A three-dimensional （3D） mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micr...A three-dimensional （3D） mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors （VEGFs）, and the discrete part of tumour cells （TCs） and blood vessel networks. The simulation shows the dynamic process of avascular tumour growth from a fewinitial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of the TCs, more and more host vessels collapse due to the stress caused by the growing tumour. In addition, the consumption of oxygen expands with the enlarged tumour region. The study also discusses the effects of certain factors on tumour growth, including the density and configuration of pre- existing vessel networks and the blood oxygen content. The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumour metastasis and the initialization of tumour angiogenesis.展开更多
In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed...In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts.Moreover,a lower bound estimate of the spreading speed is given.Then,we prove that the traveling wavefronts with large speeds are globally exponentially stable,when the initial perturbation around the traveling wavefronts decays exponentially asχ→-∞,but the initial perturbation can be arbitrarily large in other locations.The adopted methods are the weighted energy and the squeezing technique.展开更多
基金supported by the National 973 Basic Research Program of China(No.2013CB733800)the National Natural Science Foundation of China(Nos.11272091 and 11102113)
文摘A three-dimensional （3D） mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors （VEGFs）, and the discrete part of tumour cells （TCs） and blood vessel networks. The simulation shows the dynamic process of avascular tumour growth from a fewinitial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of the TCs, more and more host vessels collapse due to the stress caused by the growing tumour. In addition, the consumption of oxygen expands with the enlarged tumour region. The study also discusses the effects of certain factors on tumour growth, including the density and configuration of pre- existing vessel networks and the blood oxygen content. The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumour metastasis and the initialization of tumour angiogenesis.
基金supported by NSF of China(11861056)NSF of Gansu Province(21JR7RA121)+1 种基金Department of Education of Gansu Province:Youth Doctoral Fund Project(2021QB-018)Northwest Normal University:Starting Fund for Doctoral Research(202103101204)。
文摘In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts.Moreover,a lower bound estimate of the spreading speed is given.Then,we prove that the traveling wavefronts with large speeds are globally exponentially stable,when the initial perturbation around the traveling wavefronts decays exponentially asχ→-∞,but the initial perturbation can be arbitrarily large in other locations.The adopted methods are the weighted energy and the squeezing technique.
