The goal of in vivo histology is to extract biologically relevant metrics from MRI data¹. In the neuroimaging domain this includes characterising white matter fibres in terms of orientation, distribution and g-ratio, or determining the myelo- and cyto-architecture within the cortex. This task requires advanced biophysical models to relate the measured MRI signal to the underlying tissue microstructure. It has previously been shown, through theoretical modelling and experimental validation, that the signal decay in gradient recalled echoes (GRE) exhibits higher order temporal behaviour² that is dependent on a variety of intra-voxel microstructural metrics, e.g. fibre orientation, axonal and extra-cellular volumes, compartment-specific susceptibility etc. The fact that such biophysical models depend on an array of parameters makes their inversion to extract biologically-relevant microstructural metrics ill-posed and particularly problematic when dealing with noisy data. In addition, higher order information is typically only accessible through the acquisition of long TE data, leading to extended protocol durations. Here we use adaptive smoothing to generate maps of both the first and second order components of the temporal decay of the GRE signal from short TE (maximally 18.6ms) data using a time-efficient multi-parameter mapping³ (MPM) protocol.Data were acquired on a 7T Magnetom system (Siemens Healthcare, Germany) as part of a whole brain MPM protocol³ with 800µm isotropic resolution. Multi-echo spoiled gradient echo (SPGR) data were acquired with predominantly proton density (PDw; flip angle = 6⁰), T1- (29⁰) or magnetisation transfer (MTw; 6⁰ plus a 4ms Gaussian pulse 2kHz off-resonance prior to excitation) weighting. Each had a TR of 25.5ms and echoes were acquired with 2.3ms echo-spacing from TE = 2.5ms to TE = 14ms (MTw) or 18.6ms (PDw and T1w). The protocol duration was just under 25 minutes and additionally provided data to generate quantitative maps of magnetisation transfer, longitudinal relaxation rate and effective proton density (not shown here) including correction of B₁⁺ inhomogeneity. Extending the ESTATICS approach⁴, a common temporal decay with first and second order components (orthogonalised with respect to each other) was assumed for all contrasts, while allowing variable signal amplitude for each. This was done twice: with and without adaptive smoothing of the weighted SPGR volumes prior to the calculation of the decay components. The adaptive smoothing aims to boost SNR while preserving anatomical boundaries, even on a fine scale. This is achieved through a multi-scale smoothing procedure that defines adaptive local weights to estimate a weighted signal average.Maps of the first order component of the signal decay were of high quality, e.g. figure 1A, B. The benefit of adaptive smoothing is primarily seen in the second order component of the signal decay (figure 1: C versus D). As expected from theoretical analysis², this second order component is higher in fibre pathways that are orthogonal to the main field (figure 2). This can be seen by comparing the map (figure 2C, D) with the corresponding fibre orientation vectors derived from a diffusion weighted dataset (figure 2A, B) acquired from the same participant in a different imaging session at 3T.Adaptive smoothing improves estimation of the second order component of the temporal decay of the GRE signal. This allowed stable estimation of this component to be made from a time efficient protocol with a maximum TE of just 18.6ms and a protocol duration of just 25 minutes. The MPM protocol additionally provides further quantitative information leading to a rich data set with which to investigate brain microstructure. In agreement with theory, high values for the second order component of the signal decay are seen in fibre pathways perpendicular to the main field. Further understanding the microstructural components dominating this higher order component of the GRE signal decay will be the focus of future work.