摘要
Rationale: There is accumulating evidence that a group of stem/progenitor cells (SPCs) maintain alveolar epithelial integrity. Pulmonary emphysema is characterized by the histological finding of the loss of alveolar epithelial integrity along with corresponding bronchiolar fibrosis. Objectives: Based on the concept of autopoiesis (the capacity to produce oneself), we proposed a mathematical model in the maintenance of alveolar epithelial integrity as related to the genesis of pulmonary emphysema and fibrosis. Methods: A tessellation automaton model was used to describe the autopoietic dynamics of the bronchiolo-alveolar epithelial surface. The alveolar septal volume en-closed by the epithelial surface is a distributed system of discrete elements, which move by random walk in the manner of Brownian motion. Assuming that the numbers of components and events in the automaton are large, an approximate theoretical treatment in terms of differential equations is possible, allowing a set of partial differential equations to be produced. Results: 1) Assuming the loss of progenitor cells through the epithelial-mesenchymal transition (EMT), a sharp bifurcation between two qualitatively distinct regions of the phase space (one that is repaired completely, and another that has disappeared entirely) clearly appeared. 2) Thus, from the system of discrete and spatial partial differential equations, we obtained a system of ordinary differential equations in equilibrium conditions that defined a close relationship between the degree of emphysema, the density of alveolar septal fibroblasts, and the mean concentration of SPCs. Conclusions: A mathematical model of the autopoietic maintenance of the alveolar epithelial surface suggested a close relationship between alveolar emphysema and fibrosis and EMT in lungs affected by chronic obstructive pulmonary disease.
Rationale: There is accumulating evidence that a group of stem/progenitor cells (SPCs) maintain alveolar epithelial integrity. Pulmonary emphysema is characterized by the histological finding of the loss of alveolar epithelial integrity along with corresponding bronchiolar fibrosis. Objectives: Based on the concept of autopoiesis (the capacity to produce oneself), we proposed a mathematical model in the maintenance of alveolar epithelial integrity as related to the genesis of pulmonary emphysema and fibrosis. Methods: A tessellation automaton model was used to describe the autopoietic dynamics of the bronchiolo-alveolar epithelial surface. The alveolar septal volume en-closed by the epithelial surface is a distributed system of discrete elements, which move by random walk in the manner of Brownian motion. Assuming that the numbers of components and events in the automaton are large, an approximate theoretical treatment in terms of differential equations is possible, allowing a set of partial differential equations to be produced. Results: 1) Assuming the loss of progenitor cells through the epithelial-mesenchymal transition (EMT), a sharp bifurcation between two qualitatively distinct regions of the phase space (one that is repaired completely, and another that has disappeared entirely) clearly appeared. 2) Thus, from the system of discrete and spatial partial differential equations, we obtained a system of ordinary differential equations in equilibrium conditions that defined a close relationship between the degree of emphysema, the density of alveolar septal fibroblasts, and the mean concentration of SPCs. Conclusions: A mathematical model of the autopoietic maintenance of the alveolar epithelial surface suggested a close relationship between alveolar emphysema and fibrosis and EMT in lungs affected by chronic obstructive pulmonary disease.
