Biphasic modeling of brain tumor biomechanics and response to radiation treatment

Heterogeneous Mechanical Stress and Interstitial Fluid Flow Predictions Derived from DCE-MRI for Rat U251N Orthotopic Gliomas

Mechanical stress and fluid flow influence glioma cell phenotype in vitro, but measuring these quantities in vivo continues to be challenging. The purpose of this study was to predict these quantities in vivo, thus providing insight into glioma physiology and potential mechanical biomarkers that may improve glioma detection, diagnosis, and treatment. Image-based finite element models of human U251N orthotopic glioma in athymic rats were developed to predict structural stress and interstitial flow in and around each animal's tumor. In addition to accounting for structural stress caused by tumor growth, our approach has the advantage of capturing fluid pressure-induced structural stress, which was informed by in vivo interstitial fluid pressure (IFP) measurements. Because gliomas and the brain are soft, elevated IFP contributed substantially to tumor structural stress, even inverting this stress from compressive to tensile in the most compliant cases. The combination of tumor growth and elevated IFP resulted in a concentration of structural stress near the tumor boundary where it has the greatest potential to influence cell proliferation and invasion. MRI-derived anatomical geometries and tissue property distributions resulted in heterogeneous interstitial fluid flow with local maxima near cerebrospinal fluid spaces, which may promote tumor invasion and hinder drug delivery. In addition, predicted structural stress and interstitial flow varied markedly between irradiated and radiation-naïve animals. Our modeling suggests that relative to tumors in stiffer tissues, gliomas experience unusual mechanical conditions with potentially important biological (e.g., proliferation and invasion) and clinical consequences (e.g., drug delivery and treatment monitoring).

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.

Sustained Physiological Stretch Induces Abdominal Skin Growth in Pregnancy

Supraphysiological stretches are exploited in skin expanders to induce tissue growth for autologous implants. As pregnancy is associated with large levels of sustained stretch, we investigated whether skin growth occurs in pregnancy. Therefore, we combined a mechanical model of skin and the observations from suction experiments on several body locations of five pregnant women at different gestational ages. The measurements show a continuous increase in stiffness, with the largest change observed during the last trimester. A comparison with numerical simulations indicates that the measured increase in skin stiffness is far below the level expected for the corresponding deformation of abdominal skin. A new set of simulations accounting for growth could rationalize all observations. The predicted amount of tissue growth corresponds to approximately 40% area increase before delivery. The results of the simulations also offered the opportunity to investigate the biophysical cues present in abdominal skin along gestation and to compare them with those arising in skin expanders. Alterations of the skin mechanome were quantified, including tissue stiffness, hydrostatic and osmotic pressure of the interstitial fluid, its flow velocity and electrical potential. The comparison between pregnancy and skin expansion highlights similarities as well as differences possibly influencing growth and remodeling.

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.

Tumor growth and population modeling in a toxicant-stressed random environment

When examining some factors that contribute to the growth or decline of a population or tumor, it is essential to consider a random hypothesis. By analyzing the effects of stress on a population (or volume of tumor growth) in a random environment, we develop stochastic models describing the dynamics of the population (or tumor growth) based on random adjustments to the population's intrinsic growth rate, carrying capacity, and harvesting efforts (or tumor treatments). Apart from the models' ability to capture fluctuations, the availability of a shape parameter in the models gives it the flexibility to describe a variety of population/tumor data with different shapes. The distribution of the stressed population size with or without harvesting (or treatments) is derived and used to calculate the maximum expected amount of harvests that can be taken from the population without depleting resources in the long run (or the minimum amount of chemotherapy needed to cause shrinkage or eradication of a tumor). The work done is applied to analyze tumor growth using published data comprising of the volume of breast tumor obtained by orthotopically implanting LM2-[Formula: see text] cells into the right inguinal mammary fat pads of 6- to 8-week-old female Severe Combined Immuno-Deficient mice.

Predicting stress and interstitial fluid pressure in tumors based on biphasic theory

The uncontrolled proliferation of cancer cells causes the growth of the tumor mass. Consequently, the normal surrounding tissue exerts a compressive force on the tumor mass to oppose its expansion. These stresses directly promote tumor metastasis and invasion and affect drug delivery. In the past, the mechanical behavior of solid tumors has been extensively studied using linear elastic and nonlinear hyperelastic constitutive models. In this study, we develop a two-dimensional biomechanical model based on the biphasic assumption of the solid matrix and fluid phase of the tissues. Heterogeneous vasculature and nonuniform blood perfusion are also investigated by incorporating in the model a necrotic core and a well-vascularized zone. The findings of our study demonstrate a significant difference between the linear and nonlinear tissue responses to stress, while the interstitial fluid pressure (IFP) distribution is found to be independent of the constitutive model. The proposed biphasic model may be useful for elasticity imaging techniques aiming at predicting stress and IFP in tumors.

A position- and time-dependent pressure profile to model viscoelastic mechanical behavior of the brain tissue due to tumor growth

This study proposed a computational framework to calculate the resultant position- and time-dependent pressure profile on the brain tissue due to tumor growth. A finite element (FE) patch of the brain tissue was constructed and an inverse dynamic FE-optimization algorithm was used to calculate its viscoelastic mechanical properties under compressive uniaxial loading. Two patient-specific post-tumor resection FE models were input to the FE-optimization algorithm to calculate the optimized 3rd-order position-dependent and normal distribution time-dependent pressure profile parameters. The optimized viscoelastic material properties, the most suitable simulation time, and the optimized 3rd-order position- and -time-dependent pressure profiles were calculated.

Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model

Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.

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.

Live 3D imaging and mapping of shear stresses within tissues using incompressible elastic beads

To investigate the role of mechanical constraints in morphogenesis and development, we have developed a pipeline of techniques based on incompressible elastic sensors. These techniques combine the advantages of incompressible liquid droplets, which have been used as precise in situ shear stress sensors, and of elastic compressible beads, which are easier to tune and to use. Droplets of a polydimethylsiloxane mix, made fluorescent through specific covalent binding to a rhodamin dye, are produced by a microfluidics device. The elastomer rigidity after polymerization is adjusted to the tissue rigidity. Its mechanical properties are carefully calibrated in situ, for a sensor embedded in a cell aggregate submitted to uniaxial compression. The local shear stress tensor is retrieved from the sensor shape, accurately reconstructed through an active contour method. In vitro, within cell aggregates, and in vivo, in the prechordal plate of the zebrafish embryo during gastrulation, our pipeline of techniques demonstrates its efficiency to directly measure the three dimensional shear stress repartition within a tissue.

Inducing Biomechanical Heterogeneity in Brain Tumor Modeling by MR Elastography: Effects on Tumor Growth, Vascular Density and Delivery of Therapeutics

Simple Summary

Biomechanical forces aggravate brain tumor progression. In this study, magnetic resonance elastography (MRE) is employed to extract tissue biomechanical properties from five glioblastoma patients and a healthy subject, and data are incorporated in a mathematical model that simulates tumor growth. Mathematical modeling enables further understanding of glioblastoma development and allows patient-specific predictions for tumor vascularity and delivery of drugs. Incorporating MRE data results in a more realistic intratumoral distribution of mechanical stress and anisotropic tumor growth and a better description of subsequent events that are closely related to the development of stresses, including heterogeneity of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Abstract

The purpose of this study is to develop a methodology that incorporates a more accurate assessment of tissue mechanical properties compared to current mathematical modeling by use of biomechanical data from magnetic resonance elastography. The elastography data were derived from five glioblastoma patients and a healthy subject and used in a model that simulates tumor growth, vascular changes due to mechanical stresses and delivery of therapeutic agents. The model investigates the effect of tumor-specific biomechanical properties on tumor anisotropic growth, vascular density heterogeneity and chemotherapy delivery. The results showed that including elastography data provides a more realistic distribution of the mechanical stresses in the tumor and induces anisotropic tumor growth. Solid stress distribution differs among patients, which, in turn, induces a distinct functional vascular density distribution—owing to the compression of tumor vessels—and intratumoral drug distribution for each patient. In conclusion, incorporating elastography data results in a more accurate calculation of intratumoral mechanical stresses and enables a better mathematical description of subsequent events, such as the heterogeneous development of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Magnetic Compression of Tumor Spheroids Increases Cell Proliferation In Vitro and Cancer Progression In Vivo

A growing tumor is submitted to ever-evolving mechanical stress. Endoscopic procedures add additional constraints. However, the impact of mechanical forces on cancer progression is still debated. Herein, a set of magnetic methods is proposed to form tumor spheroids and to subject them to remote deformation, mimicking stent-imposed compression. Upon application of a permanent magnet, the magnetic tumor spheroids (formed from colon cancer cells or from glioblastoma cells) are compressed by 50% of their initial diameters. Such significant deformation triggers an increase in the spheroid proliferation for both cell lines, correlated with an increase in the number of proliferating cells toward its center and associated with an overexpression of the matrix metalloproteinase-9 (MMP-9). In vivo peritoneal injection of the spheroids made from colon cancer cells confirmed the increased aggressiveness of the compressed spheroids, with almost a doubling of the peritoneal cancer index (PCI), as compared with non-stimulated spheroids. Moreover, liver metastasis of labeled cells was observed only in animals grafted with stimulated spheroids. Altogether, these results demonstrate that a large compression of tumor spheroids enhances cancer proliferation and metastatic process and could have implications in clinical procedures where tumor compression plays a role.

Inverse dynamic finite element-optimization modeling of the brain tumor mass-effect using a variable pressure boundary

BACKGROUND AND OBJECTIVE

Statistical atlases of brain structure can potentially contribute in the surgical and radiotherapeutic treatment planning for the brain tumor patients. However, the current brain image-registration methods lack of accuracy when it comes to the mass-effect caused by tumor growth. Numerical simulations, such as finite element method (FEM), allow us to calculate the resultant pressure and deformation in the brain tissue due to tumor growth, and to predict the mass-effect. To date, however, the pressure boundary in the brain tissue due to tumor growth has been simply presented as a constant profile throughout the entire tumor outer surface that resulted in discrepancy between the patient imaging data and brain atlases.

METHODS

In this study, we employed a fully-coupled inverse dynamic FE-optimization method to estimate the resultant variable pressure boundary due to tumor resection surgery. To do that, magnetic resonance imaging data of two patients' pre- and post-tumor resection surgery were registered, segmented, volume-meshed, and prepared for fully-coupled inverse dynamic FE-optimization simulations. Two different pressure boundaries were defined on the brain cavity after tumor resection including: a) a constant pressure boundary and b) a variable pressure boundary. The inverse FE-optimization algorithm was used to find the optimum constant and variable pressure boundaries that result in the least distance between the surface-nodes of the post-surgery brain cavity and pre-surgery tumor.

RESULTS

The results revealed that a variable pressure boundary causes a considerably lower mean percentage error compared to a constant pressure one; hence, it can more effectively address the realistic boundary in tumor resection surgery and predict the mass-effect.

CONCLUSIONS

The proposed variable pressure boundary can be a robust tool that allows batch processing to register the brains with tumors to statistical atlases of normal brains and construction of brain tumor atlases. This approach is also computationally inexpensive and can be coupled to any FE software to run. The findings of this study have implications for not only predicting the accurate pressure boundary and mass-effect before tumor resection surgery, but also for predicting some clinical symptoms of brain cancers and presenting useful tools for APPLICATIONs in image-guided neurosurgery.

A computational model of glioma reveals opposing, stiffness-sensitive effects of leaky vasculature and tumor growth on tissue mechanical stress and porosity

A biphasic computational model of a growing, vascularized glioma within brain tissue was developed to account for unique features of gliomas, including soft surrounding brain tissue, their low stiffness relative to brain tissue, and a lack of draining lymphatics. This model is the first to couple nonlinear tissue deformation with porosity and tissue hydraulic conductivity to study the mechanical interaction of leaky vasculature and solid growth in an embedded glioma. The present model showed that leaky vasculature and elevated interstitial fluid pressure produce tensile stress within the tumor in opposition to the compressive stress produced by tumor growth. This tensile effect was more pronounced in softer tissue and resulted in a compressive stress concentration at the tumor rim that increased when tumor was softer than host. Aside from generating solid stress, fluid pressure-driven tissue deformation decreased the effective stiffness of the tumor while growth increased it, potentially leading to elevated stiffness in the tumor rim. A novel prediction of reduced porosity at the tumor rim was corroborated by direct comparison with estimates from our in vivo imaging studies. Antiangiogenic and radiation therapy were simulated by varying vascular leakiness and tissue hydraulic conductivity. These led to greater solid compression and interstitial pressure in the tumor, respectively, the former of which may promote tumor infiltration of the host. Our findings suggest that vascular leakiness has an important influence on in vivo solid stress, stiffness, and porosity fields in gliomas given their unique mechanical microenvironment.

Imaging acute effects of bevacizumab on tumor vascular kinetics in a preclinical orthotopic model of U251 glioma

The effect of a human vascular endothelial growth factor antibody on the vasculature of human tumor grown in rat brain was studied. Using dynamic contrast-enhanced magnetic resonance imaging, the effects of intravenous bevacizumab (Avastin; 10 mg/kg) were examined before and at postadministration times of 1, 2, 4, 8, 12 and 24 h (N = 26; 4-5 per time point) in a rat model of orthotopic, U251 glioblastoma (GBM). The commonly estimated vascular parameters for an MR contrast agent were: (i) plasma distribution volume (v_p ), (ii) forward volumetric transfer constant (K^trans ) and (iii) reverse transfer constant (k_ep ). In addition, extracellular distribution volume (V_D ) was estimated in the tumor (V_D-tumor ), tumor edge (V_D-edge ) and the mostly normal tumor periphery (V_D-peri ), along with tumor blood flow (TBF), peri-tumoral hydraulic conductivity (K) and interstitial flow (Flux) and tumor interstitial fluid pressure (TIFP). Studied as % changes from baseline, the 2-h post-treatment time point began showing significant decreases in v_p , V_D-tumor, V_D-edge and V_D-peri , as well as K, with these changes persisting at 4 and 8 h in v_p , K, V_{D-tumor, -edge} and _-peri (t-tests; p < 0.05-0.01). Decreases in K^trans were observed at the 2- and 4-h time points (p < 0.05), while interstitial volume fraction (v_e ; = K^trans /k_ep ) showed a significant decrease only at the 2-h time point (p < 0.05). Sustained decreases in Flux were observed from 2 to 24 h (p < 0.01) while TBF and TIFP showed delayed responses, increases in the former at 12 and 24 h and a decrease in the latter only at 12 h. These imaging biomarkers of tumor vascular kinetics describe the short-term temporal changes in physical spaces and fluid flows in a model of GBM after Avastin administration.

In silico investigations of intratumoral heterogeneous interstitial fluid pressure

Recent preclinical studies have shown that interstitial fluid pressure (IFP) within tumors can be heterogeneous Andersen et al. (2019). In that study tumors of two xenograft models, respectively, HL-16 cervical carcinoma and Panc-1 pancreatic carcinoma, were investigated. Significant heterogeneity in IFP was reported and it was proposed that this was associated with division of tissue into compartments separated by thick connective tissue bands for the HL-16 tumors and with dense collagen-rich extracellular matrix for the Panc-1 tumors. The purpose of the current work is to explore these experimental observations by using in silico generated tumor models. We consider a mathematical multiphase model which accounts for tumor cells, fibroblasts and interstitial fluid. The model has been trained to comply with experimental in vitro results reported in Shieh et al. (2011) which has identified autologous chemotaxis, ECM remodeling, and cell-fibroblast interaction as drivers for invasive tumor cell behavior. The in silico model is informed with parameters that characterize the leaky intratumoral vascular network, the peritumoral lymphatics which collect the fluid, and the density of ECM as represented through the hydraulic conductivity of the interstitial space. Heterogeneous distribution of solid stress may result in heterogeneous compression of blood vessels and, thus, heterogeneous vascular density inside the tumor. To mimic this we expose the in silico tumor to an intratumoral vasculature whose net effect of density of blood vesssels and vessel wall conductivity is varied through a 2D Gaussian variogram constrained such that the resulting IFPs lie within the range as reported from the preclinical study. The in silico cervical carcinoma model illustrates that sparse ECM was associated with uniform intratumoral IFP in spite of heterogeneous microvascular network, whereas compartment structures resulted in more heterogeneous IFP. Similarly, the in silico pancreatic model shows that heterogeneity in the microvascular network combined with dense ECM structure prevents IFP to even out and gives rise to heterogeneous IFP. The computer model illustrates how a heterogeneous invasive front might form where groups of tumor cells detach from the primary tumor and form isolated islands, a behavior which is natural to associate with metastatic propensity. However, unlike experimental studies, the current version of the in silico model does not show an association between metastatic propensity and elevated IFP.

Challenges of applying multicellular tumor spheroids in preclinical phase

The three-dimensional (3D) multicellular tumor spheroids (MCTs) model is becoming an essential tool in cancer research as it expresses an intermediate complexity between 2D monolayer models and in vivo solid tumors. MCTs closely resemble in vivo solid tumors in many aspects, such as the heterogeneous architecture, internal gradients of signaling factors, nutrients, and oxygenation. MCTs have growth kinetics similar to those of in vivo tumors, and the cells in spheroid mimic the physical interaction of the tumors, such as cell-to-cell and cell-to-extracellular matrix interactions. These similarities provide great potential for studying the biological properties of tumors and a promising platform for drug screening and therapeutic efficacy evaluation. However, MCTs are not well adopted as preclinical tools for studying tumor behavior and therapeutic efficacy up to now. In this review, we addressed the challenges with MCTs application and discussed various efforts to overcome the challenges.

Decompressive craniectomy of post-traumatic brain injury: an in silico modelling approach for intracranial hypertension management

Traumatic brain injury (TBI) causes brain edema that induces increased intracranial pressure and decreased cerebral perfusion. Decompressive craniectomy has been recommended as a surgical procedure for the management of swollen brain and intracranial hypertension. Proper location and size of a decompressive craniectomy, however, remain controversial and no clinical guidelines are available. Mathematical and computational (in silico) models can predict the optimum geometric conditions and provide insights for the brain mechanical response following a decompressive craniectomy. In this work, we present a finite element model of post-traumatic brain injury and decompressive craniectomy that incorporates a biphasic, nonlinear biomechanical model of the brain. A homogenous pressure is applied in the brain to represent the intracranial pressure loading caused by the tissue swelling and the models calculate the deformations and stresses in the brain as well as the herniated volume of the brain tissue that exits the skull following craniectomy. Simulations for different craniectomy geometries (unilateral, bifrontal and bifrontal with midline bar) and sizes are employed to identify optimal clinical conditions of decompressive craniectomy. The reported results for the herniated volume of the brain tissue as a function of the intracranial pressure loading under a specific geometry and size of craniectomy are exceptionally relevant for decompressive craniectomy planning.

Biomechanical modelling of spinal tumour anisotropic growth

Biomechanical abnormalities of solid tumours involve stiffening of the tissue and accumulation of mechanical stresses. Both abnormalities affect cancer cell proliferation and invasiveness and thus, play a crucial role in tumour morphology and metastasis. Even though, it has been known for more than two decades that high mechanical stresses reduce cancer cell proliferation rates driving growth towards low-stress regions, most biomechanical models of tumour growth account for isotropic growth. This cannot be valid, however, in tumours that grow within multiple host tissues of different mechanical properties, such as the spine. In these cases, structural heterogeneity would result in anisotropic growth of tumours. To this end, we present a biomechanical, biphasic model for anisotropic growth of spinal tumours. The model that accounts for both the fluid and the solid phase of the tumour was used to predict the evolution of solid stress and interstitial fluid pressure in intramedullary spinal tumours and highlight the differences between isotropic and anisotropic growth. Varying the degree of anisotropy, we found considerable differences in the shape of the tumours, leading to tumours of more realistic ellipsoidal shapes.

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.

Fluids and their mechanics in tumour transit: shaping metastasis

Metastasis is a dynamic succession of events involving the dissemination of tumour cells to distant sites within the body, ultimately reducing the survival of patients with cancer. To colonize distant organs and, therefore, systemically disseminate within the organism, cancer cells and associated factors exploit several bodily fluid systems, which provide a natural transportation route. Indeed, the flow mechanics of the blood and lymphatic circulatory systems can be co-opted to improve the efficiency of cancer cell transit from the primary tumour, extravasation and metastatic seeding. Flow rates, vessel size and shear stress can all influence the survival of cancer cells in the circulation and control organotropic seeding patterns. Thus, in addition to using these fluids as a means to travel throughout the body, cancer cells exploit the underlying physical forces within these fluids to successfully seed distant metastases. In this Review, we describe how circulating tumour cells and tumour-associated factors leverage bodily fluids, their underlying forces and imposed stresses during metastasis. As the contribution of bodily fluids and their mechanics raises interesting questions about the biology of the metastatic cascade, an improved understanding of this process might provide a new avenue for targeting cancer cells in transit.

Mechanical stress-induced autophagic response: A cancer-enabling characteristic?

Metastasis is the leading cause of cancer mortality. Throughout the cascade of metastasis, cancer cells are exposed to both chemical and mechanical cues which influence their migratory behavior and survival. Mechanical forces in the milieu of cancer may arise due to excessive growth of cells in a confinement as in case of solid tumors, interstitial flows within tumors and due to blood flow in the vasculature as in case of circulating tumor cells. The focus of this review is to highlight the mechanical forces prevalent in the cancer microenvironment and discuss the impact of mechanical stresses on cancer progression, with special focus on mechanically induced autophagic response in cancer cells. Autophagy is a cellular homeostatic mechanism that a cell employs not only for recycling of damaged organelles and turnover of proteins involved in cellular migration but also as an adaptive response to survive through unfavourable stresses. Elucidation of the role of mechanically triggered autophagic response may lead to a better understanding of the mechanobiological aspects of metastatic cancer and unravelling the associated signaling mechanochemical pathways may hint at potential therapeutic targets.

On the Impact of Chemo-Mechanically Induced Phenotypic Transitions in Gliomas

Tumor microenvironment is a critical player in glioma progression, and novel therapies for its targeting have been recently proposed. In particular, stress-alleviation strategies act on the tumor by reducing its stiffness, decreasing solid stresses and improving blood perfusion. However, these microenvironmental changes trigger chemo-mechanically induced cellular phenotypic transitions whose impact on therapy outcomes is not completely understood. In this work we analyze the effects of mechanical compression on migration and proliferation of glioma cells. We derive a mathematical model of glioma progression focusing on cellular phenotypic plasticity. Our results reveal a trade-off between tumor infiltration and cellular content as a consequence of stress-alleviation approaches. We discuss how these novel findings increase the current understanding of glioma/microenvironment interactions and can contribute to new strategies for improved therapeutic outcomes.

Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical cues in the microenvironment. Recent studies have shown that miR-451 regulates downstream molecules including AMPK/CAB39/MARK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of the main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this complex process of cell proliferation and invasion and its response to conventional treatment, we propose a mathematical model that analyzes the intracellular dynamics of the miR-451-AMPK- mTOR-cell cycle signaling pathway within a cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress in response to fluctuating glucose levels. We show how up- or down-regulation of components in these pathways affects the key cellular decision to infiltrate or proliferate in a complex microenvironment in the absence and presence of time delays and stochastic noise. Glycosylated chondroitin sulfate proteoglycans (CSPGs), a major component of the extracellular matrix (ECM) in the brain, contribute to the physical structure of the local brain microenvironment but also induce or inhibit glioma invasion by regulating the dynamics of the CSPG receptor LAR as well as the spatiotemporal activation status of resident astrocytes and tumor-associated microglia. Using a multi-scale mathematical model, we investigate a CSPG-induced switch between invasive and non-invasive tumors through the coordination of ECM-cell adhesion and dynamic changes in stromal cells. We show that the CSPG-rich microenvironment is associated with non-invasive tumor lesions through LAR-CSGAG binding while the absence of glycosylated CSPGs induce the critical glioma invasion. We illustrate how high molecular weight CSPGs can regulate the exodus of local reactive astrocytes from the main tumor lesion, leading to encapsulation of non-invasive tumor and inhibition of tumor invasion. These different CSPG conditions also change the spatial profiles of ramified and activated microglia. The complex distribution of CSPGs in the tumor microenvironment can determine the nonlinear invasion behaviors of glioma cells, which suggests the need for careful therapeutic strategies.

Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI

Previous studies to simulate brain tumor progression, often investigate either temporal changes in cancer cell density or the overall tissue-level growth of the tumor mass. Here, we developed a computational model to bridge these two approaches. The model incorporates the tumor biomechanical response at the tissue level and accounts for cellular events by modeling cancer cell proliferation, infiltration to surrounding tissues, and invasion to distant locations. Moreover, acquisition of high resolution human data from anatomical magnetic resonance imaging, diffusion tensor imaging and perfusion imaging was employed within the simulations towards a realistic and patient specific model. The model predicted the intratumoral mechanical stresses to range from 20 to 34 kPa, which caused an up to 4.5 mm displacement to the adjacent healthy tissue. Furthermore, the model predicted plausible cancer cell invasion patterns within the brain along the white matter fiber tracts. Finally, by varying the tumor vascular density and its invasive outer ring thickness, our model showed the potential of these parameters for guiding the timing (83–90 days) of cancer cell distant invasion as well as the number (0–2 sites) and location (temportal and/or parietal lobe) of the invasion sites.

Understanding the relationship between cell death and tissue shrinkage via a stochastic agent-based model

Cell death, a process which can occur both naturally and in response to insult, is both a complex and diverse phenomenon. Under some circumstances, dying cells actively contract and cause their neighbors to rearrange and maintain tissue integrity. Under other circumstances, dying cells leave behind gaps, which results in tissue separation. A better understanding of how the cellular scale features of cell death manifest on the population scale has implications ranging from morphogenesis to tumor response to treatment. However, the mechanistic relationship between cell death and population scale shrinkage is not well understood, and computational methods for studying these relationships are not well established. Here we propose a mechanically robust agent-based cell model designed to capture the implications of cell death on the population scale. In our agent-based model, algorithmic rules applied on the cellular level emerge on the population scale where their effects are quantified. To better quantify model uncertainty and parameter interactions, we implement a recently developed technique for conducting a variance-based sensitivity analysis on the stochastic model. From this analysis and subsequent investigation, we find that cellular scale shrinkage has the largest influence of all model parameters tested, and that by adjusting cellular scale shrinkage population shrinkage varies widely even across simulations which contain the same fraction of dying cells. We anticipate that the methods and results presented here are a starting point for significant future investigation toward quantifying the implications of different mechanisms of cell death on population and tissue scale behavior.

Reengineering the Physical Microenvironment of Tumors to Improve Drug Delivery and Efficacy: From Mathematical Modeling to Bench to Bedside

Physical forces have a crucial role in tumor progression and cancer treatment. The application of principles of engineering and physical sciences to oncology has provided powerful insights into the mechanisms by which these forces affect tumor progression and confer resistance to delivery and efficacy of molecular, nano-, cellular, and immuno-medicines. Here, we discuss the mechanics of the solid and fluid components of a tumor, with a focus on how they impede the transport of therapeutic agents and create an abnormal tumor microenvironment (TME) that fuels tumor progression and treatment resistance. We also present strategies to reengineer the TME by normalizing the tumor vasculature and the extracellular matrix (ECM) to improve cancer treatment. Finally, we summarize various mathematical models that have provided insights into the physical barriers to cancer treatment and revealed new strategies to overcome these barriers.

Pirfenidone normalizes the tumor microenvironment to improve chemotherapy

Normalization of the tumor microenvironment by selectively targeting components of the tumor extracellular matrix has been recently proposed to have the potential to decompress tumor blood vessels, increase vessel perfusion and thus, improve drug delivery and the efficacy of cancer therapy. Therefore, we now need to identify safe and well tolerated pharmaceutical agents that are able to remodel the microenvironment of solid tumors and enhance chemotherapy. In this study, we repurposed Pirfenidone, a clinically approved anti-fibrotic drug for the treatment of idiopathic pulmonary fibrosis, to investigate its possible role on tumor microenvironment normalization. Using two orthotopic mammary tumor models we demonstrate that Pirfenidone reduces collagen and hyaluronan levels and, as a result, significantly increases blood vessel functionality and perfusion and improves the anti-tumor efficacy of doxorubicin. Reduction of extracellular matrix components were mediated via TGFβ signaling pathway inhibition due to downregulation of TGFβ1, COL1A1, COL3A1, HAS2, HAS3 expression levels. Our findings provide evidence that repurposing Pirfenidone could be used as a promising strategy to enhance drug delivery to solid tumors by normalizing the tumor microenvironment.

Sonic-hedgehog pathway inhibition normalizes desmoplastic tumor microenvironment to improve chemo- and nanotherapy

Targeting the rich extracellular matrix of desmoplastic tumors has been successfully shown to normalize collagen and hyaluronan levels and re-engineer intratumoral mechanical forces, improving tumor perfusion and chemotherapy. As far as targeting the abundant cancer-associated fibroblasts (CAFs) in desmoplastic tumors is concerned, while both pharmacologic inhibition of the sonic-hedgehog pathway and genetic depletion of fibroblasts have been employed in pancreatic cancers, the results between the two methods have been contradictory. In this study, we employed vismodegib to inhibit the sonic-hedgehog pathway with the aim to i) elucidate the mechanism of how CAFs depletion improves drug delivery, ii) extent and evaluate the potential use of sonic-hedgehog inhibitors to breast cancers, and iii) investigate whether sonic-hedgehog inhibition improves not only chemotherapy, but also the efficacy of the most commonly used breast cancer nanomedicines, namely Abraxane® and Doxil®. We found that treatment with vismodegib normalizes the tumor microenvironment by reducing the proliferative CAFs and in cases the levels of collagen and hyaluronan. These modulations re-engineered the solid and fluid stresses in the tumors, improving blood vessel functionality. As a result, the delivery and efficacy of chemotherapy was improved in two models of pancreatic cancer. Additionally, vismodegib treatment significantly improved the efficacy of both Abraxane and Doxil in xenograft breast tumors. Our results suggest the use of vismodegib, and sonic hedgehog inhibitors in general, to enhance cancer chemo- and nanotherapy.

Tranilast-induced stress alleviation in solid tumors improves the efficacy of chemo- and nanotherapeutics in a size-independent manner

Accumulation of mechanical stresses during cancer progression can induce blood and lymphatic vessel compression, creating hypo-perfusion, hypoxia and interstitial hypertension which decrease the efficacy of chemo- and nanotherapies. Stress alleviation treatment has been recently proposed to reduce mechanical stresses in order to decompress tumor vessels and improve perfusion and chemotherapy. However, it remains unclear if it improves the efficacy of nanomedicines, which present numerous advantages over traditional chemotherapeutic drugs. Furthermore, we need to identify safe and well-tolerated pharmaceutical agents that reduce stress levels and may be added to cancer patients' treatment regimen. Here, we show mathematically and with a series of in vivo experiments that stress alleviation improves the delivery of drugs in a size-independent manner. Importantly, we propose the repurposing of tranilast, a clinically approved anti-fibrotic drug as stress-alleviating agent. Using two orthotopic mammary tumor models, we demonstrate that tranilast reduces mechanical stresses, decreases interstitial fluid pressure (IFP), improves tumor perfusion and significantly enhances the efficacy of different-sized drugs, doxorubicin, Abraxane and Doxil, by suppressing TGFβ signaling and expression of extracellular matrix components. Our findings strongly suggest that repurposing tranilast could be directly used as a promising strategy to enhance, not only chemotherapy, but also the efficacy of cancer nanomedicine.

Experimental measurements and mathematical modeling towards quantification of brain swelling stress

Traumatic brain injury results in brain tissue swelling which can be a life threatening condition due to skull confinement. While previous efforts successfully measured the exhibited volume change in brain tissue swelling, no data exist to provide information about the exhibited stresses. In this study, confined compression mechanical testing was employed to measure swelling stress in murine brain tissue samples by varying the ionic concentration of the bathing solutions. Subsequently, computer simulations of the experimental protocol were employed to confirm a triphasic mathematical model describing the effect and provide insights into the experimental data. We measured the swelling stress to be in the range of 1.2-6.7kPa (9.0-50.2mmHg) depending on the ionic strength of the bathing solution, while a good correspondence was demonstrated among the experimentally measured and simulated responses. Furthermore, the mathematical model featured the osmotic pressure as the primary contributor to the swelling stress, while a parametric analysis showed that the densities of the intracellular fixed charges and of the non-permeable solutes significantly affect the swelling stress.

Three-dimensional Image-based Mechanical Modeling for Predicting the Response of Breast Cancer to Neoadjuvant Therapy

The use of quantitative medical imaging data to initialize and constrain mechanistic mathematical models of tumor growth has demonstrated a compelling strategy for predicting therapeutic response. More specifically, we have demonstrated a data-driven framework for prediction of residual tumor burden following neoadjuvant therapy in breast cancer that uses a biophysical mathematical model combining reaction-diffusion growth/therapy dynamics and biomechanical effects driven by early time point imaging data. Whereas early work had been based on a limited dimensionality reduction (two-dimensional planar modeling analysis) to simplify the numerical implementation, in this work, we extend our framework to a fully volumetric, three-dimensional biophysical mathematical modeling approach in which parameter estimates are generated by an inverse problem based on the adjoint state method for numerical efficiency. In an in silico performance study, we show accurate parameter estimation with error less than 3% as compared to ground truth. We apply the approach to patient data from a patient with pathological complete response and a patient with residual tumor burden and demonstrate technical feasibility and predictive potential with direct comparisons between imaging data observation and model predictions of tumor cellularity and volume. Comparisons to our previous two-dimensional modeling framework reflect enhanced model prediction of residual tumor burden through the inclusion of additional imaging slices of patient-specific data.

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.