The Dependence of the Apparent Diffusion Coefficient on Voxel Location and Calculation Method

1
The Dependence of the Apparent Diffusion
Coefficient on Voxel Location and Calculation
Method Lars Ewell1, Naren Vijayakumar2 2007
Meeting of the American Society for Therapeutic
Radiation and Oncology (ASTRO) Los Angeles
Convention Center Los Angeles, CA 10/30/07 (1)
Department of Radiation Oncology, University of
Arizona Health Science Center. (2) Department of
Electrical and Computer Engineering, University
of Arizona.
Abstract
Diffusion Weighted Magnetic Resonance Imaging
(DWMRI) has the potential to effectively monitor
radiation therapy. Utilizing axial DWMRI scans
of the human brain, we have calculated Apparent
Diffusion Coefficients (ADCs) using a number of
different methods. We have utilized an ADC map,
as well as averaging the Region Of Interest (ROI)
for different diffusion values. Employing the
first method, we see a difference in near surface
regions of the brain, when using two or three
b-values. The second method yields little
difference. The differences between all four
methods are summarized.

Figure 4 Voxel Division
Figure 4 Voxel Division
Introduction The application of Diffusion
Weighted Magnetic Resonance Imaging (DWMRI) has
recently expanded from use mainly in ischemia to
radiation oncology (1,2). It is hypothesized
that as effective cancer therapy progresses,
cellular breakdown leads to increased water
mobility, which can be measured/monitored using
the Apparent Diffusion Coefficient (ADC).
Calculation of the ADC requires at least two T2
weighted images b0 and b gt 0 s/mm2. If the ADC
is calculated on a pixel by pixel basis, the
resultant image is known as an ADC map. In
oncology, a Region Of Interest (ROI) containing
suspected disease is often chosen, and the ADC of
this entire region is longitudinally monitored.
While the ADC map can give a qualitative
indication of disease progression, an ADC for an
ROI can also be quantitatively determined by
averaging the pixel intensity in the ADC map for
an ROI. However, this is not the same as
determining the ADC via averaging the pixel
intensity for the ROI in the scans with different
b-values. The differences between these two
methods are examined. In addition to this
distinction, it is possible to utilize more than
two b-values in the determination of an ADC.
Past studies have found little difference between
using two (properly chosen) or more b-values in
determining an ADC in the brain(3,4). However,
these studies did not compare the brain surface
to the brain interior. We have looked at a
number of patients and have compared the ADCs of
the brain surface, with ADCs of the brain
interior. Finally, we have also investigated
the density of sulci in the human brain, as it
relates to calculation of ADCs (5)
Table 1 ADC Calculation Results
b)
a)

Results In five different scan sets, the medial
and lateral voxels were separated, and the ratio
of ADC using three b-values (0, 520 and
850s/mm2), ADC3 (as in Figure 1b), to that using
two b-values (0 and 850s/mm2), ADC2 (as in
Figure 1a) were compared. The division of the
voxels can be seen in Figure 4. The results of
the comparisons can be seen in Table 1.
Figure 3c The ADC for the ROI is determined by
averaging the pixel intensities for different
b-values (see text).
Figure 3b ROI in b850s/mm2 T2 Weighted image.
Figure 3a ROI in b0 T2 Weighted image.

ADC Calculation
Discussion As can bee seen in Table 1, the ratio
of ADC3/ADC2 is approximately 1 (within
uncertainty/SD) for both medial and lateral
voxels using Method 1 and Method 2. A slight
decrease in the ratio is observed for the lateral
voxels using Method 1. For some of the most
lateral voxels, a significant fraction of the
area is background (dark). The ADC calculation
in such an area may have ambiguous meaning,
resulting in the observed deviation.
Methods and Materials
When using two b-values (0 and, e.g., 850 s/mm2)
the ADC is determined as the log of the ratio of
pixel intensities i.e. ADC -(1/b)ln(Ii/Io)
with b b-value for the diffusion weighted scan,
Ii the pixel intensity in the diffusion weighted
scan, and Io the pixel intensity of the
non-diffusion weighted (b0) scan. Since
diffusion weighting lowers signal intensity, the
ratio in the log argument is less than one, and
the ADC is in general gt0.
In order to determine the ADC, a minimum of two
diffusion b-values are needed 1 non-diffusion,
b0, and another diffusion weighted, bgt0. If
just two b-values are used, e.g., 0 and 1,000
s/mm2, the log of the ratio of the pixel
intensity as a function of b-value is plotted.
The slope of the line is the ADC. This is
depicted in Figure 1a. If three values are used,
a least squares fit to the three data points is
completed. This is depicted in Figure 1b.
If an ADC map has been generated, the ADC for an
ROI can be determined by averaging the pixel
intensity within the ROI. This is depicted in
Figure 2. This is referred to as Method 1. An
alternative method of calculating the ADC
involves averaging the pixel intensities of the
ROI in the non-diffusion weighted scan (b0), and
the diffusion weighted scan ( b850s/mm2), and
then determining the resultant slope. This is
depicted in Figure 3. This is referred to as
Method 2.
Conclusion When determining Apparent Diffusion
Coefficients in the human brain, it is likely
sufficient to use either Method 1, or Method
2 in the calculation. In addition, it is also
likely sufficient to use just two b-values. If
an extreme lateral area is under consideration,
it may be more accurate to use Method 2 and/or
three b-values in the calculation.

• References
• Ross, B. D, et al., Evaluation of Cancer Therapy
  Using Diffusion Magnetic Resonance Imaging,
  Molecular Cancer Therapeutics., 2, 581587, June
  2003.
• Theilmann R, et al, Changes in Water Mobility
  Measured by Diffusion MRI Predict Response of
  Metastatic Breast Cancer to Chemotherapy.
  Neoplasia 20046831-7.
• Burdette JH et al. Calculation of Apparent
  Diffusion Coefficients in Brain Using Two-Point
  and Six-Point Methods., Journal of Computer
  Assisted Tomography 199822792-794.
• Xing D et al., Optimized Diffusion-Weighting
  for Measurement of Apparent Diffusion Coefficient
  in Human Brain. Magnetic Resonance Imaging
  199715771-784.
• Ewell L., Watchman C and Wharton K. Sulci
  density map to aid in use of apparent diffusion
  coefficient for therapy evaluation, Magnetic
  Resonance Imaging, In Press.

Figure 1a Determination of the Apparent
Diffusion Coefficient (ADC) using two b-values.
The slope of the line is the ADC.
Figure 1b Determination of the ADC using three
b-values. The line is a least squares fit to the
data. The slope of the line is the ADC.