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

Microneedle-Based Electrochemical Array Patch for Ultra-Antifouling and Ultra-Anti-Interference Monitoring of Subcutaneous Oxygen

Oxygen saturation is a crucial indicator in the management of various diseases and in preoperative diagnosis, and the detection of oxygen content is valuable in guiding clinical treatment. However, as the classical and dominant oxygen detection strategies, current photoelectric oximeters and electrochemical-based blood gas analyzers often suffer from significant interindividual variation and poor compliance, respectively. In recent years, wearable microneedles (MNs) for analyzing biomarkers in interstitial fluid (ISF) have received great attention and recognition mainly for the reason that the content of the substances distributed in ISF has a better correlation with that in blood circulation compared with other body fluids such as sweat and saliva. Herein, an MN-based electrochemical array system was developed for continuous subcutaneous oxygen sensing, in which gold-modified commercial acupuncture MNs were used as the sensing units, and a tailored mini-workstation, a nonwoven fabric, and a water and air isolation membrane were integrated to fabricate a wearable array patch. Notably, a multifunctional swelling resin with good biocompatibility was adopted to decorate the MN surface as a protective layer and as an electrolyte gel. The swelling resin featured the ability to reduce epidermis secretions during the sensor array penetrating the skin and to decrease the interference of other biomolecules in ISF for oxygen assay during measurement. This proposed array patch can perform the subcutaneous oxygen analysis in the physiological range of 6-150 mmHg with high sensitivity (0.3817 μA/mmHg) and low theoretical limit of detection (5.06 mmHg). It also showed decent stability and selectivity in the presence of several kinds of exogenous and endogenous substances. Finally, the patch accomplished continual monitoring of the subcutaneous oxygen content during long-term physical exercise, showing great potential in providing warning about the hypoxia status of the human body. It could be foreseen that this high-performance patch will play an active role in respiratory disease evaluation, surgical monitoring, and public health care.

Computer model coupling hemodynamics and oxygen transport in the coronary capillary network: Pulsatile vs. non-pulsatile analysis

BACKGROUND AND OBJECTIVE

Oxygen transport in the heart is crucial, and its impairment can lead to pathological conditions such as hypoxia, ischemia, and heart failure. However, investigating oxygen transport in the heart using in vivo measurements is difficult due to the small size of the coronary capillaries and their deep embedding within the heart wall.

METHODS

In this study, we developed a novel computational modeling framework that integrates a 0-D hemodynamic model with a 1-D mass transport model to simulate oxygen transport in/across the coronary capillary network.

RESULTS

The model predictions agree with analytical solutions and experimental measurements. The framework is used to simulate the effects of pulsatile vs. non-pulsatile behavior of the capillary hemodynamics on oxygen-related metrics such as the myocardial oxygen consumption (MVO2) and oxygen extraction ratio (OER). Compared to simulations that consider (physiological) pulsatile behaviors of the capillary hemodynamics, the OER is underestimated by less than 9% and the MVO2 is overestimated by less than 5% when the pulsatile behaviors are ignored in the simulations. Statistical analyses show that model predictions of oxygen-related quantities and spatial distribution of oxygen without consideration of the pulsatile behaviors do not significantly differ from those that considered such behaviors (p-values >0.05).

CONCLUSIONS

This finding provides the basis for reducing the model complexity by ignoring the pulsatility of coronary capillary hemodynamics in the computational framework without a substantial loss of accuracy when predicting oxygen-related metrics.

Myocardial Perfusion Imaging by Cardiovascular Magnetic Resonance: Research Progress and Current Implementation

Cardiovascular diseases pose a significant health and economic burden worldwide, with coronary artery disease still recognized as a major problem. It is closely associated with hypertension, diabetes, obesity, smoking, lack of exercise, poor diet, and excessive alcohol consumption, which may lead to macro- and microvascular abnormalities in the heart. Coronary artery stenosis reduces the local supply of oxygen and nutrients to the myocardium and results in reduced levels of myocardial perfusion, which can lead to more severe conditions and irreversible damage to myocardial tissues. Therefore, accurate evaluation of myocardial perfusion abnormalities in patients with these risk factors is critical. As technology advances, magnetic resonance myocardial perfusion imaging has become more accurate at evaluating the myocardial microcirculation and has shown a powerful ability to detect myocardial ischemia. The purpose of this review is to summarize the principle, research progress of acquisition and analysis, and clinical implementation of cardiovascular magnetic resonance (CMR) myocardial perfusion imaging.

Extracellular acidification augments sclerostin and osteoprotegerin production by Ocy454 mouse osteocytes

Osteocytes sense the microenvironmental stimuli, including mechanical stress, and regulate bone resorption by osteoclasts and bone formation by osteoblasts. Diabetes and cancer metastasis to bone raise l-lactic acid in the bone tissue, causing acidification. Here, we investigated the effects of l-lactic acid and extracellular acidification on the function of mouse Ocy454 osteocytes. L- and d-lactic acid with low chiral selectivity and acidification of the medium raised the production of sclerostin and osteoprotegerin by Ocy454 cells. The mRNA expression of their genes increased after either treatment of L- and d-lactic acid or acidification of the medium. Furthermore, the conditioned medium of Ocy454 cells cultured in an acidic environment suppressed the induction of alkaline phosphatase activity in MC3T3-E1 cells, which was recovered by the anti-sclerostin antibody. While it is reported that HDAC5 inhibits the transcription of the sclerostin gene, extracellular acidification reduced the nuclear localization of HDAC5 in Ocy454 cells. While calmodulin kinase II (CaMKII) is known to phosphorylate and induce extranuclear translocation of HDAC5, KN-62, an inhibitor of CaMKII lowered the expression of the sclerostin gene in Ocy454 cells. Collectively, extracellular acidification is a microenvironmental factor that modulates osteocyte functions.

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.

Intact carbonic acid is a viable protonating agent for biological bases

Carbonic acid H2CO3 (CA) is a key constituent of the universal CA/bicarbonate/CO2 buffer maintaining the pH of both blood and the oceans. Here we demonstrate the ability of intact CA to quantitatively protonate bases with biologically-relevant pKas and argue that CA has a previously unappreciated function as a major source of protons in blood plasma. We determine with high precision the temperature dependence of pKa(CA), pKa(T) = -373.604 + 16,500/T + 56.478 ln T. At physiological-like conditions pKa(CA) = 3.45 (I = 0.15 M, 37 °C), making CA stronger than lactic acid. We further demonstrate experimentally that CA decomposition to H2O and CO2 does not impair its ability to act as an ordinary carboxylic acid and to efficiently protonate physiological-like bases. The consequences of this conclusion are far reaching for human physiology and marine biology. While CA is somewhat less reactive than (H+)aq, it is more than 1 order of magnitude more abundant than (H+)aq in the blood plasma and in the oceans. In particular, CA is about 70× more abundant than (H+)aq in the blood plasma, where we argue that its overall protonation efficiency is 10 to 20× greater than that of (H+)aq, often considered to be the major protonating agent there. CA should thus function as a major source for fast in vivo acid-base reactivity in the blood plasma, possibly penetrating intact into membranes and significantly helping to compensate for (H+)aq's kinetic deficiency in sustaining the large proton fluxes that are vital for metabolic processes and rapid enzymatic reactions.

Simulation of the Perfusion of Contrast Agent Used in Cardiac Magnetic Resonance: A Step Toward Non-invasive Cardiac Perfusion Quantification

This work presents a new mathematical model to describe cardiac perfusion in the myocardium as acquired by cardiac magnetic resonance (CMR) perfusion exams. The combination of first pass (or contrast-enhanced CMR) and late enhancement CMR is a widely used non-invasive exam that can identify abnormal perfused regions of the heart via the use of a contrast agent (CA). The exam provides important information to the diagnosis, management, and prognosis of ischemia and infarct: perfusion on different regions, the status of microvascular structures, the presence of fibrosis, and the relative volume of extracellular space. This information is obtained by inferring the spatiotemporal dynamics of the contrast in the myocardial tissue from the acquired images. The evaluation of these physiological parameters plays an important role in the assessment of myocardial viability. However, the nature of cardiac physiology poses great challenges in the estimation of these parameters. Briefly, these are currently estimated qualitatively via visual inspection of images and comparison of relative brightness between different regions of the heart. Therefore, there is a great urge for techniques that can help to quantify cardiac perfusion. In this work, we propose a new mathematical model based on multidomain flow in porous media. The model is based on a system of partial differential equations. Darcy's law is used to obtain the pressure and velocity distribution. CA dynamics is described by reaction-diffusion-advection equations in the intravascular space and in the interstitial space. The interaction of fibrosis and the CA is also considered. The new model treats the domains as anisotropic media and imposes a closed loop of intravascular flow, which is necessary to reproduce the recirculation of the CA. The model parameters were adjusted to reproduce clinical data. In addition, the model was used to simulate different scenarios: normal perfusion; endocardial ischemia due to stenosis in a coronary artery in the epicardium; and myocardial infarct. Therefore, the computational model was able to correlate anatomical features, stenosis and the presence of fibrosis, with functional ones, cardiac perfusion. Altogether, the results suggest that the model can support the process of non-invasive cardiac perfusion quantification.

Integrative model of coronary flow in anatomically based vasculature under myogenic, shear, and metabolic regulation

Coronary blood flow is regulated to match the oxygen demand of myocytes in the heart wall. Flow regulation is essential to meet the wide range of cardiac workload. The blood flows through a complex coronary vasculature of elastic vessels having nonlinear wall properties, under transmural heterogeneous myocardial extravascular loading. To date, there is no fully integrative flow analysis that incorporates global and local passive and flow control determinants. Here, we provide an integrative model of coronary flow regulation that considers the realistic asymmetric morphology of the coronary network, the dynamic myocardial loading on the vessels embedded in it, and the combined effects of local myogenic effect, local shear regulation, and conducted metabolic control driven by venous O₂ saturation level. The model predicts autoregulation (approximately constant flow over a wide range of coronary perfusion pressures), reduced heterogeneity of regulated flow, and presence of flow reserve, in agreement with experimental observations. Furthermore, the model shows that the metabolic and myogenic regulations play a primary role, whereas shear has a secondary one. Regulation was found to have a significant effect on the flow except under extreme (high and low) inlet pressures and metabolic demand. Novel outcomes of the model are that cyclic myocardial loading on coronary vessels enhances the coronary flow reserve except under low inlet perfusion pressure, increases the pressure range of effective autoregulation, and reduces the network flow in the absence of metabolic regulation. Collectively, these findings demonstrate the utility of the present biophysical model, which can be used to unravel the underlying mechanisms of coronary physiopathology.

A computational model of myocardial microcirculation including interstitial flow

Contributions of interstitial fluid (ISF) flow within the myocardial microcirculation is not well understood despite its importance due to difficulties in measurements. For analysing a contribution of interstitial fluid flow within myocardial microcirculation, we developed a computational model of myocardial microcirculation by introducing convection by the ISF flow into an existing myocardial microcirculation model, and performed simulations with varied ISF flows in normal and hypoperfusion conditions. Simulation results show that the ISF flow has a contribution only with low capillary flow. This might suggest partial comensation of oxygen supply by the ISF flow under ischemic conditions.

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.

Spatiotemporal distribution modeling of PET tracer uptake in solid tumors

OBJECTIVE

Distribution of PET tracer uptake is elaborately modeled via a general equation used for solute transport modeling. This model can be used to incorporate various transport parameters of a solid tumor such as hydraulic conductivity of the microvessel wall, transvascular permeability as well as interstitial space parameters. This is especially significant because tracer delivery and drug delivery to solid tumors are determined by similar underlying tumor transport phenomena, and quantifying the former can enable enhanced prediction of the latter.

METHODS

We focused on the commonly utilized FDG PET tracer. First, based on a mathematical model of angiogenesis, the capillary network of a solid tumor and normal tissues around it were generated. The coupling mathematical method, which simultaneously solves for blood flow in the capillary network as well as fluid flow in the interstitium, is used to calculate pressure and velocity distributions. Subsequently, a comprehensive spatiotemporal distribution model (SDM) is applied to accurately model distribution of PET tracer uptake, specifically FDG in this work, within solid tumors.

RESULTS

The different transport mechanisms, namely convention and diffusion from vessel to tissue and in tissue, are elaborately calculated across the domain of interest and effect of each parameter on tracer distribution is investigated. The results show the convection terms to have negligible effect on tracer transport and the SDM can be solved after eliminating these terms.

CONCLUSION

The proposed framework of spatiotemporal modeling for PET tracers can be utilized to comprehensively assess the impact of various parameters on the spatiotemporal distribution of PET tracers.

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.

Modeling the Behavior of Red Blood Cells within the Caudal Vein Plexus of Zebrafish

Due to the important biological role of red blood cells (RBCs) in vertebrates, the analysis of reshaping and dynamics of RBCs motion is a critical issue in physiology and biomechanics. In this paper the behavior of RBCs within the immature capillary plexus during embryonic development of zebrafish has been analyzed. Relying on the fact that zebrafish embryos are small and optically transparent, it is possible to image the blood flow. In this way the anatomy of blood vessels is monitored along with the circulation throughout their development. Numerical simulations were performed using a specific numerical model that combines fluid flow simulation, modeling of the interaction of individual RBCs immersed in blood plasma with the surrounding fluid and modeling the deformation of individual cells. The results of numerical simulations are in accordance with the in vivo observed region of interest within the caudal vein plexus of the zebrafish embryo. Good agreement of results demonstrates the capabilities of the developed numerical model to predict and analyze the motion and deformation of RBCs in complex geometries. The proposed model (methodology) will help to elucidate different rheological and hematological related pathologies and finally to design better treatment strategies.

Distinct functional roles of cardiac mitochondrial subpopulations revealed by a 3D simulation model

Experimental characterization of two cardiac mitochondrial subpopulations, namely, subsarcolemmal mitochondria (SSM) and interfibrillar mitochondria (IFM), has been hampered by technical difficulties, and an alternative approach is eagerly awaited. We previously developed a three-dimensional computational cardiomyocyte model that integrates electrophysiology, metabolism, and mechanics with subcellular structure. In this study, we further developed our model to include intracellular oxygen diffusion, and determined whether mitochondrial localization or intrinsic properties cause functional variations. For this purpose, we created two models: one with equal SSM and IFM properties and one with IFM having higher activity levels. Using these two models to compare the SSM and IFM responses of [Ca(2+)], tricarboxylic acid cycle activity, [NADH], and mitochondrial inner membrane potential to abrupt changes in pacing frequency (0.25-2 Hz), we found that the reported functional differences between these subpopulations appear to be mostly related to local [Ca(2+)] heterogeneity, and variations in intrinsic properties only serve to augment these differences. We also examined the effect of hypoxia on mitochondrial function. Under normoxic conditions, intracellular oxygen is much higher throughout the cell than the half-saturation concentration for oxidative phosphorylation. However, under limited oxygen supply, oxygen is mostly exhausted in SSM, leaving the core region in an anoxic condition. Reflecting this heterogeneous oxygen environment, the inner membrane potential continues to decrease in IFM, whereas it is maintained to nearly normal levels in SSM, thereby ensuring ATP supply to this region. Our simulation results provide clues to understanding the origin of functional variations in two cardiac mitochondrial subpopulations and their differential roles in maintaining cardiomyocyte function as a whole.

The Pathway for Oxygen: Tutorial Modelling on Oxygen Transport from Air to Mitochondrion: The Pathway for Oxygen

The 'Pathway for Oxygen' is captured in a set of models describing quantitative relationships between fluxes and driving forces for the flux of oxygen from the external air source to the mitochondrial sink at cytochrome oxidase. The intervening processes involve convection, membrane permeation, diffusion of free and heme-bound O2 and enzymatic reactions. While this system's basic elements are simple: ventilation, alveolar gas exchange with blood, circulation of the blood, perfusion of an organ, uptake by tissue, and consumption by chemical reaction, integration of these pieces quickly becomes complex. This complexity led us to construct a tutorial on the ideas and principles; these first PathwayO2 models are simple but quantitative and cover: (1) a 'one-alveolus lung' with airway resistance, lung volume compliance, (2) bidirectional transport of solute gasses like O2 and CO2, (3) gas exchange between alveolar air and lung capillary blood, (4) gas solubility in blood, and circulation of blood through the capillary syncytium and back to the lung, and (5) blood-tissue gas exchange in capillaries. These open-source models are at Physiome.org and provide background for the many respiratory models there.

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.

The effect of hydrogen gas evolution of magnesium implant on the postimplantation mortality of rats

Background/Objective

Hydrogen gas cavity is formed during in vivo degradation of magnesium implants. In many studies, the gas cavity is mostly punctured out subcutaneously. However, this procedure becomes inapplicable in certain internal surgeries; therefore, the effect of this gas cavity is worth further assessment.

Methods

In this study, we investigated the effect of hydrogen gas evolution on the mortality of rats and analysed the whole body capacity to relieve the gas. Porous pure-magnesium implants were implanted in the femoral bone defect of adult Sprague-Dawley rats up to 18 days, and their survival rate was calculated while the gas cavity size was measured, and its effect was analysed with support of radiographic and blood analysis.

Results

The gas cavity was rapidly formed surrounding the implantation site and obviously decreased the rats' survival rate. The gas was observed to swell the surrounding implantation site by filling the loose compartments and then dispersing subcutaneously to other areas.

Conclusion

The rat's whole body capacity was unable to tolerate the rapid and persistent hydrogen gas cavity formation as shown by high postimplantation mortality.

Blood Flow Versus Hematocrit in Optimization of Oxygen Transfer to Tissue During Fluid Resuscitation

The effectiveness of fluid resuscitation regimens in hemorrhagic trauma is assessed based on its ability to increase oxygen concentration in tissue. Fluid resuscitation using both crystalloids and colloids fluids, creates a dilemma due to its opposing effects on oxygen transfer. It increases blood flow thereby augmenting oxygen transport but it also dilutes the blood simultaneously and reduces oxygen concentration thereby reducing oxygen transport. In this work we have studied these two opposing effects of fluid therapy on oxygen delivery to tissue. A mathematical model of oxygen diffusion from capillaries to tissue and its distribution in tissue was developed and integrated into a previously developed hemodynamic model. The capillary-tissue model was based on the Krogh structure. Compared to other models, fewer simplifying assumptions were made leading to different boundary conditions and less constraints, especially regarding capillary oxygen content at its venous end. Results showed that oxygen content in blood is the dominant factor in oxygen transport to tissue and its effect is greater than the effect of flow. The integration of the capillary/tissue model with the hemodynamic model that links administered fluids with flow and blood dilution indicated that fluid resuscitation may reduce oxygen transport to tissue.

Extracellular hemoglobin: the case of a friend turned foe

Hemoglobin (Hb) is a highly conserved molecule present in all life forms and functionally tied to the complexity of aerobic organisms on earth in utilizing oxygen from the atmosphere and delivering to cells and tissues. This primary function sustains the energy requirements of cells and maintains cellular homeostasis. Decades of intensive research has presented a paradigm shift that shows how the molecule also functions to facilitate smooth oxygen delivery through the cardiovascular system for cellular bioenergetic homeostasis and signaling for cell function and defense. These roles are particularly highlighted in the binding of Hb to gaseous molecules carbon dioxide (CO₂), nitric oxide (NO) and carbon monoxide (CO), while also serving indirectly or directly as sources of these signaling molecules. The functional activities impacted by Hb outside of bioenergetics homeostasis, include fertilization, signaling functions, modulation of inflammatory responses for defense and cell viability. These activities are efficiently executed while Hb is sequestered safely within the confines of the red blood cell (rbc). Outside of rbc confines, Hb disaggregates and becomes a danger molecule to cell survival. In these perpectives, Hb function is broadly dichotomous, either a friend in its natural environment providing and facilitating the means for cell function or foe when dislocated from its habitat under stress or pathological condition disrupting cell function. The review presents insights into how this dichotomy in function manifests.

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.

Effects of gas exchange on acid-base balance

This paper describes the interactions between ventilation and acid-base balance under a variety of conditions including rest, exercise, altitude, pregnancy, and various muscle, respiratory, cardiac, and renal pathologies. We introduce the physicochemical approach to assessing acid-base status and demonstrate how this approach can be used to quantify the origins of acid-base disorders using examples from the literature. The relationships between chemoreceptor and metaboreceptor control of ventilation and acid-base balance summarized here for adults, youth, and in various pathological conditions. There is a dynamic interplay between disturbances in acid-base balance, that is, exercise, that affect ventilation as well as imposed or pathological disturbances of ventilation that affect acid-base balance. Interactions between ventilation and acid-base balance are highlighted for moderate- to high-intensity exercise, altitude, induced acidosis and alkalosis, pregnancy, obesity, and some pathological conditions. In many situations, complete acid-base data are lacking, indicating a need for further research aimed at elucidating mechanistic bases for relationships between alterations in acid-base state and the ventilatory responses.

Regulation of cellular gas exchange, oxygen sensing, and metabolic control

Cells must continuously monitor and couple their metabolic requirements for ATP utilization with their ability to take up O2 for mitochondrial respiration. When O2 uptake and delivery move out of homeostasis, cells have elaborate and diverse sensing and response systems to compensate. In this review, we explore the biophysics of O2 and gas diffusion in the cell, how intracellular O2 is regulated, how intracellular O2 levels are sensed and how sensing systems impact mitochondrial respiration and shifts in metabolic pathways. Particular attention is paid to how O2 affects the redox state of the cell, as well as the NO, H2S, and CO concentrations. We also explore how these agents can affect various aspects of gas exchange and activate acute signaling pathways that promote survival. Two kinds of challenges to gas exchange are also discussed in detail: when insufficient O2 is available for respiration (hypoxia) and when metabolic requirements test the limits of gas exchange (exercising skeletal muscle). This review also focuses on responses to acute hypoxia in the context of the original "unifying theory of hypoxia tolerance" as expressed by Hochachka and colleagues. It includes discourse on the regulation of mitochondrial electron transport, metabolic suppression, shifts in metabolic pathways, and recruitment of cell survival pathways preventing collapse of membrane potential and nuclear apoptosis. Regarding exercise, the issues discussed relate to the O2 sensitivity of metabolic rate, O2 kinetics in exercise, and influences of available O2 on glycolysis and lactate production.

Modeling serotonin uptake in the lung shows endothelial transporters dominate over cleft permeation

A four-region (capillary plasma, endothelium, interstitial fluid, cell) multipath model was configured to describe the kinetics of blood-tissue exchange for small solutes in the lung, accounting for regional flow heterogeneity, permeation of cell membranes and through interendothelial clefts, and intracellular reactions. Serotonin uptake data from the Multiple indicator dilution "bolus sweep" experiments of Rickaby and coworkers (Rickaby DA, Linehan JH, Bronikowski TA, Dawson CA. J Appl Physiol 51: 405-414, 1981; Rickaby DA, Dawson CA, and Linehan JH. J Appl Physiol 56: 1170-1177, 1984) and Malcorps et al. (Malcorps CM, Dawson CA, Linehan JH, Bronikowski TA, Rickaby DA, Herman AG, Will JA. J Appl Physiol 57: 720-730, 1984) were analyzed to distinguish facilitated transport into the endothelial cells (EC) and the inhibition of tracer transport by nontracer serotonin in the bolus of injectate from the free uninhibited permeation through the clefts into the interstitial fluid space. The permeability-surface area products (PS) for serotonin via the inter-EC clefts were ~0.3 ml·g⁻¹·min⁻¹, low compared with the transporter-mediated maximum PS of 13 ml·g⁻¹·min⁻¹ (with Km = ~0.3 μM and Vmax = ~4 nmol·g⁻¹·min⁻¹). The estimates of serotonin PS values for EC transporters from their multiple data sets were similar and were influenced only modestly by accounting for the cleft permeability in parallel. The cleft PS estimates in these Ringer-perfused lungs are less than half of those for anesthetized dogs (Yipintsoi T. Circ Res 39: 523-531, 1976) with normal hematocrits, but are compatible with passive noncarrier-mediated transport observed later in the same laboratory (Dawson CA, Linehan JH, Rickaby DA, Bronikowski TA. Ann Biomed Eng 15: 217-227, 1987; Peeters FAM, Bronikowski TA, Dawson CA, Linehan JH, Bult H, Herman AG. J Appl Physiol 66: 2328-2337, 1989) The identification and quantitation of the cleft pathway conductance from these studies affirms the importance of the cleft permeation.

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.

The roles of cerebral blood flow, capillary transit time heterogeneity, and oxygen tension in brain oxygenation and metabolism

Normal brain function depends critically on moment-to-moment regulation of oxygen supply by the bloodstream to meet changing metabolic needs. Neurovascular coupling, a range of mechanisms that converge on arterioles to adjust local cerebral blood flow (CBF), represents our current framework for understanding this regulation. We modeled the combined effects of CBF and capillary transit time heterogeneity (CTTH) on the maximum oxygen extraction fraction (OEF(max)) and metabolic rate of oxygen that can biophysically be supported, for a given tissue oxygen tension. Red blood cell velocity recordings in rat brain support close hemodynamic-metabolic coupling by means of CBF and CTTH across a range of physiological conditions. The CTTH reduction improves tissue oxygenation by counteracting inherent reductions in OEF(max) as CBF increases, and seemingly secures sufficient oxygenation during episodes of hyperemia resulting from cortical activation or hypoxemia. In hypoperfusion and states of blocked CBF, both lower oxygen tension and CTTH may secure tissue oxygenation. Our model predicts that disturbed capillary flows may cause a condition of malignant CTTH, in which states of higher CBF display lower oxygen availability. We propose that conditions with altered capillary morphology, such as amyloid, diabetic or hypertensive microangiopathy, and ischemia-reperfusion, may disturb CTTH and thereby flow-metabolism coupling and cerebral oxygen metabolism.

Consequences of hyperoxia and the toxicity of oxygen in the lung

Oxygen (O(2)) is life essential but as a drug has a maximum positive biological benefit and accompanying toxicity effects. Oxygen is therapeutic for treatment of hypoxemia and hypoxia associated with many pathological processes. Pathophysiological processes are associated with increased levels of hyperoxia-induced reactive O(2) species (ROS) which may readily react with surrounding biological tissues, damaging lipids, proteins, and nucleic acids. Protective antioxidant defenses can become overwhelmed with ROS leading to oxidative stress. Activated alveolar capillary endothelium is characterized by increased adhesiveness causing accumulation of cell populations such as neutrophils, which are a source of ROS. Increased levels of ROS cause hyperpermeability, coagulopathy, and collagen deposition as well as other irreversible changes occurring within the alveolar space. In hyperoxia, multiple signaling pathways determine the pulmonary cellular response: apoptosis, necrosis, or repair. Understanding the effects of O(2) administration is important to prevent inadvertent alveolar damage caused by hyperoxia in patients requiring supplemental oxygenation.

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.

Evaluation of cardiac oxygen consumption under hypoxia with tissue model integrating microcirculation model and cell model

Analyzing the microscopic energy balance of cardiac tissue is very important for understanding heart diseases. However, such analysis is difficult with animal experiments. Therefore, the accurate simulation model is expected to be an important tool for such research. We propose a cardiac tissue model which can reproduce accurate distribution of oxygen consumption under hypoxia. The model includes blood tissue exchange model of capillary and oxygen consumption model of cells. The capillary model is based on the model proposed by Dash et al. 2006, and the cell model is based on the model proposed by Kuzumoto et al. 2007. By analyzing the oxygen consumption of the proposed model, the relation between the oxygen consumption and the arterial oxygen concentration was found to be largely different from that of single cell model. This implies that the animal experimental data should be carefully used for constructing a biological simulation model, depending on whether the experiment is performed within a cell or a tissue.

An Improved Algorithm and Its Parallel Implementation for Solving a General Blood-Tissue Transport and Metabolism Model

Fast algorithms for simulating mathematical models of coupled blood-tissue transport and metabolism are critical for the analysis of data on transport and reaction in tissues. Here, by combining the method of characteristics with the standard grid discretization technique, a novel algorithm is introduced for solving a general blood-tissue transport and metabolism model governed by a large system of one-dimensional semilinear first order partial differential equations. The key part of the algorithm is to approximate the model as a group of independent ordinary differential equation (ODE) systems such that each ODE system has the same size as the model and can be integrated independently. Thus the method can be easily implemented in parallel on a large scale multiprocessor computer. The accuracy of the algorithm is demonstrated for solving a simple blood-tissue exchange model introduced by Sangren and Sheppard (Bull. Math. Biophys. 15:387-394, 1953), which has an analytical solution. Numerical experiments made on a distributed-memory parallel computer (an HP Linux cluster) and a shared-memory parallel computer (a SGI Origin 2000) demonstrate the parallel efficiency of the algorithm.

Disequilibrium between alveolar and end-pulmonary-capillary O2 tension in altitude hypoxia and respiratory disease: an update of a mathematical model of human respiration at altitude

We have previously formulated and validated a mathematical model specifically designed to describe human respiratory behavior at altitude. In that model, we assumed equality of alveolar and end-pulmonary-capillary oxygen tensions. However, this equality may not hold true during rapid and prolonged changes to high altitudes producing severe hypoxia as can occur in aircraft cabin decompressions and in some respiratory diseases. We currently investigate this possibility by modifying our previous model to include the dynamics of oxygen exchange across the pulmonary capillary. The updated model was validated against limited experimental data on ventilation and gas tensions in various altitude-decompression scenarios. The updated model predicts that during rapid and sustained decompressions to high altitudes the disequilibrium of gas tensions between alveolar gas and capillary blood could be 10 Torr, or larger. Neglecting this effect underestimates the severity of a decompression and its potential to produce unconsciousness and subsequent brain damage. In light of these results, we also examined the effect of this disequilibrium on the diminished oxygen diffusion capacity that can occur in some respiratory diseases. We found that decreases in diffusion capacity which would have minimal effects at sea level produced significant disequilibrium of gas tensions and a large fall in hemoglobin oxygen saturation at a cabin altitude of 4000-8000 ft. As demonstrated, this new model could serve as an important tool to examine the important physiological consequences of decompression scenarios in aircraft and the pathophysiological situations in which the equilibrium of gas tensions along the pulmonary capillary are particularly critical.

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.

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.

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.

Mathematical modeling of buffers used in myocardial preservation

OBJECTIVE

Buffers added to myocardial preservation solutions are considered to be critical for resisting myocardium pH changes from the accumulation of protons (H+). Our hypothesis is that mathematical modeling of three clinically used buffers will define their individual buffering capacities under simulated clinical conditions.

METHODS

The buffers, tromethamine (THAM), sodium bicarbonate (HCO3-), and L-histidine, were compared in terms of their buffering capacity (beta) under specific temperatures and concentrations, using a mathematical model.

RESULTS

At 37 degrees C, the maximal beta (betamax) occurred at pH 7.75 for THAM, pH 6.10 for HCO3-, and pH 5.89 for L-histidine at equimolar concentrations. A decrease in temperature moved betamax to a higher pH value for each buffer. At clinical concentrations, L-histidine provided the greatest buffering capacity followed by HCO3- and THAM, respectively.

DISCUSSION

This model permitted comparison of the above buffers under simulated clinical conditions. The assumption was that the magnitude of betamax at a given temperature determines which buffer(s) could be most effective for myocardial preservation. Also, the assumption was taken that these buffers are used in a closed system--where there is no continuous blood flow--and that the buffering ability of THAM and L-histidine were not influenced by the accumulation of CO2 as is HCO3-. THAM and L-histidine were more effective at hypothermic temperatures compared with HCO3-; however, HCO3- provided buffering at normothermic temperatures. Through the theoretical considerations of this study, we propose that combining HCO3- with THAM or L-histidine could be most efficacious for myocardial preservation during open heart surgery or organ transplantation.

Muscle oxygen uptake differs from consumption dynamics during transients in exercise

Relating external to internal respiration during exercise requires quantitative modeling analysis for reliable inferences with respect to metabolic rate. Often, oxygen transport and metabolism based on steady-state mass balances (Fick principle) and passive diffusion between blood and tissue are applied to link pulmonary to cellular respiration. Indeed, when the work rate does not change rapidly, a quasi-steady-state analysis based on the Fick principle is sufficient to estimate the rate of O2 consumption in working muscle. During exercise when the work rate changes quickly, however, non-invasive in vivo measurements to estimate muscle O2 consumption are not sufficient to characterize cellular respiration of working muscle. To interpret transient changes of venous O2 concentration, blood flow, and O2 consumption in working muscle, a mathematical model of O2 transport and consumption based on dynamic mass balances is required. In this study, a comparison is made of the differences between simulations of O2 uptake and O2 consumption within working skeletal muscle based on a dynamic model and quasi-steady-state approximations. The conditions are specified under which the quasi-steady-state approximation becomes invalid.

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.

A computational model of adipose tissue metabolism: evidence for intracellular compartmentation and differential activation of lipases

Regulation of lipolysis in adipose tissue is critical to whole body fuel homeostasis and to the development of insulin resistance. Due to the challenging nature of laboratory investigations of regulatory mechanisms in adipose tissue, mathematical models could provide a valuable adjunct to such experimental work. We have developed a computational model to analyze key components of adipose tissue metabolism in vivo in human in the fasting state. The various key components included triglyceride-fatty acid cycling, regulation of lipolytic reactions, and glyceroneogenesis. The model, consisting of spatially lumped blood and cellular compartments, included essential transport processes and biochemical reactions. Concentration dynamics for major substrates were described by mass balance equations. Model equations were solved numerically to simulate dynamic responses to intravenous epinephrine infusion. Model simulations were compared with the corresponding experimental measurements of the arteriovenous difference across the abdominal subcutaneous fat bed in humans. The model can simulate physiological responses arising from the different expression levels of lipases. Key findings of this study are as follows: (1) Distinguishing the active metabolic subdomain ( approximately 3% of total tissue volume) is critical for simulating data. (2) During epinephrine infusion, lipases are differentially activated such that diglyceride breakdown is approximately four times faster than triglyceride breakdown. (3) Glyceroneogenesis contributes more to glycerol-3-phosphate synthesis during epinephrine infusion when pyruvate oxidation is inhibited by a high acetyl-CoA/free-CoA ratio.

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.

Model of oxygen transport and metabolism predicts effect of hyperoxia on canine muscle oxygen uptake dynamics

Previous studies have shown that increased oxygen delivery, via increased convection or arterial oxygen content, does not speed the dynamics of oxygen uptake, V̇o2m, in dog muscle electrically stimulated at a submaximal metabolic rate. However, the dynamics of transport and metabolic processes that occur within working muscle in situ is typically unavailable in this experimental setting. To investigate factors affecting V̇o2m dynamics at contraction onset, we combined dynamic experimental data across working muscle with a mechanistic model of oxygen transport and metabolism in muscle. The model is based on dynamic mass balances for O2, ATP, and PCr. Model equations account for changes in cellular ATPase, oxidative phosphorylation, and creatine kinase fluxes in skeletal muscle during exercise, and cellular respiration depends on [ADP] and [O2]. Model simulations were conducted at different levels of arterial oxygen content and blood flow to quantify the effects of convection and diffusion of oxygen on the regulation of cellular respiration during step transitions from rest to isometric contraction in dog gastrocnemius muscle. Simulations of arteriovenous O2 differences and V̇o2m dynamics were successfully compared with experimental data (Grassi B, Gladden LB, Samaja M, Stary CM, Hogan MC. J Appl Physiol 85: 1394–1403, 1998; and Grassi B, Gladden LB, Stary CM, Wagner PD, Hogan MC. J Appl Physiol 85: 1404–1412, 1998), thus demonstrating the validity of the model, as well as its predictive capability. The main findings of this study are: 1) the estimated dynamic response of oxygen utilization at contraction onset in muscle is faster than that of oxygen uptake; and 2) hyperoxia does not accelerate the dynamics of diffusion and consequently muscle oxygen uptake at contraction onset due to the hyperoxia-induced increase in oxygen stores. These in silico derived results cannot be obtained from experimental observations alone.

A computational model that links non-periodic vasomotion to enhanced oxygenation in skeletal muscle

We propose a model of a capillary network in which chaotic capillary activity is crucial for efficient oxygenation of a muscle fiber. Tissue oxygenation by microcirculation is controlled by a complex pattern of opening and closing of precapillary sphincters, a phenomenon known as vasomotion. We model the individual precapillary sphincter as a non-linear oscillator that exhibits perfectly periodic vasomotion in isolation. The precapillary sphincters surrounding an active fiber are considered as a network; specific modes of interaction within this network result in complex patterns of vasomotion. In our model, efficient oxygenation of the fiber depends crucially on the mode of interaction among the vasomotions of the individual capillaries. Network interactions that lead to chaotic vasomotion are found to be essential for meeting the tissue oxygen demands precisely. Interactions that cause regular rhythmic patterns of vasomotion fail to meet oxygenation demands accurately.

Effect of chaotic vasomotion in skeletal muscle on tissue oxygenation

Vasomotion refers to spontaneous variations in the lumen size of small vessels, with a plausible role in regulation of various aspects of microcirculation. We propose a computational model of vasomotion in skeletal muscle in which the pattern of vasomotion is shown to critically determine the efficiency of oxygenation of a muscle fiber. In this model, precapillary sphincters are modeled as nonlinear oscillators. We hypothesize that these sphincters interact via exchange of vasoactive substances. As a consequence, vasomotion is described as a phenomenon associated with a network of nonlinear oscillators. As a specific instance, we model the vasomotion of precapillary sphincters surrounding an active fiber. The sphincters coordinate their rhythms so as to minimize oxygen deficit in the fiber. Our modeling studies indicate that efficient oxygenation of the fiber depends crucially on the mode of interaction among the vasomotions of individual sphincters. While chaotic forms of vasomotion enhanced oxygenation, regular patterns of vasomotion failed to meet the oxygenation demand accurately.