Quantitative sonographic imaging of human hard tissue by mathematical modelling of scanning acoustic...
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Quantitative sonographic imaging of human hard tissue by mathematical modelling of scanning acoustic microscopy data QUASIMProf. Dr. R.SaderProf.Dr.M.GrotePh.Dr. L.Beilina
Main objectivesDevelopment of quantitative sonographic imaging by mathematical modellingTesting Clinical application of ultrasound diagnostics
KSI Krmer Scientific Instruments GmbHIs a private company located in Herborn, GermanyEstablished in 1990Provide support and development for the high technology Scanning Acoustic Microscopy (SAM)Main directions are research, nondestructive testing and the process control industry ___________________________________ www.ksi-germany.com
KSI WINSAM 2000Scanning Acoustic Microscopetransmitterreceiveracoustic lenstransducerCoupling fluid(water)sample
KSI WINSAM 2000 Production and failure analysisRepeated informationDetailed informationShows processing and in-service defectsScan field300 X 300mmScanning Acoustic Microscope
Mathematical Model ofScanning Acoustic Microscopetransmitterreceiveracoustic lenstransducerCoupling fluid(water)sampleG 1C 0C(x)G 2G 2G 2
Computational AlgorithmInitial guessc=c0Solve forward problemSolve adjoint problemCompute gradientand new chIf gradient > epsstopnoyes
Adaptive AlgorithmInitial guessc=c0Solve forward problem on Kh, Tk Solve adjoint problem on Kh, Tk
Compute gradientand new chIf gradient decreasesstopnoyesInitial mesh K0Initial time partition T0
Residuals > tolrefine elements Construct new mesh Kh Construct new time partition Tkyesno
Solution of the forward problemc=0.5 inside a spherical inclusion and c=1.0 everywhere else in the domain. Isosurfaces of the computed solution are shown at different times.
Solution of the forward problemSolution of the forward problem with exact value of the parameter c=0.5 inside a spherical inclusion and c=1.0 everywhere else in the computational domain. We show isosurfaces of the computed solution at different times.
Adaptively refined meshes
Reconstructed parameterReconstructed parameter c(x) on different adaptively refined meshes. Isosurfaces of the parameter field c(x) indicating domains with a given parameter value are shown.22528 nodes, c =0.6626133 nodes, c = 0.53133138 nodes, c=0.51