A Coupled Mathematical Model of Cell Migration, Vessel Cooption and Tumour Microenvironment during the Initiation of Micrometastases.

We propose a coupled mathematical model for the detailed quantitative analyses of initial microtumour and micrometastases formation by including cancer cell migration, host vessel cooption and changes in microenvironment. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. Migration probability of a migrating cell is assumed to be influenced by local chemical microenvironment. Pre-existing vessel cooption and remodelling are introduced according to the local haemodynamical microenvironment, such as interstitial pressure and vessel wall permeability. After the tumour cells and tumour vessels distribution are updated, the chemical substances are coupled calculated with the haemodynamical environment. The simulation results clearly reproduce the tumour cells migrate and proliferate along the pre-existing vessels at the very early stage of growth, which are consistent with many published experimental observations. In addition, the model demonstrates the interactions of tumour cells with the pre-existing vessels, which are believed to be essential for initial adhesion, proliferation, invasion, and micrometastases establishment. Quantitative analysis of tumour expansion in longitudinal and transverse directions shows that the cooption and migration along host vessels will be inhibited once angiogenesis phase occurs. The influences of the ability of cell migration and the inclusion of vessel cooption on the formation of micrometastases are discussed.