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Statistical Analysis on Polarimetric Study of Lung
Cancer Cells
Suman Shrestha [1], IEEE Member,
George Giakos [1], [2], IEEE Fellow,
Tannaz Farrahi [1], Chaya Narayan [1]
[1] Dept. of Electrical and Computer Engineering,
[2] Dept. of Biomedical Engineering
The University of Akron, Akron Ohio, 44325, USAE-
mail: giakos@uakron.edu
George Livanos [3], Michael Zervakis [3]
[3] Dept. of Electronic and Computer Engineering,
Technical University of Crete,
Chania 73100, Greece
Email: michalis@display.tus.gr
Abstract— The objective of this study is the discrimination and
characterization of different lung cancer monoline cells using
statistical analysis of polarimetric backscattered signals. The
main aspect of this study is the use of the Welch’s t-test and the
p-value statistics as a representative metric for discriminating
distributions based on their mean and standard deviation. The
outcome of this study indicates that enhanced discrimination of
lung cancer samples can be obtained based on their t-test values
between different cancer samples for different geometries.
Keywords- medical diagnostics, lung cancer cell differentiation,
Welch’s t-test, p-value statistics, optical polarimetric
characterization of lung cancer cells
I. INTRODUCTION AND LITERATURE
The objective of the study is to develop efficient and
reliable techniques for early identification and discrimination
of precancerous and cancerous lung cells that can lead to
accurate diagnosis and treatment of lung cancer. In the year
2012, there were approximately 226,160 cases of lung cancer
and 160,340 deaths out of it as per the National Cancer Institute
[1]. There are mainly two types of lung cancer, small cell lung
cancer and non-small cell lung cancer, of which 87% are
diagnosed as non-small cell. A physical algorithm and a
systematic study relating the morphological, chemical and
metabolic properties of lung cancer to the physical and optical
parameters of the polarimetric detection process are missing.
For such reason, early detection of lung cancer cell has been of
paramount importance.
The common detection techniques for lung cancer are
classical imaging techniques like chest radiography (film or
digital) and computed tomography (CT). Digital radiography
provides better contrast resolution with equal or better spatial
resolution when compared to classical radiography techniques
[2]; however, these techniques still do not provide meaningful
information that can be utilized towards the early detection of
tumors. On the other hand, low-dose, spiral/helical CT can be a
promising modality for lung cancer screening. However, it is
limited to small peripheral lesions. Also, heavy smokers
develop tumors located in the central airways, and as a result,
other techniques besides CT are needed for early detection.
Optical imaging involves probing tissue with non-ionizing
radiation in the visible, near-infrared and infrared regions
(400nm-1500nm). Studying the optical properties of tissue
reveals information that can potentially characterize diseases
[3]-[5]. It can provide metabolic information combined with
anatomical information which enhances the detection process
of early cancer. White light bronchoscopy (WLB), auto-
florescence imaging (AFI) and narrow-band imaging (NBI),
high magnification bronchovideoscopy, endobronchial
ultrasound (EBUS) and optical coherence tomography (OCT)
are currently used optical imaging techniques that have been
developed to enhance the ability to diagnose NSCLC at a pre-
invasive stage. Most peripheral tumors are adenocarcinomas or
large cell carcinomas. Because of their peripheral location,
adenocarcinomas may not be caught early until they have
developed extrathoracic metastases. For example, patients may
show clinical signs of bone spread or intracranial metastatic
disease. On the other hand, squamous cell carcinoma of the
central airway is thought of as a multistep process starting from
a squamous metaplasia, which progresses to dysplasia,
followed by carcinoma in situ (CIS), finally progressing to
invasive cancer [6].
One proposed technique uses a polarimetric optical
technique to detect early lung cancer by analyzing the changes
in the optical properties of different types of cancer cells.
Recently, the polarimetric phenomenology of IR light
interaction with healthy and lung cancer cells, under
transmission and backscattering geometry, as well as in
conjunction to Polarimetric Exploratory Data Analysis (pEDA)
[7], aimed at developing efficient and reliable diagnostic
techniques, has been reported in [8]-[12]. In fact, image
formation through the detection of the polarization states of
light offers distinct advantages for a wide range of detection
and classification problems, due to the intrinsic of optical
backscattering for high contrast in different polarization
components of the backscattered light.
This paper presents the discrimination of the lung cancer
samples based on statistical analysis using t-test performed on
the polarimetric signals of lung cancer cells at different
polarization states [9]-[10]. T-test constitutes a widely used
tool for evaluating the statistical properties of a
population/distribution. It is defined by means of a statistical
978-1-4673-5791-3/13/$31.00 ©2013 IEEE
hypothesis in which the test statistic follows a Student's t
distribution if the null hypothesis is confirmed. It is adopted in
statistical analysis in order to determine if there is enough
evidence in a group of samples to infer that a certain condition
is true for the entire population; a common hypothesis is that
the actual difference between two means in relation to the
variation in the data (expressed as the standard deviation of the
difference between the means) is zero. A hypothesis test is
accurately described by three basic elements: two opposing
hypotheses characterizing the sample data, a test statistic that
follows a certain distribution and a confidence interval inside
which the extracted values confirm the basic statistical property
assumed for the population. The initial hypothesis, usually
referred to as the null hypothesis (denoted by Ho), comprises
the common assumption for the nature of the sample
observations, while the alternative hypothesis, denoted by Ha,
forms a contradiction to the null that the researcher needs to
explore. The selection of the proper test statistic for each
application depends on the sample size and the null hypothesis
on the data population. In order to calculate the confidence
interval in which there is enough evidence from the sample(s)
to reject or confirm Ho, two common tools are proposed. First,
the computed value of the test statistic can be compared with a
value from the appropriate table at a pre-specified significance
level α, where α represents the probability of rejecting Ho
when Ho is true. If the level is 0.05, the results are only 5%
likely to be outliers, given that the null hypothesis is true.
Alternatively, α can be compared with the P-value, which is
defined as the probability of the observed test statistic
calculated from the sample(s) to be extreme, given Ho is true.
P-value can be calculated from the assumed cumulative
distribution function (cdf) of the test statistic [13]. Both
methods will yield the same conclusions.
II. THEORITICAL FRAMEWORK
The Welch’s t-test and the p-value statistics has been used
as a representative metrics for discriminating polarized
measurements based on their mean value and standard
deviation. In general, the interpretation of statistical results for
the confirmation of a scientific hypothesis is inefficient,
requiring the exploitation of multiple tests and their comparison
through meta-analysis. Notice that in our study, besides other
data inconsistencies, the sample sizes are usually very small
rendering most statistical tests inefficient with high uncertainty
on the results. Non-parametric techniques have been used for
small sample sizes, but are not consistent to specific
assumptions, provide less statistical power than parametric
ones and do not fully exploit all information hidden in the data
distribution [14]. Thus, for the requirements of our analysis,
focusing on the discrimination of different cancer cells under
polarimetric phenomenology, the parametric t-test has been
adopted.
In cases where different polarization states and/or various
tissue types are considered and compared, the independent two-
sample t-test (Welch’s t-test) for equal or unequal sample sizes
and unequal variances for the population [15] has been
adopted, under the null hypothesis of equal means; the means
of the two distributions are the same, yet the two populations
cannot be discriminated. To validate the stability and the level
of significance of the t-test results, the p-value of the
distribution is considered. If the p-value is under 0.05 (the t-test
falls outside the 95% of the Student’s t-distribution) there is
strong evidence that the null hypothesis is false, implying that
the observations used are statistically significant, therefore the
means of the tested samples are different and the two
populations have distinct properties. The higher the t-test value,
the better the two distributions are discriminated.
The statistical model constructed for our analysis is
summarized as follows: Hypothesis to determine if a
population mean, μ1, is equal to another population mean μ2.
Hο: μ1 = μ2
Ha: μ1 ≠ μ2 (two-tailed test)
α=0.05
p-value = 2 * P(TS > |ts| | Hο is true) = 2 * (1 - cdf(|ts|))
(two-tailed test)
where, P: Probability of a random variable taking on the range of
values.
TS: Random variable associated with the assumed
distribution.
ts: The test statistic calculated from the samples.
cdf(): Cumulative density function of the assumed
distribution.
α (significance level): probability to reject Ho when it is
true. It represents the highest probability of incorrectly
rejecting Ho. If the p-value is less than α, reject Ho, else
accept Ho.
The formula used for calculating the Welch t-test values is
given by,
12
22
12
22
12
xx
t
ss
nn
(1)
where,
1
x
and
2
x
are the means of the first and second population
respectively.
2
1
s
and
2
2
s
are the variance of the first and second
population respectively. n1 and n2 are the number of elements
of first and second sample set respectively.
III. SAMPLES PREPARATION
Four different lung cells of a thickness of 5 um are studied:
a) normal lung cell (healthy); b) stage 2 squamous cell; c) stage
2 adenocarcinoma cell, and d) mixture of squamous cell and
adenocarcinoma cell. The cells were deposited on the surface
of their respective slides by growing them in an
epithelial monolayer morphology. The histological descriptions
of the lung cancer samples reported in this study are [11]: a)
normal human lung fibroblast cell (WI-38) line, used as a
reference; b) a sample consisting of human lung carcinoma
(NSCLC)-squamous cell carcinoma (Grade 1 well
differentiated tumors) which is human lung bronchiolar
epithelial cells with a thickness of 5 μm (NCI-H292). Tumors
showing these features are classified as squamous carcinoma;
c) a sample of human lung adenocarcinoma (H522) with mucus
production (Grade 3 very poorly differentiated tumors), with a
thickness of 5 μm. These cells are characterized as
adenocarcinoma lung cell, and; d) a mixture of human lung
squamous carcinoma (NCI-H292) and human lung
adenocarcinoma cell (H522) with 50% of each of the sample
mixed together. All cell lines are thawed, cultured in DMEM
medium (WI-38 cells and H522 cells) and RPMI-1640 medium
(NCI-H292 cells) with 10% heat-inactivated FBS (Hyclone,
Logan, UT), 100 units/ml penicillin, 100g/ml streptomycin in
5% CO2 cell culture incubator at 37 C, and used within 2-3
passes when in the log phase of growth. Culture media are
changed every day.
The layer thickness was measured for each of the cancer
samples through confocal microscopy by computing the
distance from the upper surface of the cell layer to the surface
of the slide on which the cells were grown Assuming that the
layer thicknesses of the cell lines are indicative of their
diameters (except in the case of the human fibroblast cells), the
values fall within the range of normal parameters for diameter
of eukaryotic cells (between 15μm -100 μm).
A microphotograph taken of the healthy lung cell (Panel
A), squamous carcinoma cell (Panel B), and adenocarinoma
cell (Panel C) are shown in Figs. 1.a, 1.b, 1.c.
Fig. 1a. Microphotograph of the Stage II Squamous Carcinoma
Fig. 1b. Stage II Adenocarcinoma
Fig. 1c. Mixture of Squamous Carcinoma and Adenocarcinoma (C) at 20x
magnification.
IV. EXPERIMENTAL SETUP AND ARRANGEMENT
Optical experiments previously done were mostly manual
ones and these were quite time consuming which required the
data for each state to be taken manually. In this work, Liquid
crystal (LC) devices are used which consist of electronic
control and hence are automated. This reduces considerable
time for performing the experiments. Prior to the development
of any platform, the preliminary works are the following:
LC Rotator LC Retarder LC Retarder LC Rotator Detector
Laser Polarizer Pol arizer
--------------------------------------------------------------------------------------------------------------
Generator Arm Analyzer arm
Fig. 2. System Calibration Setup
i. Calibration of the liquid crystal rotators and retarders
To obtain the calibrated voltages, first the generator arm is
calibrated; and then the analyzer arm is calibrated. The
calibration is obtained by adding each component one by one.
Appropriate rotation or retardation for all the states is achieved
by applying voltages to the devices. The states are the different
polarization states: Horizontal (H), Vertical (V), +450 linear
(P), -450 linear (M), Right circular (R) and Left circular (L).
System calibration setup is shown in Fig. 2.
ii. Calibration using known targets with known Mueller
matrix (Accuracy Test)
As the system developed was to calculate the Muller matrix
of different space materials and analyze their optical properties,
so after the liquid crystal devices (retarders and rotators) were
calibrated, these calibration voltages were first tested using
some components of known Mueller matrix. The components
used were air, Linear Horizontal Polarizer i.e. a polarizer
having its transmission axis in the horizontal direction (LHP)
and Linear Vertical Polarizer i.e. a polarizer having its
transmission axis in the vertical direction. These test
experiments were done in transmission mode, i.e., placing the
generator and the analyzer arm in the face to face direction.
Between the generator and the analyzer arm, the object to be
tested was placed. For air, no object is needed. The polarizer
(linear horizontal and vertical) used for the experiment was
specified for the wavelength range of 700 nm to 1100 nm
which is within the range of the laser that was being used. The
experimental setup for the test of the calibrated data is as
shown in Fig. 3.
Fig. 3. Experimental Setup for the Test of the Calibration Voltages
V. EXPERIMENTAL ARRANGEMENT
The experimental arrangement used in this study is
described by Fig. 4. The laser used in the experiment is a
pulsed laser to excite the cancer cells. The generator arm
consisted of a linear polarizer, liquid crystal rotator and
retarder. The analyzer arm is placed in backscattered mode
which also consisted of liquid crystal retarder and rotator and a
linear polarizer. The cancer cell to be analyzed is placed before
the analyzer arm so that the laser light interacts with it. The
backscattered signal is analyzed using a detector. A LeCroy
3GHz bandwidth oscilloscope is used to view the backscattered
signal.
Fig. 4. The U.S. Air Force Research Laboratory (AFRL)
multifunctional imaging platform
The target is mounted to a motor that can be rotated or
translated with a rotation accuracy of 0.01. The motor is used
to align the target with the laser light so that the light hits it.
The signal from the detector could be recorded from the
oscilloscope or recorded with the subroutine developed in
LabVIEW. A total of sixteen intensities are recorded for 16
measurement states. These intensities are obtained from the
combination of only 4 states in the generator and analyzer
arms. The calibration voltages for 6 different states are
calculated but only four of these states are used for the
experiment (Linear horizontal (H), Linear vertical (V), Linear
+450 (P) and Right Circular (R)). The combination of four
states in the generator and analyzer arm generates 16 intensities
calculation. The same procedure is employed for the
calculation of Mueller matrix of air, LHP and LVP while
testing the calibrated voltages.
VI. RESULTS AND DISCUSSIONS
Using the experimental arrangement of Fig. 5, the
backscattered intensities of the samples are obtained. The
“samples” for the t-test calculations are the waveforms
extracted for each polarization state for the different tissue
types utilized in the polarimetric phenomenology study. Thus,
16 waveforms are considered (one for each polarization state)
for the four histological subtypes of non-small-cell lung cancer,
which can be combined and examined in pairs. Each waveform
(distribution) is represented by the peaks and their differential
latencies of the five sub-modes observed in the spectrum, as
depicted in the following scheme:
Fig. 5. Highlighting the statistical analysis on polarimetric signals
Signals obtained under four polarization states, namely HV,
VH, PP and RR, were considered noisy and excluded from
statistical computations. Having calculated the peak values and
time intervals for the total number of the twelve remaining
states for each tissue sub-type (healthy, squamous carcinoma,
adenocarcinoma, mixture of cancers), we have completed the
pre-processing steps for the application of the statistical
analysis on the population samples. Due to the periodicity of
the signals, the time intervals were practically constant (a
significant indication of a well-established experimental
procedure). Thus, latency measurements were not further
considered in the analysis procedure as they cannot contribute
to the discrimination of different populations.
We performed two types of comparisons with different
objectives. The first one is concerned with the ability of
specific polarimetric geometry (measurement states) to
discriminate among input types. The second test considers the
utility of each polarimetric calibration and compares all 12
polarization states for a specific lung cell.
In all calculations, the p value fluctuated in very low levels
(values less than 10-4), implying that there is significant
evidence against the null hypothesis of equal means among the
populations, justifying that polarimetric phenomenology
provides increased capability to efficiently discriminate the
various cancer types considered within the experimental
procedure. In particular, the significant difference of population
means demonstrates the high degree of discrimination
regarding the optical properties of the four tissue types
examined. The following figures depict the t-test values
comparing paired populations of different tissue types under
distinct polarimetric geometries. In this set of calculations, we
attempt to estimate the differentiation of the optical properties
of the four tissue types compared to each other.
Fig. 6. t-statistic comparing normal lung cells and different lung cancer cells
under various polarimetric states.
Fig. 7. t-statistic comparing adenocarcinoma and the different lung cell types
under various polarimetric states.
These results demonstrate that the backscattered
polarimetric signal intensities through healthy lung cells are
obviously different than those from squamous carcinoma and
adenocarcinoma under all the 12 considered geometries. In
addition, light intensities measured in the experimental
waveforms are higher in healthy tissue, while the "population"
of adenocarcinoma cells has quite more different optical
properties than healthy tissue compared to the squamous
"population". The paired differences are relatively large for all
geometries, except possibly VP. In particular, the HH, VV and
PH geometries demonstrate consistently large differences
among the different tissue types.
In order to further explore the ability of the tested
geometries in discriminating different lung cell types, it was
considered the distance of t-test of different tissue types using
the same "population" as their common comparison sample
data. More specifically, we attempt to extract information on
which polarization geometry discriminates more clearly
healthy tissue from adenocarcinoma (and squamous carcinoma)
by comparing the difference of t-test values of these two
populations produced when squamous (and adenocarcinoma
respectively) or mixture of carcinoma distributions are utilized
as reference populations. The HH, PH and RH polarization
states provided high distances between the t-test values for
different tissue type, as depicted in Figs. 8 and 9.
Fig. 8. t-statistic comparisons between and adenocarcinoma under various
polarimetric states and the lung cell type as reference population (squamous or
mixture of carcinomas).
Fig. 9. t-statistic comparisons between normal lung cell and squamous
carcinoma under various polarimetric states using the same lung cell type as
reference population (adenocarcinoma or mixture of carcinomas).
Combining both tests above, it is suggested that HH and PH
geometries are potentially the most discriminative geometries.
Finally, the extremely low calculated p-values (values less
than 10-4) strongly emphasize on the high difference of the
means of the sample distributions, yet the advanced degree of
independence and discrimination of the optical properties of
the four tissue types examined.
VII. CONCLUSIONS
The results reveal that backscattered polarimetric signal
contributions offer distinct discrimination signatures among
different cell samples, under all the 12 examined geometries. In
particular, the geometries of PH and RH measurement states
yield better discrimination of the tested cell types. In fact, the
low p-values on the comparisons emphasize the strong
confidence on the discrimination of the four lung cell samples
under examination, based on their optical properties. It is
anticipated, that longer integration times would allow us to
capture more detailed waveforms, increasing further the
statistical confidence of this study.
ACKNOWLEDGMENT
George Giakos would like to acknowledge that
measurements were obtained using The U.S. Air Force
Research Laboratory (AFRL) multifunctional imaging
platform.
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Appendix A
TABLE 1. STATISTICAL ANALYSIS OF MUELLER MATRIX FOR AIR, LHP AND LVP.
