Coupled Numerical Study Of Tumour Growth And Development

Tumours pose a great threat to human health and life. It is a serious problem to study the pathological process and the therapeutic strategies of tumours. There are many physiological processes included in the tumour growth and development, such as avascular phase, angiogenesis, and vascular phase. The interactions between tumour cells and endothelial cells with the complex microenvironment inside the tumour are present throughout every developmental process. At the same time, the microenvironment, including chemical factors, nutrients, and haemodynamic information, will change with the growing tumours. Therefore, the decoupled models which focus on one of the developmental processes cannot provide the dynamic responses during the whole growth. We coupled tumour growth, angiogenesis with blood perfusion in this study and established a dynamic feedback system of many factors, to provide foundational understandings for researches of tumour pathological phenomena and anti-angiogenic therapy.The main works include:1. the model of tumour growth and invasion in the avascular phaseThe mathematical modeling for avascular tumour growth is presented by using a continuum-discrete hybrid model. The continuum equations are used to describe the concentration changing of oxygen, extra-cellular matrix and matrix-degrading enzyme. The discrete model is used to simulate the dynamics of tumour cells in cell life cycle, including mutation, mitosis, proliferate, migrate and apoptosis. The parameters which control the interactions of tumour cells and the abnormal microenvironment are regulated to obtain different morphologies of tumour invasion.2. the model of mature remodeling of tumour neo-capillariesWe consider the mechanical environment inside the tumour and the haemodynamics through the vascular network, which are two important factors influencing the vessel collapse and remodeling. First, the tumour vasculature is generated under the mechanical environment which includes the traction between endothelial cells, the viscous-elastic force of extra-cellular matrix and the external forces. The angiogenic model is then improved by removing the pre-defined tumour-region dependent branching law to avoid artificial intervention of the growing neo-capillaries. The two dimensional coupled flow model is carried out on the updated network to analyze the haemodynamics. The intravascular blood flow and the interstitial fluid flow are coupled by transvascular flow. The wall shear stress of each vessel segment is obtained from the haemodynamic calculation to form the criterion of vessel collapse. Based on the WSS criterion, we incorporate the immature vessel collapse with the tumour angiogenesis model to establish the remodeling process of neo-capillary network.3. the coupled model of tumour growth, vessel growth and blood perfusionWe couple the tumour growth, vessel growth and blood perfusion into one close feedback system based on the above two decoupled models, by considering the dynamic changes of chemical substances and the balance of haemodynamics. The haemodynamic calculation is carried out on the updated network, which coupled the intravascular flow, tranvascular flow and interstitial flow. The neo-capillary network is remodeled according to the WSS criterion for vessel collapse. We analyze the growth history of tumour cells and mature vasculature, and the changes of chemical substances (including oxygen, vascular endothelial growth factor, extra-cellular matrix, and matrix-depredating enzymes) and haemodynamic parameters (including intravascular pressure, intravascular flow velocity, interstitial pressure, and interstitial flow velocity). The dynamic feedback mechanism between tumour growth and vessel growth in the coupled model is discussed. To access the system stability of the current model, we change the initial distribution of tumour cells and network, analyze the system sensitivity to certain parameters and discuss the reasonability of remodeling criterion for vessel collapse.4. application the coupled model to anti-angiogenic therapyThe coupled mathematical model of tumour growth and angiogenesis is established under the effects of anti-angiogenic factors and pro-angiogenic factors, to study the inhibition of anti-angiogenic factor Angiostatin (AS) and anti-angiogenic drug Endostatin (ES) on the neo-vasculature inside and outside the tumour, and the arrested tumour growth and invasion. We analyze the changes of chemical substances and the haemodynamic information, and the effects of anti-angiogenic factor and drug on the reduced endothelial cells and inhibited tumour growth. The mechanisms and curative effects of anti-angiogenic therapy are discussed.Major innovations in this study:1. We coupled the tumour growth, angiogenesis and blood perfusion into one model, and simulated the main features of the dynamic process of tumour growth and the changes of corresponding microenvironment and haemodynamic information. Based on the coupling model, it is possible to not only study the feedback phenomena between factors, but also investigate the influence of certain parameters or variation on the whole dynamic process to the overall tumour growth. The model validations were carried out on the coupled system, which demonstrated the advantages of coupled model in wide applicability and good stability. Finally, an application of coupled model to anti-angiogenic therapy was presented.2. In the decoupled model (the model of tumour growth and invasion at the avascular phase, and the model of vessel remodeling) and the coupled model, we both removed some pre-defined model conditions. The tumour growth and vessel growth were coupled and controlled only through the changing microenvironment and the feedback of haemodynamics. This principle was applied throughout the whole study.3. In the simulation of neo-capillary network remodeling, we considered vessel collapse and remodeling under the effects of mechanical environment in matrix and haemodynamics in the vasculature. The above innovations are not reported at present.