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On Some Probabilistic Aspects of Diffusion Models for Tissue Growth

机译：关于组织生长扩散模型的一些概率方面

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Understanding of tissue growth is in its nature multidisciplinary, since it varies from cancer diagnostics, imageprocessing, fractal analysis to regular and non-regular heat flows. By medical sciences it was requested to better understoodthe tissue grow relation to mathematical modelling (stochastic geometry, fractal growth, diffusions). It is clear, thatdeterministic fractal is not an appropriate model for cancer growth. Stochastic fractal is more appropriate, however, avalidation measure should be developed for better comparability with advanced stochastic geometry model, e.g. Quermass-interaction process. Moreover, relation temperature-geometry of the tissue is studied. We have partial results, whereit is observed, that benign alterations and malignant tumors originating from glandular tissues (e.g.mammary, prostatic,pancreatic) are naturally modelled by non-standard diffusions. For standard diffusions, fair approximation is provided byanalytical models based on convective heat transfer in infinite tissues volume (e.g. model given by Perl 1962, later extendedby [1]).
机译：对组织生长的了解本质上是多学科的，因为它从癌症诊断，图像处理，分形分析到规则和不规则的热流不等。医学界要求更好地理解组织生长与数学建模（随机几何，分形增长，扩散）的关系。显然，确定性分形不是癌症生长的合适模型。随机分形更合适，但是，应开发一种验证措施，以更好地与高级随机几何模型（例如， Quermass交互过程。此外，研究了组织的关系温度-几何形状。我们观察到部分结果表明，通过非标准扩散自然可以对源自腺体组织（例如乳腺，前列腺，胰腺）的良性改变和恶性肿瘤进行建模。对于标准扩散，通过基于无限组织中对流换热的分析模型（例如，Perl 1962给出的模型，随后扩展为[1]），可以通过分析模型提供合理的近似值。

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