Numerical modelling of the ultrasound effect on bone fracture healing

• Κύριος συγγραφέας: Γρίβας, Κωνσταντίνος
• Άλλοι συγγραφείς: Πολύζος, Δημοσθένης
• Μορφή: Thesis
• Γλώσσα: English
• Έκδοση: 2016
• Θέματα: Bone healing; Ultrasound; Modelling; Οστεογένεση; Υπέρηχος; Αριθμητική επίλυση; 616.710 6

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.