Abstract
The quest for a deeper understanding of the cancer growth and spread process focuses on the naturally multiscale nature of cancer invasion, which requires an appropriate multiscale modeling and analysis approach. The cross-talk between the dynamics of the cancer cell population on the tissue scale (macroscale) and the proteolytic molecular processes along the tumor border on the cell scale (microscale) plays a particularly important role within the invasion processes, leading to dramatic changes in tumor morphology and influencing the overall pattern of cancer spread. Building on the multiscale moving boundary framework proposed in Trucu et al. (Multiscale Model. Simul 11(1): 309-335), in this work we propose a new formulation of this process involving a novel derivation of the macro scale boundary movement law based on micro-dynamics, involving a transport equation combined with the level-set method. This is explored numerically in a novel finite element macro-micro framework based on cut-cells.
Highlights
Involving a wide range of cross-related processes occurring on several spatio-temporal scales, cancer cell invasion in human tissue is one of the hallmarks of cancer [36], playing a crucial role in the overall development of a growing malignant tumour
The tissue-scale progression of tumour morphology is captured here in a multiscale moving boundary approach where the contribution arriving from the cell scale activity to the cancer invasion pattern is realised by the micro scale matrix degraded enzymes (MDEs) dynamics, which, for its part, is induced by the cancer macro-dynamics. This was recently applied to the extended context in which, rather than the matrix metalloproteinases (MMPs) dynamics, the urokinase plasminogen activator (uPA) is considered as the proteolytic system, and has led to biologically relevant results [53]
We present a two-scale model for cancer invasion that involves a double feedback loop to link the dynamics occurring at two different spatial scales explored by the following two modelling components: a macroscopic component describing the population of cancer cells and extracellular matrix at tissue-scale and a microscopic component describing the dynamics of a generic matrix-degrading enzyme molecular population whose cell-scale takes place at the leading edge of the tumour
Summary
Involving a wide range of cross-related processes occurring on several spatio-temporal scales, cancer cell invasion in human tissue is one of the hallmarks of cancer [36], playing a crucial role in the overall development of a growing malignant tumour. A important role in cancer invasion is played by the MDEs (such as the MMPs) that are secreted from the outer proliferating rim and released within the tumour peritumoural microenvironment This gives the cancer invasion a moving boundary character, and to that end several level set approaches were recently proposed to study the tumour progression both in homogeneous environments [32, 43, 44, 45, 80] and in complex heterogeneous tissues [46]. The tissue-scale progression of tumour morphology is captured here in a multiscale moving boundary approach where the contribution arriving from the cell scale activity to the cancer invasion pattern is realised by the micro scale MDEs dynamics (occurring along the tumour invasive edge), which, for its part, is induced by the cancer macro-dynamics This was recently applied to the extended context in which, rather than the MMPs dynamics, the uPA is considered as the proteolytic system, and has led to biologically relevant results [53].
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