Quantitative sonographic imaging of human hard tissue by mathematical modelling of scanning acoustic microscopy data

QUASIM

Prof. Dr. R.Sader

Prof.Dr.M.Grote

Ph.Dr. L.Beilina

Main objectives

• Development of quantitative sonographic imaging by mathematical modelling

• Testing

• Clinical application of ultrasound diagnostics

KSI – Krämer Scientific Instruments GmbH

• Is a private company located in Herborn, Germany• Established in 1990• Provide support and development for the high

technology Scanning Acoustic Microscopy (SAM)• Main directions are research, nondestructive

testing and the process control industry

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www.ksi-germany.com

KSI WINSAM 2000Scanning Acoustic Microscope

transmitter receiver

acoustic lens transducer

Coupling fluid

(water)

sample

  KSI WINSAM 2000

Production and failure analysis

Repeated information Detailed information

Shows processing and in-service defects

Scan field300 X 300

mmScanning Acoustic Microscope

Mathematical Model ofScanning Acoustic Microscope

transmitter receiver

acoustic lens transducer

Coupling fluid

(water)

sample

G 1

C 0

C(x)

G 2

G 2 G 2

Computational mesh

Computational Algorithm

Initial guessc=c0

Solve forward problem

Solve adjoint problem

Compute gradientand new ch

If gradient > eps

stop

no yes

Adaptive Algorithm

Initial guessc=c0

Solve forward problem on Kh, Tk

Solve adjoint problem on Kh, Tk

Compute gradientand new ch

If gradient decreases

stop

no yes

Initial mesh K0

Initial time partition T0

Residuals > tolrefine elements

Construct new mesh Kh

Construct new time partition Tk

yesno

Solution of the forward problem

c=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 problem

Solution 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 parameter

Reconstructed 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 =0.66 26133 nodes, c = 0.531 33138 nodes, c=0.51