Impairment of blood volume restitution after large hemorrhage: a mathematical model

A mathematical model tests possible mechanisms for the progressive failure of blood volume restitution seen after larger hemorrhages ( > 26%) with increasing changes in plasma osmolality. After 10% hemorrhage, the model requires a decrease in net hydrostatic capillary pressure, the release of solute into the extracellular space, and the release of Na+ and K+ from a bound pool in equilibrium with the interstitium to match the experimental data. The solute and released cations expand the interstitium to drive the restitution of volume and protein from 3 to 24 h. After 30% hemorrhage, the best prediction of the average experimental responses occurs when the Na(+)-K(+)-adenosinetriphosphatase (ATPase) in the cell membrane is inhibited by 38.7% from 0.8 to 3 h, and the proportionality between capillary pressure and blood volume is reduced by 68% from its value for 10% hemorrhage. When the change in plasma osmolality is doubled after 30% hemorrhage, an increase in the inhibition of the ATPase to 85% and extension of its duration to 24 h are necessary to match experimental findings. The associated defect in sodium transport may occur after large hemorrhage so that sodium and water move into cells. This response may oppose osmotically driven expansion of the interstitium and thus account for the failure of restitution.