Diffusion MRI of Brain Tissue: Importance of Axonal Trajectory

Obtaining microstructural information non-invasively on brain tissue remains a challenge. Diffusion magnetic resonance imaging (dMRI) is an imaging method that can provide such information. That includes geometrical considerations of nerve cells projections, axons, that are present in the white matter of the human brain. Axons carry information encoded into electrical impulses to other cells. The thesis deals with estimating parameters of the axonal trajectories, modeled as one-dimensional pathways, from the dMRI signal. That is achieved in two steps: constructing a forward model to predict the dMRI signal and, vice versa, estimating the tissue parameters from dMRI signal by solving the so-called inverse problem. The proposed forward model employs a spectral analysis of dMRI signal. This formulation enables signal prediction for any gradient waveform and helps to identify the physical characteristics of the underlying system that are preserved in the dMRI signal. The physical properties are represented in so-called diffusion spectra whereas gradient waveforms, that sensitizes the signal, are in the encoding spectra. To mimic biologically plausible axonal trajectories, axonal trajectories were modeled by a 1D-toy model that incorporates harmonic waves with variable degree of randomness. Different numerical methods for computation of diffusion spectra were compared, and the resulting spectra were characterized by a phenomenological model incorporating three parameters. It was not possible to estimate the exact parameters of the 1D-toy model from diffusion spectra. Nonetheless, it was possible to estimate their statistical descriptors, namely microscopic orientation dispersion and dispersion-weighted wavelength. Solving the inverse problem posed a major challenge. The phenomenological model of the diffusion spectra was incorporated in a forward model of the diffusion-weighted signal perpendicular to the trajectory and applied to a state-of-the-art data acquired in human brain white matter of a healthy volunteer. It was not possible to estimate all the parameters of the phenomenological model but by constraining the parameters to plausible values we could estimate the last that was within the range predicted by histology. Incorporating trajectory-parameters in the model of white matter diffusion yielded fit residuals as small as those obtained with current state-of-the-art models assuming parallel, straight, and cylindrical cylinders. However, the cylinder model predicted axon diameters far outside the range expected from histology. We conclude that neglecting the axonal trajectories leads to biased models of axons in brain white matter.MRI can serve as an example of successfully applied fundamental research from physics to biological sciences, humanities, chemistry or medicine. Biomolecules in biochemistry can be probed with atomic resolution. Nanomaterials in material sciences, porous rocks in geology, cell structures or tissues in biology and medicine can be examined. Statistical analysis of MRI signal can reveal functional state of the brain and is relevant in e.g. psychology. This thesis deals mainly with applications within medical sciences. Diffusion magnetic resonance imaging (dMRI) unravels the tissue microstructure, i.e. the structure of tissue on the micrometer length scale. At this scale, the arrangement of cells and other biologically relevant structures emerges as a new property from a deeper, biochemical, scale. Microstructural appearance is often defining feature of biological tissues and is intertwined with their biological behavior, which is a highly interesting information from a medical point of view. In this project, we study in a systematic way, often neglected, geometrical aspects of axons called axonal trajectories. Axons are the wiring of the brain. Based on microscopical images we proposed their representation, inspected their properties and forecasted the outcome of a diffusion measurement. The inverse question, whether the information on the axonal trajectories can be inferred from the outcome of measurement, and whether they could be neglected, was answered as well. The results suggest that non-straight axonal trajectories need to be considered in the of representations of axons, although to estimate them reliably the practical diffusion measurements need to be improved. The estimated properties of axonal trajectories were congruent to the gold-standard method, microscopy. Same methodology applied to the investigation of axonal trajectories can be employed in other problems in the dMRI field and may also lead to better understanding of the nature of the results of the diffusion measurements in the human tissue. Potentially, novel biomarkers that could help to diagnose diseases could be discovered. Generally, dMRI is an interesting research field where potential breakthrough could be made. It probes the microstructural region that is highly important from the biological point of view, has a solid foundation in physical theory, allows for large variety of possible arrangements of the dMRI experiments and is not as widespread as other imaging modalities

Applications of diffusion MRI: Tensor-valued encoding, time-dependent diffusion, and histological validation

Diffusion MRI (dMRI) sensitizes the MR signal to the diffusion of water molecules at the microscopic level and thereby non-invasively probes tissue microstructure. This is relevant when determining biological properties of tissues, for example, cancer type and its malignancy. The problem is, however, that dMRI lacks sensitivity and specificity to distinct microstructural features because an image voxel contains vast number of different features that are mapped onto relatively few dMRI observables. To tackle this issue, we aimed at solving two gaps in current knowledge—the first was related to what microstructural aspects are of most importance and the second to how adding new observables to the dMRI measurement could improve brain tumor imaging.In this work, we first investigate the biological underpinnings of dMRI observables—focusing on the degree to which larger-scale microstructural arrangements are of relevance. In Paper I, we investigated the effects of non-straight propagation of axons and found that they are indistinguishable from those originating from the diameter of a straight axon, at least for typical measurements with a clinical scanner. We propose that the use of short diffusion times could help separate them. In Paper II, in a comparison between histology and microimaging of meningioma brain tumors, we quantified to what degree the common biological interpretation of one of the most used dMRI observable holds—mean diffusivity (MD) as reflecting cell density and fractional anisotropy reflecting tissue anisotropy. We found that the local variability in MD was explained in minority of the samples whereas FA in majority by the common interpretations. We suggested additional relevant features such as tumor vascularization, psammoma bodies, microcysts or tissue cohesivity for explaining MD variability.Second, we examined whether a framework that introduces a new measurement observable brings value in intracranial tumor imaging. This new variable is termed the b-tensor shape and is derived from the tensor-valued dMRI paradigm. In Paper IV, we adjusted and shortened by 40 % (from 5 to 3 minutes) a tensor-valued dMRI protocol for clinical imaging of intracranial tumors and applied it to characterize to a wide range of different intracranial tumors. The protocol was also used in clinical studies of patients with intracranial tumors—gliomas and meningiomas—in Paper III and Paper V, respectively. In Paper III, we found that using so-called spherical b-tensor encoding leads to enhanced conspicuity of glioma hyperintensities to white matter in all patients and on average the signal-intensity-ratio increased by 28 %. In Paper V we found that it may also inform on meningiomas preoperatively. The standard deviation of isotropic kurtosis was associated with tumor grade and with and the 10th percentiles of the mean and anisotropic kurtoses with firm tumor consistency. Preoperative knowledge of the consistency is important for the neurosurgeons when choosing the optimal surgical procedure

ROBUST DECISION FOREST INFERENCE ALGORITHM IN PRESENCE OF MISSING FEATURE VALUES

Presented herein is a novel algorithm for inference on decision forest models that increases the robustness of the decisions in the presence of missing features in the data. The proposed algorithm ensures that tree decisions are supported by a minimal amount of non-missing features. Experiments have demonstrated that the proposed algorithm not only increases the robustness of the model, but also increase the model’s predictive performance

MONITORING OF FEATURE-DISTRIBUTION SHIFT IN PRODUCTION ENVIRONMENT

A fundamental problem faces with network traffic is that the traffic is dynamic and evolves over time. Presented herein is a tool for monitoring feature distribution shift and possible efficacy implications. The tool takes advantage of the fact that labels are available on the training set, but not available in the production environment where the labelling cannot be done on the fly. The tool implicitly provides estimates of feature robustness to time shift for each feature

MACHINE LEARNING FOR THING DETECTION, BEHAVIOR ANALYTICS, AND THREAT DETECTION: AN EFFICIENT ELIMINATION METHOD OF REDUNDANT FEATURE-SUBSETS

Techniques are described herein to efficiently detect redundant features in a machine learning process. The techniques are able to compute feature redundancy not only for a single feature at a time, but for any subset of features without the need to naively train and evaluate a classifier for each combination of features

Elasto-plastic material model of oak at two moisture content levels

The mechanical properties of wood show a very high dependence on the moisture content (MC). A consideration of MC in numerical simulations increases the applicability of such prediction with respect to application and moisture states of the wood material. The goal of this work is to develop an accurate orthotropic elasto-plastic model for oak wood (Quercus robur L.) at two different MC levels applicable for finite element analysis (FEA). To achieve this goal, the following steps were carried out: (a) in-house standard specimens tests in compression, tension, and shear and in all three orthogonal directions, followed by three-point bending, where all specimens were conditioned to a 12 and 25.6% MC, prior to the mechanical test; (b) integration of all obtained material characteristics into the consistent numerical material models; (c) validation of the developed material models by comparing the numerically predicted values with the experimental ones; and (d) iterative calibration of the material models by adjusting the individual material characteristics to minimize error using a reference. Material models were successfully developed with the following mean relative errors: 5.2% for 12% MC and 5.8% for 25.6% MC, respectively. Both numerical material models consistently predicted the oak elasto-plastic response that can be easily integrated into any FEA.OA-hybri