Simple accurate mathematical models of blood HbO2 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other models

2,3-Diphosphoglyceric Acid Alleviating Hypoxic-Ischemic Brain Damage through p38 MAPK Modulation

Neonatal hypoxic-ischemic encephalopathy (HIE) is a critical condition characterized by significant brain damage due to insufficient blood flow and oxygen delivery at birth, leading to high rates of neonatal mortality and long-term neurological deficits worldwide. 2,3-Diphosphoglyceric acid (2,3-DPG), a small molecule metabolite prevalent in erythrocytes, plays an important role in regulating oxygen delivery, but its potential neuroprotective role in hypoxic-ischemic brain damage (HIBD) has yet to be fully elucidated. Our research reveals that the administration of 2,3-DPG effectively reduces neuron damage caused by hypoxia-ischemia (HI) both in vitro and in vivo. We observed a notable decrease in HI-induced neuronal cell apoptosis, attributed to the downregulation of Bax and cleaved-caspase 3, alongside an upregulation of Bcl-2 expression. Furthermore, 2,3-DPG significantly alleviates oxidative stress and mitochondrial damage induced by oxygen-glucose deprivation/reperfusion (OGD/R). The administration of 2,3-DPG in rats subjected to HIBD resulted in a marked reduction in brain edema and infarct volume, achieved through the suppression of neuronal apoptosis and neuroinflammation. Using RNA-seq analysis, we validated that 2,3-DPG offers protection against neuronal apoptosis under HI conditions by modulating the p38 MAPK pathway. These insights indicated that 2,3-DPG might act as a promising novel therapeutic candidate for HIE.

Dissolved Oxygen Relevantly Contributes to Systemic Oxygenation During Venovenous Extracorporeal Membrane Oxygenation Support

When determining extracorporeal oxygen transfer (V ML O 2 ) during venovenous extracorporeal membrane oxygenation (VV ECMO) dissolved oxygen is often considered to play a subordinate role due to its poor solubility in blood plasma. This study was designed to assess the impact of dissolved oxygen on systemic oxygenation in patients with acute respiratory distress syndrome (ARDS) on VV ECMO support by differentiating between dissolved and hemoglobin-bound extracorporeal oxygen transfer. We calculated both extracorporeal oxygen transfer based on blood gas analysis using the measuring energy expenditure in extracorporeal lung support patients (MEEP) protocol and measured oxygen uptake by the native lung with indirect calorimetry. Over 20% of V ML O 2 and over 10% of overall oxygen uptake (VO 2 total ) were realized as dissolved oxygen. The transfer of dissolved oxygen mainly depended on ECMO blood flow (BF ML ). In patients with severely impaired lung function dissolved oxygen accounted for up to 28% of VO 2 total . A clinically relevant amount of oxygen is transferred as physically dissolved fraction, which therefore needs to be considered when determining membrane lung function, manage ECMO settings or guiding the weaning procedure.

Quantitative Model-Based Assessment of Multiple Sickle Cell Disease Therapeutic Approaches Alone and in Combination

Three sickle cell disease (SCD) treatment strategies, stabilizing oxygenated hemoglobin (oxyHb), lowering 2,3-BPG, and inducing fetal hemoglobin (HbF) expression aim to prevent red blood cell (RBC) sickling by reducing tense-state sickle hemoglobin that contributes to polymer formation. Induction of 30% HbF is seen as the gold standard because 30% endogenous expression is associated with a lack of symptoms. However, the level of intervention required to achieve equivalent polymerization protection by the other strategies is uncertain, and there is little understanding of how these approaches could work in combination. We sought to develop an oxygen saturation model that could assess polymerization protection of all three approaches alone or in combination by extending the Monod-Wymann-Changeux model to include additional mechanisms. Applying the model to monotherapies suggests 51% sickle hemoglobin (HbS) occupancy with an oxyHb stabilizer or lowering RBC 2,3 BPG concentrations to 1.8 mM would produce comparable polymerization protection as 30% HbF. The model predictions are consistent with observed clinical response to the oxyHb stabilizer voxelotor and the 2,3-BPG reducer etavopivat. The model also suggests combination therapy will have added benefit in the case of dose limitations, as is the case for voxelotor, which the model predicts could be combined with 20% HbF or 2,3-BPG reduction to 3.75 mM to reach equivalent protection as 30% HbF. The proposed model represents a unified framework that is useful in supporting decisions in preclinical and early clinical development and capable of evolving with clinical experience to gain new and increasingly confident insights into treatment strategies for SCD.

Neuroinflammation increases oxygen extraction in a mouse model of Alzheimer's disease

BACKGROUND

Neuroinflammation, impaired metabolism, and hypoperfusion are fundamental pathological hallmarks of early Alzheimer's disease (AD). Numerous studies have asserted a close association between neuroinflammation and disrupted cerebral energetics. During AD progression and other neurodegenerative disorders, a persistent state of chronic neuroinflammation reportedly exacerbates cytotoxicity and potentiates neuronal death. Here, we assessed the impact of a neuroinflammatory challenge on metabolic demand and microvascular hemodynamics in the somatosensory cortex of an AD mouse model.

METHODS

We utilized in vivo 2-photon microscopy and the phosphorescent oxygen sensor Oxyphor 2P to measure partial pressure of oxygen (pO2) and capillary red blood cell flux in cortical microvessels of awake mice. Intravascular pO2 and capillary RBC flux measurements were performed in 8-month-old APPswe/PS1dE9 mice and wildtype littermates on days 0, 7, and 14 of a 14-day period of lipopolysaccharide-induced neuroinflammation.

RESULTS

Before the induced inflammatory challenge, AD mice demonstrated reduced metabolic demand but similar capillary red blood cell flux as their wild type counterparts. Neuroinflammation provoked significant reductions in cerebral intravascular oxygen levels and elevated oxygen extraction in both animal groups, without significantly altering red blood cell flux in capillaries.

CONCLUSIONS

This study provides evidence that neuroinflammation alters cerebral oxygen demand at the early stages of AD without substantially altering vascular oxygen supply. The results will guide our understanding of neuroinflammation's influence on neuroimaging biomarkers for early AD diagnosis.

Erythrocyte metabolism

Our aim is to present an updated overview of the erythrocyte metabolism highlighting its richness and complexity. We have manually collected and connected the available biochemical pathways and integrated them into a functional metabolic map. The focus of this map is on the main biochemical pathways consisting of glycolysis, the pentose phosphate pathway, redox metabolism, oxygen metabolism, purine/nucleoside metabolism, and membrane transport. Other recently emerging pathways are also curated, like the methionine salvage pathway, the glyoxalase system, carnitine metabolism, and the lands cycle, as well as remnants of the carboxylic acid metabolism. An additional goal of this review is to present the dynamics of erythrocyte metabolism, providing key numbers used to perform basic quantitative analyses. By synthesizing experimental and computational data, we conclude that glycolysis, pentose phosphate pathway, and redox metabolism are the foundations of erythrocyte metabolism. Additionally, the erythrocyte can sense oxygen levels and oxidative stress adjusting its mechanics, metabolism, and function. In conclusion, fine-tuning of erythrocyte metabolism controls one of the most important biological processes, that is, oxygen loading, transport, and delivery.

Thermodynamic limitations on brain oxygen metabolism: physiological implications

Recent thermodynamic modelling indicates that maintaining the brain tissue ratio of O2 to CO2 (abbreviated tissue O2 /CO2 ) is critical for preserving the entropy increase available from oxidative metabolism of glucose, with a fall of that available entropy leading to a reduction of the phosphorylation potential and impairment of brain energy metabolism. This provides a novel perspective for understanding physiological responses under different conditions in terms of preserving tissue O2 /CO2 . To enable estimation of tissue O2 /CO2 in the human brain, a detailed mathematical model of O2 and CO2 transport was developed, and applied to reported physiological responses to different challenges, asking: how well is tissue O2 /CO2 preserved? Reported experimental results for increased neural activity, hypercapnia and hypoxia due to high altitude are consistent with preserving tissue O2 /CO2 . The results highlight two physiological mechanisms that control tissue O2 /CO2 : cerebral blood flow, which modulates tissue O2 ; and ventilation rate, which modulates tissue CO2 . The hypoxia modelling focused on humans at high altitude, including acclimatized lowlanders and Tibetan and Andean adapted populations, with a primary finding that decreasing CO2 by increasing ventilation rate is more effective for preserving tissue O2 /CO2 than increasing blood haemoglobin content to maintain O2 delivery to tissue. This work focused on the function served by particular physiological responses, and the underlying mechanisms require further investigation. The modelling provides a new framework and perspective for understanding how blood flow and other physiological factors support energy metabolism in the brain under a wide range of conditions. KEY POINTS: Thermodynamic modelling indicates that preserving the O2 /CO2 ratio in brain tissue is critical for preserving the entropy change available from oxidative metabolism of glucose and the phosphorylation potential underlying energy metabolism. A detailed model of O2 and CO2 transport was developed to allow estimation of the tissue O2 /CO2 ratio in the human brain in different physiological states. Reported experimental results during hypoxia, hypercapnia and increased oxygen metabolic rate in response to increased neural activity are consistent with maintaining brain tissue O2 /CO2 ratio. The hypoxia modelling of high-altitude acclimatization and adaptation in humans demonstrates the critical role of reducing CO2 with increased ventilation for preserving tissue O2 /CO2 . Preservation of tissue O2 /CO2 provides a novel perspective for understanding the function of observed physiological responses under different conditions in terms of preserving brain energy metabolism, although the mechanisms underlying these functions are not well understood.

Revisiting cardiac output estimated noninvasively from oxygen uptake during exercise: an exploratory hypothesis-generating replication study

Stringer et al. [J Appl Physiol (1985) 82: 908-912, 1997] developed a method from invasive data to estimate cardiac output during incremental exercise testing based on Fick's principle. The authors proposed that the arterio-mixed venous oxygen content difference increases linearly with percentage of maximal O2 consumption. We hypothesized an S-shaped pattern in the published data and calculated the inflection point of this curve and of the standard resting oxygen dissociation curve. Using a partial F test, we compared the linear model with a third-order polynomial model, which showed a better fit to the data [F(2,101) = 9.5, P < 0.001]. This finding was reproduced in a dataset published by Åstrand et al. in 1964 [F(2, 122) = 10.6, P < 0.001]. The inflection point of the curve coincided with the lactate acidosis threshold [first ventilatory threshold (VT1)] as measured by Stringer et al. (VT1 at 50% and inflection point at 56% [95% CI, 52.9 to 60.7] of maximal O2 consumption). The inflection point of the standard resting oxygen dissociation curve was calculated at a partial pressure of 21.5 mmHg and a saturation of 36%, matching the "critical capillary Po2" concept of Stringer et al. (21.2 mmHg). We conclude that the arterio-mixed venous oxygen content difference increases in an S-shaped manner with percentage of maximal oxygen consumption and that the inflection point of this curve may correspond to VT1 and that of the in vivo oxygen dissociation curve. Further research is needed to confirm these findings and improve the method.NEW & NOTEWORTHY In 1997, Stringer, Hansen, and Wasserman developed a method for estimating cardiac output during incremental exercise testing. They observed that the arterio-mixed venous oxygen content difference increases linearly with the percentage of maximal O2 consumption. This increase may be better modelled by an S-shaped function, the inflection point of which may be related to the first ventilatory threshold and the inflection point of the oxygen dissociation curve. This finding may help to improve the method.

The oxygen dissociation curve of blood in COVID-19-An update

An impressive effect of the infection with SARS-Co-19 is the impairment of oxygen uptake due to lung injury. The reduced oxygen diffusion may potentially be counteracted by an increase in oxygen affinity of hemoglobin. However, hypoxia and anemia associated with COVID-19 usually decrease oxygen affinity due to a rise in [2,3-bisphosphoglycerate]. As such, COVID-19 related changes in the oxygen dissociation curve may be critical for oxygen uptake and supply, but are hard to predict. A Pubmed search lists 14 publications on oxygen affinity in COVID-19. While some investigations show no changes, three large studies found an increased affinity that was related to a good prognosis. Exact causes remain unknown. The cause of the associated anemia in COVID-19 is under discussion. Erythrocytes with structural alterations of membrane and cytoskeleton have been observed, and virus binding to Band 3 and also to ACE2 receptors in erythroblasts has been proposed. COVID-19 presentation is moderate in many subjects suffering from sickle cell disease. A possible explanation is that COVID-19 counteracts the unfavorable large right shift of the oxygen dissociation curve in these patients. Under discussion for therapy are mainly affinity-increasing drugs.

Measuring the Resting Energy Expenditure in Children on Extracorporeal Membrane Oxygenation: A Prospective Pilot Study

Both overfeeding and underfeeding critically ill children are problematic. This prospective pilot study evaluated the resting energy expenditure in infants and children requiring extracorporeal membrane oxygenation (ECMO) support. An indirect calorimeter was used to measure oxygen consumption (VO 2 ) and carbon dioxide production (VCO 2 ) from the mechanical ventilator. Blood gases were used to determine VO 2 and VCO 2 from the ECMO circuit. Values from the mechanical ventilator and ECMO circuit were added, and the resting energy expenditure (REE) (Kcal/kg/day) was calculated. Measurements were obtained > 24 hours after ECMO support was initiated (day 2 of ECMO), 1 day before ECMO discontinuation or transfer, and 1 day after decannulation. Data were compared with the predicted energy expenditure. Seven patients aged 3 months to 13 years were included. The REE varied greatly both above and below predicted values, from 26 to 154 KCal/kg/day on day 2 of ECMO support. In patients with septic shock, the REE was > 300% above the predicted value on day 2 of ECMO. Before ECMO discontinuation, two of six (33%) children continued to have a REE > 110% of predicted. Three patients had measurements after decannulation, all with a REE < 90% of predicted. REE measurements can be obtained by indirect calorimetry in children receiving ECMO support. ECMO may not provide metabolic rest for all children as a wide variation in REE was observed. For optimal care, individual testing should be considered to match calories provided with the metabolic demand.

Reply to Böning et al. Comment on “Ceruti et al. Temporal Changes in the Oxyhemoglobin Dissociation Curve of Critically Ill COVID-19 Patients. J. Clin. Med. 2022, 11, 788”

We would like to thank Böning et al. for all the important issues raised in the present commentary [...]

Comment on Ceruti et al. Temporal Changes in the Oxyhemoglobin Dissociation Curve of Critically Ill COVID-19 Patients. J. Clin. Med. 2022, 11, 788

Ceruti et al. describe in their article very low standard half saturation pressures (P50) in COVID-19 patients, calculated with the Dash et al. equations. By using the Hill equation and Severinghaus' coefficients we obtained normal values. The authors who do not present a pathophysiological cause for their results should explain this discrepancy. Independent of the absolute values a continuous moderate decrease of P50 in the surviving patients might be of clinical importance.

Estimating the best fraction of inspired oxygen for calculation of PaO2/FiO2 ratio in acute respiratory distress syndrome due to COVID-19 pneumonia

BACKGROUND

The ratio of partial pressure of oxygen in arterial blood (PaO2) to the fraction of inspiratory oxygen concentration (FiO2) is an indicator of pulmonary shunt fraction. PaO2/FiO2 (P/F) ratio is used to classify severity of acute respiratory distress syndrome (ARDS). With the same shunt fraction, P/F ratio decreases with increases in FiO2 which may lead to errors in classifying severity of ARDS. The effect of FiO2 on P/F ratio has not been investigated in COVID-19 pneumonia. In this study, we estimated the best FiO2 for the calculation of P/F ratio in a sample of patients with ARDS due to COVID-19 pneumonia.

MATERIALS AND METHODS

Blood gas and ventilatory data of 108 COVID-19 ARDS patients were analyzed in a cross-sectional observational study. Using Oxygen Status Algorithm the calculated shunt fraction served a basis for calculating P/F ratio for different FiO2. The severity of ARDS determined by P/F ratios at each FiO2s was compared with the shunt-based severity to find the optimum FiO2 for calculation of P/F ratio so the resulting classification has the best match with the reference classification.

RESULTS

A FiO2 of 1.0 for calculation of P/F ratio and ARDS classification showed the best match with shunt-based ARDS classification. A regression model was obtained with the PaO2, patient's original FiO2, Hemoglobin concentration, and SaO2 as the independent predictors of the P/F ratio for the FiO2 of 1.0.

CONCLUSION

This study shows a FiO2 of 1.0 as the best value for correct calculation of P/F ratio and proper classification of ARDS.

Hemodynamic and metabolic changes during hypercapnia with normoxia and hyperoxia using pCASL and TRUST MRI in healthy adults

Blood oxygenation level-dependent (BOLD) or arterial spin labeling (ASL) MRI with hypercapnic stimuli allow for measuring cerebrovascular reactivity (CVR). Hypercapnic stimuli are also employed in calibrated BOLD functional MRI for quantifying neuronally-evoked changes in cerebral oxygen metabolism (CMRO₂). It is often assumed that hypercapnic stimuli (with or without hyperoxia) are iso-metabolic; increasing arterial CO₂ or O₂ does not affect CMRO₂. We evaluated the null hypothesis that two common hypercapnic stimuli, 'CO₂ in air' and carbogen, are iso-metabolic. TRUST and ASL MRI were used to measure the cerebral venous oxygenation and cerebral blood flow (CBF), from which the oxygen extraction fraction (OEF) and CMRO₂ were calculated for room-air, 'CO₂ in air' and carbogen. As expected, CBF significantly increased (9.9% ± 9.3% and 12.1% ± 8.8% for 'CO₂ in air' and carbogen, respectively). CMRO₂ decreased for 'CO₂ in air' (-13.4% ± 13.0%, p < 0.01) compared to room-air, while the CMRO₂ during carbogen did not significantly change. Our findings indicate that 'CO₂ in air' is not iso-metabolic, while carbogen appears to elicit a mixed effect; the CMRO₂ reduction during hypercapnia is mitigated when including hyperoxia. These findings can be important for interpreting measurements using hypercapnic or hypercapnic-hyperoxic (carbogen) stimuli.

Modeling the oxygen transport to the myocardium at maximal exercise at high altitude

Exposure to high altitude induces a decrease in oxygen pressure and saturation in the arterial blood, which is aggravated by exercise. Heart rate (HR) at maximal exercise decreases when altitude increases in prolonged exposure to hypoxia. We developed a simple model of myocardial oxygenation in order to demonstrate that the observed blunting of maximal HR at high altitude is necessary for the maintenance of a normal myocardial oxygenation. Using data from the available scientific literature, we estimated the myocardial venous oxygen pressure and saturation at maximal exercise in two conditions: (1) with actual values of maximal HR (decreasing with altitude); (2) with sea-level values of maximal heart rate, whatever the altitude (no change in HR). We demonstrated that, in the absence of autoregulation of maximal HR, myocardial tissue oxygenation would be incompatible with life above 6200 m-7600 m, depending on the hypothesis concerning a possible increase in coronary reserve (increase in coronary blood flow at exercise). The decrease in maximal HR at high altitude could be explained by several biological mechanisms involving the autonomic nervous system and its receptors on myocytes. These experimental and clinical observations support the hypothesis that there exists an integrated system at the cellular level, which protects the myocardium from a hazardous disequilibrium between O₂  supply and O₂ consumption at high altitude.

Temporal Changes in the Oxyhemoglobin Dissociation Curve of Critically Ill COVID-19 Patients

Critical COVID-19 is a life-threatening disease characterized by severe hypoxemia with complex pathophysiological mechanisms that are not yet completely understood. A pathological shift in the oxyhemoglobin curve (ODC) was previously described through the analysis of p50, intended as the oxygen tension at which hemoglobin is saturated by oxygen at 50%. The aim of this study was to analyze Hb-O₂ affinity features over time in a cohort of critically ill COVID-19 patients, through the analysis of ODC p50 behavior. A retrospective analysis was performed; through multiple arterial blood gas (ABG) analyses, each p50 was calculated and normalized according to PaCO₂, pH and temperature; patients' p50 evolution over time was reported, comparing the first 3 days (early p50s) with the last 3 days (late p50s) of ICU stay. A total of 3514 ABG analyses of 32 consecutive patients were analyzed. The majority of patients presented a left shift over time (p = 0.03). A difference between early p50s and late p50s was found (20.63 ± 2.1 vs. 18.68 ± 3.3 mmHg, p = 0.03); median p50 of deceased patients showed more right shifts than those of alive patients (24.1 vs. 18.45 mmHg, p = 0.01). One-way ANOVA revealed a p50 variance greater in the early p50s (σ² = 8.6) than in the late p50s (σ² = 3.84), associated with a reduction over time (p < 0.001). Comparing the Hb-O₂ affinity in critically ill COVID-19 patients between ICU admission and ICU discharge, a temporal shift in the ODC was observed.

Interactive, Visual Simulation of a Spatio-Temporal Model of Gas Exchange in the Human Alveolus

In interdisciplinary fields such as systems biology, good communication between experimentalists and theorists is crucial for the success of a project. Theoretical modeling in physiology usually describes complex systems with many interdependencies. On one hand, these models have to be grounded on experimental data. On the other hand, experimenters must be able to understand the interdependent complexities of the theoretical model in order to interpret the model's results in the physiological context. We promote interactive, visual simulations as an engaging way to present theoretical models in physiology and to make complex processes tangible. Based on a requirements analysis, we developed a new model for gas exchange in the human alveolus in combination with an interactive simulation software named Alvin. Alvin exceeds the current standard with its spatio-temporal resolution and a combination of visual and quantitative feedback. In Alvin, the course of the simulation can be traced in a three-dimensional rendering of an alveolus and dynamic plots. The user can interact by configuring essential model parameters. Alvin allows to run and compare multiple simulation instances simultaneously. We exemplified the use of Alvin for research by identifying unknown dependencies in published experimental data. Employing a detailed questionnaire, we showed the benefits of Alvin for education. We postulate that interactive, visual simulation of theoretical models, as we have implemented with Alvin on respiratory processes in the alveolus, can be of great help for communication between specialists and thereby advancing research.

Accuracy and Reliability of Commercial Wrist-Worn Pulse Oximeter During Normobaric Hypoxia Exposure Under Resting Conditions

Purpose: The present study analyzed peripheral blood oxygen saturation (S_pO₂) and heart rate (HR) measurements taken on the Garmin fēnix® 5X Plus watch, comparing them to measurements taken on a standard medical-grade pulse oximeter during normobaric hypoxia exposure under resting conditions. Methods: Thirteen women (mean ± SD: Age 20 ± 1 years, height 165 ± 5 cm, mass, 67 ± 9 kg) and ten men (mean ± SD: Age 21 ± 3 years, height 177 ± 6 cm, mass 78 ± 11 kg) sat inside a customized environmental chamber while the fraction of inspired oxygen (F_IO₂) was adjusted to simulate altitudes of 12,000; 10,000; 8,000; 6,000; and 900 ft. The novel commercial device (Garmin fēnix®) and a medical-grade pulse oximeter (Nonin® 7500) were used to measure S_pO₂ and HR in triplicate at each simulated altitude. Bland-Altman analyses were used to assess differences between methods. Results: Bland-Altman analysis indicated 3.3% bias for S_pO₂ measurements taken on the Garmin fēnix® at 12,000 ft of simulated altitude (limits of agreement: -1.9-8.6%). Mean differences in S_pO₂ measurements were smaller at the remaining simulated altitudes, where bias measurements ranged from 0.7% to 0.8%. The Garmin fēnix® also underestimated heart rate, but those discrepancies were minimal (bias measurements at all simulated altitude exposures were < 1.0 bpm). Conclusions: With the exception of readings taken at 12,000 ft of simulated altitude, the Garmin fēnix® exhibits minimal overestimation of S_pO₂ and minimal underestimation of HR during simulated altitude exposure. These data suggest the Garmin fēnix® watch may be a viable method to monitor S_pO₂ and HR under most ambient environmental conditions.

The Affinity of Hemoglobin for Oxygen Is Not Altered During COVID-19

Background: A computational proteomic analysis suggested that SARS-CoV-2 might bind to hemoglobin (Hb). The authors hypothesized that this phenomenon could result in a decreased oxygen (O₂) binding and lead to hemolytic anemia as well. The aim of this work was to investigate whether the affinity of Hb for O₂ was altered during COVID-19. Methods: In this retrospective, observational, single-center study, the blood gas analyses of 100 COVID-19 patients were compared to those of 100 non-COVID-19 patients. Fifty-five patients with carboxyhemoglobin (HbCO) ≥8% and 30 with sickle cell disease (SCD) were also included ("positive controls" with abnormal Hb affinity). P₅₀ was corrected for body temperature, pH, and PCO₂. Results: Patients did not differ statistically for age or sex ratio in COVID-19 and non-COVID-19 groups. Median P₅₀ at baseline was 26 mmHg [25.2-26.8] vs. 25.9 mmHg [24-27.3], respectively (p = 0.42). As expected, P₅₀ was 22.5 mmHg [21.6-23.8] in the high HbCO group and 29.3 mmHg [27-31.5] in the SCD group (p < 0.0001). Whatever the disease severity, samples from COVID-19 to non-COVID-19 groups were distributed on the standard O₂-Hb dissociation curve. When considering the time-course of P₅₀ between days 1 and 18 in both groups, no significant difference was observed. Median Hb concentration at baseline was 14 g.dl^-1 [12.6-15.2] in the COVID-19 group vs. 13.2 g.dl^-1 [11.4-14.7] in the non-COVID-19 group (p = 0.006). Among the 24 COVID-19 patients displaying anemia, none of them exhibited obvious biological hemolysis. Conclusion: There was no biological argument to support the hypothesis that SARS-CoV-2 could alter O₂ binding to Hb.

Suitable CO2 Solubility Models for Determination of the CO2 Removal Performance of Oxygenators

CO₂ removal via membrane oxygenators during lung protective ventilation has become a reliable clinical technique. For further optimization of oxygenators, accurate prediction of the CO₂ removal rate is necessary. It can either be determined by measuring the CO₂ content in the exhaust gas of the oxygenator (sweep flow-based) or using blood gas analyzer data and a CO₂ solubility model (blood-based). In this study, we determined the CO₂ removal rate of a prototype oxygenator utilizing both methods in in vitro trials with bovine and in vivo trials with porcine blood. While the sweep flow-based method is reliably accurate, the blood-based method depends on the accuracy of the solubility model. In this work, we quantified performances of four different solubility models by calculating the deviation of the CO₂ removal rates determined by both methods. Obtained data suggest that the simplest model (Loeppky) performs better than the more complex ones (May, Siggaard-Anderson, and Zierenberg). The models of May, Siggaard-Anderson, and Zierenberg show a significantly better performance for in vitro bovine blood data than for in vivo porcine blood data. Furthermore, the suitability of the Loeppky model parameters for bovine blood (in vitro) and porcine blood (in vivo) is evaluated.

Bulk volume susceptibility difference between deoxyhemoglobin and oxyhemoglobin for HbA and HbS: A comparative study

PURPOSE

Sickle cell anemia is a blood disorder that alters the morphology and the oxygen affinity of the red blood cells. Cerebral oxygen extraction fraction measurements using quantitative BOLD contrast have been used for assessing inadequate oxygen delivery and the subsequent risk of ischemic stroke in sickle cell anemia. The BOLD signal in MRI studies relies on Δ χ do , the bulk volume susceptibility difference between fully oxygenated and fully deoxygenated blood. Several studies have measured Δ χ do for normal hemoglobin A (HbA). However, it is not known whether the value is different for sickle hemoglobin. In this study, Δ χ do was measured for both HbA and sickle hemoglobin.

METHODS

Six sickle cell anemia patients and 6 controls were recruited. Various blood oxygenation levels were achieved through in vivo manipulations to keep the blood close to its natural state. To account for the differences in oxygen affinity, Hill's equations were used to translate partial pressure of oxygen to oxygen saturation for HbA, sickle hemoglobin, and fetal hemoglobin (HbF) separately. The pH and PCO₂ corrections were performed. Temperature and magnetic field drift were controlled for. A multivariate generalized linear mixed model with random participant effect was used.

RESULTS

Assuming that Δ χ do is similar for HbA and HbF and that Δ χ metHb is 5/4 of Δ χ do for HbA, it was found that the Δ χ do values for HbA and sickle hemoglobin were not statistically significantly different from each other.

CONCLUSION

The same Δ χ do value can be used for both types of hemoglobin in quantitative BOLD analysis.

Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points

Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient-specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least-squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application.

Single-cell O2 exchange imaging shows that cytoplasmic diffusion is a dominant barrier to efficient gas transport in red blood cells

Blood is routinely tested for gas-carrying capacity (total hemoglobin), but this cannot determine the speed at which red blood cells (RBCs) exchange gases. Such information is critical for evaluating the physiological fitness of RBCs, which have very limited capillary transit times (<1 s) for turning over substantial volumes of gas. We developed a method to quantify gas exchange in individual RBCs and used it to show that restricted diffusion, imposed by hemoglobin crowding, is a major barrier to gas flows. Consequently, hematological disorders manifesting a change in cell shape or hemoglobin concentration have uncharted implications on gas exchange, which we illustrate using inherited anemias. With its single-cell resolution, the method can identify physiologically inferior subpopulations, providing a clinically useful appraisal of blood quality.

Disorders of oxygen transport are commonly attributed to inadequate carrying capacity (anemia) but may also relate to inefficient gas exchange by red blood cells (RBCs), a process that is poorly characterized yet assumed to be rapid. Without direct measurements of gas exchange at the single-cell level, the barriers to O₂ transport and their relationship with hematological disorders remain ill defined. We developed a method to track the flow of O₂ in individual RBCs by combining ultrarapid solution switching (to manipulate gas tension) with single-cell O₂ saturation fluorescence microscopy. O₂ unloading from RBCs was considerably slower than previously estimated in acellular hemoglobin solutions, indicating the presence of diffusional barriers in intact cells. Rate-limiting diffusion across cytoplasm was demonstrated by osmotically induced changes to hemoglobin concentration (i.e., diffusive tortuosity) and cell size (i.e., diffusion pathlength) and by comparing wild-type cells with hemoglobin H (HbH) thalassemia (shorter pathlength and reduced tortuosity) and hereditary spherocytosis (HS; expanded pathlength). Analysis of the distribution of O₂ unloading rates in HS RBCs identified a subpopulation of spherocytes with greatly impaired gas exchange. Tortuosity imposed by hemoglobin was verified by demonstrating restricted diffusivity of CO₂, an acidic gas, from the dissipative spread of photolytically uncaged H⁺ ions across cytoplasm. Our findings indicate that cytoplasmic diffusion, determined by pathlength and tortuosity, is a major barrier to efficient gas handling by RBCs. Consequently, changes in RBC shape and hemoglobin concentration, which are common manifestations of hematological disorders, can have hitherto unrecognized and clinically significant implications on gas exchange.

A procedure for determining subject-specific pulse oxygen saturation response

The oxyhemoglobin dissociation curve describes the relationship between the partial pressure of oxygen and the percent of hemoglobin saturated with oxygen and varies with chemical and physical factors that differ for every patient. If variability could be determined, patient-specific oxygen therapy could be administered. We have developed a procedure for characterizing variations in the oxygen dissociation curve. The purpose of this study was to validate this procedure in surgical patients. The procedure uses an automated system to alter oxygen therapy during surgery, within safe operational levels, and fit to Hill's equation non-invasive measurements of end-tidal oxygen and peripheral pulse oxygen saturation. The best-fit parameters for the Hill equation, estimated by iterative least squares, provide an apparent dissociation curve, meaningful of the patient-specific pulse oximeter response. Thirty-nine patients participated in this study. Using patient-specific parameter values increases correlation when compared with standard values. The procedure improved the model fit of patient saturation values significantly in 19 patients. This paper has demonstrated a procedure for determining patient-specific pulse oximeter response. This procedure determined best-fit parameters resulting in a significantly improved fit when compared with standard values. These best-fit parameters increased the coefficient of determination R² in all cases. Graphical Abstract This patient-specific procedure improves fit significantly compared to standard estimates.

Differences in alveolo-capillary equilibration in healthy subjects on facing O2 demand

Oxygen diffusion across the air-blood barrier in the lung is commensurate with metabolic needs and ideally allows full equilibration between alveolar and blood partial oxygen pressures. We estimated the alveolo-capillary O2 equilibration in 18 healthy subjects at sea level at rest and after exposure to increased O2 demand, including work at sea level and on hypobaric hypoxia exposure at 3840 m (PA ~ 50 mmHg). For each subject we estimated O2 diffusion capacity (DO2), pulmonary capillary blood volume (Vc) and cardiac output ([Formula: see text]). We derived blood capillary transit time [Formula: see text] and the time constant of the equilibration process ([Formula: see text], β being the slope of the hemoglobin dissociation curve). O2 equilibration at the arterial end of the pulmonary capillary was defined as [Formula: see text]. Leq greately differed among subjects in the most demanding O2 condition (work in hypoxia): lack of full equilibration was found to range from 5 to 42% of the alveolo-capillary PO2 gradient at the venous end. The present analysis proves to be sensible enough to highlight inter-individual differences in alveolo-capillary equilibration among healthy subjects.

The effect of flow on blood oxygen level dependent (R* 2 ) MRI of orthotopic lung tumors

PURPOSE

Blood oxygen level dependent (BOLD) MRI based on R 2 * measurements can provide insights into tumor vascular oxygenation. However, measurements are susceptible to blood flow, which may vary accompanying a hyperoxic gas challenge. We investigated flow sensitivity by comparing R 2 * measurements with and without flow suppression (fs) in 2 orthotopic lung xenograft tumor models.

METHODS

H460 (n = 20) and A549 (n = 20) human lung tumor xenografts were induced by surgical implantation of cancer cells in the right lung of nude rats. MRI was performed at 4.7T after tumors reached 5 to 8 mm in diameter. A multiecho gradient echo MRI sequence was acquired with and without spatial saturation bands on each side of the imaging plane to evaluate the effect of flow on R 2 * . fs and non-fs R 2 * MRI measurements were interleaved during an oxygen breathing challenge (from air to 100% O₂ ). T 2 * -weighted signal intensity changes (ΔSI(%)) and R 2 * measurements were obtained for regions of interest and on a voxel-by-voxel basis and discrepancies quantified with Bland-Altman analysis.

RESULTS

Flow suppression affected ΔSI(%) and R 2 * measurements in each tumor model. Average discrepancy and limits of agreement from Bland-Altman analyses revealed greater flow-related bias in A549 than H460.

CONCLUSION

The effect of flow on R 2 * , and hence BOLD, was tumor model dependent with measurements being more sensitive in well-perfused A549 tumors.

The Relation Between Capillary Transit Times and Hemoglobin Saturation Heterogeneity. Part 2: Capillary Networks

Brain metabolism is highly dependent on continuous oxygen supply. Cortical microvascular networks exhibit heterogeneous blood flow, leading to non-uniform tissue oxygenation and capillary hemoglobin saturation. We recently proposed capillary outflow saturation heterogeneity (COSH) to represent effects of heterogeneity on oxygen supply to tissue regions most vulnerable to hypoxia, and showed that diffusive oxygen exchange among red blood cells within capillaries and among capillaries (diffusive interaction) significantly reduces COSH in simplified geometrical configurations. Here, numerical simulations of oxygen transport in capillary network geometries derived from mouse somatosensory cortex are presented. Diffusive interaction was found to reduce COSH by 41 to 62% compared to simulations where diffusive interaction was excluded. Hemoglobin saturation drop across the microvascular network is strongly correlated with red blood cell transit time, but the coefficient of variation of saturation drop is approximately one third lower. Unexpectedly, the radius of the tissue cylinder supplied by a capillary correlates weakly with the anatomical tissue cylinder radius, but strongly with hemoglobin saturation. Thus, diffusive interaction contributes greatly to the microcirculation's ability to achieve tissue oxygenation, despite heterogeneous capillary transit time and hematocrit distribution. These findings provide insight into the effects of cerebral small vessel disease on tissue oxygenation and brain function.

Accounting for oxygen in the renal cortex: a computational study of factors that predispose the cortex to hypoxia

We develop a pseudo-three-dimensional model of oxygen transport for the renal cortex of the rat, incorporating both the axial and radial geometry of the preglomerular circulation and quantitative information regarding the surface areas and transport from the vasculature and renal corpuscles. The computational model was validated by simulating four sets of published experimental studies of renal oxygenation in rats. Under the control conditions, the predicted cortical tissue oxygen tension ([Formula: see text]) or microvascular oxygen tension (µPo2) were within ±1 SE of the mean value observed experimentally. The predicted [Formula: see text] or µPo2 in response to ischemia-reperfusion injury, acute hemodilution, blockade of nitric oxide synthase, or uncoupling mitochondrial respiration, were within ±2 SE observed experimentally. We performed a sensitivity analysis of the key model parameters to assess their individual or combined impact on the predicted [Formula: see text] and µPo2. The model parameters analyzed were as follows: 1) the major determinants of renal oxygen delivery ([Formula: see text]) (arterial blood Po2, hemoglobin concentration, and renal blood flow); 2) the major determinants of renal oxygen consumption (V̇o2) [glomerular filtration rate (GFR) and the efficiency of oxygen utilization for sodium reabsorption (β)]; and 3) peritubular capillary surface area (PCSA). Reductions in PCSA by 50% were found to profoundly increase the sensitivity of [Formula: see text] and µPo2 to the major the determinants of [Formula: see text] and V̇o2. The increasing likelihood of hypoxia with decreasing PCSA provides a potential explanation for the increased risk of acute kidney injury in some experimental animals and for patients with chronic kidney disease.

Equations for O2 and CO2 solubilities in saline and plasma: combining temperature and density dependences

Solubilities of respiratory gasses in water, saline, and plasma decrease with rising temperatures and solute concentrations. Henry's Law, C = α·P, states that the equilibrium concentration of a dissolved gas is solubility times partial pressure. Solubilities in the water of a solution depend on temperature and the content of other solutes. Blood temperatures may differ more than 20°C between skin and heart, and an erythrocyte will undergo that range as blood circulates. The concentrations of O₂ and CO₂ are the driving forces for diffusion, exchanges, and for reactions. We provide an equation for O₂ and CO₂ solubilities, α, that allows for continuous changes in temperature, T, and solution density, ρ, in dynamically changing states:[Formula: see text]This two-exponential expression with a density scalar γ, and a density exponent β, accounts for solubility changes due to density changes of an aqueous solution. It fits experimental data on solubilities in water, saline, and plasma over temperatures from 20 to 40°C, and for plasma densities, ρ_sol up to 1.020 g/ml with ~0.3% error. The amounts of additional bound O₂ (to Hb) and CO₂ (bicarbonate and carbamino) depend on the concentrations in the local water space and the reaction parameters. During exercise, solubility changes are large; both ρ_sol and T change rapidly with spatial position and with time. In exercise hemoconcentration plasma, ρ_sol exceeds 1.02, whereas T may range over 20°C. The six parameters for O₂ and the six for CO₂ are constants, so solubilities are calculable continuously as T and ρ_sol change.NEW & NOTEWORTHY Solubilities for oxygen and carbon dioxide are dependent on the density of the solution, on temperature, and on the partial pressure. We provide a brief equation suitable for hand calculators or mathematical modeling, accounting for these factors over a wide range of temperatures and solution densities for use in rapidly changing conditions, such as extreme exercise or osmotic transients, with better than 0.5% accuracy.

A mechanistic physicochemical model of carbon dioxide transport in blood

A number of mathematical models have been produced that, given the Pco₂ and Po₂ of blood, will calculate the total concentrations for CO₂ and O₂ in blood. However, all these models contain at least some empirical features, and thus do not represent all of the underlying physicochemical processes in an entirely mechanistic manner. The aim of this study was to develop a physicochemical model of CO₂ carriage by the blood to determine whether our understanding of the physical chemistry of the major chemical components of blood together with their interactions is sufficiently strong to predict the physiological properties of CO₂ carriage by whole blood. Standard values are used for the ionic composition of the blood, the plasma albumin concentration, and the hemoglobin concentration. All K_m values required for the model are taken from the literature. The distribution of bicarbonate, chloride, and H⁺ ions across the red blood cell membrane follows that of a Gibbs-Donnan equilibrium. The system of equations that results is solved numerically using constraints for mass balance and electroneutrality. The model reproduces the phenomena associated with CO₂ carriage, including the magnitude of the Haldane effect, very well. The structural nature of the model allows various hypothetical scenarios to be explored. Here we examine the effects of 1) removing the ability of hemoglobin to form carbamino compounds; 2) allowing a degree of Cl^- binding to deoxygenated hemoglobin; and 3) removing the chloride (Hamburger) shift. The insights gained could not have been obtained from empirical models.

NEW & NOTEWORTHY

This study is the first to incorporate a mechanistic model of chloride-bicarbonate exchange between the erythrocyte and plasma into a full physicochemical model of the carriage of carbon dioxide in blood. The mechanistic nature of the model allowed a theoretical study of the quantitative significance for carbon dioxide transport of carbamino compound formation; the putative binding of chloride to deoxygenated hemoglobin, and the chloride (Hamburger) shift.

The Bohr Effect Is Not a Likely Promoter of Renal Preglomerular Oxygen Shunting

The aim of this study was to evaluate whether possible preglomerular arterial-to-venous oxygen shunting is affected by the interaction between renal preglomerular carbon dioxide and oxygen transport. We hypothesized that a reverse (venous-to-arterial) shunting of carbon dioxide will increase partial pressure of carbon dioxide and decrease pH in the arteries and thereby lead to increased oxygen offloading and consequent oxygen shunting. To test this hypothesis, we employed a segment-wise three-dimensional computational model of coupled renal oxygen and carbon dioxide transport, wherein coupling is achieved by shifting the oxygen-hemoglobin dissociation curve in dependence of local changes in partial pressure of carbon dioxide and pH. The model suggests that primarily due to the high buffering capacity of blood, there is only marginally increased acidity in the preglomerular vasculature compared to systemic arterial blood caused by carbon dioxide shunting. Furthermore, effects of carbon dioxide transport do not promote but rather impair preglomerular oxygen shunting, as the increase in acidity is higher in the veins compared to that in the arteries. We conclude that while substantial arterial-to-venous oxygen shunting might take place in the postglomerular vasculature, the net amount of oxygen shunted at the preglomerular vasculature appears to be marginal.

Comparison of tissue oximeters on a liquid phantom with adjustable optical properties

The SafeBoosC trial showed that cerebral oximetry combined with a treatment guideline can reduce the the burden of hypoxia in neonates by 50% [Brit. Med. J.350, g7635 (2015)]. However, guidelines based on oximetry by one oximeter are not directly usable by other oximeters. We made a blood-lipid phantom simulating the neonatal head to determine the relation between oxygenation values obtained by different oximeters. We calculated coefficients for easy conversion from one oximeter to the other. We additionally determined the corresponding SafeBoosC intervention thresholds at which we measured an uncertainty of up to 9.2% when varying hemoglobin content from 25μM to 70μM. In conclusion, this paper makes the comparison of absolute values obtained by different oximeters possible.

IN SILICO MODELING OF THE REDOX METABOLISM IN HUMAN ERYTHROCYTES

There was elaborated the mathematical model of erythrocytes metabolism, including glycolysis (Embden-Meyerhof pathway), pentose phosphate pathway, metHb restoration pathway, Н2О2 metabolism reaction. The final model includes 50 reactions and 60 metabolites. Within the model was studied the change of activity of some enzymes and concentrations of metabolites in stationary state, that take part in the processes of utilization of oxygen active forms and restoration of metgemoglobin, depending on amount of exogenous and endogenous Н2О2. There was demonstrated the threshold character of changes of the many studied parameters, that testifies that the cells can be practically in physiological state at the change of external conditions for rather long time. There was carried out an assessment of redox-state of erythrocytes at oxidizing load: was demonstrated the change of EGSSG/2GSH, ENADP+/NADPH and ENAD+/NADH from the concentration of endogenous Н2О2. There was established that in the studied diapason of concentrations of endogenous Н2О2 was observed the high slope of the change of EGSSG/2GSH, that was not observed for ENADP+/NADPH and the other redox-pairs. The results of modeling coincide with existing views on the functioning of enzymes of antioxidant protection in human erythrocytes and testify to the possibility of practical use of the model