Mathematical modeling of ovarian cancer treatments: sequencing of surgery and chemotherapy

Ovarian cancer has long been one of the most common forms of cancer in women. The main treatment for ovarian cancer comprises a combination of surgery and chemotherapy. In an effort to improve treatment strategies, a variety of mathematical models have been developed in the literature. In this paper, we consider a simple mathematical model that incorporates tumor growth as well as the effects of chemotherapeutic and surgical treatments in ovarian cancer. We consider several growth models and combine them with different cell-kill hypotheses. Surgery is assumed to eliminate a fixed fraction of tumor cells instantaneously. We discuss how different models predict the optimal sequencing of chemotherapeutic and surgical treatments. This work has been carried out in the context of ovarian cancer; however, the results may also be useful for other kind of cancers.     

Coupling biomechanics to a cellular level model: an approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.     

3D Multi-Cell Simulation of Tumor Growth and Angiogenesis

We present a 3D multi-cell simulation of a generic simplification of vascular tumor growth which can be easily extended and adapted to describe more specific vascular tumor types and host tissues. Initially, tumor cells proliferate as they take up the oxygen which the pre-existing vasculature supplies. The tumor grows exponentially. When the oxygen level drops below a threshold, the tumor cells become hypoxic and start secreting pro-angiogenic factors. At this stage, the tumor reaches a maximum diameter characteristic of an avascular tumor spheroid. The endothelial cells in the pre-existing vasculature respond to the pro-angiogenic factors both by chemotaxing towards higher concentrations of pro-angiogenic factors and by forming new blood vessels via angiogenesis. The tumor-induced vasculature increases the growth rate of the resulting vascularized solid tumor compared to an avascular tumor, allowing the tumor to grow beyond the spheroid in these linear-growth phases. First, in the linear-spherical phase of growth, the tumor remains spherical while its volume increases. Second, in the linear-cylindrical phase of growth the tumor elongates into a cylinder. Finally, in the linear-sheet phase of growth, tumor growth accelerates as the tumor changes from cylindrical to paddle-shaped. Substantial periods during which the tumor grows slowly or not at all separate the exponential from the linear-spherical and the linear-spherical from the linear-cylindrical growth phases. In contrast to other simulations in which avascular tumors remain spherical, our simulated avascular tumors form cylinders following the blood vessels, leading to a different distribution of hypoxic cells within the tumor. Our simulations cover time periods which are long enough to produce a range of biologically reasonable complex morphologies, allowing us to study how tumor-induced angiogenesis affects the growth rate, size and morphology of simulated tumors.     

A mathematical algorithm that computes breast cancer sizes and doubling times detected by screening

This paper presents a mathematical algorithm that computes the sizes and growth rates of breast cancer detected in a hypothetical population that is screened for the disease. The algorithm works by simulating the outcomes of the hypothetical population twice, first without screening and then with screening. The simulation without screening relies on an underlying model of the natural history of the disease. The simulation with screening uses this natural history model to track the growth of breast tumors backwards in the time starting from the time they would have been detected without screening. The method of tracking tumor growth backward in time is different from methods that track tumor growth forward in time by starting from an estimated time of tumor onset. The screening algorithm combines the natural history model, the method tracking of tumor growth backward in time, the age group, the interval between screening exams, and the detection threshold of the screening exam to compute the joint distribution of tumor size and growth rate among screen-detected and interval patients. The algorithm also computes the sensitivity and leadtime distribution. It allows for arbitrary age groups, detection thresholds and screening intervals and may contribute to the design of future screening trials.     

Modeling and computer simulations of tumor growth and tumor response to radiotherapy

A model of tumor growth and tumor response to radiation is introduced in which each tumor cell is taken into account individually. Each cell is assigned a set of radiobiological parameters, and the status of each cell is checked in discrete intervals. Tumor proliferation is governed by the cell cycle times of tumor cells, the growth fraction, the apoptotic capacity of the tumor, and the degree of tumor angiogenesis. The response of tumor cells to radiation is determined by the radiosensitivities and the oxygenation status. Computer simulation is performed on a 3D rigid cubic lattice, starting out from a single tumor cell. Random processes are simulated by Monte Carlo methods. Short cell cycle time, high growth fraction, and tumor angiogenesis all increase tumor proliferation rates. Accelerated time-dose patterns result in lower total doses needed for tumor control, but the extent of dose reduction depends on the kinetics and the radiosensitivities of tumor cells. Tumor angiogenesis alters fully oxygenated and hypoxic fractions within the tumor and subsequently affects the radiation response. It is demonstrated for selected radiobiological parameters that the simulation tools are suitable to quantitatively assess the total doses needed for tumor control. Using the simulation tools, it is feasible to simulate time-dependent effects during fractionated radiotherapy and to compare different time-dose patterns in terms of their tumor control.     

A Comparison and Catalog of Intrinsic Tumor Growth Models

Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are several competing canonical tumor growth models that are often implemented, how to determine which of the models should be used for which tumor types remains an open question. In this work, we determine the best fit growth dynamics and associated parameter ranges for ten different tumor types by fitting growth functions to at least five sets of published experimental growth data per type of tumor. These time-series tumor growth data are used to determine which of the five most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor.     

Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro

We present a three-dimensional individual cell-based, biophysical model to study the effect of normal and malfunctioning growth regulation and control on the spatial-temporal organization of growing cell populations in vitro. The model includes explicit representations of typical epithelial cell growth regulation and control mechanisms, namely 1), a cell-cell contact-mediated form of growth inhibition; 2), a cell-substrate contact-dependent cell-cycle arrest; and 3), a cell-substrate contact-dependent programmed cell death (anoikis). The model cells are characterized by experimentally accessible biomechanical and cell-biological parameters. First, we study by variation of these cell-specific parameters which of them affect the macroscopic morphology and growth kinetics of a cell population within the initial expanding phase. Second, we apply selective knockouts of growth regulation and control mechanisms to investigate how the different mechanisms collectively act together. Thereby our simulation studies cover the growth behavior of epithelial cell populations ranging from undifferentiated stem cell populations via transformed variants up to tumor cell lines in vitro. We find that the cell-specific parameters, and in particular the strength of the cell-substrate anchorage, have a significant impact on the population morphology. Furthermore, they control the efficacy of the growth regulation and control mechanisms, and consequently tune the transition from controlled to uncontrolled growth that is induced by the failures of these mechanisms. Interestingly, however, we find the qualitative and quantitative growth kinetics to be remarkably robust against variations of cell-specific parameters. We compare our simulation results with experimental findings on a number of epithelial and tumor cell populations and suggest in vitro experiments to test our model predictions.     

肿瘤血管新生的数值模拟

利用Overture开发肿瘤血管新生模型的计算程序,使用有限差分法模拟肿瘤血管新生过程中,血管内皮细胞在细胞间基质中的增生和迁徙,阐明了血管内皮生长因子和血管新生因子的调节机制.针对三种调节因子的不同组合下的模型进行数值模拟,对比说明三种因子在肿瘤血管新生中的不同作用.模型计算结果与病理学现象实验一致.     

Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis

Tumor anti-angiogenesis is a cancer treatment approach that aims at preventing the primary tumor from developing its own vascular network needed for further growth. In this paper the problem of how to schedule an a priori given amount of angiogenic inhibitors in order to minimize the tumor volume is considered for three related mathematical formulations of a biologically validated model developed by Hahnfeldt et al. [1999. Tumor development under angiogenic signalling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 59, 4770-4775]. Easily implementable piecewise constant protocols are compared with the mathematically optimal solutions. It is shown that a constant dosage protocol with rate given by the averaged optimal control is an excellent suboptimal protocol for the original model that achieves tumor values that lie within 1% of the theoretically optimal values. It is also observed that the averaged optimal dose is decreasing as a function of the initial tumor volume.     

Opposing Roles of Mitogenic and Stress Signaling Pathways in the Induction of Cancer Dormancy

Cancer dormancy is a poorly understood stage of cancer progression. However, the ability to control this step of the disease offers novel therapeutic opportunities. Here we summarize recent findings that implicate the extracellular matrix and adhesion receptor signaling in the escape or induction of tumor dormancy. We further review evidence suggesting that imbalances in the activity ratio of ERK to p38 signaling may determine the fate (i.e. tumorigenicity vs. dormancy) of different carcinoma cells. Special attention is placed on the mechanisms that p38 signaling regulates during the induction of dormancy and how modulation of these pathways may offer a therapeutic opportunity. We also review evidence for a novel drug-resistance mechanism in dormant tumor cells that when blocked may enable killing of dormant tumor cells. Finally, we explore the notion that dormancy of tumor cells may be the result of a selective adaptive response that allows disseminated tumor cells to pause their growth and cope with stress signaling imposed by dissemination and/or treatment until growth can be restored.     

Multi-scale agent-based brain cancer modeling and prediction of TKI treatment response: Incorporating EGFR signaling pathway and angiogenesis

ABSTRACT: BACKGROUND: The epidermal growth factor receptor (EGFR) signaling pathway and angiogenesis in brain cancer act as an engine for tumor initiation, expansion and response to therapy. Since the existing literature does not have any models that investigate the impact of both angiogenesis and molecular signaling pathways on treatment, we propose a novel multi-scale, agent-based computational model that includes both angiogenesis and EGFR modules to study the response of brain cancer under tyrosine kinase inhibitors (TKIs) treatment. RESULTS: The novel angiogenesis module integrated into the agent-based tumor model is based on a set of reaction--diffusion equations that describe the spatio-temporal evolution of the distributions of micro-environmental factors such as glucose, oxygen, TGFalpha, VEGF and fibronectin. These molecular species regulate tumor growth during angiogenesis. Each tumor cell is equipped with an EGFR signaling pathway linked to a cell-cycle pathway to determine its phenotype. EGFR TKIs are delivered through the blood vessels of tumor microvasculature and the response to treatment is studied. CONCLUSIONS: Our simulations demonstrated that entire tumor growth profile is a collective behaviour of cells regulated by the EGFR signaling pathway and the cell cycle. We also found that angiogenesis has a dual effect under TKI treatment: on one hand, through neo-vasculature TKIs are delivered to decrease tumor invasion; on the other hand, the neo-vasculature can transport glucose and oxygen to tumor cells to maintain their metabolism, which results in an increase of cell survival rate in the late simulation stages.     

Simulating tumor growth in confined heterogeneous environments

The holy grail of computational tumor modeling is to develop a simulation tool that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies. In order to develop such a predictive model, one must account for many of the complex processes involved in tumor growth. One interaction that has not been incorporated into computational models of neoplastic progression is the impact that organ-imposed physical confinement and heterogeneity have on tumor growth. For this reason, we have taken a cellular automaton algorithm that was originally designed to simulate spherically symmetric tumor growth and generalized the algorithm to incorporate the effects of tissue shape and structure. We show that models that do not account for organ/tissue geometry and topology lead to false conclusions about tumor spread, shape and size. The impact that confinement has on tumor growth is more pronounced when a neoplasm is growing close to, versus far from, the confining boundary. Thus, any clinical simulation tool of cancer progression must not only consider the shape and structure of the organ in which a tumor is growing, but must also consider the location of the tumor within the organ if it is to accurately predict neoplastic growth dynamics.     

The Tumor Growth Paradox and Immune System-Mediated Selection for Cancer Stem Cells

Cancer stem cells (CSCs) drive tumor progression, metastases, treatment resistance, and recurrence. Understanding CSC kinetics and interaction with their nonstem counterparts (called tumor cells, TCs) is still sparse, and theoretical models may help elucidate their role in cancer progression. Here, we develop a mathematical model of a heterogeneous population of CSCs and TCs to investigate the proposed “tumor growth paradox”—accelerated tumor growth with increased cell death as, for example, can result from the immune response or from cytotoxic treatments. We show that if TCs compete with CSCs for space and resources they can prevent CSC division and drive tumors into dormancy. Conversely, if this competition is reduced by death of TCs, the result is a liberation of CSCs and their renewed proliferation, which ultimately results in larger tumor growth. Here, we present an analytical proof for this tumor growth paradox. We show how numerical results from the model also further our understanding of how the fraction of cancer stem cells in a solid tumor evolves. Using the immune system as an example, we show that induction of cell death can lead to selection of cancer stem cells from a minor subpopulation to become the dominant and asymptotically the entire cell type in tumors.     

Inhibition of the MtTF4 tumor growth by dexamethasone

It is known that estradiol, but not progesterone or dihydrotestosterone, slows down the growth of the MtTF4 tumor. In the present paper, it is shown that: (1) this tumor contains glucocorticoid receptors, (2) its growth is also inhibited by treatment with dexamethasone (Dex), and (3) the growth rate of a cell line and several clones established from the tumor is negatively controlled by Dex 10(-7) M in culture medium containing 10% gelding serum. Unlike estradiol, Dex does not induce cell hypertrophy. This work suggests that the inhibition of the MtTF4 tumor growth by Dex may be due in part to a direct action on tumor cells and, taking into consideration previous reports, it allows us to forward the hypothesis that both Dex and estradiol inhibit MtTF4 tumor growth in two different ways.     

Parameter estimation in a Gompertzian stochastic model for tumor growth

The problem of estimating parameters in the drift coefficient when a diffusion process is observed continuously requires some specific assumptions. In this paper, we consider a stochastic version of the Gompertzian model that describes in vivo tumor growth and its sensitivity to treatment with antiangiogenic drugs. An explicit likelihood function is obtained, and we discuss some properties of the maximum likelihood estimator for the intrinsic growth rate of the stochastic Gompertzian model. Furthermore, we show some simulation results on the behavior of the corresponding discrete estimator. Finally, an application is given to illustrate the estimate of the model parameters using real data.     

Modeling and testing treated tumor growth using cubic smoothing splines

Human tumor xenograft models are often used in preclinical study to evaluate the therapeutic efficacy of a certain compound or a combination of certain compounds. In a typical human tumor xenograft model, human carcinoma cells are implanted to subjects such as severe combined immunodeficient (SCID) mice. Treatment with test compounds is initiated after tumor nodule has appeared, and continued for a certain time period. Tumor volumes are measured over the duration of the experiment. It is well known that untreated tumor growth may follow certain patterns, which can be described by certain mathematical models. However, the growth patterns of the treated tumors with multiple treatment episodes are quite complex, and the usage of parametric models is limited. We propose using cubic smoothing splines to describe tumor growth for each treatment group and for each subject, respectively. The proposed smoothing splines are quite flexible in modeling different growth patterns. In addition, using this procedure, we can obtain tumor growth and growth rate over time for each treatment group and for each subject, and examine whether tumor growth follows certain growth pattern. To examine the overall treatment effect and group differences, the scaled chi-squared test statistics based on the fitted group-level growth curves are proposed. A case study is provided to illustrate the application of this method, and simulations are carried out to examine the performances of the scaled chi-squared tests.     

Individual-based modelling of angiogenesis inside three-dimensional porous biomaterials

This paper presents a simulation modelling framework to study the growth of blood vessels and cells through a porous tissue engineering scaffold. The model simulates the migration of capillaries and the formation of a vascular network through a single pore of a tissue engineering scaffold when it is embedded in living tissue. The model also describes how the flow of blood through the network changes as growth proceeds. Results are given for how the different strategies of seeding the pore with cells affects the extent of vascularisation. Also simulations are made to compare results where the values of different model parameters are varied such as the pore dimensions, the density of endothelial cells seeded into the pore, and the release rate of growth factor from the scaffold into the pore. The modelling framework described in this paper is useful for exploring experimental strategies for producing well-vascularised tissue engineered constructs, and is therefore potentially important to the field of regenerative medicine.     

microRNA-214在恶性肿瘤中的表达及相关性的研究进展

微小RNA(microRNA,miRNA)是广泛存在于动植物中的一类不编码蛋白质的短小的单链RNA分子,一般由22个核苷酸组成,它们可以特异性地结合mRNA并通过降解或抑制其翻译而在转录后水平调控基因表达。miRNA的表达及功能可影响许多表观遗传学特征,其功能涉及细胞的发生、生长、发育、分化和凋亡过程,在肿瘤的形成和进展过程中扮演重要角色。microRNA-214(miRNA-214,miR-214)参与肝癌、乳腺癌、宫颈癌、卵巢癌、恶性黑色素瘤、胃癌、胶质瘤、儿童骨肉瘤等恶性肿瘤的发生发展,以及与肿瘤细胞的侵袭及转移密切相关。miRNA-214在不同的肿瘤中表达水平并不相同,miRNA-214在不同肿瘤中的差异表达是通过调控某个或者某些癌基因及抑癌基因而实现其参与肿瘤的发生发展、侵袭及转移的作用。因此,本文主要通过阅读大量国内外文献,总结和概括了miRNA-214参与部分恶性肿瘤发生发展的机制。虽然目前对于miRNA的理论研究已经日渐完善和成熟,但是怎样将这些研究结果应用于临床,怎样能够更准确、更便捷的通过对miRNA的检测达到对疾病的诊断、治疗以及预后评估,想必一定会成为将来研究的热点,我们期待一种新型的恶性肿瘤的分子标志物会使越来越多的肿瘤患者获益。     

PPAR??激动剂罗格列酮对人乳腺癌细胞生长 抑制及诱导凋亡作用研究

目的:观察氧化酶体激活物增殖受体(PPARγ)激动剂罗格列酮(ROZ)在体外激活PPARγ后对MCF-7细胞的生长抑制及诱导凋亡作用。方法:MTT法检测ROZ对MCF-7细胞的生长抑制作用;集落形成实验观察ROZ对MCF-7细胞集落形成的影响;不同浓度ROZ作用72h,Hoechst33342染色观察MCF-7细胞的形态变化,流式细胞光度分析术(FCM)检测凋亡细胞百分率以及ROZ对细胞周期的影响;Western blot方法检测ROZ对MCF-7细胞Bcl-2、Caspase-3表达的影响。结果:ROZ可呈剂量依赖性抑制MCF-7细胞的生长及集落形成。ROZ浓度为6×10-5M和3×10-4M时则G1期细胞数明显增加,S期相应减少。Hoechst33342染色经ROZ处理的肿瘤细胞染色质呈颗粒状,且有凋亡小体出现。FCM检测结果显示,ROZ作用72h凋亡细胞数达22.05%。Western blot提示ROZ可抑制Bcl-2表达,促进Caspase3表达。结论:ROZ在体外可抑制MCF-7细胞的增殖并诱导其凋亡,这可能与其抑制Bcl-2表达、促进caspase3表达有关。提示ROZ有望成为乳腺癌治疗药或肿瘤治疗的辅助用药,PPARγ有潜力成为肿瘤治疗的新靶点。