Department of Mathematical Sciences "G.L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy.
Department of Mathematics, University of Pavia, Via Ferrata 5, 27100, Pavia, Italy.
Biomech Model Mechanobiol. 2022 Oct;21(5):1483-1509. doi: 10.1007/s10237-022-01602-4. Epub 2022 Jul 30.
Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.
脑肿瘤是最致命的癌症类型之一，因为它们具有很强的侵袭周围组织的能力和对常见治疗方法的广泛耐药性。因此，通过数学和计算模型来再现脑微观结构的异质性非常重要，这些模型可以为研究癌症进展提供强大的工具。然而，只有少数模型包括对脑组织的适当力学和本构描述，而这对于预测病理学的进展以及分析肿瘤生长过程中和（可能）手术切除后健康组织的重新组织可能是相关的。为了通过力学丰富脑癌生长的描述，在本文中，我们提出了一个明确包含脑超弹性的数学多相模型。我们发现，我们的力学描述可以评估生长中的肿瘤对周围健康组织的影响，量化其增殖引起的位移、变形和应力。同时，力学变量的知识可用于模拟应激诱导的生长抑制，以及由于肿瘤引起的变形而适当修改白质束的优先方向。最后，我们的模型模拟在个性化框架中实现，该框架允许包含真实的大脑几何形状、从成像数据重建的患者特定扩散和渗透率张量，并根据癌症生长引起的力学变形对其进行修改。
