基于THB样条的局部自适应等几何分析在Cahn-Hilliard相场肿瘤生长建模中的应用
Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines
- University of Pavia（帕维亚大学）
- Università degli Studi di Firenze（佛罗伦萨大学）
- University of A Coruña（拉科鲁尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本研究采用基于Cahn-Hilliard方程的相场模型，结合局部自适应等几何分析和THB样条，高效模拟肿瘤生长，并在MRI重建的乳房模型上验证了其预测能力。
中文摘要 AI 辅助
在生理相关条件下，使用数学和计算模型预测生物系统中的肿瘤动力学仍然是一个具有挑战性的问题。基于相场（扩散界面）公式的连续介质模型已被证明是控制肿瘤动力学和多物种相互作用的有效建模策略。在此框架内，本研究探讨了基于Cahn-Hilliard（CH）方程的肿瘤生长模型。该公式涉及一个四阶微分算子，对近似空间提出了更高的连续性要求，以实现良定的原始变分公式。为了应对这一挑战，我们使用等几何分析（IGA），该方法通过基于样条的基函数固有地满足这一要求，并消除了标准有限元离散化中常用的混合或辅助变量方法的需要。此外，采用具有截断层次B样条（THB样条）的局部自适应IGA方案，以在保持精度的同时降低计算成本。该模型首先在标准基准案例上进行评估，然后应用于从磁共振成像（MRI）数据重建的器官尺度、患者特异性乳房几何模型。我们的结果表明，该模型再现了已知的肿瘤形态，从球状模式到指状生长。一系列数值实验进一步展示了不同模型参数选择所产生的肿瘤动力学多样性。我们的研究结果表明，基于CH的相场肿瘤生长模型与局部自适应IGA框架相结合具有预测潜力。
英文摘要
Predicting tumor dynamics in biological systems under physiologically relevant conditions using mathematical and computational models remains a challenging problem. Continuum models based on phase-field (diffuse-interface) formulations have proven to be an effective modeling strategy to govern tumor dynamics and interactions of multiple species. Within this framework, the present work investigates a tumor growth model based on the Cahn-Hilliard (CH) equation. The formulation involves a fourth-order differential operator that imposes higher continuity requirement on approximation spaces for a well-defined primal variational formulation. To address this challenge, we use isogeometric analysis (IGA), which inherently satisfies this requirement through spline-based basis functions and eliminates the need for mixed or auxiliary-variable approaches commonly used in standard finite element discretizations. Additionally, a locally adaptive IGA scheme with truncated hierarchical B-splines (THB-splines) is used to reduce computational cost while maintaining accuracy. The model is first evaluated on standard benchmark cases and then applied to an organ-scale, patient-specific geometric model of the breast reconstructed from magnetic resonance imaging (MRI) data. Our results show that the model reproduces known tumor morphologies, ranging from a spheroidal pattern to fingered growth. A series of numerical experiments further shows the diversity of tumor dynamics produced by different model parameter choices. Our findings demonstrate the predictive potential of the CH-based phase-field tumor growth model integrated with a locally adaptive IGA framework.
