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28 May 2015 Ex vivo characterization of normal and adenocarcinoma colon samples by Mueller matrix polarimetry
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Mueller matrix polarimetry along with polar decomposition algorithm was employed for the characterization of ex vivo normal and adenocarcinoma human colon tissues by polarized light in the visible spectral range (425–725 nm). Six derived polarization metrics [total diattenuation (DT), retardance (RT), depolarization (ΔT), linear diattenuation (DL), retardance (δ), and depolarization (ΔL)] were compared for normal and adenocarcinoma colon tissue samples. The results show that all six polarimetric properties for adenocarcinoma samples were significantly higher as compared to the normal samples for all wavelengths. The Wilcoxon rank sum test illustrated that total retardance is a good candidate for the discrimination of normal and adenocarcinoma colon samples. Support vector machine classification for normal and adenocarcinoma based on the four polarization properties spectra (ΔT, ΔL, RT,and δ) yielded 100% accuracy, sensitivity, and specificity, while both DT and DL  showed 66.6%, 33.3%, and 83.3% accuracy, sensitivity, and specificity, respectively. The combination of polarization analysis and given classification methods provides a framework to distinguish the normal and cancerous tissues.



Precancerous polyps initiate the majority of colon cancer,1 which is one of the major causes of cancer-related deaths.2 The detection of such precancerous polyps at an early stage, followed by surgical removal during colonoscopy, can greatly enhance the survival rates and patient’s quality of life. However, the diagnosis of precancerous polyps at early stage by white light colonoscopy is very challenging.3 Polypectomy is still considered to be a standard diagnostic technique for colon cancer, which has its own set of shortcomings. In this technique, excision of a polyp for biopsy followed by histopathology needs extensive examination of biopsy samples by microscope for several morphological changes (such as nuclear and cellular enlargement, increased variation in nuclear size and shape, and increased concentration of chromatin4) that occur during the development of cancer in the polyp. Therefore, the performance of polypectomy is greatly dependent on the expertise of the surgeon/pathologist besides its noninvasive nature. Moreover, the excision of multi polyps and their histopathology along with identification of clear circumferential margins during surgery for colon cancer further complicate this procedure. Therefore, it demands a noninvasive automated modality to overcome the above mentioned issues.

Polarized light for cancer diagnosis is gathering increased interest due to frequently observed contrasts in polarization parameters between normal and malignant tissues. It has great advantages compared to other optical techniques in signal strength and sensitivity to cellular structures, and thus conveys rich morphological and functional information about the biological tissue. Many studies implementing polarimetric contrasts in various biomedical fields such as dermatology, ophthalmology, gynecology, etc., have already been carried out. Various dermatological diseases such as lupus lesions and malignant moles are identified by polarimetric measurement.5,6 Jacques et al. reported that surgical excision of skin cancers can be guided using polarized light and developed a handheld polarization camera for this purpose.7 Polarization images of precancerousoral tissues in hamster cheek pouches showed considerable differences in depolarization and retardance images between normal and precancerous tissues.8 Polarized light has been used for extraction of quantitative information about the size of cell nuclei from imaging the human epithelial tissue.4 Shukla and Pradhan showed that depolarization power is sensitive to morphological changes in the normal and dysplastic states of epithelial cervical tissue.9 Contrast in polarization properties such as retardance, diattenuation, and depolarization has been observed for hepatic tissue,10 connective tissue,11 cervical precancer,12 myocardium samples,13 and gastric tissues.14 Pierangelo et al. have correlated various histological variants of human colon tumor to depolarization using multispectral Mueller matrix polarimetry.15,16 Robust statistical analysis along with suitable classification of healthy and cancerous colon tissues in conjunction with the Mueller matrix polarimetry technique is of paramount importance for implementation of the technique at the clinical level. Mueller matrix polarimetry is not exhausted much with suitable statistical analysis, particularly the studies conducted by Pierangelo et al. for colon cancer detection.

In this study, we have investigated the relative contrasts of polarization properties (retardance, diattenuation, and depolarization) for ex vivo normal and adenocarcinoma human colon tissue samples using Mueller matrix polarimetry in the complete visible spectral region (425–725 nm). For statistical analysis, Wilcoxon rank sum was employed for the selection of suitable polarimetric metrics for the classification of normal and adenocarcinoma colon samples. We have used a support vector machine (SVM) for classification of our data, and discussed the sensitivity and specificity in detail. The results may have important biomedical applications, specifically in the automated noninvasive diagnosis of cancer.


Materials and Methods


Microscopic Structure of Colon Tissue

In this study, we have compared the polarimetric properties of adenocarcinoma and normal colon tissues. Colon tissue is composed of three main layers: mucosa, submucosa, and muscularispropria17,18 that can be clearly seen in the microscopic image of a normal colon tissue as shown in Fig. 1. Mucosa can be further divided into: (a) the superficial one cell thick epithelium layer; (b) the lamina propria, which is composed of a loose network of collagen fibers and blood capillaries; and (c) the muscularis mucosa, which is a thin layer of smooth muscles and separates mucosa from submucosa. Submucosa contains a dense network of collagen fibers, blood vessels, and lymphatic vessels but no glands are present. Muscularis propria is composed of muscular tissue and separates submucosa from serosa, which is the inner lipid layer and contains cells that produce lubricating fluid for friction reduction.19 Sometimes serosa is termed as the fourth layer of colon tissue.

Fig. 1

Microscopic image of normal colon tissue sample with 20× objective lens showing its different layers: the mucosa (M), the submucosa (SM), and muscularis propria (MP).


Approximately 90%–95% of malignant tumors of the colorectal system are derived from epithelial cells, usually in the large intestine.20 Adenocarcinomas are derived from the glandular epithelium. The main characteristic of adenocarcinoma tissue is the significant nuclear enlargement compared to normal tissue as observed in both light scattering spectroscopy and morphometric measurements.19


Sample Preparation

A total of 24 colon tissue samples obtained from 24 different patients were examined in this study. Samples were categorized into two classes, one having 16 adenocarcinoma colon tissue samples and the other with 8 normal colon tissue samples. These tissue samples were either removed by biopsy or partial colectomy. Each tissue sample was fixed in formalin, embedded in paraffin and sliced in 3-μm thick sections using Leica microtome. These tissue samples were fixed on glass slides, stained with hematoxylin and eosin (H&E) and covered with a glass coverslip. Polarimetric analysis was sequentially performed on same tissue slides after their pathological evaluation.


Mueller Matrix Polarimeter

In this study, we have used a computer-controlled Mueller matrix spectro-polarimetery system (Axometrics, Huntsville, Alabama; schematic is shown in Fig. 2). A low-noise xenon lamp (150 W) is used as the input light source. Any wavelength in the range of 400–800 nm can be selected with a built-in diffraction grating monochromator with an accuracy of ±0.5nm. The light source is coupled to the polarization state generator (PSG) via fiber-optic cable. PSG generates various desired polarization states for sample illumination. The beam illumination diameter was 6 mm at the sample. After interacting with the sample the light is passed through a polarization state analyzer (PSA) which is connected to a computer.

Fig. 2

Schematic diagram of Mueller matrix polarimeter consists of light source (L), polarization state generator (PSG), sample (S), polarization state analyzer (PSA), and detector (D).


All samples were illuminated with four different input polarization states with a beam diameter of 6 mm. An average of three measurements for each tissue sample was considered to minimize the experimental fluctuation. The input polarization states include horizontal polarization (H:[1100]T), vertical polarization (V:[1100]T), linear +45deg polarization (P:[1010]T), and right circular polarization (R:[1001]T). After interaction with the sample, each polarization state was analyzed on four different polarization states. Thus, a total of 16 combinations were obtained. These include: HH, HV, HP, HR, VH, VV, VP, VR, PH, PV, PP, PR, RH, RV, RP, and RR, in which the first letters indicate the polarization states of the PSG, while the second letter indicates the polarization state analyzed by PSA. For example, “HV” means the incident polarization state is horizontal (H:[1100]T), which is analyzed onto vertical polarized light(V:[1100]T). A Mueller matrix was constructed using these 16 raw measurements.10


Polar Decomposition

The input Stokes vector Si is changed to the output Stokes vector S0 by polarization transfer function of the sample which can be written mathematically as S0=M Si, where M is the 4×4 Mueller matrix. The Mueller matrix contains the complete polarimetric fingerprints of the sample in “lumped” form. Various decomposition methods are used to individually retrieve these polarimetric properties. Polar decomposition21 is widely used in tissue polarimetry and is briefly discussed below.

The Mueller matrix of the sample can be expressed as the product of three basis matrices describing the three basic medium polarization properties as given below:

where MΔ is the depolarization matrix, MR is the retardance matrix, and MD is the diattenuation matrix. The derived polarization parameters are expected to be influenced by the choice of the basis matrices’ ordering due to the noncommuting nature of matrix multiplication.22 However, recent studies have shown that such ambiguity can be exclusively minimal under certain conditions such as very thin samples where multiple scattering is exceedingly negligible.23

The total depolarization ΔT and linear depolarization ΔL are calculated from the depolarization matrix MΔ, as given

where “tr” represents “trace” and mΔ is a 3×3 submatrix formed by omitting the first row and column of the full matrix MΔ

The retardance matrix MR is decoupled to calculate the total retardance R and linear retardance δ, as given


Total diattenuation DT and linear diattenuation DL are calculated from the first row of the experimental Mueller matrix as


Further details on polar decomposition can be found in the literature.8,24


Statistical Analysis

Tissue samples were divided into normal and cancerous groups based on histopathological reports. The nonparametric Wilcoxon rank-sum test was utilized to compare various polarimetric properties of the two groups with a significance level of 0.05. An SVM algorithm was employed for classification of the samples on the basis of contrast in the polarimetric properties.25 Statistical parameters such as accuracy, sensitivity, specificity, Mathew correlation coefficient, and F-measure were calculated from SVM. All data processing and statistical data analysis was performed using MATLAB®.


Results and Discussion

First, the experimental system is validated in the wavelength range of 400–800 nm (25-nm step size) for the standard samples (linear polarizer and retarder; quarter wave plate (QWP) at 632.8 nm) of known polarization properties. The Mueller matrix for each sample was measured and then decomposed via a polar decomposition method and corresponding polarization properties were extracted. Linear retardance of a retarder is presented in Fig. 3(a), while linear diattenuation of the polarizer is shown in Fig. 3(b). Analyses of Fig. 3 demonstrate that the error in both DL and δ reduces with wavelength. A maximum of 1.1% error exists in the calculation of both linear diattenuation and retardance as shown in Fig. 3. It may be noted that the error bars for linear retardance are smaller than the symbols used in Fig. 3(b) and are, therefore, not visible. The small error and almost no fluctuations in the standard samples of retarder that behave as QWP at 632.8 nm [indicated in Fig. 3(a)] and linear polarizer validate the excellent performance of the Mueller matrix polarimetric system and decomposition algorithms.

Fig. 3

(a) Linear retardance of retarder [quarter-wave plate (QWP) at 632.8 nm as indicated] and linear diattenuation of polarizer (b) in the spectral range from 400 to 800 nm.


Comparison of total and linear depolarization for normal and adenocarcinoma colon samples at seven different wavelengths (425–725 nm) is illustrated in Fig. 4. Each numerical value of the polarimetric parameter shown in Fig. 4 (and subsequent figures) corresponds to the average value taken over all samples belonging to normal and cancerous groups. It is noted that both total and linear depolarizations are significantly higher for adenocarcinoma samples as compared to normal colon tissue samples at all investigated wavelengths. Furthermore, no overlap in the error bars between cancerous and normal samples was observed. Significant contrast in depolarization suggests that it can be exploited for discriminating adenocarcinoma from normal tissue samples. Linear depolarization has values similar to the total depolarization values over the entire spectral range. This indicates that linear depolarization is the main contributor of total depolarization for both cancerous and normal tissue samples.

Fig. 4

Total (a) and linear (b) depolarization comparison for normal (rectangle) and adenocarcinoma (star) colon samples at different wavelengths (425–725 nm).


The observed contrast in depolarization can be correlated to the morphological changes that occur at histological and molecular levels in the transition from the normal to malignant phase of tissue. The distortion of normal microarchitecture in cancerous tissue samples can be easily seen from the comparison of colon tissue images shown in Fig. (5). Contrary to normal tissue [Fig. 5(a)], the carcinoma tissues have malignant glands of variable sizes, nuclear stratification of the cells lining the glands [Fig. 5(b)] and disorganized fibrous stroma Fig. 5(c). The increase in depolarization for cancerous tissue samples can be correlated to these alterations as reported in other studies.2627.28.29

Fig. 5

Images of 3-μm thick normal (a) and cancerous (b and c) colon tissues with 40× objective lens. Malignant glands of variable sizes and disorganized fibrous stroma in (b and c) can be seen.


Figure 6 depicts the total and linear retardance, while Fig. 7 shows the total and linear diattenuation for normal and adenocarcinoma tissue samples. It can be noted that both retardance and diattenuation are higher for carcinoma tissues as compared to normal tissues. However, the contrast in retardance for both groups is considerably higher than diattenuation. Retardation of polarized light in biological tissues is primarily attributed to the optical anisotropy of the collagen fibers. The network of these fibers is disturbed in the malignant colorectal tissue30 as illustrated in Fig. 5. Boosted collagen metabolism31 and enhanced collagen density in colon adenocarcinoma have been observed by electron microscopy,32 which amplifies the retardance of such tissues.

Fig. 6

Total (a) and linear (b) retardance for normal (rectangle) and carcinoma (star) tissues in the spectral range (425–725 nm).


Fig. 7

Total (a) and linear (b) diattenuation for normal (rectangle) and carcinoma (star) tissues against wavelength.


The positions of the average output Stoke vectors of linearly (H, V, P, R) and circularly (RC, LC) polarized light have been compared for both normal and cancerous tissue groups. The results, shown in Fig. 8, provide a quantitative fingerprint of the contrast in the polarimetric parameters of both groups.

Fig. 8

Comparison of positions of average output Stokes vector of linearly (a) and circularly (b) polarized light on Poincare sphere for normal and adenocarcinoma tissues.


Table 1 illustrates a typical comparison between an experimental Mueller matrix and the decomposed diattenuation MD, retardance MR and depolarization MΔ basis matrices for adenocarcinoma and normal colon samples at 425 nm. The diagonal elements of the Mueller matrices are significantly higher than the off diagonal elements indicating the high depolarization nature of colon tissue samples. It is interesting to note that an identical relation between the diagonal elements of the Mueller matrix is followed by both adenocarcinoma and normal colon tissues, i.e.,

for both types of samples. This is typical of the Rayleigh scattering regime, where the circularly polarized incident light is depolarized faster than linearly polarized incident light. Further, in turbid media such as biological tissues, the depolarization of incident linearly polarized light is primarily caused by randomization of the field vector’s direction due to scattering. Therefore, we believe that the linear depolarization in such a situation will be the same for any orientation of the incident linear polarization vector resulting in M22=M33.33 The same trend is observed in other studies for various tissues.15,19,34

Table 1

Comparison of experimental Mueller matrix and its decomposed basis matrices for cancerous and normal tissues at 425 nm.

Adenocarcinoma sampleNormal sample

In order to assess the performance of the above mentioned polarization method to differentiate normal and adenocarcinoma colon tissue samples, we have employed the Wilcoxon rank sum test and SVM for classification.35 We have performed the Wilcoxon rank sum test and SVM over all the six measured polarization properties of each individual sample and over each wavelength.

Figure 9 demonstrates the p values obtained by the Wilcoxon test for six polarimetric properties at different wavelengths with a significance level of p0.05. Polarization properties with p0.05 can be utilized for discrimination of normal and adenocarcinoma colon samples with higher than 95% confidence level. From Fig. 9, we conclude that depolarization and retardance are good candidates for the discrimination of normal and adenocarcinoma colon samples.

Fig. 9

P values obtained from Wilcoxon rank sum test for all six polarimetric properties at various wavelengths.


We have employed SVM classifier for further investigation to confirm the capability of the measured polarization metrics for classification of normal and adenocarcinoma colon samples. Different performance parameters including test accuracy, sensitivity, specificity, Mathew’s correlation coefficient (MCC), and F-measure were used to evaluate the performance of SVM. SVM was individually applied over the spectrum of six polarization properties and also with different combinations of these properties for all 24 samples. Table 2 shows that SVM classified the interrogated polarization properties very well except for total and linear diattenuations. From Table 2, it can be noted that SVM provides 100% test accuracy, sensitivity, and specificity, respectively, for four polarization properties including ΔT, ΔL, RT and δ. Contrarily, SVM provided 66.6% test accuracy, 33.3% sensitivity, and 83% specificity for both DT and DL. Furthermore, MCC and F-measure were found to be unity for the abovementioned four polarization properties, while for DT and DL they were resulted in not-a-number as shown in Table 2. Then, we have combined different polarization properties and applied SVM to each combination. In this case, SVM successfully discriminated the normal and adenocarcinoma colon samples with 100% test accuracy, sensitivity, specificity, and with MCC and F-measure were found to be unity. From Table 2, it is obvious that SVM fully categorized (100%) normal and adenocarcinoma colon samples for all kinds of combinations of polarization properties, even when total and linear diattenuations were included in these combinations. The “bad classification” of normal and adenocarcinoma colon tissue samples by SVM for total and linear diattenuations may be attributed to the overlapping of error bars for these polarization properties. Overall, we conclude that the better performance of SVM provided the confidence in the classification methodology we have acquired for the detection of normal and adenocarcinoma human colon tissue samples.

Table 2

Support vector machine (SVM)-based classification of normal and cancerous colon tissue samples.

PropertyAccuracy (%)Sensitivity (%)Specificity (%)MCCF measure

aNAN stands for not a number.



We have exploited polarized light for the differentiation of ex vivo normal and adenocarcinoma human colon tissue samples in the visible spectral range (425–725 nm). Histopathological slides were prepared from 24 human colon tissues including normal and adenocarcinoma samples for both pathology and polarimetry studies. Mueller matrix analysis along with polar decomposition method was employed for extraction and analysis of polarization metrics.inline-formula Our results show that the extracted polarization properties, namely ΔT, ΔL, DT, DL, RT, and δ, for adenocarcinoma colon tissue samples were significantly higher compared to the normal colon tissue samples. The performance of the detection method was further assessed by Wilcoxon rank sum test and SVM. Wilcoxon rank sum test illustrated that retardance and depolarization are good candidates for the discrimination of normal and adenocarcinoma colon samples. Moreover, SVM classifier showed a better performance for distinguishing normal and adenocarcinoma colon samples for all polarization properties except DT and DL. Our results show that SVM provided 100% accuracy, sensitivity, and specificity for ΔT, ΔL, RT and, δ individually as well as for any combination of above mentioned six polarization properties.


Professor Dr. Anwar (Anwar Clinical Laboratory, Swat, Pakistan) is gratefully acknowledged for providing us with ex vivo colon tissue samples and his valuable histopathological opinion. This work was supported by IT Endowment and Telecom Fund, PIEAS, Pakistan.



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Iftikhar Ahmad received his MSc degree in medical physics from PIEAS, Pakistan, in 2007. Currently he is pursuing his PhD studies. He is the recipient of IT and EF postgraduate scholarship and an exchange program scholarship for the University of Toronto. His work focuses on the polarimetric characterization of biological tissues. This is his third first-author publication.

Manzoor Ahmad has been working as an assistant professor at the Department of Physics, Islamia College (University), Peshawar. He completed his PhD from Pakistan Institute of Engineering and Applied Sciences (PIEAS) in 2014 under an indigenous scholarship sponsored by the higher education commission of Pakistan. He used polarized light for tissue characterization during his research. His research interests include polarized light imaging, elastic light scattering, diffuse reflectance, and Monte Carlo modeling of light propagation through tissues.

Karim Khan received his MS degree in medical physics from PIEAS University Islamabad, Pakistan, in 2007. He is working as a senior scientist in SINOR Cancer Hospital Swat. Currently, he is doing his PhD in the field of biophotonics at PEAS. His main field of interest is tissue polarimetry.

Sumara Ashraf is pursuing her PhD in the field of biomedical optics and polarimetry at PIEAS, Pakistan. She is the recipient of “Indigenous PhD Scholarship, Pakistan” and an exchange program scholarship for the University of Toronto. She worked as part of Dr. Alex Vitkin’s Laboratory on noninvasive glucose monitoring using polarized light.

Shakil Ahmad received his MS degree in nuclear medicine from PIEAS in 1997. He is working as the director of SINOR Cancer Hospital, Pakistan. His main field of interest is sonography imaging and nuclear imaging.

Masroor Ikram received his MSc degree in physics from Quaid-i-Azam University, Islamabad, Pakistan, and his PhD in laser physics from the University of Cambridge, Cambridge, UK, in 1990. Currently, he is the professor of physics and director (academics) of the Pakistan Institute of Engineering and Applied Sciences, Islamabad, Pakistan. His main research area is biophotonics, which include biomaterials, optical imaging, polarimetry, and photodynamic therapy.

© 2015 Society of Photo-Optical Instrumentation Engineers (SPIE) 1083-3668/2015/$25.00 © 2015 SPIE
Iftikhar Ahmad, Manzoor Ahmad, Karim Khan, Sumara Ashraf, Shakil Ahmad, and Masroor Ikram "Ex vivo characterization of normal and adenocarcinoma colon samples by Mueller matrix polarimetry," Journal of Biomedical Optics 20(5), 056012 (28 May 2015).
Published: 28 May 2015

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