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A numerical study of the nonsteady transport of gases in the pulmonary capillaries. (English) Zbl 0621.92007

A mathematical model is formulated for simulating the unsteady transport of gases in the blood flowing through the pulmonary capillaries. The formulation takes into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion of the species due to haemoglobin. A time dependent situation is created by allowing to vary suddenly the partial pressures of the gases either in the venous blood or in the alveolar air.
A numerical technique is described to solve the resulting time-dependent system of nonlinear coupled partial differential equations with the physiologically relevant boundary, entrance and initial conditions. The time required by the gases to achieve equilibrium is computed. It is shown that the dissolved oxygen takes longest in reaching equilibration whereas the carbon dioxide is the fastest. The various physiologically relevant unsteady situations have been examined.

MSC:

92Cxx Physiological, cellular and medical topics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
76Z05 Physiological flows
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