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Tissue differentiation and bone regeneration in an osteotomized mandible: a computational analysis of the latency period

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Abstract

Mandibular symphyseal distraction osteogenesis is a common clinical procedure to modify the geometrical shape of the mandible for correcting problems of dental overcrowding and arch shrinkage. In spite of consolidated clinical use, questions remain concerning the optimal latency period and the influence of mastication loading on osteogenesis within the callus prior to the first distraction of the mandible. This work utilized a mechano-regulation model to assess bone regeneration within the callus of an osteotomized mandible. A 3D model of the mandible was reconstructed from CT scan data and meshed using poroelastic finite elements (FE). The stimulus regulating tissue differentiation within the callus was hypothesized to be a function of the strain and fluid flow computed by the FE model. This model was then used to analyse tissue differentiation during a 15-day latency period, defined as the time between the day of the osteotomy and the day when the first distraction is given to the device. The following predictions are made: (1) the mastication forces generated during the latency period support osteogenesis in certain regions of the callus, and that during the latency period the percentage of progenitor cells differentiating into osteoblasts increases; (2) reducing the mastication load by 70% during the latency period increases the number of progenitor cells differentiating into osteoblasts; (3) the stiffness of new tissue increases at a slower rate on the side of bone callus next to the occlusion of the mandibular ramus which could cause asymmetries in the bone tissue formation with respect to the middle sagittal plane. Although the model predicts that the mastication loading generates such asymmetries, their effects on the spatial distribution of callus mechanical properties are insignificant for typical latency periods used clinically. It is also predicted that a latency period of longer than a week will increase the risk of premature bone union across the callus.

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, 70126, Bari, Italy

    A. Boccaccio & C. Pappalettere

  2. Trinity Centre for Bioengineering, Department of Mechanical and Manufacturing Engineering, Trinity College Dublin, Dublin 2, Ireland

    A. Boccaccio, P. J. Prendergast & D. J. Kelly

Authors
  1. A. Boccaccio
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  2. P. J. Prendergast
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  3. C. Pappalettere
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  4. D. J. Kelly
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Corresponding author

Correspondence to D. J. Kelly.

Appendix A

Appendix A

1.1 Evaluation of the symmetry coefficient

The callus consists of eight layers of elements. Its axial stiffness along 1 direction can be described by schematizing the callus as a set of springs arranged in series. Each spring will have a length equal to the thickness of each layer. If E(L i ), i = {1, 2, 3, …,8}, is the mean value of the Young’s modulus calculated in L i layer, and E equivalent is the Young’s modulus in the 1 direction for the whole bone callus model, the C S symmetry coefficient is given by:

$$ C_{{\text{S}}} = \frac{{|E_{{{\text{left}}}} - E_{{{\text{right}}}} |}} {{E_{{{\text{equivalent}}}} }}100 $$
(8)

where E left, E right and E equivalent are given by:

$$ \begin{aligned}{} E_{{{\text{left}}}} = \frac{{\frac{{S_{{{\text{TOT}}}} }} {2}}} {{S_{L} {\sum\nolimits_1^4 {\frac{1} {{E(L_{i} )}}} }}} \\ E_{{{\text{right}}}} = \frac{{\frac{{S_{{{\text{TOT}}}} }} {2}}} {{S_{L} {\sum\nolimits_5^8 {\frac{1} {{E(L_{i} )}}} }}} \\ E_{{{\text{equivalent}}}} = \frac{{S_{{{\text{TOT}}}} }} {{S_{L} {\sum\nolimits_1^8 {\frac{1} {{E(L_{i} )}}} }}} \\ \end{aligned} $$
(9)

and where S L and S TOT are the thickness of each layer of elements and of the entire model, respectively. Considering that S L  = S TOT /8, therefore Eq. 9 can be rewritten as:

$$ \begin{aligned}{} E_{{{\text{left}}}} = \frac{4} {{{\sum\nolimits_1^4 {\frac{1} {{E(L_{i} )}}} }}} \\ E_{{{\text{right}}}} = \frac{4} {{{\sum\nolimits_5^8 {\frac{1} {{E(L_{i} )}}} }}} \\ E_{{{\text{equivalent}}}} = \frac{8} {{{\sum\nolimits_1^8 {\frac{1} {{E(L_{i} )}}} }}} \\ \end{aligned} $$
(10)

It is known that Eq. 10 (corresponding to the so called Reuss’ model) underestimate the elastic modulus. Another possible way of estimating the Young’s modulus could be to perform a FE analysis of a compression test of the gap every analysis step. However, such a strategy would be significantly more expensive in terms of computation.

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Boccaccio, A., Prendergast, P.J., Pappalettere, C. et al. Tissue differentiation and bone regeneration in an osteotomized mandible: a computational analysis of the latency period. Med Biol Eng Comput 46, 283–298 (2008). https://doi.org/10.1007/s11517-007-0247-1

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