The effect of realistic geometries on the susceptibility‐weighted MR signal in white matter

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Myelin microstructure in white matter (WM) is important for healthy brain function and in neurological disease. In human and animal brains, normal myelin formation supports healthy development and promotes vital processes such as neuroplasticity 1. In contrast, abnormal myelin conditions, such as demyelination, are associated with many forms of neuropathology such as multiple sclerosis 2. Given myelin's important role in brain function, a long‐standing goal in human neuroscience has been to noninvasively estimate properties of myelin—its volume fraction in WM, or more specifically, intact myelin volume fraction—from the MR signal.
There are a number of MR‐based markers of myelin, including multicompartment T1, JOURNAL/mrim/04.02/01445475-201801000-00049/math_49MM1/v/2017-12-21T175206Z/r/image-png , and magnetization transfer mapping 3. In addition, myelin has a magnetic susceptibility χ that is offset to its environment. This arises from myelin's unique chemical composition and ordering of phospholipids within the myelin sheath structure. Following empirical works demonstrating that the frequency dependent MR signal (e.g., spectroscopic imaging) may reflect localized differences in magnetic susceptibility χ7, recent studies have shown that the magnetic susceptibility of myelin strongly influences the gradient echo (GRE) signal, including both signal phase and magnitude 10.
Several biophysical models of WM based on myelin microstructure have been used to interpret the measured GRE signal. Factors influencing this signal include relative volume fractions of myelin and intra‐/extra‐axonal water, g‐ratio (thickness of the myelin sheath), magnetization exchange with myelin water, the presence of paramagnetic iron and the magnetic susceptibility of myelin 4. Moreover, there is recent evidence that myelin exhibits susceptibility anisotropy, where the magnetic susceptibility depends on the orientation of the phospholipids in myelin with respect to the magnetic field, B04.
The present study focuses on the specific geometry of the myelinated axon and its effect upon the susceptibility‐weighted signal. Existing models use nested cylinders to describe axons, assuming circular geometries 4. In reality, a diversity of axonal shapes and myelin geometries exist in WM. While simulations using circular shapes benefit from simplicity, the effects of this assumption have not been studied. Given the role that shape has in altering the field perturbations caused by susceptibility‐shifted structures, shape is a potential confound in the extraction of microstructure parameters (e.g., myelin thickness).
Myelinated axons perpendicular to the main magnetic field were modeled in two dimensions with several variations. First, we modeled single axons and axon bundles using circular geometries. Next, we modeled the role of myelin shape on the MR signal by distorting circular geometries. We considered more realistic geometries by using a structural template of myelin microstructure derived from electron microscopy (EM) data. Finally, the signal predictions of circular and EM‐based geometries were evaluated against data acquired in a mouse model of demyelination.

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