We present a multicompartmental model for an oxygen-carbon dioxide transport system. The compartmental equations and their lumped parameters are derived through space averaging of the corresponding distributed model. The model can predict compartmental distributions of oxygen and carbon dioxide partial pressures, oxygen-hemoglobin saturation, and pH. Other unique features include the effects of the radial distribution of partial pressures and the difference in metabolic rates between vessel wall and tissue. A model for the cat brain, based on this formulation, is compared with results of experiments and with two types of earlier models: one without space averaging and one without carbon dioxide transport. The results suggest that space averaging the convective terms significantly affects the behavior of the model. This is consistent with conclusions from our earlier oxygen-only model. Our observations also demonstrate, however, significant differences between the results from the oxygen-carbon dioxide model and the oxygen-only model. For instance, at low blood flow rates or at low level of oxygen input, predicted oxygen partial pressures can differ by as much as 30% between the two models. Results obtained from the present model are supported by available experimental findings.

Animals↗

PubMedDate not supplied

Incorporating vessel taper and compliance properties in Navier-Stokes based blood flow models.

A popular and useful technique used to model blood flow in cardiovascular simulations is to divide each blood vessel into a series of segments, each with its own lumped resistance, inertance, and compliance parameters. The values of these parameters are usually obtained through a simplification of the Navier-Stokes equations for fluid flow. However, the simplification often ignores the nonlinear and convective terms of the equations, resulting in errors in the parameter values, especially in the value found for resistance per unit length. We report a new method for the calculation of vessel resistance per unit length which takes into account the effects of vessel taper and wall compliance. It is shown that these effects can be addressed by the addition of two time-varying terms to the calculation of resistance per unit length. One term, due to vessel taper, is proportional to volumetric flow rate Q. The other term, due to vessel compliance, is proportional to delta p/delta t. These variables are readily available in computer simulations of blood flow in lumped parameter systems. Using data for the descending aorta, the new parameter values, when averaged over a cardiac cycle, compare favorably with results in the literature.

Animals↗

PubMedDate not supplied

O2-Hb reaction kinetics and the Fåhraeus effect during stagnant, hypoxic, and anemic supply deficit.

We modified our previous computer model of O2 and CO2 transport in the cerebral microcirculation to include nonequilibrium O2-Hb kinetics and the Fåhraeus effect (reduced tube hematocrit in small microvessels). The model is a steady-state multicompartmental simulation which includes three arteriolar compartments, three venular compartments, and one capillary compartment. Three different types of oxygen deficits (stagnant, hypoxic, and anemic conditions) were simulated by respectively reducing blood flow, arterial O2 saturation, and systemic hematocrit to one half of normal. Microcirculatory distributions for PO2, PCO2, O2 saturation and deviations from equilibrium, and the O2 and CO2 fluxes for each compartment were predicted for the three O2 supply deficits. Differences were found for O2 extraction ratios and relative contributions of arteriolar, venular, and capillary gas fluxes for each type of deficit. The Fåhraeus effect and O2-Hb kinetics reduced O2 extraction in all cases and altered microcirculatory gas distributions depending on the specific type of O2 supply deficits. The modified model continues to predict that capillaries are the major site where gas exchange takes place, and demonstrates that the Fåhraeus effect and nonequilibrium O2-Hb kinetics are important mechanisms that should not be neglected in O2 and CO2 transport modeling. While this model provides useful insight regarding the influence of the Fahraeus effect and O2-Hb kinetics under steady state, the addition of a distributed and dynamic simulation should further elucidate the effects of the brain's heterogeneous properties and transient behavior.

Algorithms↗