Vascular tumor growth and treatment: Consequences of polyclonality,competition and dynamic vascular support

 A mathematical model is presented to describe the evolution of a vascular tumor in response to traditional chemotherapeutic treatment. Particular attention is paid to the effects of a dynamic vascular support system in a tumor comprised of competing cell populations that differ in proliferation rates and drug susceptibility. The model consists of a system of partial differential equations governing intratumoral drug concentration, cancer cell density, and blood vessel density. The balance between cell proliferation and death along with vessel production and destruction within the tumor generates a velocity field which drives the expansion or regression of the neoplasm. Radially symmetric solutions are obtained for the case when only one cell type is present and when the proportion of the tumor occupied by blood vessels remains constant. The stability of these solutions to asymmetric perturbations and to a small semi-drug resistant cell population is then investigated. The analysis shows that drug concentrations which are sufficient to insure eradication of a spherical tumor may be inadequate for the successful treatment of non-spherical tumors. When the drug is continuously infused, linear analysis predicts that whether or not a cure is possible is crucially dependent on the proliferation rate of the semi-resistant cells and on the competitive effect of the sensitive cells on the resistant population. When the blood vessel density is allowed to change dynamically, the model predicts a dramatic increase in the tumors growth and decrease in its response to therapy. Received: 4 August 2000 / Revised version: 13 July 2001 / Published online: 21 February 2002     

Numerical simulation of a stochastic model for cancerous cells submitted to chemotherapy

A stochastic model is proposed to study the problem of inherent resistance by cell populations when chemotherapeutic agents are used to control tumor growth. Stochastic differential equations are introduced and numerically integrated to simulate expected response to the chemotherapeutic strategies as a function of different parameters. Satisfactory demonstration runs of the model indicate that it could represent a useful tool in verifying the results of experimental and clinical chemotherapy courses and planning treatment strategies. Some types of behaviour are illustrated graphically.Work supported by the C.N.R. Grants: 85.02652.01; 86.02116.01     

Immune mechanism of the antitumor effects generated by bortezomib

Bortezomib, a proteasome inhibitor, is a chemotherapeutic drug that is commonly used to treat a variety of human cancers. The antitumor effects of bortezomib-induced tumor cell immunogenicity have not been fully delineated. In this study, we examined the generation of immune-mediated antitumor effects in response to treatment by bortezomib in a murine ovarian tumor model. We observed that tumor-bearing mice that were treated with bortezomib had CD8(+) T cell-mediated inhibition of tumor growth. Furthermore, the comparison of tumor cell-based vaccines that were produced from tumor cells treated or untreated with bortezomib showed vaccination with drug-treated tumor cell-based vaccines elicited potent tumor-specific CD8(+) T cell immune response with improved therapeutic antitumor effect in tumor-bearing mice. Conversely, the untreated tumor cell-based vaccines led to no appreciable antitumor response. Treatment of tumor cells with bortezomib led to the upregulation of Hsp60 and Hsp90 on the cell surface and promoted their phagocytosis by dendritic cells (DCs). However, cell surface expression of Hsp60, instead of Hsp90, is the more important determinant of whether bortezomib-treated tumor cells can generate tumor-specific CD8(+) T cells. CD11c(+) DCs that were treated with bortezomib in vitro had enhanced phagocytic activities. In addition, CD11c(+) DCs from bortezomib-treated tumor-bearing mice had increased maturation. At lower concentrations, bortezomib had no inhibitory effects on T cell proliferation. Taken together, our data indicate that bortezomib can render tumor cells immunogenic by upregulating the cell surface expression of heat shock protein 60 and heat shock protein 90, as well as improve DC function, which results in potent immune-mediated antitumor effects.     

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.     

Autowaves in a model of invasive tumor growth

A mathematical model for invasive tumor growth is proposed, which takes into account cell division, death, and motility. The model includes local cell density and the distribution of nutrient (oxygen) concentration. Cancer cells die in the absence of nutrients; therefore, the distribution of oxygen in tissue substantially affects both the tumor proliferation rate and its structure. The model adequately describes the experimentally measured rate of tumor proliferation. The existence of autowave solutions is demonstrated, and their properties are investigated. The results are compared with the properties of the Kolmogorov-Petrovskii-Piskunov and Fisher equations. It is shown that the nutrient distribution influences the selection of speed and the convergence of the initial conditions to the automodel solution.     

Immune Response to Combination Therapy for Non-Hodgkin Lymphomas

A parametric model of tumor response to combination therapy in the presence of an immune system is described. Synergistic mechanisms which induce tumor regression are simulated with a coupled set of equations. The simulations are first compared to tumor history data obtained with a SCID mouse model to determine key parameters; predictions are then made for an immune-competent animal. The minimum immune cell birth rate relative to malignant B-cell birth rate necessary to induce tumor regression is determined, and optimization of drug combinations in the presence of an immune response is explored. The delayed effect of an immune response relative to drug scheduling is examined, and a mechanism for disease transformation in heterogeneous tumors is proposed.     

Interactions between macrophages and T-lymphocytes: tumor sneaking through intrinsic to helper T cell dynamics

In a mathematical model of the cellular immune response we investigate immune reactions to tumors that are introduced in various doses. The model represents macrophage T-lymphocyte interactions that generate cytotoxic macrophages and cytotoxic T-lymphocytes. In this model antigens (tumors) can induce infinitely large T-lymphocyte effector populations because effector T-lymphocytes are capable of repeated proliferation and we have omitted immunosuppression. In this (proliferative) model small doses of weakly antigenic tumors grow infinitely large (i.e. sneak through) eliciting an immune response of limited magnitude. Intermediate doses of the same tumor induce larger immune responses and are hence rejected. Large doses of the tumor break through, but their progressive growth is accompanied by a strong immune response involving extensive lymphocyte proliferation. Similarly a more antigenic tumor is rejected in intermediate doses and breaks through in large doses. Initially small doses however lead to tumor dormancy. Thus although the model is devoid of explicit regulatory mechanisms that limit the magnitude of its response (immunosuppression is such a mechanism), the immune response to large increasing tumors may either be a stable reaction of limited magnitude (experimentally known as tolerance or unresponsiveness) or a strong and ever increasing reaction. Unresponsiveness can evolve because in this model net T-lymphocyte proliferation requires the presence of a minimum number of helper T cells (i.e. a proliferation threshold). Unresponsiveness is caused by depletion of helper T cell precursors.     

Human adipose tissue derived mesenchymal stem cells are resistant to several chemotherapeutic agents

Human adipose derived mesenchymal stem cells (ADMSCs) are multipotential stem cells, originated from the vascular stromal compartment of fat tissues which can be used as an alternative cell source for many different cell therapies. However, their response to chemotherapeutic agants remains unknown. Here we assessed the acute direct effects of individual chemotherapeutic drug on ADMSCs. Using an in vitro culture system, the response of ADMSCs to the three chemotherapeutic agents cisplatin, comptothecin and vincristine was determined in comparison with that of testicular germ cell tumour (TGCT) cell line. The recovery of cell numbers following exposure to chemotherapeutic agents were also evaluated. Our results showed that human ADMSCs were resistant to chemo-therapeutic agents which are commonly used in clinic, the full recovery was seen respectively in ADMSCs after the drug treatment. Moreover, ADMSCs maintained their stem cell characteristics in vitro after the exposure to all chemotherapeutic agents.     

A Mathematical Model for the Effects of HER2 Overexpression on Cell Proliferation in Breast Cancer

We present a mathematical model to study the effects of HER2 over-expression on cell proliferation in breast cancer. The model illustrates the proliferative behavior of cells as a function of HER2 and EGFR receptors numbers, and the growth factor EGF. This mathematical model comprises kinetic equations describing the cell surface binding of EGF growth factor to EGFR and HER2 receptors, coupled to a model for the dependence of cell proliferation rate on growth factor receptors binding. The simulation results from this model predict: (1) a growth advantage associated with excess HER2 receptors; (2) that HER2-over-expression is an insufficient parameter to predict the proliferation response of cancer cells to epidermal growth factors; and (3) the EGFR receptor expression level in HER2-over-expressing cells plays a key role in mediating the proliferation response to receptor-ligand signaling. This mathematical model also elucidates the interaction and roles of other model parameters in determining cell proliferation rate of HER2-over-expressing cells.     

Diffusion model of tumor vascularization and growth

A diffusion model of tumor growth, vascularization and necrosis is used to analyze experimental data describing the temporal changes in tumor cell and blood vessel radial distributions in a host-tissue field transplanted with a fibrosarcoma. The experimental results showed a peak density of vessels occurring at the advancing migration front of the tumor and a decline in the vessel surface area at the tumor center with time. The peak density of tumor cells shifts away from the tumor center with time. These dynamic changes can be explained by a mathematical model which views the process as one of diffusion and proliferation in time and space. Coupled diffusion equations with nonlinear source and sink terms describe the proliferation, death, and migration of tumor cells and vascular surface area. The concept of an angiogenic factor elaborated by tumor cells is incorporated.     

A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets

Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler–Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.     

Reaction-diffusion approach to modeling of the spread of early tumors along linear or tubular structures

We consider a system composed of a tubular sheet of early tumor cells, occupying the surface of a structure existing in the organism. We assume that the cells have a potential for proliferation in response to a growth factor. This model can be thought of as representing an early stage (pre-in situ) of tumor evolution. A biomedical example of such process might be the atypical adenomatous hyperplasia in the lung. Destabilization of the equilibrium in such system represents initial invasion of cancer. We are looking for a transition from a slightly perturbed equilibrium state to uncontrolled and irregular growth. We examine a mathematical model of a population of cells distributed over a linear or tubular structure. Growth of cells is regulated by a growth factor, which can diffuse over the structure. Aside from this, production of cells and of the growth factor is governed by a pair of ordinary differential equations. Equation for the cell number follows from an accepted model of cell cycle. Equation for the bounded receptor particle number follows from a time-continuous Markov process. We demonstrate existence of the solutions of the complete model, using the method of invariant rectangles. We find conditions under which diffusion causes destabilization of the spatially homogeneous steady state, leading to exponential growth and apparently chaotic spatial patterns, following a period of almost constancy. This phenomenon may serve as a mathematical explanation of "unexpected" rapid growth and invasion of temporarily stable structures composed of cancer cells.     

Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model

Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely growing in the culture medium and subjected to an external mechanical pressure induced by a Dextran solution. The growth curves of the model are compared to the experimental data, with good agreement for both the experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is presented at the end of the paper. This new law is validated against experimental data and provides better results compared to other expressions in the literature.     

T cells contribute to tumor progression by favoring pro-tumoral properties of intra-tumoral myeloid cells in a mouse model for spontaneous melanoma

Tumors affect myelopoeisis and induce the expansion of myeloid cells with immunosuppressive activity. In the MT/ret model of spontaneous metastatic melanoma, myeloid cells are the most abundant tumor infiltrating hematopoietic population and their proportion is highest in the most aggressive cutaneous metastasis. Our data suggest that the tumor microenvironment favors polarization of myeloid cells into type 2 cells characterized by F4/80 expression, a weak capacity to secrete IL-12 and a high production of arginase. Myeloid cells from tumor and spleen of MT/ret mice inhibit T cell proliferation and IFNγ secretion. Interestingly, T cells play a role in type 2 polarization of myeloid cells. Indeed, intra-tumoral myeloid cells from MT/ret mice lacking T cells are not only less suppressive towards T cells than corresponding cells from wild-type MT/ret mice, but they also inhibit more efficiently melanoma cell proliferation. Thus, our data support the existence of a vicious circle, in which T cells may favor cancer development by establishing an environment that is likely to skew myeloid cell immunity toward a tumor promoting response that, in turn, suppresses immune effector cell functions.     

Targeting mitochondria as a therapeutic target in cancer

Knowledge of re-programming in cancer cells with metabolic differences from their normal counterparts has resulted in new examination of therapeutic approaches. Several studies of the role of tumor mitochondria in cancer have led to the development of non-genotoxic therapies which target mitochondrial proteins, function. The now well-established functions of mitochondria in apoptosis provide novel targets for tumor cell suicide. Mitochondria serve as a central hub for responses to cellular stress as well as injury. The alterations in cancer cells which result in protection from apoptosis can be targeted to inhibit proliferation. Because of the reprogramming of cancer cell metabolism involving increased glycolysis, it appears that blocking InsP(3)R Ca(2+) release or adaptive pathways in response to hypoxia by targeting HIF-1 or metabolic enzymes encoded by the HIF-1 gene represents a feasible therapeutic approach to cancer. A very early in vitro event found in tumor cells following resveratrol addition is an increase in intracellular Ca(2+), measurable within seconds. Ca(2+) release is also observed with non-toxic flavonoids and a goal to identify the sentinel targets of resveratrol as a model compound involved in calcium activation seems worthwhile. New findings of the relationship between autophagy and apoptosis are discussed. The contribution of reactive oxygen species (ROS) generated by mitochondria is also considered. New data as to how cyclophilins and VDAC are involved in mitochondrial hexokinase protection of factors that induce apoptosis are reviewed. In addition, chemotherapeutic approaches based on Akt-activated mTORC1 are described, and their relationship to the role of aerobic glycolysis in this protection.     

MiR-206 suppresses the deterioration of intrahepatic cholangiocarcinoma and promotes sensitivity to chemotherapy by inhibiting interactions with stromal CAFs

Background: Intrahepatic cholangiocarcinoma (iCCA) is a highly malignant subtype of cholangiocarcinoma (CCA) with poor prognosis. In iCCA, the interplay between the stroma and tumor cells results in resistance to adjuvant chemotherapy. Increasing evidence indicates that miR-206 participates in tumor progression, but its role in iCCA is still unclear. The aim of this study was to identify dysregulated miR-206 expression in iCCA and to further explore the underlying mechanism.Methods: MiR-206 expression was proven to be downregulated in iCCA tissues by qPCR, and its correlation with clinical characteristics and prognosis was investigated. iCCA-derived cancer-associated fibroblast cells (CAFs) and normal fibroblast cells (NFs) were isolated and identified. MiR-206 was knocked in or down in CAFs and CCA cells, respectively, to explore the role of miR-206, and coculture of these treated CCAs and CAFs was conducted to explore the effects of miR-206 on their mutual promoting effects. Exosomes carrying miR-206 and an orthotopic mouse model were used to determine the inhibitory effects of miR-206 on iCCA deterioration in vivo.Results: We confirmed that miR-206 is a suppressor of iCCA. Overexpressing miR-206 in CCA cells inhibited cell proliferation, migration and invasion. When cocultured with CCA cells, NFs downregulated miR-206 expression, and NFs were susceptible to transforming into CAFs. Moreover, CAFs promoted CCA cell malignant behaviors and gemcitabine resistance. Overexpressing miR-206 in CAFs or CCA cells inhibited this mutual promoting effect. Additionally, when delivered by exosomes, miR-206 suppressed tumor deterioration. And combined with gemcitabine, this treatment resulted in a longer survival time.Conclusion: Our study explained that the interaction between CCA cells and CAFs promoted iCCA deterioration. As a suppressive factor, miR-206 inhibited aggressive characteristics and gemcitabine resistance by interfering with this mutual promoting effect. This research elucidated the molecular mechanism underlying the unfavorable chemotherapeutic response of patients with iCCA, which provided a promising target for iCCA treatment.     

Role of Constitutive Behavior and Tumor-Host Mechanical Interactions in the State of Stress and Growth of Solid Tumors

Mechanical forces play a crucial role in tumor patho-physiology. Compression of cancer cells inhibits their proliferation rate, induces apoptosis and enhances their invasive and metastatic potential. Additionally, compression of intratumor blood vessels reduces the supply of oxygen, nutrients and drugs, affecting tumor progression and treatment. Despite the great importance of the mechanical microenvironment to the pathology of cancer, there are limited studies for the constitutive modeling and the mechanical properties of tumors and on how these parameters affect tumor growth. Also, the contribution of the host tissue to the growth and state of stress of the tumor remains unclear. To this end, we performed unconfined compression experiments in two tumor types and found that the experimental stress-strain response is better fitted to an exponential constitutive equation compared to the widely used neo-Hookean and Blatz-Ko models. Subsequently, we incorporated the constitutive equations along with the corresponding values of the mechanical properties - calculated by the fit - to a biomechanical model of tumor growth. Interestingly, we found that the evolution of stress and the growth rate of the tumor are independent from the selection of the constitutive equation, but depend strongly on the mechanical interactions with the surrounding host tissue. Particularly, model predictions - in agreement with experimental studies - suggest that the stiffness of solid tumors should exceed a critical value compared with that of the surrounding tissue in order to be able to displace the tissue and grow in size. With the use of the model, we estimated this critical value to be on the order of 1.5. Our results suggest that the direct effect of solid stress on tumor growth involves not only the inhibitory effect of stress on cancer cell proliferation and the induction of apoptosis, but also the resistance of the surrounding tissue to tumor expansion.     

The Complex Role of AR Signaling After Cytotoxic Insult: Implications for Cell Cycle Based Chemotherapeutics

Prostatic adenocarcinomas are dependent on androgen receptor (AR) signaling for growth and progression, in part through the ability of AR to induce G1-S phase cell cycle transition. Hormonal therapies that inhibit AR activity are the first line of intervention for disseminated disease, and are initially quite effective; however, recurrent, incurable tumors ultimately arise with restored AR function. Given the importance of AR in governing the potentiation of this tumor type, there has been a dedicated interest in dissecting the mechanisms by which AR promotes prostate cancer proliferation and survival. Recent studies have challenged the utility of manipulating AR activity to enhance cell death in combination with genotoxic insult. Herein, the role of AR in controlling cell cycle progression and paradoxical roles of AR in survival signals are considered, as are the potential implications of these findings for chemotherapeutic response. Although there is much to be resolved, the present data suggest that knowledge of AR action in promoting cellular proliferation can be utilized for the design of coordinate strategies that maximize cell death in response to cytotoxic chemotherapeutics.