Model Of Cancer Growth Research Articles

Inhibition of the insulin-like growth factor-1 receptor potentiates acute effects of castration in a rat model for prostate cancer growth in bone

Prostate cancer (PCa) patients with bone metastases are primarily treated with androgen deprivation therapy (ADT). Less pronounced ADT effects are seen in metastases than in primary tumors. To test if acute effects of ADT was enhanced by concurrent inhibition of pro-survival insulin-like growth factor 1 (IGF-1), rats were inoculated with Dunning R3327-G tumor cells into the tibial bone marrow cavity and established tumors were treated with castration in combination with IGF-1 receptor (IGF-1R) inhibitor NVP-AEW541, or by each treatment alone. Dunning R3327-G cells were stimulated by androgens and IGF-1 in vitro. In rat tibia, Dunning R3327-G cells induced bone remodeling, identified through increased immunoreactivity of osteoblast and osteoclast markers. Tumor cells occasionally grew outside the tibia, and proliferation and apoptotic rates a few days after treatment were evaluated by scoring BrdU- and caspase-3-positive tumor cells inside and outside the bone marrow cavity, separately. Apoptosis was significantly induced outside, but unaffected inside, the tibial bone by either castration or NVP-AEW541, and the maximum increase (2.7-fold) was obtained by the combined treatment. Proliferation was significantly reduced by NVP-AEW541, independently of growth site, although the maximum decrease (24%) was observed when NVP-AEW541 was combined with castration. Tumor cell IGF-1R immunoreactivity was evaluated in clinical PCa bone metastases (n = 61), and positive staining was observed in most cases (74%). In conclusion, IGF-1R inhibition may be evaluated in combination with ADT in patients with metastatic PCa, or in combination with therapies for the subsequent development of castration-resistant disease, although diverse responses could be anticipated depending on metastasis site.

Positivity Preserving Nonstandard Finite Difference Schemes Applied to Cancer Growth Model

When one solves differential equations, modeling biological or physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. In this work, we introduce explicit finite difference schemes based on the nonstandard discretization method to approximate solution of the cross-diffusion system from bioscience. The proposed schemes improve the accuracy and guarantee the positivity requirement, as is demanded for the solution of such system. We apply new methods for numerical integration of the cancer growth model for illustrating the performance of them.

Mechanistic Model for Cancer Growth and Response to Chemotherapy.

Cancer treatment has developed over the years; however not all patients respond to this treatment, and therefore further research is needed. In this paper, we employ mathematical modeling to understand the behavior of cancer and its interaction with therapy. We study a drug delivery and drug-cell interaction model along with cell proliferation. Due to the fact that cancer cells grow when there are enough nutrients and oxygen, proliferation can be a barrier against a response to therapy. To understand the effect of this factor, we perform numerical simulations of the model for different values of the parameters with a continuous delivery of the drug. The numerical results showed that cancer dies after short apoptotic cycles if the cancer is highly vascularized or if the penetration of the drug is high. This suggests promoting angiogenesis or perfusion of the drug. This result is similar to the situation where proliferation is not considered since the constant release of drug overcomes the growth of the cells and thus the effect of proliferation can be neglected.

Abstract 2709: Mathematical modeling for prediction of secondary BRCA1 and BRCA2 mutations in ovarian cancers with deleterious germline BRCA1 and BRCA2 mutations

Abstract Background: DNA damaging agents such as cisplatin or carboplatin and poly(ADP-ribose) polymerase inhibitors (PARPi) have clinical activity in germline BRCA1 and BRCA2 mutation-associated ovarian cancers. However, BRCA1 or BRCA2-mutated tumors often develop resistance to these drugs. Restoration of BRCA function due to secondary BRCA mutations has been recognized as one of the clinical resistance mechanisms. The aim of this mathematical analysis is to study the emergence and frequency of secondary BRCA mutations in a cohort of BRCA-deficient in silico ovarian cancer-positive cases. Methods: We develop a 2D stochastic cell-cycle specific mathematical model of BRCA-deficient ovarian cancer growth and progression prior to and post-treatment, which includes debulking surgery, platinum-based chemotherapy or PARPi. This is a continuum model based on a combination of ordinary differential equations using Gompertzian growth kinetics subject to random discrete-time jump processes. This approach enables us to reflect the inter-individual heterogeneity in disease progression and drug administration reported in published data. Calculations are performed for in silico cancer-positive growth curves in which the inception of the first ovarian malignant cell is assumed to have already occurred. Results: Our modeling approach generates an empirical cumulative distribution of disease-free survival times prior to recurrence or disease progression, given the heterogeneous cancer progression illustrated by our in silico cohort. Our preliminary computational results indicate that an initially rare resistant cell clone carrying a secondary BRCA mutation pre-exists to treatment in circa 90% of the simulated progression curves. For the remaining 10% of the simulated curves, it is more likely that the secondary mutations are acquired during chemotherapy or PARPi via increased mutation rates, possibly conferred by the increasing amount of damaged DNA lesions caused by the cancer treatment. Conclusions: Our mathematical model provides some insight on the dynamics of secondary BRCA mutations that cannot be accessed through existing genomic analysis methods, as current DNA sequencing depth thresholds cannot detect the presence of rare tumor cell clones carrying such mutations. We predict that a large proportion of initially resistant cell clones with restored BRCA function more likely originate prior to rather than post-treatment. If such clones get selected for by subsequent platinum-based chemotherapy or PARPi in a Darwinian fashion, our model generates an empirical distribution of disease-free survival times prior to recurrence. This may have direct implications on the possible duration of subsequent treatment response in our simulated ovarian cancer-positive population. Citation Format: Dana-Adriana Botesteanu, Doron Levy, Jung-Min Lee. Mathematical modeling for prediction of secondary BRCA1 and BRCA2 mutations in ovarian cancers with deleterious germline BRCA1 and BRCA2 mutations. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 2709.

Sunitinib treatment reduces tumor growth and limits changes in microvascular properties after minor surgical intervention in an in vivo model of secondary breast cancer growth in bone.

Surgical interventions can alter the balance between pro- and anti-angiogenic growth factors and thereby modulate tumor growth. Since the microcirculatory properties of tumors underlie organ-specific differences, the microhemodynamic characteristics of bone metastasis have not yet been fully described. Angiogenesis inhibitors are increasingly being used to treat advanced stages of cancer. We hypothesized that the anti-angiogenic drug sunitinib abrogates alterations in microvascular properties following a minor surgical intervention in an in vivo model of secondary breast cancer growth in the bone. Intravital microscopy was performed over 25 days using a xenograft model of breast cancer tumor growth in the bone to determine changes in microvascular properties during sunitinib treatment. Mastectomy was performed on day 5 to evaluate the effect of a minor surgical trauma on tumor growth and microvascular properties. Anti-angiogenic therapy resulted in reduced tumor growth, decreased vascular density, and increased vascular diameters. Blood flow velocity remained constant while microvascular permeability temporarily increased after the surgical intervention. Administration of sunitinib reduced tumor growth and altered microcirculatory properties in a time-dependent manner. The observed dramatic increase in microvascular permeability after the surgical intervention may have implications for local tumor growth, and metastatic dissemination. J. Surg. Oncol. 2016;113:515-521. © 2016 Wiley Periodicals, Inc.

Models of cancer growth

In this paper we present a simple mathematical model of cancer growth. The model is discrete, it is a linear map (T) on three dimensional Eucledian vector space. But for some values of the parameters there exists a linear vector field on three dimensional Eucledian vector space whose time one map is T. We can analyze what happens to the flow of this vector field on one of the coordinate hyperplanes (see Fig. 5 in Sect. 4). In words this figure depicts, that if you have a bad ratio of growth inhibitor to growth factor cancer grows and if you have a good ratio cancer is eradicated. We can modify the dynamical system to model giving chemo therapy or immune therapy and discuss the consequences. We fit the model predictions to a Gompertz function and this gives a good fit for some values of the parameters (see Figs. 1, 2, 3 and 4). A main topic of the present paper is a mass action kinetic model for cancer growth. This gives a three dimensional ODE model, for which the first orthant is positively invariant. We discretize the linearization of this nonlinear ODE and with appropriate parameter definitions we recover the model T of Sect. 1. For some parameter values the model T induces a two dimensional map of the plane, see Sect. 5 .

Dynamics of a Data Based Ovarian Cancer Growth and Treatment Model with Time Delay

We present a simple model that describes ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. The tumor growth is governed by Droop’s cell quota model, a mathematical expression developed in ecology. Here, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. We present mathematical analysis of the model, including proving positivity of the solutions so that they are biologically meaningful, as well as discussing local and global stability. The mathematical model can be employed to fit both on-treatment and off-treatment preclinical data using the same biologically relevant parameters. We also state an open mathematical question.

Abstract PD1-4: Somatic leukemogenic mutations associated with infiltrating white blood cells in breast cancer patients

Abstract Background: In the last few decades, theoretical models of cancer growth and progression have long focused on the aberrations of cancer cells alone, such as the abnormal mitotic and invasive characteristics of cancer cells. More recent research across multiple solid tumors suggests a critical interplay between solid tumors and immune regulating cells. Mounting evidence suggests that the immune system can tip the scales of cancer progression, eliciting either an anti-tumor or pro-tumor immune response depending upon varying stimulating and inhibitory factors. Here, we are the first to demonstrate novel mutations including leukemogenic mutations among tumor infiltrating lymphocytes in breast cancer patients. Methods: We obtained 17 primary breast cancer samples from patients who presented for either a lumpectomy or mastectomy as part of an IRB approved biospecimen protocol. Of the 17 patient samples, 13 had triple negative breast cancer, 2 had ER+, HER2+ disease, and 2 had ER+, HER2- disease. In the 17 samples, we used fluorescent activated cell sorting to separate CD45-positive hematopoietic cells from CD45-negative epithelial cells. We then performed exome sequencing of tumor-infiltrating hematopoietic cells to investigate for the presence of pathogenic mutations in tumor-associated leukocytes. In this first step, we identified candidate mutations in known cancer genes, including BCOR, NOTCH2, TET2, NF1, EZH2, and JAK1. As a validation step, we then performed capture-based sequencing of tumor-infiltrating leukocytes in 20 breast cancer samples matched to each patient’s germline DNA sample (buccal swab). In 10 of the 20 patients, we identified and validated somatic mutations. Of note, 6 of these patients harbored mutations known to be associated with leukemia, including DNTM3A, TET2, and BCOR. Most of these mutations were present in at least 5-20% of reads. This suggests that these mutations were present in enriched subclones and were not rare alleles occurring in a minority of hematopoietic stem cells. Lastly, we performed 454 deep sequencing analysis of microdissected tumor DNA samples and confirmed the absence of these mutations in breast cancer cells. Conclusion: Our data demonstrate somatic mutations in tumor infiltrating leukocytes in breast tumors which were not identified in matched germline or tumor DNA samples. Notably, some of these mutations have been implicated in the pathogenesis of lymphoid and myeloid malignancies. This observation suggests a unique relationship between cancer cells and mutant infiltrating leukocytes. We are now investigating the functional interaction between cancer cells and hematopoietic cells. Our findings reframe our understanding of carcinogenesis and offer novel opportunities for cancer detection and treatment. Citation Format: Elizabeth A Comen, Maria Kleppe, Hannah Wen, Britta Weigelt, Lennart Bastian, Brian Blum, Franck T Rapaport, Matt Keller, Nicolas Socci, Agnes Viale, Daoqi You, Robert Benezra, Edi Brogi, Jorge Reis-Filho, Michael Berger, Ross Levine, Larry Norton. Somatic leukemogenic mutations associated with infiltrating white blood cells in breast cancer patients [abstract]. In: Proceedings of the Thirty-Seventh Annual CTRC-AACR San Antonio Breast Cancer Symposium: 2014 Dec 9-13; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2015;75(9 Suppl):Abstract nr PD1-4.

How Bad is it Doc? the Varying Predictions of ODE Cancer Growth Models

Cancer is the second most common cause of death in the US. While mathematical models are often used to predict progression of the disease and treatment outcomes, we don’t yet know how to accurately model tumor growth. Several ODE models (exponential, Mendelsohn, logistic, linear, surface, Bertalanff y, and Gompertz) have been proposed to model tumor growth. We examined the predictions of the models both for untreated growth and growth during treatment with chemotherapy. We compared the predicted maximum volume of the tumor, the doubling time, and the amount of chemotherapy needed to end tumor growth for each of the models and found that the predictions vary dramatically. This work highlights the need for detailed experiments to aid in choosing appropriate cancer growth models.

A validated mathematical model of tumor growth including tumor-host interaction, cell-mediated immune response and chemotherapy.

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. The tumor-immune and the tumor-host interactions are characterized to reproduce experimental results. A thorough dynamical analysis of the model is carried out, showing its capability to explain theoretical and empirical knowledge about tumor development. A chemotherapy treatment reproducing different experiments is also introduced. We believe that this simple model can serve as a foundation for the development of more complicated and specific cancer models.

A stochastic model of cancer growth subject to an intermittent treatment with combined effects: reduction in tumor size and rise in growth rate.

A model of cancer growth based on the Gompertz stochastic process with jumps is proposed to analyze the effect of a therapeutic program that provides intermittent suppression of cancer cells. In this context, a jump represents an application of the therapy that shifts the cancer mass to a return state and it produces an increase in the growth rate of the cancer cells. For the resulting process, consisting in a combination of different Gompertz processes characterized by different growth parameters, the first passage time problem is considered. A strategy to select the inter-jump intervals is given so that the first passage time of the process through a constant boundary is as large as possible and the cancer size remains under this control threshold during the treatment. A computational analysis is performed for different choices of involved parameters. Finally, an estimation of parameters based on the maximum likelihood method is provided and some simulations are performed to illustrate the validity of the proposed procedure.

Distribution of chaos and periodic spikes in a three-cell population model of cancer

We study complex oscillations generated by the de Pillis-Radunskaya model of cancer growth, a model including interactions between tumor cells, healthy cells, and activated immune system cells. We report a wide-ranging systematic numerical classification of the oscillatory states and of their relative abundance. The dynamical states of the cell populations are characterized here by two independent and complementary types of stability diagrams: Lyapunov and isospike diagrams. The model is found to display stability phases organized regularly in old and new ways: Apart from the familiar spirals of stability, it displays exceptionally long zig-zag networks and intermixed cascades of two- and three-doubling flanked stability islands previously detected only in feedback systems with delay. In addition, we also characterize the interplay between continuous spike-adding and spike-doubling mechanisms responsible for the unbounded complexification of periodic wave patterns. This article is dedicated to Prof. Hans Jurgen Herrmann on the occasion of his 60th birthday.

Abstract 2890: Mechanistic evaluation of the anti-tumor activities of 2-fluorofucose alone and in combination with anti-idiotype vaccination

Abstract Fucose is a sugar that is widely incorporated in cellular glycoconjugates and has been implicated for roles in tumor progression and metastasis. An analog of fucose, 2-fluorofucose, has been shown to have activity in vitro and in vivo as an inhibitor of glycoconjugate fucosylation and has shown promising antitumor activity in cancer growth models as well as potentiation of the protective effect of a mouse B cell lymphoma idiotype vaccine against challenge by live A20 lymphoma cells (Okeley N.M. et al, PNAS 110, 5404-5409, 2013). The effects of 2-fluorofucose that mediate these activities was explored in vitro and in vivo. In vitro, we found that 2-fluorofucose is rapidly converted to GDP-2-fluorofucose, the active species that inhibits the de novo pathway for fucosylation of protein glycans. The molecule accumulates within cancer cells, and is retained with a half-life in the range of 20 hours. In vivo, evaluation of the effect of 2-fluorofucose treatment on the fucosylation and proliferation state of xenografts showed reduced LCA lectin binding by western blot and IHC, and reduced Ki-67 staining, suggesting a lower mitotic index in these tumors. Adoptive transfer experiments were undertaken in order to shed light onto potential mechanisms for the antitumor effects of 2-fluorofucose when used in a cancer vaccine setting. These studies were performed in mice that were immunized with an A20 idiotype vaccine in the presence or absence of 2-fluorofucose, prior to tumor challenge. The antitumor effects obtained when serum from 2-fluorofucose treated animals was injected into non-vaccinated mice suggested a role for defucosylated antibodies with enhanced ADCC activities. In addition, T cell depletion studies demonstrated that 2-fluorofucose stimulated a CD4+ T cell involvement in in the protection against tumor engraftment. These results suggest multifactorial roles for the activities of 2-fluorofucose as an anticancer agent and as a stimulator of vaccine activity. Citation Format: Nicole M. Okeley, Weiping Zeng, Matthew R. Levengood, Julie A. McEarchern, Mechthild Jonas, Steven Duniho, Peter D. Senter, Che L. Law. Mechanistic evaluation of the anti-tumor activities of 2-fluorofucose alone and in combination with anti-idiotype vaccination. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 2890. doi:10.1158/1538-7445.AM2014-2890

Stochastic Modeling of Inter & Intra Stage Dependent Cancer Growth under Chemotherapy through Trivariate Poisson Processes

This study has proposed a Stochastic Model for cancer growth under chemotherapy with the assumptions of the growth, transition and loss parameters of different stages are inter and intra dependent. A trivariate Poisson process approach has been adopted for modeling the three stage cancer growth by considering the stages of cells in the tumor namely normal cell, mutant cell and malignant cell in the presence and absence of chemotherapy during time 't'. Stochastic differential equations were obtained and the three dimensional joint probability functions along with related statistical measures were derived. Model behavior was analysed through numerical data.

Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences

We design nonstandard finite difference (NSFD) schemes which are unconditionally dynamically consistent with respect to the positivity property of solutions of cross-diffusion equations in biosciences. This settles a problem that was open for quite some time. The study is done in the setting of three concrete and highly relevant cross-diffusion systems regarding tumor growth, convective predator–prey pursuit and evasion model and reaction–diffusion–chemotaxis model. It is shown that NSFD schemes used for classical reaction–diffusion equations, such as the Fisher equation, for which the solutions enjoy the positivity property, are not appropriate for cross-diffusion systems. The reliable NSFD schemes are therefore obtained by considering a suitable implementation on the cross-diffusive term of Mickens’ rule of nonlocal approximation of nonlinear terms, apart from his rule of complex denominator function of discrete derivatives. We provide numerical experiments that support the theory as well as the power of the NSFD schemes over the standard ones. In the case of the cancer growth model, we demonstrate computationally that our NSFD schemes replicate the property of traveling wave solutions of developing shocks observed in Marchant et al. (2000).

Stochastic Resonance for a Cancer Growth System Subjected to Correlated Multiplicative and Additive Noises

In the present paper, the phenomena of stochastic resonance (SR) for a stochastic cancer development system that is driven by correlated multiplicative and additive noises is investigated. By using the fast descent method and the two-state theory, the expression of the signal-to-noise ratio (SNR) is obtained. Numerical results show that conventional SR occurs in the cancer growth model under different values of the system parameters. If the correlation strength between the two noises is positive or negative, the effects of the addictive noise intensity, the multiplicative noise intensity, and the correlated noise strength on the SNR are different.

What Comes First: The Food or the Nutrient? Executive Summary of a Symposium1–3

This article summarizes background materials and presentations at a symposium that considered the issue of the role of foods and dietary patterns vs. nutrients in relation to chronic disease risk. A model of food synergy is presented as a basis for studying whole foods and dietary patterns. Findings from a series of studies of walnuts were presented and support the concept that walnuts are a healthy food, with specific benefits in a mouse model of breast cancer growth, reductions in cardiovascular disease risk factors in humans, and motor performance and in vitro, in vivo, and ex vivo cellular response to challenge in an aged-rat model.

A mathematical model for pancreatic cancer growth and treatments

Pancreatic cancer is one of the most deadly types of cancer and has extremely poor prognosis. This malignancy typically induces only limited cellular immune responses, the magnitude of which can increase with the number of encountered cancer cells. On the other hand, pancreatic cancer is highly effective at evading immune responses by inducing polarization of pro-inflammatory M1 macrophages into anti-inflammatory M2 macrophages, and promoting expansion of myeloid derived suppressor cells, which block the killing of cancer cells by cytotoxic T cells. These factors allow immune evasion to predominate, promoting metastasis and poor responsiveness to chemotherapies and immunotherapies. In this paper we develop a mathematical model of pancreatic cancer, and use it to qualitatively explain a variety of biomedical and clinical data. The model shows that drugs aimed at suppressing cancer growth are effective only if the immune induced cancer cell death lies within a specific range, that is, the immune system has a specific window of opportunity to effectively suppress cancer under treatment. The model results suggest that tumor growth rate is affected by complex feedback loops between the tumor cells, endothelial cells and the immune response. The relative strength of the different loops determines the cancer growth rate and its response to immunotherapy. The model could serve as a starting point to identify optimal nodes for intervention against pancreatic cancer.

Avoiding healthy cells extinction in a cancer model

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed.

Mathematical Model of Colorectal Cancer with Monoclonal Antibody Treatments

We present a new mathematical model of colorectal cancer growth and its response to monoclonal-antibody (mAb) therapy. Although promising, most mAb drugs are still in trial phases, and the possible variations in the dosing schedules of those currently approved for use have not yet been thoroughly explored. To investigate the effectiveness of current mAb treatment schedules, and to test hypothetical treatment strategies, we have created a system of nonlinear ordinary differential equations (ODE) to model colorectal cancer growth and treatment. The model includes tumor cells, elements of the host's immune response, and treatments. Model treatments include the chemotherapy agent irinotecan and one of two monoclonal antibodies - cetuximab, which is FDA-approved for colorectal cancer, and panitumumab, which is still being evaluated in clinical trials. The model incorporates patient-specific parameters to account for individual variations in immune system strength and in medication efficacy against the tumor. We have simulated outcomes for groups of virtual patients on treatment protocols for which clinical trial data are available, using a range of biologically reasonable patient-specific parameter values. Our results closely match clinical trial results for these protocols. We also simulated experimental dosing schedules, and have found new schedules which, in our simulations, reduce tumor size more effectively than current treatment schedules. Additionally, we examined the system's equilibria and sensitivity to parameter values. In the absence of treatment, tumor evolution is most affected by the intrinsic tumor growth rate and carrying capacity. When treatment is introduced, tumor growth is most affected by drug-specific PK/PD parameters.