Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular Bone
A trabecular bone consists of trabeculae whose mechanical properties differ significantly from the surrounding marrow, therefore an ultrasonic wave propagating within the bone structure is strongly scattered. The aim of this paper was to evaluate the contribution of the first, second and higher orde...
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Institute of Fundamental Technological Research Polish Academy of Sciences
2013-11-01
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| Series: | Archives of Acoustics |
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| Online Access: | https://acoustics.ippt.pan.pl/index.php/aa/article/view/224 |
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| author | Janusz WÓJCIK Jerzy LITNIEWSKI Andrzej NOWICKI |
| author_facet | Janusz WÓJCIK Jerzy LITNIEWSKI Andrzej NOWICKI |
| author_sort | Janusz WÓJCIK |
| collection | DOAJ |
| description | A trabecular bone consists of trabeculae whose mechanical properties differ significantly from the surrounding marrow, therefore an ultrasonic wave propagating within the bone structure is strongly scattered. The aim of this paper was to evaluate the contribution of the first, second and higher order scattering (multiple scattering) into the total scattering of ultrasound in a trabecular bone. The scattering due to the interconnections between thick trabeculae, usually neglected in trabecular bone models, has been also studied. The basic element in our model of the trabecular bone was an elastic cylinder with a various finite-length and diameter as well as orientation. The applied model was taking into account variation of both, elements size and their spatial configuration. The field scattered on the bone model was evaluated by solving numerically the integral form of the generalized Sturm-Liouville equation describing a scalar wave in inhomogeneous and lossy media. For the scattered fields calculated numerically the effective cross-sections were determined. The influence of absorption on the scattering coefficients was demonstrated. The results allowed to conclude that within the frequency range from 0.5 to 1.5 MHz contribution of the second order scattering to the effective backscattering cross-section is at least 500 times lower than that due to the first order scattering. It was noticed that for a frequency higher than 1.5 MHz fast growth of the backscattering (reflection) coefficients, calculated for the second order scattering, occurs. |
| format | Article |
| id | doaj-art-92c4f04e08ea4990ab0ef3e30a5ab164 |
| institution | DOAJ |
| issn | 0137-5075 2300-262X |
| language | English |
| publishDate | 2013-11-01 |
| publisher | Institute of Fundamental Technological Research Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Acoustics |
| spelling | doaj-art-92c4f04e08ea4990ab0ef3e30a5ab1642025-08-20T03:13:08ZengInstitute of Fundamental Technological Research Polish Academy of SciencesArchives of Acoustics0137-50752300-262X2013-11-01354Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular BoneJanusz WÓJCIK0Jerzy LITNIEWSKI1Andrzej NOWICKI2Institute of Fundamental Technological Research Polish Academy of SciencesInstitute of Fundamental Technological Research Polish Academy of SciencesInstitute of Fundamental Technological Research Polish Academy of SciencesA trabecular bone consists of trabeculae whose mechanical properties differ significantly from the surrounding marrow, therefore an ultrasonic wave propagating within the bone structure is strongly scattered. The aim of this paper was to evaluate the contribution of the first, second and higher order scattering (multiple scattering) into the total scattering of ultrasound in a trabecular bone. The scattering due to the interconnections between thick trabeculae, usually neglected in trabecular bone models, has been also studied. The basic element in our model of the trabecular bone was an elastic cylinder with a various finite-length and diameter as well as orientation. The applied model was taking into account variation of both, elements size and their spatial configuration. The field scattered on the bone model was evaluated by solving numerically the integral form of the generalized Sturm-Liouville equation describing a scalar wave in inhomogeneous and lossy media. For the scattered fields calculated numerically the effective cross-sections were determined. The influence of absorption on the scattering coefficients was demonstrated. The results allowed to conclude that within the frequency range from 0.5 to 1.5 MHz contribution of the second order scattering to the effective backscattering cross-section is at least 500 times lower than that due to the first order scattering. It was noticed that for a frequency higher than 1.5 MHz fast growth of the backscattering (reflection) coefficients, calculated for the second order scattering, occurs.https://acoustics.ippt.pan.pl/index.php/aa/article/view/224multi-scatteringrandom complex structurestrabecular bone model |
| spellingShingle | Janusz WÓJCIK Jerzy LITNIEWSKI Andrzej NOWICKI Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular Bone Archives of Acoustics multi-scattering random complex structures trabecular bone model |
| title | Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular Bone |
| title_full | Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular Bone |
| title_fullStr | Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular Bone |
| title_full_unstemmed | Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular Bone |
| title_short | Example of Structure Modeling and Analysis of Ultrasound Scattering for Trabecular Bone |
| title_sort | example of structure modeling and analysis of ultrasound scattering for trabecular bone |
| topic | multi-scattering random complex structures trabecular bone model |
| url | https://acoustics.ippt.pan.pl/index.php/aa/article/view/224 |
| work_keys_str_mv | AT januszwojcik exampleofstructuremodelingandanalysisofultrasoundscatteringfortrabecularbone AT jerzylitniewski exampleofstructuremodelingandanalysisofultrasoundscatteringfortrabecularbone AT andrzejnowicki exampleofstructuremodelingandanalysisofultrasoundscatteringfortrabecularbone |