Page 45 - Vibrational Spectroscopic Imaging for Biomedical Applications

22 Cha pte r O n e

associated with TMA dataset pixels that do not contain tissue, all
boxes without any pixels classified as stroma or epithelium are not
included in calculations. Any cancerous TMA cores that do not con-
tain epithelium or do not have a clear pathology diagnosis are also
not considered. To distinguish cancerous and normal TMA cores, the
fraction of boxes containing at least 50 percent epithelium for each
box size is calculated for each TMA core. Average values for cancer-
ous and normal TMA cores are compared (Fig. 1.8a), and standard
deviation error bars indicate that there is a clear distinction in epithe-
lial content between cancer and normal TMA cores for all box dimen-
sions. An optimal cutoff for selection of cancerous TMA cores is
determined from the standard deviation values for each tissue class
by the relationship

d σ
C = N (1.2)
d σ
N C

where d = distance of the cutoff from the mean of the cancer TMA
C
cores
d = distance of the cutoff from the mean of the adjacent nor-
N
mal TMA cores
σ = standard deviation for cancer TMA cores
C
σ = standard deviation for adjacent normal TMA cores.
N
An optimal cutoff point is calculated for each box size from 1 × 1
pixel to 12 × 12 pixels. Optimal operating points for each box size
are found by Eq. (1.2) to account for the lower variance of the average
fraction of boxes with more than 50 percent epithelium in adjacent
normal TMA cores. A least squares linear trendline is fit to the opti-
mal cutoff point for each box size to compute the operating line in
Fig. 1.8a.
The absence of overlap of standard deviations for each box size
indicates that each of these metrics should provide similar separation
of cancer and adjacent normal TMA cores. The standard deviations
for the cancer and normal TMA classes are relatively constant, regard-
less of box size. Therefore, it is feasible to reduce these 12-box-size
metrics to a single parameter to facilitate more rapid TMA core clas-
sification. This is accomplished by applying a least squares linear fit
to each core for the fraction of boxes containing at least 50 percent
epithelium versus box size dataset and computing the offset (y-intercept)
value. A single offset value can then be selected as a cutoff, where all
TMA core datasets with an offset above this value are classified as
cancer. Since cancer TMA cores have a greater fraction of boxes con-
taining at least 50 percent epithelium, these cores will also have a
greater offset value. The offset cutoff for cancer determination
can be altered to adjust the classification sensitivity and specificity.