A compartmental model for oxygen-carbon dioxide coupled transport in the microcirculation

Abstract

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.

A Compartmental Model for Oxygen Transport in Brain Microcirculation in the Presence of Blood Substitutes

“…Ye et al (1992) have described an averaging procedure to derive equations from the spatially distributed to a compartment model. Using this procedure, Ye and his coworkers have also proposed a compartmental M. SHARAN AND A. S. POPEL model in the microcirculation, similar to ours, for oxygen transport (Ye et al, 1993) and combined oxygen and carbon dioxide transport (Ye et al, 1994(Ye et al, , 1998.…”

“…The vascular bed is represented as a series of vascular compartments surrounded by a tissue compartment (Fig. 1), which is similar to that of Sharan et al (1998a) and Ye et al (1994). The vascular bed consists of m arteriolar and m venular compartments, and a capillary compartment.…”

Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

“…23 This fits with current trends toward open-source software and widespread collaboration in research. Models including the O 2 -CO 2 interactions were presented by Huang and Hellums 44 and Ye et al, 67 but for different reasons neither of their approaches lends itself to the quantitative analysis of experimental data from transients in venous P O 2 or tracer 15 O-oxygen in positron emission tomography (PET) imaging studies. The model of 44 accounts for radial diffusion, but is computationally slow, making it impractical for routine fitting of experimental time courses from PET imaging studies by automated iterative parameter adjustment optimization.…”

“…The model of 44 accounts for radial diffusion, but is computationally slow, making it impractical for routine fitting of experimental time courses from PET imaging studies by automated iterative parameter adjustment optimization. The model of Ye et al 67 was compartmental, thereby failing to account for axial gradients along the capillary, and therefore lacking the critical narrow impulse response required to fit high-resolution data of the sort analyzed by Deussen and Bassingthwaighte 27 and Li et al 51 The current model solves the first of these problems by an approximation (for radial diffusion) and by using highly efficient computational algorithms for Hb/HbO and for the blood-tissue exchange, and the second by using very efficient partial rather than ordinary differential equations.…”

“…44 Their model tested very well against the data on 1.5 mm diameter tubes from Dorson and Voorhees 28 on O 2 and CO 2 exchange. Fortunately the fluxes across walls of arterioles and venules are small, 44,67 so finding an exact correction is not critical. As for intra-tissue diffusion, with half-intercapillary distances of about 8 microns in the heart, 6 the diffusion relaxation times are short enough (τ = R 2 /2D or about 30 ms maximum) that the radial gradients are almost dissipated within one time step for the numerical solution, allowing us to consider them negligible within the shorter distances across each of the radial regions.…”