiency of the mouse hypothalamus using the measurements derived from the Allen Brain Atlas. This figure indicates that the hypothalamus is organized such that Eq. (1) is among the highest values that are possible although it is not the unique efficient packing. The configurations on the left and right show example configurations from different low- and high-efficiency bins. Two different hypothalamus sub-regions are highlighted in green and red to show their changes in position. (B) The histogram of efficiencies of 48,300 randomly packed hypothalamus sub-regions superimposed upon histogram from panel (A). These configurations are randomly generated and not optimized for efficiency. Comparing the two histograms shows that the true network is among the most efficient of optimized networks, which together are more efficient than an ensemble of randomly configured theoretical hypothalamic networks.