Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federico II, Piazzale Tecchio 80, Napoli 80125, Italy.
Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federico II, Piazzale Tecchio 80, Napoli 80125, Italy.
J Biomech. 2020 Dec 2;113:110122. doi: 10.1016/j.jbiomech.2020.110122. Epub 2020 Nov 10.
Modeling flow field in tumor regions interstitial space is of primary importance, because of the importance of advection in macromolecule drug delivery. Its deformation has also to be taken into account because of the forces caused by the fluid; if the tumor region is not isothermal, this deformation can be also strongly affected by temperature fields. In this paper, the effects of thermal boundary conditions on a tumor region periphery with an internal heat source are investigated. The tumor region is modeled as a deformable sphere, in which two phases can be distinguished. The fluid phase is the interstitial fluid, while the rest of the tumor is modeled as the solid phase, including also capillaries and tissues. Transient-state governing equations for mass, momentum and energy are written for both phases, by also considering tumor deformation under the linear elastic material assumption. A situation of Tumor Blood Flow (TBF) rapid decay, in which vascular pressure rapidly approaches to zero, is considered, while the heat source is modeled as a fourth-grade radial-decay function. Boundary conditions for the energy equation are varied on the external surface of the sphere, in order to appreciate the effects of the surrounding on flow and temperature fields inside the tumor. After scaling equations, a finite-element scheme is employed for the numerical solution. Comparisons with analytical solutions from literature show a good agreement. Results are shown for different dimensionless parameters that are referred to temperature, volumetric strain, pressure and velocity, showing in which case external boundary conditions strongly affect tumor region flow fields and a third-kind boundary condition is needed.
对肿瘤区域间质空间的流场进行建模至关重要，因为在大分子药物输送中，扩散非常重要。由于流体产生的力，肿瘤区域的变形也必须考虑在内；如果肿瘤区域不是等温的，这种变形也会受到温度场的强烈影响。本文研究了热边界条件对具有内部热源的肿瘤区域外围的影响。肿瘤区域被建模为一个可变形的球体，可以区分两个相。流体相是间质液，而肿瘤的其余部分被建模为固体相，包括毛细血管和组织。通过在线性弹性材料假设下考虑肿瘤变形，为两个相写出了质量、动量和能量的瞬态控制方程。考虑了一种肿瘤血流（TBF）快速衰减的情况，其中血管压力迅速接近零，而热源被建模为四阶径向衰减函数。为了了解周围环境对肿瘤内部流动和温度场的影响，在球体的外部表面上改变了能量方程的边界条件。对方程进行了缩放后，采用有限元方案进行数值求解。与文献中的解析解进行比较，结果吻合良好。针对不同的无量纲参数（与温度、体积应变、压力和速度有关）展示了结果，表明在何种情况下外部边界条件会强烈影响肿瘤区域的流场，需要使用第三类边界条件。
