![]() ![]() Fifth row: maps of DTI-derived and MAP-MRI-derived propagator anisotropy (PA) maps are illustrated. Fourth row: three non- Gaussianity indices (from left to right: three-dimensional, parallel with and perpendicular to the principal eigenvector of the diffusion tensor) are illustrated. The cube-root of the return-to-the-origin probability (RTOP), and the square root of the return-to-the-axis probability (RTAP) are provided so that these quantities have the same dimension with the return-to-the-plane probability (RTPP). Third row: three zero displacement probabilities are shown. First two rows: traditional DTI-derived maps of non-diffusion attenuated signal (S 0), direction encoded color (DEC), fractional anisotropy (FA), mean diffusivity (MD), and diffusivities along (D //) and perpendicular ( D ⊥) to the principal eigenvector. Traditional DTI and MAP-MRI-derived parameter coronal maps of marmoset brain. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.Ĭopyright © 2013 Elsevier Inc. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. In this case, we'll want to use a lambda expression without using its parameters.įirst, let's create the doNothingAtAll method: private static void doNothingAtAll(Object.Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. ![]() This simple case can't be expressed with a method reference, because the printf method requires 3 parameters in our case, and using createBicyclesList().forEach() would only allow the method reference to infer one parameter (the Bicycle object).įinally, let's explore how to create a no-operation function that can be referenced from a lambda expression. "Bike brand is '%s' and frame size is '%d'%n", Let's see an example of this limitation: createBicyclesList().forEach(b -> ( Their main limitation is a result of what's also their biggest strength: the output from the previous expression needs to match the input parameters of the referenced method signature.
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