Fluid and protein exchange in microvascular networks: Importance of modelling heterogeneity in geometrical and biophysical properties.

KEY POINTS: Microvascular network architecture defines coupling of fluid and protein exchange. Network arrangements markedly reduce capillary hydrostatic pressures and resting fluid movement at the same time as increasing the capacity for change The presence of vascular remodelling or angiogenesis puts constraints of network behaviour The sites of fluid and protein exchange can be segregated to different portions of the network Although there is a net filtration of fluid from a network of exchange vessels, there are specific areas where fluid moves into the circulation (reabsorption) and, when protein is moving into tissue, the amount is insufficient under basal conditions to result in changes in oncotic pressure. ABSTRACT: Integration of functional results obtained across scales, from chemical signalling to the whole organism, is a daunting task requiring the marriage of experimental data with mathematical modelling. In the present study, a novel coupled computational fluid dynamics model is developed incorporating fluid and protein transport using measurements in an in vivo frog (Rana pipiens) mesenteric microvascular network. The influences of network architecture and exchange are explored systematically under the common assumptions of structurally and functionally identical microvessels (Homogeneous Scenario) or microvessels classified by position in flow (Class Uniform Scenario), which are compared with realistic microvascular network components (Heterogeneous Scenario). The model incorporates ten quantities that vary within a microvessel; pressure boundary conditions are calibrated against experimental measurements. The Homogeneous Scenario standard model showed that assuming a single 'typical' capillary hides the influence of vessels arranged into a network architecture, where capillary hydrostatic pressures (pT ) are reduced, resulting in both a nonuniform distribution of blood flow and reduced volume flow rate (Jf,T ). In the Class Uniform Scenario pT was further attenuated to produce a ∼60% reduction in Jf,T . Finally, the Heterogeneous Scenario, incorporating measures of individual vessel surface area, demonstrates additional lowering of pT from inlet values favouring a >70% reduction of Jf,T in the face of a ∼120% increase in protein movement into the tissues relative to the Homogeneous Scenario. Beyond the impacts of network architecture, an unanticipated finding was the influence of a blind-end microvessel on model convergence, indicating a profound influence of the largely unexplored dynamics of vascular remodelling on tissue perfusion.

A Theoretical Approach for the Electrochemical Characterization of Ciliary Epithelium.

The ciliary epithelium (CE) is the primary site of aqueous humor (AH) production, which results from the combined action of ultrafiltration and ionic secretion. Modulation of ionic secretion is a fundamental target for drug therapy in glaucoma, and therefore it is important to identify the main factors contributing to it. As several ion transporters have been hypothesized as relevant players in CE physiology, we propose a theoretical approach to complement experimental methods in characterizing their role in the electrochemical and fluid-dynamical conditions of CE. As a first step, we compare two model configurations that differ by (i) types of transporters included for ion exchange across the epithelial membrane, and by (i) presence or absence of the intracellular production of carbonic acid mediated by the carbonic anhydrase enzyme. The proposed model configurations do not include neurohumoral mechanisms such as P2Y receptor-dependent, cAMP, or calcium-dependent pathways, which occur in the ciliary epithelium bilayer and influence the activity of ion transporters, pumps, and channels present in the cell membrane. Results suggest that one of the two configurations predicts sodium and potassium intracellular concentrations and transmembrane potential much more accurately than the other. Because of its quantitative prediction power, the proposed theoretical approach may help relate phenomena at the cellular scale, that cannot be accessed clinically, with phenomena occurring at the scale of the whole eye, for which clinical assessment is feasible.