Effects of anatomical constraints on tumor growth

Configuration of fibrous and adipose tissues in the cavernous sinus

Objective

Three-dimensional anatomical appreciation of the matrix of the cavernous sinus is one of the crucial necessities for a better understanding of tissue patterning and various disorders in the sinus. The purpose of this study was to reveal configuration of fibrous and adipose components in the cavernous sinus and their relationship with the cranial nerves and vessels in the sinus and meningeal sinus wall.

Materials and Methods

Nineteen cadavers (8 females and 11 males; age range, 54–89 years; mean age, 75 years) were prepared as transverse (6 sets), coronal (3 sets) and sagittal (10 sets) plastinated sections that were examined at both macroscopic and microscopic levels.

Results

Two types of the web-like fibrous networks were identified and localized in the cavernous sinus. A dural trabecular network constituted a skeleton-frame in the sinus and contributed to the sleeves of intracavernous cranial nerves III, IV, V₁, V₂ and VI. A fine trabecular network, or adipose tissue, was the matrix of the sinus and was mainly distributed along the medial side of the intracavernous cranial nerves, forming a dumbbell-shaped adipose zone in the sinus.

Conclusions

This study revealed the nature, fine architecture and localization of the fine and dural trabecular networks in the cavernous sinus and their relationship with intracavernous cranial nerves and vessels. The results may be valuable for better understanding of tissue patterning in the cranial base and better evaluation of intracavernous disorders, e.g. the growth direction and extent of intracavernous tumors.

Biopotential signals of breast cancer versus tumor types and proliferation stages

Clinical studies have shown compelling data of elevated biopotential signals recorded noninvasively from the breasts of women with breast cancer. While these data are compelling and show a strong potential for use in the noninvasive early detection of breast cancer, there remains significant knowledge gaps which must be addressed before this technology can be routinely used for breast cancer detection. A diffusion-drift model is developed to study the spatial and temporal characteristics of the biopotential signals of breast tumors taking into account the morphology and cell division stages. The electric signals of the most common tumor types-papillary, compact, and comedo-are also considered. The largest biopotential signal is observed from the compact tumor, while the smallest signal is observed from the papillary type. The results also show an increase in the time duration of the generated biopotential signals when cancer cells start their transitions at different time instants. The spatial and temporal variations of the biopotential signals are correlated with the tumor pattern which can have important implications for breast cancer detection.

Nonlinear modelling of cancer: bridging the gap between cells and tumours

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

Growing heterogeneous tumors in silico

An in silico tool that can be utilized in the clinic to predict neoplastic progression and propose individualized treatment strategies is the holy grail of computational tumor modeling. Building such a tool requires the development and successful integration of a number of biophysical and mathematical models. In this paper, we work toward this long-term goal by formulating a cellular automaton model of tumor growth that accounts for several different inter-tumor processes and host-tumor interactions. In particular, the algorithm couples the remodeling of the microvasculature with the evolution of the tumor mass and considers the impact that organ-imposed physical confinement and environmental heterogeneity have on tumor size and shape. Furthermore, the algorithm is able to account for cell-level heterogeneity, allowing us to explore the likelihood that different advantageous and deleterious mutations survive in the tumor cell population. This computational tool we have built has a number of applications in its current form in both predicting tumor growth and predicting response to treatment. Moreover, the latent power of our algorithm is that it also suggests other tumor-related processes that need to be accounted for and calls for the conduction of new experiments to validate the model's predictions.

A new computational tool for the phenomenological analysis of multipassage tumor growth curves

Multipassage experiments are performed by subcutaneous implantation in lab animals (usually mice) of a small number of cells from selected human lines. Tumor cells are then passaged from one mouse to another by harvesting them from a growing tumor and implanting them into other healthy animals. This procedure may be extremely useful to investigate the various mechanisms involved in the long term evolution of tumoral growth. It has been observed by several researchers that, contrary to what happens in in vitro experiments, there is a significant growth acceleration at each new passage. This result is explained by a new method of analysis, based on the Phenomenological Universalities approach. It is found that, by means of a simple rescaling of time, it is possible to collapse all the growth curves, corresponding to the successive passages, into a single curve, belonging to the Universality Class U2. Possible applications are proposed and the need of further experimental evidence is discussed.

Modeling tumor cell shedding

Cell shedding is an important step in the development of tumor invasion and metastasis. It influences growth saturation, latency, and tumor surface roughness. In spite of careful experiments carried out using multicellular tumor spheroids (MTS), the effects of the shedding process are not yet completely understood. Using a simulational model, we study how the nature and intensity of cell shedding may influence tumor morphology and examine the dependence of the total number of shed cells with the relevant parameters, finding the ranges that maximize cell detachment. These ranges correspond to intermediate values of the adhesion, for which we observe the emergence of a rough tumor surface. They are also likely to maximize the probability of generating invasion and metastases. Using numerical values taken from experiments, we find that the shedding-induced reduction in the growth rate is not intense enough to lead to latency, except when cell adhesion is assumed to be very weak. This suggests that the presence of inhibitors is a necessary condition for the observed MTS growth saturation.

An imaging-based tumour growth and treatment response model: investigating the effect of tumour oxygenation on radiation therapy response

A multiscale tumour simulation model employing cell-line-specific biological parameters and functional information derived from pre-therapy PET/CT imaging data was developed to investigate effects of different oxygenation levels on the response to radiation therapy. For each tumour voxel, stochastic simulations were performed to model cellular growth and therapeutic response. Model parameters were fitted to published preclinical experiments of head and neck squamous cell carcinoma (HNSCC). Using the obtained parameters, the model was applied to a human HNSCC case to investigate effects of different uniform and non-uniform oxygenation levels and results were compared for treatment efficacy. Simulations of the preclinical studies showed excellent agreement with published data and underlined the model's ability to quantitatively reproduce tumour behaviour within experimental uncertainties. When using a simplified transformation to derive non-uniform oxygenation levels from molecular imaging data, simulations of the clinical case showed heterogeneous tumour response and variability in radioresistance with decreasing oxygen levels. Once clinically validated, this model could be used to transform patient-specific data into voxel-based biological objectives for treatment planning and to investigate biologically optimized dose prescriptions.

Cancer growth: predictions of a realistic model

Simulations of avascular cancer growth are performed using experimental values of the relevant parameters. This permits a realistic assessment of the influence of these parameters on cancer growth dynamics. In general, an early exponential growth phase is followed by a linear regime (as observed in recent experiments), while the thickness of the viable cell layer remains approximately constant. Contrary to some predictions, a transition to latency is not observed.

Nonlinear simulation of the effect of microenvironment on tumor growth

In this paper, we present and investigate a model for solid tumor growth that incorporates features of the tumor microenvironment. Using analysis and nonlinear numerical simulations, we explore the effects of the interaction between the genetic characteristics of the tumor and the tumor microenvironment on the resulting tumor progression and morphology. We find that the range of morphological responses can be placed in three categories that depend primarily upon the tumor microenvironment: tissue invasion via fragmentation due to a hypoxic microenvironment; fingering, invasive growth into nutrient rich, biomechanically unresponsive tissue; and compact growth into nutrient rich, biomechanically responsive tissue. We found that the qualitative behavior of the tumor morphologies was similar across a broad range of parameters that govern the tumor genetic characteristics. Our findings demonstrate the importance of the impact of microenvironment on tumor growth and morphology and have important implications for cancer therapy. In particular, if a treatment impairs nutrient transport in the external tissue (e.g., by anti-angiogenic therapy) increased tumor fragmentation may result, and therapy-induced changes to the biomechanical properties of the tumor or the microenvironment (e.g., anti-invasion therapy) may push the tumor in or out of the invasive fingering regime.

Classification scheme for phenomenological universalities in growth problems in physics and other sciences

A classification in universality classes of broad categories of phenomenologies, belonging to physics and other disciplines, may be very useful for a cross fertilization among them and for the purpose of pattern recognition and interpretation of experimental data. We present here a simple scheme for the classification of nonlinear growth problems. The success of the scheme in predicting and characterizing the well known Gompertz, West, and logistic models, suggests to us the study of a hitherto unexplored class of nonlinear growth problems.

An integrated computational/experimental model of tumor invasion

The intracellular and extracellular dynamics that govern tumor growth and invasiveness in vivo remain poorly understood. Cell genotype and phenotype, and nutrient, oxygen, and growth factor concentrations are key variables. In previous work, using a reaction-diffusion mathematical model based on variables that directly describe tumor cell cycle and biology, we formulated the hypothesis that tumor morphology is determined by the competition between heterogeneous cell proliferation caused by spatial diffusion gradients, e.g., of cell nutrients, driving shape instability and invasive tumor morphologies, and stabilizing mechanical forces, e.g., cell-to-cell and cell-to-matrix adhesion. To test this hypothesis, we here obtain variable-based statistics for input to the mathematical model from in vitro human and rat glioblastoma cultures. A linear stability analysis of the model predicts that glioma spheroid morphology is marginally stable. In agreement with this prediction, for a range of variable values, unbounded growth of the tumor mass and invasion of the environment are observed in vitro. The mechanism of invasion is recursive subspheroid component development at the tumor viable rim and separation from the parent spheroid. Results of computer simulations of the mathematical model closely resemble the morphologies and spatial arrangement of tumor cells from the in vitro model. We propose that tumor morphogenesis in vivo may be a function of marginally stable environmental conditions caused by spatial variations in cell nutrients, oxygen, and growth factors, and that controlling these conditions by decreasing spatial gradients could benefit treatment outcomes, whereas current treatment, and especially antiangiogenic therapy, may trigger spatial heterogeneity (e.g., local hypoxia), thus causing invasive instability.

Markovian model of growth and histologic progression in prostate cancer

Models, based on bio-physical and biological considerations, may be very helpful as support tools for traditional diagnostic methodologies and interpretation of statistical data in oncology. This is particularly true when the neoplastic progression and differentiation are rather simple and regular, such as in the case of prostatic adenocarcinomas. Using clinical data as a "statistical ensemble," we propose here a Markovian model to forecast the tumor progression. After validation with clinical data, the model is applied to the determination of the temporal evolution of the risk of metastasis.

Inhibition of vascularization in tumor growth

The transition to a vascular phase is a prerequisite for fast tumor growth. During the avascular phase, the neoplasm feeds only from the (relatively few) existing nearby blood vessels. During angiogenesis, the number of capillaries surrounding and infiltrating the tumor increases dramatically. A model which includes physical and biological mechanisms of the interactions between the tumor and vascular growth describes the avascular-vascular transition. Numerical results agree with clinical observations and predict the influence of therapies aiming to inhibit the transition.

Competition effects in the dynamics of tumor cords

A general feature of cancer growth is the cellular competition for available nutrients. This is also the case for tumor cords, neoplasms forming cylindrical structures around blood vessels. Experimental data show that, in their avascular phase, cords grow up to a limit radius of about 100 microm, reaching a quasi-steady-state characterized by a necrotized area separating the tumor from the surrounding healthy tissue. Here we use a set of rules to formulate a model that describes how the dynamics of cord growth is controlled by the competition of tumor cells among themselves and with healthy cells for the acquisition of essential nutrients. The model takes into account the mechanical effects resulting from the interaction between the multiplying cancer cells and the surrounding tissue. We explore the influence of the relevant parameters on the tumor growth and on its final state. The model is also applied to investigate cord deformation in a region containing multiple nutrient sources and to predict the further complex growth of the tumor.