Laboratoire de Physique Statistique, Ecole Normale Superieure, UPMC Université Paris 06, Université Paris Diderot, CNRS, Paris, France.
J Theor Biol. 2011 Dec 7;290:46-59. doi: 10.1016/j.jtbi.2011.08.029. Epub 2011 Sep 1.
Current diagnostic methods for skin cancers are based on some morphological characteristics of the pigmented skin lesions, including the geometry of their contour. The aim of this article is to model the early growth of melanoma accounting for the biomechanical characteristics of the tumor micro-environment, and evaluating their influence on the tumor morphology and its evolution. The spatial distribution of tumor cells and diffusing molecules are explicitly described in a three-dimensional multiphase model, which incorporates general cell-to-cell mechanical interactions, a dependence of cell proliferation on contact inhibition, as well as a local diffusion of nutrients and inhibiting molecules. A two-dimensional model is derived in a lubrication limit accounting for the thin geometry of the epidermis. First, the dynamical and spatial properties of planar and circular tumor fronts are studied, with both numerical and analytical techniques. A WKB method is then developed in order to analyze the solution of the governing partial differential equations and to derive the threshold conditions for a contour instability of the growing tumor. A control parameter and a critical wavelength are identified, showing that high cell proliferation, high cell adhesion, large tumor radius and slow tumor growth correlate with the occurrence of a contour instability. Finally, comparing the theoretical results with a large amount of clinical data we show that our predictions describe accurately both the morphology of melanoma observed in vivo and its variations with the tumor growth rate. This study represents a fundamental step to understand more complex microstructural patterns observed during skin tumor growth. Its results have important implications for the improvement of the diagnostic methods for melanoma, possibly driving progress towards a personalized screening.
目前用于皮肤癌诊断的方法基于色素性皮肤病变的某些形态特征，包括其轮廓的几何形状。本文的目的是模拟黑色素瘤的早期生长，考虑肿瘤微环境的生物力学特征，并评估它们对肿瘤形态及其演变的影响。肿瘤细胞和扩散分子的空间分布在一个三维多相模型中被明确描述，该模型结合了一般的细胞间力学相互作用、细胞增殖对接触抑制的依赖性，以及营养物质和抑制分子的局部扩散。在考虑到表皮的薄几何形状的润滑极限中推导出二维模型。首先，使用数值和分析技术研究了平面和圆形肿瘤前缘的动力学和空间特性。然后开发了一个 WKB 方法，以便分析控制偏微分方程的解，并推导出生长肿瘤轮廓不稳定性的阈值条件。确定了一个控制参数和一个临界波长，表明高细胞增殖、高细胞黏附、大肿瘤半径和缓慢的肿瘤生长与轮廓不稳定性的发生相关。最后，将理论结果与大量临床数据进行比较，表明我们的预测准确地描述了体内观察到的黑色素瘤的形态及其随肿瘤生长速度的变化。这项研究代表了理解皮肤肿瘤生长过程中观察到的更复杂微观结构模式的基本步骤。其结果对黑色素瘤诊断方法的改进具有重要意义，可能会推动个性化筛查的进展。
