Growth, modelling and remodelling of biological tissue

Abstract

It is the aim of this work to present an accurate way of modelling, growth and remodelling processes within the framework of continuum biomechanics. Therefore, a multiphase continuum approach is used for the material modelling, where the cells and the extracellular matrix are represented by the solid constituent, and the extracellular liquids are summarised as the fluid constituents. Furthermore, biological processes only occur if the involved cells are sufficiently supported by metabolites (oxygen, vitamins, nutrients, etc.), which are needed for cell metabolic processes. Therefore, a single, non-mechanical quantity is introduced to summarise the metabolites inside the extracellular liquids. This approach provides the necessary thermodynamic restrictions which are evaluated for avascular tumour growth and bone remodelling.

To understand the mechanism of growth and remodelling and its consequences, the mechanics as well as the cell dynamics must be considered. In this regard, the Systems Biology aims at investigating the intra- and extracellular signalling pathways, which are involved in the mechanotransduction and trigger the metabolic processes. Using modern computational methods allows for the combination of systems-biological and biomechanical methods within an integrated approach. In this context, Scientific Workflow technology provides an excellent platform to allow for the integration of existing legacy applications from different vendors into an integrative simulation workflow. Therefore, the existing applications are extended or wrapped by a webservice interface, which is then invoked by the workflow instances. This radically new approach allows for a straight-forward merging of computational models from different scales and provides the possibility to further expand each model individually. To reveal the capability of the multi-field growth model, three-dimensional (3-d) simulation examples of both phenomena are presented. This allows the integrated use of separated numerical applications as webservices for each simulation part, which are controlled by a workflow management system. By replacing the phenomenological bone remodelling algorithm with a biologically motivated cell population model, the benefits of this method are demonstrated.

Es ist das Ziel dieser Arbeit, die Wachstums- und Strukturänderungsprozesse in biologischen Geweben im Rahmen der Kontinuumsbiomechanik möglichst genau abzubilden. Zur Beschreibung des Materialverhaltens wird ein zweiphasiges Kontinuumsmodell verwendet. Dabei repräsentiert die feste Phase Zellen und extrazelluläre Matrix, und die extrazellulären Flüssigkeiten werden in einer flüssigen Phase zusammengefasst. Darüber hinaus wird berücksichtigt, dass biologische Prozesse nur stattfinden, wenn die verantwortlichen Zellen ausreichend mit den für ihren Stoffwechsel notwendigen Nährstoffen versorgt sind. Um die gelösten Nährstoffe zu berücksichtigen, wird die Wachstumsenergie als eine gemittelte, nicht-mechanische Größe eingeführt, die die für den Zellstoffwechsel zur Verfügung stehende chemische Energie angibt. Durch dieses Konzept reduziert sich die Anzahl der zu berücksichtigenden Feldgrößen. Das ermöglicht eine vereinfachte Auswertung der Entropieungleichung. Gekoppelte drei-dimensionale Finite-Elemente-Simulationen von avaskulärem Tumorwachstum und durch Belastung verursachter Knochenumbau demonstrieren die Leistungsfähigkeit dieser Herangehensweise.