Mathematical model of NO and O2 transport in an arteriole facilitated by hemoglobin based O2 carriers

A model of anemic tissue perfusion after blood transfusion shows critical role of endothelial response to shear stress stimuli

Although some of the cardiovascular responses to changes in hematocrit (Hct) are not fully quantified experimentally, available information is sufficient to build a mathematical model of the consequences of treating anemia by introducing RBCs into the circulation via blood transfusion. We present such a model, which describes how the treatment of normovolemic anemia with blood transfusion impacts oxygen (O₂) delivery (DO₂, the product of blood O₂ content and arterial blood flow) by the microcirculation. Our analysis accounts for the differential response of the endothelium to the wall shear stress (WSS) stimulus, changes in nitric oxide (NO) production due to modification of blood viscosity caused by alterations of both hematocrit (Hct) and cell free layer thickness, as well as for their combined effects on microvascular blood flow and DO₂. Our model shows that transfusions of 1- and 2-unit of blood have a minimal effect on DO₂ if the microcirculation is unresponsive to the WSS stimulus for NO production that causes vasodilatation increasing blood flow and DO₂. Conversely, in a fully WSS responsive organism, blood transfusion significantly enhances blood flow and DO₂, because increased viscosity stimulates endothelial NO production causing vasodilatation. This finding suggests that evaluation of a patients' pretransfusion endothelial WSS responsiveness should be beneficial in determining the optimal transfusion requirements for treating patients with anemia.NEW & NOTEWORTHY Transfusion of 1 or 2 units of blood accounts for about 3/4 of the world blood consumption of 119 million units per year, whereas a current world demand deficit is on the order of 100 million units. Therefore, factors supporting the practice of transfusing 1 unit instead of 2 are of interest, given their potential to expand the number of interventions without increasing blood availability. Our mathematical model provides a physiological support for this practice.

Two-dimensional mathematical modelling of retinal oxygen transport and recommending treatment options

This paper presents a novel two-dimensional (2D) computational modeling of the retinal oxygen delivery, transport, and consumption analysis. The 2D modeling allows the division of the retina into four layers to address different flow profiles. The retina domain was meshed using the ICEM CFD mesher, while the ANSYS Fluent was used to calculate the transport phenomena for the four different layers. Clinical cases such as diabetes and sickle cell anaemia denoting the effects of decreasing retinal blood flow and hemoglobin's oxygen affinity were investigated. The simulation results showed that for a healthy retina in light and dark conditions, the outer retina is in danger of hypoxia at thickness >197.56μm. However, the treatment of severe ischaemia using extreme hyperoxia seems beneficial for retinal thickness >197.56μm but harmful for thickness <122.75μm. The reduction of hemoglobin's oxygen affinity at low blood flow regimes could not improve the retina's oxygen levels. The study supports the oxygen toxicity hypothesis that hypoxia causes retina degeneration and estimates the retinal thickness and lighting conditions (dark or light) this may occur.

Acute kidney function and morphology following topload administration of recombinant hemoglobin solution

There is a 0.138% incidence of adverse reactions related to blood transfusion. Transfusion-related acute lung injury, immunosuppression, fever, pathogen transmission, and hemolytic transfusion reactions are the most common ones. Synthetic oxygen carriers have been developed to deal with blood shortages and for use in the field where stored blood was not available. They were also designed to be pathogen free, including unknown viruses. In this study, we used Male Golden Syrian Hamsters implemented with a dorsal window chamber to determine how infusion of three different, genetically crosslinked recombinant acellular hemoglobin (rHb) solutions with different oxygen affinities and nitric oxide kinetics affect mean arterial pressure (MAP), heart rate (HR), kidney function, and kidney structure. We found that the administration of all three rHb solutions caused mild hypertension and bradycardia 30 minutes after infusion. However, acute changes in glomerular filtration rate (GFR) were not detected, even though histological analysis was performed 72 hours after treatment revealed some structural changes. All the rHb solutions resulted in hypertension 30 minutes after a 10% topload administration. Regardless of their properties, the presence of acellular Hb causes significant alterations to kidney tissue.

Systems biology of HBOC-induced vasoconstriction

Vasoconstriction is a major adverse effect of HBOCs. The use of a single drug for attenuating HBOC-induced vasoconstriction has been tried with limited success. Since HBOC causes disruptions at multiple levels of organization in the vascular system, a systems approach is helpful to explore avenues to counteract the effects of HBOC at multiple levels by targeting multiple sites in the system. A multi-target approach is especially appropriate for HBOC-induced vasoconstriction, because HBOC disrupts the cascade of amplification by NO-cGMP signaling and protein phosphorylation, ultimately resulting in vasoconstriction. Targeting multiple steps in the cascade may alter the overall gain of amplification, thereby limiting the propagation of disruptive effects through the cascade. As a result, targeting multiple sites may accomplish a relatively high overall efficacy at submaximal drug doses. Identifying targets and doses for developing a multi-target combination HBOC regimen for oxygen therapeutics requires a detailed understanding of the systems biology and phenotypic heterogeneity of the vascular system at multiple layers of organization, which can be accomplished by successive iterations between experimental studies and mathematical modeling at multiple levels of vascular systems and organ systems. Towards this goal, this article addresses the following topics: a) NO-scavenging by HBOC, b) HBOC autoxidation-induced reactive oxygen species generation and endothelial barrier dysfunction, c) NO- cGMP signaling in vascular smooth muscle cells, d) NO and cGMP-dependent regulation of contractile filaments in vascular smooth muscle cells, e) phenotypic heterogeneity of vascular systems, f) systems biology as an approach to developing a multi-target HBOC regimen.

Simulation of NO and O2 transport facilitated by polymerized hemoglobin solutions in an arteriole that takes into account wall shear stress-induced NO production

A mathematical model was developed to study nitric oxide (NO) and oxygen (O(2)) transport in an arteriole and surrounding tissues exposed to a mixture of red blood cells (RBCs) and hemoglobin (Hb)-based O(2) carriers (HBOCs). A unique feature of this model is the inclusion of blood vessel wall shear stress-induced production of endothelial-derived NO, which is very sensitive to the viscosity of the RBC and HBOC mixture traversing the blood vessel lumen. Therefore in this study, a series of polymerized bovine Hb (PolyHb) solutions with high viscosity, varying O(2) affinities, NO dioxygenation rate constants and O(2) dissociation rate constants that were previously synthesized and characterized by our group was evaluated via mathematical modeling, in order to investigate the effect of these biophysical properties on the transport of NO and O(2) in an arteriole and its surrounding tissues subjected to anemia with the commercial HBOC Oxyglobin® and cell-free bovine Hb (bHb) serving as appropriate controls. The computer simulation results indicated that transfusion of high viscosity PolyHb solutions promoted blood vessel wall shear stress dependent generation of the vasodilator NO, especially in the blood vessel wall and should transport enough NO inside the smooth muscle layer to activate vasodilation compared to the commercial HBOC Oxyglobin® and cell-free bHb. However, NO scavenging in the arteriole lumen was unavoidable due to the intrinsic high NO dioxygenation rate constant of the HBOCs being studied. This study also observed that all PolyHbs could potentially improve tissue oxygenation under hypoxic conditions, while low O(2) affinity PolyHbs were more effective in oxygenating tissues under normoxic conditions compared with high O(2) affinity PolyHbs. In addition, all ultrahigh molecular weight PolyHbs displayed higher O(2) transfer rates than the commercial HBOC Oxyglobin® and cell-free bHb. Therefore, these results suggest that ultrahigh molecular weight PolyHb solutions could be used as safe and efficacious O(2) carriers for use in transfusion medicine. It also suggests that future generations of PolyHb solutions should possess lower NO dioxygenation reaction rate constants in order to reduce NO scavenging, while maintaining high solution viscosity to take advantage of wall shear stress-induced NO production. Taken together, we suggest that this mathematical model can be used to predict the vasoactivity of HBOCs and help guide the design and optimization of the next generation of HBOCs for use in transfusion medicine.

Influence of tissue metabolism and capillary oxygen supply on arteriolar oxygen transport: a computational model

We present a theoretical model for steady-state radial and longitudinal oxygen transport in arterioles containing flowing blood (plasma and red blood cells) and surrounded by living tissue. This model combines a detailed description of convective and diffusive oxygen transport inside the arteriole with a novel boundary condition at the arteriolar lumen surface, and the results provide new mass transfer coefficients for computing arteriolar O(2) losses based on far-field tissue O(2) tension and in the presence of spatially distributed capillaries. A numerical procedure is introduced for calculating O(2) diffusion from an arteriole to a continuous capillary-tissue matrix immediately adjacent to the arteriole. The tissue O(2) consumption rate is assumed to be constant and capillaries act as either O(2) sources or sinks depending on the local O(2) environment. Using the model, O(2) saturation (SO(2)) and tension (PO(2)) are determined for the intraluminal region of the arteriole, as well as for the extraluminal region in the neighbouring tissue. Our model gives results that are consistent with available experimental data and previous intraluminal transport models, including appreciable radial decreases in intraluminal PO(2) for all vessel diameters considered (12-100 μm) and slower longitudinal decreases in PO(2) for larger vessels than for smaller ones, and predicts substantially less diffusion of O(2) from arteriolar blood than do models with PO(2) specified at the edge of the lumen. The dependence of the new mass transfer coefficients on vessel diameter, SO(2) and far-field PO(2) is calculated allowing their application to a wide range of physiological situations. This novel arteriolar O(2) transport model will be a vital component of future integrated models of microvascular regulation of O(2) supply to capillary beds and the tissue regions they support.

Integration of cardiovascular regulation by the blood/endothelium cell-free layer

The cell-free layer (CFL) width separating red blood cells in flowing blood from the endothelial cell membrane is shown to be a regulator of the balance between nitric oxide (NO) production by the endothelium and NO scavenging by blood hemoglobin. The CFL width is determined by hematocrit (Hct) and the vessel wall flow velocity gradient. These factors and blood and plasma viscosity determine vessel wall shear stress which regulates the production of NO in the vascular wall. Mathematical modeling and experimental findings show that vessel wall NO concentration is a strong nonlinear function of Hct and that small Hct variations have comparatively large effects on blood pressure regulation. Furthermore, NO concentration is a regulator of inflammation and oxygen metabolism. Therefore, small, sustained perturbations of Hct may have long-term effects that can promote pro-hypertensive and pro-inflammatory conditions. In this context, Hct and its variability are directly related to vascular tone, peripheral vascular resistance, oxygen transport and delivery, and inflammation. These effects are relevant to the analysis and understanding of blood pressure regulation, as NO bioavailability regulates the contractile state of blood vessels. Furthermore, regulation of the CFL is a direct function of blood composition therefore understanding of its physiology relates to the design and management of fluid resuscitation fluids. From a medical perspective, these studies propose that it should be of clinical interest to note small variations in patient's Hct levels given their importance in modulating the CFL width and therefore NO bioavailability. WIREs Syst Biol Med 2011 3 458-470 DOI: 10.1002/wsbm.150

The effect of small changes in hematocrit on nitric oxide transport in arterioles

We report the development of a mathematical model that quantifies the effects of small changes in systemic hematocrit (Hct) on the transport of nitric oxide (NO) in the microcirculation. The model consists of coupled transport equations for NO and oxygen (O2) and accounts for both shear-induced NO production by the endothelium and the effect of changing systemic Hct on the rate of NO production and the rate of NO scavenging by red blood cells. To incorporate the dependence of the plasma layer width on changes in Hct, the model couples the hemodynamics of blood in arterioles with NO and O2 transport in the plasma layer. A sensitivity analysis was conducted to determine the effects of uncertain model parameters (the thicknesses of endothelial surface layers and diffusion coefficients of NO and O2 in muscle tissues and vascular walls) on the model's predictions. Our analysis reveals that small increases in Hct may raise NO availability in the vascular wall. This finding sheds new light on the experimental data that show that the blood circulation responds to systematic increases of Hct in a manner that is consistent with increasing NO production followed by a plateau.

Diaspirin cross-linked hemoglobin infusion did not influence base deficit and lactic acid levels in two clinical trials of traumatic hemorrhagic shock patient resuscitation

BACKGROUND

Diaspirin cross-linked hemoglobin (DCLHb) has demonstrated a pressor effect that could adversely affect traumatic hemorrhagic shock patients through diminished perfusion to vital organs, causing base deficit (BD) and lactate abnormalities.

METHODS

Data from two parallel, multicenter traumatic hemorrhagic shock clinical trials from 17 US Emergency Departments and 27 European Union prehospital services using DCLHb, a hemoglobin-based resuscitation fluid.

RESULTS

In the 219 patients, the mean age was 37.3 years, 64% of the patients sustained a blunt injury, 48% received DCLHb resuscitation, and the overall 28-day mortality rate was 36.5%. BD data did not differ by treatment group (DCLHb vs. normal saline [NS]) at any time point. Study entry BD was higher in patients who died when compared with survivors in both studies (US: -14.7 vs. -9.3 and European Union: -11.1 vs. -4.1 mEq/L, p < 0.003) and at the first three time points after resuscitation. No differences in BD based on treatment group were observed in either those who survived or those who died from the hemorrhagic shock. US lactate data did not differ by treatment group (DCLHb vs. NS) at any time point. Study entry lactates were higher in US patients who ultimately died when compared with survivors (82.4 vs. 56.1 mmol/L, p < 0.003) and at all five postresuscitation time points. No lactate differences were observed between DCLHb and NS survivors or in those who died based on treatment group.

CONCLUSIONS

Although patients who died had more greatly altered perfusion than those who survived, DCLHb treatment of traumatic hemorrhagic shock patients was not associated with BD or lactate abnormalities that would indicate poor perfusion.