Phenomenological modeling of tumor diameter growth based on a mixed effects model

Over the last few years, taking advantage of the linear kinetics of the tumor growth during the steady-state phase, tumor diameter-based rather than tumor volume-based models have been developed for the phenomenological modeling of tumor growth. In this study, we propose a new tumor diameter growth model characterizing early, late and steady-state treatment effects. Model parameters consist of growth rhythms, growth delays and time constants and are meaningful for biologists. Biological experiments provide in vivo longitudinal data. The latter are analyzed using a mixed effects model based on the new diameter growth function, to take into account inter-mouse variability and treatment factors. The relevance of the tumor growth mixed model is firstly assessed by analyzing the effects of three therapeutic strategies for cancer treatment (radiotherapy, concomitant radiochemotherapy and photodynamic therapy) administered on mice. Then, effects of the radiochemotherapy treatment duration are estimated within the mixed model. The results highlight the model suitability for analyzing therapeutic efficiency, comparing treatment responses and optimizing, when used in combination with optimal experiment design, anti-cancer treatment modalities.     

Model-Based Tumor Growth Dynamics and Therapy Response in a Mouse Model of De Novo Carcinogenesis

Tumorigenesis is a complex, multistep process that depends on numerous alterations within the cell and contribution from the surrounding stroma. The ability to model macroscopic tumor evolution with high fidelity may contribute to better predictive tools for designing tumor therapy in the clinic. However, attempts to model tumor growth have mainly been developed and validated using data from xenograft mouse models, which fail to capture important aspects of tumorigenesis including tumor-initiating events and interactions with the immune system. In the present study, we investigate tumor growth and therapy dynamics in a mouse model of de novo carcinogenesis that closely recapitulates tumor initiation, progression and maintenance in vivo. We show that the rate of tumor growth and the effects of therapy are highly variable and mouse specific using a Gompertz model to describe tumor growth and a two-compartment pharmacokinetic/ pharmacodynamic model to describe the effects of therapy in mice treated with 5-FU. We show that inter-mouse growth variability is considerably larger than intra-mouse variability and that there is a correlation between tumor growth and drug kill rates. Our results show that in vivo tumor growth and regression in a double transgenic mouse model are highly variable both within and between subjects and that mathematical models can be used to capture the overall characteristics of this variability. In order for these models to become useful tools in the design of optimal therapy strategies and ultimately in clinical practice, a subject-specific modelling strategy is necessary, rather than approaches that are based on the average behavior of a given subject population which could provide erroneous results.     

The human tumor clonogenic assay as a model system in cell biology

The human tumor stem cell (clonogenic) assay (HTCA) is a soft agar system designed for growing fresh human tumor specimens in vitro. The assay has been extensively used in studies both of individual patients' response to chemotherapy and for screening new agents. The technical limitations of this assay have been extensively discussed. The use of this test as a model system to study fundamentals of tumor cell growth has not been stressed. The potentials and limitations of this assay for the study of the regulation of tumor growth are presented.     

Predictive Modeling of Neuroblastoma Growth Dynamics in Xenograft Model After Bevacizumab Anti-VEGF Therapy

Neuroblastoma is the leading cause of cancer death in young children. Although treatment for neuroblastoma has improved, the 5-year survival rate of patients still remains less than half. Recent studies have indicated that bevacizumab, an anti-VEGF drug used in treatment of several other cancer types, may be effective for treating neuroblastoma as well. However, its effect on neuroblastoma has not been well characterized. While traditional experiments are costly and time-consuming, mathematical models are capable of simulating complex systems quickly and inexpensively. In this study, we present a model of vascular tumor growth of neuroblastoma IMR-32 that is complex enough to replicate experimental data across a range of tumor cell properties measured in a suite of in vitro and in vivo experiments. The model provides quantitative insight into tumor vasculature, predicting a linear relationship between vasculature and tumor volume. The tumor growth model was coupled with known pharmacokinetics and pharmacodynamics of the VEGF blocker bevacizumab to study its effect on neuroblastoma growth dynamics. The results of our model suggest that total administered bevacizumab concentration per week, as opposed to dosage regimen, is the major determining factor in tumor suppression. Our model also establishes an exponentially decreasing relationship between administered bevacizumab concentration and tumor growth rate.     

Modeling the effects of vasculature evolution on early brain tumor growth

Mathematical modeling of both tumor growth and angiogenesis have been active areas of research for the past several decades. Such models can be classified into one of two categories: those that analyze the remodeling of the vasculature while ignoring changes in the tumor mass, and those that predict tumor expansion in the presence of a non-evolving vasculature. However, it is well accepted that vasculature remodeling and tumor growth strongly depend on one another. For this reason, we have developed a two-dimensional hybrid cellular automaton model of early brain tumor growth that couples the remodeling of the microvasculature with the evolution of the tumor mass. A system of reaction-diffusion equations has been developed to track the concentration of vascular endothelial growth factor (VEGF), Ang-1, Ang-2, their receptors and their complexes in space and time. The properties of the vasculature and hence of each cell are determined by the relative concentrations of these key angiogenic factors. The model exhibits an angiogenic switch consistent with experimental observations on the upregulation of angiogenesis. Particularly, we show that if the pathways that produce and respond to VEGF and the angiopoietins are properly functioning, angiogenesis is initiated and a tumor can grow to a macroscopic size. However, if the VEGF pathway is inhibited, angiogenesis does not occur and tumor growth is thwarted beyond 1-2mm in size. Furthermore, we show that tumor expansion can occur in well-vascularized environments even when angiogenesis is inhibited, suggesting that anti-angiogenic therapies may not be sufficient to eliminate a population of actively dividing malignant cells.     

Cellular automaton of idealized brain tumor growth dynamics

A novel cellular automaton model of proliferative brain tumor growth has been developed. This model is able to simulate Gompertzian tumor growth over nearly three orders of magnitude in radius using only four microscopic parameters. The predicted composition and growth rates are in agreement with a test case pooled from the available medical literature. The model incorporates several new features, improving previous models, and also allows ready extension to study other important properties of tumor growth, such as clonal competition.     

Kinetic model for designing a cancer therapy

A kinetic model has been developed to study cancer growth. Cancer growth has been considered as interaction between various independent but interacting compartments. The model considers cell growth and metastasis resulting in the formation of new tumor masses. Using certain representative parameter values, cell growth has been modeled in the absence and the presence of various cancer therapies. Based on this analysis, the critical parameters involved in cancer development have been identified. This model may thus be useful in studying and designing a cancer therapy using the data obtained from specific in vitro experiments.     

Polyphenols in brewed green tea inhibit prostate tumor xenograft growth by localizing to the tumor and decreasing oxidative stress and angiogenesis

It has been demonstrated in various animal models that the oral administration of green tea (GT) extracts in drinking water can inhibit tumor growth, but the effects of brewed GT on factors promoting tumor growth, including oxidant damage of DNA and protein, angiogenesis and DNA methylation, have not been tested in an animal model. To explore these potential mechanisms, brewed GT was administered instead of drinking water to male severe combined immunodeficiency (SCID) mice with androgen-dependent human LAPC4 prostate cancer cell subcutaneous xenografts. Tumor volume was decreased significantly in mice consuming GT, and tumor size was significantly correlated with GT polyphenol (GTP) content in tumor tissue. There was a significant reduction in hypoxia-inducible factor 1-alpha and vascular endothelial growth factor protein expression. GT consumption significantly reduced oxidative DNA and protein damage in tumor tissue as determined by 8-hydroxydeoxyguanosine/deoxyguanosine ratio and protein carbonyl assay, respectively. Methylation is known to inhibit antioxidative enzymes such as glutathione S-transferase pi to permit reactive oxygen species promotion of tumor growth. GT inhibited tumor 5-cytosine DNA methyltransferase 1 mRNA and protein expression significantly, which may contribute to the inhibition of tumor growth by reactivation of antioxidative enzymes. This study advances our understanding of tumor growth inhibition by brewed GT in an animal model by demonstrating tissue localization of GTPs in correlation with inhibition of tumor growth. Our results suggest that the inhibition of tumor growth is due to GTP-mediated inhibition of oxidative stress and angiogenesis in the LAPC4 xenograft prostate tumor in SCID mice.     

Repression of malignant tumor progression upon pharmacologic IGF1R blockade in a mouse model of insulinoma

NVP-AEW541, a specific ATP-competitive inhibitor of the insulin-like growth factor-1 receptor (IGF1R) tyrosine kinase, has been reported to interfere with tumor growth in various tumor transplantation models. We have assessed the efficacy of NVP-AEW541 in repressing tumor growth and tumor progression in the Rip1Tag2 transgenic mouse model of pancreatic β-cell carcinogenesis. In addition, we have tested NVP-AEW541 in Rip1Tag2;RipIGF1R double-transgenic mice which show accelerated tumor growth and increased tumor malignancy compared with Rip1Tag2 single-transgenic mice. Previously, we have shown that high levels of IGF-2, a high-affinity ligand for IGF1R, are required for Rip1Tag2 tumor cell survival and tumor growth. Unexpectedly, treatment of Rip1Tag2 mice with NVP-AEW541 in prevention and intervention trials neither did affect tumor growth nor tumor cell proliferation and apoptosis. Yet, it significantly repressed progression to tumor malignancy, that is, the rate of the transition from differentiated adenoma to invasive carcinoma. Treatment of Rip1Tag2;RipIGF1R double-transgenic mice resulted in moderately reduced tumor volumes and increased rates of tumor cell apoptosis. Sustained expression of IGF-2 and of the IGF-2-binding form of insulin receptor (IR-A) in tumor cells suggests a compensatory role of IR-A upon IGF1R blockade. The results indicate that inhibition of IGF1R alone is not sufficient to efficiently block insulinoma growth and imply an overlapping role of IGF1R and insulin receptor in executing mitogenic and survival stimuli elicited by IGF-2. The reduction of tumor invasion upon IGF1R blockade on the other hand indicates a critical function of IGF1R signaling for the acquisition of a malignant phenotype.     

Reduced tumor incidence, metastatic potential, and cytokine responsiveness of nm23-transfected melanoma cells

Reduced expression of the nm23 gene in certain rodent model systems and human breast tumors has been correlated with high tumor metastatic potential. To investigate the functional effects of nm23 expression, we have transfected a constitutive murine nm23-1 expression construct into highly metastatic K-1735 TK murine melanoma cells. TK clones expressing the exogenous nm23-1 construct exhibited a reduced incidence of primary tumor formation, significant reductions in tumor metastatic potential independent of tumor cell growth, and altered responses to the cytokine transforming growth factor beta 1 in soft agar colonization assays, compared with control-transfected TK clones. In contrast, nm23-1-transfected TK clones exhibited no significant differences in intrinsic tumor cell growth, i.e., primary tumor size in vivo, anchorage-dependent growth rate in vitro, and anchorage-independent colony formation in soft agar in vitro. The data demonstrate a suppressive effect of nm23 on several aspects of the cancer process, including tumor metastasis.     

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.     

Chronic bacterial osteomyelitis suppression of tumor growth requires innate immune responses

Clinical studies over the past several years have reported that metastasis-free survival times in humans and dogs with osteosarcoma are significantly increased in patients that develop chronic bacterial osteomyelitis at their surgical site. However, the immunological mechanism by which osteomyelitis may suppress tumor growth has not been investigated. Therefore, we used a mouse model of osteomyelitis to assess the effects of bone infection on innate immunity and tumor growth. A chronic Staphylococcal osteomyelitis model was established in C3H mice and the effects of infection on tumor growth of syngeneic DLM8 osteosarcoma were assessed. The effects of infection on tumor angiogenesis and innate immunity, including NK cell and monocyte responses, were assessed. We found that osteomyelitis significantly inhibited the growth of tumors in mice, and that the effect was independent of the infecting bacterial type, tumor type, or mouse strain. Depletion of NK cells or monocytes reversed the antitumor activity elicited by infection. Moreover, infected mice had a significant increase in circulating monocytes and numbers of tumor associated macrophages. Infection suppressed tumor angiogenesis but did not affect the numbers of circulating endothelial cells. Therefore, we concluded that chronic localized bacterial infection could elicit significant systemic antitumor activity dependent on NK cells and macrophages.     

Optimal control of tumor size used to maximize survival time when cells are resistant to chemotherapy.

The high failure rates encountered in the chemotherapy of some cancers suggest that drug resistance is a common phenomenon. In the current study, the tumor burden during therapy is used to slow the growth of the drug-resistant cells, thereby maximizing the survival time of the host. Three types of tumor growth model are investigated--Gompertz, logistic, and exponential. For each model, feedback controls are constructed that specify the optimal tumor mass as a function of the size of the resistant subpopulation. For exponential and logistic tumor growth, the tumor burden during therapy is shown to have little impact upon survival time. When the tumor is in Gompertz growth, therapies maintaining a large tumor burden double and sometimes triple the survival time under aggressive therapies. Aggressive therapies aim for a rapid reduction in the sensitive cell subpopulation. These conclusions are not dependent upon the values of the model constants that determine the mass of resistant cells. Since treatments maintaining a high tumor burden are optimal for Gompertz tumor growth and close to optimal for exponential and logistic tumor growth, it may no longer be necessary to know the growth characteristics of a tumor to schedule anticancer drugs.     

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.     

Synthesis and biological evaluation of dimeric cinnamaldehydes as potent antitumor agents

It has been reported that 2-hydroxycinnamaldehyde and 2-benzoyl-oxycinnamaldehyde inhibited the activity of farnesyl protein transferase, angiogenesis, cell-cell adhesion, and tumor growth in vivo model. In order to improve its anti-tumor activity, dimeric cinnamaldehydes have been synthesized based on 2-hydroxycinnamaldehyde. The synthesized compounds strongly inhibited the growth of human colon tumor cells with GI50 values of 0.6-10 microM. Especially, 2-piperazine derivative blocked in vivo growth of human colon tumor xenograft in nude mice at 10 mg/kg. It was found that their anti-tumor effects induce apoptosis and cell cycle arrest at G2/M phase by the compounds. It was confirmed by detection of apoptosis markers such as activated caspase-3 and cleaved PARP, and cell cycle analysis. The dimeric compounds also inhibited Cdc25B phosphatase which is essential for preinitiating G2/M transition and S phase progression.     

Nuclear architecture supports integration of physiological regulatory signals for transcription of cell growth and tissue-specific genes during osteoblast differentiation

Metastatic model of human tumor xenografts have been developed using orthotopic transplantation of histologically intact tissue (onplantation) of lung, stomach, colon, pancreatic, prostate and bladder carcinomas. These models represent the entire process of the metastasis, consisting of local tumor growth, vascular and lymphatic invasion at the local site, flow in the vessels and lymphatic, extravasation at the metastatic organs, and seeding and growth at relevant metastatic sites. Orthotopically transplanted human small-cell lung carcinoma displayed a different chemosensitivity pattern compared with the subcutaneous transplanted model, suggesting different pharmacodynamics between the orthotopic lung and the ectopic subcutaneous sites. The intact-tissue orthotopic-onplantation model seems to be useful to study the mechanism of metastasis for discovery of antimetastatic agents and for the patient tumors and for this treatment design.     

Influence of interstitial fluid dynamics on growth and therapy of angiogenic tumor. Analysis by mathematical model

We have developed a spatially distributed mathematical model of angiogenic tumor growth in tissue with account of interstitial fluid dynamics and bevacizumab monotherapy. In this model the process of neovascularization is initiated by tumor cells in a state of metabolic stress, vascular endothelial growth factor (VEGF) being its main mediator. The model takes into consideration the convection flows arising in dense tissue due to active proliferation and migration of tumor cells as well as interstitial fluid inflow from blood vascular system, its outflow through lymphatic system and redistribution in the area of tumor growth. The work considers the diffusive approximation of interstitial fluid dynamics in tumor and normal tissue. Numerical study of the model showed that in absence of therapy a peritumoral edema is formed due to the increase of interstitial fluid inflow from angiogenic capillaries. In the case of rapid interstitial fluid outflow through lymphatic system and its fast transport from necrotic zone to normal tissue the regimes of full growth stop are observed in case of low-invasive tumor. Under bevacizumab monotherapy the peritumoral edema vanishes and low-invasive tumor may not only decelerate its growth, but also start shrinking for a large range of parameters.