This thesis introduces TLM as a new method for modelling medical ultrasound wave propagation. Basic TLM theory is presented and how TLM is related to Huygens principle is discussed. Two dimensional TLM modelling is explained in detail and one dimensional and three dimensional TLM modelling are explained.

Implementing TLM in single CPU computers and parallel computers is discussed and several algorithms are presented together with their advantages and disadvantages. Inverse TLM and modelling non linear wave propagation and different types of mesh are discussed. A new idea for modelling TLM as a digital filter is presented and removing the boundary effect based on digital filter modelling of TLM is discussed.

Some modelling experiments such as : 1) Focusing mirror. 2) Circular mirror. 3) Array transducers. 4) Doppler effect.

are presented and how to use TLM to model these experiments is explained. A new low sampling rate theory for TLM modelling is proposed and verified. This new theory makes the modelling of a much larger spaces practical on a given hardware platform.