{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T18:27:58Z","timestamp":1763836078732,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,3,17]],"date-time":"2016-03-17T00:00:00Z","timestamp":1458172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Computational studies on the evaluation of bone status in cases of pathologies have gained significant interest in recent years. This work presents a parametric and systematic numerical study on ultrasound propagation in cortical bone models to investigate the effect of changes in cortical porosity and the occurrence of large basic multicellular units, simply called non-refilled resorption lacunae (RL), on the velocity of the first arriving signal (FAS). Two-dimensional geometries of cortical bone are established for various microstructural models mimicking normal and pathological tissue states. Emphasis is given on the detection of RL formation which may provoke the thinning of the cortical cortex and the increase of porosity at a later stage of the disease. The central excitation frequencies 0.5 and 1 MHz are examined. The proposed configuration consists of one point source and multiple successive receivers in order to calculate the FAS velocity in small propagation paths (local velocity) and derive a variation profile along the cortical surface. It was shown that: (a) the local FAS velocity can capture porosity changes including the occurrence of RL with different number, size and depth of formation; and (b) the excitation frequency 0.5 MHz is more sensitive for the assessment of cortical microstructure.<\/jats:p>","DOI":"10.3390\/ma9030205","type":"journal-article","created":{"date-parts":[[2016,3,17]],"date-time":"2016-03-17T11:35:47Z","timestamp":1458214547000},"page":"205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Computational Study of the Effect of Cortical Porosity on Ultrasound Wave Propagation in Healthy and Osteoporotic Long Bones"],"prefix":"10.3390","volume":"9","author":[{"given":"Vassiliki","family":"T. Potsika","sequence":"first","affiliation":[{"name":"Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantinos","family":"N. Grivas","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Theodoros","family":"Gortsas","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gianluca","family":"Iori","sequence":"additional","affiliation":[{"name":"Berlin-Brandenburg School for Regenerative Therapies, Charit\u00e9-Universit\u00e4tsmedizin Berlin, Augustenburger Platz 1, 13353 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vasilios","family":"C. Protopappas","sequence":"additional","affiliation":[{"name":"Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0573-1622","authenticated-orcid":false,"given":"Kay","family":"Raum","sequence":"additional","affiliation":[{"name":"Berlin-Brandenburg School for Regenerative Therapies, Charit\u00e9-Universit\u00e4tsmedizin Berlin, Augustenburger Platz 1, 13353 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Demosthenes","family":"Polyzos","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dimitrios","family":"I. Fotiadis","sequence":"additional","affiliation":[{"name":"Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece"},{"name":"Foundation for Research and Technology\u2013Hellas, Institute of Molecular Biology and Biotechnology, Department of Biomedical Research, GR 45110 Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,3,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Laugier, P., and Ha\u00efat, G. (2010). Bone Quantitative Ultrasound, Springer.","DOI":"10.1007\/978-94-007-0017-8"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/TUFFC.2014.6722615","article-title":"Influence of Porosity, Pore Size, and Cortical Thickness on the Propagation of Ultrasonic Waves Guided Through the Femoral Neck Cortex: A Simulation Study","volume":"61","author":"Rohde","year":"2014","journal-title":"IEEE Trans. Ultras. Ferroel. Freq. Control"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1016\/j.ultrasmedbio.2010.01.008","article-title":"Potential of first arriving signal to assess cortical bone geometry at the hip with QUS: A model based study","volume":"36","author":"Grondin","year":"2010","journal-title":"Ultrasound Med. Biol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1121\/1.2756758","article-title":"Ultrasonically determined thickness of long cortical bones: two-dimensional simulations of in vitro experiments","volume":"122","author":"Moilanen","year":"2007","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.bone.2013.01.015","article-title":"Longitudinal elastic properties and porosity of cortical bone tissue vary with age in human proximal femur","volume":"53","author":"Malo","year":"2013","journal-title":"Bone"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1016\/j.ultras.2013.09.015","article-title":"Quantification of guided mode propagation in fractured long bones","volume":"54","author":"Xu","year":"2014","journal-title":"Ultrasonics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1060","DOI":"10.1121\/1.3605566","article-title":"A numerical study on the propagation of Rayleigh and guided waves in cortical bone according to Mindlin\u2019s Form II gradient elastic theory","volume":"130","author":"Papacharalampopoulos","year":"2011","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.bone.2011.02.021","article-title":"Experimental and simulation results on the effect of cortical bone mineralization in ultrasound axial transmission measurements: A model for fracture healing ultrasound monitoring","volume":"48","author":"Machado","year":"2011","journal-title":"Bone"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2264","DOI":"10.1016\/j.jbiomech.2012.06.003","article-title":"Spatial distribution of tissue level properties in human a femoral cortical bone","volume":"45","author":"Rohrbach","year":"2012","journal-title":"J. Biomech."},{"key":"ref_10","unstructured":"Potsika, V.T., Vavva, M.G., and Protopappas, V.C. (2014). Computational Medicine in Data Mining and Modeling, Springer."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2614","DOI":"10.1121\/1.4869691","article-title":"Measuring the wavenumber of guided modes in waveguides with linearly varying thickness","volume":"135","author":"Moreau","year":"2014","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1016\/j.ultrasmedbio.2006.02.001","article-title":"Guided ultrasound wave propagation in intact and healing long bones","volume":"32","author":"Protopappas","year":"2006","journal-title":"Ultras. Med. Biol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.bone.2014.04.014","article-title":"Ultrasound backscatter measurements of intact human proximal femurs\u2014Relationships of ultrasound parameters with tissue structure and mineral density","volume":"64","author":"Malo","year":"2014","journal-title":"Bone"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bourgnon, \u0391., Sitzer, \u0391., Chabraborty, A., Rohde, K., Varga, P., Wendlandt, R., and Raum, K. (2014, January 3\u20136). Impact of microscale properties measured by 50-MHz acoustic microscopy on mesoscale elastic and ultimate mechanical cortical bone properties. Proceedings of IEEE International Ultrasonics Symposium, Chicago, IL, USA.","DOI":"10.1109\/ULTSYM.2014.0156"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1088\/0967-3334\/23\/4\/313","article-title":"Guided ultrasonic waves in long bones: modelling, experiment and application","volume":"23","author":"Nicholson","year":"2002","journal-title":"Physiol. Meas."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1121\/1.1480836","article-title":"Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: a 2d simulation study","volume":"112","author":"Bossy","year":"2002","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2439","DOI":"10.1121\/1.2769619","article-title":"Ultrasonically determined thickness of long cortical bones: Three-dimensional simulations of in vitro experiments","volume":"122","author":"Moilanen","year":"2007","journal-title":"J. Acoust. Soc. Amer."},{"key":"ref_18","first-page":"1","article-title":"Modeling of femoral neck cortical bone for the numerical simulation of ultrasound propagation","volume":"40","author":"Grimal","year":"2013","journal-title":"Ultrasound Med. Biol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1016\/j.bone.2011.08.002","article-title":"Change in porosity is the major determinant of the variation of cortical bone elasticity at the millimeter scale in aged women","volume":"49","author":"Granke","year":"2011","journal-title":"Bone"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF02407161","article-title":"Age changes in bone mineralization, cortical thickness, and haversian canal area","volume":"31","author":"Thompson","year":"1980","journal-title":"Calcif. Tissue Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4324","DOI":"10.1121\/1.4712021","article-title":"Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method","volume":"131","author":"Treeby","year":"2012","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Laugier, P., and Haiat, G. (2010). Bone Quantitative Ultrasound, Springer.","DOI":"10.1007\/978-94-007-0017-8"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2469","DOI":"10.1121\/1.2766779","article-title":"Attenuation in trabecular bone: A comparison between numerical simulation and experimental results in human femur","volume":"122","author":"Bossy","year":"2007","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/j.ultrasmedbio.2005.02.001","article-title":"Comparison of three ultrasonic axial transmission methods for bone assessment","volume":"31","author":"Muller","year":"2005","journal-title":"Ultrasound Med. Biol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.ultrasmedbio.2007.09.002","article-title":"Ultrasound transmission loss across transverse and oblique bone fractures: An in vitro study","volume":"34","author":"Dodd","year":"2008","journal-title":"Ultrasound Med. Biol."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Potsika, V., Spiridon, I., and Protopappas, V. (2014, January 3\u20136). Computational study of the influence of callus porosity on ultrasound propagation in healing bones. Proceedings of 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, USA.","DOI":"10.1109\/EMBC.2014.6943683"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1016\/j.ultras.2013.09.002","article-title":"Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones","volume":"54","author":"Potsika","year":"2014","journal-title":"Ultrasonics"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.ultrasmedbio.2006.07.038","article-title":"Assessment of the cortical bone thickness using ultrasonic guided waves: modelling and in vitro study","volume":"33","author":"Moilanen","year":"2007","journal-title":"Ultrasound Med. Biol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1007\/s11914-014-0205-4","article-title":"Ultrasound to Assess Bone Quality","volume":"12","author":"Raum","year":"2014","journal-title":"Curr. Osteoporos. Rep."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1088\/0031-9155\/51\/3\/017","article-title":"Site-matched assessment of structural and tissue properties of cortical bone using scanning acoustic microscopy and synchrotron radiation \u03bcCT","volume":"51","author":"Raum","year":"2006","journal-title":"Phys. Med. Biol."},{"key":"ref_31","unstructured":"Potsika, V.T., Gortsas, T., Grivas, \u039a.\u039d., Protopappas, V.C., Vavva, M.G., Raum, K.D., Polyzos, D., and Fotiadis, D.I. (,  2014). Computational modeling of guided ultrasound wave propagation in healthy and osteoporotic bones. \u0395L\u0395\u039c\u0392\u0399\u039f 6th National Conference, Patras, Greece."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1007\/s11914-014-0218-z","article-title":"Changes in the Degree of Mineralization with Osteoporosis and its Treatment","volume":"12","author":"Roschger","year":"2014","journal-title":"Curr. Osteoporos. Rep."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1007\/s00223-002-2113-3","article-title":"Does quantitative ultrasound of bone reflect more bone mineral density than bone microarchitecture","volume":"74","author":"Cortet","year":"2004","journal-title":"Calcif. Tissue Int."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1933","DOI":"10.1016\/j.ultrasmedbio.2007.05.022","article-title":"Frequency Dependence of Ultrasonic Attenuation in Bovine Cortical Bone: An In Vitro Study","volume":"33","author":"Sasso","year":"2007","journal-title":"Ultrasound Med. Biol."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/9\/3\/205\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:20:54Z","timestamp":1760210454000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/9\/3\/205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,17]]},"references-count":34,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,3]]}},"alternative-id":["ma9030205"],"URL":"https:\/\/doi.org\/10.3390\/ma9030205","relation":{},"ISSN":["1996-1944"],"issn-type":[{"type":"electronic","value":"1996-1944"}],"subject":[],"published":{"date-parts":[[2016,3,17]]}}}