Katarzyna A. Rejniak

Hybrid models of tumor growth

Cancer is a complex, multiscale process in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The multiscale nature of cancer requires mathematical modeling approaches that can handle multiple intracellular and extracellular factors acting on different time and space scales. Hybrid models provide a way to integrate both discrete and continuous variables that are used to represent individual cells and concentration or density fields, respectively. Each discrete cell can also be equipped with submodels that drive cell behavior in response to microenvironmental cues. Moreover, the individual cells can interact with one another to form and act as an integrated tissue. Hybrid models form part of a larger class of individual‐based models that can naturally connect with tumor cell biology and allow for the integration of multiple interacting variables both intrinsically and extrinsically and are therefore perfectly suited to a systems biology approach to tumor growth. WIREs Syst Biol Med 2011 3 115–125 DOI: 10.1002/wsbm.102

Microenvironment driven invasion: a multiscale multimodel investigation.

Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional and morphological changes at the cellular and tissue scale. The importance of interactions between tumour cells and their microenvironment is currently of great interest in experimental as well as computational modelling. Both the immediate microenvironment (e.g. cell–cell signalling or cell–matrix interactions) and the extended microenvironment (e.g. nutrient supply or a host tissue structure) are thought to play crucial roles in both tumour progression and suppression. In this paper we focus on tumour invasion, as defined by the emergence of a fingering morphology, which has previously been shown to be dependent upon harsh microenvironmental conditions. Using three different modelling approaches at two different spatial scales we examine the impact of nutrient availability as a driving force for invasion. Specifically we investigate how cell metabolism (the intrinsic rate of nutrient consumption and cell resistance to starvation) influences the growing tumour. We also discuss how dynamical changes in genetic makeup and morphological characteristics, of the tumour population, are driven by extreme changes in nutrient supply during tumour development. The simulation results indicate that aggressive phenotypes produce tumour fingering in poor nutrient, but not rich, microenvironments. The implication of these results is that an invasive outcome appears to be co-dependent upon the evolutionary dynamics of the tumour population driven by the microenvironment.

Current Advances in Mathematical Modeling of Anti-Cancer Drug Penetration into Tumor Tissues

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Current trends in mathematical modeling of tumor–microenvironment interactions: a survey of tools and applications

In its simplest description, a tumor is comprised of an expanding population of transformed cells supported by a surrounding microenvironment termed the tumor stroma. The tumor microcroenvironment has a very complex composition, including multiple types of stromal cells, a dense network of various extracellular matrix (ECM) fibers interpenetrated by the interstitial fluid and gradients of several chemical species that either are dissolved in the fluid or are bound to the ECM structure. In order to study experimentally such complex interactions between multiple players, cancer is dissected and considered at different scales of complexity, such as protein interactions, biochemical pathways, cellular functions or whole organism studies. However, the integration of information acquired from these studies into a common description is as difficult as the disease itself. Computational models of cancer can provide cancer researchers with invaluable tools that are capable of integrating the complexity into organizing principles as well as suggesting testable hypotheses. We will focus in this Minireview on mathematical models in which the whole cell is a main modeling unit. We will present a current stage of such cell-focused mathematical modeling incorporating different stromal components and their interactions with growing tumors, and discuss what modeling approaches can be undertaken to complement the in vivo and in vitro experimentation.

A single cell-based model of the ductal tumour microarchitecture.

The preinvasive intraductal tumours, such as the breast or prostate carcinomas, develop in many different architectural forms. There are, however, no experimental models explaining why cancer cells grow in these various configurations. We use a mathematical model to compare different proliferative conditions that can lead to such distinct microarchitectures. In order to simulate different scenarios of tumour growth, we employed a single cell-based technique that allows us to model development of the whole tumour tissue by focusing on biomechanical processes of individual cells and on communication between cells and their microenvironment. Formation of four specific intraductal tumour patterns, micropapillary, cribriform, tufting and solid, are presented in this paper together with a discussion on gradual dedifferentiation of ductal epithelial cells that gives rise to these distinct carcinomas. We introduce two versions of our cell-based model to show that the obtained results do not depend on a particularly chosen cell structure.

Cellular modeling of cancer invasion: Integration of in silico and in vitro approaches

Cancer invasion is one of the hallmarks of cancer and a prerequisite for cancer metastasis. However, the invasive process is very complex, depending on multiple correlated intrinsic and environmental factors, and thus is difficult to study experimentally in a fully controlled way. Therefore, there is an increased demand for interdisciplinary integrated approaches combining laboratory experiments with multiscale in silico modeling. In this review, we will summarize current computational techniques applicable to model cancer invasion in silico, with a special focus on a class of individual‐cell‐based models developed in our laboratories. We also discuss their integration with traditional and novel in vitro experimentation, including new invasion assays whose design was inspired by computational modeling. J. Cell. Physiol. 227: 431–438, 2012.

A Computational Study of the Development of Epithelial Acini: II. Necessary Conditions for Structure and Lumen Stability

Simple epithelial tissues are organized as single layers of tightly packed cells that surround hollow lumens and form selective barriers separating different internal compartments of the body. The maintenance of epithelial structure and its function requires tight coordination and control of all the life processes of epithelial cells via cell-to-cell communication and signaling. These well-balanced cellular systems are, however, quite often disturbed by genetic or environmental cues that may lead to the formation of epithelial tumors (carcinomas). In fact, more than a half of all diagnosed tumors are initiated from epithelial cells. It is, therefore, important to gain a greater understanding of the factors that form and maintain the epithelial structure, as well as the features of the acinar structure that are modified during cancer development as observable in experimental and clinical research. We address these questions using the bio-mechanical model of the developing hollow epithelial acini introduced in Rejniak and Anderson (Bull. Math. Biol. 70:677–712, 2008). Here, we propose several scenarios involving various bio-mechanical interactions between neighboring cells that result in abnormal acinar development. Whenever possible, we compare our computational results with known experimental cases of mutant acini.

Pyruvate sensitizes pancreatic tumors to hypoxia-activated prodrug TH-302

BackgroundHypoxic niches in solid tumors harbor therapy-resistant cells. Hypoxia-activated prodrugs (HAPs) have been designed to overcome this resistance and, to date, have begun to show clinical efficacy. However, clinical HAPs activity could be improved. In this study, we sought to identify non-pharmacological methods to acutely exacerbate tumor hypoxia to increase TH-302 activity in pancreatic ductal adenocarcinoma (PDAC) tumor models.ResultsThree human PDAC cell lines with varying sensitivity to TH-302 (Hs766t > MiaPaCa-2 > SU.86.86) were used to establish PDAC xenograft models. PDAC cells were metabolically profiled in vitro and in vivo using the Seahorse XF system and hyperpolarized 13C pyruvate MRI, respectively, in addition to quantitative immunohistochemistry. The effect of exogenous pyruvate on tumor oxygenation was determined using electroparamagnetic resonance (EPR) oxygen imaging. Hs766t and MiaPaCa-2 cells exhibited a glycolytic phenotype in comparison to TH-302 resistant line SU.86.86. Supporting this observation is a higher lactate/pyruvate ratio in Hs766t and MiaPaCa xenografts as observed during hyperpolarized pyruvate MRI studies in vivo. Coincidentally, response to exogenous pyruvate both in vitro (Seahorse oxygen consumption) and in vivo (EPR oxygen imaging) was greatest in Hs766t and MiaPaCa models, possibly due to a higher mitochondrial reserve capacity. Changes in oxygen consumption and in vivo hypoxic status to pyruvate were limited in the SU.86.86 model. Combination therapy of pyruvate plus TH-302 in vivo significantly decreased tumor growth and increased survival in the MiaPaCa model and improved survival in Hs766t tumors.ConclusionsUsing metabolic profiling, functional imaging, and computational modeling, we show improved TH-302 activity by transiently increasing tumor hypoxia metabolically with exogenous pyruvate. Additionally, this work identified a set of biomarkers that may be used clinically to predict which tumors will be most responsive to pyruvate + TH-302 combination therapy. The results of this study support the concept that acute increases in tumor hypoxia can be beneficial for improving the clinical efficacy of HAPs and can positively impact the future treatment of PDAC and other cancers.

Linking changes in epithelial morphogenesis to cancer mutations using computational modeling.

Most tumors arise from epithelial tissues, such as mammary glands and lobules, and their initiation is associated with the disruption of a finely defined epithelial architecture. Progression from intraductal to invasive tumors is related to genetic mutations that occur at a subcellular level but manifest themselves as functional and morphological changes at the cellular and tissue scales, respectively. Elevated proliferation and loss of epithelial polarization are the two most noticeable changes in cell phenotypes during this process. As a result, many three-dimensional cultures of tumorigenic clones show highly aberrant morphologies when compared to regular epithelial monolayers enclosing the hollow lumen (acini). In order to shed light on phenotypic changes associated with tumor cells, we applied the bio-mechanical IBCell model of normal epithelial morphogenesis quantitatively matched to data acquired from the non-tumorigenic human mammary cell line, MCF10A. We then used a high-throughput simulation study to reveal how modifications in model parameters influence changes in the simulated architecture. Three parameters have been considered in our study, which define cell sensitivity to proliferative, apoptotic and cell-ECM adhesive cues. By mapping experimental morphologies of four MCF10A-derived cell lines carrying different oncogenic mutations onto the model parameter space, we identified changes in cellular processes potentially underlying structural modifications of these mutants. As a case study, we focused on MCF10A cells expressing an oncogenic mutant HER2-YVMA to quantitatively assess changes in cell doubling time, cell apoptotic rate, and cell sensitivity to ECM accumulation when compared to the parental non-tumorigenic cell line. By mapping in vitro mutant morphologies onto in silico ones we have generated a means of linking the morphological and molecular scales via computational modeling. Thus, IBCell in combination with 3D acini cultures can form a computational/experimental platform for suggesting the relationship between the histopathology of neoplastic lesions and their underlying molecular defects.

The Role of Tumor Tissue Architecture in Treatment Penetration and Efficacy: An Integrative Study

Despite the great progress that has been made in understanding cancer biology and the potential molecular targets for its treatment, the majority of drugs fail in the clinical trials. This may be attributed (at least in part) to the complexity of interstitial drug transport in the patient’s body, which is hard to test experimentally. Similarly, recent advances in molecular imaging have led to the development of targeted biomarkers that can predict pharmacological responses to therapeutic interventions. However, both the drug and biomarker molecules need to access the tumor tissue and be taken up into individual cells in concentrations sufficient to exert the desired effect. To investigate the process of drug penetration at the mesoscopic level we developed a computational model of interstitial transport that incorporates the biophysical properties of the tumor tissue, including its architecture and interstitial fluid flow, as well as the properties of the agents. This model is based on the method of regularized Stokeslets to describe the fluid flow coupled with discrete diffusion-advection-reaction equations to model the dynamics of the drugs. Our results show that the tissue cellular porosity and density influence the depth of penetration in a non-linear way, with sparsely packed tissues being traveled through more slowly than the denser tissues. We demonstrate that irregularities in the cell spatial configurations result in the formation of interstitial corridors that are followed by agents leading to the emergence of tissue zones with less exposure to the drugs. We describe how the model can be integrated with in vivo experiments to test the extravasation and penetration of the targeted biomarkers through the tumor tissue. A better understanding of tissue- or compound-specific factors that limit the penetration through the tumors is important for non-invasive diagnoses, chemotherapy, the monitoring of treatment responses, and the detection of tumor recurrence.