| Περίληψη: | Bone healing is an extremely complex procedure. During this process several cellular
and molecular mechanisms take place. The main objective of this PhD dissertation was the
development of a novel standard computational framework that successfully simulates tissue
differentiation during fracture healing and investigates the influence of Low Intensity Pulsed
Ultrasound (LIPUS) on bone healing, giving an insight into the exact mechanisms that lead to
the acceleration of bone regeneration.
The present PhD work was implemented in three phases. During the first phase a new
and simple Meshless Local Boundary Integral Equation Method (LBIE) was developed in
order to solve the linear and nonlinear mesenchymal stem cells’ proliferation problem so as
to conclude which of the two is the most representative case.
Furthermore, during the second stage a hybrid biological mathematical model, based on
that of Peiffer et al. (2011), was explicated. This model consists of a) a system of partial
differential equations (PDEs) which describes the spatiotemporal evolution of cells, growth
factors, tissues and ultrasound acoustic pressure and b) a system of velocity equations that
depicts the development of the blood vessel network. The effect of Ultrasound on this
multiscale model was taken into consideration so as to primarily affect Vascular Endothelial
Growth Factor (VEGF) transport, which is in accordance with previous in-vitro studies on
human cells.
Finally, the third phase regards the presentation of a micromechano-biological model
based on that of Lacroix and Prendergast (2002) enhanced with all the terms that introduce
the effect of ultrasound in fracture healing. In this direction, the model includes an iterative
procedure, which combines a mechanical model accounting for the effect of mechanical
loading over time, a biological model for the evolution of mesenchymal stem cells and the
hybrid biological model established during the second phase.
The innovative aspects of this PhD thesis are a) the development of a new biological
and micromechano-biological numerical model that simulates bone solidification under the
presence of ultrasound and b) the implementation of a new and simple Meshless LBIE for the
simulation of the mesenchymal stem cells’ proliferation.
Therefore it could be regarded as a step towards the ultrasonic assessment of bone
fracture healing. The development of experiments of ultrasound application on rodent
fracture along with the promotion of a more comprehensive theoretical framework could further improve our understanding on the role of ultrasound in the enhancement of the
healing course.
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