A Mathematical Model of Idiopathic Pulmonary Fibrosis

Abstract

Idiopathic pulmonary fibrosis (IPF) is a disease of unknown etiology, and life expectancy of 3-5 years after diagnosis. The incidence rate in the United States is estimated as high as 15 per 100,000 persons per year. The disease is characterized by repeated injury to the alveolar epithelium, resulting in inflammation and deregulated repair, leading to scarring of the lung tissue, resulting in progressive dyspnea and hypoxemia. The disease has no cure, although new drugs are in clinical trials and two agents have been approved for use by the FDA. In the present paper we develop a mathematical model based on the interactions among cells and proteins that are involved in the progression of the disease. The model simulations are shown to be in agreement with available lung tissue data of human patients. The model can be used to explore the efficacy of potential drugs.

Calibrations and validations of biological models with an application on the renal fibrosis

“…In order to model different cells dispersion and cytokines' diffusion (due to the renal fibrosis progression) shown in Figure , a system of convection‐diffusion equations has been used in Hao et al The equation for each species C i (1 ≤ i ≤ N ) has the following form: where is the diffusion/dispersion coefficient and is a function which models all the species' interactions in the molecular networks as shown in Figure . We will not write explicitly here for each C i (see Hao et al for more details). The system of diffusion equations, Equation (1), is solved by the central difference scheme of finite difference method in discretizing the space coupled with the forward Euler method in discretizing the time.…”

“…This mathematical model is based on the network of cells and cytokines of renal fibrosis progression which is represented by a system of partial differential equations (PDEs) in a section of the kidney tissue. More recently Hao et al extended this model to Idiopathic pulmonary fibrosis (IPF) and used it to explore the efficacy of drugs. These computational models enable predictions of fibrosis progression and can provide a systematic way to quantify the precision medicine for fibrosis patients.…”

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

“…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. In [162] a mathematical model for idiopathic pulmonary fibrosis have been derived. The model is based on the interactions among cells and proteins that are involved in the progression of the disease.…”

A mathematical model of skeletal muscle regeneration

“…While this problem is widespread and occurs often, little work has been done to investigate the potential role of mathematics in alleviating the issue. Some mathematical models have been constructed to simulate the response of diseased tissue to continual, disease‐driven damage, such as Dell'Acqua and Castiglione's model for Duchenne muscular dystrophy and Hao, Marsh, and Friedman's model for idiopathic pulmonary fibrosis . In Dell'Acqua and Castiglione, a mathematical model is used to examine the mesoscopic interactions in the damage and healing cycles of the mdx mouse.…”

“…Besides modeling a qualitatively different scenario than that of skeletal muscle regeneration, this model does not take into account the various cells that constitute healthy muscle tissue, such as myoblasts and satellite cells, nor does it differentiate between classically and alternatively activated macrophages, which have been shown to have different and complementary functions in muscle repair . The model in Hao et al considers specific cells, such as myofibroblasts, fibroblasts, and the two subsets of macrophages but represents a qualitatively different process: Not only is there a difference in the healing process of diseased versus disease‐free tissue but healing of lung tissue also involves different cells and interactions between cells than healing of skeletal muscle tissue.…”