A model for cell migration in tumour growth |
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| Affiliation: | 1. DIMA, University of Genoa, Via Dodecaneso 35, 16146 Genoa, Italy;2. DIBRIS, University of Genoa, Via Opera Pia 13, 16145 Genoa, Italy;1. State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China;2. Tunnel and Underground Engineering Research Center of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China;1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore;2. School of Astranautics and Aeronautics, University of Electronic Science and Technology, Chengdu 611732, PR China |
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| Abstract: | Tumour growth results, in particular, from cell–cell interaction and tumour and healthy cell proliferation. The complexity of the cellular microenvironment may then be framed within the theory of mixtures by looking at cell populations as the constituents of a mixture. In this paper the balance equations are reviewed to account for directionality onto a collective migration of the tumour cell population, via an attractive force of the chemotactic type, in addition to the customary pressure term. The density of tumour cells turns out to be governed by a hyperbolic differential equation. By neglecting, as usual, the inertia term it follows that the density satisfies a backward, or forward, diffusion equation according as the attraction, or pressure effect, prevails. Uniqueness of the solution to the backward equation is investigated and a family of solutions is described. An estimate is given for the growth rate of a tumour profile. |
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| Keywords: | Tumour growth Cell migration Cell populations Mixtures Backward diffusion equation |
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