Modeling bone regeneration around endosseous implants

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Dit proefschrift is goedgekeurd door de promotor:Prof.dr.ir. C. VuikCopromotor Dr.ir. F.J. VermolenSamenstelling promotiecommissie:Rector Magnificus,Prof.dr.ir. C. Vuik,Dr.ir. F.J. Vermolen,Prof.Dr. J.M. García-Aznar,Prof.Dr. M.A. Zhuravkov,Prof.dr.ir. H.H. Weinans,Dr. A. Madzvamuse,Dr. L. Geris,Prof.dr.ir. C.W. Oosterlee,voorzitterTechnische Universiteit Delft, promotorTechnische Universiteit Delft, copromotorUniversidad de ZaragozaBelarusian State UniversityTechnische Universiteit DelftUniversity of SussexKatholieke Universiteit LeuvenTechnische Universiteit Delft, reservelidModeling bone regeneration around endosseous implants.Dissertation at Delft University of Technology.Copyright c○ 2012 by P.A. ProkharauThe work described in this thesis was financially supported by the DelftInstitute of Applied Mathematics (DIAM) of the Delft University of Technology.ISBN 978-94-6203-171-5Cover design by Maxim Molokov and Pavel Prokharau. Painting by MaryjaProkharava.Printed in the Netherlands by Wöhrmann Print Service.
to my parents, Masha and Paulinka
Page 1: Modeling bone regeneration around e
Page 6 and 7: viSummaryentiate into other cell ph
Page 9 and 10: SamenvattingModelleren van botregen
Page 13 and 14: CONTENTSSummarySamenvattingvix1 Int
Page 15: CONTENTSxv5.3.7 Treatment of the re
Page 18 and 19: 2 Chapter 1. IntroductionNecrotic p
Page 20 and 21: 4 Chapter 1. Introductionorganisms.
Page 22 and 23: 6 Chapter 1. Introductionenhances f
Page 24 and 25: 8 Chapter 1. IntroductionGómez-Ben
Page 26 and 27: 10 Chapter 1. Introductionstability
Page 28: 12 Chapter 1. Introductionand bioch
Page 31 and 32: 2.2. Biological model 15this chapte
Page 35 and 36: 2.3. Stability analysis 19The equat
Page 37 and 38: 2.3. Stability analysis 21χ = α m
Page 39 and 40: 2.3. Stability analysis 23Let us de
Page 41 and 42: 2.3. Stability analysis 25Remark 2.
Page 43 and 44: 2.3. Stability analysis 27where⎛
Page 45 and 46: 2.3. Stability analysis 29Lemma 2.1
Page 47 and 48: 2.3. Stability analysis 31Since k n
Page 49 and 50: 2.3. Stability analysis 332.3.4 Cor
Page 51 and 52: 2.3. Stability analysis 35The other
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2.3. Stability analysis 37polynomia
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2.3. Stability analysis 39This cond
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2.4. Numerical results 41or in the
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2.4. Numerical results 43but such t
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2.5. Conclusions 45ical simulations
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48 Chapter 3. Evolutionary cell dif
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3.4. Numerical simulations 71T= 6 d
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3.4. Numerical simulations 73T= 6 d
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3.5. Discussion and conclusions 75c
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3.5. Discussion and conclusions 77o
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CHAPTER 4Moving boundary model fore
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4.2. Recent mathematical models 81o
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4.3. Moving boundary model 834.3 Mo
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4.3. Moving boundary model 85Assume
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4.3. Moving boundary model 87concen
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4.3. Moving boundary model 89classi
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4.3. Moving boundary model 91zero).
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4.4. Model validation 93geometry of
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4.4. Model validation 95Table 4.1:
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4.4. Model validation 97Table 4.2:
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4.4. Model validation 99c m0.2c tot
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4.4. Model validation 101c m0.2c to
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4.4. Model validation 105ub=0.15 da
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4.4. Model validation 109t=42 days
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4.4. Model validation 111t=6 days0.
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4.4. Model validation 113the end of
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4.4. Model validation 115randomday
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4.4. Model validation 1174.4.3.2 Co
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4.4. Model validation 119L nz=10nz=
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4.4. Model validation 121log 10 err
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4.4. Model validation 123log 10 err
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4.5. Results and discussion 125Area
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4.5. Results and discussion 127t=15
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4.6. Conclusions 129bone formation
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132 Chapter 5. Numerical algorithmi
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134 Chapter 5. Numerical algorithmT
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136 Chapter 5. Numerical algorithm5
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138 Chapter 5. Numerical algorithmp
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140 Chapter 5. Numerical algorithmO
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142 Chapter 5. Numerical algorithmw
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144 Chapter 5. Numerical algorithmo
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146 Chapter 5. Numerical algorithmf
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150 Chapter 5. Numerical algorithmN
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152 Chapter 5. Numerical algorithmd
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156 Chapter 5. Numerical algorithmI
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158 Chapter 5. Numerical algorithmi
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160 Chapter 5. Numerical algorithmL
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166 Chapter 5. Numerical algorithmN
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168 Chapter 5. Numerical algorithmn
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170 Chapter 5. Numerical algorithmw
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172 Chapter 5. Numerical algorithmc
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180 Chapter 5. Numerical algorithma
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186 Chapter 6. Conclusions and outl
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188 Chapter 6. Conclusions and outl
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190 Appendix At=7 days0.5c m0.201.4
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192 Appendix Awhere ⃗n is the out
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194 Appendix BRemark B.1. Since the
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196 Appendix BCase 1b are valid.Cas
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198 AcknowledgmentTheda Olsder has
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BIBLIOGRAPHY[1] I. Abrahamsson, T.
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BIBLIOGRAPHY 203[20] P. Colella, D.
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BIBLIOGRAPHY 205[42] L. Geris, J. V
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BIBLIOGRAPHY 207[64] P. Mayer-Kucku
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BIBLIOGRAPHY 209[89] U. Simon, P. A
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