Training data distribution significantly impacts the estimation of tissue microstructure with machine learning.

PURPOSE: Supervised machine learning (ML) provides a compelling alternative to traditional model fitting for parameter mapping in quantitative MRI. The aim of this work is to demonstrate and quantify the effect of different training data distributions on the accuracy and precision of parameter estimates when supervised ML is used for fitting. METHODS: We fit a two- and three-compartment biophysical model to diffusion measurements from in-vivo human brain, as well as simulated diffusion data, using both traditional model fitting and supervised ML. For supervised ML, we train several artificial neural networks, as well as random forest regressors, on different distributions of ground truth parameters. We compare the accuracy and precision of parameter estimates obtained from the different estimation approaches using synthetic test data. RESULTS: When the distribution of parameter combinations in the training set matches those observed in healthy human data sets, we observe high precision, but inaccurate estimates for atypical parameter combinations. In contrast, when training data is sampled uniformly from the entire plausible parameter space, estimates tend to be more accurate for atypical parameter combinations but may have lower precision for typical parameter combinations. CONCLUSION: This work highlights that estimation of model parameters using supervised ML depends strongly on the training-set distribution. We show that high precision obtained using ML may mask strong bias, and visual assessment of the parameter maps is not sufficient for evaluating the quality of the estimates.

Comparative analysis of signal models for microscopic fractional anisotropy estimation using q-space trajectory encoding.

Microscopic diffusion anisotropy imaging using diffusion-weighted MRI and multidimensional diffusion encoding is a promising method for quantifying clinically and scientifically relevant microstructural properties of neural tissue. Several methods for estimating microscopic fractional anisotropy (µFA), a normalized measure of microscopic diffusion anisotropy, have been introduced but the differences between the methods have received little attention thus far. In this study, the accuracy and precision of µFA estimation using q-space trajectory encoding and different signal models were assessed using imaging experiments and simulations. Three healthy volunteers and a microfibre phantom were imaged with five non-zero b-values and gradient waveforms encoding linear and spherical b-tensors. Since the ground-truth µFA was unknown in the imaging experiments, Monte Carlo random walk simulations were performed using axon-mimicking fibres for which the ground truth was known. Furthermore, parameter bias due to time-dependent diffusion was quantified by repeating the simulations with tuned waveforms, which have similar power spectra, and with triple diffusion encoding, which, unlike q-space trajectory encoding, is not based on the assumption of time-independent diffusion. The truncated cumulant expansion of the powder-averaged signal, gamma-distributed diffusivities assumption, and q-space trajectory imaging, a generalization of the truncated cumulant expansion to individual signals, were used to estimate µFA. The gamma-distributed diffusivities assumption consistently resulted in greater µFA values than the second order cumulant expansion, 0.1 greater when averaged over the whole brain. In the simulations, the generalized cumulant expansion provided the most accurate estimates. Importantly, although time-dependent diffusion caused significant overestimation of µFA using all the studied methods, the simulations suggest that the resulting bias in µFA is less than 0.1 in human white matter.

On the potential for mapping apparent neural soma density via a clinically viable diffusion MRI protocol.

Diffusion MRI is a valuable tool for probing tissue microstructure in the brain noninvasively. Today, model-based techniques are widely available and used for white matter characterisation where their development is relatively mature. Conversely, tissue modelling in grey matter is more challenging, and no generally accepted models exist. With advances in measurement technology and modelling efforts, a clinically viable technique that reveals salient features of grey matter microstructure, such as the density of quasi-spherical cell bodies and quasi-cylindrical cell projections, is an exciting prospect. As a step towards capturing the microscopic architecture of grey matter in clinically feasible settings, this work uses a biophysical model that is designed to disentangle the diffusion signatures of spherical and cylindrical structures in the presence of orientation heterogeneity, and takes advantage of B-tensor encoding measurements, which provide additional sensitivity compared to standard single diffusion encoding sequences. For the fast and robust estimation of microstructural parameters, we leverage recent advances in machine learning and replace conventional fitting techniques with an artificial neural network that fits complex biophysical models within seconds. Our results demonstrate apparent markers of spherical and cylindrical geometries in healthy human subjects, and in particular an increased volume fraction of spherical compartments in grey matter compared to white matter. We evaluate the extent to which spherical and cylindrical geometries may be interpreted as correlates of neural soma and neural projections, respectively, and quantify parameter estimation errors in the presence of various departures from the modelling assumptions. While further work is necessary to translate the ideas presented in this work to the clinic, we suggest that biomarkers focussing on quasi-spherical cellular geometries may be valuable for the enhanced assessment of neurodevelopmental disorders and neurodegenerative diseases.

Modeling Fibrillogenesis of Collagen-Mimetic Molecules.

One of the most robust examples of self-assembly in living organisms is the formation of collagen architectures. Collagen type I molecules are a crucial component of the extracellular matrix, where they self-assemble into fibrils of well-defined axial striped patterns. This striped fibrillar pattern is preserved across the animal kingdom and is important for the determination of cell phenotype, cell adhesion, and tissue regulation and signaling. The understanding of the physical processes that determine such a robust morphology of self-assembled collagen fibrils is currently almost completely missing. Here, we develop a minimal coarse-grained computational model to identify the physical principles of the assembly of collagen-mimetic molecules. We find that screened electrostatic interactions can drive the formation of collagen-like filaments of well-defined striped morphologies. The fibril axial pattern is determined solely by the distribution of charges on the molecule and is robust to the changes in protein concentration, monomer rigidity, and environmental conditions. We show that the striped fibrillar pattern cannot be easily predicted from the interactions between two monomers but is an emergent result of multibody interactions. Our results can help address collagen remodeling in diseases and aging and guide the design of collagen scaffolds for biotechnological applications.

Microscopic susceptibility anisotropy imaging.

PURPOSE: The gradient-echo MR signal in brain white matter depends on the orientation of the fibers with respect to the external magnetic field. To map microstructure-specific magnetic susceptibility in orientationally heterogeneous material, it is thus imperative to regress out unwanted orientation effects. METHODS: This work introduces a novel framework, referred to as microscopic susceptibility anisotropy imaging, that disentangles the 2 principal effects conflated in gradient-echo measurements, (a) the susceptibility properties of tissue microenvironments, especially the myelin microstructure, and (b) the axon orientation distribution relative to the magnetic field. Specifically, we utilize information about the orientational tissue structure inferred from diffusion MRI data to factor out the B0 -direction dependence of the frequency difference signal. RESULTS: A human pilot study at 3 T demonstrates proxy maps of microscopic susceptibility anisotropy unconfounded by fiber crossings and orientation dispersion as well as magnetic field direction. The developed technique requires only a dual-echo gradient-echo scan acquired at 1 or 2 head orientations with respect to the magnetic field and a 2-shell diffusion protocol achievable on standard scanners within practical scan times. CONCLUSIONS: The quantitative recovery of microscopic susceptibility features in the presence of orientational heterogeneity potentially improves the assessment of microstructural tissue integrity.