Corrigendum: Measurement of guided mode wavenumbers in soft tissue–bone mimicking phantoms using ultrasonic axial transmission

Human soft tissue is an important factor that influences the assessment of human long bones using quantitative ultrasound techniques. To investigate such influence, a series of soft tissue-bone phantoms (a bone-mimicking plate coated with a layer of water, glycerol or silicon rubber) were ultrasonically investigated using a probe with multi-emitter and multi-receiver arrays in an axial transmission configuration. A singular value decomposition signal processing technique was applied to extract the frequency-dependent wavenumbers of several guided modes. The results indicate that the presence of a soft tissue-mimicking layer introduces additional guided modes predicted by a fluid waveguide model. The modes propagating in the bone-mimicking plate covered by the soft-tissue phantom are only slightly modified compared to their counterparts in the free bone-mimicking plate, and they are still predicted by an elastic transverse isotropic two-dimensional waveguide. Altogether these observations suggest that the soft tissue-bone phantoms can be modeled as two independent waveguides. Even in the presence of the overlying soft tissue-mimicking layer, the modes propagating in the bone-mimicking plate can still be extracted and identified. These results suggest that our approach can be applied for the purpose of the characterization of the material and structural properties of cortical bone.