Multiscale modelling of solid tumour growth: the effect of collagen micromechanics

Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

Modelling the Tumour Microenvironment, but What Exactly Do We Mean by "Model"?

The Oxford English Dictionary includes 17 definitions for the word "model" as a noun and another 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For instance, "model railways" refer to replicas of railways and trains at a smaller scale and a "model student" refers to an exemplary individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning for model. Even if the context is narrowed, specifically, to research related to the tumour microenvironment, "model" can be understood in a wide variety of ways, from an animal model to a mathematical expression. This paper presents a review of different "models" of the tumour microenvironment, as grouped by different definitions of the word into four categories: model organisms, in vitro models, mathematical models and computational models. Then, the frequencies of different meanings of the word "model" related to the tumour microenvironment are measured from numbers of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequencies of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, particularly xenografts and mouse models, are the most commonly used "models", the number of these entries has been slowly decreasing. Mathematical models, as well as prognostic and risk models, follow in frequency, and these have been growing in use.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

Combined Influence of Nutrient Supply Level and Tissue Mechanical Properties on Benign Tumor Growth as Revealed by Mathematical Modeling

A continuous mathematical model of non-invasive avascular tumor growth in tissue is presented. The model considers tissue as a biphasic material, comprised of a solid matrix and interstitial fluid. The convective motion of tissue elements happens due to the gradients of stress, which change as a result of tumor cells proliferation and death. The model accounts for glucose as the crucial nutrient, supplied from the normal tissue, and can reproduce both diffusion-limited and stress-limited tumor growth. Approximate tumor growth curves are obtained semi-analytically in the limit of infinite tissue hydraulic conductivity, which implies instantaneous equalization of arising stress gradients. These growth curves correspond well to the numerical solutions and represent classical sigmoidal curves with a short initial exponential phase, subsequent almost linear growth phase and a phase with growth deceleration, in which tumor tends to reach its maximum volume. The influence of two model parameters on tumor growth curves is investigated: tissue hydraulic conductivity, which links the values of stress gradient and convective velocity of tissue phases, and tumor nutrient supply level, which corresponds to different permeability and surface area density of capillaries in the normal tissue that surrounds the tumor. In particular, it is demonstrated, that sufficiently low tissue hydraulic conductivity (intrinsic, e.g., to tumors arising from connective tissue) and sufficiently high nutrient supply can lead to formation of giant benign tumors, reaching tens of centimeters in diameter, which are indeed observed clinically.

Compressive Remodeling Alters Fluid Transport Properties of Collagen Networks - Implications for Tumor Growth

Biomechanical alterations to the tumor microenvironment include accumulation of solid stresses, extracellular matrix (ECM) stiffening and increased fluid pressure in both interstitial and peri-tumoral spaces. The relationship between interstitial fluid pressurization and ECM remodeling in vascularized tumors is well characterized, while earlier biomechanical changes occurring during avascular tumor growth within the peri-tumoral ECM remain poorly understood. Type I collagen, the primary fibrous ECM constituent, bears load in tension while it buckles under compression. We hypothesized that tumor-generated compressive forces cause collagen remodeling via densification which in turn creates a barrier to convective fluid transport and may play a role in tumor progression and malignancy. To better understand this process, we characterized the structure-function relationship of collagen networks under compression both experimentally and computationally. Here we show that growth of epithelial cancers induces compressive remodeling of the ECM, documented in the literature as a TACS-2 phenotype, which represents a localized densification and tangential alignment of peri-tumoral collagen. Such compressive remodeling is caused by the unique features of collagen network mechanics, such as fiber buckling and cross-link rupture, and reduces the overall hydraulic permeability of the matrix.

A quantitative in silico platform for simulating cytotoxic and nanoparticle drug delivery to solid tumours

The role of tumour-host mechano-biology and the mechanisms involved in the delivery of anti-cancer drugs have been extensively studied using in vitro and in vivo models. A complementary approach is offered by in silico models, which can also potentially identify the main factors affecting the transport of tumour-targeting molecules. Here, we present a generalized three-dimensional in silico modelling framework of dynamic solid tumour growth, angiogenesis and drug delivery. Crucially, the model allows for drug properties-such as size and binding affinity-to be explicitly defined, hence facilitating investigation into the interaction between the changing tumour-host microenvironment and cytotoxic and nanoparticle drugs. We use the model to qualitatively recapitulate experimental evidence of delivery efficacy of cytotoxic and nanoparticle drugs on matrix density (and hence porosity). Furthermore, we predict a highly heterogeneous distribution of nanoparticles after delivery; that nanoparticles require a high porosity extracellular matrix to cause tumour regression; and that post-injection transvascular fluid velocity depends on matrix porosity, and implicitly on the size of the drug used to treat the tumour. These results highlight the utility of predictive in silico modelling in better understanding the factors governing efficient cytotoxic and nanoparticle drug delivery.

In-silico dynamic analysis of cytotoxic drug administration to solid tumours: Effect of binding affinity and vessel permeability

The delivery of blood-borne therapeutic agents to solid tumours depends on a broad range of biophysical factors. We present a novel multiscale, multiphysics, in-silico modelling framework that encompasses dynamic tumour growth, angiogenesis and drug delivery, and use this model to simulate the intravenous delivery of cytotoxic drugs. The model accounts for chemo-, hapto- and mechanotactic vessel sprouting, extracellular matrix remodelling, mechano-sensitive vascular remodelling and collapse, intra- and extravascular drug transport, and tumour regression as an effect of a cytotoxic cancer drug. The modelling framework is flexible, allowing the drug properties to be specified, which provides realistic predictions of in-vivo vascular development and structure at different tumour stages. The model also enables the effects of neoadjuvant vascular normalisation to be implicitly tested by decreasing vessel wall pore size. We use the model to test the interplay between time of treatment, drug affinity rate and the size of the vessels’ endothelium pores on the delivery and subsequent tumour regression and vessel remodelling. Model predictions confirm that small-molecule drug delivery is dominated by diffusive transport and further predict that the time of treatment is important for low affinity but not high affinity cytotoxic drugs, the size of the vessel wall pores plays an important role in the effect of low affinity but not high affinity drugs, that high affinity cytotoxic drugs remodel the tumour vasculature providing a large window for the normalisation of the vascular architecture, and that the combination of large pores and high affinity enhances cytotoxic drug delivery efficiency. These results have implications for treatment planning and methods to enhance drug delivery, and highlight the importance of in-silico modelling in investigating the optimisation of cancer therapy on a personalised setting.

One of the main challenges in optimising cancer therapy is understanding the in-vivo cancer environment and how it changes over time. The efficacy of chemotherapeutic drugs is known to be strongly dependent on blood vessel wall properties and the architecture of the developing tumour vasculature, which in turn are dependent on biochemical and mechanical interactions between cancer cells and their microenvironment. Here we present a novel in-silico modelling framework of dynamic tumour growth, angiogenesis and drug delivery, and we use it to explore biophysical factors governing the efficient delivery of cytotoxic drugs to solid tumours. We find that the time of treatment and vessel permeability are important factors for the efficacy of chemical agents with low binding affinity, that high affinity drugs can impact the tumour vasculature remodelling and bring vascular structure back to a more normalised state, and that the combination of large-sized vessel wall pores and high affinity enhances cytotoxic drug delivery and efficacy. These results have implications for treatment planning and optimisation, and show how in-silico models can be used to help understand and optimise cancer therapy.

Predicting the role of microstructural and biomechanical cues in tumor growth and spreading

A continuum porous media model is developed for elucidating the role of the mechanical cues in regulating tumor growth and spreading. It is shown that stiffer matrices and higher cell-matrix adhesion limit tumor growth and spreading toward the surrounding tissue. Higher matrix porosities, conversely, favor the growth and the dissemination of tumor cells. This model could be used for predicting the response of malignant masses to novel therapeutic agents affecting directly the tumor microenvironment and its micromechanical cues.

Automated Classification of Breast Cancer Stroma Maturity From Histological Images

OBJECTIVE

The tumor microenvironment plays a crucial role in regulating tumor progression by a number of different mechanisms, in particular, the remodeling of collagen fibers in tumor-associated stroma, which has been reported to be related to patient survival. The underlying motivation of this work is that remodeling of collagen fibers gives rise to observable patterns in hematoxylin and eosin (H&E) stained slides from clinical cases of invasive breast carcinoma that the pathologist can label as mature or immature stroma. The aim of this paper is to categorise and automatically classify stromal regions according to their maturity and show that this classification agrees with that of skilled observers, hence providing a repeatable and quantitative measure for prognostic studies.

METHODS

We use multiscale basic image features and local binary patterns, in combination with a random decision trees classifier for classification of breast cancer stroma regions-of-interest (ROI).

RESULTS

We present results from a cohort of 55 patients with analysis of 169 ROI. Our multiscale approach achieved a classification accuracy of 84%.

CONCLUSION

This work demonstrates the ability of texture-based image analysis to differentiate breast cancer stroma maturity in clinically acquired H&E-stained slides at least as well as skilled observers.

Multiscale biphasic modelling of peritumoural collagen microstructure: The effect of tumour growth on permeability and fluid flow

We present an in-silico model of avascular poroelastic tumour growth coupled with a multiscale biphasic description of the tumour–host environment. The model is specified to in-vitro data, facilitating biophysically realistic simulations of tumour spheroid growth into a dense collagen hydrogel. We use the model to first confirm that passive mechanical remodelling of collagen fibres at the tumour boundary is driven by solid stress, and not fluid pressure. The model is then used to demonstrate the influence of collagen microstructure on peritumoural permeability and interstitial fluid flow. Our model suggests that at the tumour periphery, remodelling causes the peritumoural stroma to become more permeable in the circumferential than radial direction, and the interstitial fluid velocity is found to be dependent on initial collagen alignment. Finally we show that solid stresses are negatively correlated with peritumoural permeability, and positively correlated with interstitial fluid velocity. These results point to a heterogeneous, microstructure-dependent force environment at the tumour–peritumoural stroma interface.

The Solid Mechanics of Cancer and Strategies for Improved Therapy

Tumor progression and response to treatment is determined in large part by the generation of mechanical stresses that stem from both the solid and the fluid phase of the tumor. Furthermore, elevated solid stress levels can regulate fluid stresses by compressing intratumoral blood and lymphatic vessels. Blood vessel compression reduces tumor perfusion, while compression of lymphatic vessels hinders the ability of the tumor to drain excessive fluid from its interstitial space contributing to the uniform elevation of the interstitial fluid pressure. Hypoperfusion and interstitial hypertension pose major barriers to the systemic administration of chemotherapeutic agents and nanomedicines to tumors, reducing treatment efficacies. Hypoperfusion can also create a hypoxic and acidic tumor microenvironment that promotes tumor progression and metastasis. Hence, alleviation of intratumoral solid stress levels can decompress tumor vessels and restore perfusion and interstitial fluid pressure. In this review, three major types of tissue level solid stresses involved in tumor growth, namely stress exerted externally on the tumor by the host tissue, swelling stress, and residual stress, are discussed separately and details are provided regarding their causes, magnitudes, and remedies. Subsequently, evidence of how stress-alleviating drugs could be used in combination with chemotherapy to improve treatment efficacy is presented, highlighting the potential of stress-alleviation strategies to enhance cancer therapy. Finally, a continuum-level, mathematical framework to incorporate these types of solid stress is outlined.

A Validated Multiscale In-Silico Model for Mechano-sensitive Tumour Angiogenesis and Growth

Vascularisation is a key feature of cancer growth, invasion and metastasis. To better understand the governing biophysical processes and their relative importance, it is instructive to develop physiologically representative mathematical models with which to compare to experimental data. Previous studies have successfully applied this approach to test the effect of various biochemical factors on tumour growth and angiogenesis. However, these models do not account for the experimentally observed dependency of angiogenic network evolution on growth-induced solid stresses. This work introduces two novel features: the effects of hapto- and mechanotaxis on vessel sprouting, and mechano-sensitive dynamic vascular remodelling. The proposed three-dimensional, multiscale, in-silico model of dynamically coupled angiogenic tumour growth is specified to in-vivo and in-vitro data, chosen, where possible, to provide a physiologically consistent description. The model is then validated against in-vivo data from murine mammary carcinomas, with particular focus placed on identifying the influence of mechanical factors. Crucially, we find that it is necessary to include hapto- and mechanotaxis to recapitulate observed time-varying spatial distributions of angiogenic vasculature.

Production of a Self-Aligned Scaffold, Free of Exogenous Material, from Dermal Fibroblasts Using the Self-Assembly Technique

Many pathologies of skin, especially ageing and cancer, involve modifications in the matrix alignment. Such tissue reorganization could have impact on cell behaviour and/or more global biological processes. Tissue engineering provides accurate study model by mimicking the skin and it allows the construction of versatile tridimensional models using human cells. It also avoids the use of animals, which gave sometimes nontranslatable results. Among the various techniques existing, the self-assembly method allows production of a near native skin, free of exogenous material. After cultivating human dermal fibroblasts in the presence of ascorbate during two weeks, a reseeding of these cells takes place after elevation of the resulting stroma on a permeable ring and culture pursued for another two weeks. This protocol induces a clear realignment of matrix fibres and cells parallel to the horizon. The thickness of this stretched reconstructed tissue is reduced compared to the stroma produced by the standard technique. Cell count is also reduced. In conclusion, a new, easy, and inexpensive method to produce aligned tissue free of exogenous material could be used for fundamental research applications in dermatology.