Mechanistic Modeling Quantifies The Influence Of Tumor Growth Kinetics On The Response To Anti-Angiogenic Treatment

Thomas D. Gaddy, Stacey D. Finley

Abstract

Tumors exploit angiogenesis, the formation of new blood vessels from pre-existing vasculature, in order to obtain nutrients required for continued growth and proliferation. Targeting factors that regulate angiogenesis, including the potent promoter vascular endothelial growth factor (VEGF), is therefore an attractive strategy for inhibiting tumor growth. Systems biology modeling enables us to identify tumor-specific properties that influence the response to those anti-angiogenic strategies. Here, we build on our previous systems biology model of VEGF transport and kinetics in tumor-bearing mice to include a tumor compartment whose volume depends on the “angiogenic signal” produced when VEGF binds to its receptors on tumor endothelial cells. We trained and validated the model using in vivo measurements of xenograft tumor volume to produce a model that accurately predicts the tumor's response to anti-angiogenic treatment. We applied the model to investigate how tumor growth kinetics influence the response to anti-angiogenic treatment targeting VEGF. Based on multivariate regression analysis, we found that certain intrinsic kinetic parameters that characterize the growth of tumors could successfully predict response to anti-VEGF treatment. This model is a useful tool for predicting which tumors will respond to anti-VEGF treatment, complementing pre-clinical in vivo studies.

Link: http://biorxiv.org/content/early/2017/05/10/136531

3D Hybrid Modelling of Vascular Network Formation

3D hybrid modeling of vascular network formation

Holger Perfahl, Barry D Hughes, Tomas Alaracon, Philip K Maini, Mark C Lloyd, Matthias Reuss, Helen M Byrne

Abstract

We develop an agent-based model of vasculogenesis, the de novo formation of blood vessels. Endothelial cells in the vessel network are viewed as linearly elastic spheres and are of two types: vessel elements are contained within the network; tip cells are located at endpoints. Tip cells move in response to forces due to interactions with neighbouring vessel elements, the local tissue environment, chemotaxis and a persistence force modeling their tendency to continue moving in the same direction. Vessel elements experience similar forces but not chemotaxis. An angular persistence force representing local tissue interactions stabilises buckling instabilities due to proliferation. Vessel elements proliferate, at rates that depend on their degree of stretch: elongated elements proliferate more rapidly than compressed elements. Following division, new cells are more likely to form new sprouts if the parent vessel is highly compressed and to be incorporated into the parent vessel if it is stretched. 

Model simulations reproduce key features of vasculogenesis. Parameter sensitivity analyses reveal significant changes in network size and morphology on varying the chemotactic sensitivity of tip cells, and the sensitivities of the proliferation rate and sprouting probability to mechanical stretch. Varying chemotactic sensitivity also affects network directionality. Branching and network density are influenced by the sprouting probability. Glyphs depicting multiple network properties show how network quantities change over time and as model parameters vary. We also show how glyphs constructed from in vivo data could be used to discriminate between normal and tumour vasculature and, ultimately, for model validation. We conclude that our biomechanical hybrid model generates vascular networks similar to those generated from in vitro and in vivo experiments.

Link:	arXiv:1610.00661 [q-bio.QM]

Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature

Artem Kaznatcheev, Robert Vander Velde, Jacob G Scott, David Basanta

 

Abstract

Background: Tumours are diverse ecosystems with persistent heterogeneity in various cancer hallmarks like self-sufficiency of growth factor production for angiogenesis and reprogramming of energy-metabolism for aerobic glycolysis. This heterogeneity has consequences for diagnosis, treatment, and disease progression. Methods: We introduce the double goods game to study the dynamics of these traits using evolutionary game theory. We model glycolytic acid production as a public good for all tumour cells and oxygen from vascularization via VEGF production as a club good benefiting non-glycolytic tumour cells. This results in three viable phenotypic strategies: glycolytic, angiogenic, and aerobic non-angiogenic. Results: We classify the dynamics into three qualitatively distinct regimes: (1) fully glycolytic, (2) fully angiogenic, or (3) polyclonal in all three cell types. The third regime allows for dynamic heterogeneity even with linear goods, something that was not possible in prior public good models that considered glycolysis or growth-factor production in isolation. Conclusion: The cyclic dynamics of the polyclonal regime stress the importance of timing for anti-glycolysis treatments like lonidamine. The existence of qualitatively different dynamic regimes highlights the order effects of treatments. In particular, we consider the potential of vascular renormalization as a neoadjuvant therapy before follow up with interventions like buffer therapy.

Link: doi: http://dx.doi.org/10.1101/067488

 

 

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silica insights

J. C. L. Alfonso, A. Kohn-Luque, T. Stylianopoulos, F. Feuerhake, A. Deutsch, H. Hatzikirou

There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve functional tumour-associated blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation medi- ated by vascular targeting agents that induce occlusion/collapse of tumour blood vessels. In contrast, the therapeutic intention of normalising the abnormal structure and function of tumour vascular net- works, e.g. via alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and radiation therapy efficacy. Although both strategies have shown therapeutic potential, it remains unclear why they often fail to control glioma invasion into the surrounding healthy brain tissue. To shed light on this issue, we propose a mathematical model of glioma invasion focusing on the interplay between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells and modulations of the functional tumour vasculature. Vaso-modulatory interventions are modelled by varying the degree of vaso-occlusion. We discovered the existence of a critical cell proliferation/diffusion ratio that separates glioma invasion re- sponses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the tumour front speed and increase the infiltration width, for those in the other regime the invasion speed increases and infiltration width decreases. We show how these in silico findings can be used to guide individualised approaches of vaso-modulatory treatment strategies and thereby improve success rates.

Link:arXiv:1604.05082http://arxiv.org/abs/1604.05082

Cancer therapeutic potential of combinatorial immuno- and vaso-modulatory interventions

Cancer therapeutic potential of combinatorial immuno- and vaso-modulatory interventions 

H. Hatzikirou, J. C. L. Alfonso, S. Muhle, C. Stern, S. Weiss, M. Meyer-Hermann

Currently, most of the basic mechanisms governing tumor-immune system interactions, in combination with modulations of tumor-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of vascularized tumor growth, where the main novelty is the modelling of the interplay between functional tumor vasculature and effector recruitment dynamics. Parameters are calibrated on the basis of different in vivo Rag1-/- and wild-type (WT) BALB/c murine tumor growth experiments. The model analysis supports that vasculature normalization can be a plausible and effective strategy to treat cancer when combined with appropriate immuno-stimulation. We find that improved levels of functional vasculature, potentially mediated by vascular normalization or stress alleviation strategies, can provide beneficial outcomes in terms of tumor burden reduction and control. Normalization of tumor blood vessels opens a therapeutic window of opportunity to augment the anti- tumor immune responses, as well as to reduce the intratumoral immunosuppression and hypoxia due to vascular abnormalities. The potential success of normalizing tumor vasculature closely depends on the effector cell recruitment dynamics and tumor sizes. Furthermore, an arbitrary increase of initial effector cell concentration does not necessarily imply tumor control, and we evidence the existence of an optimal effector concentration range for tumor shrinkage. Based on these findings, we suggest a theory-driven therapeutic proposal that optimally combines immune- and vaso-modulatory interventions.

http://arxiv.org/abs/1505.05670

Computational Screening of Angiogenesis Model Variants Predicts that Differential Chemotaxis Helps Tip Cells Move to the Sprout Tip and Accelerates Sprouting

Margriet M. Palm, Marchien G. Dallinga, Erik van Dijk, Ingeborg Klaassen, Reinier O. Schlingemann, Roeland M.H. Merks

(Submitted on 20 Sep 2014)

Angiogenesis involves the formation of new blood vessels by sprouting or splitting of existing blood vessels. During sprouting, a highly motile type of endothelial cell, called the tip cell, migrates from the blood vessels followed by stalk cells, an endothelial cell type that forms the body of the sprout. In vitro models and computational models can recapitulate much of the phenomenology of angiogenesis in absence of tip and stalk cell differentiation. Therefore it is unclear how the presence of tip cells contributes to angiogenesis. To get more insight into how tip cells contribute to angiogenesis, we extended an existing computational model of vascular network formation based on the cellular Potts model with tip and stalk differentiation, without making a priori assumptions about the specific rules that tip cells follow. We then screened a range of model variants, looking for rules that make tip cells (a) move to the sprout tip, and (b) change the morphology of the angiogenic networks. The screening predicted that if tip cells respond less effectively to an endothelial chemoattractant than stalk cells, they move to the tips of the sprouts, which impacts the morphology of the networks. A comparison of this model prediction with genes expressed differentially in tip and stalk cells revealed that the endothelial chemoattractant Apelin and its receptor APJ may match the model prediction. To test the model prediction we inhibited Apelin signaling in our model and in an in vitro model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting. Based on the prediction of the computational model, we propose that the differential expression of Apelin and APJ yields a "self-generated" gradient mechanisms that accelerates the extension of the sprout.

 link: http://arxiv.org/abs/1409.5895

Mesoscopic and continuum modelling of angiogenesis

Fabian Spill, Pilar Guerrero, Tomas Alarcon, Philip K. Maini, Helen M. Byrne

(Submitted on 22 Jan 2014)

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells.

http://arxiv.org/abs/1401.5701

Global Dormancy of Metastases due to Systemic Inhibition of Angiogenesis

Cancer does not always develop to become a clinically manifest disease. Most of the population actually carries small occult tumors that remain asymptomatic and undetectable. Here, we propose a theoretical study of this phenomenon by defining and simulating a novel mathematical model able to describe the development of a population of tumors at the organism scale. After demonstrating the model can explain experimental data on metastatic development, we go on to test the hypothesis of global dormancy resulting from inhibitory signaling interactions among the tumors. These interactions are targeted against the tumor's vascular support development (angiogenesis), known to be essential for tumor growth, by means of inhibitory molecules released in the circulation. By quantifying their consequences on the establishment of metastases and maintenance of the dormant state, our model shows for the first time how a previously unrecognized phenomenon - systemic inhibition of angiogenesis (SIA) - regulates tumor development. We show SIA alone is not sufficient for global dormancy but can suppress the growth of the total metastatic burden, even to the point of producing an equilibrium state with low and stable total cancerous mass.

Sebastien Benzekry, Alberto Gandolfi, Philip Hahnfeldt

Link: http://hal.inria.fr/hal-00868592/

A recent physical approach to angiogenesis modeling: mixture models

Angiogenesis modeling has generally tended towards (1) discrete models of individual sprout tip cells (cellular automata, Plank-Sleeman free-swimming models, etc.), or (2) continuum models of the evolving blood vessel density. At the Mathways into Cancer II workshop last week, I learned of a new approach using mixture (or phase field) models: computational voxels are treated as a conserved mixture of water, matrix, and endothelial cells. Applying conservation laws to each of these phases, plus an energy formulation of how the phases mix, leads to fourth-order Cahn-Hilliard equations for the mixture components. These require some fairly tricky numerics to solve correctly, but the results can be beautiful. And notably, it allows the inclusion of sophisticated cell and tissue mechanics.

Without further ado, I present two papers (by two different groups) on this new approach to angiogenesis modeling, combined as hybrid models with "traditional" sprout tip agents:

Capillary networks in tumor angiogenesis: From discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis
Guillermo Vilanova, Ignasi Colominas, Hector Gomez

Abstract: Tumor angiogenesis, the growth of new capillaries from preexisting ones promoted by the starvation and hypoxia of cancerous cell, creates complex biological patterns. These patterns are captured by a hybrid model that involves high-order partial differential equations coupled with mobile, agent-based components. The continuous equations of the model rely on the phase-field method to describe the intricate interfaces between the vasculature and the host tissue. The discrete equations are posed on a cellular scale and treat tip endothelial cells as mobile agents. Here, we put the model into a coherent mathematical and algorithmic framework and introduce a numerical method based on isogeometric analysis that couples the discrete and continuous descriptions of the theory. Using our algorithms, we perform numerical simulations that show the development of the vasculature around a tumor. The new method permitted us to perform a parametric study of the model. Furthermore, we investigate different initial configurations to study the growth of the new capillaries. The simulations illustrate the accuracy and efficiency of our numerical method and provide insight into the dynamics of the governing equations as well as into the underlying physical phenomenon.

Preprint / advance copy: http://dx.doi.org/10.1002/cnm.2552

(AFAIK) The first work using this approach was by Rui Travasso and colleagues in 2011, with a focus on the role of mechanistic modeling in driving biological hypotheses:

Tumor Angiogenesis and Vascular Patterning: A Mathematical Model
Rui D. M. Travasso et al.

Abstract: Understanding tumor induced angiogenesis is a challenging problem with important consequences for diagnosis and treatment of cancer. Recently, strong evidences suggest the dual role of endothelial cells on the migrating tips and on the proliferating body of blood vessels, in consonance with further events behind lumen formation and vascular patterning. In this paper we present a multi-scale phase-field model that combines the benefits of continuum physics description and the capability of tracking individual cells. The model allows us to discuss the role of the endothelial cells' chemotactic response and proliferation rate as key factors that tailor the neovascular network. Importantly, we also test the predictions of our theoretical model against relevant experimental approaches in mice that displayed distinctive vascular patterns. The model reproduces the in vivo patterns of newly formed vascular networks, providing quantitative and qualitative results for branch density and vessel diameter on the order of the ones measured experimentally in mouse retinas. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of different parameters in this process, hence underlining the necessary collaboration between mathematical modeling, in vivo imaging and molecular biology techniques to improve current diagnostic and therapeutic tools.

Open access: http://dx.doi.org/10.1371/journal.pone.0019989