{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T10:06:37Z","timestamp":1788516397345,"version":"build-2803163510"},"reference-count":19,"publisher":"Wiley","issue":"10","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000054","name":"National Cancer Institute","doi-asserted-by":"publisher","award":["R01CA193378"],"award-info":[{"award-number":["R01CA193378"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["J Applied Clin Med Phys"],"published-print":{"date-parts":[[2021,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Objective<\/jats:title><jats:p>The objective of this article is to introduce a simplified and swift method to satisfactorily estimate the half\u2010value layers (HVL), quarter\u2010value layer (QVL), and tenth\u2010value layer (TVL) from the x\u2010ray spectra emitted by any diagnostic radiology or kV radiotherapy x\u2010ray tubes.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>A CdTe x\u2010ray and Gamma detector (X\u2010123 CdTe, AmpTek Inc.) is used to measure the x\u2010ray spectra at four different x\u2010ray energies (low, mid, high energy x\u2010rays) with different external filtering. The software \u201c<jats:italic>SpekCalc GUI\u201d<\/jats:italic> (Developed in McGill University, Montreal, Canada) is also used to obtain the simulated x\u2010ray spectra. Both measured and simulated spectra are used to compute the HVL thicknesses of Aluminum by a mathematical method presented in this article. Next, the HVL thicknesses for corresponding tube potentials are also measured by calibrated ionization chamber and varying thicknesses of aluminum plates. Finally, the computed and measured HVL, QVL, and TVL thicknesses are compared to evaluate the efficacy of the presented method.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>The results show acceptable concordance between computed and measured quantities. The disagreement rates between measured HVL and the values derived mathematically from the x\u2010ray spectra are 10 to 90\u00a0micrometers of Aluminum at tube potentials of 31\u00a0kV to 120\u00a0kV. As it is shown, a negligible discrepancy is observed between the analytical estimation and the experimental assessments.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>The HVL is an essential component in the evaluation of the quality of an x\u2010ray beam. However, its measurement could occasionally be challenging, time\u2010consuming, or uncertain due to some technical difficulties. Although the scope of this study is not to undermine the value of conventional and widely accepted practice to determine the HVL thickness, the introduced method provides the fast, more convenient, and comparably reliable technique to estimate the HVL, QVL, and TVL by employing the given x\u2010ray spectrum.<\/jats:p><\/jats:sec>","DOI":"10.1002\/acm2.13385","type":"journal-article","created":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T14:47:10Z","timestamp":1630507630000},"page":"320-328","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Mathematical estimation of half\u2010value layer thicknesses"],"prefix":"10.1002","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1956-0879","authenticated-orcid":false,"given":"Farid H.","family":"Omoumi","sequence":"first","affiliation":[{"name":"The School of Electrical and Computer Engineering The University of Oklahoma Norman Oklahoma USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xizeng","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Radiology University of Alabama at Birmingham Birmingham Alabama USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad U.","family":"Ghani","sequence":"additional","affiliation":[{"name":"The School of Electrical and Computer Engineering The University of Oklahoma Norman Oklahoma USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Molly D.","family":"Wong","sequence":"additional","affiliation":[{"name":"The School of Electrical and Computer Engineering The University of Oklahoma Norman Oklahoma USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuhua","family":"Li","sequence":"additional","affiliation":[{"name":"The School of Electrical and Computer Engineering The University of Oklahoma Norman Oklahoma 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