Jan Demol

Towards a quantitative understanding of oxygen tension and cell density evolution in fibrin hydrogels

The in vitro culture of hydrogel-based constructs above a critical size is accompanied by problems of unequal cell distribution when diffusion is the primary mode of oxygen transfer. In this study, an experimentally-informed mathematical model was developed to relate cell proliferation and death inside fibrin hydrogels to the local oxygen tension in a quantitative manner. The predictive capacity of the resulting model was tested by comparing its outcomes to the density, distribution and viability of human periosteum derived cells (hPDCs) that were cultured inside fibrin hydrogels in vitro. The model was able to reproduce important experimental findings, such as the formation of a multilayered cell sheet at the hydrogel periphery and the occurrence of a cell density gradient throughout the hydrogel. In addition, the model demonstrated that cell culture in fibrin hydrogels can lead to complete anoxia in the centre of the hydrogel for realistic values of oxygen diffusion and consumption. A sensitivity analysis also identified these two parameters, together with the proliferation parameters of the encapsulated cells, as the governing parameters for the occurrence of anoxia. In conclusion, this study indicates that mathematical models can help to better understand oxygen transport limitations and its influence on cell behaviour during the in vitro culture of cell-seeded hydrogels.

Computed tomography-based joint locations affect calculation of joint moments during gait when compared to scaling approaches

Hip joint moments are an important parameter in the biomechanical evaluation of orthopaedic surgery. Joint moments are generally calculated using scaled generic musculoskeletal models. However, due to anatomical variability or pathology, such models may differ from the patients anatomy, calling into question the accuracy of the resulting joint moments. This study aimed to quantify the potential joint moment errors caused by geometrical inaccuracies in scaled models, during gait, for eight test subjects. For comparison, a semi-automatic computed tomography (CT)-based workflow was introduced to create models with subject-specific joint locations and inertial parameters. 3D surface models of the femora and hemipelves were created by segmentation and the hip joint centres and knee axes were located in these models. The scaled models systematically located the hip joint centre (HJC) up to 33.6 mm too inferiorly. As a consequence, significant and substantial peak hip extension and abduction moment differences were recorded, with, respectively, up to 23.1% and 15.8% higher values in the image-based models. These findings reaffirm the importance of accurate HJC estimation, which may be achieved using CT- or radiography-based subject-specific modelling. However, obesity-related gait analysis marker placement errors may have influenced these results and more research is needed to overcome these artefacts.

Modelling of in vitro mesenchymal stem cell cultivation, chondrogenesis and osteogenesis

Hydrogels present an interesting three-dimensional culture environment for tissue engineering applications. Fibrin for example has been used for culturing many cell types, a.o. mesenchymal progenitor cells. Furthermore, several studies have explored the potential of fibrin to induce chondrogenesis or osteogenesis [Worster, 2001; Catelas, 2006; Matziolis, 2006]. Mathematical modelling can be used to enhance the understanding of these processes and can propose the optimal culture conditions for each process. In this study, a mathematical model is developed encapsulating the essential aspects of bone and cartilage tissue engineering processes.