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.

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.

Multiscale modeling of solid stress and tumor cell invasion in response to dynamic mechanical microenvironment

Mathematical models can provide a quantitatively sophisticated description of tumor cell (TC) behaviors under mechanical microenvironment and help us better understand the role of specific biophysical factors based on their influences on the TC behaviors. To this end, we propose an off-lattice cell-based multiscale mathematical model to describe the dynamic growth-induced solid stress during tumor progression and investigate the influence of the mechanical microenvironment on TC invasion. At the cellular level, cell-cell and cell-matrix interactive forces depend on the mechanical properties of the cells and the cancer-associated fibroblasts in the stroma, respectively. The constitutive relationship between the interactive forces and cell migrations obeys the Hooke's law and damping effects. At the tissue level, the integrated growth-induced forces caused by proliferating cells within the simulation region are balanced by the external forces applied by the surrounding host tissues. Then, the cell movements are calculated according to the Newton's second law of motion, and the morphology of TC invasion is updated. The simulation results reveal the continuous changes of the macroscopic mechanical forces due to the interactions among the structural components and the microscopic environmental factors. Moreover, the simulation results demonstrate the adverse effect of the stiffness of tumor tissue on tumor growth and invasion. A decrease in the stiffness of tumor and matrix can promote TCs to proliferate at a much faster rate and invade into the surrounding healthy tissue more easily, whereas an increase in the stiffness can lead to an aggressive morphology of tumor invasion. We envision that the proposed model can be served as a quantitative theoretical platform to study the underlying biophysical role of the mechanical microenvironmental factors during tumor invasion and metastasis.

Mechanical Compression Regulates Brain Cancer Cell Migration Through MEK1/Erk1 Pathway Activation and GDF15 Expression

Mechanical compression is a common abnormality of brain tumors that has been shown to be responsible for the severe neurological defects of brain cancer patients representing a negative prognostic factor. Indeed, it is of note that patients that undergo resection exhibited higher survival rates than those subjected to biopsy only, suggesting that compressive forces generated during brain tumor growth play a key role in tumor progression. Despite the importance of mechanical compression in brain tumors, there is a lack of studies examining its direct effects on brain cancer cells and the mechanisms involved. In the present study, we used two brain cancer cell lines with distinct metastatic potential, the less aggressive H4 and the highly aggressive A172 cell lines, in order to study the effect of compression on their proliferative and migratory ability. Specifically, we used multicellular tumor spheroids (MCS) embedded in agarose matrix to show that compression strongly impaired their growth. Using mathematical modeling, we estimated the levels of compressive stress generated during the growth of brain MCS and then we applied the respective stress levels on brain cancer cell monolayers using our previously established transmembrane pressure device. By performing a scratch assay, we found that compression strongly induced the migration of the less aggressive H4 cells, while a less pronounced effect was observed for A172 cells. Analysis of the gene expression profile of both cell lines revealed that GDF15 and small GTPases are strongly regulated by mechanical compression, while GDF15 was further shown to be necessary for cells to migrate under compression. Through a phospho-proteomic screening, we further found that compressive stimulus is transmitted through the MEK1/Erk1 signaling pathway, which is also necessary for the migration of brain cancer cells. Finally, our results gave the first indication that GDF15 could regulate and being regulated by MEK1/Erk1 signaling pathway in order to facilitate the compression-induced brain cancer cell migration, rendering them along with small GTPases as potential targets for future anti-metastatic therapeutic innovations to treat brain tumors.

Capillary flow and mechanical buckling in a growing annular bacterial colony

A growing bacterial colony is a dense suspension of an increasing number of cells capable of individual as well as collective motion. After inoculating Pseudomonas aeruginosa over an annular area on an agar plate, we observe the growth and spread of the bacterial population, and model the process by considering the physical effects that account for the features observed. Over a course of 10-12 hours, the majority of bacteria migrate to and accumulate at the edges. We model the capillary flow induced by imbalanced evaporation flux as the cause for the accumulation, much like the well-known coffee stain phenomenon. Simultaneously, periodic buckles or protrusions occur at the inner edge. These buckles indicate that the crowding bacteria produce a jam, transforming the densely packed population at the inner edge to a solid state. The continued bacterial growth produces buckles. Subsequently, a ring of packed bacteria behind the inner edge detach from it and break into pieces, forming bacterial droplets. These droplets slowly coalesce while they continually grow and collectively surf on the agar surface in the region where the colony had previously spread over. Our study shows a clear example of how fluid dynamics and elasto-mechanics together govern the bacterial colony pattern evolution.

Finite Element Modeling of Avascular Tumor Growth Using a Stress-Driven Model

Tumor growth being a multistage process has been investigated from different aspects. In the present study, an attempt is made to represent a constitutive-structure-based model of avascular tumor growth in which the effects of tensile stresses caused by collagen fibers are considered. Collagen fibers as a source of anisotropy in the structure of tissue are taken into account using a continuous fiber distribution formulation. To this end, a finite element modeling is implemented in which a neo-Hookean hyperelastic material is assigned to the tumor and its surrounding host. The tumor is supplied with a growth term. The growth term includes the effect of parameters such as nutrient concentration on the tumor growth and the tumor's solid phase content in the formulation. Results of the study revealed that decrease of solid phase is indicative of decrease in growth rate and the final steady-state value of tumor's radius. Moreover, fiber distribution affects the final shape of the tumor, and it could be used to control the shape and geometry of the tumor in complex morphologies. Finally, the findings demonstrated that the exerted stresses on the tumor increase as time passes. Compression of tumor cells leads to the reduction of tumor growth rate until it gradually reaches an equilibrium radius. This finding is in accordance with experimental data. Hence, this formulation can be deployed to evaluate both the residual stresses induced by growth and the mechanical interactions with the host tissue.

Biphasic modeling of brain tumor biomechanics and response to radiation treatment

Biomechanical forces are central in tumor progression and response to treatment. This becomes more important in brain cancers where tumors are surrounded by tissues with different mechanical properties. Existing mathematical models ignore direct mechanical interactions of the tumor with the normal brain. Here, we developed a clinically relevant model, which predicts tumor growth accounting directly for mechanical interactions. A three-dimensional model of the gray and white matter and the cerebrospinal fluid was constructed from magnetic resonance images of a normal brain. Subsequently, a biphasic tissue growth theory for an initial tumor seed was employed, incorporating the effects of radiotherapy. Additionally, three different sets of brain tissue properties taken from the literature were used to investigate their effect on tumor growth. Results show the evolution of solid stress and interstitial fluid pressure within the tumor and the normal brain. Heterogeneous distribution of the solid stress exerted on the tumor resulted in a 35% spatial variation in cancer cell proliferation. Interestingly, the model predicted that distant from the tumor, normal tissues still undergo significant deformations while it was found that intratumoral fluid pressure is elevated. Our predictions relate to clinical symptoms of brain cancers and present useful tools for therapy planning.

Stress-mediated progression of solid tumors: effect of mechanical stress on tissue oxygenation, cancer cell proliferation, and drug delivery

Oxygen supply plays a central role in cancer cell proliferation. While vascular density increases at the early stages of carcinogenesis, mechanical solid stresses developed during growth compress tumor blood vessels and, thus, drastically reduce not only the supply of oxygen, but also the delivery of drugs at inner tumor regions. Among other effects, hypoxia and reduced drug delivery compromise the efficacy of radiation and chemo/nanotherapy, respectively. In the present study, we developed a mathematical model of tumor growth to investigate the interconnections among tumor oxygenation that supports cancer cell proliferation, the heterogeneous accumulation of mechanical stresses owing to tumor growth, the non-uniform compression of intratumoral blood vessels due to the mechanical stresses, and the insufficient delivery of oxygen and therapeutic agents because of vessel compression. We found that the high vascular density and increased cancer cell proliferation often observed in the periphery compared to the interior of a tumor can be attributed to heterogeneous solid stress accumulation. Highly vascularized peripheral regions are also associated with greater oxygenation compared with the compressed, less vascularized inner regions. We also modeled the delivery of drugs of two distinct sizes, namely chemotherapy and nanomedicine. Model predictions suggest that drug delivery is affected negatively by vessel compression independently of the size of the therapeutic agent. Finally, we demonstrated the applicability of our model to actual geometries, employing a breast tumor model derived from MR images.

The role of mechanical forces in tumor growth and therapy

Tumors generate physical forces during growth and progression. These physical forces are able to compress blood and lymphatic vessels, reducing perfusion rates and creating hypoxia. When exerted directly on cancer cells, they can increase cells' invasive and metastatic potential. Tumor vessels-while nourishing the tumor-are usually leaky and tortuous, which further decreases perfusion. Hypoperfusion and hypoxia contribute to immune evasion, promote malignant progression and metastasis, and reduce the efficacy of a number of therapies, including radiation. In parallel, vessel leakiness together with vessel compression causes a uniformly elevated interstitial fluid pressure that hinders delivery of blood-borne therapeutic agents, lowering the efficacy of chemo- and nanotherapies. In addition, shear stresses exerted by flowing blood and interstitial fluid modulate the behavior of cancer and a variety of host cells. Taming these physical forces can improve therapeutic outcomes in many cancers.

Evolution of osmotic pressure in solid tumors

The mechanical microenvironment of solid tumors includes both fluid and solid stresses. These stresses play a crucial role in cancer progression and treatment and have been analyzed rigorously both mathematically and experimentally. The magnitude and spatial distribution of osmotic pressures in tumors, however, cannot be measured experimentally and to our knowledge there is no mathematical model to calculate osmotic pressures in the tumor interstitial space. In this study, we developed a triphasic biomechanical model of tumor growth taking into account not only the solid and fluid phase of a tumor, but also the transport of cations and anions, as well as the fixed charges at the surface of the glycosaminoglycan chains. Our model predicts that the osmotic pressure is negligible compared to the interstitial fluid pressure for values of glycosaminoglycans (GAGs) taken from the literature for sarcomas, melanomas and adenocarcinomas. Furthermore, our results suggest that an increase in the hydraulic conductivity of the tumor, increases considerably the intratumoral concentration of free ions and thus, the osmotic pressure but it does not reach the levels of the interstitial fluid pressure.

Role of constitutive behavior and tumor-host mechanical interactions in the state of stress and growth of solid tumors

Mechanical forces play a crucial role in tumor patho-physiology. Compression of cancer cells inhibits their proliferation rate, induces apoptosis and enhances their invasive and metastatic potential. Additionally, compression of intratumor blood vessels reduces the supply of oxygen, nutrients and drugs, affecting tumor progression and treatment. Despite the great importance of the mechanical microenvironment to the pathology of cancer, there are limited studies for the constitutive modeling and the mechanical properties of tumors and on how these parameters affect tumor growth. Also, the contribution of the host tissue to the growth and state of stress of the tumor remains unclear. To this end, we performed unconfined compression experiments in two tumor types and found that the experimental stress-strain response is better fitted to an exponential constitutive equation compared to the widely used neo-Hookean and Blatz-Ko models. Subsequently, we incorporated the constitutive equations along with the corresponding values of the mechanical properties - calculated by the fit - to a biomechanical model of tumor growth. Interestingly, we found that the evolution of stress and the growth rate of the tumor are independent from the selection of the constitutive equation, but depend strongly on the mechanical interactions with the surrounding host tissue. Particularly, model predictions - in agreement with experimental studies - suggest that the stiffness of solid tumors should exceed a critical value compared with that of the surrounding tissue in order to be able to displace the tissue and grow in size. With the use of the model, we estimated this critical value to be on the order of 1.5. Our results suggest that the direct effect of solid stress on tumor growth involves not only the inhibitory effect of stress on cancer cell proliferation and the induction of apoptosis, but also the resistance of the surrounding tissue to tumor expansion.

Effects of internal pressure and surface tension on the growth-induced wrinkling of mucosae

Surface wrinkling of mucosae is crucial for the biological functions of many living tissues. In this paper, we investigate the instability of a cylindrical tube consisting of a mucosal layer and a submucosal layer. Our attention is focused on the effects of internal pressure and surface tension on the critical condition and mode number of surface wrinkling induced by tissue growth. It is found that the internal pressure plays a stabilizing role but basically has no effect on the critical mode number. Surface tension also stabilizes the system and reduces the critical mode number of surface patterns. Besides, the thinner the mucosal layer, the more significant the effect of surface tension. This work may help gain insights into the surface wrinkling and morphological evolution of such tubular organs as airways and esophagi.

Coevolution of solid stress and interstitial fluid pressure in tumors during progression: implications for vascular collapse

The stress harbored by the solid phase of tumors is known as solid stress. Solid stress can be either applied externally by the surrounding normal tissue or induced by the tumor itself due to its growth. Fluid pressure is the isotropic stress exerted by the fluid phase. We recently showed that growth-induced solid stress is on the order of 1.3 to 13.0 kPa (10-100 mmHg)--high enough to cause compression of fragile blood vessels, resulting in poor perfusion and hypoxia. However, the evolution of growth-induced stress with tumor progression and its effect on cancer cell proliferation in vivo is not understood. To this end, we developed a mathematical model for tumor growth that takes into account all three types of stresses: growth-induced stress, externally applied stress, and fluid pressure. First, we conducted in vivo experiments and found that growth-induced stress is related to tumor volume through a biexponential relationship. Then, we incorporated this information into our mathematical model and showed that due to the evolution of growth-induced stress, total solid stress levels are higher in the tumor interior and lower in the periphery. Elevated compressive solid stress in the interior of the tumor is sufficient to cause the collapse of blood vessels and results in a lower growth rate of cancer cells compared with the periphery, independently from that caused by the lack of nutrients due to vessel collapse. Furthermore, solid stress in the periphery of the tumor causes blood vessels in the surrounding normal tissue to deform to elliptical shapes. We present histologic sections of human cancers that show such vessel deformations. Finally, we found that fluid pressure increases with tumor growth due to increased vascular permeability and lymphatic impairment, and is governed by the microvascular pressure. Crucially, fluid pressure does not cause vessel compression of tumor vessels.

Perspective: Flicking with flow: Can microfluidics revolutionize the cancer research?

According to the World Health Organization, cancer is one of the leading causes of death worldwide. Cancer research, in its all facets, is truly interdisciplinary in nature, cutting across the fields of fundamental and applied sciences, as well as biomedical engineering. In recent years, microfluidics has been applied successfully in cancer research. There remain, however, many elusive features of this disease, where microfluidic systems could throw new lights. In addition, some inherent features of microfluidic systems remain unexploited in cancer research. In this article, we first briefly review the advancement of microfluidics in cancer biology. We then describe the biophysical aspects of cancer and outline how microfluidic system could be useful in developing a deeper understanding on the underlying mechanisms. We next illustrate the effects of the confined environment of microchannel on cellular dynamics and argue that the tissue microconfinement could be a crucial facet in tumor development. Lastly, we attempt to highlight some of the most important problems in cancer biology, to inspire next level of microfluidic applications in cancer research.