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

A dynamic computational network model for the role of nitric oxide and the myogenic response in microvascular flow regulation

OBJECTIVES

The effect of NO on smooth muscle cell contractility is crucial in regulating vascular tone, blood flow, and O₂ delivery. Quantitative predictions for interactions between the NO production rate and the myogenic response for microcirculatory blood vessels are lacking.

METHODS

We developed a computational model of a branching microcirculatory network with four representative classes of resistance vessels to predict the effect of endothelium-derived NO on the microvascular pressure-flow response. Our model links vessel scale biotransport simulations of NO and O₂ delivery to a mechanistic model of autoregulation and myogenic tone in a simplified microcirculatory network.

RESULTS

The model predicts that smooth muscle cell NO bioavailability significantly contributes to resting vascular tone of resistance vessels. Deficiencies in NO seen during hypoxia or ischemia lead to a decreased vessel diameter for all classes at a given intravascular pressure. At the network level, NO deficiencies lead to an increase in pressure drop across the vessels studied, a downward shift in the pressure-flow curve, and a decrease in the effective range of the autoregulatory response.

CONCLUSIONS

Our model predicts the steady state and transient behavior of resistance vessels to perturbations in blood pressure, including effects of NO bioavailability on vascular regulation.

Theoretical analysis of vascular regulatory mechanisms contributing to retinal blood flow autoregulation

PURPOSE

To study whether impaired retinal autoregulation is a risk factor for glaucoma, the relationship between vascular regulatory mechanisms and glaucoma progression needs to be investigated. In this study, a vascular wall mechanics model is used to predict the relative importance of regulatory mechanisms in achieving retinal autoregulation.

METHODS

Resistance vessels are assumed to respond to changes in pressure, shear stress, carbon dioxide (CO2), and the downstream metabolic state communicated via conducted responses. Model parameters governing wall tension are fit to pressure and diameter data from porcine retinal arterioles. The autoregulation pressure range for control and elevated levels of IOP is predicted.

RESULTS

The factor by which flow changes as the blood pressure exiting the central retinal artery is varied between 28 and 40 mm Hg is used to indicate the degree of autoregulation (1 indicates perfect autoregulation). In the presence of only the myogenic response mechanism, the factor is 2.06. In the presence of the myogenic and CO2 responses, the factor is 1.22. The combination of myogenic, shear, CO2, and metabolic responses yields the best autoregulation (factor of 1.10).

CONCLUSIONS

Model results are compared with flow and pressure data from multiple patient studies, and the combined effects of the metabolic and CO2 responses are predicted to be critical for achieving retinal autoregulation. When IOP is elevated, the model predicts a decrease in the autoregulation range toward low perfusion pressure, which is consistent with observations that glaucoma is associated with decreased perfusion pressure.

A model of NO/O2 transport in capillary-perfused tissue containing an arteriole and venule pair

The goal of this study was to investigate the complex co-transport of nitric oxide (NO) and oxygen (O2) in a paired arteriole-venule, surrounded by capillary-perfused tissue using a computer model. Blood flow was assumed to be steady in the arteriolar and venular lumens and to obey Darcy's law in the tissue. NO consumption rate was assumed to be constant in the core of the arteriolar and venular lumen and to decrease linearly to the endothelium. Average NO consumption rate by capillary blood in a unit tissue volume was assumed proportional to the blood flux across the volume. Our results predict that: (1) the capillary bed, which connects the arteriole and venule, facilitates the release of O2 from the vessel pair to the surrounding tissue; (2) decreasing the distance between arteriole and venule can result in a higher NO concentration in the venular wall than in the arteriolar wall; (3) in the absence of capillaries in the surrounding tissue, diffusion of NO from venule to arteriole contributes little to NO concentration in the arteriolar wall; and (4) when capillaries are added to the simulation, a significant increase of NO in the arteriolar wall is observed.

Simultaneous blood-tissue exchange of oxygen, carbon dioxide, bicarbonate, and hydrogen ion

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 (O2) and carbon dioxide (CO2) in the blood-tissue exchange system of the heart. Since the pH variation in blood and tissue influences the transport and exchange of O2 and CO2 (Bohr and Haldane effects), and since most CO2 is transported as HCO3(-) (bicarbonate) via the CO2 hydration (buffering) reaction, the transport and exchange of HCO3(-) and H+ are also simulated along with that of O2 and CO2. Furthermore, the model accounts for the competitive nonlinear binding of O2 and CO2 with the hemoglobin inside the red blood cells (nonlinear O2-CO2 interactions, Bohr and Haldane effects), and myoglobin-facilitated transport of O2 inside the parenchymal cells. The consumption of O2 through cytochrome-c oxidase reaction inside the parenchymal cells is based on Michaelis-Menten kinetics. The corresponding production of CO2 is determined by respiratory quotient (RQ), depending on the relative consumption of carbohydrate, protein, and fat. The model gives a physiologically realistic description of O2 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 O2 consumption.

Numerical studies on the effect of lowering temperature on the oxygen transport during brain hypothermia resuscitation

There have been arguments about the advantage and shortcoming of hypothermia on the brain resuscitation during circulation arrest. People usually accepted that hypothermia may decrease the cerebral oxygen demands, which is beneficial for the patient to sustain longer time when subjected to a hypoxia. However, there are also quite a few disputes claiming that the blood viscosity would increase with the reduction of temperature, which may lead to an increase of cerebral vascular resistance and thus worsen the hypoxia state. To resolve this critical issue, a heat transfer model was established to characterize the thermal response of brain tissue during hypothermia resuscitation. Combined with this model, a compartmental model taking account of the temperature effect was further developed to analyze the transient oxygen partial pressure (PO(2)) distribution over the successive branches of the vascular network during circulation arrest. Using the morphological and physiological data of a sheep brain, effects of lowering temperature on the oxygen consumption dynamics were studied. Calculations indicated that the lower the temperature, the slower the decreasing rate for the PO(2). Although immediately lowering the brain temperature may induce an evident increase in blood viscosity and subsequently a decrease in blood flow rate, which is responsible for oxygen delivery, it seems to always result in a monotonic increase of PO(2). The results show a good qualitative accord with the experimental data. They also present better understanding on the transient oxygen transport in brain hypothermia during circulation arrest.

A compartmental model for oxygen transport in brain microcirculation in the presence of blood substitutes

A compartmental model is developed for oxygen (O(2)) transport in brain microcirculation in the presence of blood substitutes (hemoglobin-based oxygen carriers). The cerebrovascular bed is represented as a series of vascular compartments, on the basis of diameters, surrounded by a tissue compartment. A mixture of red blood cells (RBC) and plasma/extracellular hemoglobin solution flows through the vascular bed from the arterioles through the capillaries to the venules. Oxygen is transported by convection in the vascular compartments and by diffusion in the surrounding tissue where it is utilized. Intravascular resistance and the diffusive loss of oxygen from the arterioles to the tissue are incorporated in the model. The model predicts that most of the O(2) transport occurs at the level of capillaries. Results computed from the present model in the presence of hemoglobin-based oxygen carriers are consistent with those obtained from the earlier validated model (Sharan et al., 1989, 1998a) on oxygen transport in brain circulation in the absence of extracellular hemoglobin. We have found that: (a) precapillary PO(2) gradients increase as PO(2) in the arterial blood increases, P(50 p) (oxygen tension at 50% saturation of hemoglobin with O(2) in plasma) decreases, i.e. O(2) affinity of the extracellular hemoglobin is increased, the flow rate of the mixture decreases, hematocrit decreases at constant flow, metabolic rate increases, and intravascular transport resistance in the arterioles is neglected; (b) precapillary PO(2) gradients are not sensitive to (i) intracapillary transport resistance, (ii) cooperativity (n(p)) of hemoglobin with oxygen in plasma, (iii) hemoglobin concentration in the plasma and (iv) hematocrit when accounting for viscosity variation in the flow; (c) tissue PO(2) is not sensitive to the variation of intravascular transport resistance in the arterioles. We also found that tissue PO(2) is a non-monotonic function of the Hill coefficient n(p) for the extracellular hemoglobin with a maximum occurring when n(p) equals the blood Hill coefficient. The results of the computations give estimates of the magnitudes of the increases in tissue PO(2) as arterial PO(2) increases,P(50 p) increases, flow rate increases, hematocrit increases, hemoglobin concentration in the plasma increases, metabolic rate decreases, the capillary mass transfer coefficient increases or the intracapillary transport resistance decreases.

Dependence of oxygen delivery on blood flow in rat brain: a 7 tesla nuclear magnetic resonance study

Magnetic resonance imaging (MRI) and spectroscopy (MRS) were used at a magnetic field strength of 7 T to measure CBF and CMRO2 in the sensorimotor cortex of mature rats at different levels of cortical activity. In rats maintained on morphine anesthesia, transitions to lower activity and higher activity states were produced by administration of pentobarbital and nicotine, respectively. Under basal conditions of morphine sulfate anesthesia, CBF was 0.75 +/- 0.09 mL x g(-1) x min(-1) and CMRO2 was 3.15 +/- 0.18 micromol x g(-1) x min(-1). Administration of sodium pentobarbital reduced CBF and CMRO2 by 66% +/- 16% and 61% +/- 6%, respectively (i.e., "deactivation"). In contrast, administration of nicotine hydrogen tartrate increased CBF and CMRO2 by 41% +/- 5% and 30% +/- 3%, respectively (i.e., "activation"). The resting values of CBF and CMRO2 for alpha-chloralose anesthetized rats were 0.40 +/- 0.09 mL x g(-1) x min(-1) and 1.51 +/- 0.06 micromol x g(-1) x min(-1), respectively. Upon forepaw stimulation, CBF and CMRO2 were focally increased by 34% +/- 10% and 26% +/- 12%, respectively, above the resting nonanesthetized values (i.e., "activation"). Incremental changes in CBF and CMRO2, when expressed as a percentage change for "deactivation" and "activation" from the respective control conditions, were linear (R2 = 0.997) over the entire range examined with the global and local perturbations. This tight correlation for cerebral oxygen delivery in vivo is supported by a recent model where the consequence of a changing effective diffusivity of the capillary bed for oxygen, D, has been hypothetically shown to be linked to alterations in CMRO2 and CBF. This assumed functional characteristic of the capillary bed can be theoretically assessed by the ratio of fractional changes in D with respect to changes in CBF, signified by omega. A value 0.81 +/- 0.23 was calculated for omega with the in vivo data presented here, which in turn corresponds to a supposition that the effective oxygen diffusivity of the capillary bed is not constant but presumably varies to meet local requirements in oxygen demand in a similar manner with both "deactivation" and "activation."

Incorporating O2-Hb reaction kinetics and the Fåhraeus effect into a microcirculatory O2-CO2 transport model

The influence of O2-Hb reaction kinetics and the Fåhraeus effect on steady state O2 and CO2 transport in cat brain microcirculation was investigated using our refined multicompartmental model. The most important model predictions include: 1) capillaries are the sites in the microcirculation where the effect of O2-Hb kinetics is most pronounced; 2) while there is only a small difference between equilibrium and actual oxygen saturation, this effect is not negligible; 3) O2-Hb kinetics tends to make the PO2 level at the venous entrance higher than in venules; 4) the influence of the Fåhraeus effect leads to a lower tissue PO2 level than in venules and the outlet vein. The resultant decline in tissue PO2 may lead to a decrease in O2 consumption rate and extraction ratio; 5) although the Fåhraeus effect changes the ratio between arteriolar flux and capillary flux, incorporating the Fåhraeus effect and O2-Hb kinetics into the simulation does not change our previous conclusion, that most of the O2 and CO2 exchange takes place at the capillary level; 6) in general, influences of O2-Hb kinetics and Fåhraeus effect are synergistic; 7) a model that excludes these two mechanisms might overestimate the tissue oxygenation level especially during severe hypoxia.