利用血管生成模型计算实体肿瘤内的血液动力学

肿瘤血管生成(Tumor-induced Angiogenesis)是指在实体肿瘤细胞诱导下毛细血管的生长以及肿瘤中血液微循环的建立。肿瘤内血液、组织液等流体流动在肿瘤药物输运过程中扮演着重要作用,而这些流动受到肿瘤内微血管网络结构的直接影响。目前要获得精确的肿瘤内外的毛细血管拓扑结构存在一定困难,因此给肿瘤内的血液动力学研究带来困难。本文根据肿瘤内外的复杂生理特性,建立肿瘤内外血管生成的二维离散模型,在获得相对真实的毛细血管网络拓扑结构基础上对肿瘤内的血液动力学进行初步计算,数值计算的结果加深了对肿瘤的复杂生理特性的理解,同时也给肿瘤内的药物输运给予一定的提示。     

Experimental study of two-phase flow in three sandstones. II. Capillary pressure curve measurement and relative permeability pore space capillary models

By means of the porous plate method and mercury porosimetry intrusion tests, capillary pressure curves of three different sandstones were measured. The testing results have been exploited jointly with three relative permeability models of the pore space capillary type (Burdine’s model type), these models are widely used and in rather distinct fields. To do so, capillary pressure has been correlated to saturation degree using six of the most popular relations encountered in the literature. Model predictions were systematically compared to the experimentally measured relative permeabilities presented in the first part of this work. Comparison indicated that the studied models underestimate the water relative permeability and over-estimate that of the non-wetting phase. Moreover, this modeling proves to be unable to locate the significant points that are the limits of fields of saturation where the variation of the relative permeabilities becomes consequent. We also showed that, if pore structure is modeled as a “bundle of capillary tubes”, model predications are independent of the capillary pressure curve measuring method.     

INSTABILITY OF COUPLED THERMO-SOLUTE CAPILLARY CONVECTION IN LIQUID BRIDGE AND CONTROL BY ROTATING MAGNETIC FIELD

浮区法因具有无坩埚接触污染的生长优点而成为生长高完整性和高均匀性单晶材料的重要技术.但熔体中存在的毛细对流会给浮区法晶体生长带来极大挑战,这是由于对流的不稳定会导致晶体微观瑕疵的产生和宏观条纹等缺陷的形成.为了提高浮区法生长单晶材料的品质,研究浮区法晶体生长中毛细对流特性及如何控制其不稳定性显得尤为重要.本文采用数值模拟的方法对半浮区液桥内Si_xGe_1-x体系中存在的热质毛细对流展开研究并施加旋转磁场对其进行控制.结果表明：纯溶质毛细对流表现为二维轴对称模式,温度场主要由热扩散作用决定,而浓度场则由对流和溶质扩散共同支配;纯热毛细对流呈现三维稳态非轴对称流动,浓度分布与熔体内热毛细对流的流向密切相关,等温线在对流较大的区域发生弯曲;耦合溶质与热毛细对流则为三维周期性旋转振荡流.施加旋转磁场后,熔体周向速度沿径向向外增大,熔体内浓度场和流场均呈现二维轴对称分布.     

On study of horizontal thin film flow of Sisko fluid due to surface tension gradient

The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method (ADM). The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile, and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.     

Biochemomechanical poroelastic theory of avascular tumor growth

Tumor growth is a complex process involving genetic mutations, biochemical regulations, and mechanical deformations. In this paper, a thermodynamics-based nonlinear poroelastic theory is established to model the coupling among the mechanical, chemical, and biological mechanisms governing avascular tumor growth. A volumetric growth law accounting for mechano-chemo-biological coupled effects is proposed to describe the development of solid tumors. The regulating roles of stresses and nutrient transport in the tumor growth are revealed under different environmental constraints. We show that the mechano-chemo-biological coupling triggers anisotropic and heterogeneous growth, leading to the formation of layered structures in a growing tumor. There exists a steady state in which tumor growth is balanced by resorption. The influence of external confinements on tumor growth is also examined. A phase diagram is constructed to illustrate how the elastic modulus and thickness of the confinements jointly dictate the steady state of tumor volume. Qualitative and quantitative agreements with experimental observations indicate the developed model is capable of capturing the essential features of avascular tumor growth in various environments.     

双自由面溶质?热毛细液层的不稳定性

溶质?热毛细对流是流体界面的浓度和温度分布不均导致的表面张力梯度驱动的流动, 它主要存在于空间微重力环境、小尺度流动等表面张力占主导的情况中, 例如晶体生长、微流控、合金浇筑凝固、有机薄液膜生长等. 对其流动进行稳定性分析具有重要意义. 本文采用线性稳定性理论研究了双自由面溶质?热毛细液层对流的不稳定性, 得到了两种负毛细力比(η)下的临界Marangoni数与Prandtl数(Pr)的函数关系, 并分析了临界模态的流场和能量机制. 研究发现: 溶质?热毛细对流和纯热毛细对流的临界模态有较大的差别, 前者是同向流向波、逆向流向波、展向稳态模态和逆向斜波, 后者是逆向斜波和逆向流向波. 在Pr较大时, Pr增加会降低流动稳定性; 在其他参数下, Pr增加会增强流动稳定性. 在中低Pr, 溶质毛细力使流动更加不稳定; 在大Pr时, 溶质毛细力的出现可能使流动更加稳定; 在其他参数下, 溶质毛细力会减弱流动稳定性. 流动稳定性不随η单调变化. 在多数情况下, 扰动浓度场与扰动温度场都是相似的. 能量分析表明: 扰动动能的主要能量来源是表面张力做功, 但其中溶质毛细力和热毛细力做功的正负性与参数有关.      

Numerical Investigation of Magnetic Nanoparticles Distribution Inside a Cylindrical Porous Tumor Considering the Influences of Interstitial Fluid Flow

A numerical simulation of interstitial fluid flow and blood flow and diffusion of magnetic nanoparticles (MNPs) are developed, based on the governing equations for the fluid flow, i.e., the continuity and momentum and mass diffusion equations, to a tissue containing two-dimensional cylindrical tumor. The tumor is assumed to be rigid porous media with a necrotic core, interstitial fluid and two capillaries with arterial pressure input and venous pressure output. Blood flow through the capillaries and interstitial fluid flow in tumor tissues are carried by extended Poiseuille’s law and Darcy’s law, respectively. Transvascular flows are also described using Starling’s law. MNPs diffuse by interstitial fluid flow in tumor. The finite difference method has been used to simulate interstitial fluid pressure and velocity, blood pressure and velocity and diffusion of MNPs injected inside a biological tissue during magnetic fluid hyperthermia (MFH). Results show that the interstitial pressure has a maximum value at the center of the tumor and decreases toward the first capillary. The reduction continues between two capillaries, and interstitial pressure finally decreases in direction of the tumor perimeter. This study also shows that decreasing in intercapillary distance may cause a decrease in interstitial pressure. Furthermore, multi-site injection of nanoparticles has better effect on MFH.     

非饱和土力学理论的研究进展

回顾了非饱和土有效应力的发展,目前普遍认同采用两个应力变量来建立本构模型,且对基质吸力中毛细和粘吸两部分作用进行了阐述。分析了非饱和土强度问题,包括抗剪强度和抗拉强度。讨论了非饱和土的本构模型问题,包括基于净应力和基质吸力的弹塑性模型,基于Bishop有效应力和基质吸力的水力力学耦合弹塑性模型,以及双孔隙结构的模型。最后探讨了热力学方法和多孔介质理论在非饱和土中的应用,基于多孔介质理论在多场耦合条件下土体复杂的行为是当前值得研究的问题。     

内皮抑素抑制肿瘤血管生成的数值模拟

数值模拟抗血管生成药物内皮抑素对肿瘤血管生成的抑制效应. 建立内皮抑素作用下肿瘤内外血管生成的二维、三维离散数学模型,模型中考虑内皮抑素的抑制作用、内皮细胞自身的增殖、促血管生成因子TAF和Fibronectin对内皮细胞产生的趋化性和趋触性以及内皮细胞自身扩散引起的随机性运动,数值模拟肿瘤内外微血管网的生成过程. 模拟结果表明,抗血管生成药物内皮抑素对肿瘤内外血管生成的速度、成熟度以及血管分支数量均有明显的抑制作用,从而有效地抑制肿瘤新生血管的形成. 该模型能够较好地模拟内皮抑素对肿瘤血管内皮细胞迁移与增殖的抑制效应,为临床抗血管生成治疗肿瘤提供有益的信息.      

表面张力液柱中粘性引起的模分裂

本文证明粘性会使得表面张力所维持的无限长液柱运动模发生分裂(或称分叉),结果是每个轴对称模一次分裂为无穷个。这种现象类似于原生物理学中的 Zeemen 和 Stark效应。无粘条件下的不稳定模分裂后还出现可数无穷个负势能的稳定模,这是关于连续系统模稳定性的 Hare 和 Chandrasekhar 势能判据的一个反例,并解释其物理意义。     

Motion of a gas inclusion in a capillary under the action of vibration

The motion of gas inclusions in a liquid-filled duct under the action of vibration for comparable cross-sectional dimensions of the inclusion and the duct is studied. Two limiting cases of inclusion motion differing with respect to the drag mechanism are considered. For low velocities, it is assumed that the drag is mainly determined by the capillary forces and the friction in the liquid film separating the gas inclusion from the duct wall. As the inclusion velocity increases, the main contribution to the drag is made by such mechanisms as flow separation, the formation of a low-pressure region in the wake, etc. It is demonstrated that due to the vibration a gas inclusion traveling in a capillary under the action of steady forces is halted at certain points of the capillary. The capillary behaves like a filter, impermeable for inclusions smaller than a certain threshold size. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 85–92, May–June, 1998. The work received financial support from the Russian Foundation for Basic Research (project No.96-01-01813).     

Local Bifurcation for Steady Periodic Capillary Water Waves with Constant Vorticity

We study periodic capillary waves at the free surface of water in a flow with constant vorticity over a flat bed. Using bifurcation theory the local existence of waves of small amplitude is proved even in the presence of stagnation points in the flow. We also derive the dispersion relation.     

Sessile drop deformations under an impinging jet

The problem of steady axisymmetric deformations of a liquid sessile drop on a flat solid surface under an impinging gas jet is of interest for understanding the fundamental behavior of free surface flows as well as for establishing the theoretical basis in process design for the Aerosol \({{\rm Jet}^{\circledR}}\) direct-write technology. It is studied here numerically using a Galerkin finite-element method, by computing solutions of Navier–Stokes equations. For effective material deposition in Aerosol \({{\rm Jet}^{\circledR}}\) printing, the desired value of Reynolds number for the laminar gas jet is found to be greater than ~500. The sessile drop can be severely deformed by an impinging gas jet when the capillary number is approaching a critical value beyond which no steady axisymmetric free surface deformation can exist. Solution branches in a parameter space show turning points at the critical values of capillary number, which typically indicate the onset of free surface shape instability. By tracking solution branches around turning points with an arc-length continuation algorithm, critical values of capillary number can be accurately determined. Near turning points, all the free surface profiles in various parameter settings take a common shape with a dimple at the center and bulge near the contact line. An empirical formula for the critical capillary number for sessile drops with \({45^{\circ}}\) contact angle is derived for typical ranges of jet Reynolds number and relative drop sizes especially pertinent to Aerosol \({{\rm Jet}^{\circledR}}\) printing.     

Mathematical modeling of anisotropic avascular tumor growth

Cancer represents one the most challenging problems in medicine and biology nowadays, and is being actively addressed by many researchers from different areas of knowledge. The increasing development of sophisticated mathematical models and computer-based procedures has had a positive impact on our understanding of cancer-related mechanisms and the design of anticancer treatment strategies. However, further investigation and experimentation are still required to completely elucidate the tumor-associated mechanical responses, as well as the effect of mechanical forces on the net tumor growth. In this work we develop a theoretical framework in the context of continuum mechanics to investigate the anisotropic growth of avascular tumor spheroids. To that end, a specific anisotropic growth deformation tensor is considered, which also describes an isotropic growth law as a particular case. Mixtures theory and the notion of multiple natural configurations are then used to formulate a mathematical model of avascular tumor growth. More precisely, mass, momentum balance and nutrients diffusion equations are derived, where solid tumors are assumed as hyperelastic and compressible materials. Moreover, mechanical interactions with a rigid extracellular matrix (ECM) are considered, and the mechanical modulation of growing tumors in a rigid surrounding tissue is investigated by means of numerical simulations. Finally, the model results are compared with experimental data previously reported in the literature.     

A model of liquid phase sintering by the homogenization

We study the first stage of liquid phase sintering, when the particles rearrangement due to capillary forces is over. We give the boundary value problem satisfied by the displacement field of points of the medium in the phase of elastic compression of solid particles, for given capillary forces acting as a density of external forces, by using the homogenization method and we characterize the mechanical behavior of this constrained medium from the material properties of each elementary components.     

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.     

Application of the TVD scheme to the nonlinear instability analysis of a capillary jet

In the past, when either the perturbation‐type method or direct‐simulation approach was used to analyse capillary jets, the governing equations, which are parabolic in time and elliptic in space, were simplified or linearized. In the present study, the convective derivative term and a full, nonlinear form of the capillary pressure term are retained in the governing equations to investigate nonlinear effects on the break‐up of capillary jets. In this work, the TVD (i.e. total variation diminishing) scheme with flux‐vector splitting is applied to obtain the solutions of the system of nonlinear equations in a matrix form. Numerical results show that the present nonlinear model predicts longer jet break‐up lengths and slower growth rates for capillary jets than the previous linear model does. Comparing with other measurements from past literatures, the nonlinear results are consistent with the experimental data and appear more accurate than the linear analysis. In the past, the classic perturbation‐type analyses assumed constant growth rates for the fundamental and all harmonic components. By contrast, the present model is able to capture the local features of growth rates, which are not spatially and temporally constant. Copyright © 2006 John Wiley & Sons, Ltd.     

Free surface deformation due to a source or a sink in Stokes flow

Free surface shape and cusp formation are analyzed by considering two-dimensional viscous flow due to a line source or a line sink below the free surface where the strength of source/sink is given arbitrarily. In the analysis, the Stokes' approximation is used and surface tension effects are included, but gravity is neglected. The solution is obtained analytically by using conformal mapping and complex function theory. From the solution, shapes of the free surface are shown and the formation of a cusp on the free surface is discussed. As the capillary number decreases in negative, the free surface shape becomes singular and in a real fluid a cusp should form on the free surface below some negative critical capillary number. Typically, streamline patterns for some capillary numbers are also shown. As the small capillary number vanishes, the solution is reduced to a linearized potential flow solution.     

On a Nonlinear Model for Tumor Growth: Global in Time Weak Solutions

We investigate the dynamics of a class of tumor growth models known as mixed models. The key characteristic of these type of tumor growth models is that the different populations of cells are continuously present everywhere in the tumor at all times. In this work we focus on the evolution of tumor growth in the presence of proliferating, quiescent and dead cells as well as a nutrient. The system is given by a multi-phase flow model and the tumor is described as a growing continuum Ω with boundary ?Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation.     

Theory of water waves in an elastic vessel

Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Based on this new finding, a theory of parametric resonance is developed in detail to explain the on-set of the prominent circumferential capillary waves. Numerical computation is also carried out and the results agree generally with the experiments. Analysis and numerical computation are also presented to explain the generation of axisymmetric low-frequency gravity waves by the high-frequency external excitation.