抗血管生成治疗抑制实体肿瘤细胞生长的数值模拟:应用血管生成与肿瘤生长的耦合数学模型

为研究抗血管生成因子angiostatin和抗血管生成药物endostatin对肿瘤血管生成和肿瘤细胞的抑制作用,建立耦合肿瘤血管生长、肿瘤生长和血液灌注的数学模型．模拟结果显示抗血管生成因子angiostatin和抗血管生成药物endostatin可明显抑制血管生成和减少肿瘤细胞数量,从而起到改善肿瘤组织内部异常微环境的作用．模型可作为肿瘤抗血管生成治疗的一种理论研究．     

抗血管生成药物Endostantin作用下实体肿瘤血管生成的数值模拟:考虑基质力学环境及血管生成抑素的影响

为研究抗血管生成药物Endostatin作用下,肿瘤血管生成过程中基质力学环境及血管生成抑素的影响,考虑内皮细胞(EC)和细胞外基质(ECM)两相,耦合抗血管生成药物Endostatin和血管生成抑素Angiostatin的抑制效应,建立肿瘤内外血管生成的二维数值模型.抗血管生成因子Angiostatin和药物Endostatin耦合作用时,可明显降低肿瘤组织内的微血管密度,对肿瘤快速生长起到一定的抑制作用.所给出的模型,可以较好模拟基质力学环境影响下,肿瘤抗血管生成因子对内皮细胞迁移和增殖的抑制作用.     

Neuropilin-1与胃癌发生、发展及血管生成的关系

目的探讨胃癌组织中Neuropilin-1、VEGF的表达与胃癌生物学行为及血管生成的关系和意义.方法应用免疫组化ElivisionTM法检测正常胃黏膜、上皮内瘤变、胃癌组织中Neuropilin-1、VEGF、CD34的表达并测定MVD,回顾分析胃癌患者的临床病理资料.结果胃癌组织中Neuropilin-1、VEGF的表达及MVD高于正常胃黏膜和上皮内瘤变组织,且与胃癌淋巴结转移、浸润程度密切相关.Neuropilin-1、VEGF表达阳性组的MVD高于各自阴性组.两者表达呈正相关关系,联合表达时MVD增高.结论 Neuropilin-1、VEGF、血管生成参与了胃癌发生、浸润与转移;Neuropilin-1、VEGF参与了胃癌的血管生成;表达存在协同作用;联合表达时血管生成的效应增强.Neuropilin-1作为肿瘤抗血管治疗的靶点具有一定的价值.     

弹性动脉血管中血液流动特性的模拟和分析

研究了两个不同的非牛顿血液流动模型:低粘性剪切简单幂律模型和低粘性剪切及粘弹性振荡流的广义Maxwell模型．同时利用这两个非牛顿模型和牛顿模型,研究了磁场中刚性和弹性直血管中血液的正弦型脉动．在生理学条件下,大动脉中血液的弹性对其流动性态似乎并不产生影响,单纯低粘性剪切模型可以逼真地模拟这种血液流动．利用高剪切幂律模型模拟弹性血管中的正弦型脉动流,发现在同一压力梯度下,与牛顿流体相比较,幂律流体的平均流率和流率变化幅度都更小．控制方程用Crank-Niclson方法求解．弹性动脉中血液受磁场作用是产生此结果的直观原因．在主动脉生物流的模拟中,与牛顿流体模型比较,发现在匹配流率曲线上,幂律模型的平均壁面剪切应力增大,峰值壁面剪切应力减小．讨论了弹性血管横切磁场时的血液流动,评估了血管形状和表面不规则等因素的影响．     

血液动力学中血管流激波与驻波的相互作用

血液动力学问题是生物力学心血管系统中的重要研究课题.血管内斑块处,血管截面和血管壁的材质发生变化,对血液流动产生重要影响.血液流动中基本波及其相互作用对探究血液流动的规律、生理学意义及与疾病的关系有着重要的意义.本文研究血液动力学血液流动简化数学模型的基本波的相互作用.血管流模型是3×3非严格双曲型方程组.构造性地得到了初值为三段常状态时,血管流问题的解,即解决了激波与驻波的相互作用问题.特别地,给出四种后前激波与驻波的相互作用的结果.     

锥形血管入口区域内管壁与血液的耦合运动

本文研究了锥形血管入口区域内血管壁与血液间的耦合问题。对具有锥度角的弹性血管入口区域内的管壁运动和血液流动建立的相互耦合作用的数学模型，在满足相应的边界条件下求得了一组血液流动的速度分布公式、压力分布公式以及管壁运动公式，得出了一些重要的结论。     

主动脉弓及分支血管内非稳态血流分析

运用流体力学中的三维非定常Navier-Stokes方程作为血液流动的控制方程,并采用计算流体力学方法对人体主动脉弓及分支血管内非Newton(牛顿)血液黏度模型下血流进行瞬态数值模拟.分析了一个心动周期内不同时刻血流动力学特征参数的分布对动脉粥样硬化斑块形成的影响,并与Newton血液黏度模型下的血管壁面压力和壁面切应力特征参数进行对比.结果表明:与Newton血液模型相比,非Newton血液模型下血流分布更符合真实血流特性;在心动收缩期,分支血管外侧壁附近存在面积较大的低速涡流区,该区域内血管壁面压力与壁面切应力具有较大的变化量,血液中的血小板、脂质和纤维蛋白等易沉积,血管内壁易疲劳损伤并发生血管重构,促使动脉粥样硬化斑块形成;而在心动舒张期,分支血管内血流速度分布均匀,血管壁面压力与壁面切应力变化量较小,血管壁受到较小的应力作用,对动脉粥样硬化斑块形成的作用较小.     

二维离散数学模型模拟肿瘤内外血管生成

建立九点差分格式的二维离散数学模型,模拟肿瘤内外的血管生成,模型扩展了内皮细胞沿9个方向运动,考虑存在两根母血管的情况下,耦合内皮细胞在肿瘤内外不同力学环境下的随机、趋化和趋触性运动,数值生成了肿瘤内外异构的血管网.结果表明,该模型可以产生相对真实的具有接近肿瘤病理生理特性的血管网,可为临床研究提供有益的信息.     

脉象的血管位移波理论

本文从医学和力学的分析解释出发,提出采用粘弹性简支梁的数学模型研究血管的位移波,得到了位移波与血管弹性以及血管、血液粘性耗散之间的关系,并讨论了中医脉学中滑脉、浮脉、沉脉类与血管位移波之间的对应关系.计算结果和超声波实测结果十分符合.     

一类非定常流的奇异有限元分析

且引言在生物流体力学中,由于血流具有轴对称性,常常采用圆柱坐标系来研究血管内的血液流动．本文采用〔门中描述血液流动的N－S方程及其相应的定解条件：N－S方程：其中V为血液的轴向速度,V为血液的径向速度,坐标圆点取在血管入口处的截面中心x轴沿管的轴向,广轴沿管的径向,户与厂无关．＊一nU厂。U几U凤．边界条件：初始条件：ul。－。一u。（r,x）,叫t＿。一v。（r,x）,tEI一［0,TI（l．6）此定解问题中,N－S方程在r—0处具有奇异性质,这给数值分析带来了一定的困难．有关二维稳态和非稳态奇异问题有限元方法的研究,…     

A Dynamic Programming Approach for Approximate Optimal Control for Cancer Therapy

In the last 15 years, tumor anti-angiogenesis became an active area of research in medicine and also in mathematical biology, and several models of dynamics and optimal controls of angiogenesis have been described. We use the Hamilton–Jacobi approach to study the numerical analysis of approximate optimal solutions to some of those models earlier analysed from the point of necessary optimality conditions in the series of papers by Ledzewicz and Schaettler.     

A numerical method for nonconvex multi-objective optimal control problems

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang–bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions.     

A mixed radiotherapy and chemotherapy model for treatment of cancer with metastasis

In this paper, a mathematical model of cancer treatment, in the form of a system of ordinary differential equations, by chemotherapy and radiotherapy where there is metastasis from a primary to a secondary site has been proposed and analyzed. The interaction between immune cells and cancer cells has been examined, and the chemotherapy agent has been considered as a predator on both normal and cancer cells. The metastasis may be time delayed. For better investigation of the treatment process and based on physical investigation, the immanent effects of inputs on cancer dynamic have been investigated. It is supposed that the interaction between NK cells and tumor cells changes during the chemotherapy. This novel approach is useful not only to gain a broad understanding of the specific system dynamics but also to guide the development of combination therapies. The analysis is carried out both analytically (where possible) and numerically. By considering such immanent effects, the tumor‐free equilibrium point will be stable at the end of treatment, and the tumor can not recur again, and the patient will totally recover. So, the present analysis suggests that a proper treatment method should change the dynamics of the cancer instead of only reducing the population of cancer cells. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulations of the electrostatic field,temperature, and tissue damage generated by multiple electrodes for electrochemical treatment

Integrated analysis of the spatial distributions of the electric potential, electric field, temperature, and tissue damage generated by multiple arrays of straight needle electrodes inserted into tumors is highly significant for improving the effectiveness of electrochemical treatment. In this study, we simulated the spatial profiles generated by multiple electrodes inserted individually into a tumor and multiple pairs of straight needle electrodes inserted in a tumor surrounded by healthy tissue. Poisson nonlinear and Laplace equations were used to calculate the electric potential in the tumor and the surrounding healthy tissue, respectively. The stationary bioheat transfer equation of Pennes was used to calculate the temperature in both tissues. The percentage tissue damage was computed in each biological medium for each electrode array shape. Numerical simulations showed that the non-homogeneous spatial distributions of the temperature (above 40°C) generated by different types of multiple pairs of straight needle electrodes covered the whole tumor volume. Spatial profiles of this physical magnitude were generated by multiple straight needle electrodes, which were individually inserted into the tumor and partially covered by its volume. In addition, the simulations showed that multiple pairs of electrodes led to tumor damage percentages above 80%. By contrast, multiple electrodes inserted individually in the tumor induced damage percentages below 25%. We conclude that multiple pairs of straight needle electrodes may be applied to deep-seated solid tumors in treatment with electrochemical therapy considering their theoretically calculated high tumor damage percentages.     

Modelling of tumor cells regression in response to chemotherapeutic treatment

The proposed model describes the interaction among normal, immune and tumor cells in a tumor with a chemotherapeutic drug, using a system of four coupled partial differential equations. The dimensions of the tumor and initial conditions of tumor cells are chosen under the assumption that the tumor is already large enough in size to be detectable with the available clinical devices. The pattern of distribution of tumor cells is drafted on the basis of clinical observations. The stability of the system is established with tumor and tumor-free equilibria. The process of tumor regression with the introduction of different diffusion coefficients of tumor and immune cells is considered along with normal cells of tissue without any diffusive movement. It is shown that the results of chemotherapy treatment are in agreement with Jeff’s phenomenon. The response of three different levels of immune system strength to the pulsed chemotherapy are investigated. It is observed that the tumor performs better if a chemotherapeutic drug is injected near the invasive fronts of the tumor.     

A risk-based modeling approach for radiation therapy treatment planning under tumor shrinkage uncertainty

Robust optimization approaches have been widely used to address uncertainties in radiation therapy treatment planning problems. Because of the unknown probability distribution of uncertainties, robust bounds may not be correctly chosen, and a risk of undesirable effects from worst-case realizations may exist. In this study, we developed a risk-based robust approach, embedded within the conditional value-at-risk representation of the dose-volume constraint, to deal with tumor shrinkage uncertainty during radiation therapy. The objective of our proposed model is to reduce dose variability in the worst-case scenarios as well as the total delivered dose to healthy tissues and target dose deviations from the prescribed dose, especially, in underdosed scenarios. We also took advantage of adaptive radiation therapy in our treatment planning approach. This fractionation technique considers the response of the tumor to treatment up to a particular point in time and reoptimizes the treatment plan using an estimate of tumor shrinkage. The benefits of our model were tested in a clinical lung cancer case. Four plans were generated and compared: static, nominal-adaptive, robust-adaptive, and conventional robust (worst-case) optimization. Our results showed that the robust-adaptive model, which is a risk-based model, achieved less dose variability and more control on the worst-case scenarios while delivering the prescribed dose to the tumor target and sparing organs at risk. This model also outperformed other models in terms of tumor dose homogeneity and plan robustness.     

Fast Statistical Surrogates for Dynamical 3D Computer Models of Brain Tumors

Understanding how malignant brain tumors are formed and evolve has direct consequences on the development of efficient methods for their early detection and treatment. Adequate mathematical models for brain tumor growth and invasion can be helpful in clarifying some aspects of the mechanism responsible for the tumor. These mathematical models are typically implemented in computer models, which can be used for computer experimentation to study how changes in inputs, such as growth and diffusion parameters, affect the evolution of the virtual brain tumor. The computer model considered in this article is defined on a three-dimensional (3D) anatomically accurate digital representation of the human brain, which includes white and gray matter, and on a time interval of hundreds of days to realistically simulate the tumor development. Consequently, this computer model is very computationally intensive and only small-size computer experiments can be conducted, corresponding to a small sample of inputs. This article presents a computationally efficient multidimensional kriging method to predict the evolution of the virtual brain tumor at new inputs, conditioned on the virtual brain tumor data available from the small-size computer experiment. The analysis shows that this prediction can be more accurate than a computationally competing model.     

Uncertainty and Option Value in Land Allocation Problems

In intensity-modulated radiation therapy (IMRT) not only is the shape of the beam controlled, but combinations of open and closed multileaf collimators modulate the intensity as well. In this paper, we offer a mixed integer programming approach which allows optimization over beamlet fluence weights as well as beam and couch angles. Computational strategies, including a constraint and column generator, a specialized set-based branching scheme, a geometric heuristic procedure, and the use of disjunctive cuts, are described. Our algorithmic design thus far has been motivated by clinical cases. Numerical tests on real patient cases reveal that good treatment plans are returned within 30 minutes. The MIP plans consistently provide superior tumor coverage and conformity, as well as dose homogeneity within the tumor region while maintaining a low irradiation to important critical and normal tissues.     

Stochastic stability and state shifts for a time-delayed cancer growth system subjected to correlated multiplicative and additive noises

In the present paper, we investigate the stationary probability distribution(SPD) and the mean treatment time of a time-delayed cancer growth system induced by cross-correlated intrinsic and extrinsic noises. Our main results show that the resonant-like phenomenon of the mean first-passage time (MFPT) appears in the tumor cell growth model due to the interaction of all kinds of noises and time delay. Due to the existence of the resonant-like peak value, by increasing the intensity of multiplicative noise and time delay, it is possible to restrain effectively the development of the cancer cells and enhance the stability of the system. During the process of controlling the diffusion of the tumor cells, it contributes to inhibiting the development of cancer by increasing the cross-correlated noise strength and weakening the additive noise intensity and time delay. Meanwhile, the proper multiplicative noise intensity is conducive to the process of inhibition. Conversely, in the process of exterminating cancer cells of a large density, it can exert positive effects on eliminating the tumor cells by increasing noises intensities and the value of time delay.     

Qualitative analysis of an integro-differential equation model of periodic chemotherapy

An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined.