Proceedings of the International Conference DAYS on DIFFRACTION 2014, pp. 215–219 978-1-4799-6699-8/14/$31.00 c ⃝ IEEE 2014 Diffraction of electromagnetic wave on skin capillary Ivan Starkov, Zbynˇ ek Raida SIX Research Centre, Brno University of Technology, Brno, Czech Republic; e-mail: starkov@feec.vutbr.cz Alexander Starkov Institute of Refrigeration and Biotechnology, University ITMO, St.Petersburg, Russia We have formulated and solved the problem of elec- tromagnetic wave diffraction on skin blood vessel. As an important result of our investigation, it is es- tablished that the amplitude of the scattered field is proportional to the square of the capillary area. For the case of long waves, the reflected field is lin- early dependent on the depth position of the capil- lary. The proposed approach would eliminate fun- damental uncertainties in the modeling of biological tissues. 1 Introduction The human skin is the largest organ in the body. At the same time, it is a very intricate tissue that exhibits complex material behavior. Due to poten- tial applications in medical diagnostic, therapeu- tic and surgical procedures, the understanding of optical/electromagnetic properties of biological tis- sues is an active and important research topic. In this work, we have proposed a theoretical model for the diffraction of electromagnetic wave on the skin blood vessel. In order to correctly build the model of hu- man skin describing its optical and electromagnetic properties, it is necessary to understand biological features of this system (see Fig. 1). The upper layer of the skin with thickness h e is the epider- mis which is multilayered epithelium [1]. Radiation incident from the air firstly goes through the epi- dermis where the highest dielectric constant corre- sponds to the melanin. By virtue of this, optical properties of the epidermis can be considered equal to those of the melanin with a refractive index of 1.44 [2]. The next layer in the skin tissue is dermis. At the interface of the dermis some part of the radi- ation is reflected while the rest goes inside. Below the dermis is the subcutaneous fat which possesses a high absorption coefficient and reflection from which is insignificant [3]. Thus, we can consider the thickness of the dermis as infinite. The blood vessel is situated in the dermis at a depth of h and is rep- resented by the cylinder of arbitrary cross section with center at point M 0 . The fact that the capillary has walls is taken into account. The cylinder axis is considered parallel to the interface. The typical value of the radius for blood capillaries lays in the range 0.05–0.1 mm. In turn, the wavelength of the incident electromagnetic field for medical purposes is around 1 cm. As a consequence, in this paper the problem of diffraction on the capillary located in the layered media is investigated in the long- wave approximation. For convenience, we denote quantities related to air, epidermis, dermis, vessel, and capillary wall by the indexes {a, e, d, v, w}, re- spectively. The absence of index implies a general dependence. 2 The problem statement As a starting point, we consider the system of Maxwell’s equations ∇× E = iω c μ H , ∇× H = - iω c ε E . (1) Any plane electromagnetic wave can be represented by the superposition of two waves: the first with vector E inc is perpendicular to the plane of inci- dence, while the second lies in this plane. The approach in both cases is similar and we restrict ourselves by the consideration of TE waves. That is, we assume that E inc = U inc e y . Here e y is the unit basis vector of the Cartesian coordinate system chosen so that the xy plane coincides with the skin interface. From the geometry of the system, it fol- lows that the total electric field E will be oriented in the same direction, i.e. E = U e y . For electromagnetic waves of the same polar- ization, the system (1) can be reduced to the Helmholtz’s equation [5] ∆U + k 2 U =0. (2)