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

Using mathematical modelling and AI to improve delivery and efficacy of therapies in cancer

Mathematical modelling has proven to be a valuable tool in predicting the delivery and efficacy of molecular, antibody-based, nano and cellular therapy in solid tumours. Mathematical models based on our understanding of the biological processes at subcellular, cellular and tissue level are known as mechanistic models that, in turn, are divided into continuous and discrete models. Continuous models are further divided into lumped parameter models - for describing the temporal distribution of medicine in tumours and normal organs - and distributed parameter models - for studying the spatiotemporal distribution of therapy in tumours. Discrete models capture interactions at the cellular and subcellular levels. Collectively, these models are useful for optimizing the delivery and efficacy of molecular, nanoscale and cellular therapy in tumours by incorporating the biological characteristics of tumours, the physicochemical properties of drugs, the interactions among drugs, cancer cells and various components of the tumour microenvironment, and for enabling patient-specific predictions when combined with medical imaging. Artificial intelligence-based methods, such as machine learning, have ushered in a new era in oncology. These data-driven approaches complement mechanistic models and have immense potential for improving cancer detection, treatment and drug discovery. Here we review these diverse approaches and suggest ways to combine mechanistic and artificial intelligence-based models to further improve patient treatment outcomes.

Validating the predictions of mathematical models describing tumor growth and treatment response

Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer mechanisms and personalize disease management. To address these limitations, individualized cancer forecasts have been shown to predict tumor growth and therapeutic response, inform treatment optimization, and guide experimental efforts. These predictions are obtained via computer simulations of mathematical models that are constrained with data from a patient's cancer and experiments. This book chapter addresses the validation of these mathematical models to forecast tumor growth and treatment response. We start with an overview of mathematical modeling frameworks, model selection techniques, and fundamental metrics. We then describe the usual strategies employed to validate cancer forecasts in preclinical and clinical scenarios. Finally, we discuss existing barriers in validating these predictions along with potential strategies to address them.

A 3D Computational Study on the Formation and Progression of Tumor Cells in Diffuse Gastric Cancer

Hereditary diffuse gastric cancer is characterized by an increased risk of diffuse gastric cancer and lobular breast cancer, and is caused by pathogenic germline variants of E-cadherin and α -E-catenin, which are key regulators of cell-cell adhesion. However, how the loss of cell-cell adhesion promotes cell dissemination remains to be fully understood. Therefore, a three-dimensional computer model was developed to describe the initial steps of diffuse gastric cancer development. In this model, we have implemented a cellular Potts approach that contemplates cell adhesion to other cells and to the extracellular matrix, cell extrusion from the gastric epithelia, and subsequent proliferation. We demonstrate that early disease features are determined by decreased adhesion of mutant cells to their normal epithelial neighbors, with concomitant increased attachment to matrix components. Importantly, our simulation shows how mechanical pressure and uncontrolled proliferation of mutant cells lead to modifications in cell shape and in gastric gland morphology. In conclusion, this work underscores the potential of computational models to elucidate the role of cellular and noncellular components in gastric cancer that may be relevant targets in therapeutic interventions.

Hybrid model of tumor growth, angiogenesis and immune response yields strategies to improve antiangiogenic therapy

Solid tumors harbor a complex and dynamic microenvironment that hinders the delivery and efficacy of therapeutic interventions. In this study, we developed and utilized a hybrid, discrete-continuous mathematical model to explore the interplay between solid tumor growth, immune response, tumor-induced angiogenesis, and antiangiogenic drugs. By integrating published data with anti-angiogenic drugs, we elucidate three primary mechanisms by which anti-angiogenesis influences tumor progression and treatment outcomes: reduction in tumor growth rate by mitigating and temporally delaying angiogenesis, normalization of blood vessel structure and function, and improving immune cell extravasation and activation. Our results indicate a significant increase in functional blood vessels and perfusion following anti-angiogenic treatment, which in turn improves the intratumoral distribution of immune cells. The normalization window, or optimal time frame for anti-angiogenic drug administration, and the dose of the drug arise naturally in the model and are highlighted as crucial factors in maximizing treatment benefits. Prolonged anti-angiogenic treatment triggers cancer cell migration into healthy tissue and induces immunosuppression due to hypoxia, potentially leading to negative effects because these cancer cells will rapidly proliferate upon treatment termination. In conclusion, the positive contribution of anti-angiogenic treatment must balance the possible negative effects by choosing a proper treatment protocol as well as combining it with proper anti-cancer treatment. Our findings provide valuable insights and a framework for the design of protocols with anti-angiogenic treatment, targeted immunotherapy, and non-targeted anti-cancer therapies.

Mechanical forces inducing oxaliplatin resistance in pancreatic cancer can be targeted by autophagy inhibition

Pancreatic cancer remains one of the most lethal malignancies, with limited treatment options and poor prognosis. A common characteristic among pancreatic cancer patients is the biomechanically altered tumor microenvironment (TME), which among others is responsible for the elevated mechanical stresses in the tumor interior. Although significant research has elucidated the effect of mechanical stress on cancer cell proliferation and migration, it has not yet been investigated how it could affect cancer cell drug sensitivity. Here, we demonstrated that mechanical stress triggers autophagy activation, correlated with increased resistance to oxaliplatin treatment in pancreatic cancer cells. Our results demonstrate that inhibition of autophagy using hydroxychloroquine (HCQ) enhanced the oxaliplatin-induced apoptotic cell death in pancreatic cancer cells exposed to mechanical stress. The combined treatment of HCQ with losartan, a known modulator of mechanical abnormalities in tumors, synergistically enhanced the therapeutic efficacy of oxaliplatin in murine pancreatic tumor models. Furthermore, our study revealed that the use of HCQ enhanced the efficacy of losartan to alleviate mechanical stress levels and restore blood vessel integrity beyond its role in autophagy modulation. These findings underscore the potential of co-targeting mechanical stresses and autophagy as a promising therapeutic strategy to overcome drug resistance and increase chemotherapy efficacy.

AMBER: A Modular Model for Tumor Growth, Vasculature and Radiation Response

Computational models of tumor growth are valuable for simulating the dynamics of cancer progression and treatment responses. In particular, agent-based models (ABMs) tracking individual agents and their interactions are useful for their flexibility and ability to model complex behaviors. However, ABMs have often been confined to small domains or, when scaled up, have neglected crucial aspects like vasculature. Additionally, the integration into tumor ABMs of precise radiation dose calculations using gold-standard Monte Carlo (MC) methods, crucial in contemporary radiotherapy, has been lacking. Here, we introduce AMBER, an Agent-based fraMework for radioBiological Effects in Radiotherapy that computationally models tumor growth and radiation responses. AMBER is based on a voxelized geometry, enabling realistic simulations at relevant pre-clinical scales by tracking temporally discrete states stepwise. Its hybrid approach, combining traditional ABM techniques with continuous spatiotemporal fields of key microenvironmental factors such as oxygen and vascular endothelial growth factor, facilitates the generation of realistic tortuous vascular trees. Moreover, AMBER is integrated with TOPAS, an MC-based particle transport algorithm that simulates heterogeneous radiation doses. The impact of radiation on tumor dynamics considers the microenvironmental factors that alter radiosensitivity, such as oxygen availability, providing a full coupling between the biological and physical aspects. Our results show that simulations with AMBER yield accurate tumor evolution and radiation treatment outcomes, consistent with established volumetric growth laws and radiobiological understanding. Thus, AMBER emerges as a promising tool for replicating essential features of tumor growth and radiation response, offering a modular design for future expansions to incorporate specific biological traits.

A convolutional attention model for predicting response to chemo-immunotherapy from ultrasound elastography in mouse tumor models

BACKGROUND

In the era of personalized cancer treatment, understanding the intrinsic heterogeneity of tumors is crucial. Despite some patients responding favorably to a particular treatment, others may not benefit, leading to the varied efficacy observed in standard therapies. This study focuses on the prediction of tumor response to chemo-immunotherapy, exploring the potential of tumor mechanics and medical imaging as predictive biomarkers. We have extensively studied "desmoplastic" tumors, characterized by a dense and very stiff stroma, which presents a substantial challenge for treatment. The increased stiffness of such tumors can be restored through pharmacological intervention with mechanotherapeutics.

METHODS

We developed a deep learning methodology based on shear wave elastography (SWE) images, which involved a convolutional neural network (CNN) model enhanced with attention modules. The model was developed and evaluated as a predictive biomarker in the setting of detecting responsive, stable, and non-responsive tumors to chemotherapy, immunotherapy, or the combination, following mechanotherapeutics administration. A dataset of 1365 SWE images was obtained from 630 tumors from our previous experiments and used to train and successfully evaluate our methodology. SWE in combination with deep learning models, has demonstrated promising results in disease diagnosis and tumor classification but their potential for predicting tumor response prior to therapy is not yet fully realized.

RESULTS

We present strong evidence that integrating SWE-derived biomarkers with automatic tumor segmentation algorithms enables accurate tumor detection and prediction of therapeutic outcomes.

CONCLUSIONS

This approach can enhance personalized cancer treatment by providing non-invasive, reliable predictions of therapeutic outcomes.

Metachromin C, a marine-derived natural compound, shows potential in antitumor activity

Metachromin C was first isolated from the marine sponge Hippospongia metachromia and has been reported to possess potent cytotoxicity against leukemia cells. However, its antitumor activity and possible mechanisms in pancreatic cancer remain unclear. The effects of Metachromin C on cell viability were estimated using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT) assay. The compound demonstrated a cytotoxic effect on four pancreatic cancer cell lines (PANC-1, BxPC-3, MiaPaCa-2, and AsPC-1). The significant S phase arrest observed with Metachromin C treatment suggests its impact on DNA replication machinery. Metachromin C might interfere with the binding of Topoisomerase I (TOPO I) to DNA, inhibit TOPO I activity, prevent DNA relaxation, cause DNA damage, and consequently activate the DNA repair pathway. Additionally, anti-migration and anti-invasion abilities of Metachromin C were confirmed using the transwell assay. It also inhibited angiogenesis in human endothelial cells by reducing cell proliferation, migration, and disrupting tube formation. Moreover, Metachromin C dose-dependently inhibited the growth of intersegmental vessels, subintestinal vessels, and the caudal vein plexus in a zebrafish embryo model, confirming its inhibitory effect on new vessel formation in vivo. Taken together, Metachromin C could not only inhibit the growth of pancreatic cancer cells but also act as an anti-angiogenic compound simultaneously.

A three-dimensional, discrete-continuum model of blood pressure in microvascular networks

We present a 3D discrete-continuum model to simulate blood pressure in large microvascular tissues in the absence of known capillary network architecture. Our hybrid approach combines a 1D Poiseuille flow description for large, discrete arteriolar and venular networks coupled to a continuum-based Darcy model, point sources of flux, for transport in the capillary bed. We evaluate our hybrid approach using a vascular network imaged from the mouse brain medulla/pons using multi-fluorescence high-resolution episcopic microscopy (MF-HREM). We use the fully-resolved vascular network to predict the hydraulic conductivity of the capillary network and generate a fully-discrete pressure solution to benchmark against. Our results demonstrate that the discrete-continuum methodology is a computationally feasible and effective tool for predicting blood pressure in real-world microvascular tissues when capillary microvessels are poorly defined.

Stabilizing Tumor-Resident Mast Cells Restores T-Cell Infiltration and Sensitizes Sarcomas to PD-L1 Inhibition

PURPOSE

To explore the cellular cross-talk of tumor-resident mast cells (MC) in controlling the activity of cancer-associated fibroblasts (CAF) to overcome tumor microenvironment (TME) abnormalities, enhancing the efficacy of immune-checkpoint inhibitors in sarcoma.

EXPERIMENTAL DESIGN

We used a coculture system followed by further validation in mouse models of fibrosarcoma and osteosarcoma with or without administration of the MC stabilizer and antihistamine ketotifen. To evaluate the contribution of ketotifen in sensitizing tumors to therapy, we performed combination studies with doxorubicin chemotherapy and anti-PD-L1 (B7-H1, clone 10F.9G2) treatment. We investigated the ability of ketotifen to modulate the TME in human sarcomas in the context of a repurposed phase II clinical trial.

RESULTS

Inhibition of MC activation with ketotifen successfully suppressed CAF proliferation and stiffness of the extracellular matrix accompanied by an increase in vessel perfusion in fibrosarcoma and osteosarcoma as indicated by ultrasound shear wave elastography imaging. The improved tissue oxygenation increased the efficacy of chemoimmunotherapy, supported by enhanced T-cell infiltration and acquisition of tumor antigen-specific memory. Importantly, the effect of ketotifen in reducing tumor stiffness was further validated in sarcoma patients, highlighting its translational potential.

CONCLUSIONS

Our study suggests the targeting of MCs with clinically administered drugs, such as antihistamines, as a promising approach to overcome resistance to immunotherapy in sarcomas.

Investigating the synergistic effects of immunotherapy and normalization treatment in modulating tumor microenvironment and enhancing treatment efficacy

We developed a comprehensive mathematical model of cancer immunotherapy that takes into account: i) Immune checkpoint blockers (ICBs) and the interactions between cancer cells and the immune system, ii) characteristics of the tumor microenvironment, such as the tumor hydraulic conductivity, interstitial fluid pressure, and vascular permeability, iii) spatial and temporal variations of the modeled components within the tumor and the surrounding host tissue, iv) the transport of modeled components through the vasculature and between the tumor-host tissue with convection and diffusion, and v) modeling of the tumor draining lymph nodes were the antigen presentation and the development of cytotoxic immune cells take place. Our model successfully reproduced experimental data from various murine tumor types and predicted immune system profiling, which is challenging to achieve experimentally. It showed that combination of ICB therapy and normalization treatments, that aim to improve tumor perfusion, decreases interstitial fluid pressure and increases the concentration of both innate and adaptive immune cells at the tumor center rather than the periphery. Furthermore, using the model, we investigated the impact of modeled components on treatment outcomes. The analysis found that the number of functional vessels inside the tumor region and the ICB dose administered have the largest impact on treatment outcomes.

Enhanced perfusion following exposure to radiotherapy: A theoretical investigation

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features and blood perfusion in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies.

Applied Electric Fields Polarize Initiation and Growth of Endothelial Sprouts

Therapeutic electric fields (EFs) are applied to the epidermis to accelerate the healing of chronic epidermal wounds and promote skin transplantation. While research has emphasized understanding the role of EFs in polarizing the migration of superficial epidermal cells, there are no reports describing the effect of EFs on polarization of the underlying vasculature. We explored the effects of EFs on the growth of endothelial sprouts, precursors to functional blood vessels. We discovered that DC EFs of the same magnitude near wounded epidermis polarize initiation, growth, and turning of endothelial sprouts toward the anode. While EFs polarize sprouts, they do not change the frequency of primary sprout or branch formation. Unidirectional electrical pulses also polarize sprouts based on their time-averaged EF magnitude. Sprout polarization occurs antiparallel to the direction of electrically driven water flow (electro-osmosis) and is consistent with the direction of sprout polarization induced by pressure-driven flow. These results support the role of EFs in controlling the direction of neovascularization during the healing of soft tissues and tissue engineering.

COMMBINI: an experimentally-informed COmputational Model of Macrophage dynamics in the Bone INjury Immunoresponse

Bone fracture healing is a well-orchestrated but complex process that involves numerous regulations at different scales. This complexity becomes particularly evident during the inflammatory stage, as immune cells invade the healing region and trigger a cascade of signals to promote a favorable regenerative environment. Thus, the emergence of criticalities during this stage might hinder the rest of the process. Therefore, the investigation of the many interactions that regulate the inflammation has a primary importance on the exploration of the overall healing progression. In this context, an in silico model named COMMBINI (COmputational Model of Macrophage dynamics in the Bone INjury Immunoresponse) has been developed to investigate the mechano-biological interactions during the early inflammatory stage at the tissue, cellular and molecular levels. An agent-based model is employed to simulate the behavior of immune cells, inflammatory cytokines and fracture debris as well as their reciprocal multiscale biological interactions during the development of the early inflammation (up to 5 days post-injury). The strength of the computational approach is the capacity of the in silico model to simulate the overall healing process by taking into account the numerous hidden events that contribute to its success. To calibrate the model, we present an in silico immunofluorescence method that enables a direct comparison at the cellular level between the model output and experimental immunofluorescent images. The combination of sensitivity analysis and a Genetic Algorithm allows dynamic cooperation between these techniques, enabling faster identification of the most accurate parameter values, reducing the disparity between computer simulation and histological data. The sensitivity analysis showed a higher sensibility of the computer model to the macrophage recruitment ratio during the early inflammation and to proliferation in the late stage. Furthermore, the Genetic Algorithm highlighted an underestimation of macrophage proliferation by in vitro experiments. Further experiments were conducted using another externally fixated murine model, providing an independent validation dataset. The validated COMMBINI platform serves as a novel tool to deepen the understanding of the intricacies of the early bone regeneration phases. COMMBINI aims to contribute to designing novel treatment strategies in both the biological and mechanical domains.

Computational simulations of tumor growth and treatment response: Benefits of high-frequency, low-dose drug regimens and concurrent vascular normalization

Implementation of effective cancer treatment strategies requires consideration of how the spatiotemporal heterogeneities within the tumor microenvironment (TME) influence tumor progression and treatment response. Here, we developed a multi-scale three-dimensional mathematical model of the TME to simulate tumor growth and angiogenesis and then employed the model to evaluate an array of single and combination therapy approaches. Treatments included maximum tolerated dose or metronomic (i.e., frequent low doses) scheduling of anti-cancer drugs combined with anti-angiogenic therapy. The results show that metronomic therapy normalizes the tumor vasculature to improve drug delivery, modulates cancer metabolism, decreases interstitial fluid pressure and decreases cancer cell invasion. Further, we find that combining an anti-cancer drug with anti-angiogenic treatment enhances tumor killing and reduces drug accumulation in normal tissues. We also show that combined anti-angiogenic and anti-cancer drugs can decrease cancer invasiveness and normalize the cancer metabolic microenvironment leading to reduced hypoxia and hypoglycemia. Our model simulations suggest that vessel normalization combined with metronomic cytotoxic therapy has beneficial effects by enhancing tumor killing and limiting normal tissue toxicity.

Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radiotherapy treatment

We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell and determines its proliferative capacity, apoptosis propensity and response to treatment. Our study is based on numerical bifurcation analysis and dynamical simulations of a system of coupled, non-local (in phenotypic "space") partial differential equations that link the phenotypic evolution of the tumour cells to local tissue oxygen levels. In our formulation, we consider a 1D geometry where oxygen is supplied by a blood vessel located on the domain boundary and consumed by the tumour cells as it diffuses through the tissue. For biologically relevant parameter values, the system exhibits multiple steady states; in particular, depending on the initial conditions, the tumour is either eliminated ("tumour-extinction") or it persists ("tumour-invasion"). We conclude by using the model to investigate tumour responses to radiotherapy, and focus on identifying radiotherapy strategies which can eliminate the tumour. Numerical simulations reveal how phenotypic heterogeneity evolves during treatment and highlight the critical role of tissue oxygen levels on the efficacy of radiation protocols that are commonly used in the clinic.

Combined anti-angiogenic and cytotoxic treatment of a solid tumour: In silico investigation of a xenograft animal model's digital twin

Anti-angiogenic (AA) treatments have received significant research interest due to the key role of angiogenesis in cancer progression. AA agents can have a strong effect on cancer regression, by blocking new vessels and reducing the density of the existing vasculature. Moreover, in a process termed vascular normalisation, AA drugs can improve the abnormal structure and function of the tumour vasculature, enhancing the delivery of chemotherapeutics to the tumour site. Despite their promising potential, an improved understanding of AA treatments is necessary to optimise their administration as a monotherapy or in combination with other cancer treatments. In this work we present an in silico multiscale cancer model which is used to systematically interrogate the role of individual mechanisms of action of AA drugs in tumour regression. Focus is placed on the reduction of vascular density and on vascular normalisation through a parametric study, which are considered either as monotherapies or in combination with conventional/metronomic chemotherapy. The model is specified to data from a mammary carcinoma xenograft in immunodeficient mice, to enhance the physiological relevance of model predictions. Our results suggest that conventional chemotherapy might be more beneficial when combined with AA treatments, hindering tumour growth without causing excessive damage on healthy tissue. Notably, metronomic chemotherapy has shown significant potential in stopping tumour growth with minimal toxicity, even as a monotherapy. Our findings underpin the potential of our in silico framework for non-invasive and cost-effective evaluation of treatment strategies, which can enhance our understanding of combined therapeutic strategies and contribute towards improving cancer treatment management.

Convection-Enhanced Delivery In Silico Study for Brain Cancer Treatment

Brain cancer therapy remains a formidable challenge in oncology. Convection-enhanced delivery (CED) is an innovative and promising local drug delivery method for the treatment of brain cancer, overcoming the challenges of the systemic delivery of drugs to the brain. To improve our understanding about CED efficacy and drug transport, we present an in silico methodology for brain cancer CED treatment simulation. To achieve this, a three-dimensional finite element formulation is utilized which employs a brain model representation from clinical imaging data and is used to predict the drug deposition in CED regimes. The model encompasses biofluid dynamics and the transport of drugs in the brain parenchyma. Drug distribution is studied under various patho-physiological conditions of the tumor, in terms of tumor vessel wall pore size and tumor tissue hydraulic conductivity as well as for drugs of various sizes, spanning from small molecules to nanoparticles. Through a parametric study, our contribution reports the impact of the size of the vascular wall pores and that of the therapeutic agent on drug distribution during and after CED. The in silico findings provide useful insights of the spatio-temporal distribution and average drug concentration in the tumor towards an effective treatment of brain cancer.

Investigation of cancer response to chemotherapy: a hybrid multi-scale mathematical and computational model of the tumor microenvironment

Tumor microenvironment (TME) is a multi-scale biological environment that can control tumor dynamics with many biomechanical and biochemical factors. Investigating the physiology of TME with a heterogeneous structure and abnormal functions not only can achieve a deeper understanding of tumor behavior but also can help develop more efficient anti-cancer strategies. In this work, we develop a hybrid multi-scale mathematical model of TME to simulate the progression of a three-dimensional tumor and elucidate its response to different chemotherapy approaches. The chemotherapy approaches include multiple low dose (MLD) of anti-cancer drug, maximum tolerated dose (MTD) of anti-cancer drug, combination therapy of MLD and anti-angiogenic drug, and combination therapy of MTD and anti-angiogenic drug. The results show that combining anti-angiogenic agent with anti-cancer drug increases the performance of cancer treatment and decreases side effects for normal tissue. Indeed, the vascular normalization caused by anti-angiogenic therapy improves anti-cancer drug delivery for both MLD and MTD approaches. The results show that anti-cancer drug administered in a lower dose than the maximum tolerated dose repetitively over a long period treats cancer with a considerable performance and fewer side effects. We also show that tumor morphology and distribution of cancer cell phenotypes can be considered as the characteristics to distinguish different chemotherapy approaches. This robust model can be applied to predict the behavior of any type of cancer and quantify cancer response to different chemotherapy approaches. The computational results of cancer response to chemotherapy are in good agreement with experimental measurements.

Navigating Multi-Scale Cancer Systems Biology Towards Model-Driven Clinical Oncology and Its Applications in Personalized Therapeutics

Rapid advancements in high-throughput omics technologies and experimental protocols have led to the generation of vast amounts of scale-specific biomolecular data on cancer that now populates several online databases and resources. Cancer systems biology models built using this data have the potential to provide specific insights into complex multifactorial aberrations underpinning tumor initiation, development, and metastasis. Furthermore, the annotation of these single- and multi-scale models with patient data can additionally assist in designing personalized therapeutic interventions as well as aid in clinical decision-making. Here, we have systematically reviewed the emergence and evolution of (i) repositories with scale-specific and multi-scale biomolecular cancer data, (ii) systems biology models developed using this data, (iii) associated simulation software for the development of personalized cancer therapeutics, and (iv) translational attempts to pipeline multi-scale panomics data for data-driven in silico clinical oncology. The review concludes that the absence of a generic, zero-code, panomics-based multi-scale modeling pipeline and associated software framework, impedes the development and seamless deployment of personalized in silico multi-scale models in clinical settings.

ING5 Inhibits Migration and Invasion of Esophageal Cancer Cells by Downregulating the IL-6/CXCL12 Signaling Pathway

Esophageal squamous cell carcinoma (ESCC) is a common cancer in East Asia and in other parts of the world and exhibits a poor prognosis. Growth inhibitor 5 (ING5) is a new member of the growth inhibitor (ING) protein family and is involved in many important cellular functions, such as the cell cycle, apoptosis, and chromatin remodeling. As a newly discovered tumor suppressor, ING5 has been shown to inhibit lung cancer proliferation and distant metastasis through the AKT pathway. In lung cancer tumors, ING5 can attenuate the ability of cancer cells to invade normal tumor-adjacent tissues. However, ING5 has rarely been studied in ESCC. Here, we found that in ESCC EC-109 cancer cells, ING5 overexpression inhibited cell proliferation and tumor invasion, whereas, in ESCC TE-1 cancer cells, ING5 knockdown promoted cell invasion. In a nude mouse xenograft model, ING5 overexpression inhibited tumor growth and the invasion ability of ESCC cells. Further studies revealed that ING5 overexpression inhibited IL-6/CXCL12 expression at both the mRNA and protein levels as well as morphological changes. We found for the first time that ING5 inhibits ESCC cell migration and invasion by downregulating the IL-6/CXCL12 signaling pathway.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

Chemo-mechanistic multi-scale model of a three-dimensional tumor microenvironment to quantify the chemotherapy response of cancer

Exploring efficient chemotherapy would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. As in vivo experimental methods are unable to isolate or control individual factors of the TME, and in vitro models often cannot include all the contributing factors, some questions are best addressed with mathematical models of systems biology. In this study, we establish a multi-scale mathematical model of the TME to simulate three-dimensional tumor growth and angiogenesis and then implement the model for an array of chemotherapy approaches to elucidate the effect of TME conditions and drug scheduling on controlling tumor progression. The hyperglycemic condition as the most common disorder for cancer patients is considered to evaluate its impact on cancer response to chemotherapy. We show that combining antiangiogenic and anticancer drugs improves the outcome of treatment and can decrease accumulation of the drug in normal tissue and enhance drug delivery to the tumor. Our results demonstrate that although both concurrent and neoadjuvant combination therapies can increase intratumoral drug exposure and therapeutic accuracy, neoadjuvant therapy surpasses this, especially against hyperglycemia. Our model provides mechanistic explanations for clinical observations of tumor progression and response to treatment and establishes a computational framework for exploring better treatment strategies.

Phenotypic variation modulates the growth dynamics and response to radiotherapy of solid tumours under normoxia and hypoxia

In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in which cells are structured by a stemness level, which varies continuously between stem-like and terminally differentiated behaviours. Cell evolution is driven by proliferation and death, as well as advection and diffusion with respect to the stemness structure variable. Here, the magnitude and sign of the advective flux are allowed to vary with the oxygen level. We use the model to investigate how the environment, in particular oxygen levels, affects the tumour's population dynamics and composition, and its response to radiotherapy. We use a combination of numerical and analytical techniques to quantify how under physiological oxygen levels the cells evolve to a differentiated phenotype and under low oxygen level (i.e., hypoxia) they de-differentiate. Under normoxia, the proportion of cancer stem cells is typically negligible and the tumour may ultimately become extinct whereas under hypoxia cancer stem cells comprise a dominant proportion of the tumour volume, enhancing radio-resistance and favouring the tumour's long-term survival. We then investigate how such phenotypic heterogeneity impacts the tumour's response to treatment with radiotherapy under normoxia and hypoxia. Of particular interest is establishing how the presence of radio-resistant cancer stem cells can facilitate a tumour's regrowth following radiotherapy. We also use the model to show how radiation-induced changes in tumour oxygen levels can give rise to complex re-growth dynamics. For example, transient periods of hypoxia induced by damage to tumour blood vessels may rescue the cancer cell population from extinction and drive secondary regrowth.

Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis

Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid arthritis. The structure of the resulting vessel networks determines their ability to deliver nutrients and remove waste products from biological tissues. Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data. Specifically, we propose a topological data analysis (TDA) pipeline for systematic analysis of the model. TDA is a vibrant and relatively new field of computational mathematics for studying the shape of data. We compute topological and standard descriptors of model simulations generated by different parameter values. We show that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology. The methodologies proposed here are widely applicable to other synthetic and experimental data including wound healing, development, and plant biology.

Exosomes in Angiogenesis and Anti-angiogenic Therapy in Cancers

Angiogenesis is the process through which new blood vessels are formed from pre-existing ones. Exosomes are involved in angiogenesis in cancer progression by transporting numerous pro-angiogenic biomolecules like vascular endothelial growth factor (VEGF), matrix metalloproteinases (MMPs), and microRNAs. Exosomes promote angiogenesis by suppressing expression of factor-inhibiting hypoxia-inducible factor 1 (HIF-1). Uptake of tumor-derived exosomes (TEX) by normal endothelial cells activates angiogenic signaling pathways in endothelial cells and stimulates new vessel formation. TEX-driven cross-talk of mesenchymal stem cells (MSCs) with immune cells blocks their anti-tumor activity. Effective inhibition of tumor angiogenesis may arrest tumor progression. Bevacizumab, a VEGF-specific antibody, was the first antiangiogenic agent to enter the clinic. The most important clinical problem associated with cancer therapy using VEGF- or VEFGR-targeting agents is drug resistance. Combined strategies based on angiogenesis inhibitors and immunotherapy effectively enhances therapies in various cancers, but effective treatment requires further research.

Drug delivery to solid tumors with heterogeneous microvascular networks: Novel insights from image-based numerical modeling

The present study examines chemotherapy by incorporating multi-scale mathematical modeling to predict drug delivery and its effects. This approach leads to a more-realistic physiological tumor model than is possible with previous approaches, as it obtains the capillary network geometry from an image, and also considers the tumor's necrotic core, drug binding, and cellular uptake. Modeling of the fluid flow and drug transport is then performed in the extracellular matrix. The results demonstrate a 10% drop in the fraction of killed cancer cells 69% rather than the 79% reported earlier for a tumor of similar geometry a more-accurate value. This study examines how tumor-related parameters including the necrotic core size and tumor size, and also drug-related parameters drug dosage, binding affinity of drug, and drug degradation can affect the delivery of the drug to solid tumors. Results indicate that concentration of drug are high in the tumor, low in normal tissue, and remarkably low in the necrotic core. Results also offer a treatment of tumors with smaller necrotic core. Tumor size, which implies the tumor progression, has a considerable impact on treatment outcomes, so to be more effective, treatment should be applied at a specific size of tumor. It is demonstrated that binding affinity of drugs to cell-surface receptors and drug dosage have significant impact on treatment efficacy, so they should be regulated based on a balanced quantification between maximum treatment efficacy and minimum side effects. On the other hand, considering the effects of drug degradation in the model has not significant effect on treatment efficacy. The findings of the present study provide insight into the mechanism of drug delivery to solid tumors based on analyzing the effective parameters and modeling how their behavior in the tumor microenvironment affects treatment efficacy.

Transport of nanoparticles in magnetic targeting: Comparison of magnetic, diffusive and convective forces and fluxes in the microvasculature, through vascular pores and across the interstitium

Magnetic nanoparticle targeting in tumor areas is examined by an integrated consideration of the transport steps from the microcirculation to the vascular walls, through their pores and into the interstitium. Brownian, flow- and magnetically induced forces and fluxes are compared on the basis of order-of-magnitude estimates and numerical simulations. The main resistance to nanoparticle transport is found to be within the interstitium, since fluxes there are much smaller than the extravasation fluxes, and the latter are much smaller than the convective-diffusive ones within the microvasculature. For typical nanoparticle sizes, magnetic properties and strengths of magnetic fields as in MRI equipment, magnetic targeting is rather unlikely to play a significant role in directing nanoparticles towards vascular walls or through vascular pores. However, magnetic drift can have an effect within the interstitium and a tangible overall outcome, despite the fact that typical magnetic forces are smaller than Brownian ones or interstitial flow convective forces. The reason behind such an effect has to do with the much larger length scales involved in interstitial transport. Magnetic drift creates a front of large nanoparticle concentrations, flooding the inadequately perfused and poorly accessible tumor area. On the basis of time-scale estimates, it is suggested that sequential cycles of magnetic nanoparticle dosage may help in more efficient access of cell layers ever closer to the tumor center. The present results may assist in the quest for optimal parameters and conditions, given the conflicting requirements for particles small enough to evade hydrodynamic and steric hindrances in vascular pores and the interstitium, yet large enough to bear a substantial magnetic load.

From tumour perfusion to drug delivery and clinical translation of in silico cancer models

In silico cancer models have demonstrated great potential as a tool to improve drug design, optimise the delivery of drugs to target sites in the host tissue and, hence, improve therapeutic efficacy and patient outcome. However, there are significant barriers to the successful translation of in silico technology from bench to bedside. More precisely, the specification of unknown model parameters, the necessity for models to adequately reflect in vivo conditions, and the limited amount of pertinent validation data to evaluate models' accuracy and assess their reliability, pose major obstacles in the path towards their clinical translation. This review aims to capture the state-of-the-art in in silico cancer modelling of vascularised solid tumour growth, and identify the important advances and barriers to success of these models in clinical oncology. Particular emphasis has been put on continuum-based models of cancer since they - amongst the class of mechanistic spatio-temporal modelling approaches - are well-established in simulating transport phenomena and the biomechanics of tissues, and have demonstrated potential for clinical translation. Three important avenues in in silico modelling are considered in this contribution: first, since systemic therapy is a major cancer treatment approach, we start with an overview of the tumour perfusion and angiogenesis in silico models. Next, we present the state-of-the-art in silico work encompassing the delivery of chemotherapeutic agents to cancer nanomedicines through the bloodstream, and then review continuum-based modelling approaches that demonstrate great promise for successful clinical translation. We conclude with a discussion of what we view to be the key challenges and opportunities for in silico modelling in personalised and precision medicine.

A multi-scale model for determining the effects of pathophysiology and metabolic disorders on tumor growth

The search for efficient chemotherapy drugs and other anti-cancer treatments would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. Because in vivo experimental methods are unable to isolate or control individual factors of the TME and in vitro models often do not include all the contributing factors, some questions are best addressed with systems biology mathematical models. In this work, we present a new fully-coupled, agent-based, multi-scale mathematical model of tumor growth, angiogenesis and metabolism that includes important aspects of the TME spanning subcellular-, cellular- and tissue-level scales. The mathematical model is computationally implemented for a three-dimensional TME, and a double hybrid continuous-discrete (DHCD) method is applied to solve the governing equations. The model recapitulates the distinct morphological and metabolic stages of a solid tumor, starting with an avascular tumor and progressing through angiogenesis and vascularized tumor growth. To examine the robustness of the model, we simulated normal and abnormal blood conditions, including hyperglycemia/hypoglycemia, hyperoxemia/hypoxemia, and hypercarbia/hypocarbia - conditions common in cancer patients. The results demonstrate that tumor progression is accelerated by hyperoxemia, hyperglycemia and hypercarbia but inhibited by hypoxemia and hypoglycemia; hypocarbia had no appreciable effect. Because of the importance of interstitial fluid flow in tumor physiology, we also examined the effects of hypo- or hypertension, and the impact of decreased hydraulic conductivity common in desmoplastic tumors. The simulations show that chemotherapy-increased blood pressure, or reduction of interstitial hydraulic conductivity increase tumor growth rate and contribute to tumor malignancy.

An in silico hybrid continuum-/agent-based procedure to modelling cancer development: Interrogating the interplay amongst glioma invasion, vascularity and necrosis

This paper develops a three-dimensional in silico hybrid model of cancer, which describes the multi-variate phenotypic behaviour of tumour and host cells. The model encompasses the role of cell migration and adhesion, the influence of the extracellular matrix, the effects of oxygen and nutrient availability, and the signalling triggered by chemical cues and growth factors. The proposed in silico hybrid modelling framework combines successfully the advantages of continuum-based and discrete methods, namely the finite element and agent-based method respectively. The framework is thus used to realistically model cancer mechano-biology in a multiscale fashion while maintaining the resolution power of each method in a computationally cost-effective manner. The model is tailored to simulate glioma progression, and is subsequently used to interrogate the balance between the host cells and small sized gliomas, while the go-or-grow phenotype characteristic in glioblastomas is also investigated. Also, cell-cell and cell-matrix interactions are examined with respect to their effect in (macroscopic) tumour growth, brain tissue perfusion and tumour necrosis. Finally, we use the in silico framework to assess differences between low-grade and high-grade glioma growth, demonstrating significant differences in the distribution of cancer as well as host cells, in accordance with reported experimental findings.

Engineering Patient-on-a-Chip Models for Personalized Cancer Medicine

Traditional in vitro and in vivo models typically used in cancer research have demonstrated a low predictive power for human response. This leads to high attrition rates of new drugs in clinical trials, which threaten cancer patient prognosis. Tremendous efforts have been directed towards the development of a new generation of highly predictable pre-clinical models capable to reproduce in vitro the biological complexity of the human body. Recent advances in nanotechnology and tissue engineering have enabled the development of predictive organs-on-a-chip models of cancer with advanced capabilities. These models can reproduce in vitro the complex three-dimensional physiology and interactions that occur between organs and tissues in vivo, offering multiple advantages when compared to traditional models. Importantly, these models can be tailored to the biological complexity of individual cancer patients resulting into biomimetic and personalized cancer patient-on-a-chip platforms. The individualized models provide a more accurate and physiological environment to predict tumor progression on patients and their response to drugs. In this chapter, we describe the latest advances in the field of cancer patient-on-a-chip, and discuss about their main applications and current challenges. Overall, we anticipate that this new paradigm in cancer in vitro models may open up new avenues in the field of personalized - cancer - medicine, which may allow pharmaceutical companies to develop more efficient drugs, and clinicians to apply patient-specific therapies.

An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model

The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D inclusion and embedded into the 3D tissue through a suitable coupling method, which allows for nonmatching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex morphology, physiology, and flow patterns in the neovasculature, which are challenging and computationally expensive to resolve with a discrete, 1D angiogenesis and blood flow model. Moreover, it is questionable if a discrete representation generates any useful additional insight. By contrast, our model may be classified as a hybrid vascular multiphase tumor growth model in the sense that a discrete, 1D representation of the preexisting vasculature is coupled with a continuum model describing angiogenesis. It is based on an originally avascular model which has been derived via the thermodynamically constrained averaging theory. The new model enables us to study mass transport from the preexisting vasculature into the neovasculature and tumor tissue. We show by means of several illustrative examples that it is indeed capable of reproducing important aspects of vascular tumor growth phenomenologically.

Three-dimensional tumor growth in time-varying chemical fields: a modeling framework and theoretical study

Background

Contemporary biological observations have revealed a large variety of mechanisms acting during the expansion of a tumor. However, there are still many qualitative and quantitative aspects of the phenomenon that remain largely unknown. In this context, mathematical and computational modeling appears as an invaluable tool providing the means for conducting in silico experiments, which are cheaper and less tedious than real laboratory experiments.

Results

This paper aims at developing an extensible and computationally efficient framework for in silico modeling of tumor growth in a 3-dimensional, inhomogeneous and time-varying chemical environment. The resulting model consists of a set of mathematically derived and algorithmically defined operators, each one addressing the effects of a particular biological mechanism on the state of the system. These operators may be extended or re-adjusted, in case a different set of starting assumptions or a different simulation scenario needs to be considered.

Conclusion

In silico modeling provides an alternative means for testing hypotheses and simulating scenarios for which exact biological knowledge remains elusive. However, finer tuning of pertinent methods presupposes qualitative and quantitative enrichment of available biological evidence. Validation in a strict sense would further require comprehensive, case-specific simulations and detailed comparisons with biomedical observations.

A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation

Mechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty, we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an individual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the individual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. We discuss applications of the model, such as determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.

Modelling the transport of fluid through heterogeneous, whole tumours in silico

Cancers exhibit spatially heterogeneous, unique vascular architectures across individual samples, cell-lines and patients. This inherently disorganised collection of leaky blood vessels contribute significantly to suboptimal treatment efficacy. Preclinical tools are urgently required which incorporate the inherent variability and heterogeneity of tumours to optimise and engineer anti-cancer therapies. In this study, we present a novel computational framework which incorporates whole, realistic tumours extracted ex vivo to efficiently simulate vascular blood flow and interstitial fluid transport in silico for validation against in vivo biomedical imaging. Our model couples Poiseuille and Darcy descriptions of vascular and interstitial flow, respectively, and incorporates spatially heterogeneous blood vessel lumen and interstitial permeabilities to generate accurate predictions of tumour fluid dynamics. Our platform enables highly-controlled experiments to be performed which provide insight into how tumour vascular heterogeneity contributes to tumour fluid transport. We detail the application of our framework to an orthotopic murine glioma (GL261) and a human colorectal carcinoma (LS147T), and perform sensitivity analysis to gain an understanding of the key biological mechanisms which determine tumour fluid transport. Finally we mimic vascular normalization by modifying parameters, such as vascular and interstitial permeabilities, and show that incorporating realistic vasculatures is key to modelling the contrasting fluid dynamic response between tumour samples. Contrary to literature, we show that reducing tumour interstitial fluid pressure is not essential to increase interstitial perfusion and that therapies should seek to develop an interstitial fluid pressure gradient. We also hypothesise that stabilising vessel diameters and permeabilities are not key responses following vascular normalization and that therapy may alter interstitial hydraulic conductivity. Consequently, we suggest that normalizing the interstitial microenvironment may provide a more effective means to increase interstitial perfusion within tumours.

The structure of tumours varies widely, with dense and chaotically-formed networks of blood vessels that differ between each individual tumour and even between different regions of the same tumour. This atypical environment can inhibit the delivery of anti-cancer therapies. Computational tools are urgently required which facilitate a deeper understanding of the relationship between blood vessel architectures and therapeutic response. We have developed a computational framework which integrates the complex tumour vascular architecture to predict fluid transport across all lengths scales in whole tumours. We apply our model to two tumour cell-lines and show that differences in their inherent vascular structures influence flow through cancerous tissue. We also use our platform to predict the fluid dynamic response following vascular normalization therapy in realistic, static tumour networks and show that the response is dependent on tumour vascular architecture. We hypothesise that therapy may alter the permeability of interstitial tissue to fluid transport and show that lowering interstitial fluid pressure is not a necessary therapeutic outcome to increase tumour perfusion.

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.

Multiscale Tumor Modeling With Drug Pharmacokinetic and Pharmacodynamic Profile Using Stochastic Hybrid System

Effective cancer treatment strategy requires an understanding of cancer behavior and development across multiple temporal and spatial scales. This has resulted into a growing interest in developing multiscale mathematical models that can simulate cancer growth, development, and response to drug treatments. This study thus investigates multiscale tumor modeling that integrates drug pharmacokinetic and pharmacodynamic (PK/PD) information using stochastic hybrid system modeling framework. Specifically, (1) pathways modeled by differential equations are adopted for gene regulations at the molecular level; (2) cellular automata (CA) model is proposed for the cellular and multicellular scales. Markov chains are used to model the cell behaviors by taking into account the gene expression levels, cell cycle, and the microenvironment. The proposed model enables the prediction of tumor growth under given molecular properties, microenvironment conditions, and drug PK/PD profile. Simulation results demonstrate the effectiveness of the proposed approach and the results agree with observed tumor behaviors.

Angiogenic Factors produced by Hypoxic Cells are a leading driver of Anastomoses in Sprouting Angiogenesis-a computational study

Angiogenesis - the growth of new blood vessels from a pre-existing vasculature - is key in both physiological processes and on several pathological scenarios such as cancer progression or diabetic retinopathy. For the new vascular networks to be functional, it is required that the growing sprouts merge either with an existing functional mature vessel or with another growing sprout. This process is called anastomosis. We present a systematic 2D and 3D computational study of vessel growth in a tissue to address the capability of angiogenic factor gradients to drive anastomosis formation. We consider that these growth factors are produced only by tissue cells in hypoxia, i.e. until nearby vessels merge and become capable of carrying blood and irrigating their vicinity. We demonstrate that this increased production of angiogenic factors by hypoxic cells is able to promote vessel anastomoses events in both 2D and 3D. The simulations also verify that the morphology of these networks has an increased resilience toward variations in the endothelial cell's proliferation and chemotactic response. The distribution of tissue cells and the concentration of the growth factors they produce are the major factors in determining the final morphology of the network.

Modeling mechanical inhomogeneities in small populations of proliferating monolayers and spheroids

Understanding the mechanical behavior of multicellular monolayers and spheroids is fundamental to tissue culture, organism development, and the early stages of tumor growth. Proliferating cells in monolayers and spheroids experience mechanical forces as they grow and divide and local inhomogeneities in the mechanical microenvironment can cause individual cells within the multicellular system to grow and divide at different rates. This differential growth, combined with cell division and reorganization, leads to residual stress. Multiple different modeling approaches have been taken to understand and predict the residual stresses that arise in growing multicellular systems, particularly tumor spheroids. Here, we show that by using a mechanically robust agent-based model constructed with the peridynamic framework, we gain a better understanding of residual stresses in multicellular systems as they grow from a single cell. In particular, we focus on small populations of cells (1-100 s) where population behavior is highly stochastic and prior investigation has been limited. We compare the average strain energy density of cells in monolayers and spheroids using different growth and division rules and find that, on average, cells in spheroids have a higher strain energy density than cells in monolayers. We also find that cells in the interior of a growing spheroid are, on average, in compression. Finally, we demonstrate the importance of accounting for stochastic fluctuations in the mechanical environment, particularly when the cellular response to mechanical cues is nonlinear. The results presented here serve as a starting point for both further investigation with agent-based models, and for the incorporation of major findings from agent-based models into continuum scale models when explicit representation of individual cells is not computationally feasible.

A Network Model to Explore the Effect of the Micro-environment on Endothelial Cell Behavior during Angiogenesis

Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.

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.