During the first years of life, the human brain undergoes dynamic spatially-heterogeneous changes, involving differentiation of neuronal types, dendritic arborization, axonal ingrowth, outgrowth and retraction, synaptogenesis, and myelination. To better quantify these changes, this article presents a method for probing tissue microarchitecture by characterizing water diffusion in a spectrum of length scales, factoring out the effects of intra-voxel orientation heterogeneity. Our method is based on the spherical means of the diffusion signal, computed over gradient directions for a fixed set of diffusion weightings (i.e., b-values). We decompose the spherical mean series at each voxel into a spherical mean spectrum (SMS), which essentially encodes the fractions of spin packets undergoing fine- to coarse-scale diffusion processes, characterizing hindered and restricted diffusion stemming respectively from extra- and intra-neurite water compartments. From the SMS, multiple orientation distribution invariant indices can be computed, allowing for example the quantification of neurite density, microscopic fractional anisotropy ($mu$FA), per-axon axial/radial diffusivity, and free/restricted isotropic diffusivity. We show maps of these indices for baby brains, demonstrating that microscopic tissue features can be extracted from the developing brain for greater sensitivity and specificity to development related changes. Also, we demonstrate that our method, called spherical mean spectrum imaging (SMSI), is fast, accurate, and can overcome the biases associated with other state-of-the-art microstructure models.
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