Trace DWI and ADC map

What is the Trace DW image? How does it differ from the ADC map?  

As described in a previous Q&A, the typical diffusion-weighted imaging protocol begins with production of a baseline b0 image obtained with all diffusion-sensitizing gradients turned off. Immediately thereafter, diffusion gradients are applied individually and in various combinations to produce a set of source images sensitized to diffusion along various directions. At least three sets of source images must be obtained. These may be along the laboratory x-, y-, and z-axes or in three arbitrary perpendicular orientations. More modern schemes typically obtain source images in 6, 20 or more directions, but three is the minimum. 

b0 image

Diffusion source images obtained with gradients applied along the x-, y-, and z-directions.

If So is the signal intensity of a point in the b0 image, and the directionally-specific diffusion coefficients at the same point are Dxx, Dyy, and Dzz, the signal intensities of the x-, y-, and z-direction source images are given by 

The individual source images are not usually viewed separately, but combined into a single final set for diagnosis. These combined images are known by various names: diffusion-weighted images, isotropic images, or trace images. The most common method of image combination is to take the geometric mean:

Trace DW image

In a prior Q&A we explained that biological tissues are anisotropic. They have multiple diffusion coefficients that vary by direction and are represented by the diffusion tensor, a 3x3 array of numbers. The term "trace" comes from matrix algebra where it means the sum of diagonal elements of such an array. The trace of the diffusion tensor (Dtrace) equals (Dxx + Dyy + Dzz). Using the average value of the trace, (Dxx + Dyy + Dzz)/3, reduces the multi-directional diffusivity at each point into a single number that can be considered a consolidated apparent diffusion coefficient (ADC). Thus the terms average trace and ADC are often used interchangeably.

Trace DWI of stroke

The signal intensity of each voxel in a Trace DW image is inversely related to its ADC value. Lesions that restrict diffusion (strokes, abscesses, etc.) lower the ADC and appear bright. Conversely, substances with unrestricted diffusion and high ADC's (like cerebrospinal fluid) appear dark.

The Trace DW image is not a map of diffusion; it is only diffusion-weighted, a fact implicit in its name. Trace DW images possess considerable T2-weighting. As such, lesions with either very long or very short T2 values may "contaminate" the Trace DW images, making them appear "artificially" bright or dark. These important phenomena are known as "T2-shine-through" and "T2-black-out", the subject of later Q&A's. 

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T2-effects can be mathematically removed from the DW image to create a pure parametric image of apparent diffusion coefficients (the "ADC Map"). The ADC Map is created by dividing the signal from the trace-DW image (SDWI) by the signal (So) from each corresponding point in the b0 image and then taking logarithms:

ADC map of stroke

The ADC map is a pure display of consolidated ADC values. Because it is mathematically calculated it appears "pixel-ly" with "spots" scattered in the air around the subject.  The signal intensities are opposite to those of the Trace-DW image, which can be a source of confusion. Tissues with short ADC values (like the stroke) appear dark, while materials like CSF with long ADC values appear bright.

Advanced Discussion (show/hide)»

Although 3-direction source DW imaging is still performed as described above, higher quality images can be obtained using more directions. We typically use at 6 directions for routine DWI, and 20 or more if performing diffusion tensor imaging (DTI). The trace of the diffusion tensor is computed from these multi-directional source images using a linear regression estimation technique that improves accuracy and signal-to-noise. The "trace" is rotationally invariant, meaning that it is the same regardless of which projections are used to measure it.

As described above, the ADC map is processed from the b0 and source DW images. On some scanners a "noise level" or similar thresholding parameter must be selected to determine which pixels are selected to produce the final map.

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References
     Minati L, Weglarz WP. Physical foundations, models, and methods of diffusion magnetic resonance imaging of the brain: a review. Concepts Magn Reson 2007; 30A:278-307.
     Mukherjee P, Berman JI, Chung SW, et al. Diffusion tensor MR imaging and fiber tractography: theoretic underpinnings. AJNR Am J Neuroradiol 2008; 29:632-640.     
     Schaefer PW, Grant PE, Gonzalez RG. Diffusion-weighted MR imaging of the brain. Radiology 2000; 217:331-345.

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Related Questions
     How do you make a DW image?
     Which diseases are "bright" on DW imaging and why?
     If a stroke is bright on a standard DW image, why is it dark on the ADC map? 

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