Abstract—Guided wave propagation has gained significant interest in the ultrasonic evaluation of bone. Previous computational and experimental studies are based on the theory describing guided wave propagation in a free two-dimensional plate (Lamb wave theory). In this work, we modify the boundary conditions so as to take the effect of the overlying soft tissues into account. A two-dimensional model of a bone- mimicking plate (density 1500Kg/m 3 , Young’s modulus 14GPa, cortical thickness 4mm) was developed. The fracture callus tissue was modeled as an inhomogeneous material consisting of six ossification regions with properties changing during the healing period. The bone was assumed immersed in blood (fluid-loaded boundary conditions). The ultrasound transmitter and receiver (1MHz) were placed on each side of the callus, equidistant from it at a 35mm in-between distance. First, we investigated the propagation velocity of the first arriving signal (FAS) using traditional time-domain analysis. Next, the velocity dispersion of the guided wave modes was represented in the time-frequency (t-f) domain of the signal. Characterization of the propagating guided modes was carried out by incorporating the theoretical leaky Lamb wave dispersion curves. Comparing with previous results obtained from free intact and healing plates, it was found that the surrounding soft tissues have a significant effect on the dispersion of guided waves. The effect was less pronounced on the FAS propagation velocity. However, leaky Lamb waves were again sensitive to the material and mechanical changes during the simulated healing process. In conclusion, the application of realistic boundary conditions provides an improved approach to interpreting clinical measurements. I. INTRODUCTION uantitative determination of bone mechanical properties is a crucial issue not only for the assessment of degenerative diseases such as osteoporosis, but also for Manuscript received June, 30, 2006. M. G. Vavva is with the Department of Material Science and Engineering, University of Ioannina, and the Unit of Medical Technology and Intelligent Information Systems, Computer Science Department, University of Ioannina, GR 45 110 Ioannina, Greece (e-mail: mvavva@cc.uoi.gr). V. C. Protopappas is with the Department of Medical Physics, Medical School, University of Ioannina and the Unit of Medical Technology and Intelligent Information Systems, Computer Science Department, University of Ioannina, GR 45 110 Ioannina, Greece (e-mail: me00642@cc.uoi.gr). D. I. Fotiadis is with the Unit of Medical Technology and Intelligent Information Systems, Computer Science Department, University of Ioannina, Greece, and also with the Biomedical Research Institute – FORTH, GR 45 110 Ioannina, Greece (e-mail: fotiadis@cs.uoi.gr). D. Polyzos is with the Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26 500, Greece (e-mail: polyzos@mech.upatras.gr). the objective evaluation of fracture healing. The so-called axial transmission technique has been developed to serve that purpose by measuring the ultrasound velocity of the waves propagating through the long axis of the bone. This technique allows for the evaluation of long bones like tibia and radius. A transmitter and a receiver are placed along the bone axis either in contact with the skin [1] or through implantation directly onto the bone surface [2,3]. The apparent velocity is specified by the transit time of the first arriving signal (FAS) at the receiver and the propagation distance. The correlation between the FAS velocity and the properties of bone, such as mineral density, cortical thickness and elastic modulus, has been clarified experimentally [4,5] and by computed simulations [6-9]. Clinical [10] and animal [2,3] research, as well as simulations of two-dimensional (2-D) bone models [11], aiming at the assessment of the fracture healing process, have indicated that the FAS velocity increases during the healing period. In addition, both experimental immersion techniques on acrylic plates and in vivo applications [12] have been carried out in order to elucidate the effect of the surrounding soft tissue and the width of the fracture gap on the FAS propagation velocity. However, the FAS wave corresponds to a “surface wave” when the wavelength is smaller than the thickness of the cortex, and therefore its velocity reflects only the properties of the cortex along a subsurface region. Conversely, when the wavelength of the transmitted wave is larger than the cortical thickness, the bone acts as a waveguide supporting the propagation of guided wave modes [13]. Guided waves have recently been regarded as a significant tool in the ultrasound evaluation of bone status since they are sensitive to both the mechanical and geometrical properties of the propagation medium. Computational studies on 2-D bone models [6,9] and experimental research [4,9,14,15] have been performed to investigate guided wave propagation by making use of the Lamb wave theory (the theory that describes guided waves in free 2-D plates) [13]. As opposed to the above mentioned studies which focused on osteoporosis, we recently demonstrated that guided waves can be also useful in monitoring the fracture healing process [1]. A free 2-D isotropic healing bone model was developed and the investigation of guided wave propagation was based on time-frequency (t-f) signal analysis. However, all the Two-Dimensional Modeling of Guided Ultrasound Wave Propagation in Intact and Healing Bones Immersed in Fluid Maria G. Vavva, Vasilios C. Protopappas, Member, IEEE, Dimitrios I. Fotiadis, Member, IEEE, and Demos Polyzos Q