Abstract
The design of experiments (DOE) is a valuable method for studying the influence of one or more factors on the outcome of computer experiments. There is no limit to the number of times a computer experiment can be run, but they are often time-consuming. Moreover, the number of parameters in a computer model is often very large and the range of variation for each of these parameters is often quite extensive. The DOE provides the statistical tools necessary for choosing a minimum amount of parameter combinations resulting in as much information as possible about the computer model. In this chapter, several designs and analysing methods are explained. At the end of the chapter, these designs and methods are applied to a mechanobiological model describing tooth movement.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Carlier, A., Chai, Y.C., Moesen, M., Theys, T., Schrooten, J., Van Oosterwyck, H., Geris, L.: Designing optimal calcium phosphate scaffold-cell combinations using an integrative model-based approach. Acta Biomater. 7, 3573–3585 (2011)
Dar, F.H., Meakin, J.R., Aspden, R.M.: Statistical methods in finite element analysis. J. Biomech. 35, 1155–1161 (2002)
Ebden, M.: Gaussian processes for regression: a quick introduction. Lecture Notes (2008)
Eriksson, O., Tegnér, J.: Modeling and model simplification to facilitate biological insights and predictions. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Chem (2016, this volume)
Fang, K.T.: The uniform design: application of number-theoretic methods in experimental design. Acta Mathematicae Applicatae Sinica 3, 363–372 (1980)
Fang, K.T., Li, R., Sudijanto, A.: Design and Modeling for Computer Experiments. Chapman & Hall/CRC, Boca Raton (2006)
Fisher, R.A.: The Design of Experiments. Oliver & Boyd, Edinburgh (1935)
Garant, P.R. (ed.): Oral Cells and Tissues. Quintessence Publishing, Hanover Park (2003)
Geris, L., Gerisch, A., Maes, C., Carmeliet, G., Weiner, R., Vander Sloten, J., Van Oosterwyck, H.: Mathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results. MBEC 44, 280–289 (2006)
Geris, L., Gerisch, A., Sloten, J.V., Weiner, R., Van Oosterwyck, H.: Angiogenesis in bone fracture healing: a bioregulatory model. J. Theory Biol. 251(1), 137–158 (2008)
Henneman, S., Von den Hoff, J.W., Maltha, J.C.: Mechanobiology of tooth movement. Eur. J. Orthod. 30(3), 299–306 (2008)
Isaksson, H., van Donkelaar, C.C., Huiskes, R., Ito, K.: A mechano-regulatory bone-healing model incorporating cell-phenotype specific activity. J. Theory Biol. 252, 230–246 (2008a)
Isaksson, H., van Donkelaar, C.C., Huiskes, R., Yao, J., Ito, K.: Determining the most important cellular characteristics for fracture healing using design of experiments methods. J. Theory Biol. 255(1), 26–39 (2008)
Kanzaki, H., Chiba, M., Shimizu, Y., Mitani, H.: Periodontal ligament cells under mechanical stress induce osteoclastogenesis by receptor activator of nuclear factor kappab ligand up-regulation via prostaglandin e2 synthesis. J. Bone Miner. Res. 17(2), 210–220 (2002)
Kimoto, S., Matsuzawa, M., Matsubara, S., Komatsu, T., Uchimura, N., Kawase, T., Saito, S.: Cytokine secretion of periodontal ligament fibroblasts derived from human deciduous teeth: effect of mechanical stress on the secretion of transforming growth factor-beta 1 and macrophage colony stimulating factor. J. Periodontal Res. 34(5), 235–243 (1999)
Kirk, P., Silk, D., Stumpf, M.P.H.: Reverse engineering under uncertainty. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Chem (2016, this volume)
Krishnan, V., Davidovitch, Z.: Cellular, molecular, and tissue-level reactions to orthodontic force. Am. J. Orthod. Dentofacial Orthop. 129(4), 469.e1-469.32 (2006)
Krishnan, V., Davidovitch, Z.: On a path to unfolding the biological mechanisms of orthodontic tooth movement. J. Dent. Res. 88(7), 597–608 (2009)
Lacroix, D.: Simulation of tissue differentiation during fracture healing. PhD thesis, University of Dublin (2001)
Lin, C.L., Chang, S.H., Chang, W.J., Kuo, Y.C.: Factorial analysis of variables influencing mechanical characteristics of a single tooth implant placed in the maxilla using finite element analysis and the statistics-based taguchi method. Eur. J. Oral Sci. 115, 408–416 (2007)
Lundstedt, T., Seifert, E., Abramo, L., Thelin, B., Nyström, A., Pettersen, J., Bergman, R.: Experimental design and optimization. Chemom. Intell. Lab. 42(2), 3–40 (1998)
MacKay, D.J.C.: Introduction to gaussian processes. Lecture Notes (1998)
Malandrino, A., Planell, J., Lacroix, D.: Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression, flexion and axial rotation. J. Biomech. 42, 2780–2788 (2009)
Mannakee, B.K., Ragsdale, A.P., Transtrum, M.K., Gutenkunst, R.N.: Sloppiness and the geometry of parameter space. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Chem (2016, this volume)
Marotti, G.: The osteocyte as a wiring transmission system. J. Musculoskelet. Neuronal. Interact. 1(2), 133–136 (2000)
Montgomery, D.C.: Design and analysis of experiments, 7th edn. Wiley, New York (1997)
Myers, R.H., Montgomery, D.C.: Response surface methodology: process and product optimization using designed experiments. Wiley, New York (1995)
Nishijima, Y., Yamaguchi, M., Kojima, T., Aihara, N., Nakajima, R., Kasai, K.: Levels of RANKL and OPG in gingival crevicular fluid during orthodontic tooth movement and effect of compression force on releases from periodontal ligament cells in vitro. Orthod. Craniofac. Res. 9(2), 63–70 (2006)
Pfeilschifter, J., Diel, I., Scheppach, B., Bretz, A., Krempien, R., Erdmann, J., Schmid, G., Reske, N., Bismar, H., Seck, T., Krempien, B., Ziegler, R.: Concentration of transforming growth factor beta in human bone tissue: relationship to age, menopause, bone turnover, and bone volume. J. Bone Miner. Res. 13(4), 716–730 (1998)
Pinkerton, M.N., Wescott, D.C., Gaffey, B.J., Beggs, K.T., Milne, T.J., Meikle, M.C.: Cultured human periodontal ligament cells constitutively express multiple osteotropic cytokines and growth factors, several of which are responsive to mechanical deformation. J. Periodontal Res. 43(3), 343–351 (2008)
Pivonka, P., Zimak, J., Smith, D.W., Gardiner, B.S., Dunstan, C.R., Sims, N.A., Martin, T.J., Mundy, G.R.: Model structure and control of bone remodeling: a theoretical study. Bone 43(2), 249–263 (2008)
Provatidis, C.G.: An analytical model for stress analysis of a tooth in translation. Int. J. Eng. Sci. 39, 1361–1381 (2001)
Rinchuse, D.J., Rinchuse, D.J., Sosovicka, M.F., Robison, J.M., Pendleton, R.: Orthodontic treatment of patients using bisphosphonates: a report of 2 cases. Am. J. Orthod. Dentofacial Orthop. 131(3), 321–326 (2007)
Saltelli, A., Chan, K., Scott, E.M. (eds.): Sensitivity Analysis. Wiley, New York (2000)
Sandberg, M., Vuorio, T., Hirvonen, H., Alitalo, K., Vuorio, E.: Enhanced expression of tgf-beta and c-fos mrnas in the growth plates of developing human long bones. Development 102(3), 461–470 (1988)
Santner, T.J., Williams, B.J., Notz, W.I.: The Design and Analysis of Computer Experiments. Springer, New York (2003)
Van Schepdael, A., Vander Sloten, J., Geris, L.: A mechanobiological model of orthodontic tooth movement. Biomech. Model Mechanobiol. 12(2), 249–265 (2013)
Van Schepdael, A., Vander Sloten, J., Geris, L.: Mechanobiological modeling can explain orthodontic tooth movement: three case studies. J. Biomech. 46(3), 470–477 (2013)
Wescott, D.C., Pinkerton, M.N., Gaffey, B.J., Beggs, K.T., Milne, T.J., Meikle, M.C.: Osteogenic gene expression by human periodontal ligament cells under cyclic tension. J. Dent. Res. 86(12), 1212–1216 (2007)
Yamaguchi, M., Aihara, N., Kojima, T., Kasai, K.: Rankl increase in compressed periodontal ligament cells from root resorption. J. Dent. Res. 85(8), 751–756 (2006)
Yang, K., Teo, E.C., Fuss, F.K.: Application of Taguchi method in optimization of cervical ring cage. J. Biomech. 40, 3251–3256 (2007)
Acknowledgments
The authors acknowledge support from European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement n279100 (An Van Schepdael and Liesbet Geris). Aurélie Carlier is a Fellow of the Research Foundation Flanders (FWO).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Conflict of Interest
Conflict of Interest
The authors declare that they have no conflict of interest.
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Van Schepdael, A., Carlier, A., Geris, L. (2016). Sensitivity Analysis by Design of Experiments. In: Geris, L., Gomez-Cabrero, D. (eds) Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-21296-8_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21295-1
Online ISBN: 978-3-319-21296-8
eBook Packages: EngineeringEngineering (R0)