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

Abstract

A detailed nonlinear four-region (red blood cell, plasma, interstitial fluid, and parenchymal cell) axially distributed convection-diffusion-permeation-reaction-binding computational model is developed to study the simultaneous transport and exchange of oxygen (O 2 ) and carbon dioxide (CO 2 ) in the blood-tissue exchange system of the heart. Since the pH variation in blood and tissue influences the transport and exchange of O 2 and CO 2 (Bohr and Haldane effects), and since most CO 2 is transported as (bicarbonate) via the CO 2 hydration (buffering) reaction, the transport and exchange of and H + are also simulated along with that of O 2 and CO 2 . Furthermore, the model accounts for the competitive nonlinear binding of O 2 and CO 2 with the hemoglobin inside the red blood cells (nonlinear O 2 -CO 2 interactions, Bohr and Haldane effects), and myoglobin-facilitated transport of O 2 inside the parenchymal cells. The consumption of O 2 through cytochrome-c oxidase reaction inside the parenchymal cells is based on MichaelisMenten kinetics. The corresponding production of CO 2 is determined by respiratory quotient (RQ), depending on the relative consumption of carbohydrate, protein, and fat. The model gives a physiologically realistic description of O 2 transport and metabolism in the microcirculation of the heart. Furthermore, because model solutions for tracer transients and steady states can be computed highly efficiently, this model may be the preferred vehicle for routine data analysis where repetitive solutions and parameter optimization are required, as is the case in PET imaging for estimating myocardial O 2 consumption.

Bayesian flux balance analysis applied to a skeletal muscle metabolic model

“…The convection term depends on the difference of total arterial C a,tot and venous C b,tot concentrations of the species, where "total" means that in the oxygen and carbon dioxide concentrations, the oxy-hemoglobin, carbamino-hemoglobin and bicarbonate concentrations are taken into account in addition to the free dissolved concentrations (Dash & Bassingthwaighte, 2006;Lai et al, 2006). The factor Q(t) represents the blood flow, and F is the mixing ratio.…”

“…The values for the arterial concentrations C a were taken from Dash & Bassingthwaighte (2006) (see also Appendix A, Table 3). To set up the likelihood model, we assumed a standard deviation of 5% for the arterial concentration values.…”

“…The 26 biochemical reactions implemented in the model are listed in Table 2. Table 3 specifies the type of transport flux (facilitated or passive) between blood and tissue for each species in the blood domain, and gives the numerical values (from Dash & Bassingthwaighte (2006)) for the arterial blood concentrations. In our calculations, the units for the concentrations are mmol/l, for the reaction and transport fluxes mmol/min and for the blood flow l/min.…”

Modeling Oxygen and Carbon Dioxide Transport and Exchange Using a Closed Loop Circulatory System

“…The model accounts for hemoglobin saturation, the simultaneous binding of o 2 CO 2 . H + , 2,3-DPG to hemoglobin, and temperature effects [1,2]. Invertible Hill-type saturation equations facilitate rapid calculation of respiratory gas redistribution among the plasma, red blood cell and issue that occur along the concentration gradients in the lung and in the capillary-tissue exchange regions.…”

“…Hemoglobin dissociation curves were developed that described the fraction of O 2 and CO 2 bound to Hb in the steady state as a function of P O2 , P CO2 . pH, 2,3-DPG and temperature [1], These expressions were used to describe the steady state transport of O 2 and CO 2 as well as H + and HCO 3 − in a blood-tissue exchange model with convective transport and axial diffusion in the capillary along with exchange and metabolism in the surrounding tissue region [2].The model presented in this study accounts for ventilatory exchange between outside air and lung alveoli, exchange with alveolar capillary blood, convective transport in arteries, the exchange in tissue capillaries and arterioles, and return of venous blood to the lungs. The model describes transport of O 2 and CO 2 to tissue as influenced by respiration rate, composition of inspired gas, H + and CO 2 production and O 2 consumption in tissue and buffering in the blood.…”