Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures

Modeling brain dynamics in brain tumor patients using the virtual brain

Presurgical planning for brain tumor resection aims at delineating eloquent tissue in the vicinity of the lesion to spare during surgery. To this end, noninvasive neuroimaging techniques such as functional MRI and diffusion-weighted imaging fiber tracking are currently employed. However, taking into account this information is often still insufficient, as the complex nonlinear dynamics of the brain impede straightforward prediction of functional outcome after surgical intervention. Large-scale brain network modeling carries the potential to bridge this gap by integrating neuroimaging data with biophysically based models to predict collective brain dynamics. As a first step in this direction, an appropriate computational model has to be selected, after which suitable model parameter values have to be determined. To this end, we simulated large-scale brain dynamics in 25 human brain tumor patients and 11 human control participants using The Virtual Brain, an open-source neuroinformatics platform. Local and global model parameters of the Reduced Wong-Wang model were individually optimized and compared between brain tumor patients and control subjects. In addition, the relationship between model parameters and structural network topology and cognitive performance was assessed. Results showed (1) significantly improved prediction accuracy of individual functional connectivity when using individually optimized model parameters; (2) local model parameters that can differentiate between regions directly affected by a tumor, regions distant from a tumor, and regions in a healthy brain; and (3) interesting associations between individually optimized model parameters and structural network topology and cognitive performance

Mathematical biomedicine and modeling avascular tumor growth

In this chapter we review existing continuum models of avascular tumor growth, explaining howthey are inter related and the biophysical insight that they provide. The models range in complexity and include one-dimensional studies of radiallysymmetric growth, and two-dimensional models of tumor invasion in which the tumor is assumed to comprise a single population of cells. We also present more detailed, multiphase models that allow for tumor heterogeneity. The chapter concludes with a summary of the different continuum approaches and a discussion of the theoretical challenges that lie ahead

ORGAN SPECIFIC VASCULAR RESPONSE TO FIBROSIS AFFECTS BREAST CANCER METASTATIC ORGANOTROPISM

The solid tumor microenvironment, pre-metastatic niche, and fibrotic environment are known to have significant biochemical and biomechanical similarities to the fibrotic environment. All have significantly increased levels of factors such as TGFβ, HIF1α, TNFα, PDGF, VEGF, FGF, interleukins and other growth factors that are known to be pro-tumorigenic. Clinical and basic science research has shown that fibrosis presents an environment that favors tumor growth, such as hepatocellular carcinoma being commonly preceded by liver cirrhosis, or bleomycin induced lung fibrosis enhancing pulmonary metastasis in mouse models of breast cancer. In addition to the evidence indicating that fibrosis enhances primary tumor growth and metastasis it is also well characterized that primary tumor metastasis has specific organotropism, for example breast cancer commonly spreads to the lungs, brain, bone, liver and lymph nodes. However, whether non-organtropic fibrosis can redirect metastasis to the damaged organ has not been investigated. To elucidate the fibrotic effect on tumor organotropism we induced fibrosis in the organotropic lungs and in the non-organotropic kidney of two mouse models of breast cancer, the 4T1 murine cancer cell line model and the genetic MMTV-Pymt model, both of which are known to metastasize. Using histopathology, microarrays, gene expression by polymerase chain reaction, ELISA, chemokine array, and in vitro experiments we demonstrate that despite the pro-tumorigenic environment, kidney fibrosis does not redirect metastasis to the non-organotropic damaged organ. However, mice with kidney fibrosis had increased metastasis to their lungs. Furthermore, we found that kidney fibrosis increases the circulating levels of the pro-angiogenic factor Angiopoietin 2 that increased vascular permeability of the lungs, but not the kidneys. In fact, while fibrotic lungs showed decreased expression of endothelial tight gap junction protein Claudin-5, the fibrotic kidneys had an elevated expression of Claudin-5. Our findings suggest that despite the similarities between fibrosis, the tumor microenvironment and the pre-metastatic niche, that while it can enhance tropic metastatic disease, it cannot redirect organotropism indicating that other factors must be involved in directing organotropism. Here we report that tumor organotropism may be a result of organ specific vascular responses to excess circulating factors and increased fibrotic factors. These findings indicate that organotropism is directly related to and as a result of organ specific vascular alterations

Determining the neurotransmitter concentration profile at active synapses

Establishing the temporal and concentration profiles of neurotransmitters during synaptic release is an essential step towards understanding the basic properties of inter-neuronal communication in the central nervous system. A variety of ingenious attempts has been made to gain insights into this process, but the general inaccessibility of central synapses, intrinsic limitations of the techniques used, and natural variety of different synaptic environments have hindered a comprehensive description of this fundamental phenomenon. Here, we describe a number of experimental and theoretical findings that has been instrumental for advancing our knowledge of various features of neurotransmitter release, as well as newly developed tools that could overcome some limits of traditional pharmacological approaches and bring new impetus to the description of the complex mechanisms of synaptic transmission