Evolution of Statistic Moments of 2D-Distributions of Biological Liquid Crystal Net Mueller Matrix Elements in the Process of Their Birefringent Structure Changes
This research is aimed to investigate the reliability of Mueller-matrix differentiation of birefringence change of optically thick layers of biological liquid crystals at the early stages of the change in their physiological state. This is performed by measuring the set of skewness and kurtosis values of Mueller matrix image of the phase element in various points of the object under investigation. 1. Introduction Among many methods of optical diagnostics of organic phase-inhomogeneous object a new technique—laser polarimetry [1]—has been formulated within recent 10 years. It enables to obtain information about optical anisotropy [2–5] of biological tissues (BT) in the form of coordinate distributions of BT Mueller matrix elements, azimuths, and ellipticities of their object field polarization. To analyze this polarimetric information the following model approach was elaborated [1, 2, 6–13]:(i)all the variety of human BT can be represented as four main types—connective, muscle, epithelial, and nerve tissues;(ii)morphological structure of any BT type is regarded as a 2-component amorphous-crystalline structure; (iii)the crystalline component or extracellular matrix is an architectonic net consisting of coaxial cylindrical protein (collagen, myosin, elastin, etc.) fibrils;(iv)optically, the protein fibrils possess the properties of uniaxial birefringent crystals;(v)interaction of laser radiation with the BT layer is considered in the single scattering approximation, when the attenuation factor corresponds to . Specifically, the above mentioned model was used for finding and substantiating the interconnections between the ensemble of statistic moments of the 1st–4th orders that characterize the orientation-phase structure (distribution of optical axes and phase shifts of protein fibrils networks directions) of birefringent BT architectonics and that of 2D distributions of the elements of the corresponding Mueller matrix [6, 10]. It was determined [8, 11] that the 3rd and the 4th statistic moments of coordinate distributions of “phase” matrix elements ( , , ) are the most sensitive to the change (dystrophic and oncological processes) of optical anisotropy of protein crystals. These statistic moments characterize the BT extracellular matrix birefringence. On this basis the criteria of early diagnostics of muscle dystrophy, precancer states of connective tissue, collagenosis, and so forth were determined. However, such techniques do not take into account the coordinate heterogeneity of orientation-phase structure of protein crystals nets of the BT layer as
References
[1]
A. G. Ushenko and V. P. Pishak, Coherent-Domain Optical Methods. Biomedical Diagnostics, Environmental and Material Science, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004.
[2]
J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” Journal of Biomedical Optics, vol. 7, no. 3, pp. 359–371, 2002.
[3]
J. F. de Boer, T. E. Milner, and J. S. Nelson, Trends in Optics and Photonics (TOPS): Advances in Optical Imaging and Photon Migration, OSA, Washington, DC, USA, 1998.
[4]
M. J. Everett, K. Schoenenberger, B. W. Colston Jr., and L. B. Da Silva, “Birefringence characterization of biological tissue by use of optical coherence tomography,” Optics Letters, vol. 23, no. 3, pp. 228–230, 1998.
[5]
S. Jiao, W. Yu, G. Stoica, and L. V. Wang, “Optical-fiber-based Mueller optical coherence tomography,” Optics Letters, vol. 28, no. 14, pp. 1206–1208, 2003.
[6]
O. V. Angelsky, G. V. Demianovsky, A. G. Ushenko, D. N. Burkovets, and Yu. A. Ushenko, “Wavelet analysis of two-dimensional birefringence images of architectonics in biotissues for diagnosing pathological changes,” Journal of Biomedical Optics, vol. 9, no. 4, pp. 679–690, 2004.
[7]
O. V. Angelsky, Yu. Ya. Tomka, A. G. Ushenko, Ye. G. Ushenko, S. B. Yermolenko, and Yu. A. Ushenko, “2-D tomography of biotissues images in pre-clinic diagnostics of their pre-cancer states,” in Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies II, Proceedings of the SPIE, 2004.
[8]
O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, and Yu. A. Ushenko, “Polarization visualization and selection of biotissue image two-layer scattering medium,” Journal of Biomedical Optics, vol. 10, no. 1, Article ID 014010, 2005.
[9]
O. V. Angelsky, Yu. Ya. Tomka, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” Journal of Physics D, vol. 38, no. 23, pp. 4227–4235, 2005.
[10]
Yu. A. Ushenko, “Statistical structure of polarization-inhomogeneous images of biotissues with different morphological structures,” Ukrainian Journal of Physical Optics, vol. 6, pp. 63–70, 2005.
[11]
O. V. Angelsky, A. G. Ushenko, and Yu. A. Ushenko, “Polarization reconstruction of orientation structure of biological tissues birefringent architectonic nets by using their Mueller-matrix speckle-images,” Journal of Holography and Speckle, vol. 2, pp. 72–79, 2005.
[12]
O. V. Angelsky, P. P. Maksimyak, V. V. Ryukhtin, and S. G. Hanson, “New feasibilities for characterizing rough surfaces by optical-correlation techniques,” Applied Optics, vol. 40, no. 31, pp. 5693–5707, 2001.
[13]
O. V. Angelsky, P. P. Maksimyak, and T. O. Perun, “Optical correlation method for measuring spatial complexity in optical fields,” Optics Letters, vol. 18, no. 2, pp. 90–92, 1993.
