Numerical simulation of the influence of the poroelastic nature of human trabecular bone on ultrasonic wave propagation

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Journal o f Biomechanics 2006, Vol. 39 (Suppl 1)

5702 Mo-Tu, no. 5 (P55) Development o f a wave front removal algorithm for an ultrasonic axial transmission device used for the in vivo mechanical characterization o f cortical bone M. Sasso 1, M. Talmant 2, G. Haiat 1, P. Laugier 2, S. Naili 1. 1Universit# Paris 12, Laboratoire de M#canique Physique, UMR CNRS 7052 B2OA, Cr#teil, France, 2Laboratoire d'lmagerie Param#trique, CNRS UMR 7623, Universit# Pierre et Marie Curie- Paris 6, Paris, France In the context of bone status assessment, the axial transmission technique allows ultrasonic measurements of the elastic properties of cortical bone using a multi-element transducer. The axial transmission set up generates a diversity of propagating modes or wave types in the cortical shell. The current processing only evaluates the velocity of the first arriving signal, commonly referred to as the speed-of-sound. Later contributions are potentially valuable in respect to the mechanical characterization of the cortical bone and are not yet analysed. The issue is that all the later contributions interfere which disrupt the various mode analysis. A novel ultrasonic wave extraction algorithm using a singular value decomposition method is proposed. This algorithm aims at characterizing a given energetic low frequency contribution observed in vivo around 1 MHz. The performance of the proposed algorithm is evaluated by estimating the wave velocity of the considered wave front and is tested on 100 simulated signals. For a signal to noise ratio of 10dB, the mean error associated with this method is of 5.2%, to be compared with 34% with a classical signal analysis. The algorithm is also tested on real in vive measurements and is shown to be effective for wave extraction. The results show that it is possible to accurately determine and possibly remove the contribution of this wave front in this experimental configuration. 7533 Mo-Tu, no. 6 (P55) Patients satisfaction with the knee and ankle function after limb lenghtening - Long-term follow-up M.A. Kirjanen, A. Toom, T. Haviko. Tartu University, Clinic ef Traumatelegy and Orthopaedics, Tartu, Estonia In this study were analyzed 72 limb lengthening operations performed on 63 lower limbs in 53 patients. Ilizarov device was used. Three operation methods were compared: distraction epiphysiolysis (n=13), metaphyseal osteotomy (n=16) and corticotomy (n=43) regard the biomechanical function and patients satisfacion with functional gain at the long term follow-up- 19.4 years (range 10-29). After the limb lengthening the function of knee joint was impaired expressed in the diminishing of knee flexion mean by 79.1°±5.30 , what significantly differed from the preoperative values (p<0.0001). The degree of impaired function of the knee did not differ statistically from the used method of operation. After one year the function was significantly improved, but flexion was still 12.3°±4.00 less from the preoperative values (p=0.010). Patients from distraction epiphysiolysis group had gained almost the same level of knee flexion after one year 143°±2.10 comparing to preoperative 145°±1.70 (p =0.470). Patients with metaphyseal osteotomy had larger difference between preoperative (128.2°±7.60 ) and one year postoperative (115.0°±7.60 ) knee flexion values, but there was no statistical difference (p = 0.229). Statistically significant difference of knee flexion was found in metaphyseal corticotomy patients, so the preoperative value was 136.5°±2.60 and one year postoperative 121.70±5.60 (p=0.019). Also, the function of the ankle was decreased postoperatively in all groups. The decrease was most prominent in distraction epiphysiolysis group (-18.3°±2.40 versus -9.1°±2.40 in other groups; p=0.021). However, preoperative ankle function was restored completely after 1 year and there were no more differences between the different groups. However, patients' agreement to pass similar procedure once more (81% overall) was not associated with the objective functional result neither with the general satisfaction or satisfaction with the cosmetic results, but rather the subjective appraisal of the current pain intensity and appearance. Patients' satisfaction and agreement to repeat the procedure at the long-term follow-up did not differ between the used operation methods. Thus, all three methods can be considered useful and the final decision to choose one of them has to be based on clinical demand. 5687 Mo-Tu, no. 7 (P55) Numerical simulation of the influence of the poroelastic nature of human trabecular bone on ultrasonic wave propagation G. Haiat 1, F. Padilla 2, P. Laugier 2. 1Universit# Paris 12, Laberateire de M6canique Physique, UMR CNRS 7052 B2OA, Cr6teil, France, 2Laboratoire d'lmagerie Param#trique, CNRS UMR 7623, Universit# Pierre et Marie Curie- Paris 6, Paris, France Trabecular bone is a poroelastic medium in which the propagation of one or two longitudinal ultrasound waves has been observed (fast and slow waves),

Poster Presentations

depending of the relative orientation of the propagation direction with respect to the main direction of alignment of the trabecular network. Predictions based on analytical models have been unable so far to establish reliable relationships between bone properties and velocity and/or attenuation of the fast and the slow waves. The aim of this work is to assess the potential of computational methods as an alternative to analytical models to predict both types of compression wave in a poroelastic medium such as trabecular bone. The approach is based on a three-dimensional finite-difference timedomain (FDTD) coupled with real trabecular microstructures measured using high resolution micro computed tomography data. The influence of bone microstructure and material properties on fast and slow waves was studied (i) by using a dedicated iterative image processing algorithm (dilation, erosion) in order to modify the initial 3D microstructures and (ii) by varying the physical parameters introduced in the model (elastic stiffness coefficients cl 1 and c44 and density of the bone component). The simulations predicted the presence of both waves when the direction of propagation was parallel to the main trabecular orientation. For all samples, the fast wave disappears when bone volume fraction decreases. From the analysis of the transmitted signals, we were able to assess the dependence of velocity and amplitude of both waves on the variations of microstructure and material properties. The results suggest that the finite-difference computational method is a valuable approach to predict wave propagation in a poroelastic medium and may be a useful complimentary approach to analytical models. 5226 Mo-Tu, no. 8 (P55) In vitro studies of cancellous bones - Comparison of the prediction o f Blot's model, experiments and computer simulations M. Pakula 1,2,3, F. Padilla 1,2,3, E. Bossy 1,2,3, P. Laugier 2. 1Laboratoire d'Optique Physique, ESCPL CNRS UPR 5, Paris, France, 2Laboratoire d'lmagerie Parametrique, CNRS UMR 7623, Universite Paris 6, Paris, France, 3Institute of Environmental Mechanics & Applied Computer Science Bydgeszcz University, Bydgeszcz, Poland Quantitative ultrasound (QUS) techniques have received considerable attention during the last decade for non-invasive assessment of bone quality. However, poorly understood mechanisms implied in ultrasound wave propagation through bone require clarification, in order to improve QUS diagnostic capability and relate bone characteristics to ultrasound parameters. This paper is focused on ultrasonic propagation through cancellous bone. The aim is to compare experimental results with predictions from Biot's model and from numerical simulations based on a finite difference time domain (FDTD) algorithm for elastic wave propagation in non absorbing materials.. Ultrasonic (0.4-0.9 MHz) tests for 35 dry and water saturated specimens of trabecular bones (human femur) were performed.. Then the microarchitecture of the specimens was assessed by synchrotron microtomography (SR-~tCT). The reconstructed 3D microarchitectural models were used as an input structure for FDTD simulations. Finally, parameters like tortuosity, permeability, porosity and density of solid phase were measured using techniques dedicated to characterization of porous materials. The so called Biot-Willis porous material constants were derived based on these experimental data and formulas available for example in [Biot, J. Acoust. Soc. Am., 1962]. Experimental phase velocity (SOS) and attenuation coefficient (BUA) were then compared to FDTD and Biot's model predictions. Whereas a strong relationship was observed between measurements and 2 FDTD simulations r2os=0.74 and rnBUA-0.81, no correlation was found between SOS and nBUA predicted by Biot's model and experimental or FDTD data. In conclusion, our data suggest that Biot's model is inappropriate, even when using individually measured values of parameters such as tortuosity and permeability. In contrast, FDTD simulations using real 3D models of micro architecture provided accurate predictions of SOS and BUA, suggesting an important role of ultrasound scattering by the trabecular network in the interaction mechanism. 5115 Mo-Tu, no. 9 (P55) Ultrasonically determined thickness o f long cortical bones: Simulation study P. Moilanen, M. Talmant, P. Laugier. Laberateire d'lmagerie Param~trique, UMR CNRS 7623, Universit6 Paris 6, Paris, France Recent experimental studies have shown that an ultrasonically determined thickness (U-Th), based on a fit between measured and theoretical velocity of fundamental flexural guided wave, correlated significantly with the cortical thickness (C-Th) of human radius bones [1]. These results were, however, subjects to errors, such as variations in material and geometrical properties, which were not properly explained by the theoretical model used. The purpose of this study was to start investigating the gap between the theoretical and experimental results for real bone. Numerical model, based on 3D X-ray reconstructions of human radii in vitro (n = 29), was developed, and wave propagation