BSRT Graduate School


Mechanics27.05.2019 09:00 - 17:00 (Mon)Kay RaumCranach House 0.0043
Mechanics28.05.2019 09:00 - 17:00 (Tue)Kay RaumCranach House 0.0043
Mechanics29.05.2019 09:00 - 17:00 (Wed)Kay RaumCranach House 0.0043
Title of Event: 
Introduction to the Finite Difference Time Domain Method
Optional or Mandatory: 
This course is optional for doctoral researchers at the BSRT
booked/available (including waiting list): 
maximum number of participants: 

The goal of this course is to provide a basic introduction to the Finite Difference Time Domain Method (FDTD) and exemplary applications in quantitative ultrasound bone healing. As the course duration does not allow going into the detailed theory, it is designed as a hands-on training giving participants a chance to use and learn how to operate FDTD software (SimSonic). After a basic overview of the concepts behind FDTD, we will provide introductory training to the software that will be used later on in the course. Starting with simple examples, for which analytical solutions are known (e.g. reflection at boundaries, scattering from a spherical inclusion), will be modeled in order to demonstrate the importance of element choice and mesh refinement. Once these basic ideas are understood we will then approach real bone and cartilage geometries coming from Scanning Acoustic Microscopy (SAM) and microcomputed tomography (µCT) images. These images will be segmented (Matlab), FDTD simulation maps will be produced, mechanical properties will be included and sound propagation and backscattering will be modeled. Moreover, the effects of more detailed material properties, such as inhomogeneity and anisotropy will be investigated and compared with experimental data.


Day 1

- Introduction to SimSonic with main emphasis on musculoskeletal ultrasound application

- Hands on demo

- Revision of acoustics, mechanics, introduction to FDTD


Day 2

- Simple problems (plate, spherical inclusion) with comparison to analytical solution 

- Effect of element size, sampling rate and other parameters

- From the medical image to the FDTD geometry, simple material properties

- Examples to be modeled > (a) intact long bones, bones with pores > (b) cartilage and soft scaffold


Day 3

- Advanced material properties (example a) > material heterogeneity and anisotropy of bone tissue

- Advanced structural properties (example b) > effects of cell morphology and distribution (random vs. layered structure)

- Independent work on an individualized example

- Report preparation

- Free discussion based on topics brought by the students



Course Materials and Techniques:

- Simsonic,

- E. Bossy, M. Talmant, and P. Laugier. Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models. Journal of the Acoustical Society of America, 115(5):2314{2324, 2004. 3

- G C Cohen. Higher-order numerical methods. Springer, Berlin, 2002. 9

- D Royer and E Dieulesaint. Elastic waves in solids I. Springer-Verlag, Berlin, 2 edition, 1999. 4