Mathematical model of renal interstitial fibrosis

Hao, Wenrui; Rovin, Brad H.; Friedman, Avner

doi:10.1073/pnas.1413970111

Cited by 45 publications

(72 citation statements)

References 38 publications

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“…They satisfy a flux condition on the boundary of the blood vessels, where n is the outward normal, M 0 is the density of the monocytes in the brain capillaries, and is a function which depends on the concentration of MCP-1. By averaging these fluxes from blood vessels, we can represent (as in [56]) the immigration of macrophages into the brain tissue by a term . We assume that the incoming macrophages divide into and phenotype depending on the relative concentrations of TNF- α and IL-10 [47].…”

Section: Methodsmentioning

confidence: 99%

Mathematical model on Alzheimer’s disease

2016

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BackgroundAlzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. AD is characterized by the presence of two types of neuropathological hallmarks: extracellular plaques consisting of amyloid β-peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins. The disease affects 5 million people in the United States and 44 million world-wide. Currently there is no drug that can cure, stop or even slow the progression of the disease. If no cure is found, by 2050 the number of alzheimer’s patients in the U.S. will reach 15 million and the cost of caring for them will exceed $ 1 trillion annually.ResultsThe present paper develops a mathematical model of AD that includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. The model is represented by a system of partial differential equations. The model is used to simulate the effect of drugs that either failed in clinical trials, or are currently in clinical trials.ConclusionsBased on these simulations it is suggested that combined therapy with TNF- α inhibitor and anti amyloid β could yield significant efficacy in slowing the progression of AD.

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Section: Methodsmentioning

confidence: 99%

Mathematical model on Alzheimer’s disease

2016

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“…This framework clarifies how the interactions between the relevant cell types provide multi-stability: the dynamics can flow to the different physiological states of fibrosis or healing, depending on the severity and duration of the immune response. This approach builds on previous theoretical work regarding fibroblast activation (Hao et al, 2014), and adds to it the critical component of the fibroblast interaction with macrophages. The circuit predicts the existence of three steady-states: a state of healing associated with modest ECM production, and two fibrosis states associated with high cellularity and excessive ECM production, consistent with histopathological observations.…”

Section: Introductionmentioning

confidence: 99%

Principles of Cell Circuits for Tissue Repair and Fibrosis

Adler

Mayo

Zhou

et al. 2019

Preprint

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Tissue-repair is a protective response after injury, but repetitive or prolonged injury can lead to fibrosis, a pathological state of excessive scarring. To pinpoint the dynamic mechanisms underlying fibrosis, it is important to understand the principles of the cell circuits that carry out tissue-repair. In this study, we establish a cell-circuit framework for the myofibroblast-macrophage circuit in wound-healing, including the accumulation of scar-forming extracellular matrix. We find that fibrosis results from multi-stability between three outcomes, which we term 'hot fibrosis' characterized by many macrophages, 'cold fibrosis' lacking macrophages, and normal wound-healing. The cell-circuit framework clarifies several unexplained phenomena including the paradoxical effect of macrophage depletion, the limited time-window in which removing inflammation leads to healing, the effects of cellular senescence, and why scar maturation takes months. We define key parameters that control the transition from healing to fibrosis, which may serve as potential targets for therapeutic reduction of fibrosis.

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“…Recently a mathematical model of renal interstitial fibrosis have been proposed in [161]. The model aims at monitoring the effect of treatment by anti-fibrotic drugs that are currently being used, or undergoing clinical trials, in non-renal fibrosis.…”

Section: Models With Internal Structurementioning

confidence: 99%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Bianca

2016

Physics of Life Reviews

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Pathological fibrosis is the result of a failure in the wound healing process. The comprehension and the related modeling of the different mechanisms that trigger fibrosis is a challenge of many researchers that work in the field of medicine and biology. The modern scientific analysis of a phenomenon generally consists of three major approaches: theoretical, experimental, and computational. Different theoretical tools coming from mathematics and physics have been proposed for the modeling of the physiological and pathological fibrosis. However a complete framework is missing and the development of a general theory is required. This review aims at finding a unified approach in the modeling of fibrosis diseases that takes into account the different phenomena occurring at each level: molecular, cellular and tissue. Specifically by means of a critical analysis of the different models that have been proposed in the mathematical, computational and physical biology, from molecular to tissue scales, a multiscale approach is proposed, an approach that has been strongly recommended by top level biologists in the past decades.

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Mathematical model of renal interstitial fibrosis

Cited by 45 publications

References 38 publications

Mathematical model on Alzheimer’s disease

Mathematical model on Alzheimer’s disease

Principles of Cell Circuits for Tissue Repair and Fibrosis

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

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