Blood HbO2 and HbCO2 Dissociation Curves at Varied O2, CO2, pH, 2,3-DPG and Temperature Levels

Relationship between muscle venous blood oxygenation and near-infrared spectroscopy: quantitative analysis of the Hb and Mb contributions

A linear relationship between skeletal muscle venous ([Formula: see text]) and oxygenated (ΔHbMbO2,N) or deoxygenated (ΔHHbMbN) near-infrared spectroscopy (NIRS) signals suggest a main hemoglobin (Hb) contribution to the NIRS signal. However, experimental, and computational evidence supports a significant contribution of myoglobin (Mb) to the NIRS. Venous and NIRS measurements from a canine model of muscle oxidative metabolism (Sun Y, Ferguson BS, Rogatzki MJ, McDonald JR, Gladden LB. Med Sci Sports Exerc 48(10):2013-2020, 2016) were integrated into a computational model of muscle O2 transport and utilization to evaluate whether the relationship between venous and NIRS oxygenation can be affected by a significant Mb contribution to the NIRS signals. The mathematical model predicted well the measure of the changes of [Formula: see text] and NIRS signals for different O2 delivery conditions (blood flow, arterial O2 content) in muscle at rest (T1, T2) and during contraction (T3). Furthermore, computational analysis indicates that for adequate O2 delivery, Mb contribution to NIRS signals was significant (20%-30%) even in the presence of a linear [Formula: see text]-NIRS relationship; for a reduced O2 delivery the nonlinearity of the [Formula: see text]-NIRS relationship was related to the Mb contribution (50%). In this case (T3), the deviation from linearity is observed when O2 delivery is reduced from 1.3 to 0.7 L kg-1·min-1 ([Formula: see text] < 10 mLO2 100 mL-1) and Mb saturation decreased from 85% to 40% corresponding to an increase of the Mb contribution to ΔHHbMbN from 15% to 50% and the contribution to ΔHbMbO2,N from 0% to 30%. In contrast to a common assumption, our model indicates that both NIRS signals (ΔHHbMbN and ΔHbMbO2,N are significantly affected by Hb and Mb oxygenation changes.NEW & NOTEWORTHY Within the near-infrared spectroscopy (NIRS) signal, the contribution from hemoglobin is indistinguishable from that of myoglobin. A computation analysis indicates that a linear relationship between muscle venous oxygen content and NIRS signals does not necessarily indicate a negligible myoglobin contribution to the NIRS signal. A reduced oxygen delivery increases the myoglobin contribution to the NIRS signal. The integrative approach proposed is a powerful way to assist in interpreting the elements from which the NIRS signals are derived.

Integral assessment of gas exchange during veno-arterial ECMO: accuracy and precision of a modified Fick principle in a porcine model

Assessment of native cardiac output during extracorporeal circulation is challenging. We assessed a modified Fick principle under conditions such as dead space and shunt in 13 anesthetized swine undergoing centrally cannulated veno-arterial extracorporeal membrane oxygenation (V-A ECMO, 308 measurement periods) therapy. We assumed that the ratio of carbon dioxide elimination (V̇co₂) or oxygen uptake (V̇o₂) between the membrane and native lung corresponds to the ratio of respective blood flows. Unequal ventilation/perfusion (V̇/Q̇) ratios were corrected towards unity. Pulmonary blood flow was calculated and compared to an ultrasonic flow probe on the pulmonary artery with a bias of 99 mL/min (limits of agreement -542 to 741 mL/min) with blood content V̇o₂ and no-shunt, no-dead space conditions, which showed good trending ability (least significant change from 82 to 129 mL). Shunt conditions led to underestimation of native pulmonary blood flow (bias -395, limits of agreement -1,290 to 500 mL/min). Bias and trending further depended on the gas (O₂, CO₂) and measurement approach (blood content vs. gas phase). Measurements in the gas phase increased the bias (253 [LoA -1,357 to 1,863 mL/min] for expired V̇o₂ bias 482 [LoA -760 to 1,724 mL/min] for expired V̇co₂) and could be improved by correction of V̇/Q̇ inequalities. Our results show that common assumptions of the Fick principle in two competing circulations give results with adequate accuracy and may offer a clinically applicable tool. Precision depends on specific conditions. This highlights the complexity of gas exchange in membrane lungs and may further deepen the understanding of V-A ECMO.

A quantitative model for human neurovascular coupling with translated mechanisms from animals

Neurons regulate the activity of blood vessels through the neurovascular coupling (NVC). A detailed understanding of the NVC is critical for understanding data from functional imaging techniques of the brain. Many aspects of the NVC have been studied both experimentally and using mathematical models; various combinations of blood volume and flow, local field potential (LFP), hemoglobin level, blood oxygenation level-dependent response (BOLD), and optogenetics have been measured and modeled in rodents, primates, or humans. However, these data have not been brought together into a unified quantitative model. We now present a mathematical model that describes all such data types and that preserves mechanistic behaviors between experiments. For instance, from modeling of optogenetics and microscopy data in mice, we learn cell-specific contributions; the first rapid dilation in the vascular response is caused by NO-interneurons, the main part of the dilation during longer stimuli is caused by pyramidal neurons, and the post-peak undershoot is caused by NPY-interneurons. These insights are translated and preserved in all subsequent analyses, together with other insights regarding hemoglobin dynamics and the LFP/BOLD-interplay, obtained from other experiments on rodents and primates. The model can predict independent validation-data not used for training. By bringing together data with complementary information from different species, we both understand each dataset better, and have a basis for a new type of integrative analysis of human data.

Pathophysiology and clinical implications of the veno-arterial PCO2 gap

This article is one of ten reviews selected from the Annual Update in Intensive Care and Emergency Medicine 2021. Other selected articles can be found online at https://www.biomedcentral.com/collections/annualupdate2021 . Further information about the Annual Update in Intensive Care and Emergency Medicine is available from https://link.springer.com/bookseries/8901 .

Oxygen Pathway Limitations in Patients With Chronic Thromboembolic Pulmonary Hypertension

BACKGROUND

Exertional intolerance is a limiting and often crippling symptom in patients with chronic thromboembolic pulmonary hypertension (CTEPH). Traditionally the pathogenesis has been attributed to central factors, including ventilation/perfusion mismatch, increased pulmonary vascular resistance, and right heart dysfunction and uncoupling. Pulmonary endarterectomy and balloon pulmonary angioplasty provide substantial improvement of functional status and hemodynamics. However, despite normalization of pulmonary hemodynamics, exercise capacity often does not return to age-predicted levels. By systematically evaluating the oxygen pathway, we aimed to elucidate the causes of functional limitations in patients with CTEPH before and after pulmonary vascular intervention.

METHODS

Using exercise cardiac magnetic resonance imaging with simultaneous invasive hemodynamic monitoring, we sought to quantify the steps of the O₂ transport cascade from the mouth to the mitochondria in patients with CTEPH (n=20) as compared with healthy participants (n=10). Furthermore, we evaluated the effect of pulmonary vascular intervention (pulmonary endarterectomy or balloon angioplasty) on the individual components of the cascade (n=10).

RESULTS

Peak Vo₂ (oxygen uptake) was significantly reduced in patients with CTEPH relative to controls (56±17 versus 112±20% of predicted; P<0.0001). The difference was attributable to impairments in multiple steps of the O₂ cascade, including O₂ delivery (product of cardiac output and arterial O₂ content), skeletal muscle diffusion capacity, and pulmonary diffusion. The total O₂ extracted in the periphery (ie, ΔAVo₂ [arteriovenous O₂ content difference]) was not different. After pulmonary vascular intervention, peak Vo₂ increased significantly (from 12.5±4.0 to 17.8±7.5 mL/[kg·min]; P=0.036) but remained below age-predicted levels (70±11%). The O₂ delivery was improved owing to an increase in peak cardiac output and lung diffusion capacity. However, peak exercise ΔAVo₂ was unchanged, as was skeletal muscle diffusion capacity.

CONCLUSIONS

We demonstrated that patients with CTEPH have significant impairment of all steps in the O₂ use cascade, resulting in markedly impaired exercise capacity. Pulmonary vascular intervention increased peak Vo₂ by partly correcting O₂ delivery but had no effect on abnormalities in peripheral O₂ extraction. This suggests that current interventions only partially address patients' limitations and that additional therapies may improve functional capacity.

Krogh’s capillary recruitment hypothesis, 100 years on: Is the opening of previously closed capillaries necessary to ensure muscle oxygenation during exercise?

In 1919, August Krogh published his seminal work on skeletal muscle oxygenation. Krogh’s observations indicated that muscle capillary diameter is actively regulated, rather than a passive result of arterial blood flow regulation. Indeed, combining a mathematical model with the number of ink-filled capillaries he observed in muscle cross sections taken at different workloads, Krogh was able to account for muscle tissue’s remarkably efficient oxygen extraction during exercise in terms of passive diffusion from nearby capillaries. Krogh was awarded the 1920 Nobel Prize for his account of muscle oxygenation. Today, his observations are engrained in the notion of capillary recruitment: the opening of previously closed capillaries. While the binary distinction between “closed” and “open” was key to Krogh’s model argument, he did in fact report a continuum of capillary diameters, degrees of erythrocyte deformation, and perfusion states. Indeed, modern observations question the presence of closed muscle capillaries. We therefore examined whether changes in capillary flow patterns and hematocrit among open capillaries can account for oxygen extraction in muscle across orders-of-magnitude changes in blood flow. Our four-compartment model of oxygen extraction in muscle confirms this notion and provides a framework for quantifying the impact of changes in microvascular function on muscle oxygenation in health and disease. Our results underscore the importance of capillary function for oxygen extraction in muscle tissue as first proposed by Krogh. While Krogh’s model calculations still hold, our model predictions support that capillary recruitment can be viewed in the context of continuous, rather than binary, erythrocyte distributions among capillaries.

NEW & NOTEWORTHY Oxygen extraction in working muscle is extremely efficient in view of single capillaries properties. The underlying mechanisms have been widely debated. Here, we develop a four-compartment model to quantify the influence of each of the hypothesized mechanisms on muscle oxygenation. Our results show that changes in capillary flow pattern and hematocrit can account for the high oxygen extraction observed in working muscle, while capillary recruitment is not required to account for these extraction properties.

Determination of optical properties of human tissues obtained from parotidectomy in the spectral range of 250 to 800 nm

The optical properties of human tissues are an important parameter in medical diagnostics and therapy. The knowledge of these parameters can encourage the development of automated, computer-driven optical tissue analysis methods. We determine the absorption coefficient μa and scattering coefficient μ s ' of different tissue types obtained during parotidectomy in the wavelength range of 250 to 800 nm. These values are determined by high precision integrating sphere measurements in combination with an optimized inverse Monte Carlo simulation. To conserve the optical behavior of living tissues, the optical spectroscopy measurements are performed immediately after tissue removal. Our study includes fresh samples of the ear, nose, and throat (ENT) region, as muscle tissue, nervous tissue, white adipose tissue, stromal tissue, parotid gland, and tumorous tissue of five patients. The measured behavior of adipose corresponds well with the literature, which sustains the applied method. It is shown that muscle is well supplied with blood as it features the same characteristic peaks at 430 and 555 nm in the absorption curve. The parameter μ s ' decreases for all tissue types above 570 nm. The accuracy is adequate for the purposes of providing μa and μ s ' of different human tissue types as muscle, fat, nerve, or gland tissue, which are embedded in large complex structures such as in the ENT area. It becomes possible for the first time to present reasonable results for the optical behavior of human soft tissue located in the ENT area and in the near-UV, visual, and near-infrared areas.

The relative influence of hematocrit and red blood cell velocity on oxygen transport from capillaries to tissue

OBJECTIVE

Oxygen transport to parenchymal cells occurs mainly at the microvascular level and depends on convective RBC flux, which is proportional in an individual capillary to the product of capillary hematocrit and RBC velocity. This study investigates the relative influence of these two factors on tissue PO₂ .

METHODS

A simple analytical model is used to quantify the respective influences of hematocrit, RBC velocity, and RBC flow on tissue oxygenation around capillaries. Predicted tissue PO₂ levels are compared with a detailed computational model.

RESULTS

Hematocrit is shown to have a larger influence on tissue PO₂ than RBC velocity. The effect of RBC velocity increases with distance from the arterioles. Good agreement between analytical and numerical results is obtained, and the discrepancies are explained. Significant dependence of MTCs on RBC velocity at low hematocrit is demonstrated.

CONCLUSIONS

For a given RBC flux in a capillary, the PO₂ in the surrounding tissue increases with increasing hematocrit, as a consequence of decreasing IVR to diffusive oxygen transport from RBCs to tissue. These results contribute to understanding the effects of blood flow changes on oxygen transport, such as those that occur in functional hyperemia in the brain.

The effects of capillary transit time heterogeneity on the BOLD signal

Neurovascular coupling mechanisms give rise to vasodilation and functional hyperemia upon neural activation, thereby altering blood oxygenation. This blood oxygenation level dependent (BOLD) contrast allows studies of activation patterns in the working human brain by functional MRI (fMRI). The BOLD-weighted fMRI signal shows characteristic transients in relation to functional activation, such as the so-called initial dip, overshoot, and post-stimulus undershoot. These transients are modulated by other physiological stimuli and in disease, but the underlying physiological mechanisms remain incompletely understood. Capillary transit time heterogeneity (CTH) has been shown to affect oxygen extraction, and hence blood oxygenation. Here, we examine how recently reported redistributions of capillary blood flow during functional activation would be expected to affect BOLD signal transients. We developed a three-compartment (hemoglobin, plasma, and tissue) model to predict the BOLD signal, incorporating the effects of dynamic changes in CTH. Our model predicts that the BOLD signal represents the superposition of a positive component resulting from increases in cerebral blood flow (CBF), and a negative component, resulting from elevated tissue metabolism and homogenization of capillary flows (reduced CTH). The model reproduces salient features of BOLD signal dynamics under conditions such as hypercapnia, hyperoxia, and caffeine intake, where both brain physiology and BOLD characteristics are altered. Neuroglial signaling and metabolism could affect CBF and capillary flow patterns differently. Further studies of neurovascular and neuro-capillary coupling mechanisms may help us relate BOLD signals to the firing of certain neuronal populations based on their respective BOLD "fingerprints."

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

PURPOSE

Equations for blood oxyhemoglobin (HbO2) and carbaminohemoglobin (HbCO2) dissociation curves that incorporate nonlinear biochemical interactions of oxygen and carbon dioxide with hemoglobin (Hb), covering a wide range of physiological conditions, are crucial for a number of practical applications. These include the development of physiologically-based computational models of alveolar-blood and blood-tissue O2–CO2 transport, exchange, and metabolism, and the analysis of clinical and in vitro data.

METHODS AND RESULTS

To this end, we have revisited, simplified, and extended our previous models of blood HbO2 and HbCO2 dissociation curves (Dash and Bassingthwaighte, Ann Biomed Eng 38:1683–1701, 2010), validated wherever possible by available experimental data, so that the models now accurately fit the low HbO2 saturation (SHbO2) range over a wide range of values of PCO2, pH, 2,3-DPG, and temperature. Our new equations incorporate a novel PO2-dependent variable cooperativity hypothesis for the binding of O2 to Hb, and a new equation for P50 of O2 that provides accurate shifts in the HbO2 and HbCO2 dissociation curves over a wide range of physiological conditions. The accuracy and efficiency of these equations in computing PO2 and PCO2 from the SHbO2 and SHbCO2 levels using simple iterative numerical schemes that give rapid convergence is a significant advantage over alternative SHbO2 and SHbCO2 models.

CONCLUSION

The new SHbO2 and SHbCO2 models have significant computational modeling implications as they provide high accuracy under non-physiological conditions, such as ischemia and reperfusion, extremes in gas concentrations, high altitudes, and extreme temperatures.

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

PURPOSE

Equations for blood oxyhemoglobin (HbO2) and carbaminohemoglobin (HbCO2) dissociation curves that incorporate nonlinear biochemical interactions of oxygen and carbon dioxide with hemoglobin (Hb), covering a wide range of physiological conditions, are crucial for a number of practical applications. These include the development of physiologically-based computational models of alveolar-blood and blood-tissue O2–CO2 transport, exchange, and metabolism, and the analysis of clinical and in vitro data.

METHODS AND RESULTS

To this end, we have revisited, simplified, and extended our previous models of blood HbO2 and HbCO2 dissociation curves (Dash and Bassingthwaighte, Ann Biomed Eng 38:1683–1701, 2010), validated wherever possible by available experimental data, so that the models now accurately fit the low HbO2 saturation (SHbO2) range over a wide range of values of PCO2, pH, 2,3-DPG, and temperature. Our new equations incorporate a novel PO2-dependent variable cooperativity hypothesis for the binding of O2 to Hb, and a new equation for P50 of O2 that provides accurate shifts in the HbO2 and HbCO2 dissociation curves over a wide range of physiological conditions. The accuracy and efficiency of these equations in computing PO2 and PCO2 from the SHbO2 and SHbCO2 levels using simple iterative numerical schemes that give rapid convergence is a significant advantage over alternative SHbO2 and SHbCO2 models.

CONCLUSION

The new SHbO2 and SHbCO2 models have significant computational modeling implications as they provide high accuracy under non-physiological conditions, such as ischemia and reperfusion, extremes in gas concentrations, high altitudes, and extreme temperatures.

Endurance training facilitates myoglobin desaturation during muscle contraction in rat skeletal muscle

At onset of muscle contraction, myoglobin (Mb) immediately releases its bound O₂ to the mitochondria. Accordingly, intracellular O₂ tension (P_mbO₂) markedly declines in order to increase muscle O₂ uptake (mO₂). However, whether the change in P_mbO₂ during muscle contraction modulates mO₂ and whether the O₂ release rate from Mb increases in endurance-trained muscles remain unclear. The purpose of this study was, therefore, to determine the effect of endurance training on O₂ saturation of Mb (S_mbO₂) and P_mbO₂ kinetics during muscle contraction. Male Wistar rats were subjected to a 4-week swimming training (Tr group; 6 days per week, 30 min × 4 sets per day) with a weight load of 2% body mass. After the training period, deoxygenated Mb kinetics during muscle contraction were measured using near-infrared spectroscopy under hemoglobin-free medium perfusion. In the Tr group, the mO₂peak significantly increased by 32%. Although the P_mbO₂ during muscle contraction did not affect the increased mO₂ in endurance-trained muscle, the O₂ release rate from Mb increased because of the increased Mb concentration and faster decremental rate in S_mbO₂ at the maximal twitch tension. These results suggest that the Mb dynamics during muscle contraction are contributing factors to faster O₂ kinetics in endurance-trained muscle.

Microvascular perfusion heterogeneity contributes to peripheral vascular disease in metabolic syndrome

A major challenge facing public health is the increased incidence and prevalence of the metabolic syndrome, a clinical condition characterized by excess adiposity, impaired glycaemic control, dyslipidaemia and moderate hypertension. The greatest concern for this syndrome is the profound increase in risk for development of peripheral vascular disease (PVD) in afflicted persons. However, ongoing studies suggest that reductions in bulk blood flow to skeletal muscle may not be the primary contributor to the premature muscle fatigue that is a hallmark of PVD. Compelling evidence has been provided suggesting that an increasingly spatially heterogeneous and temporally stable distribution of blood flow at successive arteriolar bifurcations in metabolic syndrome creates an environment where a large number of the pre-capillary arterioles have low perfusion, low haematocrit, and are increasingly confined to this state, with limited ability to adapt perfusion in response to a challenged environment. Single pharmacological interventions are unable to significantly restore function owing to a divergence in their spatial effectiveness, although combined therapeutic approaches to correct adrenergic dysfunction, elevated oxidant stress and increased thromboxane A2 improve perfusion-based outcomes. Integrated, multi-target therapeutic interventions designed to restore healthy network function and flexibility may provide for superior outcomes in subjects with metabolic syndrome-associated PVD.

A dynamic model of oxygen transport from capillaries to tissue with moving red blood cells

Most oxygen required to support the energy needs of vertebrate tissues is delivered by diffusion from microvessels. The presence of red blood cells (RBCs) makes blood flow in the microcirculation highly heterogeneous. Additionally, flow regulation mechanisms dynamically respond to changes in tissue energy demand. These spatiotemporal variations directly affect the supply of oxygen to parenchymal cells. Due to various limiting assumptions, current models of oxygen transport cannot fully capture the consequences of complex hemodynamic effects on tissue oxygenation and are often not suitable for studying unsteady phenomena. With our new approach based on moving RBCs, the impact of blood flow heterogeneity on oxygen partial pressure (Po2) in the tissue can be quantified. Oxygen transport was simulated using parachute-shaped solid RBCs flowing through a capillary. With the use of a conical tissue domain with radii 19 and 13 μm, respectively, our computations indicate that Po2 at the RBC membrane exceeds Po2 between RBCs by 30 mmHg on average and that the mean plasma Po2 decreases by 9 mmHg over 50 μm. These results reproduce well recent intravascular Po2 measurements in the rodent brain. We also demonstrate that instantaneous variations of capillary hematocrit cause associated fluctuations of tissue Po2. Furthermore, our results suggest that homogeneous tissue oxygenation requires capillary networks to be denser on venular side than on arteriolar side. Our new model for oxygen transport will make it possible to quantify in detail the effects of blood flow heterogeneity on tissue oxygenation in realistic capillary networks.

Extra permeability is required to model dynamic oxygen measurements: evidence for functional recruitment?

Neural activation triggers a rapid, focal increase in blood flow and thus oxygen delivery. Local oxygen consumption also increases, although not to the same extent as oxygen delivery. This 'uncoupling' enables a number of widely-used functional neuroimaging techniques; however, the physiologic mechanisms that govern oxygen transport under these conditions remain unclear. Here, we explore this dynamic process using a new mathematical model. Motivated by experimental observations and previous modeling, we hypothesized that functional recruitment of capillaries has an important role during neural activation. Using conventional mechanisms alone, the model predictions were inconsistent with in vivo measurements of oxygen partial pressure. However, dynamically increasing net capillary permeability, a simple description of functional recruitment, led to predictions consistent with the data. Increasing permeability in all vessel types had the same effect, but two alternative mechanisms were unable to produce predictions consistent with the data. These results are further evidence that conventional models of oxygen transport are not sufficient to predict dynamic experimental data. The data and modeling suggest that it is necessary to include a mechanism that dynamically increases net vascular permeability. While the model cannot distinguish between the different possibilities, we speculate that functional recruitment could have this effect in vivo.

Modeling to link regional myocardial work, metabolism and blood flows

Given the mono-functional, highly coordinated processes of cardiac excitation and contraction, the observations that regional myocardial blood flows, rMBF, are broadly heterogeneous has provoked much attention, but a clear explanation has not emerged. In isolated and in vivo heart studies the total coronary flow is found to be proportional to the rate-pressure product (systolic mean blood pressure times heart rate), a measure of external cardiac work. The same relationship might be expected on a local basis: more work requires more flow. The validity of this expectation has never been demonstrated experimentally. In this article we review the concepts linking cellular excitation and contractile work to cellular energetics and ATP demand, substrate utilization, oxygen demand, vasoregulation, and local blood flow. Mathematical models of these processes are now rather well developed. We propose that the construction of an integrated model encompassing the biophysics, biochemistry and physiology of cardiomyocyte contraction, then combined with a detailed three-dimensional structuring of the fiber bundle and sheet arrangements of the heart as a whole will frame an hypothesis that can be quantitatively evaluated to settle the prime issue: Does local work drive local flow in a predictable fashion that explains the heterogeneity? While in one sense one can feel content that work drives flow is irrefutable, the are no cardiac contractile models that demonstrate the required heterogeneity in local strain-stress-work; quite the contrary, cardiac contraction models have tended toward trying to show that work should be uniform. The object of this review is to argue that uniformity of work does not occur, and is impossible in any case, and that further experimentation and analysis are necessary to test the hypothesis.

Magnetic resonance imaging of resting OEF and CMRO₂ using a generalized calibration model for hypercapnia and hyperoxia

We present a method allowing determination of resting cerebral oxygen metabolism (CMRO₂) from MRI and end-tidal O₂ measurements acquired during a pair of respiratory manipulations producing different combinations of hypercapnia and hyperoxia. The approach is based on a recently introduced generalization of calibrated MRI signal models that is valid for arbitrary combinations of blood flow and oxygenation change. Application of this model to MRI and respiratory data during a predominantly hyperoxic gas manipulation yields a specific functional relationship between the resting BOLD signal M and the resting oxygen extraction fraction OEF₀. Repeating the procedure using a second, primarily hypercapnic, manipulation provides a different functional form of M vs. OEF₀. These two equations can be readily solved for the two unknowns M and OEF₀. The procedure also yields the resting arterial O₂ content, which when multiplied by resting cerebral blood flow provides the total oxygen delivery in absolute physical units. The resultant map of oxygen delivery can be multiplied by the map of OEF₀ to obtain a map of the resting cerebral metabolic rate of oxygen consumption (CMRO₂) in absolute physical units. Application of this procedure in a group of seven human subjects provided average values of 0.35 ± 0.04 and 6.0 ± 0.7% for OEF₀ and M, respectively in gray-matter (M valid for 30 ms echo-time at 3T). Multiplying OEF₀ estimates by the individual values of resting gray-matter CBF (mean 52 ± 5 ml/100 g/min) and the measured arterial O₂ content gave a group average resting CMRO₂ value of 145 ± 30 μmol/100 g/min. The method also allowed the generation of maps depicting resting OEF, BOLD signal, and CMRO₂.

A COMPREHENSIVE SIMULATOR OF THE HUMAN PULMONARY SYSTEM: VALIDATION WITH DETERMINATION OF TOTALCO2AND DIAGNOSIS OF ACID-BASE ABNORMALITIES

In previous models, heart-lung-blood interactions and their physicochemical properties have not been considered in comprehensive simulators and an integrated mathematical model has not been presented. The aim of the present study is to combine different phenomena involved in the cardiopulmonary function, which are often considered separately. In this study, the variables that constitute a comprehensive model; which includes physicochemical reactions of O2and CO2in the blood and fluid compartments, V/Q, pH , body temperature and diffusion limitation in the adult human and its ability to provide realistic response under different physiological and pathophysiological conditions; have been evaluated. The new biological system model consists of two subsystems: physicochemical properties of blood and physiological subsystem models. Based on the mentioned parameters, comprehensive simulator model has been suggested as following: [Formula: see text] According to the literature, all patients [COPD (20) and asthma (20)] showed acid-base imbalances. The mathematical model has been validated by diagnosis of acid-base abnormalities via calculating the total CO2and T40HCO3in physiological and pathophysiological conditions, and then the results compared to literature experimental data. Our comprehensive model provides results consistent with dynamic and steady state responses measured in subjects undergoing physiological and pathophysiological conditions. This might enable us to deepen our understanding of the cardiopulmonary system as a whole.

Computer-assisted numerical analysis for oxygen and carbon dioxide mass transfer in blood oxygenators

A two-dimensional numeric simulator is developed to predict the nonlinear, convective-reactive, oxygen mass exchange in a cross-flow hollow fiber blood oxygenator. The numeric simulator also calculates the carbon dioxide mass exchange, as hemoglobin affinity to oxygen is affected by the local pH value, which depends mostly on the local carbon dioxide content in blood. Blood pH calculation inside the oxygenator is made by the simultaneous solution of an equation that takes into account the blood buffering capacity and the classical Henderson-Hasselbach equation. The modeling of the mass transfer conductance in the blood comprises a global factor, which is a function of the Reynolds number, and a local factor, which takes into account the amount of oxygen reacted to hemoglobin. The simulator is calibrated against experimental data for an in-line fiber bundle. The results are: (i) the calibration process allows the precise determination of the mass transfer conductance for both oxygen and carbon dioxide; (ii) very alkaline pH values occur in the blood path at the gas inlet side of the fiber bundle; (iii) the parametric analysis of the effect of the blood base excess (BE) shows that (.)V(CO₂) is similar in the case of blood metabolic alkalosis, metabolic acidosis, or normal BE, for a similar blood inlet P(CO₂), although the condition of metabolic alkalosis is the worst case, as the pH in the vicinity of the gas inlet is the most alkaline; (iv) the parametric analysis of the effect of the gas flow to blood flow ratio (QG/QB) shows that (.)V(CO₂) variation with the gas flow is almost linear up to QG/QB = 2.0. (.)V(O₂) is not affected by the gas flow as it was observed that by increasing the gas flow up to eight times, the (.)V(O₂) grows only 1%. The mass exchange of carbon dioxide uses the full length of the hollow-fiber only if Q(G) /Q(B)> 2.0, as it was observed that only in this condition does the local variation of pH and blood P(CO₂) comprise the whole fiber bundle.

Resposta da cinética de consumo de oxigênio e da eficiência mecânica delta de homens e mulheres em diferentes intensidades de esforço

INTRODUÇÃO:A eficiência mecânica delta (EMΔ ) e a cinética do consumo de oxigênio (K<img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2) são influenciadas por parâmetros metabólicos musculares e pelo transporte de <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2. O objetivo do presente estudo foi determinar a diferença na K<img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2 e na EMΔ em três intensidades de esforço nos dois gêneros. MÉTODOS: 56 sujeitos (26 mulheres) foram submetidos ao protocolo de esforço escalonado, contínuo e máximo (GxT) no cicloergômetro mecânico para determinação da potência aeróbia máxima (<img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2máx), carga máxima (Wmax), limiar anaeróbio (AT) e ponto de compensação respiratória (PCR). O AT foi determinado através dos métodos V-slope e E <img src="/img/revistas/rbme/v17n4/a13cr02.jpg" align="absmiddle" /><img src="/img/revistas/rbme/v17n4/a13cr02.jpg" align="absmiddle" />E / <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2; o PCR através da relação <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2 versus <img src="/img/revistas/rbme/v17n4/a13cr02.jpg" align="absmiddle" />E ; ambos por dois avaliadores. A EMΔ e a K <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2 foram consideradas como a inclinação entre <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2 versus Watts e <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2 versus tempo (s), respectivamente, do começo do teste até o AT (S1), do AT ao PCR (S2) e do PCR ao <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2máx (S3), determinada por análise de regressão linear. RESULTADOS: Para a EMΔ, diferenças significativas foram observadas entre S1 versus S2 (p = 0,001), S1 versus S3 (p = 0,001) e S2 versus S3 (p = 0,006). Não foi observada diferença (p = 0,060) ou interação significativa (p = 0,062) entre homens versus mulheres. Para a K <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2 diferenças significativas foram observadas entre S1 versus S3 (p = 0,001) e S2 versus S3 (p = 0,001) em ambos gêneros. Diferenças (p = 0,001) e interação significativa (p = 0,006) foram observadas entre homens versus mulheres, no último parâmetro. CONCLUSÕES: A EMΔ decresce com o incremento da intensidade de trabalho, porém, não há diferenças quando se compara homens e mulheres. Por outro lado, as mulheres apresentam K <img src="/img/revistas/rbme/v17n4/a13cr01.jpg" align="absmiddle" />2 mais rápida do que os homens.

Patient-specific modeling of dyssynchronous heart failure: a case study

The development and clinical use of patient-specific models of the heart is now a feasible goal. Models have the potential to aid in diagnosis and support decision-making in clinical cardiology. Several groups are now working on developing multi-scale models of the heart for understanding therapeutic mechanisms and better predicting clinical outcomes of interventions such as cardiac resynchronization therapy. Here we describe the methodology for generating a patient-specific model of the failing heart with a myocardial infarct and left ventricular bundle branch block. We discuss some of the remaining challenges in developing reliable patient-specific models of cardiac electromechanical activity, and identify some of the main areas for focusing future research efforts. Key challenges include: efficiently generating accurate patient-specific geometric meshes and mapping regional myofiber architecture to them; modeling electrical activation patterns based on cellular alterations in human heart failure, and estimating regional tissue conductivities based on clinically available electrocardiographic recordings; estimating unloaded ventricular reference geometry and material properties for biomechanical simulations; and parameterizing systemic models of circulatory dynamics from available hemodynamic measurements.

19F MRI oximetry: simulation of perfluorocarbon distribution impact

In (19)F MRI oximetry, a method used to image tumour hypoxia, perfluorocarbons serve as oxygenation markers. The goal of this study is to evaluate the impact of perfluorocarbon distribution and concentration in (19)F MRI oximetry through a computer simulation. The simulation studies the correspondence between (19)F measured (pO(FNMR)(2)) and actual tissue oxygen tension (pO(2)) for several tissue perfluorocarbon distributions. For this, a Krogh tissue model is implemented which incorporates the presence of perfluorocarbons in blood and tissue. That is, in tissue the perfluorocarbons are distributed homogeneously according to Gaussian diffusion profiles, or the perfluorocarbons are concentrated in the capillary wall. Using these distributions, the oxygen tension in the simulation volume is calculated. The simulated mean oxygen tension is then compared with pO(FNMR)(2), the (19)F MRI-based measure of pO(2) and with pO(0)(2), pO(2) in the absence of perfluorocarbons. The agreement between pO(FNMR)(2) and actual pO(2) is influenced by vascular density and perfluorocarbon distribution. The presence of perfluorocarbons generally gives rise to a pO(2) increase in tissue. This effect is enhanced when perfluorocarbons are also present in blood. Only the homogeneous perfluorocarbon distribution in tissue with no perfluorocarbons in blood guarantees small deviations of pO(FNMR)(2) from pO(2). Hence, perfluorocarbon distribution in tissue and blood has a serious impact on the reliability of (19)F MRI-based measures of oxygen tension. In addition, the presence of perfluorocarbons influences the actual oxygen tension. This finding may be of great importance for further development of (19)F MRI oximetry.

A metabolic model of human erythrocytes: practical application of the E-Cell Simulation Environment

The human red blood cell (RBC) has long been used for modeling of complex biological networks, for elucidation of a wide variety of dynamic phenomena, and for understanding the fundamental topology of metabolic pathways. Here, we introduce our recent work on an RBC metabolic model using the E-Cell Simulation Environment. The model is sufficiently detailed to predict the temporal hypoxic response of each metabolite and, at the same time, successfully integrates modulation of metabolism and of the oxygen transporting capacity of hemoglobin. The model includes the mechanisms of RBC maintenance as a single cell system and the functioning of RBCs as components of a higher order system. Modeling of RBC metabolism is now approaching a fully mature stage of realistic predictions at the molecular level and will be useful for predicting conditions in biotechnological applications such as long-term cold storage of RBCs.

The effect on cerebral tissue oxygenation index of changes in the concentrations of inspired oxygen and end-tidal carbon dioxide in healthy adult volunteers

BACKGROUND

A variety of near-infrared spectroscopy devices can be used to make noninvasive measurements of cerebral tissue oxygen saturation (ScO2). The ScO2 measured by the NIRO 300 spectrometer (Hamamatsu Photonics, Japan) is called the cerebral tissue oxygenation index (TOI) and is an assessment of the balance between cerebral oxygen delivery and utilization. We designed this study to investigate the effect of systemic and intracranial physiological changes on TOI.

METHODS

Fifteen healthy volunteers were studied during isocapneic hyperoxia and hypoxemia, and normoxic hypercapnea and hypocapnea. Absolute cerebral TOI and changes in oxy- and deoxyhemoglobin concentrations were measured using a NIRO 300 spectrometer. Changes in arterial oxygen saturation (SaO2), ETCO2, heart rate, mean arterial blood pressure (MBP), and middle cerebral artery blood flow velocity (Vmca) were also measured during these physiological challenges. Changes in cerebral blood volume (CBV) were subsequently calculated from changes in total cerebral hemoglobin concentration.

RESULTS

Baseline TOI was 67.3% with an interquartile range (IQR) of 65.2%-71.9%. Hypoxemia was associated with a median decrease in TOI of 7.1% (IQR -9.1% to -5.4%) from baseline (P < 0.0001) and hyperoxia with a median increase of 2.3% (IQR 2.0%-2.5%) (P < 0.0001). Hypocapnea caused a reduction in TOI of 2.1% (IQR -3.3% to -1.3%) from baseline (P < 0.0001) and hypercapnea an increase of 2.6% (IQR 1.4%-3.7%) (P < 0.0001). Changes in SaO2 (P < 0.0001), ETCO2 (P < 0.0001), CBV (P = 0.0003), and MBP (P = 0.03) were significant variables affecting TOI. Changes in Vmca (P = 0.7) and heart rate (P = 0.2) were not significant factors.

CONCLUSION

TOI is an easy-to-monitor variable that provides real-time, multisite, and noninvasive assessment of the balance between cerebral oxygen delivery and utilization. However, TOI is a complex variable that is affected by SaO2 and ETCO2, and, to a lesser extent, by MBP and CBV. Clinicians need to be aware of the systemic and cerebral physiological changes that can affect TOI to interpret changes in this variable during clinical monitoring.

Theoretical models of microvascular oxygen transport to tissue

To improve understanding of microvascular O(2) transport, theoretical modeling has been pursued for many years. The large number of studies in this area attests to the complexities (i.e., biochemical, structural, and hemodynamic) involved. This article focuses on theoretical studies from the last two decades and, in particular, on models of O(2) transport to tissue by discrete microvessels. A brief discussion of intravascular O(2) transport is first given, highlighting the physiological importance of intravascular resistance to blood-tissue O(2) transfer. This is followed by a description of the Krogh tissue cylinder model of O(2) transport by a single capillary, which is shown to remain relevant in modified forms that relax many of the original biophysical assumptions. However, there are many geometric and hemodynamic complexities that require the consideration of microvascular arrays and networks. Multivessel models are discussed that have shown the physiological importance of heterogeneities in vessel spacing, O(2) supply, red blood cell flow path, as well as interactions between capillaries and arterioles. These realistic models require sophisticated methods for solving the governing partial differential equations, and a range of solution techniques are described. Finally, the issue of experimental validation of microvascular O(2) delivery models is discussed, and new directions in O(2) transport modeling are outlined.

Quantitative evaluation of respiration induced metabolic oscillations in erythrocytes

The changes in the partial pressures of oxygen and carbon dioxide (P(O(2)) and P(CO(2))) during blood circulation alter erythrocyte metabolism, hereby causing flux changes between oxygenated and deoxygenated blood. In the study we have modeled this effect by extending the comprehensive kinetic model by Mulquiney and Kuchel [P.J. Mulquiney, and P.W. Kuchel. Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: equations and parameter refinement, Biochem. J. 1999, 342, 581-596.] with a kinetic model of hemoglobin oxy-/deoxygenation transition based on an oxygen dissociation model developed by Dash and Bassingthwaighte [R. Dash, and J. Bassingthwaighte. Blood HbO(2) and HbCO(2) dissociation curves at varied O(2), CO(2), pH, 2,3-DPG and temperature levels, Ann. Biomed. Eng., 2004, 32(12), 1676-1693.]. The system has been studied during transitions from the arterial to the venous phases by simply forcing P(O(2)) and P(CO(2)) to follow the physiological values of venous and arterial blood. The investigations show that the system passively follows a limit cycle driven by the forced oscillations of P(O(2)) and is thus inadequately described solely by steady state consideration. The metabolic system exhibits a broad distribution of time scales. Relaxations of modes with hemoglobin and Mg(2+) binding reactions are very fast, while modes involving glycolytic, membrane transport and 2,3-BPG shunt reactions are much slower. Incomplete slow mode relaxations during the 60 s period of the forced transitions cause significant overshoots of important fluxes and metabolite concentrations - notably ATP, 2,3-BPG, and Mg(2+). The overshoot phenomenon arises in consequence of a periodical forcing and is likely to be widespread in nature - warranting a special consideration for relevant systems.

Role of NADH/NAD+ transport activity and glycogen store on skeletal muscle energy metabolism during exercise: in silico studies

Skeletal muscle can maintain ATP concentration constant during the transition from rest to exercise, whereas metabolic reaction rates may increase substantially. Among the key regulatory factors of skeletal muscle energy metabolism during exercise, the dynamics of cytosolic and mitochondrial NADH and NAD+ have not been characterized. To quantify these regulatory factors, we have developed a physiologically based computational model of skeletal muscle energy metabolism. This model integrates transport and reaction fluxes in distinct capillary, cytosolic, and mitochondrial domains and investigates the roles of mitochondrial NADH/NAD+ transport (shuttling) activity and muscle glycogen concentration (stores) during moderate intensity exercise (60% maximal O2 consumption). The underlying hypothesis is that the cytosolic redox state (NADH/NAD+) is much more sensitive to a metabolic disturbance in contracting skeletal muscle than the mitochondrial redox state. This hypothesis was tested by simulating the dynamic metabolic responses of skeletal muscle to exercise while altering the transport rate of reducing equivalents (NADH and NAD+) between cytosol and mitochondria and muscle glycogen stores. Simulations with optimal parameter estimates showed good agreement with the available experimental data from muscle biopsies in human subjects. Compared with these simulations, a 20% increase (or approximately 20% decrease) in mitochondrial NADH/NAD+ shuttling activity led to an approximately 70% decrease (or approximately 3-fold increase) in cytosolic redox state and an approximately 35% decrease (or approximately 25% increase) in muscle lactate level. Doubling (or halving) muscle glycogen concentration resulted in an approximately 50% increase (or approximately 35% decrease) in cytosolic redox state and an approximately 30% increase (or approximately 25% decrease) in muscle lactate concentration. In both cases, changes in mitochondrial redox state were minimal. In conclusion, the model simulations of exercise response are consistent with the hypothesis that mitochondrial NADH/NAD+ shuttling activity and muscle glycogen stores affect primarily the cytosolic redox state. Furthermore, muscle lactate production is regulated primarily by the cytosolic redox state.

Metabolic dynamics in skeletal muscle during acute reduction in blood flow and oxygen supply to mitochondria: in-silico studies using a multi-scale, top-down integrated model

Control mechanisms of cellular metabolism and energetics in skeletal muscle that may become evident in response to physiological stresses such as reduction in blood flow and oxygen supply to mitochondria can be quantitatively understood using a multi-scale computational model. The analysis of dynamic responses from such a model can provide insights into mechanisms of metabolic regulation that may not be evident from experimental studies. For the purpose, a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics was developed to describe dynamic responses of key chemical species and reaction fluxes to muscle ischemia. The model, which incorporates key transport and metabolic processes and subcellular compartmentalization, is based on dynamic mass balances of 30 chemical species in both capillary blood and tissue cells (cytosol and mitochondria) domains. The reaction fluxes in cytosol and mitochondria are expressed in terms of a general phenomenological Michaelis-Menten equation involving the compartmentalized energy controller ratios ATP/ADP and NADH/NAD(+). The unknown transport and reaction parameters in the model are estimated simultaneously by minimizing the differences between available in vivo experimental data on muscle ischemia and corresponding model outputs in coupled with the resting linear flux balance constraints using a robust, nonlinear, constrained-based, reduced gradient optimization algorithm. With the optimal parameter values, the model is able to simulate dynamic responses to reduced blood flow and oxygen supply to mitochondria associated with muscle ischemia of several key metabolite concentrations and metabolic fluxes in the subcellular cytosolic and mitochondrial compartments, some that can be measured and others that can not be measured with the current experimental techniques. The model can be applied to test complex hypotheses involving dynamic regulation of cellular metabolism and energetics in skeletal muscle during physiological stresses such as ischemia, hypoxia, and exercise.

A model of autoregulated blood flow in the cerebral vasculature

The circle of Willis is a ring-like arterial structure located in the base of the brain, and is responsible for the distribution of oxygenated blood throughout the cerebral mass. Among the general population, approximately 50 per cent have a complete circle of Willis; for the others a multitude of possible anatomical variations are present, with absent or hypoplastic vessels being common. Certain conditions such as a build-up of atherosclerotic plaque on the arterial wall can result in ischaemic damage and stroke-like symptoms. A three-dimensional computer model has been developed based on the results of magnetic resonance imaging data, incorporating a numerical algorithm to simulate the body's autoregulation mechanism, such that oxygen delivery to the cerebral territories can be predicted in response events, leading to a reduction in cerebral blood flow. Sample results are presented for combinations of occlusion and stenosis.

Modeling cellular metabolism and energetics in skeletal muscle: large-scale parameter estimation and sensitivity analysis

Skeletal muscle plays a major role in the regulation of whole-body energy metabolism during physiological stresses such as ischemia, hypoxia, and exercise. Current experimental techniques provide relatively little in vivo data on dynamic responses of metabolite concentrations and metabolic fluxes in skeletal muscle to such physiological stimuli. As a complementary approach to experimental measurements and as a framework for quantitatively analyzing available in vivo data, a physiologically based model of skeletal muscle cellular metabolism and energetics is developed. This model, which incorporates key transport and reaction processes, is based on dynamic mass balances of 30 chemical species in capillary (blood) and tissue (cell) domains. The reaction fluxes in the cellular domain are expressed in terms of a generalized Michaelis?Menten equation involving energy controller ratios ATP/ADP and ATP/ADP and NADH/NAD+ . This formalism introduces a large number of unknown parameters ( approximately 90). Estimating these parameters from in vivo sparse data and evaluating dynamic sensitivities of the model outputs with respect to these parameters is a challenging problem. Parameter estimation is accomplished using an efficient, nonlinear, constraint-based, optimization algorithm that minimizes differences between available experimental data and corresponding model outputs by explicitly utilizing equality constraints on resting fluxes and concentrations. With the estimated parameter values, the model is able to simulate dynamic responses to reduced blood flow (ischemia) of key metabolite concentrations and metabolic fluxes, both measured and nonmeasured. A general parameter sensitivity analysis is carried out to determine and characterize the parameters having the most and least effects on the measured outputs.

Modeling oxygen and carbon dioxide transport and exchange using a closed loop circulatory system

The binding and buffering of O2 and CO2 in the blood influence their exchange in lung and tissues and their transport through the circulation. To investigate the binding and buffering effects, a model of blood-tissue gas exchange is used. The model accounts for hemoglobin saturation, the simultaneous binding of O2, CO2, H+, 2,3-DPG to hemoglobin, and temperature effects. Invertible Hill-type saturation equations facilitate rapid calculation of respiratory gas redistribution among the plasma, red blood cell and tissue that occur along the concentration gradients in the lung and in the capillary-tissue exchange regions. These equations are well-suited to analysis of transients in tissue metabolism and partial pressures of inhaled gas. The modeling illustrates that because red blood cell velocities in the flowing blood are higher than plasma velocities after a transient there can be prolonged differences between RBC and plasma oxygen partial pressures. The blood-tissue gas exchange model has been incorporated into a higher level model of the circulatory system plus pulmonary mechanics and gas exchange using the RBC and plasma equations to account for pH and CO2 buffering in the blood.

Subject-specific model estimation of cardiac output and blood volume during hemorrhage

We have developed a novel method for estimating subject-specific hemodynamics during hemorrhage. First, a mathematical model representing a closed-loop circulation and baroreceptor feedback system was parameterized to match the baseline physiology of individual experimental subjects by fitting model results to 1 min of pre-injury data. This automated parameterization process matched pre-injury measurements within 1.4 +/- 1.3% SD. Tuned parameters were then used in similar open-loop models to simulate dynamics post-injury. Cardiac output (CO) estimates were obtained continuously using post-injury measurements of arterial blood pressure (ABP) and heart rate (HR) as inputs to the first open-loop model. Secondarily, total blood volume (TBV) estimates were obtained by summing the blood volumes in all the circulatory segments of a second open-loop model that used measured CO as an additional input. We validated the estimation method by comparing model CO results to flowprobe measurements in 14 pigs. Overall, CO estimates had a Bland-Altman bias of -0.30 l/min with upper and lower limits of agreement 0.80 and -1.40 l/min. The negative bias is likely due to overestimation of the peripheral resistance response to hemorrhage. There was no reference measurement of TBV; however, the estimates appeared reasonable and clearly predicted survival versus death during the post-hemorrhage period. Both open-loop models ran in real time on a computer with a 2.4 GHz processor, and their clinical applicability in emergency care scenarios is discussed.

Pulsatile Blood Flow and Oxygen Transport Past a Circular Cylinder

The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the x direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter (α), pulsation amplitude (A), and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure O2 and air. The flow and concentration fields were computed for Re=5, 10, and 40, 0≤A≤0.75, α=0.25, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as A and α are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure O2 feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small A) for both feed-gas mixtures. The time averaged Sherwood number, Sh̿, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with A. Little change is observed with varying α for the ranges investigated. The effect of pulsatility on Sh̿ is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.

Pulsatile Blood Flow and Gas Exchange Across a Cylindrical Fiber Array

The pulsatile blood flow and gas transport of oxygen and carbon dioxide through a cylindrical array of microfibers are numerically simulated. Blood is modeled as a homogeneous Casson fluid, and hemoglobin molecules in blood are assumed to be in local equilibrium with oxygen and carbon dioxide. It is shown that flow pulsatility enhances gas transport and the amount of gas exchange is sensitive to the blood flow field across the fibers. The steady Sherwood number dependence on Reynolds number was shown to have a linear relation consistent with experimental findings. For most cases, an enhancement in gas transport is accompanied with an increase in flow resistance. Maximum local shear stress is provided as a possible indicator of thrombosis, and the computed shear stress is shown to be below the threshold value for thrombosis formation for all cases evaluated.

Roles of hemoglobin Allostery in hypoxia-induced metabolic alterations in erythrocytes: simulation and its verification by metabolome analysis

When erythrocytes are exposed to hypoxia, hemoglobin (Hb) stabilizes in the T-state by capturing 2,3-bisphosphoglycerate. This process could reduce the intracellular pool of glycolytic substrates, jeopardizing cellular energetics. Recent observations suggest that hypoxia-induced activation of glycolytic enzymes is correlated with their release from Band III (BIII) on the cell membrane. Based on these data, we developed a mathematical model of erythrocyte metabolism and compared hypoxia-induced differences in predicted activities of the enzymes, their products, and cellular energetics between models with and without the interaction of Hb with BIII. The models predicted that the allostery-dependent Hb interaction with BIII accelerates consumption of upstream glycolytic substrates such as glucose 6-phosphate and increases downstream products such as phosphoenolpyruvate. This prediction was consistent with metabolomic data from capillary electrophoresis mass spectrometry. The hypoxia-induced alterations in the metabolites resulted from acceleration of glycolysis, as judged by increased conversion of [(13)C]glucose to [(13)C]lactate. The allostery-dependent interaction of Hb with BIII appeared to contribute not only to maintenance of energy charge but also to further synthesis of 2,3-bisphosphoglycerate, which could help sustain stabilization of T-state Hb during hypoxia. Furthermore, such an activation of glycolysis was not observed when Hb was stabilized in R-state by treating the cells with CO. These results suggest that Hb allostery in erythrocytes serves as an O(2)-sensing trigger that drives glycolytic acceleration to stabilize intracellular energetics and promote the ability to release O(2) from the cells.

Multi-organ system model of O2 and CO2 transport during isocapnic and poikilocapnic hypoxia

A multi-organ systems model of O(2) and CO(2) transport is developed to analyze the control of ventilation and blood flow during hypoxia. Among the aspects of the control processes that this model addressed are possible mechanisms responsible for the second phase of the ventilatory hypoxic response to mild hypoxia, i.e., hypoxic ventilatory decline (HVD). Species mass transport processes are described by compartmental mass balances in brain, heart, skeletal muscle, and "other tissues" connected in parallel via the circulation. In pulmonary and systemic capillaries and in the vasculature connecting the systemic tissues, species transport processes are represented by a one-dimensional, convection-dispersion model. The effects of bicarbonate acid-base buffering, hemoglobin, and myoglobin on the transport processes are included. The model incorporates feedback control mechanisms through a cardiorespiratory control system in which peripheral and central chemoreceptors sense O(2) and CO(2) partial pressures. Model simulations of the ventilatory responses to isocapnic and poikilocapnic hypoxia show two phases with distinct dynamics. A fast phase is discernable immediately after switching from normoxic to hypoxic conditions, while a delayed slow phase (HVD) typically becomes manifested after several minutes. Model simulations allow quantitative evaluation of several proposed mechanisms to account for HVD. Under isocapnic hypoxia, simulations indicate that an increase in brain blood flow has no effect on HVD, but that HVD can be entirely described by central ventilatory depression (CVD). Under poikilocapnic hypoxia, the hypocapnia caused by hypoxic hyperventilation has no effect on HVD.

Relating pulmonary oxygen uptake to muscle oxygen consumption at exercise onset: in vivo and in silico studies

Assessment of the rate of muscle oxygen consumption, UO(2m), in vivo during exercise involving a large muscle mass is critical for investigating mechanisms regulating energy metabolism at exercise onset. While UO(2m) is technically difficult to obtain under these circumstances, pulmonary oxygen uptake, VO(2p), can be readily measured and used as a proxy to UO(2m). However, the quantitative relationship between VO(2p) and UO(2m) during the nonsteady phase of exercise in humans, needs to be established. A computational model of oxygen transport and utilization--based on dynamic mass balances in blood and tissue cells--was applied to quantify the dynamic relationship between model-simulated UO(2m) and measured VO(2p) during moderate (M), heavy (H), and very heavy (V) intensity exercise. In seven human subjects, VO(2p) and muscle oxygen saturation, StO(2m), were measured with indirect calorimetry and near infrared spectroscopy (NIRS), respectively. The dynamic responses of VO(2p) and StO(2m) at each intensity were in agreement with previously published data. The response time of muscle oxygen consumption, tauUO(2m) estimated by direct comparison between model results and measurements of StO(2m) was significantly faster (P < 0.001) than that of pulmonary oxygen uptake, tauVO(2p) (M: 13 +/- 4 vs. 65 +/- 7 s; H: 13 +/- 4 vs. 100 +/- 24 s; V: 15 +/- 5 vs. 82 +/- 31 s). Thus, by taking into account the dynamics of oxygen stores in blood and tissue and determining muscle oxygen consumption from muscle oxygenation measurements, this study demonstrates a significant temporal dissociation between UO(2m) and VO(2p) at exercise onset.

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.

Multiscale modeling of cardiac cellular energetics

Multiscale modeling is essential to integrating knowledge of human physiology starting from genomics, molecular biology, and the environment through the levels of cells, tissues, and organs all the way to integrated systems behavior. The lowest levels concern biophysical and biochemical events. The higher levels of organization in tissues, organs, and organism are complex, representing the dynamically varying behavior of billions of cells interacting together. Models integrating cellular events into tissue and organ behavior are forced to resort to simplifications to minimize computational complexity, thus reducing the model's ability to respond correctly to dynamic changes in external conditions. Adjustments at protein and gene regulatory levels shortchange the simplified higher-level representations. Our cell primitive is composed of a set of subcellular modules, each defining an intracellular function (action potential, tricarboxylic acid cycle, oxidative phosphorylation, glycolysis, calcium cycling, contraction, etc.), composing what we call the "eternal cell," which assumes that there is neither proteolysis nor protein synthesis. Within the modules are elements describing each particular component (i.e., enzymatic reactions of assorted types, transporters, ionic channels, binding sites, etc.). Cell subregions are stirred tanks, linked by diffusional or transporter-mediated exchange. The modeling uses ordinary differential equations rather than stochastic or partial differential equations. This basic model is regarded as a primitive upon which to build models encompassing gene regulation, signaling, and long-term adaptations in structure and function. During simulation, simpler forms of the model are used, when possible, to reduce computation. However, when this results in error, the more complex and detailed modules and elements need to be employed to improve model realism. The processes of error recognition and of mapping between different levels of model form complexity are challenging but are essential for successful modeling of large-scale systems in reasonable time. Currently there is to this end no established methodology from computational sciences.