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Standard isentropic acoustic models do not include the dissipative effects of viscous friction and heat conduction. These viscothermal effects can be important, for example in models of small acoustic transducers. Viscothermal acoustics can be modeled in arbitrary geometries with models that contain four or fivecoupled fields. Therefore, these fully coupled models are computationally costly.O nt he other hand, efficient approximate viscothermal acoustic models exist, butthese are only applicable to certain simplified geometries. Anew approximate model is presented which fills the gapbetween these twoextremes. This newmodel can be used for arbitrary geometries and has acomputational efficiencywhich is higher than the full model and lower than the models with geometrical constraints. The newmodel is derivedand demonstrated on several problems, including acoustic-structure interaction problems.

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Structural vibration testing might be a promising method to study the mechanical properties of spinal motion segments as an alternative to imaging and spinal manipulation techniques. Structural vibration testing is a non-destructive measurement technique that measures the response of a system to an applied vibration as a function of frequency, and allows determination of modal parameters such as resonance frequencies (ratio between stiffness and mass), vibration modes (pattern of motion) and damping. The objective of this study was to determine if structural vibration testing can reveal the resonance frequencies that correspond to the mode shapes flexion-extension, lateroflexion and axial rotation of lumbar motion segments, and to establish whether resonance frequencies can discriminate specific structural alterations of the motion segment. Therefore, a shaker was used to vibrate the upper vertebra of 16 goat lumbar motion segments, while the response was obtained from accelerometers on the transverse and spinous processes and the anterior side of the upper vertebra. Measurements were performed in three conditions: intact, after dissection of the ligaments and after puncturing the annulus fibrosus. The results showed clear resonance peaks for flexion-extension, lateral bending and axial rotation for all segments. Dissection of the ligaments did not affect the resonance frequencies, but puncturing the annulus reduced the resonance frequency of axial rotation. These results indicate that vibration testing can be utilised to assess the modal parameters of lumbar motion segments, and might eventually be used to study the mechanical properties of spinal motion segments in vivo.

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