MBI Publications

MBI Publications for Avner Friedman (74)

  • P. Srinivasan, X. Liu and A. Friedman
    Hematocrit effects on nitric oxide flux over the surface of red blood cells
    (In Preparation)

    Abstract

  • H. Coskun, D. Kniss and A. Friedman
    Quantitative analysis of fat cell fate determination
    PNAS

    Abstract

  • H. Kang, A. Friedman and P. Nana-Sinkam
    A mathematical model for miR-9, let-7, and EMT in lung cancer
    (Submitted)

    Abstract

  • G. Cracium, A. Brown and A. Friedman
    A Dynamical System Model of Transport of Neurofilaments in Axons
    Journal of Theoretical BiologyVol. 237 No. 3 (2005) pp. 316-322

    Abstract

  • G. Cracium, B. Aguda and A. Friedman
    Mathematical Analysis of a Modular Network Coordinating the Cell Cycle and Apoptosis
    Mathematical Biosciences an dEngineeringVol. 2 No. 3 (2005) pp. 473-485

    Abstract

  • G. Cracium, A. Friedman and G. Cracium
    A Model of Intracellular Transport of Particles in an Axon
    Journal of Mathematical BiologyVol. 51 No. 2 (2005) pp. 217-246

    Abstract

  • A. Friedman and G. Cracium
    Approximate Traveling Waves in Linear Reaction-Hyperbolic Equations
    SIAM Journal on Mathematical AnalysisVol. 38 No. 3 (2006) pp. 741-758

    Abstract

  • A. Friedman, G. Fulci, E. Chiocca , J. Tian and J. Wang
    Glioma Virotherapy: The effects of innate immune suppression and increased viral replication capacity
    Cancer ResearchVol. 66 (2006) pp. 2314-2319

    Abstract

  • P. Goel, J. Sneyd and A. Friedman
    Homogenization of the Cell Cytoplasm: The Calcium Bidomain Equations
    SIAM Multiscale Modeling and SimulationVol. 5 No. 4 (2006) pp. 1045-1062

    Abstract

  • A. Friedman, G. Fulci, E. Chiocca , J. Tian and J. Wang
    Glioma Virotherapy: The effects of innate immune suppression and increased viral replication capacity
    Cancer ResearchVol. 66 (2006) pp. 2314-2319

    Abstract

  • X. Liu, P. Srinivasan, E. Collard, P. Grajdeanu, J. Zweier and A. Friedman
    Oxygen regulates the flux of nitric oxide diffusion across the vascular wall,
    Conference Proceedings, American Heart Association Scientific Sessions (2007)

    Abstract

  • B. Szomolay, T. Eubank, R. Roberts, C. Marsh and A. Friedman
    Modeling Inhibition of breast cancer growth by GM-CSF: A mathematical model
    Bulletin of Mathematical Biology (2008) (Submitted)

    Abstract

  • Y. Kim, S. Lawler, M. Nowicki, E. Chiocca and A. Friedman
    A mathematical model of Brain tumor: pattern formation of glioma cells outside the tumor spheroid core
    J Theo BiolVol. 260 (2008) pp. 259-371 (Submitted)

    Abstract

  • P. Grajdeanu, R. Schugart, A. Friedman, C. Valentine and B. Rovin
    A mathematical model of venous neointimal hyperplasia
    Theoretical Biology and Medical ModellingVol. 5 (2008)

    Abstract

  • E. Green and A. Friedman
    The extensional flow of a thin sheet of incompressible, transversely isotropic fluid
    European Journal of Applied MathematicsVol. 19 No. 3 (2008) pp. 225-257

    Abstract

    Motivated by the aim of modelling the mechanical behaviour of biological gels (such as collagen gels) which have a fibrous microstructure, we consider the extensional flow of a thin two-dimensional film of incompressible, transversely isotropic viscous fluid. Neglecting inertia, and the effects of gravity and surface tension, leading-order equations are derived from a perturbation expansion of the full flow problem in powers of the (small) inverse aspect ratio. The existence and uniqueness of the solution of the reduced system of equations for small times is then proven. Special cases, in which the solution may be determined explicitly, are considered and we discuss the physical interpretation of the results.
  • Y. Kim, S. Lim, S. Raman, O. Simonetti and A. Friedman
    Blood flow in a compliant vessel by the immersed boundary method
    Annals of Biomedical Engineering (2008) (Submitted)

    Abstract

  • R. Zhao, A. Friedman, R. Schugart and C. Sen
    Wound angiogenesis as a function of tissue oxygen tension - a mathematical model
    PNAS USAVol. 105 (2008) pp. 2628-2633

    Abstract

  • A. Friedman, J. Turner and B. Szomolay
    A model on the influence of age on immunity with Mycobacterium tuberculosis
    Exp. GerontolVol. 43 No. 4 (2008) pp. 275-285

    Abstract

  • B. Aguda, Y. Kim, M. Piper-Hunter, A. Friedman and C. Marsh
    MicroRNA Regulation of a Cancer Network: Consequences of the Feedback Loops Involving miR-17-92, E2F, and Myc
    PNASVol. 105 No. 50 (2008) pp. 19678-19683

    Abstract

  • P. Grajdeanu, R. Schugart, A. Friedman, D. Birmingham, D. Birmingham and B. Rovin
    The dynamics of SLE nephritis under immunosuppressive therapy: A mathematical model
    (2008) (Submitted)

    Abstract

  • P. Grajdeanu, R. Schugart, A. Friedman, C. Valentine, A. Agarwal and B. Rovin
    A mathematical model of venous neointimal hyperplasia formation
    Theoretical Biology and Medical ModellingVol. 5 No. 2 (2008)

    Abstract

  • X. Liu, P. Srinivasan, E. Collard, P. Grajdeanu, J. Zweier and A. Friedman
    Nitric oxide diffusion rate is reduced in the aortic wall
    Biophysical JournalVol. 94 No. 5 (2008) pp. 1880-1889

    Abstract

  • B. Aguda, Y. Kim, M. Piper-Hunter, A. Friedman and C. Marsh
    MicroRNA Regulation of a Cancer Network: Consequences of the Feedback Loops Involving miR-17-92, E2F, and Myc
    PNASVol. 105 No. 50 (2008) pp. 19678-19683

    Abstract

    The transcription factors E2F and Myc participate in the control of cell proliferation and apoptosis, and can act as oncogenes or tumor suppressors depending on their levels of expression. Positive feedback loops in the regulation of these factors are predicted-and recently shown experimentally-to lead to bistability, which is a phenomenon characterized by the existence of low and high protein levels ("off" and "on" levels, respectively), with sharp transitions between levels being inducible by, for example, changes in growth factor concentrations. E2F and Myc are inhibited at the posttranscriptional step by members of a cluster of microRNAs (miRs) called miR-17-92. In return, E2F and Myc induce the transcription of miR-17-92, thus forming a negative feedback loop in the interaction network. The consequences of the coupling between the E2F/Myc positive feedback loops and the E2F/Myc/miR-17-92 negative feedback loop are analyzed using a mathematical model. The model predicts that miR-17-92 plays a critical role in regulating the position of the off-on switch in E2F/Myc protein levels, and in determining the on levels of these proteins. The model also predicts large-amplitude protein oscillations that coexist with the off steady state levels. Using the concept and model prediction of a "cancer zone," the oncogenic and tumor suppressor properties of miR-17-92 is demonstrated to parallel the same properties of E2F and Myc.
  • P. Grajdeanu, R. Schugart, A. Friedman, C. Valentine, A. Agarwal and B. Rovin
    A mathematical model of venous neointimal hyperplasia formation
    Theoretical Biology and Medical ModellingVol. 5 No. 2 (2008)

    Abstract

    In hemodialysis patients, the most common cause of vascular access failure is neointimal hyperplasia of vascular smooth muscle cells at the venous anastomosis of arteriovenous fistulas and grafts. The release of growth factors due to surgical injury, oxidative stress and turbulent flow has been suggested as a possible mechanism for neointimal hyperplasia.
    In this work, we construct a mathematical model which analyzes the role that growth factors might play in the stenosis at the venous anastomosis. The model consists of a system of partial differential equations describing the influence of oxidative stress and turbulent flow on growth factors, the interaction among growth factors, smooth muscle cells, and extracellular matrix, and the subsequent effect on the stenosis at the venous anastomosis, which, in turn, affects the level of oxidative stress and degree of turbulent flow. Computer simulations suggest that our model can be used to predict access stenosis as a function of the initial concentration of the growth factors inside the intimal-luminal space.
    The proposed model describes the formation of venous neointimal hyperplasia, based on pathogenic mechanisms. The results suggest that interventions aimed at specific growth factors may be successful in prolonging the life of the vascular access, while reducing the costs of vascular access maintenance. The model may also provide indication of when invasive access surveillance to repair stenosis should be undertaken.
  • X. Liu, P. Srinivasan, E. Collard, P. Grajdeanu, J. Zweier and A. Friedman
    Nitric Oxide Diffusion Rate is Reduced in the Aortic Wall
    Biophysical JournalVol. 94 No. 5 (2008) pp. 1880-1889q

    Abstract

    Endogenous nitric oxide (NO) plays important physiological roles in the body. As a small diatomic molecule, NO has been assumed to freely diffuse in tissues with a diffusion rate similar to that in water. However, this assumption has not been tested experimentally. In this study, a modified Clark-type NO electrode attached with a customized aorta holder was used to directly measure the flux of NO diffusion across the aortic wall at 37°C. Experiments were carefully designed for accurate measurements of the apparent NO diffusion coefficient D and the partition coefficient α in the aortic wall. A mathematical model was presented for analyzing experimental data. It was determined that α = 1.15 ± 0.11 and D = 848 ± 45 μm2/s (n = 12). The NO diffusion coefficient in the aortic wall is nearly fourfold smaller than the reported diffusion coefficient in solution at 37°C, indicating that NO diffusion in the vascular wall is no longer free, but markedly dependent on the environment in the tissue where these NO molecules are. These results imply that the NO diffusion rate in the vascular wall may be upregulated and downregulated by certain physiological and/or pathophysiological processes affecting the composition of tissues.
  • Y. Kim, S. Lawler, M. Nowicki, E. Chiocca and A. Friedman
    A mathematical model of Brain tumor: pattern formation of glioma cells outside the tumor spheroid core
    J Theo BiolVol. 260 (2009) pp. 259-371

    Abstract

    Glioblastoma is the most common and the most aggressive type of brain cancer. The median survival time from the time of diagnosis is approximately one year. Invasion of glioma cells from the core tumor into the surrounding brain tissue is a major reason for treatment failure: these migrating cells are not eliminated in surgical resection and cause tumor recurrence. Variations are seen in number of invading cells, and in the extent and patterns of migration. Cells can migrate diffusely and can also be seen as clusters of cells distinct from the main tumor mass. This kind of clustering is also evident in vitro using 3D spheroid models of glioma invasion. This has been reported for U87 cells stably expressing the constitutively active EGFRVIII mutant receptor, often seen expressed in glioblastoma. In this case the cells migrate as clusters rather than as single cells migrating in a radial pattern seen in control wildtype U87 cells. Several models have been suggested to explain the different modes of migration, but none of them, so far, has explored the important role of cell€“cell adhesion. The present paper develops a mathematical model which includes the role of adhesion and provides an explanation for the various patterns of cell migration. It is shown that, depending on adhesion, haptotactic, and chemotactic parameters, the migration patterns exhibit a gradual shift from branching to dispersion, as has been reported experimentally.
  • J. Day, A. Friedman and L. Schlesinger
    Modeling the immune rheostat of macrophages in the lung in response to infection
    Proc. Natl Acad Sci USAVol. 106 No. 27 (2009) pp. 11246-11251

    Abstract

    In the lung, alternatively activated macrophages (AAM) form the first line of defense against microbial infection. Due to the highly regulated nature of AAM, the lung can be considered as an immunosuppressive organ for respiratory pathogens. However, as infection progresses in the lung, another population of macrophages, known as classically activated macrophages (CAM) enters; these cells are typically activated by IFN-. CAM are far more
    effective than AAM in clearing the microbial load, producing proinflammatory cytokines and antimicrobial defense mechanisms necessary to mount an adequate immune response. Here, we are concerned with determining the first time when the population of CAM becomes more dominant than the population of AAM. This proposed €˜€˜switching time€™€™ is explored in the context of Mycobacterium tuberculosis (MTb) infection. We have developed a mathematical model that describes the interactions among cells, bacteria, and cytokines involved in the activation of both AAM and CAM. The model, based on a system of differential equations, represents a useful tool to analyze strategies for reducing the switching time, and to generate hypotheses for experimental testing.
  • C. Xue, A. Friedman and C. Sen
    A mathematical model of ischemic cutaneous wounds
    PNASVol. 106 No. 39 (2009) pp. 16782-16787

    Abstract

    Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia, primarily caused by peripheral artery diseases, represents a major complicating factor in cutaneous wound healing. In this work, we sought to develop a mathematical model of ischemic dermal wounds. The model consists of a coupled system of partial differential equations in the partially healed region, with the wound boundary as a free boundary. The extracellular matrix (ECM) is assumed to be viscoelastic, and the free boundary moves with the velocity of the ECM at the boundary. The model equations involve the concentration of oxygen, PDGF and VEGF, the densities of macrophages, fibroblasts, capillary tips and sprouts, and the density and velocity of the ECM. Simulations of the model demonstrate how ischemic conditions may limit macrophage recruitment to the wound-site and impair wound closure. The results are in general agreement with experimental findings.
  • Y. Kim, S. Lim, S. Raman, O. Simonetti and A. Friedman
    Blood flow in a compliant vessel by the immersed boundary method
    Annals of Biomedical EngineeringVol. 37 No. 5 (2009) pp. 927-942

    Abstract

    In this paper we develop a computational approach to analyze hemodynamics in the aorta; this may serve as a useful tool in the development of noninvasive methods to detect early onset of diseases such as aneurysms and stenosis in major blood vessels. We introduce a mathematical model which describes the interaction of blood flow with the aortic wall; this model is based on the immersed boundary method. A two-dimensional vessel model is constructed, the velocity at the inlet is prescribed based on the information from the Magnetic Resonance Imaging data measured in the aorta of a healthy subject, and the velocity at the outlet is prescribed by driving the pressure level reproduced from the literature. The mathematical model is validated by comparing with well-known solutions of the viscous incompressible Navierâ???Stokes equations, i.e., Womersley flow. The hysteresis behavior in the pressureâ???diameter relation is observed when the viscoelastic material property of the arterial wall is taken into consideration. Five different shapes of aortic wall are considered for comparison of the flow patterns inside the aorta: one for the normal aorta, two for the dilated aorta, and two for the constrictive aorta.
  • A. Matzavinos, C. Kao, E. Green, A. Sutradhar, M. Miller and A. Friedman
    Modelling oxygen transport in surgical tissue transfer
    PNASVol. 106 No. 29 (2009) pp. 12091-12096

    Abstract

  • H. Coskun, T. Summerfield, D. Kniss and A. Friedman
    Mathematical Modeling of Preadipocyte Fate Determination
    Journal of Theoretical BiologyVol. 265 No. 1 (2010)

    Abstract

  • Y. Kim and A. Friedman
    Interaction of tumor with its microenvironment : A Mathematical Model
    Bulletin of Mathematical BiologyVol. 72 No. 5 (2010) pp. 1029-1068

    Abstract

  • Y. Kim and A. Friedman
    Interaction of tumor with its microenvironment: A Mathematical Model
    Bulletin of Mathematical BiologyVol. 72 No. 5 (2010) pp. 1029-1068

    Abstract

    This paper is concerned with early development of transformed epithelial cells (TECs) in the presence of fibroblasts in the tumor microenvironment. These two types of cells interact by means of cytokines such as transforming growth factor (TGF-beta) and epidermal growth factor (EGF) secreted, respectively, by the TECs and the fibroblasts. As this interaction proceeds, TGF-beta induces fibroblasts to differentiate into myofibroblasts which secrete EGF at a larger rate than fibroblasts. We monitor the entire process in silico, in a setup which mimics experiments in a Tumor Chamber Invasion Assay, where a semi-permeable membrane coated by extracellular matrix (ECM) is placed between two chambers, one containing TECs and another containing fibroblasts. We develop a mathematical model, based on a system of PDEs, that includes the interaction between TECs, fibroblasts, myofibroblasts, TGF-beta, and EGF, and we show how model parameters affect tumor progression. The model is used to generate several hypotheses on how to slow tumor growth and invasion. In an Appendix, it is proved that the mathematical model has a unique global in-time solution.
  • Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman
    Transformed Epithelias cells (TEC) and fibroblasts/myofibroblasts interaction in Breast Tumor: A Mathematical Model and Experiments
    Journal of Mathematical BiologyVol. 61 No. 3 (2010) pp. 401-421

    Abstract

    It is well known that tumor and its microenvironment, or stroma, interact with each other and that this interaction plays a critical role in tumor initiation, growth, and metastasis. This interaction consists of complex relations between tumor cells, stromal cells such as fibroblasts, epithelial cells and immunocytes, the vascular system, the extracellular matrix, and cytokines secreted by the cells. Understanding these relationships may lead to new therapeutic approaches to cancer. In the present paper, we consider tumor-stroma crosstalk in a simple in vitro situation which involves interaction between tumor epithelial cells from breast cancer and a microenvironment consisting of just fibroblasts. The two populations of cells are separated by a semi-permeable membrane that allows only cytokines to cross over. We develop a mathematical model that includes two critical growth factors: TGF-beta, produced by the tumor cells, and EGF, secreted by the fibroblasts. The TGF-beta modifies the microenvironment by transforming fibroblasts into myofibroblasts. Myofibroblasts secrete higher concentrations of EGF than fibroblasts, thereby, increasing the proliferation of tumor cells. Thus already in this simple setup one sees a mutual interaction between tumor cells and their microenvironment. We conducted experiments which show good agreement with the model's simulations, hence confirming the model's ability to predict aspects of tumor cell behavior in response to signaling from fibroblasts.
  • X. Liu, P. Srinivasan, E. Collard, P. Grajdeanu, K. Lok, S. Boyle, A. Friedman and J. Zweier
    Oxygen regulates the effective diffusion distance of nitric oxide in the aortic wall
    Free Radic Biol MedVol. 48 No. 4 (2010) pp. 554-559

    Abstract

    Endothelium-derived nitric oxide (NO) is critical in maintaining vascular tone. Accumulating evidence shows that NO bioavailability is regulated by oxygen concentration. However, it is unclear to what extent the oxygen concentration regulates NO bioavailability in the vascular wall. In this study, a recently developed experimental setup was used to measure the NO diffusion flux across the aortic wall at various oxygen concentrations. It was observed that for a constant NO concentration at the endothelial surface, the measured NO diffusion flux out of the adventitial surface at [O2] = 0 μM is around fivefold greater than at [O2] = 150 μM, indicating that NO is consumed in the aortic wall in an oxygen-dependent manner. Analysis of experimental data shows that the rate of NO consumption in the aortic wall is first order with respect to [NO] and first order with respect to [O2], and the rate constant k1 was determined as (4.0 ± 0.3) — 103 Mˆ’1 sˆ’1. Computer simulations demonstrate that NO concentration distribution significantly changes with oxygen concentration and the effective NO diffusion distance at low oxygen level ([O2] ‰ 25 μM) is significantly longer than that at high oxygen level ([O2] = 200 μM). These results suggest that oxygen-dependent NO consumption may play an important role in dilating blood vessels during hypoxia by increasing the effective NO diffusion distance.
  • P. Grajdeanu, R. Schugart, A. Friedman, D. Birmingham and B. Rovin
    Mathematical framework for human SLE Nephritis: disease dynamics and urine biomarkers
    Theoretical Biology and Medical ModellingVol. 7 No. 14 (2010)

    Abstract

    Although the prognosis for Lupus Nephritis (LN) has dramatically improved with aggressive immunosuppressive therapies, these drugs carry significant side effects. To improve the effectiveness of these drugs, biomarkers of renal flare cycle could be used to detect the onset, severity, and responsiveness of kidney relapses, and to modify therapy accordingly. However, LN is a complex disease and individual biomarkers have so far not been sufficient to accurately describe disease activity. It has been postulated that biomarkers would be more informative if integrated into a pathogenic-based model of LN.
    This work is a first attempt to integrate human LN biomarkers data into a model of kidney inflammation. Our approach is based on a system of differential equations that capture, in a simplified way, the complexity of interactions underlying disease activity. Using this model, we have been able to fit clinical urine biomarkers data from individual patients and estimate patient-specific parameters to reproduce disease dynamics, and to better understand disease mechanisms. Furthermore, our simulations suggest that the model can be used to evaluate therapeutic strategies for individual patients, or a group of patients that share similar data patterns.
    We show that effective combination of clinical data and physiologically based mathematical modeling may provide a basis for more comprehensive modeling and improved clinical care for LN patients.
  • J. Day, L. Schlesinger and A. Friedman
    Tuberculosis research: Going forward with a powerful "Translation Systems Biology" approach
    Tuberculosis (Edinb)Vol. 90 No. 1 (2010) pp. 7-8

    Abstract

    Due to the complexity of the immune response to a Mycobacterium tuberculosis infection, identifying new, effective therapies and vaccines to combat it has been a problematic issue. Although many advances have been made in understanding particular mechanisms involved, they have, to date, proved insufficient to provide real breakthroughs in this area of tuberculosis research. The term €œTranslational Systems Biology€? has been formally proposed to describe the use of experimental findings combined with mathematical modeling and/or engineering principles to understand complex biological processes in an integrative fashion for the purpose of enhancing clinical practice. This opinion piece discusses the importance of using a translational systems biology approach for tuberculosis research as a means by which to go forward with the potential for significant breakthroughs to occur.
  • A. Friedman, B. Hu and C. Xue
    Analysis of a mathematical model of ischemic cutaneous wounds
    SIAM J. Math. Anal.Vol. 42 No. 5 (2010) pp. 2013-2040

    Abstract

  • Y. Kim, A. Friedman, J. Wallace, F. Li and M. Ostrowski
    Transformed Epithelial cells (TEC) and fibroblasts/myofibroblasts interaction in Breast Tumor: A Mathematical Model and Experiments
    Journal of Mathematical BiologyVol. 61 No. 3 (2010)

    Abstract

  • H. Jain, S. Clinton, A. Bhinder and A. Friedman
    Mathematical modeling of prostate cancer progression in response to androgen ablation therapy
    Proc Natl Acad Sci.Vol. 108 No. 49 (2011) pp. 19701-19706

    Abstract

  • M. Eisenberg, Y. Kim, R. Li, W. Ackerman, D. Kniss and A. Friedman
    Modeling the effects of myoferlin on tumor cell invasion
    Proc Natl Acad Sci USAVol. 108 No. 50 (2011) pp. 20078-20083

    Abstract

  • B. Aguda, Y. Kim, H. Kim, A. Friedman and H. Fine
    Qualitative network modeling of the MYC-p53 control system of cell proliferation and differentiation
    Biophysical JournalVol. 101 No. 9 (2011) pp. 2082-2091

    Abstract

  • Y. Kim, S. Roh, S. Lawler and A. Friedman
    miR451 and AMPK mutual antagonism in glioma cells migration and proliferation
    PLoS OneVol. 6 No. 12 (2011)

    Abstract

  • A. Friedman and Y. Kim
    Tumor cells proliferation and migration under the influence of their microenvironment
    Mathematical Biosciences and EngineeringVol. 8 No. 2 (2011) pp. 373-385

    Abstract

    It is well known that tumor microenvironment affects tumor growth and metastasis: Tumor cells may proliferate at different rates and migrate in different patterns depending on the microenvironment in which they are embedded. There is a huge literature that deals with mathematical models of tumor growth and proliferation, in both the avascular and vascular phases. In particular, a review of the literature of avascular tumor growth (up to 2006) can be found in Lolas [8] (G. Lolas, Lecture Notes in Mathematics, Springer Berlin / Heidelberg, 1872, 77 (2006)). In this article we report on some of our recent work. We consider two aspects, proliferation and of migration, and de- scribe mathematical models based on in vitro experiments. Simulations of the models are in agreement with experimental results. The models can be used to generate hypotheses regarding the development of drugs which will confine tumor growth.
  • J. Day, A. Friedman and L. Schlesinger
    Modeling the host response to inhalation anthrax
    J Theor BiolVol. 276 No. 1 (2011) pp. 199-208

    Abstract

    Inhalation anthrax, an often fatal infection, is initiated by endospores of the bacterium Bacillus anthracis, which are introduced into the lung. To better understand the pathogenesis of an inhalation anthrax infection, we propose a two-compartment mathematical model that takes into account the documented early events of such an infection. Anthrax spores, once inhaled, are readily taken up by alveolar phagocytes, which then migrate rather quickly out of the lung and into the thoracic/mediastinal lymph nodes. En route, these spores germinate to become vegetative bacteria. In the lymph nodes, the bacteria kill the host cells and are released into the extracellular environment where they can be disseminated into the blood stream and grow to a very high level, often resulting in the death of the infected person. Using this framework as the basis of our model, we explore the probability of survival of an infected individual. This is dependent on several factors, such as the rate of migration and germination events and treatment with antibiotics.
  • A. Friedman and C. Xue
    A mathematical model of chronic wounds
    Mathematical Biosciences and EngineeringVol. 8 No. 2 (2011) pp. 253-261

    Abstract

  • A. Friedman and A. Yakubu
    Fatal disease and demographic Allee effect: population persistence and extinction
    Journal of Biological Dynamics (2011) (In Press)

    Abstract

  • H. Jain, S. Clinton, A. Bhinder and A. Friedman
    Impact of androgen ablation treatment on mutation acquisition in prostate cancer
    Proc Natl Acad Sci (2011) (In Press)

    Abstract

  • M. Eisenberg, Y. Kim, R. Li, W. Ackerman, D. Kniss and A. Friedman
    Mechanistic modeling of a novel cancer protein: myoferlin effects on tumor cell invasion
    Proc Natl Acad SciVol. 108 No. 50 (2011) pp. 20078-20083

    Abstract

  • E. Green, A. Bassom and A. Friedman
    A mathematical model for cell-induced gel compaction in vitro
    Mathematical Models and Methods in Applied Sciences (2012) (Accepted)

    Abstract

  • A. Friedman, B. Hu and C. Xue
    A three dimensional model of chronic wound healing: analysis and computation
    DCDS-B (2012) (In Preparation)

    Abstract

  • C. Xue, C. Chou, C. Kao, C. Sen and A. Friedman
    Propagation of Cutaneous Thermal Injury: A Mathematical Model
    Wound Repair and RegenVol. 20 No. 1 (2012) pp. 114-122

    Abstract

  • B. Szomolay, T. Eubank, R. Roberts, C. Marsh and A. Friedman
    Modeling inhibition of breast cancer growth by GM-CSF
    J. of Theor. Biol. (2012) (Accepted)

    Abstract

  • J. Tian, A. Friedman, J. Wang and E. Chiocca
    Modeling the Effects of Resection, Radiation and Chemotherapy in Glioblastoma
    Journal of Neuro-OncologyVol. 91 No. 3 (2012) pp. 287-293

    Abstract

  • J. Day, A. Friedman and L. Schlesinger
    Modeling the immune rheostat of macrophages in the lung in response to infection.
    Proc. Natl Acad Sci USAVol. 106 No. 27 (2012) pp. 11246-11251

    Abstract

  • P. Budu-Grajdeanu, R. Schugart, A. Friedman, D. Birmingham and B. Rovin
    Predicting renal interstitial inflammation levels using urine biomarkers and artificial neural networks
    (2012) (In Preparation)

    Abstract

  • C. Xue, C. Chou, C. Kao, C. Sen and A. Friedman
    Propagation of Cutaneous Thermal Injury: A Mathematical Model
    Wound Repair and RegenVol. 20 No. 1 (2012) pp. 114-122

    Abstract

  • C. Xue, A. Friedman and B. Hu
    A three dimensional model of chronic wound healing: analysis and computation
    DCDS-B (2012) (Submitted)

    Abstract

  • H. Jain and A. Friedman
    Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy
    Discrete Cont Dyn-B (2012) (Under Revision)

    Abstract

  • P. Goel, A. Sherman and A. Friedman
    Multiscale modeling of electrical and intracellular activity in the pancreas: The islet Tridomain equations
    SIAM Multiscale Modeling and SimulationVol. 7 (2012) pp. 1609-1642

    Abstract

  • D. Chen and A. Friedman
    Analysis of a two-phase free boundary problem for a parabolic-hyperbolic system: an application to tumor growth.
    (2012) (Submitted)

    Abstract

  • R. Leander, S. Dai, L. Schlesinger and A. Friedman
    A Mathematical Model of CR3/TLR2 Crosstalk in the context of Francisella Tularensis infection
    PLoS Comput Biol (2012) (Under Revision)

    Abstract

  • R. Leander and A. Friedman
    Modulation of the cAMP response by G alpha i and G beta gamma: a computational study of G protein signaling in immune cells
    PLoS One (2012) (Under Review)

    Abstract

  • D. Chen, J. Roda, C. Marsh, T. Eubank and A. Friedman
    Hypoxia Inducible Factors-mediated inhibition of cancer by GM-CSF: A mathematical model
    (2012) (Under Review)

    Abstract

  • D. Chen, J. Roda, C. Marsh, T. Eubank and A. Friedman
    Hypoxia inducible factors mediated-inhibition of cancer by GM-CSF: A mathematical model
    Bulletin of Mathematical Biology (2012)

    Abstract

    Under hypoxia, tumor cells, and tumor-associated macrophages produce VEGF (vascular endothelial growth factor), a signaling molecule that induces angiogenesis. The same macrophages, when treated with GM-CSF (granulocyte/macrophage colony-stimulating factor), produce sVEGFR-1 (soluble VEGF receptor-1), a soluble protein that binds with VEGF and inactivates its function. The production of VEGF by macrophages is regulated by HIF-1α (hypoxia inducible factor-1α), and the production of sVEGFR-1 is mediated by HIF-2α. Recent experiments measured the effect of inhibiting tumor growth by GM-CSF treatment in mice with HIF-1α-de?cient or HIF-2α-de?cient macrophages. In the present paper, we represent these experiments by a mathematical model based on a system of partial differential equations. We show that the model simulations agree with the above experiments. The model can then be used to suggest strategies for inhibiting tumor growth. For example, the model qualitatively predicts the extent to which GM-CSF treatment in combination with a small molecule inhibitor that stabilizes HIF-2α will reduce tumor volume and angiogenesis.
  • D. Chen and A. Friedman
    A two-phase free boundary problem with discontinuous velocity: Application to tumor model
    Journal of Mathematical Analysis and Applications (2012)

    Abstract

    We consider a two-phase free boundary problem consisting of a hyperbolic equation for w and a parabolic equation for u, where w and u represent, respectively, densities of cells and cytokines in a simpli?ed tumor growth model. The tumor region Ω(t) is enclosed by the free boundary Γ(t), and the exterior of the tumor, D(t), consists of a healthy normal tissue. Due to cancer cells proliferation, the convective velocity ~v of cells is discontinuous across the free boundary; the motion of the free boundary Γ(t) is determined by ~v. We prove the existence and uniqueness of a solution to this system in the radially symmetric case for a small time interval 0 t T, and apply the analysis to the full tumor growth model.
  • H. Kang, M. Crawford, M. Fabbri, G. Nuovo, M. Garofalo, P. Nana-Sinkam and A. Friedman
    A mathematical model for microRNA in lung cancer
    PLoS OneVol. 8 No. 1 (2013)

    Abstract

    Lung cancer is the leading cause of cancer-related deaths worldwide. Lack of early detection and limited options for targeted therapies are both contributing factors to the dismal statistics observed in lung cancer. Thus, advances in both of these areas are likely to lead to improved outcomes. MicroRNAs (miRs or miRNAs) represent a class of non-coding RNAs that have the capacity for gene regulation and may serve as both diagnostic and prognostic biomarkers in lung cancer. Abnormal expression patterns for several miRNAs have been identified in lung cancers. Specifically, let-7 and miR-9 are deregulated in both lung cancers and other solid malignancies. In this paper, we construct a mathematical model that integrates let-7 and miR-9 expression into a signaling pathway to generate an in silico model for the process of epithelial mesenchymal transition (EMT). Simulations of the model demonstrate that EGFR and Ras mutations in non-small cell lung cancers (NSCLC), which lead to the process of EMT, result in miR-9 upregulation and let-7 suppression, and this process is somewhat robust against random input into miR-9 and more strongly robust against random input into let-7. We elected to validate our model in vitro by testing the effects of EGFR inhibition on downstream MYC, miR-9 and let-7a expression. Interestingly, in an EGFR mutated lung cancer cell line, treatment with an EGFR inhibitor (Gefitinib) resulted in a concentration specific reduction in c-MYC and miR-9 expression while not changing let-7a expression. Our mathematical model explains the signaling link among EGFR, MYC, and miR-9, but not let-7. However, very little is presently known about factors that regulate let-7. It is quite possible that when such regulating factors become known and integrated into our model, they will further support our mathematical model.
  • E. Martin, A. Friedman and W. Lo
    Mathematical Model of Colitis-associated Colon Cancer
    Journal of Theoretical BiologyVol. 317 (2013) pp. 2. 20-29

    Abstract

    As a result of chronic inflammation of their colon, patients with ulcerative colitis or Crohn's disease are at risk of developing colon cancer. In this paper, we consider the progression of colitis-associated colon cancer. Unlike normal colon mucosa, the inflammed colon mucosa undergoes genetic mutations, affecting, in particular, tumor suppressors TP53 and adenomatous polyposis coli (APC) gene. We develop a mathematical model that involves these genes, under chronic inflammation, as well as NF-?ºB, ?²-catenin, MUC1 and MUC2. The model demonstrates that increased level of cells with TP53 mutations results in abnormal growth and proliferation of the epithelium; further increase in the epithelium proliferation results from additional APC mutations. The model may serve as a conceptual framework for further data-based study of the early stage of colon cancer.
  • K. Liao, X. Bai and A. Friedman
    The role of CD200-CD200R in tumor immune evasion
    J. Theor. Biol. (2013) (Accepted)

    Abstract

    CD200 is a cell membrane protein that interacts with CD200 receptor (CD200R) of myeloid lineage cells. During tumor initiation and progression, CD200-positive tumor cells can interact with M1 and M2 macrophages through CD200-CD200R-compex, and downregulate IL-10 and IL-12 productions secreted primarily by M2 and M1 macrophages, respectively. In the tumor microenvironment, IL-10 inhibits the activation of cytotoxic T lymphocytes (CTL), while IL-12 enhances CTL activation. In this paper, we used a system approach to determine the combined effect of CD200-CD200R interaction on tumor proliferation by developing a mathematical model. We demonstrate that blocking CD200 on tumor cells may have opposite effects on tumor proliferation depending on the €œaffinity€? of the macrophages to form the CD200-CD200R-complex with tumor cells. Our results help understanding the complexities of tumor microenvironment.
  • K. Liao, X. Bai and A. Friedman
    The role of CD200-CD200R in tumor immune evasion.
    Journal of theoretical biologyVol. 328 (2013) pp. 65-76

    Abstract

    CD200 is a cell membrane protein that interacts with CD200 receptor (CD200R) of myeloid lineage cells. During tumor initiation and progression, CD200-positive tumor cells can interact with M1 and M2 macrophages through CD200-CD200R-compex, and downregulate IL-10 and IL-12 productions secreted primarily by M2 and M1 macrophages, respectively. In the tumor microenvironment, IL-10 inhibits the activation of cytotoxic T lymphocytes (CTL), while IL-12 enhances CTL activation. In this paper, we used a system approach to determine the combined effect of CD200-CD200R interaction on tumor proliferation by developing a mathematical model. We demonstrate that blocking CD200 on tumor cells may have opposite effects on tumor proliferation depending on the "affinity" of the macrophages to form the CD200-CD200R-complex with tumor cells. Our results help understanding the complexities of tumor microenvironment.
  • W. Lo, R. Arsenescu and A. Friedman
    Mathematical model of the roles of T cells in inflammatory bowel disease.
    Bulletin of mathematical biologyVol. 75 No. 9 (2013) pp. 1417-33

    Abstract

    Gut mucosal homeostasis depends on complex interactions among the microbiota, the intestinal epithelium, and the gut associated immune system. A breakdown in some of these interactions may precipitate inflammation. Inflammatory bowel diseases, Crohn's disease, and ulcerative colitis are chronic inflammatory disorders of the gastrointestinal tract. The initial stages of disease are marked by an abnormally high level of pro-inflammatory helper T cells, Th1. In later stages, Th2 helper cells may dominate while the Th1 response may dampen. The interaction among the T cells includes the regulatory T cells (Treg). The present paper develops a mathematical model by a system of differential equations with terms nonlocal in the space spanned by the concentrations of cytokines that represents the interaction among T cells through a cytokine signaling network. The model demonstrates how the abnormal levels of T cells observed in inflammatory bowel diseases can arise from abnormal regulation of Th1 and Th2 cells by Treg cells.
  • H. Kang, M. Crawford, M. Fabbri, G. Nuovo, M. Garofalo and A. Friedman
    A mathematical model for microRNA in lung cancer.
    PloS oneVol. 8 No. 1 (2013) pp. e53663

    Abstract

    Lung cancer is the leading cause of cancer-related deaths worldwide. Lack of early detection and limited options for targeted therapies are both contributing factors to the dismal statistics observed in lung cancer. Thus, advances in both of these areas are likely to lead to improved outcomes. MicroRNAs (miRs or miRNAs) represent a class of non-coding RNAs that have the capacity for gene regulation and may serve as both diagnostic and prognostic biomarkers in lung cancer. Abnormal expression patterns for several miRNAs have been identified in lung cancers. Specifically, let-7 and miR-9 are deregulated in both lung cancers and other solid malignancies. In this paper, we construct a mathematical model that integrates let-7 and miR-9 expression into a signaling pathway to generate an in silico model for the process of epithelial mesenchymal transition (EMT). Simulations of the model demonstrate that EGFR and Ras mutations in non-small cell lung cancers (NSCLC), which lead to the process of EMT, result in miR-9 upregulation and let-7 suppression, and this process is somewhat robust against random input into miR-9 and more strongly robust against random input into let-7. We elected to validate our model in vitro by testing the effects of EGFR inhibition on downstream MYC, miR-9 and let-7a expression. Interestingly, in an EGFR mutated lung cancer cell line, treatment with an EGFR inhibitor (Gefitinib) resulted in a concentration specific reduction in c-MYC and miR-9 expression while not changing let-7a expression. Our mathematical model explains the signaling link among EGFR, MYC, and miR-9, but not let-7. However, very little is presently known about factors that regulate let-7. It is quite possible that when such regulating factors become known and integrated into our model, they will further support our mathematical model.
  • K. Liao, X. Bai and A. Friedman
    Mathematical modeling of interleukin-27 induction of anti-tumor T cells response.
    PloS oneVol. 9 No. 3 (2014) pp. e91844

    Abstract

    Interleukin-12 is a pro-inflammatory cytokine which promotes Th1 and cytotoxic T lymphocyte activities, such as Interferon-[Formula: see text] secretion. For this reason Interleukin-12 could be a powerful therapeutic agent for cancer treatment. However, Interleukin-12 is also excessively toxic. Interleukin-27 is an immunoregulatory cytokine from the Interleukin-12 family, but it is not as toxic as Interleukin-12. In recent years, Interleukin-27 has been considered as a potential anti-tumor agent. Recent experiments in vitro and in vivo have shown that cancer cells transfected with IL-27 activate CD8+ T cells to promote the secretion of anti-tumor cytokines Interleukin-10, although, at the same time, IL-27 inhibits the secretion of Interferon-[Formula: see text] by CD8+ T cells. In the present paper we develop a mathematical model based on these experimental results. The model involves a dynamic network which includes tumor cells, CD8+ T cells and cytokines Interleukin-27, Interleukin-10 and Interferon-[Formula: see text]. Simulations of the model show how Interleukin-27 promotes CD8+ T cells to secrete Interleukin-10 to inhibit tumor growth. On the other hand Interleukin-27 inhibits the secretion of Interferon-[Formula: see text] by CD8+ T cells which somewhat diminishes the inhibition of tumor growth. Our numerical results are in qualitative agreement with experimental data. We use the model to design protocols of IL-27 injections for the treatment of cancer and find that, for some special types of cancer, with a fixed total amount of drug, within a certain range, continuous injection has better efficacy than intermittent injections in reducing the tumor load while the treatment is ongoing, although the decrease in tumor load is only temporary.
  • W. Hao and A. Friedman
    The LDL-HDL Profile Determines the Risk of Atherosclerosis: A Mathematical Model.
    PloS oneVol. 9 No. 3 (2014) pp. e90497

    Abstract

    Atherosclerosis, the leading death in the United State, is a disease in which a plaque builds up inside the arteries. As the plaque continues to grow, the shear force of the blood flow through the decreasing cross section of the lumen increases. This force may eventually cause rupture of the plaque, resulting in the formation of thrombus, and possibly heart attack. It has long been recognized that the formation of a plaque relates to the cholesterol concentration in the blood. For example, individuals with LDL above 190 mg/dL and HDL below 40 mg/dL are at high risk, while individuals with LDL below 100 mg/dL and HDL above 50 mg/dL are at no risk. In this paper, we developed a mathematical model of the formation of a plaque, which includes the following key variables: LDL and HDL, free radicals and oxidized LDL, MMP and TIMP, cytockines: MCP-1, IFN-?, IL-12 and PDGF, and cells: macrophages, foam cells, T cells and smooth muscle cells. The model is given by a system of partial differential equations with in evolving plaque. Simulations of the model show how the combination of the concentrations of LDL and HDL in the blood determine whether a plaque will grow or disappear. More precisely, we create a map, showing the risk of plaque development for any pair of values (LDL,HDL).

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