A 4D hyperspherical interpretation of q-space

[Display omitted] •Derive a 4D hyperspherical harmonic-based framework to estimate the 3D q-space signal and dODF.•Estimate rotationally invariant q-space indices using our framework, like Po and QIV.•Validate our framework using HYDI-acquired datasets, both synthetic and in vivo.•Compare our framework to existing analytical methods, specifically BFOR.•Derive a novel integral transform. 3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space.