Angiogenesis, i.e. the formation of blood vessels from existing ones, plays a vital role in bone or wound healing. The expansion of vascularization facilitates the healing process through the delivery of oxygen and nutrients to the injured site and through the removal of waste products. Clinical observations indicate that impaired angiogenesis can impede the healing process, or can result in non-healing outcomes. The computational model developed in this thesis predicts tip/stalk cell patterning, marking the initial phase of sprouting angiogenesis. Growth factors signal endothelial cells to differentiate into tip and stalk cells. Tip cells branch from the existing vessel, leading the sprout, while stalk cells proliferate and follow behind, forming the newly emerged blood vessel. Understanding tip/stalk cell patterning is vital to ensure successful angiogenesis, as an excess or deficiency in tip cells leads to improper healing. Despite several experimental studies and mathematical models exploring the signaling pathways behind tip cell selection, there is a noticeable gap regarding the effect of extracellular matrix (ECM) stiffness on this process. Given that alterations in stiffness occur in various physiological and pathological processes, comprehension of this effect is clinically relevant. This thesis aims to address the existing gap by investigating the specific influence of ECM stiffness on tip/stalk cell patterning. A computational model is created that simulates a vessel sprout under stimulation of growth factors. This model is able to predict the cell patterning over various ECM stiffness levels, and highlights the relevance of incorporating ECM stiffness in the investigation of angiogenic treatments. Enhancing the models’ accuracy and validating the ECM stiffness-dependent model predictions requires additional experimental data. However, further development of the model has great potential for deepening our understanding of angiogenesis dynamics and for facilitating the investigation of treatment strategies.

Introduction: Tibial fracture healing complications occur frequently with reported non-union rates up to 23%. Preoperative patient-specific finite element (FE) modelling of fracture fixation may help to minimize these complications. However, developing such models requires labour-intensive work including (manual) segmentation of bones from medical images, making them unpractical for clinical applications. This study aims to establish a semi-automated workflow for the development of three-dimensional (3D) patient-specific FE models of long bone fractures based on two-dimensional (2D) X-ray images and patient characteristics. Methods: A statistical shape model (SSM) of the tibia was developed based on computed tomography (CT) scans of subjects without tibial fractures. Using this model, shape parameters were correlated to patient characteristics, including gender, age, weight, and height of the subjects, using multilinear regression. Thereafter, strategies were developed to (1) fit the SSM of the tibia to a previously unseen fractured tibia based on two orthogonal X-rays and patient characteristics to estimate its intact 3D shape, and to (2) automatically model the fracture lines as detected on the X-rays in the intact tibia model. Using the automatically created geometries of the fractured tibia, FE models of the stabilized fracture were developed in Abaqus/CAE and used to investigate strains within the callus under post-operative loading conditions. The workflow was tested on one patient and the strains obtained from the FE models within the fracture region were compared to strains reported in the literature. Results: An SSM of the tibia was successfully developed based on CT scans of 25 subjects (15 male, age = 60 ± 5.5; 10 female, age = 51 ± 7.1). The first five shape modes captured 90% of the total shape variation in the studied population. Significant correlations were found between the first shape mode, which described shape changes in the tibial length, and patient gender, age, weight, and height. SSM-to-patient fitting was achieved with a mean error of 0.81 mm and a maximum error of 4.22 mm. FE analysis of the stabilized fracture predicted inter-fragmentary compressive strains between 0 and 10% with a median value of 2%. Increasing the fixation working length by 13 mm, led to a 10-fold increase in the predicted median compressive strains. Discussion and Conclusions: A workflow for the semi-automated generation of FE models of tibia fractures was successfully established. Patient-specific FE analysis results predicted strains within the fracture in a range reported for optimal bone formation. Additionally, predicted strains were highly dependent on the fixation configuration and material, most notably the fixation working length. Future work should focus on fully automating the suggested workflow and on the validation of the results. Ultimately, such a workflow could be used to formulate individualized treatment recommendations during the early pre- and post-operative phase in tibial fracture management to prevent non-union development.