Recent experimental and imaging studies suggest that the influence of gravity on the measured distribution of blood flow in the lung is largely through deformation of the parenchymal tissue. To study the contribution of hydrostatic effects to regional perfusion in the presence of tissue deformation, we have developed an anatomically structured computational model of the pulmonary circulation (arteries, capillaries, veins), coupled to a continuum model of tissue deformation, and including scale-appropriate fluid dynamics for blood flow in each vessel type. The model demonstrates that both structural and the multiple effects of gravity on the pulmonary circulation make a distinct contribution to the distribution of blood. It shows that postural differences in perfusion gradients can be explained by the combined effect of tissue deformation and extra-acinar blood vessel resistance to flow in the dependent tissue. However, gravitational perfusion gradients persist when the effect of tissue deformation is eliminated, highlighting the importance of the hydrostatic effects of gravity on blood distribution in the pulmonary circulation. Coupling of large- and small-scale models reveals variation in microcirculatory driving pressures within isogravitational planes due to extra-acinar vessel resistance. Variation in driving pressures is due to heterogeneous large-vessel resistance as a consequence of geometric asymmetry in the vascular trees and is amplified by the complex balance of pressures, distension, and flow at the microcirculatory level.

The topographic distribution of ventilation in the lungs is determined by the interaction of several factors, including lung shape, airway tree geometry, posture, and tissue deformation. Inter-species differences in lung structure-function and technical difficulty in obtaining high resolution imaging of the upright human lung mean that it is not straightforward to experimentally determine the contribution of each of these factors to ventilation distribution. We present a mathematical model for predicting the topological distribution of inhaled air in the upright healthy human lung, based on anatomically-structured model geometries and biophysical equations for model function. Gravitational deformation of the lung tissue is predicted using a continuum model. Air flow is simulated in anatomically-based conducting airways coupled to geometrically simplified terminal acinar units with varying volume-dependent compliances. The predicted ventilation distribution is hence governed by local tissue density and elastic recoil pressure, airway resistance and acinar compliance. Results suggest that there is significant spatial variation in intrinsic tissue properties in the lungs. The model confirms experimental evidence that in the healthy lungs tissue compliance has a far greater effect than airway resistance on the spatial distribution of ventilation, and hence a realistic description of tissue deformation is essential in models of ventilation.

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One contribution of 11 to a theme issue 'Multiscale modelling in biomechanics: theoretical, computational and translational challenges'. The placenta provides all the nutrients required for the fetus through pregnancy. It develops dynamically, and, to avoid rejection of the fetus, there is no mixing of fetal and maternal blood; rather, the branched placental villi 'bathe' in blood supplied from the uterine arteries. Within the villi, the feto-placental vasculature also develops a complex branching structure in order to maximize exchange between the placental and maternal circulations. To understand the development of the placenta, we must translate functional information across spatial scales including the interaction between macro-and micro-scale haemodynamics and account for the effects of a dynamically and rapidly changing structure through the time course of pregnancy. Here, we present steps towards an anatomically based and multiscale approach to modelling the feto-placental circulation. We assess the effect of the location of cord insertion on feto-placental blood flow resistance and flow heterogeneity and show that, although cord insertion does not appear to directly influence feto-placental resistance, the heterogeneity of flow in the placenta is predicted to increase from a 19.4% coefficient of variation with central cord insertion to 23.3% when the cord is inserted 2 cm from the edge of the placenta. Model geometries with spheroidal and ellipsoidal shapes, but the same volume, showed no significant differences in flow resistance or heterogeneity, implying that normal asymmetry in shape does not affect placental efficiency. However, the size and number of small capillary vessels is predicted to have a large effect on feto-placental resistance and flow heterogeneity. Using this new model as an example, we highlight the importance of taking an integrated multi-disciplinary and multiscale approach to understand development of the placenta.