Effects of pulsating heat source on interstitial fluid transport in tumor tissues

Macromolecules and drug delivery to solid  tumors is strongly
influenced by fluid flow through interstitium, and pressure-induced tissue
deformations can have a role in this. Recently, it has been shown that
temperature-induced tissue deformation can influence interstitial fluid
velocity and pressure fields, too. In this paper, the effect of
modulating-heat strategies to influence interstitial fluid transport in
tissues is analyzed. The whole tumor tissue is modeled as a deformable
porous material, where the solid phase is made up by extracellular matrix
and cells, while the fluid phase is the interstitial fluid that moves
through the solid matrix driven by fluid pressure gradient and vascular
capillaries that are modelled as uniformly interspersed fluid
point-source. Pulsating-heat generation is modeled with a time-variable
cosine function starting from a direct current approach to solve voltage
equation, for different pulsations. From the steady-state solution, a
step-variation of vascular pressure included in the model equation as a
mass source term via Starling equation is simulated. Dimensionless 1D
radial equations are numerically solved with a finite element-scheme.
Results are presented in terms of temperature, volumetric strain, pressure
and velocity profiles under different conditions. It is shown that a
modulating-heat procedure influences velocity fields, that might have a
consequence in terms of mass transport for macromolecules or drug
delivery.

大分子（macromolecules）与实体瘤（solid tumors）药物递送（drug delivery）过程，极易受组织间隙（interstitium）流体流动的影响，而压力诱导的组织变形亦在此过程中发挥重要作用。近期研究证实，温度诱导的组织变形同样可对组织间隙液流速与压力场产生调控效应。本文针对调热策略（modulating-heat strategies）调控组织间隙流体输运的作用效果展开分析。研究中将完整肿瘤组织建模为可变形多孔介质（deformable porous material）：固相由细胞外基质与细胞构成，液相则为受流体压力梯度驱动、在固相基质中流动的组织间隙液；同时将毛细血管（vascular capillaries）建模为均匀分布的流体点源（fluid point-source）。针对不同脉动频率，采用以直流方法（direct current approach）求解电压方程（voltage equation）为基础的时变余弦函数（time-variable cosine function），对脉动产热（pulsating-heat generation）过程进行建模。基于稳态解（steady-state solution），通过斯塔林方程（Starling equation）将血管压力的阶跃变化以质量源项形式纳入模型方程中进行仿真。研究采用有限元格式（finite element-scheme）对无量纲一维径向方程（dimensionless 1D radial equations）进行数值求解。研究结果以不同工况下的温度、体积应变（volumetric strain）、压力及速度分布（velocity profiles）形式呈现。结果表明，调热操作可对流体流速场产生显著调控作用，这一效应或可对大分子或药物递送的质量输运过程产生影响。