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| | == Description == | | == Description == |
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| − | Our algorithm simulates the flow of an artificial fluid through a volume whose dimensions, viscosity, and pressure tensor field are derived from a DTI volume. Specific regions of interest are chosen as sources and/or sinks, and we simulate the flow of an artificial fluid governed by the Navier-Stokes equations. The most likely connection path is then estimated using a generalized gradient vector flow (GGVF) based approach to compute the trajectory through the fluid velocity vector field that simultaneously maximizes the magnitude of the fluid velocity and its gradient along the path. Our fluid model is valid only as a theoretical framework for generating a connectivity metric and does not try to model any aspect of the underlying diffusion process.
| + | This software program creates a digital DTI phantom whose dimensions, etc... are specified by the user. The shape of the helix is defined using standard helix equations. |
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| − | [[Image:NAMICFMech_VisFig.jpg|Viscosity Map]]
| + | A helix is defined mathematically with the following parametric equations |
| | + | X = r cos t |
| | + | Y = r sin t |
| | + | Z = ct |
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| − | Viscosity maps derived from 2D slices of DTI data from human control subjects. Viscosity values were calculated from the corresponding diffusion tensor image and are color-coded according to the legend bar seen on the right side of the figure. A. Axial slice taken at the level of the internal capsule. The corpus callosum, marked with a star is a highly organized white matter tract and is therefore characterized by low viscosity. Conversely, the lateral ventricle, marked with a delta contains CSF and is highly viscous. B. A mid-sagittal slice. As in A, the corpus callosum is marked with a star and is characterized by low viscosity. In contrast, the lateral ventricular space, marked with a delta contains CSF and therefore has no architecture. Consequently, it is highly viscous.
| + | Where t is the parameterized variable and r is the radius of the helix and c is a constant giving the vertical separation of the helix’s loops. |
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| − | [[Image:NAMICFMech_PressureFig.jpg|Pressure Map]]
| + | The parameterized derivatives of the helix equation are used to calculate the local principal eigenvector and, with respect to t, are |
| | + | X’ = -r sin t |
| | + | Y’ = r cos t |
| | + | Z’ = c |
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| − | Representations of the pressure tensor derived from 2D slices from human control subjects. At each voxel in the image, the pressure force is represented by a tensor glyph, an ellipsoid whose axis is obtained from a diagonalization of the corresponding pressure tensor. The color of the ellipsoid represents the dominant diffusion direction, according to the color coded axes in the figure with the superior-inferior z-axis (blue) coming out of the page, the anterior-posterior y-axis (green) vertical, and the left-right x-axis (red) horizontal. A. A 2D axial slice taken at the level of the internal capsule. The white box marks the enlarged area shown in B. B. Enlarged view from A. The posterior limb of the corpus callosum, marked with a star is a highly organized white matter tract, and the pressure force acts on the artificial fluid co-linear with the fiber tract. In contrast, the lateral ventricular space, marked with a delta contains little structure. Consequently, the pressure force is isotropic in that region.
| + | [[Image:NAMICSingleHelix_08-02-20.jpg|Tracts Segmenting Helix Phantom]] |
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| − | [[Image:NAMICFMech_CspFig.jpg|Human Corticospinal Tracts]] | |
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| − | Segmentation results of the corticospinal tracts using our method in human control DTI images. ROIs were placed within the brainstem below the level of the crossing pontine fibers and within the corona radiata above the level of the corpus callosum. Cross-sections of the approximate location of these ROIs are shown Figure 8D, drawn in white, superimposed on the corresponding axial DEC slices. Figure 8A shows the estimated connection paths between these ROIs generated by our method. An axial slice of the tensor glyphs at the level of the mid-brain is shown for spatial reference. The tracts show a prominent lateral course at the level of the mid-pons (Figure 8A: white arrow). This corresponds to a strong lateral diffusion component at that point as seen in the directionally encoded color (DEC) image of the axial slice at the mid-pontine level (Figure 8B, 8C: white arrow). The tensor glyphs and DEC image are color-coded by the axes shown in the figure.
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| | == Key Investigators == | | == Key Investigators == |
Latest revision as of 19:54, 21 February 2008
Home < Hageman:NAMICHelixPhantom
Helical Digital DTI Phantom
Overview
This is a software utility for creating a pure digital DTI phantom based on a user specified helix shape. One of the current challenges of DTI tractography is the lack of any ground truth with which to validate a method's results. To address this problem, we have created a digital DTI phantom that allows the user to specify all aspects of the ground truth, such as dimensions, helix shape, addition of Rician noise, etc... The program creates the shape as a volume of eigensystems and, using this, outputs the appropriate number of DWI volumes based on the number of acquisitions, b-values, and gradient directions that the user has provided. The goal of this project is to fully develop this method and make it available to the NAMIC tractography group to aid their validation efforts.
Description
This software program creates a digital DTI phantom whose dimensions, etc... are specified by the user. The shape of the helix is defined using standard helix equations.
A helix is defined mathematically with the following parametric equations
X = r cos t
Y = r sin t
Z = ct
Where t is the parameterized variable and r is the radius of the helix and c is a constant giving the vertical separation of the helix’s loops.
The parameterized derivatives of the helix equation are used to calculate the local principal eigenvector and, with respect to t, are
X’ = -r sin t
Y’ = r cos t
Z’ = c
Key Investigators
- UCLA: Nathan Hageman
- UCLA: Arthur Toga, Ph.D
Project Week Results: 2008 Winter
