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Bone strength of the human distal radius under fall loading conditions : an experimental and numerical study

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(1)Bone strength of the human distal radius under fall loading conditions : an experimental and numerical study Edison Zapata. To cite this version: Edison Zapata. Bone strength of the human distal radius under fall loading conditions : an experimental and numerical study. Biomechanics [physics.med-ph]. Université Claude Bernard - Lyon I, 2015. English. �NNT : 2015LYO10275�. �tel-01424133�. HAL Id: tel-01424133 https://tel.archives-ouvertes.fr/tel-01424133 Submitted on 2 Jan 2017. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) N° d’ordre : 275 -2015. Année 2015. THESE DE L’UNIVERSITE DE LYON Délivrée par L’UNIVERSITE CLAUDE BERNARD LYON 1 ECOLE DOCTORALE MEGA DIPLOME DE DOCTORAT (Arrêté du 7 août 2006) Spécialité : Biomécanique Soutenue publiquement le 2 décembre 2015 Par :. Edison ZAPATA. Bone strength of the human distal radius under fall loading conditions an experimental and numerical study Directeur de thèse: Co-Encadrante :. David MITTON Hélène FOLLET JURY :. Lalaonirina RAKOTOMANANA Bert VAN RIETBERGEN Pascal LAUGIER Jean-Baptiste PIALAT Hélène FOLLET David MITTON. . Professeur des Universités, Université de Rennes Professeur associé, Université de Technologie d’Eindhoven Directeur de Recherche, CNRS, Paris Professeur des Universités, Université Claude Bernard Lyon 1 Chargée de recherche, INSERM, Lyon Directeur de Recherche, IFSTTAR, Lyon. Rapporteur Rapporteur Examinateur Examinateur Examinateur Examinateur. .

(3) UNIVERSITE CLAUDE BERNARD - LYON 1 Président de l’Université. M. François-Noël GILLY. Vice-président du Conseil d’Administration. M. le Professeur Hamda BEN HADID. Vice-président du Conseil des Etudes et de la Vie Universitaire. M. le Professeur Philippe LALLE. Vice-président du Conseil Scientifique. M. le Professeur Germain GILLET. Directeur Général des Services. M. Alain HELLEU. COMPOSANTES SANTE Faculté de Médecine Lyon Est – Claude Bernard. Directeur : M. le Professeur J. ETIENNE. Faculté de Médecine et de Maïeutique Lyon Sud – Charles Mérieux. Directeur : Mme la Professeure C. BURILLON. Faculté d’Odontologie Institut des Sciences Pharmaceutiques et Biologiques Institut des Sciences et Techniques de la Réadaptation Département de formation et Centre de Recherche en Biologie Humaine. Directeur : M. le Professeur D. BOURGEOIS Directeur : Mme la Professeure C. VINCIGUERRA Directeur : M. le Professeur Y. MATILLON Directeur : Mme. la Professeure A-M. SCHOTT. COMPOSANTES ET DEPARTEMENTS DE SCIENCES ET TECHNOLOGIE Faculté des Sciences et Technologies Département Biologie. Directeur : M. F. DE MARCHI Directeur : M. le Professeur F. FLEURY. Département Chimie Biochimie. Directeur : Mme Caroline FELIX. Département GEP. Directeur : M. Hassan HAMMOURI. Département Informatique Département Mathématiques. Directeur : M. le Professeur S. AKKOUCHE. Département Mécanique. Directeur : M. le Professeur H. BEN HADID. Département Physique. Directeur : M. Jean-Claude PLENET. Directeur : M. le Professeur Georges TOMANOV. UFR Sciences et Techniques des Activités Physiques et Sportives Directeur : M. Y.VANPOULLE Observatoire des Sciences de l’Univers de Lyon. Directeur : M. B. GUIDERDONI. Polytech Lyon. Directeur : M. P. FOURNIER. Ecole Supérieure de Chimie Physique Electronique. Directeur : M. G. PIGNAULT. Institut Universitaire de Technologie de Lyon 1. Directeur : M. le Professeur C. VITON. Ecole Supérieure du Professorat et de l’Education. Directeur : M. le Professeur A. MOUGNIOTTE. Institut de Science Financière et d'Assurances. Directeur : M. N. LEBOISNE. . .

(4) Bone strength of the human distal radius under fall loading conditions: an experimental and numerical study ”ƒ‰‹Ž‹–› ˆ”ƒ –—”‡• ”‡’”‡•‡– ƒ ’—„Ž‹  Š‡ƒŽ–Š ’”‘„Ž‡ ˆ‘” ‡Ž†‡”Ž›Ǥ Š‡ ƒ••‡••‡– ‘ˆ –Š‡ „‘‡ •–”‡‰–Šƒ†‘ˆ–Š‡”‹•‘ˆˆ”ƒ –—”‡„›–Š‡‰‘Ž†•–ƒ†ƒ”†‡–Š‘†ȋ—ƒŽǦ”ƒ›„•‘”’–‹‘‡–”›ǦȌ ‹•Ž‹‹–‡†Ǥ‹ ”‘Ǧˆ‹‹–‡‡Ž‡‡–‘†‡Ž•ȋρ ȌŠƒ˜‡•Š‘™–‘„‡––‡”’”‡†‹ ––Š‡„‘‡•–”‡‰–Šǡ„—– ‹–‹•‘–’‘••‹„Ž‡–‘ ‘ˆ‹”–Šƒ––Š‡›†‘„‡––‡”–Šƒ–Š‡†‡•‹–› ‡ƒ•—”‡†„›–‘‡•–‹ƒ–‡–Š‡ ”‹• ‘ˆ ˆ”ƒ –—”‡Ǥ Š—•ǡ –Š‡ ƒ‹ ‘ˆ –Š‹• –Š‡•‹• ™ƒ• –‘ ‡˜ƒŽ—ƒ–‡ ™Š‡–Š‡” ‹ Ž—†‹‰ ”‡ƒŽ‹•–‹  Ž‘ƒ†‹‰ ‘†‹–‹‘• ‘—Ž† ‹’”‘˜‡ –Š‡ Ž‡˜‡Ž ‘ˆ ’”‡†‹ –‹‘ ‘ˆ –Š‡ Ǥ ‹”•–ǡ ™‡ ”‡’”‘†— ‡† –Š‡ Ž‘ƒ†‹‰ ‘†‹–‹‘• ‘ˆ ƒ ˆ‘”™ƒ”† ˆƒŽŽ ‘ ͵ʹ ”ƒ†‹‹ ‹ ƒ ‡šǦ˜‹˜‘ ‡š’‡”‹‡–Ǥ Š‹• ‡š’‡”‹‡– Ž‡ƒ†‡† –‘ –™‘ ‰”‘—’•ǣ ‘‡ ˆ”ƒ –—”‡† ƒ† ‘‡ ‘ Ǧ ˆ”ƒ –—”‡†Ǥ Š‡ǡ ™‡ ‡˜ƒŽ—ƒ–‡† –Š‡ ’”‡†‹ –‹‘ ƒ’ƒ„‹Ž‹–› ‘ˆ ƒ •‡‰‡– ȋͻ‘ˆ–Š‡†‹•–ƒŽ”ƒ†‹—•Ȍ ”‡ƒ–‡†—•‹‰–Š‡ ‹‰Š‡•‘Ž—–‹‘’‡”‹’Š‡”ƒŽ—ƒ–‹–ƒ–‹˜‡ ‘’—–‡†‘‘‰”ƒ’Š›ǤŠ‹••‡‰‡– ™ƒ•–‡•–‡†—†‡”–Š‡ƒš‹ƒŽŽ‘ƒ†‹‰ȋ•–ƒ†ƒ”†ƒƒŽ›•‹•Ȍǡ ƒ†—†‡”ˆ‹˜‡ƒ††‹–‹‘ƒŽ‘Ǧƒš‹ƒŽ ‘ˆ‹‰—”ƒ–‹‘•Ǥ

(5) –™ƒ•ˆ‘—†–Šƒ––Š‡’”‡†‹ –‹‘ ƒ’ƒ„‹Ž‹–›‘ˆ–Š‡ •‡‰‡–  ™ƒ• ‘– ‹’”‘˜‡† „› –Š‡ ‹’Ž‡‡–ƒ–‹‘ ‘ˆ ‘Ǧƒš‹ƒŽ Ž‘ƒ†‹‰•Ǥ ‹ƒŽŽ›ǡ ƒ Š‡–‡”‘‰‡‡‘—• ‘ˆ–Š‡™Š‘Ž‡†‹•–ƒŽ”ƒ†‹—•™ƒ• ”‡ƒ–‡†—•‹‰†ƒ–ƒˆ”‘ƒ‘‡‡ƒ‘’—–‡† ‘‘‰”ƒ’Š›Ǥ Š‹• ‘†‡Ž ‘•‹†‡”• –Š‡ ˆƒŽŽ Ž‘ƒ†‹‰ ‘ˆ‹‰—”ƒ–‹‘• ‹ ‘”‹‡–ƒ–‹‘ ƒ† •’‡‡† ‘ˆ –Š‡ ‡šǦ˜‹˜‘ ‡š’‡”‹‡–Ǥ Š‡  ‘ˆ –Š‡ ™Š‘Ž‡ †‹•–ƒŽ ”ƒ†‹—• Šƒ• ƒ „‡––‡” ƒ —”ƒ › –‘ ’”‡†‹ – –Š‡ ‡š’‡”‹‡–ƒŽ ˆƒ‹Ž—”‡ Ž‘ƒ† –Šƒ –Š‡ •‡‰‡– Ǥ Š‹• •–—†› ’”‘’‘•‡• ‘”‹‰‹ƒŽ †ƒ–ƒ ˆ‘” ‘†‡Ž ˜ƒŽ‹†ƒ–‹‘†‡†‹ ƒ–‡†–‘ˆ—”–Š‡”‹’”‘˜‡‡–•‘ˆˆ”ƒ –—”‡”‹•’”‡†‹ –‹‘Ǥ ‡›™‘”†•ǣ‘‡–”‡‰–Šǡ ”ƒ –—”‡‹•ǡ‹•–ƒŽƒ†‹—•ǡ ‘”™ƒ”†ˆƒŽŽǡ ‹‹–‡Ž‡‡–‘†‡Ž•Ǥ Résistance du radius humain distal soumis à un chargement représentatif d’une chute: Etude expérimentale et numérique ‡• ˆ”ƒ –—”‡• †‡ ˆ”ƒ‰‹Ž‹–± ”‡’”±•‡–‡– — ’”‘„Ž°‡ †‡ •ƒ–± ’—„Ž‹“—‡ ’‘—” Ž‡• ’‡”•‘‡• Ÿ‰±‡•Ǥ ̵±˜ƒŽ—ƒ–‹‘ †‡ Žƒ ”±•‹•–ƒ ‡ ‘••‡—•‡ ‡– †— ”‹•“—‡ †‡ ˆ”ƒ –—”‡ ’ƒ” Žƒ ±–Š‘†‡ †‡ ”±ˆ±”‡ ‡ ȋƒ„•‘”’–‹‘ „‹Ǧ’Š‘–‘‹“—‡  ”ƒ›‘• ǡ Ȍ ‡•– Ž‹‹–±‡Ǥ ‡• ‹ ”‘Ǧ‘†°Ž‡• ‡ ±Ž±‡–• ˆ‹‹• ȋɊ Ȍ‘–‘–”±†‡‡‹ŽŽ‡—”‡•’”±†‹ –‹‘•†‡Žƒ ”±•‹•–ƒ ‡‘••‡—•‡ǡƒ‹• ‘‡’‡—– ‘ˆ‹”‡” “—ǯ‹Ž• ƒ±Ž‹‘”‡– Žǯ‡•–‹ƒ–‹‘ †— ”‹•“—‡ †‡ ˆ”ƒ –—”‡ ’ƒ” ”ƒ’’‘”–  Žƒ Ǥ ̵‘„Œ‡ –‹ˆ †‡ ‡––‡ –Š°•‡ ±–ƒ‹–†‘ †̵±˜ƒŽ—‡”•‹Žƒ’”±†‹ –‹‘’ƒ”•‹—Žƒ–‹‘—±”‹“—‡’‘—˜ƒ‹–²–”‡ƒ±Ž‹‘”±‡‡’”‡ƒ–‡ ‘’–‡ †‡• ‘†‹–‹‘• ”±ƒŽ‹•–‡• †‡ Šƒ”‰‡‡–Ǥ ‘—– †ǯƒ„‘”†ǡ Ž‡• ‘†‹–‹‘• †‡ Šƒ”‰‡‡– ‘””‡•’‘†ƒ–  —‡ Š—–‡ ˜‡”• Žǯƒ˜ƒ– ‘– ±–± ”‡’”‘†—‹–‡• •—” ͵ʹ ”ƒ†‹—• Š—ƒ‹ †ƒ• —‡ ‡š’±”‹‡–ƒ–‹‘‡šǦ˜‹˜‘Ǥ‡•”±•—Ž–ƒ–•‡š’±”‹‡–ƒ—š‘– ‘†—‹–•†‡—š‰”‘—’‡•ǣ—ˆ”ƒ –—”±‡– —‘ˆ”ƒ –—”±Ǥ—‹•ǡŽƒ ƒ’ƒ ‹–±†‡’”±†‹ –‹‘†ǯ—‘†°Ž‡Ǽ•±‰‡–ǽȋͻ†‡”ƒ†‹—•†‹•–ƒŽȌ ”±± ‡—–‹Ž‹•ƒ–—• ƒ‡”–”°•Šƒ—–‡”±•‘Ž—–‹‘ȋ ‹‰Š‡•‘Ž—–‹‘’‡”‹’Š‡”ƒŽ—ƒ–‹–ƒ–‹˜‡‘’—–‡† ‘‘‰”ƒ’Š›Ȍƒ±–±±˜ƒŽ—±‡ǤǤ‹ˆˆ±”‡–‡• ‘ˆ‹‰—”ƒ–‹‘•ȋƒš‹ƒŽ‡ȋ ‘ˆ‹‰—”ƒ–‹‘•–ƒ†ƒ”†Ȍ‡–ͷ‘Ǧ ƒš‹ƒŽ‡•Ȍ‘–±–±•‹—Ž±‡•Ǥǯ‹’Ž±‡–ƒ–‹‘†‡ Šƒ”‰‡‡–‘Ǧƒš‹ƒŽǯƒ’ƒ•ƒ±Ž‹‘”±Žƒ ƒ’ƒ ‹–±†‡ ’”±†‹ –‹‘†—‘†°Ž‡Ǽ•‡‰‡–ǽǤ ‹ƒŽ‡‡–ǡ—‘†°Ž‡Š±–±”‘‰°‡†—”ƒ†‹—• †‹•–ƒŽ‡–‹‡”ƒ±–± ”±±  ’ƒ”–‹” †ǯ— • ƒ‡” Ž‹‹“—‡ ȋ‘‡ ‡ƒ ‘’—–‡† ‘‘‰”ƒ’Š›ȌǤ ‡ ‘†°Ž‡ ƒ ’”‹• ‡ ‘’–‡Ž‡• ‘†‹–‹‘•†ǯ—‡ Š—–‡‡–‡”‡•†ǯ‘”‹‡–ƒ–‹‘‡–†‡˜‹–‡••‡Ǥ‡‘†°Ž‡†‡”ƒ†‹—•†‹•–ƒŽ ‡–‹‡” ƒ ‘–”± —‡ ‡‹ŽŽ‡—”‡ ’”±†‹ –‹‘ †‡ Žƒ Šƒ”‰‡  Žƒ ”—’–—”‡ ‡š’±”‹‡–ƒŽ‡ “—‡ Ž‡ ‘†°Ž‡ Ǽ•‡‰‡–ǽǤ‡––‡±–—†‡’”‘’‘•‡†‡•†‘±‡•‘”‹‰‹ƒŽ‡•’‘—”Žƒ˜ƒŽ‹†ƒ–‹‘†‡‘†°Ž‡•—±”‹“—‡• ’‘—”Žǯƒ±Ž‹‘”ƒ–‹‘†‡Žƒ’”±†‹ –‹‘†—”‹•“—‡†‡ˆ”ƒ –—”‡Ǥ ‘–• Ž±•ǣ±•‹•–ƒ ‡‘••‡—•‡ǡ‹•“—‡†‡ˆ”ƒ –—”‡ǡƒ†‹—•†‹•–ƒŽǡŠ—–‡ǡ‘†°Ž‡•±Ž±‡–•ˆ‹‹•Ǥ   ƒ„‘”ƒ–‘‹”‡†‡‹‘± ƒ‹“—‡‡–†‡± ƒ‹“—‡†‡•Š‘ •Ȃ̴ͻͶͲ͸ȋ

(6) ǦȌ ʹͷ˜‡—‡ ”ƒ­‘‹•‹––‡””ƒ†ǡƒ•‡ʹͶǡ͸ͻ͸͹ͷ‡†‡š ”ƒ ‡ ƒ–Š‘’Š›•‹‘Ž‘‰›ǡ‹ƒ‰‘•‹•ƒ†”‡ƒ–‡–•‘ˆ‘‡‹•‡ƒ•‡•ȂͳͲ͵͵ȋ

(7) ǦȌ ͹Ǧͳͳǡ”—‡ Ǥƒ”ƒ†‹ǡ͸ͻ͵͹ʹ›‘‡†‡šͲͺ ”ƒ ‡. . .

(8) Foreword Š‹•–Š‡•‹•™ƒ•’‡”ˆ‘”‡†‹ ‘ŽŽƒ„‘”ƒ–‹‘„‡–™‡‡–Š‡ƒ„‘”ƒ–‘‹”‡†‡‹‘± ƒ‹“—‡‡–± ƒ‹“—‡ †‡•Š‘ •ȋȌȋŒ‘‹–—‹–„‡–™‡‡–Š‡ ”‡ Š‹•–‹–—–‡‘ˆ• ‹‡ ‡ƒ†–‡ Š‘Ž‘‰›ˆ‘”–”ƒ•’‘”–ǡ †‡˜‡Ž‘’‡– ƒ† ‡–™‘”• ȋ

(9) Ȍ ƒ† ‹˜‡”•‹–± Žƒ—†‡ ‡”ƒ”† ›‘ ͳ ȋȌ ƒ† –Š‡ ƒ„‘”ƒ–‘”›ȋŒ‘‹–—‹–„‡–™‡‡–Š‡ ”‡ Š

(10) •–‹–—–‡‘ˆ ‡ƒŽ–Šƒ†‡†‹ ƒŽ‡•‡ƒ” Šȋ

(11) Ȍ ƒ†ȌǤ ‰”ƒ–ˆ‘”–Š‹•–Š‡•‹•™ƒ•’”‘˜‹†‡†„›–Š‡†‹‹•–”ƒ–‹˜‡‡’ƒ”–‡–‘ˆ ‹‡ ‡ǡ‡ Š‘Ž‘‰›ƒ†

(12) ‘˜ƒ–‹‘ ȋ

(13) 

(14) Ȍǡ ™Š‹ Š ‹• –Š‡ ‰‘˜‡”‡– ƒ‰‡ › •—’’‘”–‹‰ ˆ—†ƒ‡–ƒŽ ƒ† ƒ’’Ž‹‡† ”‡•‡ƒ” Š‹

(15) Ǥ

(16) ™‘—Ž†Ž‹‡–‘–Šƒ”ǤŠ‹Ž‹’’‡‡œ‹ǡ†‹”‡ –‘”‘ˆǡƒ†–Š‡”Ǥ ‡‘”‰‡

(17) 

(18) ǡ”‡•’‘•‹„Ž‡‘ˆ –Š‡ ‡ƒ Dz‘‡ —ƒŽ‹–› ƒ† ‹‘Ž‘‰‹ ƒŽ ƒ”‡”•dz ƒ– –Š‡

(19)  —‹– ͳͲ͵͵ ȋȌǡ ˆ‘” –Š‡‹” ‹† ™‡Ž ‘‡ƒ†ƒ ‡’–ƒ ‡‹–‘–Š‡‹”Žƒ„‘”ƒ–‘”‹‡•Ǥ

(20) ™‘—Ž†Ž‹‡–‘‡š’”‡••›•‹ ‡”‡‰”ƒ–‹–—†‡–‘›ƒ†˜‹•‘”•”Ǥƒ˜‹†‹––‘ƒ†”Ǥ ±Ž°‡ ‘ŽŽ‡– ˆ‘” –Š‡‹” ‡š ‡ŽŽ‡– ‰—‹†ƒ ‡ǡ ƒ”‹‰ ƒ† ’ƒ–‹‡ ‡Ǥ Š‡› ’”‘˜‹†‡† ‡ ’”‹ ‡Ž‡•• ƒ†˜‹ ‡• –Šƒ–

(21)  ™‹ŽŽ —†‘—„–‡†Ž›”‡‡„‡”ˆ‘”› ƒ”‡‡”‹”‡•‡ƒ” ŠǤ

(22) ™‘—Ž†Ž‹‡–‘–Šƒ”ǤƒŽƒ‘‹”‹ƒƒ‘–‘ƒƒƒǡ”Ǥ‡”–˜ƒ‹‡–„‡”‰‡ƒ†”Ǥƒ• ƒŽƒ—‰‹‡” ˆ‘”–ƒ‹‰’ƒ”–‘ˆ–Š‡Œ—”› ‘‹––‡‡Ǥ ‘ ‡ƒǦƒ—Ž ‘—šǡ ”Ǥ ”ƒ­‘‹• —„à—ˆǡ ”Ǥ –±’Šƒ‹‡ ‘—–”‘› ƒ† ”Ǥ ‡ƒǦƒ’–‹•–‡ ‹ƒŽƒ– ȋŒ—”› ‡„‡”Ȍǡ

(23) ƒ†‡‡’Ž›‰”ƒ–‡ˆ—Žˆ‘”‡˜‡”›–Š‹‰›‘—–ƒ—‰Š–†—”‹‰–Š‡•‡›‡ƒ”•ƒ†ˆ‘”ƒŽŽ›‘—”•—’’‘”–Ǥ

(24) ‘™ƒŽ•‘›‰”ƒ–‹–—†‡–‘”ǤŠ‹ŽŽ‹’’‡‡‹ŽŽƒ•ǡ™Š‘‹–”‘†— ‡‡‹–‘–Š‡ˆ‹‹–‡‡Ž‡‡–‘†‡Ž• ˆ‘”‹Œ—”›”‹•’”‡†‹ –‹‘ǡˆ‘”Š‹•‹†‘„•‡”˜ƒ–‹‘•†—”‹‰›–Š‡•‹•Ǥ

(25) ™ƒ––‘–Šƒ–Š‡–‡ Š‹ ƒŽ•—’’‘”–‘ˆ‡‹Žƒ‡„‘—„ƒ‡”ǡ˜‡•ƒ‹”‡ǡ–±’Šƒ‡”†‹œœ‘‡ǡ ‡ƒǦ — —••‘ƒ†ƒ” ƒ‰‹‘Ǥ

(26) ™ƒ––‘–ŠƒƒŽŽ›ˆ‡ŽŽ‘™Žƒ„ƒ–‡•ˆ”‘–Š‡ƒ†Ǥ

(27) •’‡ ‹ƒŽŽ›–Šƒƒ‹ŽŽ‡‘­‘ǡ Ž‘”‹‡ ‘–ƒ‰‡”ǡ ±„ƒ•–‹‡ ‹œœ‘ǡ ƒ—‡ŽŽ‡ ‡ˆ°˜”‡ǡ ƒˆƒƒ ŽŽ‘—œǡ ‘ƒ ‡•„ƒ–•ǡ ƒ• ƒŽ ƒŽŽ±‡ƒ† ƒ„‹‡‡”–Š‡–ˆ‘”–Š‡‹”ˆ”‹‡†•Š‹’ƒ†•—’’‘”–Ǥ Š‡ Žƒ•– „—– ‘– Ž‡ƒ•–ǡ

(28)  ™‘—Ž† ƒŽ•‘ Ž‹‡ –‘ ‡š–‡† › ‰”ƒ–‹–—†‡ –‘ › — ŠǦŽ‘˜‡† ’ƒ”‡–•ǡ › „‡Ž‘˜‡†ƒŽ‡–‹ƒ‡”ƒƒ†› Ž‘•‡•–ˆ”‹‡†•ǡˆ‘”–Š‡‹”— ‘†‹–‹‘ƒŽƒˆˆ‡ –‹‘ƒ†•‹ ‡”‡•—’’‘”– ‘˜‡”ƒŽŽ–Š‡•‡›‡ƒ”•Ǥ. . .

(29) Contents. ‘–‡–• . ‘”‡™‘”†ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶ ‘–‡–•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷ

(30) –”‘†— –‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͺ Šƒ’–‡”ͳǤ ͳǤͳ.

(31) –”‘†— –‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͲ. ͳǤʹ. ƒ–‘›ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳ. ͳǤʹǤͳ. ƒ–‘‹ ƒŽŽƒ‡•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳ. ͳǤʹǤʹ. Š‡‘‡•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳ. ͳǤʹǤ͵. Š‡ƒ†‹—•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳʹ. ͳǤ͵. ’‹†‡‹‘Ž‘‰›‘ˆ ”ƒ‰‹Ž‹–›ˆ”ƒ –—”‡•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͶ. ͳǤͶ. ‘‡ˆ”ƒ‰‹Ž‹–›‡•–‹ƒ–‹‘‹ Ž‹‹ •ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͷ. ͳǤͶǤͳ. —ƒŽǦ‡‡”‰›šǦ”ƒ›ƒ„•‘”’–‹‘‡–”›ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͷ. ͳǤͶǤʹ. ‘’—–‡†–‘‘‰”ƒ’Š›• ƒǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳ͹. ͳǤͶǤ͵. Š‡ ‹‰Š‡•‘Ž—–‹‘’‡”‹’Š‡”ƒŽ—ƒ–‹–ƒ–‹˜‡‘’—–‡†‘‘‰”ƒ’Š›ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͺ. ͳǤͶǤͶ. Š‡ ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͲ. ͳǤͶǤͷ. ‹•–ƒŽ”ƒ†‹—•ˆ”ƒ –—”‡•†‡• ”‹’–‹‘ƒ† Žƒ••‹ˆ‹ ƒ–‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͳ. ͳǤͷ. . –ƒ–‡‘ˆ”–ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͲ. ‘‡ˆ”ƒ‰‹Ž‹–›‡•–‹ƒ–‹‘‹”‡•‡ƒ” ŠǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹ͵. ͳǤͷǤͳ. ‡ Šƒ‹ ƒŽ‡ˆ‹‹–‹‘•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹ͵. ͳǤͷǤʹ. ‘‡

(32) ƒ‰‹‰ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͶ. ͳǤͷǤ͵. ‘’‘Ž‘‰›ƒ†ƒ–‡”‹ƒŽ’”‘’‡”–‹‡•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹ͸. ͳǤͷǤͶ. ƒ–‡”‹ƒŽŽƒ™ƒ••—’–‹‘•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤʹͻ. ͳǤͷǤͷ. ‡•Š‹‰‘’–‹‘•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵Ͳ. ͳǤͷǤ͸. ‹•‘ˆˆ”ƒ –—”‡†‡ˆ‹‹–‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͳ. ͳǤͷǤ͹. ƒ‹Ž—”‡ ”‹–‡”‹ƒǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͳ. ͳǤ͸. ‹• —••‹‘ǣ‡Ž‡ –‹‘‘ˆ–Š‡Ž‘ƒ†‹‰ ‘†‹–‹‘•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͷ. ͳǤ͹. ‘ Ž—•‹‘•ƒ†ƒ‹•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵͹. ͷ.

(33) ‘–‡–• Šƒ’–‡”ʹǤ. . š’‡”‹‡–ƒŽ ’”‘–‘ ‘Ž –‘ ”‡’”‘†— ‡ ƒ ˆ‘”™ƒ”† ˆƒŽŽ Ž‡ƒ†‹‰ –‘ ˆ”ƒ –—”‡† ƒ† ‘Ǧ. ˆ”ƒ –—”‡†”ƒ†‹‹ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͻ ʹǤͳ.

(34) –”‘†— –‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͻ. ʹǤʹ. ‡–Š‘†•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͵ͻ. ʹǤ͵. ‡•—Ž–•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶͷ. ʹǤ͵Ǥͳ. ƒš‹— ‘” ‡•ˆ”‘–Š‡‡š’‡”‹‡–ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͶͷ. ʹǤ͵Ǥʹ. ”ƒ –—”‡ ƒ•‡•ƒ†–›’‡‘ˆˆ”ƒ –—”‡•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͲ. ʹǤ͵Ǥ͵. –”ƒ‹ƒƒŽ›•‹•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͳ. ʹǤͶ. ‹• —••‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷʹ. ʹǤͷ. ‘ Ž—•‹‘•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͶ. Šƒ’–‡”͵Ǥ ͵Ǥͳ.

(35) –”‘†— –‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͷ. ͵Ǥʹ. ‡–Š‘†•ƒ†”‡•—Ž–•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͷ. ͵ǤʹǤͳ. ƒŽ‹†ƒ–‹‘–—†›ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͸Ͳ. ͵ǤʹǤʹ. ˆˆ‡ –‘ˆ–Š‡Ž‘ƒ†‹‰†‹”‡ –‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͸ͷ. ͵ǤʹǤ͵. ‹• ”‹‹ƒ–‹‘‘ˆ–Š‡‰”‘—’•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹Ͳ. ͵ǤʹǤͶ.  —”ƒ ›‘ˆ–Š‡‘†‡Ž•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹ͳ. ͵ǤʹǤͷ. ‘””‡Žƒ–‹‘•„‡–™‡‡‘†‡Žƒ†‡š’‡”‹‡–ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹ͳ. ͵ǤʹǤ͸. ••‡••‡–‘ˆ–Š‡”‹•‘ˆˆ”ƒ –—”‡ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹ʹ. ͵ǤʹǤ͹. ••‡••‡–‘ˆƒ ”‹–‡”‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹͵. ͵Ǥ͵. ‹• —••‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹͸. ͵ǤͶ. ‘ Ž—•‹‘•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹͹. Šƒ’–‡”ͶǤ. ͸ . —‡”‹ ƒŽ•–—†›ǣ‡ˆˆ‡ –‘ˆ–Š‡Ž‘ƒ†‹‰†‹”‡ –‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͷͷ. ‹‹–‡‡Ž‡‡–‘†‡Ž”‡’”‘†— ‹‰ƒ‡šǦ˜‹˜‘ˆ‘”™ƒ”†ˆƒŽŽ‘–Š‡†‹•–ƒŽ”ƒ†‹—•ǤǤǤǤǤǤǤǤǤǤǤǤ͹ͺ. ͶǤͳ.

(36) –”‘†— –‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹ͺ. ͶǤʹ. ‡–Š‘†•ƒ†”‡•—Ž–•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ͹ͻ. ͶǤ͵. ‹• —••‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͺͻ. ͶǤͶ. ‘ Ž—•‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͻͲ.

(37) ‘–‡–• . ‡‡”ƒŽ‘ Ž—•‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͻʹ ‹„Ž‹‘‰”ƒ’Š›ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͻͷ. ’’‡†‹šͳǣ‡”•‘ƒŽ‘—‹ ƒ–‹‘•ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͲͶ ’’‡†‹šʹǣ—ƒ”›‹ ”‡ ŠǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳͳ

(38) –”‘†— –‹‘ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳͳ Šƒ’‹–”‡ͳǣ‘–‡š–‡†‡Žǯ±–—†‡ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳ͵ Šƒ’‹–”‡ʹǣ”‘–‘ ‘Ž‡‡š’±”‹‡–ƒŽƒˆ‹†‡”‡’”‘†—‹”‡—‡ Š—–‡˜‡”•Ž̵ƒ˜ƒ–•—””ƒ†‹—•Š—ƒ‹ ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳͳ͹ Šƒ’‹–”‡͵ǣ–—†‡—±”‹“—‡ǣ‡ˆˆ‡–†‡Žƒ†‹”‡ –‹‘†‡ Šƒ”‰‡‡–•—”•‡‰‡–ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳʹ͵ Šƒ’‹–”‡Ͷǣ‘†°Ž‡±Ž±‡–•ˆ‹‹•”‡’”‘†—‹•ƒ–—‡ Š—–‡‡ƒ˜ƒ–•—””ƒ†‹—•†‹•–ƒŽ‡š˜‹˜‘ǤǤǤͳʹͺ ‘ Ž—•‹‘‰±±”ƒŽ‡ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳ͵ͷ ’’‡†‹š͵ǣ ƒ”ƒ‡–‡”•ˆ”‘Ǧ ƒ–ƒ† ǦǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤͳ͵ͺ. . . ͹.

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(40) –”‘†— –‹‘. Introduction. . ”ƒ‰‹Ž‹–› ˆ”ƒ –—”‡• ƒ”‡ ƒ ™‘”Ž†™‹†‡ Š‡ƒŽ–Š ’”‘„Ž‡Ǥ Š‡•‡ –›’‡• ‘ˆ ˆ”ƒ –—”‡•ǡ ™Š‹ Š ‘””‡•’‘†–‘ƒ›ˆ”ƒ –—”‡ ƒ—•‡†„›ƒˆƒŽŽˆ”‘–Š‡•–ƒ†‹‰Š‡‹‰Š–‘”Ž‡••ǡƒ”‡”‡Žƒ–‡†–‘ —†‡”Ž›‹‰†‹•‡ƒ•‡•‰‡‡”ƒ–‹‰„‘‡ˆ”ƒ‰‹Ž‹–›ǤŠ‡‘•–‡‘’‘”‘•‹•‹•‘‡‘ˆ–Š‡•‡†‹•‡ƒ•‡•Ǥ

(41) –• ’”‡˜ƒŽ‡ ‡‹™‘‡‹–Š‡Žƒ”‰‡•– ‘—–”‹‡•‹–Š‡ȋ ”ƒ ‡ǡ ‡”ƒ›ǡ

(42) –ƒŽ›ǡ’ƒ‹ƒ† Ȍ‹•‡•–‹ƒ–‡†‹‘”‡–Šƒͳʹ‹ŽŽ‹‘ ƒ•‡•ȋƒ‹•‡–ƒŽǤʹͲͳ͵ȌǤ Š‡‰‘Ž†•–ƒ†ƒ”†‡–Š‘†ˆ‘”–Š‡ Ž‹‹ ƒŽ†‹ƒ‰‘•‹•‘ˆ–Š‡‘•–‡‘’‘”‘•‹•ƒ†–Š‡‡˜ƒŽ—ƒ–‹‘ ‘ˆ–Š‡ ”‹•‘ˆˆ”ƒ –—”‡ ‹•–Š‡—ƒŽǦ”ƒ›„•‘”’–‹‘‡–”›ȋȌȋ‘”Ž† ‡ƒŽ–Š”‰ƒ‹œƒ–‹‘ ʹͲͲͶȌǤ Š‹• ‡–Š‘† ‹• „ƒ•‡† ‘ –Š‡ ‡ƒ•—”‡‡– ‘ˆ „‘‡ ‹‡”ƒŽ †‡•‹–› ƒ– †‹ˆˆ‡”‡– ƒƒ–‘‹ ƒŽ •‹–‡•Ǥ

(43) – Šƒ• „‡‡ •Š‘™ –Šƒ– –Š‹• ‡ƒ•—”‡ǡ ™Š‹ Š ‹• ƒ šǦ”ƒ› ʹ ’”‘Œ‡ –‹‘ǡ ’”‡•‡–•ƒ‹•—ˆˆ‹ ‹‡–•‡•‹„‹Ž‹–›ǡ„‡ ƒ—•‡ͷͲΨ‘ˆˆ”ƒ –—”‡•‘ —”‹’ƒ–‹‡–• ‘•‹†‡”‡† ‘‘•–‡‘’‘”‘–‹ ȋ‹”‹•‡–ƒŽǤʹͲͲͳȌǤ ‰‘‹‰”‡•‡ƒ” ŠŠƒ•’”‘’‘•‡††‹ˆˆ‡”‡–‡–Š‘†•–‘‹’”‘˜‡–Š‹••‡•‹„‹Ž‹–›Ǥ‡‘ˆ–Š‡•‡ ‡–Š‘†• ‹• –Š‡ ǡ ™Š‹ Š ‹• ƒ •—”˜‡› ‘””‡Žƒ–‹‰ †‹ˆˆ‡”‡– Ǯ”‹• ˆƒ –‘”•ǯ –‘ ‡•–‹ƒ–‡ –Š‡ ”‹• ‘ˆ ˆ”ƒ –—”‡ ‘˜‡” –‡ ›‡ƒ”•Ǥ ‘™‡˜‡”ǡ –Š‹• ‡–Š‘† †‘‡• ‘–‹–‡‰”ƒ–‡ –Š‡ ˆƒŽŽ• ƒ† –Š‡ †‹•–—”„ƒ ‡•‘ˆ–Š‡™ƒŽ‹‰‹–Š‡ƒŽ‰‘”‹–Š‘ˆ’”‡†‹ –‹‘ȋŠƒ’—”Žƒ–ʹͲͳ͵ȌǤ

(44) ‘–Š‡”™‘”†•ǡ –Š‹••—”˜‡› ƒ‘––ƒ‡‹–‘ƒ ‘—––Š‡‡š–‡”ƒŽŽ‘ƒ†‹‰ ‘†‹–‹‘•–Šƒ–‹ ”‡ƒ•‡–Š‡”‹•‘ˆ ˆ”ƒ –—”‡Ǥ ‘–Š‡” ‡–Š‘† –Šƒ– Šƒ• „‡‡ ’”‘’‘•‡† ‹• –Š‡ ƒƒŽ›•‹• „› ‹ ”‘Ǧˆ‹‹–‡ ‡Ž‡‡– ‘†‡Ž• ȋρ Ȍ ”‡ƒ–‡† —•‹‰ ƒ ‹‰Š ‡•‘Ž—–‹‘ ’‡”‹’Š‡”ƒŽ —ƒ–‹–ƒ–‹˜‡ ‘’—–‡† ‘‘‰”ƒ’Š›ȋ Ǧ’Ȍȋ‹Žƒ›’Š‹‘—‡–ƒŽǤʹͲͳͲȌǤŽŽ˜ƒŽ‹†ƒ–‹‘•–—†‹‡•Šƒ˜‡•Š‘™–Šƒ––Š‡ ‡•–‹ƒ–‹‘‘ˆ–Š‡„‘‡•–”‡‰–Š‹•„‡––‡”ƒ Š‹‡˜‡†„›–Š‡ρ ȋʹ„‡–™‡‡ͲǤ͹͵ƒ†ͲǤͻʹȌ –Šƒ —•‹‰ †‡•‹–› ‡ƒ•—”‡• ˆ”‘ –Š‡  ȋʹ „‡–™‡‡ ͲǤ͵ͳ ƒ† ͲǤ͹ͳȌȋ‹‡–„‡”‰‡ Ƭ

(45) –‘ ʹͲͳͷȌǤ‡•’‹–‡–Š‹•‰‘‘†Ž‡˜‡Ž‘ˆ’”‡†‹ –‹‘‘ˆ–Š‡„‘‡•–”‡‰–Šǡ”‡–”‘•’‡ –‹˜‡•–—†‹‡•Šƒ˜‡ ‘–’”‘˜‹†‡ƒ––Š‹•‘‡–ƒ Ž‡ƒ”‡˜‹†‡ ‡–Šƒ––Š‡‘—–’—–‘ˆρ ƒ”‡„‡––‡”’”‡†‹ –‘”• ‘ˆ–Š‡”‹•‘ˆˆ”ƒ –—”‡–Šƒ–Š‡†‡•‹–›‡ƒ•—”‡‡–•„›ȋ‹‡–„‡”‰‡Ƭ

(46) –‘ʹͲͳͷȌǤ Š‡•–ƒ†ƒ”†‡–Š‘†‘ˆρ ƒƒŽ›•‹•‹•–Š‡•–ƒ–‹ Ǧƒš‹ƒŽŽ‘ƒ†‹‰Ǥ ‘™‡˜‡”ǡ‹–Š‡ ƒ•‡‘ˆƒ ˆƒŽŽǡ˜‡Ž‘ ‹–‹‡• ƒ”‡ƒ ŠʹȀ•ǡ–Šƒ–•Š‘—Ž†„‡ ‘•‹†‡”‡†ƒ•ƒ†›ƒ‹ Ž‘ƒ†‹‰ǤŽ•‘ǡ‹–Šƒ• „‡‡•Š‘™–Šƒ–‘Ž›ͳͷΨ‘ˆ–Š‡ˆƒŽŽ ƒ•‡•ƒ”‡ƒ••‘ ‹ƒ–‡†™‹–Šƒƒš‹ƒŽŽ‘ƒ†‘–Š‡”ƒ†‹—• ȋ‡Ž–‘‡–ƒŽǤʹͲͳͲȌǤŠ—•ǡ–Š‡ƒ‹‘ˆ–Š‹•–Š‡•‹•™ƒ•–‘•–—†›–Š‡‹ˆŽ—‡ ‡‘ˆ—•‹‰”‡ƒŽ‹•–‹  ͺ .

(47)

(48) –”‘†— –‹‘  Ž‘ƒ†‹‰ ‘†‹–‹‘•ȋ†‹”‡ –‹‘ƒ†˜‡Ž‘ ‹–›Ȍǡ‹ˆ‹‹–‡‡Ž‡‡–‘†‡Ž•ˆ‘”–Š‡ƒ••‡••‡–‘ˆ „‘‡•–”‡‰–Šƒ†–Š‡ˆ”ƒ –—”‡”‹•ǤŠ‹••–—†›™ƒ• ƒ””‹‡†‘—–‹–Š”‡‡•–‡’•ǣ ‹”•–ǡ™‡†‡˜‡Ž‘’‡†ƒ‡šǦ˜‹˜‘‡š’‡”‹‡––‘”‡’”‘†— ‡ƒˆƒŽŽ ƒ•‡ǡŽ‡ƒ†‹‰–‘ˆ”ƒ –—”‡†ƒ† ‘Ǧˆ”ƒ –—”‡†”ƒ†‹‹ȋŠƒ’–‡”ʹȌǤŠ‡ ƒ•‡‘ˆ–Š‡•–—†›™ƒ•ƒˆ‘”™ƒ”†ˆƒŽŽ™‹–Š‘—–•–”‡– Š‡† Šƒ†Ǥ Š‡ ƒ‰Ž‡ „‡–™‡‡ –Š‡ ˜‘Žƒ” ˆƒ ‡ ‘ˆ –Š‡ ”ƒ†‹—• ƒ† –Š‡ ‰”‘—† ™ƒ• ͹ͷι ƒ† –Š‡ ˜‡Ž‘ ‹–›™Š‡‹’ƒ –‹‰–Š‡‰”‘—†™ƒ•ʹȀ•Ǥ ‡ ‘†ǡ™‡‡˜ƒŽ—ƒ–‡†–Š‡’”‡†‹ –‹‘ ƒ’ƒ„‹Ž‹–›‹†‹ˆˆ‡”‡– ‘†‹–‹‘•‘ˆƒ•‡‰‡– ȋͻ  †‹•–ƒŽ ”ƒ†‹—•Ȍ ”‡ƒ–‡† —•‹‰ –Š‡ Ǧ’ ȋŠƒ’–‡” ͵ȌǤ

(49) – ™ƒ• –‡•–‡† —†‡” –Š‡ ƒš‹ƒŽ Ž‘ƒ†‹‰ ȋ•–ƒ†ƒ”† ‘ˆ‹‰—”ƒ–‹‘ ‘ˆ ƒƒŽ›•‹•Ȍǡ ƒ† —†‡” ˆ‹˜‡ ƒ††‹–‹‘ƒŽ ‘Ǧƒš‹ƒŽ ‘ˆ‹‰—”ƒ–‹‘•Ǥ

(50)  –Š‡ –Š‹”† •–‡’ǡ ƒ Š‡–‡”‘‰‡‡‘—•  ‘ˆ –Š‡ ™Š‘Ž‡ †‹•–ƒŽ ”ƒ†‹—• ™ƒ• ”‡ƒ–‡† —•‹‰ †ƒ–ƒ ˆ”‘ƒ‘‡‡ƒ‘’—–‡†‘‘‰”ƒ’Š›ȋŠƒ’–‡”ͶȌǤŠ‹•‘†‡Ž•‹—Žƒ–‡†–Š‡†›ƒ‹  ‘Ǧƒš‹ƒŽŽ‘ƒ†‹‰ ‘†‹–‹‘•‘ˆ–Š‡‡šǦ˜‹˜‘‡š’‡”‹‡–”‡’”‡•‡–‹‰ƒˆ‘”™ƒ”†ˆƒŽŽ ƒ•‡ǤŠ‡ ƒ —”ƒ ›–‘’”‡†‹ ––Š‡‡š’‡”‹‡–ƒŽˆƒ‹Ž—”‡Ž‘ƒ†‘ˆ–Š‹•‘†‡Žƒ†–Š‡•‡‰‡– ™‡”‡ ‘’ƒ”‡†Ǥ  . . . ͻ.

(51) –ƒ–‡‘ˆ”–. Chapter 1. State of Art. . 1.1 Introduction Š‹• Šƒ’–‡” ˆ‘ —•‡• ‘ ’”‡•‡–‹‰ –Š‡ ”‡•‡ƒ” Š •—„Œ‡ – ƒ† ƒ ”‡˜‹‡™ ‘ˆ –Š‡ Ž‹–‡”ƒ–—”‡ ”‡Žƒ–‡†™‹–Š–Š‡ƒ••‡••‡–‘ˆ„‘‡•–”‡‰–Šƒ†„‘‡ˆ”ƒ –—”‡”‹•ǤŠ‹•”‡˜‹‡™™‹ŽŽ ‘˜‡” ƒƒ–‘‹ ƒŽǡ Ž‹‹ ƒŽƒ†„‹‘‡ Šƒ‹ ƒŽƒ•’‡ –•‘ˆ–Š‡•—„Œ‡ –Ǥ•’‡ ‹ƒŽˆ‘ —•™‹ŽŽ„‡†‘‡‘ –Š‡”ƒ†‹—•Ǥ ‹”•–ǡ„‹‘Ž‘‰‹ ƒŽƒ†ƒƒ–‘‹ ƒŽ‘–‹‘•ƒ”‡”‡‡„‡”‡†ǤŠ‡•–”— –—”‡ƒ†ˆ— –‹‘‘ˆ–Š‡ ‹˜‘Ž˜‡† ‘’‘‡–• ƒ”‡ ‡š’Žƒ‹‡†ǡ ˆ”‘ –Š‡ ‹ ”‘ Ž‡˜‡Ž –‘ –Š‡ ƒ ”‘ Ž‡˜‡ŽǤ Š‡ ‡š– •—„ Šƒ’–‡”‡š’Žƒ‹•–Š‡‡’‹†‡‹‘Ž‘‰›‘ˆ–Š‡ˆ”ƒ‰‹Ž‹–›ˆ”ƒ –—”‡•Ǥ Š‡ǡ –Š‡ „‘‡ ˆ”ƒ‰‹Ž‹–› ƒ••‡••‡– ‹• ’”‡•‡–‡†Ǥ ™‘ ƒ’’”‘ƒ Š‡• ƒ”‡ †‹• —••‡†ǣ Ž‹‹ ƒŽ ƒ†”‡•‡ƒ” ŠǤŠ‡ƒ‹•–‡ Š‹“—‡•—•‡†‘‡ƒ Šƒ’’”‘ƒ Šƒ”‡’”‡•‡–‡†Ǥ ‹ƒŽŽ›ǡ™‡†‹• —••‡†–Š‡’”‡†‹ –‹‘ ƒ’ƒ„‹Ž‹–›‘ˆ–Š‡†‹ˆˆ‡”‡––‡ Š‹“—‡•ƒ†™‡•–ƒ–‡†‘—” Š›’‘–Š‡•‹•ˆ‘”‹–•‹’”‘˜‡‡–Ǥ. ͳͲ .

(52) –ƒ–‡‘ˆ”– . 1.2 Anatomy 1.2.1 Anatomical Planes. ‡ˆ‘”‡ †‡• ”‹„‹‰ –Š‡ „‘‡• ‘ˆ –Š‡ •‡Ž‡–‘ǡ ‹– ‹• ‹’‘”–ƒ– –‘ ”‡‡„‡” –Š‡ ƒ‹ ‘˜‡–‹‘•–‘Ž‘ ƒŽ‹œ‡ƒ†’‘•‹–‹‘„‘†›’ƒ”–•ǤŠ‡›ƒ”‡•Š‘™‹–Š‡ ‹‰—”‡ͳǦͳ.  Figure 1-1ǣ‘˜‡–‹‘ˆ‘”–Š‡Ž‘ ƒŽ‹œƒ–‹‘ƒ†’‘•‹–‹‘‘ˆ–Š‡Š—ƒ„‘†›’ƒ”–• . Ilustrations: Jordi March i Nogué & Blausen.com staff: "Blausen gallery 2014". 1.2.2 The Bones ‘‡•ƒ”‡”‹‰‹†‘”‰ƒ•–Šƒ– ‘•–‹–—–‡–Š‡•‡Ž‡–‘ǤŠ‡Š—ƒ•‡Ž‡–‘‹•ˆ‘”‡†„›ʹͲ͸ „‘‡•ǡ™Š‹ Š’”‘˜‹†‡–Š‡ˆ”ƒ‡™‘”‘ˆ–Š‡„‘†›Ǥ‘‡••—’’‘”–ƒ†’”‘–‡ ––Š‡•‘ˆ–‘”‰ƒ• ‘ˆ–Š‡ „‘†›Ǥ •ƒ –‹••—‡ǡ‹– ‘•‹•–•‹ƒ‹–‡” ‡ŽŽ—Žƒ” ƒŽ ‹ˆ‹‡†ƒ–”‹šǡ ‘–ƒ‹‹‰ ‘ŽŽƒ‰‡ ˆ‹„‡”•ƒ††‹ˆˆ‡”‡––›’‡•‘ˆ ‡ŽŽǤŠ‡„‘‡‹•ƒ”‡•‡”˜‘‹”ˆ‘” ƒŽ ‹—ƒ†’Š‘•’Š‘”—•ƒ†ƒ ‘–ƒ‹‡”ˆ‘”„Ž‘‘†Ǧ’”‘†— ‹‰ ‡ŽŽ•ȋ”ƒ‡‡–ƒŽǤʹͲͳͶȌǤ ‘‡• ‰‘‡• ‘•–ƒ–Ž› –Š”‘—‰Š ƒ ‘†‡Ž‹‰ ’”‘ ‡•• ȋ”‡•Šƒ’‹‰ ƒ† ”‡•‹œ‹‰Ȍǡ –‘ ƒ†ƒ’– –Š‡ •–”— –—”‡ –‘ Ž‘ƒ†‹‰Ǥ

(53) – ƒŽ•‘ —†‡”‰‘‡• ƒ ”‡‘†‡Ž‹‰ ’”‘ ‡•• –‘ ”‡‘˜‡ ‘Ž†ǡ ƒ† –‘ ”‡’ƒ‹” ‹ ”‘Ǧ†ƒƒ‰‡•„›”‡’Žƒ ‹‰™‹–Š‡™•–”‘‰‡”„‘‡ƒ†‡‡’„‘‡•–”‡‰–Šȋ ”‘•–ͳͻͻͶȌǤ Š‡ ƒ’’”‡ ‹ƒ–‹‘ ‘ˆ –Š‹• ’Š‡‘‡ƒ ™‡”‡ •–ƒ–‡† „› ‘Žˆǡ ‹ –Š‡ Žƒ™ ƒ””›‹‰ Š‹• ƒ‡ǣ “Every change in the form and the function of a bone or in the function of the bone alone, leads to changes in its internal architecture and in its external form”ȋ‘Žˆˆͳͻͺ͸Ȍ. . . ͳͳ.

(54) –ƒ–‡‘ˆ”–  Š‡„‘‡Šƒ•–™‘ ‘’‘‡–•ǣ–Š‡ ‘”–‹ ƒŽ„‘‡ƒ†–Š‡–”ƒ„‡ —Žƒ”„‘‡ǤŠ‡ ‘”–‹ ƒŽ„‘‡ ‹•ƒ†‡•‡„‘‡™Š‹ Š ‘””‡•’‘†•‰‡‡”ƒŽŽ›–‘–Š‡‡š–‡”‹‘”•Š‡ŽŽ‘ˆ–Š‡„‘‡Ǥ

(55) –•—””‘—†• –Š‡–”ƒ„‡ —Žƒ”„‘‡ƒ†–Š‡ƒ””‘™ǤŠ‡–”ƒ„‡ —Žƒ”„‘‡ǡ™Š‹ Š‹•ƒ‡–™‘”‘ˆ–”ƒ„‡ —Žƒ” ’Žƒ–‡•ƒ†”‘†••’”‹Ž‡†‹–Š‡ƒ””‘™ȋƒ”–‡”Ƭ ƒ›‡•ͳͻ͹͹ȌǤ ‘”–‹ ƒŽ „‘‡ ‹• ”‡ ‘˜‡”‡† „› –Š‡ ’‡”‹‘•–‡—ǡ ™Š‹ Š ‹• ƒ ˆ‹„”‘—• ‘‡ –‹˜‡ –‹••—‡ •—””‘—†‹‰„‘‡ȋ ‹‰—”‡ͳǦʹȌǤ.  Figure 1-2ǣ‘‰„‘‡•–”— –—”‡•ǤIlustration: Pearson Education, Inc., publishing as Pearson Benjamin Cummings . 1.2.3 The Radius Š‡ ƒ••‡„Ž› ‘ˆ „‘‡• ˆ‘”• –Š‡ •‡Ž‡–‘ǡ ™Š‹ Š ƒ „‡ †‹˜‹†‡† ‹ –™‘ ‰”‘—’•ǣ –Š‡ ƒš‹ƒŽ •‡Ž‡–‘ ȋ ”ƒ‹—ǡ ˜‡”–‡„”ƒŽ ‘Ž—ǡ ”‹„• ƒ† •–‡”—Ȍ ƒ† –Š‡ ƒ’’‡†‹ —Žƒ” •‡Ž‡–‘ ȋ—’’‡”ƒ†Ž‘™‡”Ž‹„•ȌǤŠ‹••—„†‹˜‹•‹‘‘ˆ–Š‡•‡Ž‡–‘ ƒ„‡•‡‡‹–Š‡ ‹‰—”‡ͳǦ͵ Š‡—’’‡”Ž‹„ ƒ„‡•—„Ǧ†‹˜‹†‡†‹ƒ”ǡˆ‘”‡ƒ”ƒ†Šƒ†ǤŠ‡”ƒ†‹—•‹•Ž‘ ƒ–‡†‘–Š‡ Žƒ–‡”ƒŽ•‹†‡‘ˆ–Š‡ˆ‘”‡ƒ”„‡–™‡‡–Š‡‡Ž„‘™ƒ†–Š‡™”‹•–Œ‘‹–•Ǥ

(56) –ˆ‘”•–Š‡‡Ž„‘™Œ‘‹– ‘‹–•’”‘š‹ƒŽ‡†™‹–Š–Š‡Š—‡”—•ƒ†–Š‡—Žƒȋ ‹‰—”‡ͳǦͶȌǤ. ͳʹ .

(57) –ƒ–‡‘ˆ”– .  Figure 1-3ǣ —ƒ‡Ž‡–‘ǤIllustration: Gray’s anatomy for students, 2nd EditionǤȋ”ƒ‡‡–ƒŽǤʹͲͳͶȌ.  Figure 1-4ǣ‘‡•‹–Š‡—’’‡”Ž‹„ǤIllustration: Gray’s anatomy for student, 2nd Edition. ȋ”ƒ‡‡–ƒŽǤʹͲͳͶȌ.  . . ͳ͵.

(58) –ƒ–‡‘ˆ”–  Š‡†‹•–ƒŽ”ƒ†‹—•Šƒ•ƒ“—ƒ†”‹Žƒ–‡”ƒŽˆ‘”Ǥ

(59) –Šƒ•–™‘ƒ”–‹ —Žƒ”•—”ˆƒ ‡•ȋ‘‡ˆ‘”–Š‡ ƒ”’ƒŽ „‘‡• ƒ† ‘‡ ˆ‘” –Š‡ —ŽƒȌǤ Š‡ ƒ”’ƒŽ ƒ”–‹ —Žƒ” •—”ˆƒ ‡ ‹• ƒ”‡† „› –™‘ ˆƒ ‡–• ˆ‘” –Š‡ • ƒ’Š‘‹† ƒ† Ž—ƒ–‡Ǥ Š‡ •—”ˆƒ ‡ ˆ‘” –Š‡ —Žƒǡ ƒŽ•‘ ‘™ ƒ• –Š‡ —Žƒ” ‘– Šǡ ‹• ƒ””‘™ǡ ‘ ƒ˜‡ƒ†•‘‘–Šǡƒ†ƒ”–‹ —Žƒ–‡•™‹–Š–Š‡Š‡ƒ†‘ˆ–Š‡—ŽƒǤŠ‡‘–Š‡”•—”ˆƒ ‡•ƒ”‡–Š‡ ˜‘Žƒ”ǡ†‘”•ƒŽƒ†Žƒ–‡”ƒŽ•—”ˆƒ ‡ȋ ‹‰—”‡ͳǦͷȌǤ.  Figure 1-5 : ƒ–‘›‘ˆ–Š‡”ƒ†‹—•ǤIllustration: Gray’s anatomy for student, 2nd Edition. ȋ”ƒ‡‡–ƒŽǤʹͲͳͶȌ. 1.3 Epidemiology of Fragility fractures ˆ”ƒ‰‹Ž‹–›ˆ”ƒ –—”‡”‡•—Ž–•ˆ”‘ƒŽ‘™–”ƒ—ƒ‡˜‡–ǡ•— Šƒ•ˆƒŽŽˆ”‘•–ƒ†‹‰Š‡‹‰Š–‘”Ž‡•• ȋƒ”•ŠƒŽŽ ‡– ƒŽǤ ͳͻͻ͸ȌǤ Š‹• ‹† ‘ˆ ˆ”ƒ –—”‡ ‹• —•—ƒŽŽ› ƒ••‘ ‹ƒ–‡† ™‹–Š ‘•–‡‘’‘”‘•‹•Ǥ  ‘”†‹‰–‘–Š‡‘”Ž† ‡ƒŽ–Š”‰ƒ‹œƒ–‹‘ǡ–Š‡‘•–‡‘’‘”‘•‹•‹•ƒ†‹•‡ƒ•‡ Šƒ”ƒ –‡”‹œ‡†„› Ž‘™ „‘‡ ƒ•• ƒ† ‹ ”‘ƒ” Š‹–‡ –—”ƒŽ †‡–‡”‹‘”ƒ–‹‘ ‘ˆ „‘‡ –‹••—‡ǡ Ž‡ƒ†‹‰ –‘ ‡Šƒ ‡† „‘‡ ˆ”ƒ‰‹Ž‹–› ƒ† ‘•‡“—‡– ‹ ”‡ƒ•‡ ‹ ˆ”ƒ –—”‡ ”‹•Ǥ Š‹• †‹•‡ƒ•‡ ƒˆˆ‡ –• ͹ͷ ‹ŽŽ‹‘ ’‡‘’Ž‡ ‹ –Š‡ ‹–‡† –ƒ–‡•ǡ —”‘’‡ ƒ† ƒ’ƒ ƒ† ‹• –Š‡ ƒ—•‡ ˆ‘” ƒ– Ž‡ƒ•– ͺǤͻ ‹ŽŽ‹‘ ˆ”ƒ –—”‡• ƒ—ƒŽŽ› ™‘”Ž†™‹†‡Ǥ Š‡ ‡•–‹ƒ–‡† Ž‹ˆ‡–‹‡ ”‹• ˆ‘” ‘•–‡‘’‘”‘•‹• ‹• „‡–™‡‡ ͵Ͳ ƒ†ͶͲΨȋ‘”Ž† ‡ƒŽ–Š”‰ƒ‹œƒ–‹‘ʹͲͲͶȌǤ ͳͶ .

(60) –ƒ–‡‘ˆ”–  Š‡ ƒ™ƒ”‡‡•• ƒ„‘—– –Š‡ Š‹‰Š ‘”„‹†‹–› ƒ† ‘”–ƒŽ‹–› ƒ••‘ ‹ƒ–‡† ™‹–Š ‘•–‡‘’‘”‘–‹  ˆ”ƒ –—”‡• Šƒ†‡š‹•–‡†ˆ‘”ƒ››‡ƒ”•Ǥ ‘™‡˜‡”ǡ ’”‡˜‡–‹‘ǡ†‹ƒ‰‘•‹•ǡƒ†–”‡ƒ–‡–‘Ž› ˆ‘—† ”‡ƒŽŽ› ’”‘‰”‡•• ƒˆ–‡” –Š‡ “—ƒ–‹ˆ‹ ƒ–‹‘ ‘ˆ –Š‡ ‘•–‡‘’‘”‘•‹• „› –Š‡ “—ƒ–‹ˆ‹ ƒ–‹‘ ‘ˆ –Š‡„‘‡‹‡”ƒŽ†‡•‹–›ȋȌǤŠ‡‹•—•‡†–‘†‡ˆ‹‡ƒ–Š”‡•Š‘Ž†‘ˆˆ”ƒ –—”‡ǡ™Š‹ Š ‡ƒ• ƒ —–Ǧ‘ˆˆ ˜ƒŽ—‡ ™Š‹ Š ƒ––‡’–• –‘ ƒ’–—”‡ ‘•– ‘ˆ –Š‡ ’ƒ–‹‡–• ™‹–Š ‘•–‡‘’‘”‘–‹  ˆ”ƒ –—”‡•ȋƒ‹•ͳͻͻͶȌǤ ‹ˆˆ‡”‡– ’Šƒ”ƒ ‡—–‹ ƒŽ –”‡ƒ–‡–• Šƒ˜‡ „‡‡ ’”‘’‘•‡† ˆ‘” –Š‡ –”‡ƒ–‡– ‘ˆ –Š‡ ‘•–‡‘’‘”‘•‹•Ǥ‡‘ˆ–Š‡‘•– ‘‘ –”‡ƒ–‡–•‹• „ƒ•‡†‹–Š‡ —•‡ ‘ˆ„‹•’Š‘•’Š‘ƒ–‡ ȋ”‹‘– ‡– ƒŽǤ ʹͲͳͶȌȋ‘—š Ƭ ”‹‘– ʹͲͳͶȌǤ ‘™‡˜‡”ǡ –Š‹• –Š‡•‹• †‘‡• ‘– ˆ‘ —• ‘ –Š‡ ’Šƒ”ƒ ‡—–‹ ƒŽ –”‡ƒ–‡–•ǡ „—– ƒ‹Ž› ‹ –Š‡ †‹ƒ‰‘•‹• ‡–Š‘†• ‹˜‘Ž˜‹‰ „‹‘‡ Šƒ‹ ƒŽ ‡–Š‘†•Ǥ. 1.4 Bone fragility estimation in clinics 1.4.1 Dual-energy x-ray absorptiometry Š‡‡ƒ•—”‡‘ˆ–Š‡‹•†‘‡—•‹‰ƒ—ƒŽǦ‡‡”‰›šǦ”ƒ›ƒ„•‘”’–‹‘‡–”›• ƒȋȌǤ

(61)  –Š‹• • ƒǡ–™‘šǦ”ƒ›„‡ƒ•™‹–Š†‹ˆˆ‡”‡–‡‡”‰›Ž‡˜‡Ž•ƒ”‡ˆ‘ —•‡†ƒ––Š‡’ƒ–‹‡–ǯ•„‘‡•Ǥ Š‡ ƒ„•‘”’–‹‘ †‡’‡†• ƒ– –Š‡ •ƒ‡ –‹‡ ‘ˆ –Š‡ “—ƒ–‹–› ƒ† ƒ–—”‡ ‘ˆ –Š‡ –”ƒ˜‡”•‡† ƒ–‡”‹ƒŽǤ‡‘ˆ–Š‡–™‘‡‡”‰‹‡•™‹ŽŽ„‡ƒ‹Ž›ƒ„•‘”„‡†„›–Š‡•‘ˆ––‹••—‡ǡƒ†–Š‡‘–Š‡” ‘‡„›„‘‡Ǥˆ–‡”•‘ˆ––‹••—‡ƒ„•‘”’–‹‘‹••—„–”ƒ –‡†ǡ–Š‡ ƒ„‡†‡–‡”‹‡†Ǥ•–Š‡ ‹•ƒ‡ƒ•—”‡‹ƒʹ’”‘Œ‡ –‹‘ǡ–Š‡‡ƒ•—”‡‹†‹ ƒ–‡•–Š‡ƒ‘—–‘ˆ‹‡”ƒŽ’‡” •“—ƒ”‡ ‡–‹‡–‡”‘ˆ„‘‡Ǥȋ ‡ƒ–‡–ƒŽǤͳͻͻ͸ǢŽƒ‡Ƭ ‘‰‡ŽƒʹͲͲ͹Ȍ Ž‹‹ ƒŽ’”ƒ –‹ ‡—•‹‰–Š‹•• ƒŠƒ•„‡‡ƒ˜ƒ‹Žƒ„Ž‡•‹ ‡ͳͻͺ͹ƒ†‹–Šƒ•„‡‡—•‡†–‘’”‘˜‡ ‡ˆˆ‡ –‹˜‡‡••‘ˆ†‹ˆˆ‡”‡–’Šƒ”ƒ ‡—–‹ ƒŽ’”‘†— ––‘’”‡˜‡–„‘‡Ž‘••ȋŽƒ‡Ƭ ‘‰‡Žƒ ʹͲͲ͹ȌǤ  ‘”†‹‰ –‘ –Š‡ ‘”Ž† ‡ƒŽ–Š ”‰ƒ‹œƒ–‹‘ǡ ‘•–‡‘’‘”‘•‹• ‹• †‡ˆ‹‡† ƒ• ƒ  –Šƒ– Ž‹‡• „‡–™‡‡ ʹǤͷ •–ƒ†ƒ”† †‡˜‹ƒ–‹‘• ‘” ‘”‡ǡ „‡Ž‘™ –Š‡ ƒ˜‡”ƒ‰‡ ˜ƒŽ—‡ ˆ‘” ›‘—‰ ’‡”•‘ ȋǦ • ‘”‡ ‘ˆδǦʹǤͷȌȋƒ‹•ͳͻͻͶȌǤŠ‹• ˜ƒŽ—‡ƒ’’Ž‹‡•ˆ‘”‡ƒ•—”‡• ‘ •’‹‡ǡŠ‹’ƒ†ˆ‘”‡ƒ”Ǥ  †‡–ƒ‹Ž‡† †‡• ”‹’–‹‘ ‘ˆ Žƒ••‹ˆ‹ ƒ–‹‘ǡ ƒ ‘”†‹‰ –‘ –Š‡ ‘”Ž† ”‰ƒ‹œƒ–‹‘ ‡ˆ‹‹–‹‘ ‹• •Š‘™‹ƒ„Ž‡ͳǦͳȋŽƒ‡Ƭ ‘‰‡ŽƒʹͲͲ͹ȌǤ. . ͳͷ.

(62) –ƒ–‡‘ˆ”–  Terminology. T-score definition. Normal. T ш -1.0. Osteopenia. -2.5 < T < -1.0. Osteoporosis. Tч -2.5. Established osteoporosis. Tч -2.5 with presence of one or more fragility fracture. Table 1-1ǣŠ‡‘”Ž† ‡ƒŽ–Š”‰ƒ‹œƒ–‹‘†‡ˆ‹‹–‹‘•‘ˆ‘•–‡‘’‘”‘•‹•ƒ†‘•–‡‘’‡‹ƒǡ—•‡†–‘‹–‡”’”‡– • ƒ•‹’‘•–‡‘’ƒ—•ƒŽ™‘‡Ǥȋƒ‹•ͳͻͻͶȌǤ. Š‡ Ǧ• ‘”‡ ‹• ƒŽ —Žƒ–‡† —•‹‰ –Š‡ “—ƒ–‹‘ ͳǦͳǤ

(63) – ‡•–‹ƒ–‡• –Š‡ †‹ˆˆ‡”‡ ‡ „‡–™‡‡ –Š‡ ‡ƒ•—”‡ ‘ˆ  ‹ ƒ ’ƒ–‹‡– ƒ† –Š‡ ‡ƒ  ‹ ƒ Š‡ƒŽ–Š› ›‘—‰ ’‘’—Žƒ–‹‘ǡ ƒ† ‹• ‡š’”‡••‡†ƒ•ƒ•–ƒ†ƒ”††‡˜‹ƒ–‹‘Ǥ Ǧ• ‘”‡ ൌ. ‡ƒ•—”‡† െ ‘—‰ƒ†—Ž–‡ƒ  ‘—‰ƒ†—Ž–’‘’—Žƒ–‹‘ Equation 1-1ǣǦ ‘”‡‡•–‹ƒ–‹‘Ǥ.  ‡šƒ’Ž‡ ‘ˆ ƒ  –‡•– ”‡’‘”– ˆ‘” ƒ ˆ‘”‡ƒ” ‹• ’”‡•‡–‡† ‹ ‹‰—”‡ ͳǦ͸Ǥ Š‡ ˜ƒŽ—‡ ‡ƒ•—”‡†‘ˆ‹• ‘’ƒ”‡†™‹–Š†ƒ–ƒ‘ˆƒ•’‡ ‹ˆ‹ ’‘’—Žƒ–‹‘Ǥ. ͳ͸ .

(64) –ƒ–‡‘ˆ”– .  Figure 1-6ǣšƒ’Ž‡‘ˆƒˆ‘”‡ƒ”‡’‘”–ǤRenée Newman, ‘avoidboneloss.com’ . ‡˜‡”–Š‡Ž‡••ǡ–Š‡’”‡•‡–••‘‡’”‘„Ž‡•ˆ‘”–Š‡†‡–‡ –‹‘‘ˆ‹†‹˜‹†—ƒŽ™‹–ŠŠ‹‰Š”‹• ‘ˆ ˆ”ƒ –—”‡Ǥ

(65) †‡‡†ǡ  Šƒ˜‡ „‡‡ ”‡’‘”–‡† ƒ• ƒ –‡•– ™‹–Š ƒ Š‹‰Š •’‡ ‹ˆ‹ ‹–›ǡ „—– Ž‘™ •‡•‹–‹˜‹–›ȋƒ‹•ͳͻͻͶȌǤŠ—•ǡ™Š‡‘•–‡‘’‘”‘•‹•‹•†‡–‡ –‡†ǡ–Š‡’”‡†‹ –‹‘‘ˆ–Š‡”‹•‘ˆ ˆ”ƒ –—”‡‹•Š‹‰Šǡ„—–‹ˆ–Š‡‡ƒ•—”‡‘ˆ‹•‘”ƒŽǡ–Š‹•’”‡†‹ –‹‘”‡ƒ‹•— ‡”–ƒ‹Ǥ

(66) – Šƒ• „‡‡ •Š‘™ –Šƒ–ǡ ͷͲΨ ‘ˆ ˆ”ƒ –—”‡• ƒ”‡ ’”‡•‡–‡† ‹ ’ƒ–‹‡– †‹ƒ‰‘•‡† ƒ• ‘Ǧ ‘•–‡‘’‘”‘–‹ „›ȋ‹”‹•‡–ƒŽǤʹͲͲͶȌ 1.4.2 Computed tomography scan Š‡‘’—–‡†–‘‘‰”ƒ’Š›ȋǦ• ƒȌ‹•‘–ƒ•–ƒ†ƒ”†‹œ‡†‡–Š‘†—•‡†‹ Ž‹‹ ƒŽ’”ƒ –‹ ‡ ˆ‘” –Š‡ ƒ••‡••‡– ‘ˆ „‘‡ ˆ”ƒ‰‹Ž‹–›Ǥ ‡˜‡”–Š‡Ž‡••ǡ ‹– ‹• ˆ”‡“—‡–Ž› —•‡† –‘ ‡˜ƒŽ—ƒ–‡ –Š‡ ‘’Ž‹ ƒ–‹‘•ƒ••‘ ‹ƒ–‡†™‹–ŠƒŒ‘”ˆ”ƒ –—”‡•Ǥ–Š‡‘–Š‡”Šƒ†ǡ• ƒ‡”‹ƒ‰‹‰‹•ƒ˜‡”› ‘‘ •‘—” ‡‘ˆ†ƒ–ƒ –‘†‡˜‡Ž‘’ †‹ˆˆ‡”‡– ‘†‡Ž•–‘’”‡†‹ –„‘‡ •–”‡‰–Šȋ—„ Šƒ’–‡” ͳǤͷǤ͸ȌǤ Š‡ Ǧ• ƒ —•‡• ƒ ‘’—–‡”Ǧ’”‘ ‡‡†‡† ‘„‹ƒ–‹‘ ‘ˆ ƒ •‡”‹‡• ‘ˆ Ǧ”ƒ› ‹ƒ‰‡•ǡ –ƒ‡ ˆ”‘ †‹ˆˆ‡”‡– ƒ‰Ž‡•ǡ –‘ ’”‘†— ‡ ”‘•• •‡ –‹‘ƒŽ ‹ƒ‰‡• ‘ˆ ƒ •’‡ ‹ˆ‹  ƒ”‡ƒǤ Š‡  • ƒ. . ͳ͹.

(67) –ƒ–‡‘ˆ”–  ‰‡‡”ƒ–‡•ƒ˜‘Ž—‡‘ˆ†ƒ–ƒ–Šƒ– ƒ„‡ƒ‹’—Žƒ–‡†–‘†‡–‡ –†‹ˆˆ‡”‡–„‘†›•–”— –—”‡•Ǥ ‡šƒ’Ž‡‘ˆƒǦ• ƒƒ†ƒ ”‘••Ǧ•‡ –‹‘ƒŽƒ “—‹•‹–‹‘ȋ ‹‰—”‡ͳǦ͹Ȍ.  Figure 1-7ǣǦ ƒŠ‹ŽŽ‹’•‹‰‡—‹–›ƒ†‘‡ƒ “—‹•‹–‹‘‡šƒ’Ž‡‘ˆ–Š‡†‹•–ƒŽ”ƒ†‹—•  ȋAcquisition from the manufacturer – ‘healthcare.philips.com’ȌǤ. ‡ ‘ˆ –Š‡ ƒ†˜ƒ–ƒ‰‡• ‘ˆ –Š‡ Ǧ• ƒ ‘˜‡” ƒ –”ƒ†‹–‹‘ƒŽ Ǧ”ƒ› ”ƒ†‹‘‰”ƒ’Š› ‹• –Šƒ– –Š‡ Ǧ • ƒ‡Ž‹‹ƒ–‡•–Š‡•—’‡”’‘•‹–‹‘‘ˆ‹ƒ‰‡•‘ˆ•–”— –—”‡•‘—–•‹†‡–Š‡ƒ”‡ƒ‘ˆ‹–‡”‡•–ǤŽ•‘ǡ –Š‡ Ǧ ƒ’”‡•‡–•ƒ ‹Š‡”‡– Š‹‰ŠǦ ‘–”ƒ•– ”‡•‘Ž—–‹‘ǡ™Š‹ Š‹•—•‡ˆ—Ž–‘†‹ˆˆ‡”‡–‹ƒ–‡ –‹••—‡„›‹–•†‡•‹–›Ǥ Š‡ ƒ “—‹”‡† •–ƒ  ‘ˆ ‹ƒ‰‡• ƒ „‡ ƒƒŽ›œ‡† ‹ –Š‡ ͵ ƒ‹• ƒƒ–‘‹ ƒŽ ’Žƒ‡•ǣ š‹ƒŽǡ •ƒ‰‹––ƒŽƒ†–”ƒ•˜‡”•‡ǡ„—–ƒŽ•‘ǡ‘‘„Ž‹“—‡’Žƒ‡•™Š‡†‡ˆ‹‡†„›–Š‡—•‡”Ǥ 1.4.3 The. High. Resolution. peripheral. Quantitative. Computed. Tomography Š‡ ‹‰Š ‡•‘Ž—–‹‘ ’‡”‹’Š‡”ƒŽ —ƒ–‹–ƒ–‹˜‡ ‘’—–‡† ‘‘‰”ƒ’Š› ȋ Ǧ’Ȍ ȋ ‹‰—”‡ ͳǦͺȌ ‡˜ƒŽ—ƒ–‡• „‘‡ ƒ” Š‹–‡ –—”‡ ƒ† ‰‹˜‡• ƒ ”ƒ‰‡ ‘ˆ „‘‡ ‹‡”ƒŽ †‡•‹–› ‘ˆ –Š‡ „‘‡ ȋ‹‡–„‡”‰‡‡–ƒŽǤͳͻͻͷȌȋ ‹‰—”‡ͳǦͻȌǤ

(68) –Šƒ•„‡‡—•‡†ˆ‘” Ž‹‹ ƒŽ”‡•‡ƒ” Š–”‹ƒŽ•ǡ„—–‹–•—•‡ ƒ•ƒ Ž‹‹ ƒŽ†‹ƒ‰‘•–‹ ‡–Š‘†‹•‘–‹’Ž‡‡–‡†Ǥ. ͳͺ .

(69) –ƒ–‡‘ˆ”– .  Figure 1-8ǣ–”‡‡ǣ ‹‰Š‡•‘Ž—–‹‘’‡”‹’Š‡”ƒŽ—ƒ–‹–ƒ–‹˜‡‘’—–‡†‘‘‰”ƒ’Š› Ǧ’ǡ„› ȋò”‹ Šǡ™‹–œ‡”Žƒ†Ȍ.  Figure 1-9ǣšƒ’Ž‡‘ˆƒ Ǧ’ƒƒŽ›•‹•”‡•—Ž–ˆ‘”ƒ”ƒ†‹—•ǡ•Š‘™‹‰†‡•‹–›ƒƒ” Š‹–‡ –—”‡‡ƒ•—”‡•Ǥ. In vivoǡ –Š‹• • ƒ‡” ‡˜ƒŽ—ƒ–‡• ’‡”‹’Š‡”ƒŽ •‹–‡• ȋ†‹•–ƒŽ ”ƒ†‹—• ƒ† †‹•–ƒŽ –‹„‹ƒȌǤ

(70) – Šƒ• –™‘Ǧ †‹‡•‹‘ƒŽ†‡–‡ –‘”ȋͳͷ͵͸ȗͳʹ͹Ȍ’‹š‡Ž•‘ˆͺʹ‹ ”‘•ǡ™Š‹ Šˆƒ ‡•ƒǦ”ƒ›–—„‡ȋ ‘‹ ƒŽ „‡ƒǡ ͸ͲǡͻͲͲɊǡ•’‘–•‹œ‡ ƒ––Š‡ ˆ‘ ƒŽ’‘‹–ǣͺͲ‹ ”‘•ȌǤ

(71) – ƒŽŽ‘™•–Š‡ •‹—Ž–ƒ‡‘—• ƒ “—‹•‹–‹‘ ‘ˆ ͳͳͲ ’ƒ”ƒŽŽ‡Ž •Ž‹ ‡• ‘ˆ ͺʹ ‹ ”‘• ‹ ͵ ‹—–‡•ǡ ™Š‹ Š ‘””‡•’‘†• –‘ ƒ ”‡ ‘•–”— –‹‘‘ˆͻ–Š‹ ǤŠ‡ƒ –—ƒŽ‹””ƒ†‹ƒ–‹‘‹•˜‡”›Ž‘™ƒ†ƒ‘—–‡†–‘͵Ɋ˜’‡” ‡šƒ‹ƒ–‹‘ǤŠ‡͵†ƒ–ƒ•‡–’”‘˜‹†‡†„›–Š‡ Ǧ’ƒŽŽ‘™•–Š‡•‡’ƒ”ƒ–‹‘‘ˆƒƒŽ›•‡•‘ˆ –”ƒ„‡ —Žƒ”ƒ† ‘”–‹ ƒŽ„‘‡ƒ–’‡”‹’Š‡”ƒŽ•‹–‡•ȋ‹Žƒ›’Š‹‘—ʹͲͳʹȌǤ. . ͳͻ.

(72) –ƒ–‡‘ˆ”–  ‡ƒ•—”‡‡–• ƒ”‡ ’‡”ˆ‘”‡† ‹ –Š‡ ‘Ǧ†‘‹ƒ– ‡„‡” „‡‹‰ ‹•‡”–‡† ‹–‘ ƒ ƒ”„‘ ˆ‹„‡”•Š‡ŽŽ–‘ƒ‹–ƒ‹–Š‡ ’‘•‹–‹‘ ‹•‹†‡ –Š‡• ƒ‡”Ǥ• ‘—–˜‹‡™‹•’‡”ˆ‘”‡†’”‹‘”–‘ ƒ—ƒŽŽ›•‡–ƒ”‡ˆ‡”‡ ‡Ž‹‡ƒ––Š‡’Žƒ–‡ƒ—‘ˆ–Š‡†‹•–ƒŽ”ƒ†‹—•‘”–‹„‹ƒǤŠ‡‡ƒ•—”‡‡– ƒ”‡ƒ ‹• Ž‘ ƒ–‡† ͻǤͷ  ƒ† ʹʹǤͷ  ’”‘š‹ƒŽ –‘ –Š‡ ”‡ˆ‡”‡ ‡ Ž‹‡ ˆ‘” ”ƒ†‹—• ƒ† –‹„‹ƒǡ ”‡•’‡ –‹˜‡Ž›Ǥ 1.4.4 The FRAX Š—•ǡˆ‘”–Š‡’ƒ•–›‡ƒ”•ǡ‘‡‘ˆ–Š‡ƒ‹ ‘ ‡”•‹–Š‡ˆ‹‡Ž†Šƒ•„‡‡–Š‡†‡–‡”‹ƒ–‹‘‘ˆ ‘–Š‡”•ˆƒ –‘”• ‘–”‹„—–‹‰–‘’”‡†‹ ––Š‡ˆ”ƒ –—”‡”‹•Ǥ

(73) ‘”†‡”–‘†‡–‡”‹‡–Š‘•‡ǡ‡–ƒǦ ƒƒŽ›•‹• •–—†‹‡• Šƒ˜‡ „‡‡ ‹’Ž‡‡–‡† —•‹‰ ͳʹ ’”‘•’‡ –‹˜‡Ž› •–—†‹‡† ’‘’—Žƒ–‹‘Ǧ„ƒ•‡† ‘Š‘”–• ˆ”‘ •‡˜‡”ƒŽ ‰‡‘‰”ƒ’Š‹  –‡””‹–‘”‹‡•Ǥ ‘‡ ‘ˆ –Š‡ ƒ”‡ –Š‡ ƒ‰‡ǡ –Š‡ •‡šǡ –Š‡ „‘‡ –—”‘˜‡”ǡŽ‹ˆ‡•–›Ž‡ƒ†ˆƒ‹Ž›Š‹•–‘”›Ǥˆ–‡”–Š‹•”‹‰‘”‘—•ƒƒŽ›•‹•ǡ‘˜‡”‘”‡–ŠƒʹͷͲͲͲͲ ’ƒ–‹‡–•ǡ ƒ ƒŽ‰‘”‹–Š ‘ˆ ˆ”ƒ –—”‡ ”‹• Šƒ˜‡ „‡‡ ‡•–ƒ„Ž‹•Š‡† ƒ† ‘†‡•‡† ‹ ƒ •—”˜‡› ƒŽŽ‡† ǤŠ‡ ‡•–‹ƒ–‡•ˆ”ƒ –—”‡”‹•‘˜‡”ͳͲ›‡ƒ”•ǤŠ‡”‹•ˆƒ –‘”•ƒ”‡ȋƒ‹•‡– ƒŽǤʹͲͲͺȌǣ‰‡ǡ‡šǡ‡‹‰Š–ǡ ‡‹‰Š–ǡ”‡˜‹‘—•ˆ”ƒ –—”‡ǡƒ”‡–ˆ”ƒ –—”‡†Š‹’ȋ–Š‹•‡“—‹”‡•ˆ‘” ƒŠ‹•–‘”›‘ˆŠ‹’ˆ”ƒ –—”‡‹–Š‡’ƒ–‹‡–̵•‘–Š‡”‘”ˆƒ–Š‡”Ȍǡ—””‡–•‘‹‰ǡ Ž— ‘ ‘”–‹ ‘‹†• ȋ —””‡–Ž› ‡š’‘•—”‡ –‘ ‘”ƒŽ ‰Ž— ‘ ‘”–‹ ‘‹†•Ȍǡ Š‡—ƒ–‘‹† ƒ”–Š”‹–‹• ȋ ‘ˆ‹”‡† †‹ƒ‰‘•‹•Ȍǡ ‡ ‘†ƒ”› ‘•–‡‘’‘”‘•‹• ȋ•–”‘‰ †‹•‘”†‡”• ƒ••‘ ‹ƒ–‡† ™‹–Š ‘•–‡‘’‘”‘•‹•ǣ †‹ƒ„‡–‡• –›’‡

(74)  ‘•–‡‘‰‡‡•‹•‹’‡”ˆ‡ –ƒ‹ƒ†—Ž–•ǡ—–”‡ƒ–‡†Ž‘‰Ǧ•–ƒ†‹‰Š›’‡”–Š›”‘‹†‹•ǡŠ›’‘‰‘ƒ†‹• ‘” ’”‡ƒ–—”‡ ‡‘’ƒ—•‡ǡ Š”‘‹  ƒŽ—–”‹–‹‘ǡ ‘” ƒŽƒ„•‘”’–‹‘ ƒ† Š”‘‹  Ž‹˜‡” †‹•‡ƒ•‡ȌǡŽ ‘Š‘Ž‹•ƒ†‘‡‹‡”ƒŽ‡•‹–›ȋ ‹‰—”‡ͳǦͳͲȌǤ. ʹͲ .

(75) –ƒ–‡‘ˆ”– .  Figure 1-10ǣ ǡƒ•’”‡•‡–‡†‹–Š‡™‡„ ƒŽ —Žƒ–‹‘–‘‘ŽǤ Š––’•ǣȀȀ™™™Ǥ•Š‡ˆǤƒ Ǥ—Ȁ Ȁ–‘‘ŽǤƒ•’šǫŽƒ‰α‡. †‹†‘– ‘•‹†‡” –Š‡ ˆƒŽŽƒ• ƒ ”‹•ˆƒ –‘”Ǥ Š‡”‡ ‹•‘‡š–‡”ƒŽ‡ Šƒ‹ ƒŽ ‹ˆŽ—‡ ‡• ‘•‹†‡”‡†‹–‘–Š‡ƒŽ‰‘”‹–ŠǤŠ—•ǡ  ƒ†‘ƒ••—’–‹‘ƒ„‘—––Š‡ˆ”ƒ –—”‡”‹•„ƒ•‡† ‘‹–”‹•‹ ’”‘’‡”–‹‡•ǡ„—–™‹ŽŽ‘–ƒ••‡••–Š‡”‹•‘ˆˆ”ƒ –—”‡‹ƒˆƒŽŽ ƒ•‡ǡˆ‘”‡šƒ’Ž‡Ǥ 1.4.5 Distal radius fractures description and classification ƒ†‹—•ˆ”ƒ –—”‡•Šƒ˜‡„‡‡†‡• ”‹„‡†„›‘—–‡ƒ—•‹ ‡ͳ͹ͺ͵ȋ‡ŽŽ‘–‹‡–ƒŽǤʹͲͳ͵ȌǤŠ‡–Š‡ †‡• ”‹’–‹‘ ‘ˆ ƒŽ‘•– ƒŽŽ ‹† ‘ˆ ˆ”ƒ –—”‡• ™ƒ• †‘‡ǡ ƒ—–Š‘”• Šƒ˜‡ –”‹‡† –‘ Žƒ••‹ˆ› –Š‡ ˆ”ƒ –—”‡• ‹ ‘”†‡” –‘ †‡–‡”‹‡ –Š‡ ‘’Ž‡š‹–› ‘ˆ –Š‡ Ž‡•‹‘• ƒ† –Š‡‹” –”‡ƒ–‡–Ǥ ‡”ƒ†‡œŠƒ•’”‡•‡–‡†ƒ†‡–ƒ‹Ž‡††‡• ”‹’–‹‘‘ˆ–Š‡‡˜‘Ž—–‹‘‘ˆ–Š‹• Žƒ••‹ˆ‹ ƒ–‹‘ƒ†Š‡ ’”‘’‘•‡† –Š‡‹” ‘™ Žƒ••‹ˆ‹ ƒ–‹‘ǡ ™Š‹ Š ‹• ‘”‡ ‡ Šƒ‹ ƒŽŽ› ”‡Žƒ–‡† ȋ ‡”ƒ†‡œ ʹͲͲͳȌǤ ‡ˆ‘”‡™‡‰‡––‘–Š‡ Žƒ••‹ˆ‹ ƒ–‹‘ǡ‹–‹•‡‡†‡†–‘‡š’Žƒ‹–Š‡–”ƒ†‹–‹‘ƒŽ†‡• ”‹’–‹‘‘ˆ–Š‡ ˆ”ƒ –—”‡•Ǥ Š‹• Šƒ˜‡ „‡‡ ™‡ŽŽ ”‡•—‡† „› ‡‰ƒ”‡ ƒ† ”‡••™‡ŽŽ ȋ‡‰ƒ”‡ Ƭ ”‡••™‡ŽŽ ʹͲͳ͵Ȍǣ Colles’ fracture:š–”ƒǦƒ”–‹ —Žƒ”†‹•–ƒŽ”ƒ†‹—•ˆ”ƒ –—”‡™‹–Š†‘”•ƒŽ ‘‹—–‹‘ǡƒ‰—Žƒ–‹‘ǡ †‹•’Žƒ ‡‡–ǡ”ƒ†‹ƒŽ•Š‘”–‡‹‰ƒ†•—’‹ƒ–‹‘Ǥ Smith’s fracture:‹•–ƒŽ”ƒ†‹—•ˆ”ƒ –—”‡™‹–Š˜‘Žƒ”†‹•’Žƒ ‡‡–. . ʹͳ.

(76) –ƒ–‡‘ˆ”–  Barton’s fracture: ‹•’Žƒ ‡†ǡ —•–ƒ„Ž‡ ƒ”–‹ —Žƒ” ˆ”ƒ –—”‡• —„Ž—šƒ–‹‘ ‘ˆ –Š‡ †‹•–ƒŽ ”ƒ†‹—• ™‹–Š†‹•’Žƒ ‡‡– ‘ˆ–Š‡ ƒ”’—•ƒŽ‘‰™‹–Š–Š‡ƒ”–‹ —Žƒ”ˆ”ƒ –—”‡ˆ”ƒ‰‡–ǤŠ‡•‡ƒ›„‡ ‡‹–Š‡”†‘”•ƒŽ‘”˜‘Žƒ” Chauffeur’s fracture: ”ƒ –—”‡‘ˆ–Š‡”ƒ†‹ƒŽ•–›Ž‘‹†Ǥƒ›„‡ƒ••‘ ‹ƒ–‡†™‹–Š†‹•’Žƒ ‡‡– ‘ˆ–Š‡ ƒ”’—•ƒ†ƒ›„‡–Š‡‘Ž›„‘› ‘’‘‡–‘ˆ’‡”‹Ž—ƒ–‡‹Œ—”›Ǥ Die-punch fracture:

(77) –”ƒƒ”–‹ —Žƒ” ˆ”ƒ –—”‡ ™‹–Š †‡’”‡••‹‘ ‘ˆ –Š‡ †‘”•ƒŽ ƒ•’‡ – ‘ˆ –Š‡ Ž—ƒ–‡ˆ‘••ƒǤ Š‡’”‘„Ž‡™‹–Š–Š‹• Žƒ••‹ˆ‹ ƒ–‹‘Šƒ’’‡•’”‹ ‹’ƒŽŽ›™Š‡ƒ‹–”ƒǦƒ”–‹ —Žƒ”†‹•”—’–‹‘ ‹•‹•†‹ƒ‰‘•‡†Ǥ ‘”‡šƒ’Ž‡ǡ‹–Š‡ ƒ•‡‘ˆƒ•Ž‹‰Š–†‹‡’— Šˆ”ƒ –—”‡ǡ–Šƒ– ƒ„‡•‹’Ž› †‹ƒ‰‘•‡† ƒ• ƒ ‘ŽŽ‡•ǯ ˆ”ƒ –—”‡Ǥ Š‡ǡ ”‡•‡ƒ” Š‡”• Šƒ˜‡ ’”‘’‘•‡† –‘ —•‡ †‹ˆˆ‡”‡– Žƒ••‹ˆ‹ ƒ–‹‘• ™Š‹ Šǡ ‹ •‘‡ ƒ•‡•ǡ †‡‘–‡ ƒ ™‹†‡ •’‡ –”— ‘ˆ ˆ”ƒ –—”‡•ǡ —•‹‰ ƒ ƒŽ’ŠƒǦ —‡”‹ ƒŽ•›•–‡ȋ ‡”ƒ†‡œʹͲͲͳȌȋƒ—Žƒ‡–ƒŽǤʹͲͲ͹ȌǤ ‡˜‡”–Š‡Ž‡••ǡ‘•–‘ˆ–Š‘•‡ Žƒ••‹ˆ‹ ƒ–‹‘•–‡†–‘„‡ƒƒ–‘‹ ƒŽ†‡• ”‹’–‹‘•Ǥ

(78) –Š‹•™‘”ǡ ™‡ƒ”‡‹–‡”‡•–‡†ƒŽ•‘‹ƒ†‡• ”‹’–‹‘™Š‹ Š‡’Šƒ•‹œ‡•†‹•–ƒŽ”ƒ†‹—•ˆ”ƒ –—”‡ƒ ‘”†‹‰–‘ –Š‡‹” „‹‘‡ Šƒ‹ •Ǥ Š‹• ™ƒ• –Š‡ ™‘” †‘‡ „› —’‹–‡” ƒ† ‡”ƒ†‡œǡ ™Š‘ —•‡† ƒ „‹‘‡ Šƒ‹ ƒŽ †‡• ”‹’–‹‘ ‘ˆ –Š‡ ˆ”ƒ –—”‡• ‹ ‘”†‡” –‘ ‰‡– ƒ Žƒ••‹ˆ‹ ƒ–‹‘ ™Š‹ Š ’”‡†‹ –• •–ƒ„‹Ž‹–› ‘ˆ –Š‡ ˆ”ƒ –—”‡ ƒ† ‰‹˜‹‰ ”‡ ‘‡†ƒ–‹‘• ˆ‘” –Š‡ –”‡ƒ–‡–• ȋ —’‹–‡” Ƭ ‡”ƒ†‡œͳͻͻ͹Ȍȋ‡ŽŽ‘–‹‡–ƒŽǤʹͲͳ͵ȌǤ‡–ƒ‹Ž• ƒ„‡•‡‡‹ƒ„Ž‡ͳǦʹǤ. ʹʹ .

(79) –ƒ–‡‘ˆ”– .  Table 1-2ǣ ”ƒ –—”‡ Žƒ••‹ˆ‹ ƒ–‹‘‘ˆ–Š‡”ƒ†‹—•„› ‡”ƒ†‡œȋ ‡”ƒ†‡œʹͲͲͳȌǤ. 1.5 Bone fragility estimation in research Š‹• •—„ Šƒ’–‡” ’”‡•‡–• –Š‡ †‡ˆ‹‹–‹‘• ƒ† ‡–Š‘†‘Ž‘‰‹‡• ”‡Žƒ–‡† –‘ –Š‡ ”‡ƒ–‹‘ ‘ˆ ‘†‡Ž• ˆ‘” ƒ••‡••‹‰ „‘‡ ˆ”ƒ‰‹Ž‹–›Ǥ ‡ ’”‡•‡–‡† ‘ –Š‹• •—„ Šƒ’–‡” †‹ˆˆ‡”‡– ‘†‡Ž• ’”‡•‡–‡†‹Ž‹–‡”ƒ–—”‡Ǥ 1.5.1 Mechanical Definitions Š‡ Stress ‹• –Š‡ ”ƒ–‹‘ „‡–™‡‡ –Š‡ ƒ’’Ž‹‡† ˆ‘” ‡ ƒ† –Š‡ ”‘•• •‡ –‹‘ƒŽ ƒ”‡ƒ ™Š‡”‡ –Š‡ ˆ‘” ‡ ‹• ƒ’’Ž‹‡†Ǥ Š‡ Strain ‹• –Š‡ ”ƒ–‹‘ ‘ˆ Šƒ‰‡ ‹ †‹‡•‹‘ –‘ –Š‡ ‘”‹‰‹ƒŽ †‹‡•‹‘Ǥ Š‡”ƒ–‹‘„‡–™‡‡–‡•‹Ž‡•–”‡••ƒ†–‡•‹Ž‡•–”ƒ‹‹• ƒŽŽ‡†–Š‡Young’s modulus‘”‡Žƒ•–‹  ‘†—Ž—•Ǥ. . ʹ͵.

(80) –ƒ–‡‘ˆ”–  Š‡ strength ‘ˆ ƒ ƒ–‡”‹ƒŽ ‹• †‡ˆ‹‡† ƒ• –Š‡ ƒ„‹Ž‹–› ‘ˆ ƒ ƒ–‡”‹ƒŽ –‘ •—•–ƒ‹ Ž‘ƒ†•Ǥ Š‡ •–”‘‰‡”–Š‡ƒ–‡”‹ƒŽǡ–Š‡‰”‡ƒ–‡”–Š‡Ž‘ƒ†‹– ƒ™‹–Š•–ƒ†Ǥ‘‹–‹•–Š‡ƒ„‹Ž‹–›‘ˆ–Š‡ƒ–‡”‹ƒŽ –‘™‹–Š•–ƒ†•–”‡••™‹–Š‘—–ˆƒ‹Ž—”‡Ǥ Š‡ Poisson ratio ‹• –Š‡ ”ƒ–‹‘ „‡–™‡‡ –Š‡ –”ƒ•˜‡”•‡ ‘–”ƒ –‹‘ •–”ƒ‹ ƒ† –Š‡ Ž‘‰‹–—†‹ƒŽ‡š–‡•‹‘•–”ƒ‹Ǥ.  Figure 1-11ǣ‡ Šƒ‹ ƒŽ†‡ˆ‹‹–‹‘•ǤIllustration: van Rietbergen, CISM summer course 2013.. Š‡failure load ‹•–Š‡ˆ‘” ‡‡‡†‡†–‘”‡ƒ Š–Š‡ˆ”ƒ –—”‡‘ˆƒƒ–‡”‹ƒŽǤ 1.5.2 Bone Imaging Š‡ Žƒ••‹  ’”‘ ‡†—”‡ –‘ †‡†— ‡ –Š‡ ‡ Šƒ‹ ƒŽ ’”‘’‡”–‹‡• –Šƒ– ™‹ŽŽ „‡ —•‡† ‹ ƒ „‘‡ ‘†‡Ž‹•–‘—•‡–Š‡†ƒ–ƒˆ”‘ƒ• ƒ‡”Ǥ ‹”•–ǡ–Š‡grey levels ȋ ‘—•ˆ‹‡Ž†—‹–•ΪͳͲͲͲȌ ‡ƒ•—”‡†„›–Š‡• ƒ‡”ƒ”‡—•‡†–‘†‡†— ‡–Š‡ ›†”‘š›ƒ’ƒ–‹–‡†‡•‹–›‘ˆ‡ƒ Š˜‘š‡Ž‘ˆ–Š‡ •ƒ’Ž‡ǤŠ‡ǡ–Š‡ †‡•‹–›‘ˆŠ›†”‘š›ƒ’ƒ–‹–‡ ‹• —•‡†–‘†‡†— ‡–Š‡ ƒ’’ƒ”‡–†‡•‹–›•‹‰ –Š‹•˜ƒŽ—‡ȋ Š‹Ž‡‘‡–ƒŽǤʹͲͲͺȌǡ‹–‹•’‘••‹„Ž‡–‘†‡†— ‡ƒƒ’’”‘š‹ƒ–‡˜ƒŽ—‡ˆ‘”–Š‡‘—‰ǯ• ‘†—Ž—•Ǥ

(81) – ‹• ‹’‘”–ƒ––‘‘™–Šƒ––Š‡ ‡ƒ•—”‡†˜ƒŽ—‡† ‘ˆ‰”‡›Ž‡˜‡Ž• ‹ƒ ƒ”‡‹ˆŽ—‡ ‡†„› •‘‡ ‹ƒ‰‡ ƒ”–‹ˆƒ –•ǡ ƒ• „‡ƒ Šƒ”†‡‹‰ǡ •‘ǡ –Š‹• –‡ Š‹“—‡ ƒ ‰‹˜‡ ‘Ž› ƒ “—ƒŽ‹–ƒ–‹˜‡ ʹͶ .

Figure

Figure 1-2ǣ‘‰„‘‡•–”—…–—”‡•Ǥ Ilustration: Pearson Education, Inc., publishing as Pearson Benjamin Cummings
Figure 1-4ǣ‘‡•‹–Š‡—’’‡”Ž‹„Ǥ Illustration: Gray’s anatomy for student, 2nd Edition. ȋ”ƒ‡‡–ƒŽǤʹͲͳͶȌ
Figure 1-5 : ƒ–‘›‘ˆ–Š‡”ƒ†‹—•ǤIllustration: Gray’s anatomy for student, 2nd Edition
Table 1-1ǣŠ‡‘”Ž†‡ƒŽ–Š”‰ƒ‹œƒ–‹‘†‡ˆ‹‹–‹‘•‘ˆ‘•–‡‘’‘”‘•‹•ƒ†‘•–‡‘’‡‹ƒǡ—•‡†–‘‹–‡”’”‡– •…ƒ•‹’‘•–‡‘’ƒ—•ƒŽ™‘‡Ǥȋƒ‹•ͳͻͻͶȌǤ Š‡ Ǧ•…‘”‡ ‹• …ƒŽ…—Žƒ–‡† —•‹‰ –Š‡ “—ƒ–‹‘ ͳǦͳǤ – ‡•–‹ƒ–‡• –Š‡ †‹ˆˆ‡”‡…‡ „‡–™‡‡ –Š‡ ‡ƒ•—”‡ ‘ˆ ‹ ƒ ’ƒ–‹‡– ƒ† –Š‡ ‡ƒ ‹ ƒ
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