The invasive growth of malignant tumours as a purely mechanical process

Eaves, G.

doi:10.1002/path.1711090308

Cited by 61 publications

(18 citation statements)

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“…The higher probability of proliferation corresponds to the higher level of nutrient supply in our model. We also model explicitly the mechanical resistance for a tumor cell to migrate toward the normal, virtual tissue on the 2D lattice since it has been shown that mechanical properties of the environment affect the pattern of both proliferation and invasion (Eaves, 1973;Helmlinger et al, 1997;Oishi et al, 1998). Finally, we model explicitly the death of tumor cells (i.e.…”

Section: Emerging Patterns In Tumor Systemsmentioning

confidence: 99%

Emerging Patterns in Tumor Systems: Simulating the Dynamics of Multicellular Clusters with an Agent-based Spatial Agglomeration Model

Mansury

Kimura

Lobo

et al. 2002

Journal of Theoretical Biology

116

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Section: Emerging Patterns In Tumor Systemsmentioning

confidence: 99%

Emerging Patterns in Tumor Systems: Simulating the Dynamics of Multicellular Clusters with an Agent-based Spatial Agglomeration Model

Mansury

Kimura

Lobo

et al. 2002

Journal of Theoretical Biology

116

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“…Moreover the proposed model predicts the Gompertzian behavior on the basis of a feedback effect and a constant supply of nutri- ent for cell and this explains why, under these conditions, the MTS and the in situ tumors follow the same general growth law. ii) BIOMECHANICAL EFFECTS The heterogeneous elastic characteristics of the environment give the strongest external constraints [9]. Again the MTS are useful to study how the mechanical features of the environment can modify the growth pattern.…”

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confidence: 99%

Tumor Gompertzian growth by cellular energetic balance

Castorina

Zappalà

2006

Physica A: Statistical Mechanics and its Applications

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A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor factors. The model is successfully applied to the multicellular tumor spheroid data.A microscopic model of tumor growth in vivo is still an open problem. It requires a detailed description of cellular interactions and a control on the large variety of in situ conditions related to the distributions of nutrient, of oxygen, of growth inhibitors, of blood vessels and capillarity and to the mechanical effects due to tissue elasticity and heterogeneity. On the other hand, in spite of the previous large set of potential parameters, tumors have a peculiar growth pattern that is generally described by a Gompertzian curve [1], often considered as a pure phenomenological fit to the data. More precisely there is an initial exponential growth (until 1-3 mm in diameter) followed by the vascular Gompertzian phase [2]. Then it seems reasonable to think that cancer growth follows a general pattern that one can hope to describe by macroscopic variables, constrained by a set of environmental conditions crucial to understand the fundamental features of the growth as, for example, the shape and the maximum possible size of the tumor and the onset of the tissue invasion and metastasis. Following this line of research, for example, the universal model proposed in [3] has been recently applied to cancer [4].In this paper we consider a macroscopic model of tumor growth that: i) gives an energetic basis to the Gompertzian law; ii) clearly distinguishes among the general evolution patterns, which include feedback effects and external constraints; iii) can give indications on the different tumor phases during its evolution. The proposed macroscopic approach is not in competition with microscopic models [5], but it is a complementary instrument for the description of the tumor growth. The Gompertzian curve is solution of the equationwhere N (t) is the cell number at time t, γ is a constant and N ∞ is the theoretical saturation value for t → ∞. It is quite natural to identify the right hand side of Eq. (1) as the number of proliferating cells at time t and then to consider f p (N ) = γ ln N∞ N as the fraction of proliferating cells and 1 − f p (N ) = f np the fraction of non proliferating cells. Here, we observe the difference with respect to an exponential growth that corresponds to a N independent specific proliferation rate, typical of a system of independent cells. Instead, the logarithmic dependence observed in the Gompertzian law, can be regarded as a sort of feedback mechanism, such that the system, at any time, rearranges the growth rate and the fraction of proliferating cells according to the logarithm of the total number of cells N (t).Living tumor cells consume an amount of energy, under the form of nutrient and oxygen, which is recovered from the environment (which will be addressed in the followin...

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“…This phenomenon is considered to have resulted from an impaired rate of production and destruction of collagen fibers around the tumor lesion. Concerning the mechanism of destruction of the extracellular matrix in malignant tumors, the mechanical effect caused by the infiltration of tumor cells (Eaves 1973;Fidler et al 1978 Desmoplasia refers to the formation of excessive extracellular matrix aroound invasive tumor cells. Some invasive tumors like melanoma are seldom associated with a desmoplastic response, whereas other tumors like infiltrating ductal breast carcinoma are almost always associated with a marked desmoplastic reaction (Liotta et al 1983).…”

Section: Discussionmentioning

confidence: 99%