A Spatial Model of Tumor-Host Interaction: Application of Chemotherapy
Peter Hinow, Philip Gerlee, Lisa J. McCawley, Vito Quaranta, Madalina Ciobanu, Shizhen Wang, Jason M. Graham, Bruce P. Ayati, Jonathan Claridge, Kristin R. Swan… 展开作者
Peter Hinow, Philip Gerlee, Lisa J. McCawley, Vito Quaranta, Madalina Ciobanu, Shizhen Wang, Jason M. Graham, Bruce P. Ayati, Jonathan Claridge, Kristin R. Swanson, Mary Loveless, Alexander R. A. Anderson
备注：
revised version, 25 pages, 9 figures, minor misprints corrected
In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. When no treatment is applied the model reproduces the typical dynamics of early tumor growth. The initially avascular tumor reaches a diffusion limited size of the order of millimeters and initiates angiogenesis through the release of vascular endothelial growth factor (VEGF) secreted by hypoxic cells in the core of the tumor. This stimulates endothelial cells to migrate towards the tumor and establishes a nutrient supply sufficient for sustained invasion. To this model we apply cytostatic treatment in the form of a VEGF-inhibitor, which reduces the proliferation and chemotaxis of endothelial cells. This treatment has the capability to reduce tumor mass, but more importantly, we were able to determine that inhibition of endothelial cell proliferation is the more important of the two cellular functions targeted by the drug. Further, we considered the application of a cytotoxic drug that targets proliferating tumor cells. The drug was treated as a diffusible substance entering the tissue from the blood vessels. Our results show that depending on the characteristics of the drug it can either reduce the tumor mass significantly or in fact accelerate the growth rate of the tumor. This result seems to be due to complicated interplay between the stromal and tumor cell types and highlights the importance of considering chemotherapy in a spatial context.
A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and th…
Cytotoxic chemotherapy is a common treatment for advanced prostate cancer. These tumors are also known to rely on angiogenesis, i.e., the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical studies have been investigating antiangiogenic therapy for advanced prostate cancer, either as monotherapy or combined with standard cytotoxic protocols. However, the complex genetic alterations promoting prostate cancer growth complicate the selection of the best chemotherapeutic approach for each patient's tumor. Here, we present a mathematical model of pr…
A fundamental model of tumor growth in the presence of cytotoxic chemotherapeutic agents is formulated. The model allows to study the role of the Norton-Simon hypothesis in the context of dose-dense chemotherapy. Dose-dense protocols aim at reducing the period between courses of chemotherapy from three weeks to two weeks, in order to avoid tumor regrowth between cycles. We address the conditions under which these protocols might be more or less beneficial in comparison to less dense settings, depending on the sensitivity of the tumor cells to the cytotoxic drugs. The effects of varying other p…
Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility and death \cite{jr}, that, qualitatively reproduces commonly observed morphologies for carcinomas {\it in situ}. In the present work, we analyze the effects of distinct chemotherapeutic strategies on the patterns, scaling and growth laws obtained for such nutrient-limited model. Two kinds of chemotherapeutic strategies were considered, namely, those that kill cancer cells and those that block cell mitosis but allows the cell to survive for some time. Depending on the ch…
Case Western Reserve University（凯斯西储大学）；Picture Health（Picture Health公司）；Stony Brook University（石溪大学）；University Hospitals Cleveland Medical Center（克利夫兰大学医院医学中心）；Yale School of Medicine（耶鲁医学院）；The Cleveland Clinic Foundation (CCF)（克利夫兰诊所基金会（CCF））；New York University (NYU) Langone Medical Center（纽约大学（NYU）朗格尼医学中心）；Louis Stokes Cleveland Veterans Medical Center（路易斯·斯托克斯克利夫兰退伍军人医学中心）
Purpose: Tumor-associated vasculature differs from healthy blood vessels by its chaotic architecture and twistedness, which promotes treatment resistance. Measurable differences in these attributes may help stratify patients by likely benefit of systemic therapy (e.g. chemotherapy). In this work, we present a new category of radiomic biomarkers called quantitative tumor-associated vasculature (QuanTAV) features, and demonstrate their ability to predict response and survival across multiple cancers, imaging modalities, and treatment regimens. Experimental Design: We segmented tumor vessels and …
The majority of cancer-related fatalities are due to metastatic disease. In chemoradiotherapy, chemotherapeutic agents are administered along with radiation to increase damage to the primary tumor and control systemic disease such as metastasis. This work introduces a mathematical model to obtain optimal drug and radiation protocols in a chemoradiotherapy scheduling problem with the objective of minimizing metastatic cancer cell populations at multiple potential sites while maintaining a minimum level of damage to the primary tumor site. We derive closed-form expressions for an optimal chemoth…
Neoadjuvant chemotherapy (NAC) is a standard-of-care treatment for locally advanced triple negative breast cancer (TNBC) before surgery. The early assessment of TNBC response to NAC would enable an oncologist to adapt the therapeutic plan of a non-responding patient, thereby improving treatment outcomes while preventing unnecessary toxicities. To this end, a promising approach consists of obtaining \textsl{in silico} personalized forecasts of tumor response to NAC \textsl{via} computer simulation of mechanistic models constrained with patient-specific magnetic resonance imaging (MRI) data acqu…
We present a mathematical model, based on ordinary differential equations, for the evolution of solid tumors and their response to treatment. Specifically the effects of a cytotoxic agent and a monoclonal antibody are included as control term in the equations. The variables considered here are: the number of cancerous cells sensitive to chemotherapy, the number of cancerous cells resistant to chemotherapy, the degree of angiogenesis and the average intensity of VEGF. The rules that govern the quantities mentioned above are based on a geometrical argument: we approximate the tumor mass as a sph…
While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor response to a DNA damaging drug to study how the development of chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider cell populations that harbor pre-existing resistance to the drug, and those that acquire resistance during the course of treatment. For each of these independent scenarios, we consider one hypothetical cell l…
Tumorigenesis is a complex process that is heterogeneous and affected by numerous sources of variability. This study presents a stochastic extension of a biologically grounded tumor growth model, referred to as the Norton-Simon-Massagué (NSM) tumor growth model. We first study the uncontrolled version of the model where the effect of chemotherapeutic drug agent is absent. Conditions on the model's parameters are derived to guarantee the positivity of the tumor volume and hence the validity of the proposed stochastic NSM model. To calibrate the proposed model we utilize a maximum likelihood-bas…
Improvement of anti-tumor biotherapy effectiveness by modification of immune response with histamine H2 receptor Cimetidinum (CM) was studied using the experimental murine model of B16 F10 melanoma in vivo. It is shown that skin melanoma biotherapy by antitumor whole-cell GM-CSF-producing vaccine with the addition of CM (in dose of 25 mg/kg, daily for 5 days) increases preventive effects of vaccination. 33 % of mice did not have tumor growth within 60 days of observation. Average life span of animals exceeded those of the control group up to 68 %. Using CM-combined bio-chemotherapy doesn't imp…
While the use of combination therapy is increasing in prevalence for cancer treatment, it is often difficult to predict the exact interactions between different treatment forms, and their synergistic/antagonistic effects on patient health and therapy outcome. In this research, a system of ordinary differential equations is constructed to model nonlinear dynamics between tumor cells, immune cells, and three forms of therapy: chemotherapy, immunotherapy, and radiotherapy. This model is then used to generate optimized combination therapy plans using optimal control theory. In-silico experiments a…
The use of bacteria has been attractive to cancer researchers as drug delivery vehicle because motile bacteria are able to penetrate in tumors. In particular, the combination of therapeutic bacteria and conventional chemotherapy leads to dramatically high anti-tumor efficay. However, the mechanisms of the synergy, in part, remain unclear. To aim for understanding the mechanisms of the synergy of the combination therapy, simultaneous delivery of C. novyi-NT and chemotherapeutic agents in tumors is mathematically modeled from porous media approach. Simulated doxorubicin concentration in tumors a…
Most cancers in humans are large, measuring centimeters in diameter, composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is their homogeneity - virtually every neoplastic cell within a large cancer contains the same core set of genetic alterations, with heterogeneity confined to mutations that have emerged after the last clonal expansions. How such clones expand within the spatially-constrained three dimensional architecture of a tumor, and come t…
Prostate cancer can be lethal in advanced stages, for which chemotherapy may become the only viable therapeutic option. While there is no clear clinical management strategy fitting all patients, cytotoxic chemotherapy with docetaxel is currently regarded as the gold standard. However, tumors may regain activity after treatment conclusion and become resistant to docetaxel. This situation calls for new delivery strategies and drug compounds enabling an improved therapeutic outcome. Combination of docetaxel with antiangiogenic therapy has been considered a promising strategy. Bevacizumab is the m…
It has been recently proposed that the two "emerging" hallmarks of cancer, namely altered glucose metabolism and immune evasion, may in fact be fundamentally linked (Kareva and Hahnfeldt, 2013). This connection comes from up-regulation of glycolysis by tumor cells, which can lead to active competition for resources in the tumor microenvironment between tumor and immune cells. Here it is further proposed that cancer stem cells (CSCs) can circumvent the anti-tumor immune response by creating a 'protective shield' of non-stem cancer cells around them. This shield can protect the CSCs both by crea…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are introduced in this work in order to correctly model the physic…
In this paper we propose an ecological resilience point of view on cancer. This view is based on the analysis of a simple ODE model for the interactions between cancer and normal cells. The model presents two regimes for tumor growth. In the first, cancer arises due to three reasons: a partial corruption of the functions that avoid the growth of mutated cells, an aggressive phenotype of tumor cells and exposure to external carcinogenic factors. In this case, treatments may be effective if they drive the system to the basin of attraction of the cancer cure state. In the second regime, cancer ar…
In this paper, we study a phase-space analysis of a mathematical model of tumor growth with an immune response. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of solutions, invariance of non-negativity, nature of equilibria, local and global stability will be investigated. We study some features of behavior of one three-dimensional tumor growth model with dynamics described in terms of densities of three cells populations: tumor cells, healthy host cells and effector immune cells. We find the upper and lower bounds for th…
Magnetic hyperthermia is a new type of cancer treatment designed for overcoming resistance to chemotherapy during the treatment of solid, inaccessible human tumors. The main challenge of this technology is increasing the local tumoral temperature with minimal side effects on the surrounding healthy tissue. This work consists of an in vitro study that compared the effect of hyperthermia in response to the application of exogenous heating (EHT) sources with the corresponding effect produced by magnetic hyperthermia (MHT) at the same target temperatures. Human neuroblastoma SH-SY5Y cells were loa…
Resection of primary tumors is often followed by accelerated growth of metastases. Here we propose that this effect may be due to the fact that resection of primary tumor results in a decrease in the total systemic amount of angiogenesis stimulators, such as VEGF and bFGF. This in turn causes decrease in the systemic level of angiogenesis inhibitors, such as PF-4 and TSP-1, which at least temporarily relieves inhibition of secondary tumors, allowing them to grow. This construct is predicated on the notion that systemic level of angiogenesis inhibitors is regulated by the systemic level of angi…
Assuming that there is feedback between an expanding cancer system and its organ-typical microenvironment, we argue here that such local tumor growth is guided by co-existence rather than competition with the surrounding tissue. We then present a novel concept that understands cancer dissemination as a biological mechanism to evade the specific carrying capacity limit of its host organ. This conceptual framework allows us to relate the tumor system's volumetric growth rate to the host organ's functionality-conveying composite infrastructure, and, intriguingly, already provides useful insights …
Purpose To develop and demonstrate a novel tumor shell feature for predicting distant failure in non-small cell lung cancer (NSCLC) and cervical cancer (CC) patients. Patients and Methods The shell predictive model was constructed using pretreatment positron emission tomography (PET) images from 48 NSCLC patients received stereotactic body radiation therapy (SBRT) and 52 CC patients underwent external beam radiation therapy and concurrent chemotherapy followed with high-dose-rate intracavitary brachytherapy. A shell feature, consisting of outer voxels around the tumor boundary, was extracted f…
Cancer is one of the most common diseases worldwide, posing a serious threat to human health and leading to the deaths of a large number of people. It was observed during the drug administration in chemotherapy that immune cells, cancer cells and normal cells are killed or at least seriously injured and also in order to keep dosage of the drug at specific level in body, drug should be delivered in specific time and dosage. Therefore, to address these problems, a decision-making process is needed to identify the most appropriate treatment for cancer cases which causes killing of cancer cells by…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient and surrounded by host tissue. The introduction of cytotoxic drugs into the system serves to eliminate the tumor cells and in this setting the concentration of the cytotoxic drugs will act as the control variable. Furthermore, we allow the objective functional to depend on a free time variable, which represents the unknown treatment time to be optimized. As a…
Recent studies have identified highly tumorigenic cells with stem cell-like characteristics in human cancers, termed cancer stem cells (CSCs). CSCs are resistant to conventional radiotherapy and chemotherapy owing to their high DNA repair ability and oncogene overexpression. However, the mechanisms regulating CSC radio-resistance, particularly proton beam resistance, remain unclear. We isolated CSCs from the breast cancer cell lines MCF-7 and MDA-MB-231, which expressed the characteristic breast CSC membrane protein markers CD44+/CD24-/low, and irradiated the CSCs with pulsed proton beams. We …
In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular matrix, that occupies a spatial region close to a blood vessel whence cells get the nutrient needed for their vital functions. Growth of tumor cells takes place within a healthy host tissue, which is in turn modeled as a saturated mixture of non-proliferating cells. Interactions between these two regions are accounted for as an essential mechanism for the growth o…
We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully exponential, Gompertz, logistic, and power-law tumor growths. We have been able to include as many hallmarks of cancer as possible. We study also the dynamic response of cancer under therapy. Using our model, we can make predictions about the different outcomes when we change the parameters, and/or the initial conditions. We can determine the importance of diff…
One of the most promising strategies to treat cancer is attacking it with viruses designed to exploit specific altered pathways. Here, the effects of oncolytic virotherapy on tumors having compact, papillary and disconnected morphologies are investigated through computer simulations of a multiscale model coupling macroscopic reaction diffusion equations for the nutrients with microscopic stochastic rules for the actions of individual cells and viruses. The interaction among viruses and tumor cells involves cell infection, intracellular virus replication and release of new viruses in the tissue…
Breast Cancer is a major public health problem and the most common diagnosed malignancy in woman. There have been significant developments in clinical approaches and theoretical experimental to understand the interactions of cancer cells dynamics with the immune system, also developments on analytical and computational models to help provide insights into clinical observations for a better understanding of cancer cells, but more are needed, especially at the genetic and molecular levels mathematically. Treatments such as immunotherapy, chemotherapy, hormone therapy, radiotherapy, and gene ther…
Movement behavior of biological entities plays a crucial role in their destiny through regulating their intraspecific and interspecific interactions as well as their interaction with surrounding environment. In spite of various models for population dynamics, the effect of movement behavior and heterogeneity of environment on population dynamics has remained poorly understood. We introduced an extended version of Kolmogorov equation which captures movement behavior and translated our model to a biased random walk on percolation lattice. Then we explored the effect of mentioned topic on populat…
Oncolytic virotherapy - the use of viruses that specifically kill tumor cells - is an innovative and highly promising route for treating cancer. However, its therapeutic outcomes are mainly impaired by the host immune response to the viral infection. In the present work, we propose a multiscale mathematical model to study how the immune response interferes with the viral oncolytic activity. The model assumes that cytotoxic T cells can induce apoptosis in infected cancer cells and that free viruses can be inactivated by neutralizing antibodies or cleared at a constant rate by the innate immune …
