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Yayın An inverse source problem connected thermoacoustic imaging in multi-layer planar medium(Işık Üniversitesi, 2018-06-04) Yücel, Hazel; Uzun, Banu; Işık Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Doktora ProgramıIn this thesis, we mentioned imaging technics used today, and microwave induced thermoacoustic procedure and imaging. We made literature survey about solution of the thermoacoustic equation for homogeneous and inhomogeneous medium. We modelled the inhomogenity of medium as a multi-layer planar structure and de?ned initial condition, continuity conditions on the layer boundaries and radiation conditions at in?nity, then we derived analytical forward and inverse solution of the thermoacoustic wave equation for inhomogeneous medium with the source distribution existing in all layers. Our solution of inverse source problem is based on the methods of the Green’s functions for layered planar media. For qualitative testing and comparison of the point-spread functions associated with the conventional solution for homogeneous medium and our derived layered solutions, we performed numerical simulations. In numerical simulations ?rst we generated the measured data by using the derived forward solution for multi-layer planar medium and then we used conventional inverse solution and our derived inverse solution to image source distribution. Our simulation results showed that the conventional inverse solution based on homogeneous medium assumption, as expected, produced incorrect locations of point sources, whereas our inverse solution involving the multi-layer planar medium produced point sources at the correct source locations. Also, we showed that the performance of layered inverse solution is sensitive to the validity of the layer parameters and medium parameters used as prior information in the measured data. Our inverse solutions based on multi-layer planar media are applicable for cross-sectional 2 dimensional imaging of the organs such as breast, skin, and abdominal structure.Yayın Solution of inverse source problem in thermoacoustic imaging(Işık Üniversitesi, 2022-06-14) Elmas, Demet; Uzun, Banu; Işık Üniversitesi, Lisansüstü Eğitim Enstitüsü, Matematik Doktora ProgramıThis study aims to investigate and explore accurate analytical inverse solutions of thermoacoustic wave equation involved in microwave induced thermoacoustic imaging of breast. Using boundary conditions, we aimed to find more realistic solutions. For cross-sectional two-dimensional thermoacoustic imaging of breast, we explored solution of the wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section. To obtain the forward and inverse solutions of the thermoacoustic wave equation, we derived the Green’s function involving Bessel and Hankel functions by employing the geometrical and acoustic parameters (densities and velocities) of layered media together with temporal initial condition, radiation conditions and continuity conditions on boundaries of layers. The image reconstruction based on this approach involves the layers parameters as the a priori information which can be estimated from the acquired thermoacoustic data. To test and compare our layered solution with conventional solution based on homogeneous medium assumption, we performed simulations using numerical test phantoms consisting of sources distributed in the layered structure. After then, we derived more general integral solution for thermoacoustic wave equation in frequency domain for an arbitrary convex domain in R³.Yayın Eshelby tensors for a spherical inclusion in microstretch elastic fields(Elsevier Ltd, 2006-08) Kırış, Ahmet; İnan, EsinIn the present work, microelastic and macroelastic fields are presented for the case of spherical inclusions embedded in an infinite microstretch material using the concept of Green's functions. The Eshelby tensors are obtained for a spherical inclusion and it is shown that their forms for microelongated, micropolar and the classical cases are the proper limiting cases of the Eshelby tensors of microstretch materials.Yayın Eshelby tensors for a spherical inclusion in microelongated elastic fields(Pergamon-Elsevier Science ltd, 2005-01) Kırış, Ahmet; İnan, EsinEshelby tensors are found for a spherical inclusion in a microelongated elastic field. Here. a special micromorphic model is introduced to describe the damaged material which defines the damage as the formation and the growth of microcracks and microvoids occurred in the material at the microstructural level. To determine the new material coefficients of the model, an analogy is established between the damaged body and the composite materials and then Mori-Tanaka homogenization technique is considered to obtain overall material moduli. Following this idea, the determination of the Eshelby tensors which establish the relation between the strains of the matrix material and of the inclusion becomes the first task. Introducing the concept of eigenstrain and microeigenstrain, the general constitutive theory is given for a homogeneous isotropic centrosymmetric microelongated media with defects. Then by the use of Green's functions, micro and macro elastic fields are presented for the case of spherical inclusions embedded in an infinite microelongated material. Thus, the Eshelby tensors are obtained for a microelongated elastic field with a spherical inclusion and it is also shown that the classical Eshelby tensors can be obtained as a limit case of the microelongation.
