Submission ID: 347 Subject Classificiation: MTC Medical Tissue Characterization 1 Abstract— Using a dedicated axial transmission device and SVD-based signal processing, experimental wavenumbers were measured on bone mimicking phantoms of different geometries (plate, tube, radius shape). An estimation method based on the use of the dispersion function of an anisotropic plate model was applied to estimate elastic properties of the phantoms. This work has shown that measured data are sufficient to allow an estimation for all three considered geometries. Considering four different thicknesses for the plate geometry, a variability ranging from 5 to 15 % was found for the estimated stiffnesses with a reproducibility less than 1 %. For all phantoms, estimated stiffnesses are overall in good agreement with values obtained from reference measurements (transverse transmission). Index Terms— axial transmission, guided wave, bone, quantitative ultrasound, singular value decomposition (SVD). I. INTRODUCTION LTRASONIC guided modes propagation has been proposed as a means for cortical bone assessment. However, the presence of interfering multimodal responses in recorded signals requires sophisticated signal processing to disentangle individual modes. Towards this goal, an approach based on the singular value decomposition (SVD) of multidimensional signals recorded with an axial transmission array of emitters and receivers has been proposed and has been shown to be efficient for non dissipative materials [1]. The axial transmission technique utilizes a set of emitter(s) and receiver(s) to measure long bones, like tibia and radius. The shaft of long bones has been evidenced to act as a natural waveguide [2, 3]. A number of studies have demonstrated experimentally the potential of this technique to assess bone mechanical and structural properties [4-6]. In some studies, the signal processing techniques were adapted to identify several guided modes propagating in long bones. High order guided modes have also been observed in vitro in bovine and human bone specimens [7-9]. In this work, the SVD-based signal processing is used on experimental data obtained on a bone mimicking material with different shapes (plates, tube, bone). An estimation method is This work has been supported by ANR project ”COSTUM” 09-TECS-005- 03 (2009-2012). corresponding email: josquin.foiret@upmc.fr then applied using experimental wavenumbers in order to infer elastic properties from experimental data. All experimental data were measured using an axial transmission device with a compact probe dedicated for clinical use. II. WAVENUMBER MEASUREMENT The SVD-based signal processing technique has been described in detail in papers from our group [1, 10, 11]. Here, only the principles are recalled. The recorded signals r ij (t), with i and j the emission and reception indices ranging from 1 to N E and 1 to N R , respectively, are first Fourier-transformed. In this study, a custom made linear transducer array (Vermon, Tours, France) was used (N E = 5, N R = 32 and 1 MHz central frequency). The singular value decomposition is subsequently applied to the N E ×N R sub-matrices, i.e., the matrices R ij (f) at each frequency. The signal subspace dimension M is determined by applying a first heuristically selected threshold t 1 on the singular values. The singular values below the threshold are considered to be associated with the noise subspace. The M reception singular vectors, denoted U n , are associated with the signal subspace and are therefore a basis of the experimental guided modes. Then, the so-called Norm function is defined by the following equation ( ) ( ) 2 1 ,, , M test n n Norm fk k α α = = ∑ U e , (1) where e test (k, α) is proportional to exp(i(k+iα)x R ) with k and α the real and imaginary parts of the testing wavenumber. The vector e test (k, α) corresponds to a spatial plane wave defined on the reception array with a norm equal to 1. x 1 ith emitter jth receiver propagating medium : may be absorbing and/or anistropic e thickness emission array reception array O L = N R p x j R D x 3 x 2 x i E Fig.1 Axial transmission configuration with multi-emitters and multi-receivers arrays. The Norm-function can be interpreted using the guided Guided mode measurement on bone phantoms with realistic geometry Josquin Foiret, Jean-Gabriel Minonzio, Maryline Talmant, and Pascal Laugier CNRS - UPMC Univ Paris 6 - UMR 7623, 15 rue de l’école de médecine, 75006 Paris, France U