An Analytic Probability Density for Particle Size in Human Mastication
Identifieur interne : 003702 ( Istex/Corpus ); précédent : 003701; suivant : 003703An Analytic Probability Density for Particle Size in Human Mastication
Auteurs : F. A. Baragar Retired ; A. Van Der Bilt ; H. W. Van Der GlasSource :
- Journal of Theoretical Biology [ 0022-5193 ] ; 1996.
English descriptors
- KwdEn :
- Academic press, Analytical expression, Analytical method, Average particle size, Bilt, Biol, Breakage, Breakage function, Breakage functions, Breakage process, Breakage sites, Breakage variables, Central tendency, Comminuted food, Comminution, Comminution data, Comminution process, Complete agreement, Composite result, Cumulative distributions, Cumulative probability distribution, Data points, Density function, Dentate subject, Dentate subjects, Discrete evolution, Double logarithmic scale, Empirical function, Equivalent rate process, Food comminution, Food particle, Food particles, Glas, Good description, Human mastication, Initial phase, Initial size, Largest particle size, Lucas luke, Mastication, Masticatory process, Mathematical description, Median, Median particle size, Numerical model, Particle, Particle size, Particle size distribution, Particle sizes, Powder technol, Power function, Probability densities, Probability density, Recurrence relation, Relative particle size, Rosin rammler, Selection function, Selection variables, Silicone rubber, Simple functions, Size distribution, Size intervals, Small particles, Smaller sizes, Solid food, Test food, Tooth shape, Variable number, Various numbers, Various sieves.
- Teeft :
- Academic press, Analytical expression, Analytical method, Average particle size, Bilt, Biol, Breakage, Breakage function, Breakage functions, Breakage process, Breakage sites, Breakage variables, Central tendency, Comminuted food, Comminution, Comminution data, Comminution process, Complete agreement, Composite result, Cumulative distributions, Cumulative probability distribution, Data points, Density function, Dentate subject, Dentate subjects, Discrete evolution, Double logarithmic scale, Empirical function, Equivalent rate process, Food comminution, Food particle, Food particles, Glas, Good description, Human mastication, Initial phase, Initial size, Largest particle size, Lucas luke, Mastication, Masticatory process, Mathematical description, Median, Median particle size, Numerical model, Particle, Particle size, Particle size distribution, Particle sizes, Powder technol, Power function, Probability densities, Probability density, Recurrence relation, Relative particle size, Rosin rammler, Selection function, Selection variables, Silicone rubber, Simple functions, Size distribution, Size intervals, Small particles, Smaller sizes, Solid food, Test food, Tooth shape, Variable number, Various numbers, Various sieves.
Abstract
Abstract: In previous studies the distribution of particles sizes of chewed food has been described by an empirical function. However, at the beginning of the chewing process, when many unbroken food particles are still present in the mixture, this function failed to give a good description. In the present study, formulae were derived to characterize the distribution of chewed food particles by size as a function of the number of chewing cycles. The reduction of food particle sizes was considered too be the composite result of a selection and a breakage process. Both processes were described by simple functions. The probability densityPn+1(x) of finding a particle of sizexaftern+ 1 chewing cycles was computed fromPn(x) by selecting a proportion of particles of sizeyfromPnto be converted to particles of sizex
Url:
DOI: 10.1006/jtbi.1996.0123
Url:
DOI: 10.1006/jtbi.1996.0123
Links to Exploration step
ISTEX:6F20553B06353CBA153BEA3FBBEB4DF42EC3A6E2Le document en format XML
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sieves</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: In previous studies the distribution of particles sizes of chewed food has been described by an empirical function. However, at the beginning of the chewing process, when many unbroken food particles are still present in the mixture, this function failed to give a good description. In the present study, formulae were derived to characterize the distribution of chewed food particles by size as a function of the number of chewing cycles. The reduction of food particle sizes was considered too be the composite result of a selection and a breakage process. Both processes were described by simple functions. The probability densityPn+1(x) of finding a particle of sizexaftern+ 1 chewing cycles was computed fromPn(x) by selecting a proportion of particles of sizeyfromPnto be converted to particles of sizex</div> </front></TEI><istex><corpusName>elsevier</corpusName><keywords><teeft><json:string>comminution</json:string><json:string>probability density</json:string><json:string>breakage</json:string><json:string>bilt</json:string><json:string>particle size</json:string><json:string>mastication</json:string><json:string>biol</json:string><json:string>median particle size</json:string><json:string>glas</json:string><json:string>median</json:string><json:string>data points</json:string><json:string>food particle</json:string><json:string>food particles</json:string><json:string>central tendency</json:string><json:string>lucas luke</json:string><json:string>average particle size</json:string><json:string>breakage function</json:string><json:string>human mastication</json:string><json:string>particle size distribution</json:string><json:string>numerical model</json:string><json:string>various numbers</json:string><json:string>selection variables</json:string><json:string>selection function</json:string><json:string>breakage functions</json:string><json:string>cumulative probability distribution</json:string><json:string>comminution process</json:string><json:string>density function</json:string><json:string>smaller sizes</json:string><json:string>mathematical description</json:string><json:string>breakage process</json:string><json:string>test food</json:string><json:string>size distribution</json:string><json:string>particle</json:string><json:string>dentate subject</json:string><json:string>analytical expression</json:string><json:string>rosin rammler</json:string><json:string>breakage sites</json:string><json:string>various sieves</json:string><json:string>comminuted food</json:string><json:string>solid food</json:string><json:string>largest particle size</json:string><json:string>recurrence relation</json:string><json:string>power function</json:string><json:string>initial size</json:string><json:string>variable number</json:string><json:string>cumulative distributions</json:string><json:string>probability densities</json:string><json:string>relative particle size</json:string><json:string>tooth shape</json:string><json:string>academic press</json:string><json:string>food comminution</json:string><json:string>small particles</json:string><json:string>comminution data</json:string><json:string>double logarithmic scale</json:string><json:string>simple functions</json:string><json:string>composite result</json:string><json:string>good description</json:string><json:string>complete agreement</json:string><json:string>size intervals</json:string><json:string>analytical method</json:string><json:string>dentate subjects</json:string><json:string>silicone rubber</json:string><json:string>discrete evolution</json:string><json:string>equivalent rate process</json:string><json:string>masticatory process</json:string><json:string>breakage variables</json:string><json:string>particle sizes</json:string><json:string>initial phase</json:string><json:string>empirical function</json:string><json:string>powder technol</json:string></teeft></keywords><author><json:item><name>F.A. Baragar (retired)</name><affiliations><json:string>Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1</json:string></affiliations></json:item><json:item><name>A. van der Bilt</name><affiliations><json:string>Department of Oral-Maxillofacial Surgery, Prosthodonitcs and Special Dental Care, Utrecht University, PO Box 80037, 3508 TA, Utrecht, The Netherlands</json:string></affiliations></json:item><json:item><name>H.W. van der Glas</name><affiliations><json:string>Department of Oral-Maxillofacial Surgery, Prosthodonitcs and Special Dental Care, Utrecht University, PO Box 80037, 3508 TA, Utrecht, The Netherlands</json:string></affiliations></json:item></author><arkIstex>ark:/67375/6H6-Z7WHF3VL-L</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><abstract>Abstract: In previous studies the distribution of particles sizes of chewed food has been described by an empirical function. However, at the beginning of the chewing process, when many unbroken food particles are still present in the mixture, this function failed to give a good description. In the present study, formulae were derived to characterize the distribution of chewed food particles by size as a function of the number of chewing cycles. The reduction of food particle sizes was considered too be the composite result of a selection and a breakage process. Both processes were described by simple functions. The probability densityPn+1(x) of finding a particle of sizexaftern+ 1 chewing cycles was computed fromPn(x) by selecting a proportion of particles of sizeyfromPnto be converted to particles of sizex>yby a breakage function. Measures of central tendency—average, median, and most probable size—were obtained as a function of the number of chewing cycles. The measures of central tendency characterize the degree of food comminution during the chewing process and so can be used to quantify chewing performance. The comminution of food is described in terms of the selection and breakage functions in a convenient, efficient, analytic way, valid for all phases of the chewing process.</abstract><qualityIndicators><score>9.238</score><pdfWordCount>4814</pdfWordCount><pdfCharCount>25334</pdfCharCount><pdfVersion>1.1</pdfVersion><pdfPageCount>10</pdfPageCount><pdfPageSize>612 x 792 pts (letter)</pdfPageSize><refBibsNative>false</refBibsNative><abstractWordCount>202</abstractWordCount><abstractCharCount>1303</abstractCharCount><keywordCount>0</keywordCount></qualityIndicators><title>An Analytic Probability Density for Particle Size in Human Mastication</title><pmid><json:string>8935594</json:string></pmid><pii><json:string>S0022-5193(96)90123-X</json:string></pii><genre><json:string>research-article</json:string></genre><host><title>Journal of Theoretical Biology</title><language><json:string>unknown</json:string></language><publicationDate>1996</publicationDate><issn><json:string>0022-5193</json:string></issn><pii><json:string>S0022-5193(00)X0130-0</json:string></pii><volume>181</volume><issue>2</issue><pages><first>169</first><last>178</last></pages><genre><json:string>journal</json:string></genre></host><namedEntities><unitex><date><json:string>1996</json:string></date><geogName></geogName><orgName><json:string>Department of Oral-Maxillofacial Surgery, Prosthodontics and Special Dental Care</json:string><json:string>Utrecht University</json:string></orgName><orgName_funder></orgName_funder><orgName_provider></orgName_provider><persName></persName><placeName><json:string>Netherlands</json:string></placeName><ref_url></ref_url><ref_bibl><json:string>Slagter et al. (1993)</json:string><json:string>van der Bilt et al., 1993b</json:string><json:string>van der Glas et al., 1987</json:string><json:string>Austin et al.</json:string><json:string>Lucas & Luke, 1983</json:string><json:string>van der Glas et al., 1992</json:string><json:string>Slagter et al., 1993</json:string><json:string>van der Bilt et al., 1987</json:string><json:string>van der Bilt et al., 1987, 1993a, b, 1994</json:string><json:string>van der Glas et al.</json:string><json:string>van der Bilt et al., 1992</json:string><json:string>van der Bilt et al., 1987, 1992</json:string><json:string>van der Bilt et al. (1993a, 1994)</json:string><json:string>Voon et al. 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However, at the beginning of the chewing process, when many unbroken food particles are still present in the mixture, this function failed to give a good description. In the present study, formulae were derived to characterize the distribution of chewed food particles by size as a function of the number of chewing cycles. The reduction of food particle sizes was considered too be the composite result of a selection and a breakage process. Both processes were described by simple functions. The probability densityPn+1(x) of finding a particle of sizexaftern+ 1 chewing cycles was computed fromPn(x) by selecting a proportion of particles of sizeyfromPnto be converted to particles of sizex</p> </abstract></profileDesc><revisionDesc><change when="1996">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-09-30">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/6F20553B06353CBA153BEA3FBBEB4DF42EC3A6E2/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier converted-article found"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla" xml:lang="en"><item-info><jid>YJTBI</jid><aid>90123</aid><ce:pii>S0022-5193(96)90123-X</ce:pii><ce:doi>10.1006/jtbi.1996.0123</ce:doi><ce:copyright type="full-transfer" year="1996">Academic Press</ce:copyright></item-info><head><ce:dochead><ce:textfn>Regular article</ce:textfn></ce:dochead><ce:title>An Analytic Probability Density for Particle Size in Human Mastication</ce:title><ce:author-group><ce:author><ce:surname>Baragar (retired)</ce:surname><ce:given-name>F.A.</ce:given-name><ce:cross-ref refid="A1"><ce:sup>a</ce:sup></ce:cross-ref><ce:cross-ref refid="FN1"><ce:sup>f1</ce:sup></ce:cross-ref></ce:author><ce:author><ce:surname>van der Bilt</ce:surname><ce:given-name>A.</ce:given-name><ce:cross-ref refid="A2"><ce:sup>b</ce:sup></ce:cross-ref></ce:author><ce:author><ce:surname>van der Glas</ce:surname><ce:given-name>H.W.</ce:given-name><ce:cross-ref refid="A2"><ce:sup>b</ce:sup></ce:cross-ref></ce:author><ce:affiliation id="A1"><ce:label>a</ce:label><ce:textfn>Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1</ce:textfn></ce:affiliation><ce:affiliation id="A2"><ce:label>b</ce:label><ce:textfn>Department of Oral-Maxillofacial Surgery, Prosthodonitcs and Special Dental Care, Utrecht University, PO Box 80037, 3508 TA, Utrecht, The Netherlands</ce:textfn></ce:affiliation><ce:footnote id="FN1"><ce:label>f1</ce:label><ce:note-para>Corresponding author. E-mail: abaragar@vega.math.ualberta.ca</ce:note-para></ce:footnote></ce:author-group><ce:date-received day="8" month="12" year="1993"></ce:date-received><ce:date-accepted day="27" month="3" year="1996"></ce:date-accepted><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>In previous studies the distribution of particles sizes of chewed food has been described by an empirical function. However, at the beginning of the chewing process, when many unbroken food particles are still present in the mixture, this function failed to give a good description. In the present study, formulae were derived to characterize the distribution of chewed food particles by size as a function of the number of chewing cycles. The reduction of food particle sizes was considered too be the composite result of a selection and a breakage process. Both processes were described by simple functions. The probability density<ce:italic>P</ce:italic><ce:inf>n</ce:inf><ce:inf>+1</ce:inf>(<ce:italic>x</ce:italic>) of finding a particle of size<ce:italic>x</ce:italic>after<ce:italic>n</ce:italic>+ 1 chewing cycles was computed from<ce:italic>P</ce:italic><ce:inf><ce:italic>n</ce:italic></ce:inf>(<ce:italic>x</ce:italic>) by selecting a proportion of particles of size<ce:italic>y</ce:italic>from<ce:italic>P</ce:italic><ce:italic><ce:inf>n</ce:inf></ce:italic>to be converted to particles of size<ce:italic>x</ce:italic><<ce:italic>y</ce:italic>by a breakage function. Measures of central tendency—average, median, and most probable size—were obtained as a function of the number of chewing cycles. The measures of central tendency characterize the degree of food comminution during the chewing process and so can be used to quantify chewing performance. The comminution of food is described in terms of the selection and breakage functions in a convenient, efficient, analytic way, valid for all phases of the chewing process.</ce:simple-para></ce:abstract-sec></ce:abstract></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>An Analytic Probability Density for Particle Size in Human Mastication</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>An Analytic Probability Density for Particle Size in Human Mastication</title></titleInfo><name type="personal"><namePart type="given">F.A.</namePart><namePart type="family">Baragar (retired)</namePart><affiliation>Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1</affiliation><description>Corresponding author. E-mail: abaragar@vega.math.ualberta.ca</description><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">van der Bilt</namePart><affiliation>Department of Oral-Maxillofacial Surgery, Prosthodonitcs and Special Dental Care, Utrecht University, PO Box 80037, 3508 TA, Utrecht, The Netherlands</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">H.W.</namePart><namePart type="family">van der Glas</namePart><affiliation>Department of Oral-Maxillofacial Surgery, Prosthodonitcs and Special Dental Care, Utrecht University, PO Box 80037, 3508 TA, Utrecht, The Netherlands</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1996</dateIssued><copyrightDate encoding="w3cdtf">1996</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><abstract lang="en">Abstract: In previous studies the distribution of particles sizes of chewed food has been described by an empirical function. However, at the beginning of the chewing process, when many unbroken food particles are still present in the mixture, this function failed to give a good description. In the present study, formulae were derived to characterize the distribution of chewed food particles by size as a function of the number of chewing cycles. The reduction of food particle sizes was considered too be the composite result of a selection and a breakage process. Both processes were described by simple functions. The probability densityPn+1(x) of finding a particle of sizexaftern+ 1 chewing cycles was computed fromPn(x) by selecting a proportion of particles of sizeyfromPnto be converted to particles of sizex</abstract> <note type="content">Section title: Regular article</note><relatedItem type="host"><titleInfo><title>Journal of Theoretical Biology</title></titleInfo><titleInfo type="abbreviated"><title>YJTBI</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">19960721</dateIssued></originInfo><identifier type="ISSN">0022-5193</identifier><identifier type="PII">S0022-5193(00)X0130-0</identifier><part><date>19960721</date><detail type="volume"><number>181</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="issue-pages"><start>97</start><end>196</end></extent><extent unit="pages"><start>169</start><end>178</end></extent></part></relatedItem><identifier type="istex">6F20553B06353CBA153BEA3FBBEB4DF42EC3A6E2</identifier><identifier type="ark">ark:/67375/6H6-Z7WHF3VL-L</identifier><identifier type="DOI">10.1006/jtbi.1996.0123</identifier><identifier type="PII">S0022-5193(96)90123-X</identifier><accessCondition type="use and reproduction" contentType="copyright">©1996 Academic Press</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-HKKZVM7B-M">elsevier</recordContentSource><recordOrigin>Academic Press, ©1996</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/6F20553B06353CBA153BEA3FBBEB4DF42EC3A6E2/metadata/json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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