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Simulation of acute and chronic reaction patterns in the microcirculation

Jens Christian Brings Jacobsen 

Summary

The present thesis is concerned with simulation of acute and chronic reaction patterns in the microcirculation. It consists of three separate models. The first is a of model microvascular remodeling and growth. The assumptions are made that 1) vessels in a network adjust the relative wall-thickness so as to maintain a certain level of circumferential wall-stress. 2) They adjust the luminal radius until a certain wall shear stress is reached. At this level of wall shear stress, endothelial-derived growth influencing substances have a certain equilibrium concentration in the wall. 3) Vessels which, during the adaptation process, achieve a diameter too small for the blood cells to pass, will disappear. Allowing an immature modelnetwork consisting of capillary sized vessels to adapt according to these principles causes a mature network with arterio-venous asymmetry in vessel radii, relative wall thickness, wall transsectional area, flow velocity and wall shear stress, to emanate. The pressure declines steeply on the arterial side, protecting the central capillary bed and venous-side vessels from the high arterial pressure. By varying the sensitivity of the endothelium to shear-stress and simultaneously varying the arterial perfusion pressure, all the theoretically possible modes of the remodeling and growth can be found in each vessel in the network.
The second model is concerned with the development of a peculiar pattern of alternating dilated and constricted areas found during acute hypertension in small arteries and arterioles. A similar pattern has been observed angiographically in large muscular arteries. Characteristically, the pattern in the microcirculation appears to be functional in nature since it disappears on lowering the pressure, but reappears with the constrictions in the same locations along the vessel if the pressor agent is infused once again. A model has been developed which explains the pattern as a consequence of an instability of the cylindrical shape of the vessel, that can arise at high levels of activation of the smooth muscle cells of the wall. As found in experiments on the rat intestinal microcirculation, numerical simulations of the model shows that the length of the dilated areas scales linearly with the resting diameter of the vessel and increases with the square root of the longitudinal stress. Furthermore, the simulations show that when the relative wall thickness is decreased, the pattern becomes more like pearls on a string, resembling the pattern seen in large muscular arteries. Most importantly, the model suggests that no underlying heterogeneity in the vascular wall is necessary to explain the pattern. In the microcirculation, damage to the vascular wall is found exclusively in the dilated areas of the vessel, suggesting that the pattern has a pathophysiological significance, possibly related to the patchy fibrinoid necrosis found in the wall of small arteries and arterioles in human malignant hypertension.
The last model is concerned with a phenomenon known as arterial vasomotion. Microvessels scattered across the vascular bed exhibits spontaneous rhythmic contractions with a frequency of typically 2-10 cpm. A tube shaped plate of cells coupled through gap-junctions was developed. The model entails a description of the calcium dynamics of the SR, calcium buffering of the cytosol and various currents across the plasma membrane in each cell. Without currents across the membrane, the cells shows spontaneous calcium waves sweeping along the cytoplasm. Coupling the cells through gap-junctions causes synchronization of the membrane potential among all cells. Coordinated opening of L-type calcium channels with influx of calcium from the extracellular space, causes subsequent coordinated release of calcium release from the SR and synchronization of the cytoplasmic calcium transients among all the cells.