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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 An inverse source problem connected with thermoacoustic imaging in multi-layer planar medium(Springer, 2019-02-20) Yücel, Hazel; Ünalmış Uzun, BanuWe derived analytical forward and inverse solution of thermoacoustic wave equation for nonhomogeneous medium. We modelled the nonhomogeneous medium as a multi-layer planar medium and defined initial conditions, continuity conditions on the layer boundaries and radiation conditions at infinity assuming the source distribution existing in all layers. These solutions of thermoacoustic wave equation are based on the method of Green’s functions for layered planar media. For qualitative testing and comparison of the point-spread functions associated with the homogeneous and layered solutions, we performed numerical simulations. 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 examined whether the performance of our layered inverse solution is sensitive to medium parameters used as priority information in the measured data. Our inverse solutions based on multi-layer planar media are applicable for cross-sectional two-dimensional imaging of abdominal structure and the organs such as breast and skin.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 Çok katmanlı düzlemsel ortam için termoakustik dalga denkleminin çözümü(IEEE, 2017-06-27) Bayıntır, Hazel; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, MustafaBu çalışmada, farklı akustik parametrelere sahip çok katmanlı düzlemsel ortam için tüm katmanlarda kaynak dağılımı olduğu varsayımı altında termoakustik dalga denkleminin analitik olarak düz ve ters çözümü elde edilmiştir. Çok katmanlı düzlemsel ortam için elde edilen analitik çözüm katmanlı düzlemsel green fonksiyonlarına dayanmaktadır. Çok katmanlı düzlemsel modelleme meme, deri ve karın bölgesi görüntülemelerine uygun bir modellemedir. Elde edilen analitik çözüm ile literatürde var olan homojen ortam varsayımına dayanan çözüm her katmanda noktasal kaynak alınarak sayısal olarak karşılaştırılmıştır.Yayın Inverse solution of thermoacoustic wave equation for cylindrical layered media(Frontiers Media S.A., 2022-03-30) Elmas, Demet; Ünalmış Uzun, BanuThermoacoustic imaging is a crossbred approach taking advantages of electromagnetic and ultrasound disciplines, together. A significant number of current medical imaging strategies are based on reconstruction of source distribution from information collected by sensors over a surface covering the region to be imaged. Reconstruction in thermoacoustic imaging depends on the inverse solution of thermoacoustic wave equation. Homogeneous assumption of tissue to be imaged results in degradation of image quality. In our paper, inverse solution of the thermoacoustic wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section is investigated for cross-sectional thermoacustic imaging of breast and brain. By using Green’s functions and surface integral methods we derive an exact analytic inverse solution of thermoacoustic wave equation in frequency domain. Our inverse solution is an extension of conventional solution to layered cylindrical structures. By carrying out simulations, using numerical test phantoms consisting of thermoacoustic sources distributed in the layered model, our layered medium assumption solution was tested and benchmarked with conventional solutions based on homogeneous medium assumption in frequency domain. In thermoacoustic image reconstruction, where the medium is assumed as homogeneous medium, the solution of nonhomogeneous thermoacoustic wave equation results in geometrical distortions, artifacts and reduced image resolution due to inconvenient medium assumptions.Yayın Thermoacoustic image reconstruction based on layered tissue model(SPIE-Int Soc Optical Engineering, 2017) Bayıntır, Hazel; İdemen, Mehmet Mithat; Ünalmış Uzun, Banu; Karaman, Mustafa; Elmas, DemetWe derived analytical forward and inverse solution of thermoacoustic wave equation for inhomogeneous multi layered planar and cylindrical mediums with the source distribution existing in all layers. These solutions are applicable for imaging of organs such as breast and brain, whose structures are suitable for multi-layer modelling. For qualitative testing and comparison of the point-spread-functions associated with the homogeneous and layered solutions, we performed numerical simulations. Our simulation results show that the conventional inverse solution based on homogeneous medium assumption, as expected, produces incorrect locations of point sources and significantly increased side lobes, whereas our inverse solution involving the multi-layered medium produces point sources at the correct locations with lower side lobes.Yayın Çok katmanlı silindirik yapılar için termoakustik dalga denkleminin ters çözümü(IEEE, 2017-06-27) Elmas, Demet; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, MustafaTermoakustik görüntüleme, elektromanyetik enerji uyarımı ile ultrason dalgaları oluşumunu sağlayan yeni bir yöntemdir. Bu sistemin görüntüleme işlemi termoakustik dalga denkleminin ters çözümüne dayanmaktadır. Ters çözümde görüntülenecek dokunun homojen yapıda olduğu varsayımı, görüntü kalitesinin azalmasına neden olur. Bu çalışmada, meme ve beyinin görüntülemesinde uygulanabilecek üç boyutlu eş merkezli silindirik çok katmanlı yapılar için termoakustik dalga denkleminin analitik ters çözümü elde edilmiştir. Çözümü sayısal olarak test etmek için, noktasal kaynaklar içeren üç katmanlı fantom kullanılarak numerik simulasyonlar elde edilmiştir.
