Multi-scale lung modeling

Abstract

Multi-scale modeling of biological systems has recently become fashionable due to the growing power of digital computers as well as to the growing realization that integrative systems behavior is as important to life as is the genome. While it is true that the behavior of a living organism must ultimately be traceable to all its components and their myriad interactions, attempting to codify this in its entirety in a model misses the insights gained from understanding how collections of system components at one level of scale conspire to produce qualitatively different behavior at higher levels. The essence of multi-scale modeling thus lies not in the inclusion of every conceivable biological detail, but rather in the judicious selection of emergent phenomena appropriate to the level of scale being modeled. These principles are exemplified in recent computational models of the lung. Airways responsiveness, for example, is an organ-level manifestation of events that begin at the molecular level within airway smooth muscle cells, yet it is not necessary to invoke all these molecular events to accurately describe the contraction dynamics of a cell, nor is it necessary to invoke all phenomena observable at the level of the cell to account for the changes in overall lung function that occur following methacholine challenge. Similarly, the regulation of pulmonary vascular tone has complex origins within the individual smooth muscle cells that line the blood vessels but, again, many of the fine details of cell behavior average out at the level of the organ to produce an effect on pulmonary vascular pressure that can be described in much simpler terms. The art of multi-scale lung modeling thus reduces not to being limitlessly inclusive, but rather to knowing what biological details to leave out.

Fig. 1.

Schematic representation of the key levels of scale involved in modeling the mechanical consequences of bronchoconstriction from the level of the molecule up to the whole organ. [Reproduced with permission (44)].

Fig. 2.

Schematic illustration of the passive components of a multi-scale model of the pulmonary circulation, as presented by Burrowes and colleagues (12, 16). The arteries (red) and veins (blue) are distributed within a deforming model of the lung tissue (colored by pleural pressure for the right lung). These “large scale” components couple to the “microscale” at each precapillary artery and vein via elastic recoil and blood pressures. Q_tot is the total blood flow into an acinus, Q_cj is flow into the jth level capillary sheet, and the right hand side lists the number of sheets at each level of the ladder model. [Adapted with permission (18)].