Contribution of serial and parallel microperfusion to spatial variability in pulmonary inter- and intra-acinar blood flow

Abstract

This study presents a theoretical model of combined series and parallel perfusion in the human pulmonary acinus that maintains computational simplicity while capturing some important features of acinar structure. The model provides a transition between existing models of perfusion in the large pulmonary blood vessels and the pulmonary microcirculation. Arterioles and venules are represented as distinct elastic vessels that follow the branching structure of the acinar airways. These vessels are assumed to be joined at each generation by capillary sheets that cover the alveoli present at that generation, forming a "ladderlike" structure. Compared with a model structure in which capillary beds connect only the most distal blood vessels in the acinus, the model with combined serial and parallel perfusion provides greater capacity for increased blood flow in the lung via capillary recruitment when the blood pressure is elevated. Stratification of acinar perfusion emerges in the model, with red blood cell transit time significantly larger in the distal portion of the acinus compared with the proximal portion. This proximal-to-distal pattern of perfusion may act in concert with diffusional screening to optimize the potential for gas exchange.

Multiscale modelling of the feto–placental vasculature

“…The Fåhraeus-Lindqvist effect may play a role in the smallest blood vessels; in that case, the effective viscosity of blood is decreased in the smallest placental blood vessels. In other models of this type, the viscosity of blood is assumed to vary with vessel radius, either in a linear manner [41] or, based on empirical formulae, as a function of vessel radius and haematocrit [56]. This reduction in viscosity would reduce resistance of the smallest vessels and potentially influence the magnitude of pressure drops predicted in figure 7.…”

Pulmonary embolism: predicting disease severity

“…However, the in vivo intra-acinar vessel structure differs substantially from the large arterial and venous trees owing to vessels that regularly branch off to feed the capillary bed that enwrap the alveolated surface of the acinar airways. This combined series and parallel structure have been termed 'ladder-like' by Clark et al [13]. In this previous study, intraacinar blood flow was modelled with specific consideration of intra-acinar vessel structure, which was shown to be important for simulating increased blood flow via capillary recruitment.…”

“…There are approximately 64 000 each of arterial and venous branches, and each terminal vessel in this model is associated with a single pulmonary acinus (of which there are approximately 32 000 in the whole lung). -A simplified intra-acinar flow model [13] consisting of nine symmetric branches of intra-acinar arteries and veins coupled in a serial and parallel arrangement through a 'sheet' flow representation of the pulmonary capillaries [66]. -A model of parenchymal tissue deformation [67], to which the vascular networks are tethered.…”

“…The baseline model relies on geometrical and mathematical simplifications that are described in detail in previous studies, along with their implications on simulation results [3,13,15,42]. For example, the model does not include supernumerary arteries (SAs), which are small side branches that arise at a large branching angle from the conventional arteries (CAs) of the lung to supply the closest respiratory tissue [84] without following a matching portion of the bronchial tree.…”

“…In the smallest vessels (diameter less than 200 mm), the dominant pressure acting externally to the blood vessel was assumed to be alveolar pressure (P a ), so P tm ≈ P b − P a (P a = 0 in this study). Capillary sheet thickness was defined using a relationship analogous to equation (A 1) [13]. Equation (A 1) is assumed valid for P tm < 32 cm H 2 O, beyond which the vessel is maximally extended in the radial direction.…”