Myocardial oxygenation in isolated hearts predicted by an anatomically realistic microvascular transport model

Integrated Functions of Cardiac Energetics, Mechanics, and Purine Nucleotide Metabolism

Purine nucleotides play central roles in energy metabolism in the heart. Most fundamentally, the free energy of hydrolysis of the adenine nucleotide adenosine triphosphate (ATP) provides the thermodynamic driving force for numerous cellular processes including the actin-myosin crossbridge cycle. Perturbations to ATP supply and/or demand in the myocardium lead to changes in the homeostatic balance between purine nucleotide synthesis, degradation, and salvage, potentially affecting myocardial energetics and, consequently, myocardial mechanics. Indeed, both acute myocardial ischemia and decompensatory remodeling of the myocardium in heart failure are associated with depletion of myocardial adenine nucleotides and with impaired myocardial mechanical function. Yet there remain gaps in the understanding of mechanistic links between adenine nucleotide degradation and contractile dysfunction in heart disease. The scope of this article is to: (i) review current knowledge of the pathways of purine nucleotide depletion and salvage in acute ischemia and in chronic heart disease; (ii) review hypothesized mechanisms linking myocardial mechanics and energetics with myocardial adenine nucleotide regulation; and (iii) highlight potential targets for treating myocardial metabolic and mechanical dysfunction associated with these pathways. It is hypothesized that an imbalance in the degradation, salvage, and synthesis of adenine nucleotides leads to a net loss of adenine nucleotides in both acute ischemia and under chronic high-demand conditions associated with the development of heart failure. This reduction in adenine nucleotide levels results in reduced myocardial ATP and increased myocardial inorganic phosphate. Both of these changes have the potential to directly impact tension development and mechanical work at the cellular level. © 2024 American Physiological Society. Compr Physiol 14:5345-5369, 2024.

Disentangling the Gordian knot of local metabolic control of coronary blood flow

Recognition that coronary blood flow is tightly coupled with myocardial metabolism has been appreciated for well over half a century. However, exactly how coronary microvascular resistance is tightly coupled with myocardial oxygen consumption (MV̇o₂) remains one of the most highly contested mysteries of the coronary circulation to this day. Understanding the mechanisms responsible for local metabolic control of coronary blood flow has been confounded by continued debate regarding both anticipated experimental outcomes and data interpretation. For a number of years, coronary venous Po₂ has been generally accepted as a measure of myocardial tissue oxygenation and thus the classically proposed error signal for the generation of vasodilator metabolites in the heart. However, interpretation of changes in coronary venous Po₂ relative to MV̇o₂ are quite nuanced, inherently circular in nature, and subject to confounding influences that remain largely unaccounted for. The purpose of this review is to highlight difficulties in interpreting the complex interrelationship between key coronary outcome variables and the arguments that emerge from prior studies performed during exercise, hemodilution, hypoxemia, and alterations in perfusion pressure. Furthermore, potential paths forward are proposed to help to facilitate further dialogue and study to ultimately unravel what has become the Gordian knot of the coronary circulation.

Intra-cardiac Side-Firing Light Catheter for Monitoring Cellular Metabolism using Transmural Absorbance Spectroscopy of Perfused Mammalian Hearts

Absorbance spectroscopy of cardiac muscle provides non-destructive assessment of cytosolic and mitochondrial oxygenation via myoglobin and cytochrome absorbance respectively. In addition, numerous aspects of the mitochondrial metabolic status such as membrane potential and substrate entry can also be estimated. To perform cardiac wall transmission optical spectroscopy, a commercially available side-firing optical fiber catheter is placed in the left ventricle of the isolated perfused heart as a light source. Light passing through the heart wall is collected with an external optical fiber to perform optical spectroscopy of the heart in near real- time. The transmission approach avoids numerous surface scattering interference occurring in widely used reflection approaches. Changes in transmural absorbance spectra were deconvolved using a library of chromophore reference spectra, providing quantitative measures of all the known cardiac chromophores simultaneously. This spectral deconvolution approach eliminated intrinsic errors that may result from using common dual wavelength methods applied to overlapping absorbance spectra, as well as provided a quantitative evaluation of the goodness of fit. A custom program was designed for data acquisition and analysis, which permitted the investigator to monitor the metabolic state of the preparation during the experiment. These relatively simple additions to the standard heart perfusion system provide a unique insight into the metabolic state of the heart wall in addition to conventional measures of contraction, perfusion, and substrate/oxygen extraction.

Energy Metabolism in the Failing Right Ventricle: Limitations of Oxygen Delivery and the Creatine Kinase System

Pulmonary arterial hypertension (PAH) results in hypertrophic remodeling of the right ventricle (RV) to overcome increased pulmonary pressure. This increases the O2 consumption of the myocardium, and without a concomitant increase in energy generation, a mismatch with demand may occur. Eventually, RV function can no longer be sustained, and RV failure occurs. Beta-adrenergic blockers (BB) are thought to improve survival in left heart failure, in part by reducing energy expenditure and hypertrophy, however they are not currently a therapy for PAH. The monocrotaline (MCT) rat model of PAH was used to investigate the consequence of RV failure on myocardial oxygenation and mitochondrial function. A second group of MCT rats was treated daily with the beta-1 blocker metoprolol (MCT + BB). Histology confirmed reduced capillary density and increased capillary supply area without indications of capillary rarefaction in MCT rats. A computer model of O2 flux was applied to the experimentally recorded capillary locations and predicted a reduction in mean tissue PO2 in MCT rats. The fraction of hypoxic tissue (defined as PO2 < 0.5 mmHg) was reduced following beta-1 blocker (BB) treatment. The functionality of the creatine kinase (CK) energy shuttle was measured in permeabilized RV myocytes by sequential ADP titrations in the presence and absence of creatine. Creatine significantly decreased the KmADP in cells from saline-injected control (CON) rats, but not MCT rats. The difference in KmADP with or without creatine was not different in MCT + BB cells compared to CON or MCT cells. Improved myocardial energetics could contribute to improved survival of PAH with chronic BB treatment.

Paradoxical arteriole constriction compromises cytosolic and mitochondrial oxygen delivery in the isolated saline-perfused heart

The isolated saline-perfused heart is used extensively to study cardiac physiology. Previous isolated heart studies have demonstrated lower tissue oxygenation compared with in vivo hearts based on myoglobin oxygenation and the mitochondrial redox state. These data, consistent with small anoxic regions, suggest that the homeostatic balance between work and oxygen delivery is impaired. We hypothesized that these anoxic regions are caused by inadequate local perfusion due to a paradoxical arteriole constriction generated by a disrupted vasoregulatory network. We tested this hypothesis by applying two exogenous vasodilatory agents, adenosine and cromakalim, to relax vascular tone in an isolated, saline-perfused, working rabbit heart. Oxygenation was monitored using differential optical transmission spectroscopy and full spectral fitting. Increases in coronary flow over control with adenosine (27 ± 4 ml/min) or cromakalim (44 ± 4 ml/min) were associated with proportional spectral changes indicative of myoglobin oxygenation and cytochrome oxidase (COX) oxidation, consistent with a decrease in tissue anoxia. Quantitatively, adenosine decreased deoxymyoglobin optical density (OD) across the wall by 0.053 ± 0.008 OD, whereas the reduced form of COX was decreased by 0.039 ± 0.005 OD. Cromakalim was more potent, decreasing deoxymyoglobin and reducing the level of COX by 0.070 ± 0.019 OD and 0.062 ± 0.019 OD, respectively. These effects were not species specific, as Langendorff-perfused mouse hearts treated with adenosine demonstrated similar changes. These data are consistent with paradoxical arteriole constriction as a major source of regional anoxia during saline heart perfusion. We suggest that the vasoregulatory network is disrupted by the washout of interstitial vasoactive metabolites in vitro. NEW & NOTEWORTHY Regional tissue anoxia is a common finding in the ubiquitous saline-perfused heart but is not found in vivo. Noninvasive optical techniques confirmed the presence of regional anoxia under control conditions and demonstrated that anoxia is diminished using exogenous vasodilators. These data are consistent with active arteriole constriction, occurring despite regional anoxia, generated by a disrupted vasoregulatory network. Washout of interstitial vasoactive metabolites may contribute to the disruption of normal vasoregulatory processes in vitro.

Cardiac performance is limited by oxygen delivery to the mitochondria in the crystalloid-perfused working heart

The left ventricular working, crystalloid-perfused heart is used extensively to evaluate basic cardiac function, pathophysiology, and pharmacology. Crystalloid-perfused hearts may be limited by oxygen delivery, as adding oxygen carriers increases myoglobin oxygenation and improves myocardial function. However, whether decreased myoglobin oxygen saturation impacts oxidative phosphorylation (OxPhos) is unresolved, since myoglobin has a much lower affinity for oxygen than cytochrome c oxidase (COX). In the present study, a laboratory-based synthesis of an affordable perfluorocarbon (PFC) emulsion was developed to increase perfusate oxygen carrying capacity without impeding optical absorbance assessments. In left ventricular working hearts, along with conventional measurements of cardiac function and metabolic rate, myoglobin oxygenation and cytochrome redox state were monitored using a novel transmural illumination approach. Hearts were perfused with Krebs-Henseleit (KH) or KH supplemented with PFC, increasing perfusate oxygen carrying capacity by 3.6-fold. In KH-perfused hearts, myoglobin was deoxygenated, consistent with cytoplasmic hypoxia, and the mitochondrial cytochromes, including COX, exhibited a high reduction state, consistent with OxPhos hypoxia. PFC perfusate increased aortic output from 76 ± 6 to 142 ± 4 ml/min and increased oxygen consumption while also increasing myoglobin oxygenation and oxidizing the mitochondrial cytochromes. These results are consistent with limited delivery of oxygen to OxPhos resulting in an adapted lower cardiac performance with KH. Consistent with this, PFCs increased myocardial oxygenation, and cardiac work was higher over a wider range of perfusate Po₂. In summary, heart mitochondria are limited by oxygen delivery with KH; supplementation of KH with PFC reverses mitochondrial hypoxia and improves cardiac performance, creating a more physiological tissue oxygen delivery. NEW & NOTEWORTHY Optical absorbance spectroscopy of intrinsic chromophores reveals that the commonly used crystalloid-perfused working heart is oxygen limited for oxidative phosphorylation and associated cardiac work. Oxygen-carrying perfluorocarbons increase myocardial oxygen delivery and improve cardiac function, providing a more physiological mitochondrial redox state and emphasizing cardiac work is modulated by myocardial oxygen delivery.

Intracardiac light catheter for rapid scanning transmural absorbance spectroscopy of perfused myocardium: measurement of myoglobin oxygenation and mitochondria redox state

Absorbance spectroscopy of intrinsic cardiac chromophores provides nondestructive assessment of cytosolic oxygenation and mitochondria redox state. Isolated perfused heart spectroscopy is usually conducted by collecting reflected light from the heart surface, which represents a combination of surface scattering events and light that traversed portions of the myocardium. Reflectance spectroscopy with complex surface scattering effects in the beating heart leads to difficulty in quantitating chromophore absorbance. In this study, surface scattering was minimized and transmural path length optimized by placing a light source within the left ventricular chamber while monitoring transmurally transmitted light at the epicardial surface. The custom-designed intrachamber light catheter was a flexible coaxial cable (2.42-Fr) terminated with an encapsulated side-firing LED of 1.8 × 0.8 mm, altogether similar in size to a Millar pressure catheter. The LED catheter had minimal impact on aortic flow and heart rate in Langendorff perfusion and did not impact stability of the left ventricule of the working heart. Changes in transmural absorbance spectra were deconvoluted using a library of chromophore reference spectra to quantify the relative contribution of specific chromophores to the changes in measured absorbance. This broad-band spectral deconvolution approach eliminated errors that may result from simple dual-wavelength absorbance intensity. The myoglobin oxygenation level was only 82.2 ± 3.0%, whereas cytochrome c and cytochrome a + a₃ were 13.3 ± 1.4% and 12.6 ± 2.2% reduced, respectively, in the Langendorff-perfused heart. The intracardiac illumination strategy permits transmural optical absorbance spectroscopy in perfused hearts, which provides a noninvasive real-time monitor of cytosolic oxygenation and mitochondria redox state.NEW & NOTEWORTHY Here, a novel nondestructive real-time approach for monitoring intrinsic indicators of cardiac metabolism and oxygenation is described using a catheter-based transillumination of the left ventricular free wall together with complete spectral analysis of transmitted light. This approach is a significant improvement in the quality of cardiac optical absorbance spectroscopic metabolic analyses.

Hypoxia exposure and B-type natriuretic peptide release from Langendorff heart of rats

Aim

We studied whether available oxygen without induced mechanical stretch regulates the release of the biologically active B‐type natriuretic peptide (BNP) from Langendorff heart.

Methods

Rat hearts were isolated and perfused with a physiological Krebs–Henseleit solution at a constant hydrostatic pressure in Langendorff set‐up. The basal O₂ level of perfusate (24.4 ± 0.04 mg L⁻¹) was gradually lowered to 3.0 ± 0.01 mg L⁻¹ over 20 min using N₂ gas (n = 7). BNP and O₂ level were measured from coronary flow. During control perfusions (n = 5), the O₂ concentration was kept at 26.6 ± 0.3 mg L⁻¹.

Results

A low oxygen concentration in the perfusate was associated with a significant increase in BNP release (F = 40.4, P < 0.001). Heart rate decreased when the oxygen concentration in the perfusate reached 9.1 ± 0.02 mg L⁻¹ and continued to fall in lower oxygen concentrations (F = 14.8, P < 0.001). There was also a significant but inverse correlation between BNP and oxygen in the coronary flow (R² = 0.27, P < 0.001).

Conclusion

In the spontaneously beating Langendorff rat heart, a decreasing concentration of oxygen in the ingoing perfusion increased the secretion of BNP. The effect of oxygen was independent of mechanical stretch of the heart as it occurred even when the heart rate decreased but the pressure conditions remained constant. The difference in the oxygen capacitance of blood and Krebs–Henseleit solution appears to be a major factor affecting secretion of BNP, which is correlated with the oxygen tension of myocardial cells and affected both by the oxygen concentration and capacitance of solution perfusing the heart and by the coronary flow.

Impaired Tissue Oxygenation in Metabolic Syndrome Requires Increased Microvascular Perfusion Heterogeneity

Metabolic syndrome (MS) in obese Zucker rats (OZR) is associated with impaired skeletal muscle performance and blunted hyperemia. Studies suggest that reduced O₂ diffusion capacity is required to explain compromised muscle performance and that heterogeneous microvascular perfusion distribution is critical. We modeled tissue oxygenation during muscle contraction in control and OZR skeletal muscle using physiologically realistic relationships. Using a network model of Krogh cylinders with increasing perfusion asymmetry and increased plasma skimming, we predict increased perfusion heterogeneity and decreased muscle oxygenation in OZR, with partial recovery following therapy. Notably, increasing O₂ delivery had less impact on VO₂ than equivalent decreases in O₂ delivery, providing a mechanism for previous empirical work associating perfusion heterogeneity and impaired O₂ extraction. We demonstrate that increased skeletal muscle perfusion asymmetry is a defining characteristic of MS and must be considered to effectively model and understand blood-tissue O₂ exchange in this model of human disease.

KV7 channels contribute to paracrine, but not metabolic or ischemic, regulation of coronary vascular reactivity in swine

Hydrogen peroxide (H2O2) and voltage-dependent K(+) (KV) channels play key roles in regulating coronary blood flow in response to metabolic, ischemic, and paracrine stimuli. The KV channels responsible have not been identified, but KV7 channels are possible candidates. Existing data regarding KV7 channel function in the coronary circulation (limited to ex vivo assessments) are mixed. Thus we examined the hypothesis that KV7 channels are present in cells of the coronary vascular wall and regulate vasodilation in swine. We performed a variety of molecular, biochemical, and functional (in vivo and ex vivo) studies. Coronary arteries expressed KCNQ genes (quantitative PCR) and KV7.4 protein (Western blot). Immunostaining demonstrated KV7.4 expression in conduit and resistance vessels, perhaps most prominently in the endothelial and adventitial layers. Flupirtine, a KV7 opener, relaxed coronary artery rings, and this was attenuated by linopirdine, a KV7 blocker. Endothelial denudation inhibited the flupirtine-induced and linopirdine-sensitive relaxation of coronary artery rings. Moreover, linopirdine diminished bradykinin-induced endothelial-dependent relaxation of coronary artery rings. There was no effect of intracoronary flupirtine or linopirdine on coronary blood flow at the resting heart rate in vivo. Linopirdine had no effect on coronary vasodilation in vivo elicited by ischemia, H2O2, or tachycardia. However, bradykinin increased coronary blood flow in vivo, and this was attenuated by linopirdine. These data indicate that KV7 channels are expressed in some coronary cell type(s) and influence endothelial function. Other physiological functions of coronary vascular KV7 channels remain unclear, but they do appear to contribute to endothelium-dependent responses to paracrine stimuli.

Myocardial Po2 does not limit aerobic metabolism in the postischemic heart

Reperfused hypertrophic hearts are prone to develop reflow abnormalities, which are likely to impair O2 return to the myocardium. Yet, reflow deficit may not be the only factor determining postischemic oxygenation in the hypertrophic heart. Altered O2 demand may also contribute to hypoxia. In addition, the extent to which myocardial Po2 dictates energy and functional recovery in the reperfused heart remains uncertain. In the present study, moderately hypertrophied hearts from spontaneously hypertensive rats were subjected to ischemia-reperfusion, and the recovery time courses of pH and high-energy phosphates were followed by (31)P NMR. (1)H NMR measurement of intracellular myoglobin assessed tissue O2 levels. The present study found that the exacerbation of hypoxia in the postischemic spontaneously hypertensive rat heart arises mostly from impaired microvascular supply of O2. However, postischemic myocardial Po2, at least when it exceeds ∼18% of the preischemic level, does not limit mitochondrial respiration and high-energy phosphate resynthesis. It only passively reflects changes in the O2 supply-demand balance.

A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries

A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10-30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume.

Effects of fiber type and size on the heterogeneity of oxygen distribution in exercising skeletal muscle

The process of oxygen delivery from capillary to muscle fiber is essential for a tissue with variable oxygen demand, such as skeletal muscle. Oxygen distribution in exercising skeletal muscle is regulated by convective oxygen transport in the blood vessels, oxygen diffusion and consumption in the tissue. Spatial heterogeneities in oxygen supply, such as microvascular architecture and hemodynamic variables, had been observed experimentally and their marked effects on oxygen exchange had been confirmed using mathematical models. In this study, we investigate the effects of heterogeneities in oxygen demand on tissue oxygenation distribution using a multiscale oxygen transport model. Muscles are composed of different ratios of the various fiber types. Each fiber type has characteristic values of several parameters, including fiber size, oxygen consumption, myoglobin concentration, and oxygen diffusivity. Using experimentally measured parameters for different fiber types and applying them to the rat extensor digitorum longus muscle, we evaluated the effects of heterogeneous fiber size and fiber type properties on the oxygen distribution profile. Our simulation results suggest a marked increase in spatial heterogeneity of oxygen due to fiber size distribution in a mixed muscle. Our simulations also suggest that the combined effects of fiber type properties, except size, do not contribute significantly to the tissue oxygen spatial heterogeneity. However, the incorporation of the difference in oxygen consumption rates of different fiber types alone causes higher oxygen heterogeneity compared to control cases with uniform fiber properties. In contrast, incorporating variation in other fiber type-specific properties, such as myoglobin concentration, causes little change in spatial tissue oxygenation profiles.

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.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Crystalloid versus red blood cell-containing medium in the Langendorff-perfused isolated heart preparation

BACKGROUND

The isolated heart model is widely used for the assessment of coronary vascular response under various experimental conditions. As medium perfusate influences oxygenation conditions, coronary vascular response and myocardial consumption performance may differ between isolated hearts perfused with from with Krebs-Henseleit solution or Krebs-Henseleit mixed with red blood cells (KH-RBC).

METHODS

Coronary vascular response to endothelium-dependent and independent vasodilators as well as myocardial performance and oxygen consumption to isoproterenol infusion were compared in isolated rabbit hearts perfused with Krebs-Henseleit or KH-RBC. Krebs-Henseleit perfusate was equilibrated with 95% oxygen and 5% carbon dioxide, KH-RBC (haemoglobin 8.0 +/- 1.1 g.dl) with 20% oxygen, 5% carbon dioxide, and 75% nitrogen. The perfusion pressure was kept constant so that coronary blood flow (CBF) varied with coronary resistance. Data are mean +/- SD.

RESULTS

Bradykinin induced a greater increase in CBF in KH-RBC-perfused hearts than in Krebs-Henseleit-perfused hearts (263 +/- 78 versus 134 +/- 35% of baseline, P < 0.001). Sodium nitroprusside induced a greater increase in CBF in KH-RBC-perfused than in Krebs-Henseleit-perfused hearts (257 +/- 70 versus 174 +/- 31% of baseline, P < 0.001). The increases in myocardial performance and in oxygen consumption induced by isoproterenol were greater with KH-RBC-perfused hearts than in Krebs-Henseleit-perfused hearts. A greater myoglobin release was observed in Krebs-Henseleit-perfused hearts.

CONCLUSION

Endothelium-dependent and independent coronary flow responses are increased in KH-RBC-perfused hearts. Moreover, metabolic control of CBF is altered in Krebs-Henseleit-perfused hearts. Such differences should be taken into account when pharmacologic responses of anaesthetic agents are studied.

Computational analysis of oxygen transport in the retinal arterial network

PURPOSE

The retina has a high oxygen consumption, making it particularly vulnerable to vascular insults, impairing oxygen and nutrient supply. The aim of this study was to develop a detailed computational model for quantitative analysis of blood flow and oxygen transport in physiologically realistic retinal arterial networks. Such a model will allow us to examine the effect of topological changes in retinal vasculature on hemodynamics and oxygen distribution in the retinal circulation.

MATERIALS AND METHODS

The Navier-Stokes equations for blood flow and the convection-diffusion equation for oxygen transfer were solved numerically to obtain detailed blood flow and oxygen distribution patterns in a retinal arterial tree. The geometrical outlines of the central retinal artery and its major branches were extracted from retinal images acquired from a healthy young adult by a Zeiss FF450+ fundus camera. The reconstructed subject-specific retinal arterial network geometry was combined with a structured tree model for the distal peripheral vessels. The non-Newtonian rheological properties of blood were incorporated by using an empirical viscosity model to account for the Fahraeus-Lindqvist effect.

RESULTS

The model predicted pressure drops in the range of 11-14.6 mmHg between the inlet and outlets of the reconstructed network and non-uniform oxygen tension, which varied with the vessel diameter and distance from the optic disc. The mean oxygen saturation in retinal arteries was 93.1% for vessels larger than 50 mum in diameter and 82.2% for smaller arterioles.

CONCLUSIONS

Our numerical results are in good agreement with in vivo measurements reported in the literature, demonstrating the potential of our model for prediction of oxygen distribution and intravascular oxygen tension profiles in the retinal arterial network. This paves the way for investigating the effects of parameter variation, simulating cases not available from experimental studies.

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.

Apparent diffusivity and Taylor dispersion of water and solutes in capillary beds

A physical theory explaining the anisotropic dispersion of water and solutes in biological tissues is introduced based on the phenomena of Taylor dispersion, in which highly diffusive solutes cycle between flowing and stagnant regions in the tissue, enhancing dispersion in the direction of microvascular flow. An effective diffusion equation is derived, for which the coefficient of dispersion in the axial direction (direction of capillary orientation) depends on the molecular diffusion coefficient, tissue perfusion, and vessel density. This analysis provides a homogenization that represents three-dimensional transport in capillary beds as an effectively one-dimensional phenomenon. The derived dispersion equation may be used to simulate the transport of solutes in tissues, such as in pharmacokinetic modeling. In addition, the analysis provides a physically based hypothesis for explaining dispersion anisotropy observed in diffusion-weighted imaging (DWI) and diffusion-tensor magnetic resonance imaging (DTMRI) and suggests the means of obtaining quantitative functional information on capillary vessel density from measurements of dispersion coefficients. It is shown that a failure to account for flow-mediated dispersion in vascular tissues may lead to misinterpretations of imaging data and significant overestimates of directional bias in molecular diffusivity in biological tissues. Measurement of the ratio of axial to transverse diffusivity may be combined with an independent measurement of perfusion to provide an estimate of capillary vessel density in the tissue.

Roles of the creatine kinase system and myoglobin in maintaining energetic state in the working heart

BACKGROUND

The heart is capable of maintaining contractile function despite a transient decrease in blood flow and increase in cardiac ATP demand during systole. This study analyzes a previously developed model of cardiac energetics and oxygen transport to understand the roles of the creatine kinase system and myoglobin in maintaining the ATP hydrolysis potential during beat-to-beat transient changes in blood flow and ATP hydrolysis rate.

RESULTS

The theoretical investigation demonstrates that elimination of myoglobin only slightly increases the predicted range of oscillation of cardiac oxygenation level during beat-to-beat transients in blood flow and ATP utilization. In silico elimination of myoglobin has almost no impact on the cytoplasmic ATP hydrolysis potential (DeltaGATPase). In contrast, disabling the creatine kinase system results in considerable oscillations of cytoplasmic ADP and ATP levels and seriously deteriorates the stability of DeltaGATPase in the beating heart.

CONCLUSION

The CK system stabilizes DeltaGATPase by both buffering ATP and ADP concentrations and enhancing the feedback signal of inorganic phosphate in regulating mitochondrial oxidative phosphorylation.

Mitochondrial oxygen tension within the heart

By using a newly developed optical technique which enables non-invasive measurement of mitochondrial oxygenation (mitoPO(2)) in the intact heart, we addressed three long-standing oxygenation questions in cardiac physiology: 1) what is mitoPO(2) within the in vivo heart?, 2) is mitoPO(2) heterogeneously distributed?, and 3) how does mitoPO(2) of the isolated Langendorff-perfused heart compare with that in the in vivo working heart? Following calibration and validation studies of the optical technique in isolated cardiomyocytes, mitochondria and intact hearts, we show that in the in vivo condition mean mitoPO(2) was 35+/-5 mm Hg. The mitoPO(2) was highly heterogeneous, with the largest fraction (26%) of mitochondria having a mitoPO(2) between 10 and 20 mm Hg, and 10% between 0 and 10 mm Hg. Hypoxic ventilation (10% oxygen) increased the fraction of mitochondria in the 0-10 mm Hg range to 45%, whereas hyperoxic ventilation (100% oxygen) had no major effect on mitoPO(2). For Langendorff-perfused rat hearts, mean mitoPO(2) was 29+/-5 mm Hg with the largest fraction of mitochondria (30%) having a mitoPO(2) between 0 and 10 mm Hg. Only in the maximally vasodilated condition, did the isolated heart compare with the in vivo heart (11% of mitochondria between 0 and 10 mm Hg). These data indicate 1) that the mean oxygen tension at the level of the mitochondria within the heart in vivo is higher than generally considered, 2) that mitoPO(2) is considerably heterogeneous, and 3) that mitoPO(2) of the classic buffer-perfused Langendorff heart is shifted to lower values as compared to the in vivo heart.

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.

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.

A mathematical model of oxygen transport in intact muscle with imposed surface oscillations

A one-dimensional (1D) reaction-diffusion equation is presented to model oxygen delivery by the microcirculation and oxygen diffusion and consumption in intact muscle. This model is motivated by in vivo experiments in which oscillatory boundary conditions are used to study the mechanisms of local blood flow regulation in response to changes in the tissue oxygen environment. An exact periodic solution is presented for the 1D 'in vivo' model and shown to agree with experimental data for the case where the blood flow regulation system is not activated. Approximate low- and high-frequency solutions are presented, and the latter is shown to agree with the pure diffusion solution in the absence of sources or sinks. For the low frequencies considered experimentally, the 1D in vivo model shows that as depth increases: (i) the mean of tissue O(2) oscillations changes exponentially, (ii) the amplitude of oscillations decreases very rapidly, and (iii) the phase of oscillations remains nearly the same as that of the imposed surface oscillations. The 1D in vivo model also shows that the dependence on depth of the mean, amplitude, and phase of tissue O(2) oscillations is nearly the same for all stimulation periods >30s, implying that experimentally varying the forcing period in this range will not change the spatial distribution of the O(2) stimulation.

Microvascular transport model predicts oxygenation changes in the infarcted heart after treatment

Chronic heart failure is most commonly due to ischemic cardiomyopathy after a previous myocardial infarction (MI). Rebuilding lost myocardium to prevent heart failure mandates a neovasculature able to nourish new cardiomyocytes. Previously we have used a series of novel techniques to directly measure the ability of the scar neovasculature to deliver and exchange oxygen at 1–4 wk after MI in rats following left coronary artery ligation. In this study, we have developed a morphologically realistic mathematical model of oxygen transport in cardiac tissue to help in deciding what angiogenic strategies should be used to rebuild the vasculature. The model utilizes microvascular morphology of cardiac tissue based on available morphometric images and is used to simulate experimentally measured oxygen levels after MI. Model simulations of relative oxygenation match experimental measurements closely and can be used to simulate distributions of oxygen concentration in normal and infarcted rat hearts. Our findings indicate that both vascular density and vascular spatial distribution play important roles in cardiac tissue oxygenation after MI. Furthermore, the model can simulate relative changes in tissue oxygen levels in infarcted tissue treated with proangiogenic compounds such as losartan. From the minimum oxygen concentration myocytes need to maintain their normal function, we estimate that 2 wk after MI 29% of the myocardium is severely hypoxic and that the vascular density of the infarcted tissue should reach 75% of normal tissue to ensure that no areas of the myocardium are critically hypoxic.

Monitoring oxygen transport and tissue oxygenation

PURPOSE OF REVIEW

To review recent publications in the field of oxygen delivery and tissue oxygenation. With few exceptions, we restricted our selection to clinical studies published in the English literature.

RECENT FINDINGS

No major breakthroughs have occurred in the past decade in the diagnosis or treatment of tissue hypoxia. There is renewed interest in goal-directed resuscitation when applied early in the course of treatment. Monitoring metabolic markers of tissue hypoxia continues to hold great clinical interest, in particular, tissue PCO2, near infrared spectroscopy, base deficit and blood lactate concentration. Technical issues, however, seem to restrict the widespread use of many of these techniques.

SUMMARY

There is an urgent need to develop methods to accurately and rapidly identify patients with tissue hypoxia. Perhaps the combination of gastric tonometry, near-infrared spectroscopy, urinary PO2 and continuous measures of mixed (or central) venous O2 saturation may provide the answer. An even more formidable task is that of developing effective therapy to correct tissue hypoxia while avoiding harm to the patient.

A computational model of oxygen delivery by hemoglobin-based oxygen carriers in three-dimensional microvascular networks

A detailed computational model is developed to simulate oxygen transport from a three-dimensional (3D) microvascular network to the surrounding tissue in the presence of hemoglobin-based oxygen carriers. The model accounts for nonlinear O(2) consumption, myoglobin-facilitated diffusion and nonlinear oxyhemoglobin dissociation in the RBCs and plasma. It also includes a detailed description of intravascular resistance to O(2) transport and is capable of incorporating realistic 3D microvascular network geometries. Simulations in this study were performed using a computer-generated microvascular architecture that mimics morphometric parameters for the hamster cheek pouch retractor muscle. Theoretical results are presented next to corresponding experimental data. Phosphorescence quenching microscopy provided PO(2) measurements at the arteriolar and venular ends of capillaries in the hamster retractor muscle before and after isovolemic hemodilution with three different hemodilutents: a non-oxygen-carrying plasma expander and two hemoglobin solutions with different oxygen affinities. Sample results in a microvascular network show an enhancement of diffusive shunting between arterioles, venules and capillaries and a decrease in hemoglobin's effectiveness for tissue oxygenation when its affinity for O(2) is decreased. Model simulations suggest that microvascular network anatomy can affect the optimal hemoglobin affinity for reducing tissue hypoxia. O(2) transport simulations in realistic representations of microvascular networks should provide a theoretical framework for choosing optimal parameter values in the development of hemoglobin-based blood substitutes.

OPTICAL SPECTROSCOPY DEMONSTRATES ELEVATED INTRACELLULAR OXYGENATION IN AN ENDOTOXIC MODEL OF SEPSIS IN THE PERFUSED HEART

Recent clinical studies of patients with sepsis have shown that the delivery of adequate oxygen alone does not necessarily result in improved organ function or survival. This study was undertaken to determine if optical spectroscopy could detect higher intracellular oxygenations in isolated, perfused guinea pig hearts that have been treated with endotoxin (lipopolysaccharide [LPS]) than in controls. Four hours after intraperitoneal injection with LPS, adult guinea pigs were anesthetized, and hearts were excised and perfused in the Langendorff manner. Six control and eight LPS-exposed guinea pigs were studied. Myoglobin oxygen saturation was determined from analysis of optical reflectance spectra acquired from the left ventricular free wall. Myoglobin saturation was significantly higher at baseline with LPS than in controls (96.0% +/- 0.8% vs. 89.4% +/- 1.7%, P < 0.001). At the end of 30 s of ischemia, myoglobin saturation decreased to 15% +/- 1% in controls, but to only 60% +/- 7% in the LPS group. Myocardial performance was determined by measured left ventricular developed pressure, which was significantly depressed in the LPS-exposed hearts relative to controls (30 +/- 4 mmHg vs. 67 +/- 9 mmHg, P < 0.001). Myocardial oxygen consumption, calculated from measurements of arterial and venous PO2 and coronary flow, was lower in LPS hearts relative to controls (0.199 +/- 0.021 mL oxygen x min(-1) x g(-1) vs. 0.157 +/- 0.006 mL oxygen x min(-1) x g(-1)). In this model of sepsis in the perfused guinea pig heart, intracellular oxygenation was higher and oxygen consumption was lower than in controls. Cellular dysfunction seen in sepsis may be caused by compromised oxygen use rather than insufficient oxygen delivery. Optical spectroscopy has the potential to noninvasively monitor patients and their responses to therapy.

Linking pulmonary oxygen uptake, muscle oxygen utilization and cellular metabolism during exercise

The energy demand imposed by physical exercise on the components of the oxygen transport and utilization system requires a close link between cellular and external respiration in order to maintain ATP homeostasis. Invasive and non-invasive experimental approaches have been used to elucidate mechanisms regulating the balance between oxygen supply and consumption during exercise. Such approaches suggest that the mechanism controlling the various subsystems coupling internal to external respiration are part of a highly redundant and hierarchical multi-scale system. In this work, we present a "systems biology" framework that integrates experimental and theoretical approaches able to provide simultaneously reliable information on the oxygen transport and utilization processes occurring at the various steps in the pathway of oxygen from air to mitochondria, particularly at the onset of exercise. This multi-disciplinary framework provides insights into the relationship between cellular oxygen consumption derived from measurements of muscle oxygenation during exercise and pulmonary oxygen uptake by indirect calorimetry. With a validated model, muscle oxygen dynamic responses is simulated and quantitatively related to cellular metabolism under a variety of conditions.

Contractile effects of adenosine, coronary flow and perfusion pressure in murine myocardium

There is mixed evidence adenosine receptors (ARs) may enhance myocardial contractility, although this remains contentious. We assessed inotropic actions of adenosine (50 muM) and selective AR activation with 100 nM N (6)-cyclohexyladenosine (CHA; A(1)AR agonist), 25 nM 2-[p-(2-carboxyethyl) phenethylamino]-5'-N-ethylcarboxamidoadenosine (CGS-21680; A(2A)AR agonist) and 100 nM 2-chloro-N (6)-(3-iodobenzyl)-adenosine-5'-N-methyluronamide (Cl-IB-MECA; A(3)AR agonist) in mouse hearts perfused at constant pressure, constant flow, or conditions of stable flow and pressure (following maximal nitroprusside-mediated dilatation at constant flow). Adenosine and CGS-21680 significantly (although modestly) increased force in constant-pressure perfused hearts (</=10 mmHg elevations in systolic pressure), effects paralleled by coronary vasodilatation (</=10 ml min(-1) g(-1) elevations in flow). Neither CHA nor Cl-IB-MECA altered force or flow. With constant-flow perfusion, adenosine and CGS-21680 reduced systolic pressure in parallel with perfusion pressure. When changes in coronary flow and pressure were prevented, CGS-21680 failed to alter contractility. However, adenosine still enhanced systolic pressure up to 10 mmHg. Relations between flow, perfusion pressure and ventricular force evidence substantial Gregg effects in murine myocardium: systolic force increases transiently by approximately 1 mmHg ml(-1) min(-1) g(-1) rise in flow during the first minutes of hyperaemia and in a sustained manner (by approximately 1 mmHg mmHg(-1)) during altered perfusion pressure. These effects contribute to inotropism with AR agonism when flow/pressure is uncontrolled. In summary, we find no evidence of direct A(1) or A(3)AR-mediated inotropic responses in intact myocardium. Inotropic actions of A(2A)AR agonism appear entirely Gregg-related. Nonetheless, the endogenous agonist adenosine exerts a modest inotropic action independently of flow and perfusion pressure. The basis of this response remains to be identified.

Modeling of oxygen transport and cellular energetics explains observations on in vivo cardiac energy metabolism

Observations on the relationship between cardiac work rate and the levels of energy metabolites adenosine triphosphate (ATP), adenosine diphosphate (ADP), and phosphocreatine (CrP) have not been satisfactorily explained by theoretical models of cardiac energy metabolism. Specifically, the in vivo stability of ATP, ADP, and CrP levels in response to changes in work and respiratory rate has eluded explanation. Here a previously developed model of mitochondrial oxidative phosphorylation, which was developed based on data obtained from isolated cardiac mitochondria, is integrated with a spatially distributed model of oxygen transport in the myocardium to analyze data obtained from several laboratories over the past two decades. The model includes the components of the respiratory chain, the F₀F₁-ATPase, adenine nucleotide translocase, and the mitochondrial phosphate transporter at the mitochondrial level; adenylate kinase, creatine kinase, and ATP consumption in the cytoplasm; and oxygen transport between capillaries, interstitial fluid, and cardiomyocytes. The integrated model is able to reproduce experimental observations on ATP, ADP, CrP, and inorganic phosphate levels in canine hearts over a range of workload and during coronary hypoperfusion and predicts that cytoplasmic inorganic phosphate level is a key regulator of the rate of mitochondrial respiration at workloads for which the rate of cardiac oxygen consumption is less than or equal to approximately 12 μmol per minute per gram of tissue. At work rates corresponding to oxygen consumption higher than 12 μmol min⁻¹ g⁻¹, model predictions deviate from the experimental data, indicating that at high work rates, additional regulatory mechanisms that are not currently incorporated into the model may be important. Nevertheless, the integrated model explains metabolite levels observed at low to moderate workloads and the changes in metabolite levels and tissue oxygenation observed during graded hypoperfusion. These findings suggest that the observed stability of energy metabolites emerges as a property of a properly constructed model of cardiac substrate transport and mitochondrial metabolism. In addition, the validated model provides quantitative predictions of changes in phosphate metabolites during cardiac ischemia.

To function properly over a range of work rates, the heart must maintain its metabolic energy level within a range that is narrow relative to changes in the rate of energy utilization. Decades of observations have revealed that in cardiac muscle cells, the supply of adenosine triphosphate (ATP)—the primary currency of intracellular energy transfer—is controlled to maintain intracellular concentrations of ATP and related compounds within narrow ranges. Yet the development of a mechanistic understanding of this tight control has lagged behind experimental observation. This paper introduces a computational model that links ATP synthesis in a subcellular body called the mitochondrion with ATP utilization in the cytoplasm, and reveals that the primary control mechanism operating in the system is feedback of substrate concentrations for ATP synthesis. In other words, changes in the concentrations of the products generated by the utilization of ATP in the cell (adenosine diphosphate and inorganic phosphate) effect changes in the rate at which mitochondria utilize those products to resynthesize ATP.

Three-dimensional mitochondrial arrangement in ventricular myocytes: from chaos to order

We have developed a novel method to quantitatively analyze mitochondrial positioning in three dimensions. Using this method, we compared the relative positioning of mitochondria in adult rat and rainbow trout (Oncorhynchus mykiss) ventricular myocytes. Energetic data suggest that trout, in contrast to the rat, have two subpopulations of mitochondria in their cardiomyocytes. Therefore, we speculated whether trout cardiomyocytes exhibit two types of mitochondrial patterns. Stacks of confocal images of mitochondria were acquired in live cardiomyocytes. The images were processed and mitochondrial centers were detected automatically. The mitochondrial arrangement was analyzed by calculating the three-dimensional probability density and distribution functions describing the distances between neighboring mitochondrial centers. In the rat (8 cells with a total of 7,546 mitochondrial centers), intermyofibrillar mitochondria are highly ordered and arranged in parallel strands. These strands are separated by approximately 1.8 mum and can be found in any transversal direction relative to each other. Neighboring strands exhibit the same mitochondrial periodicity. In contrast to the rat, trout ventricular myocytes (22 cells; 5,528 mitochondrial centers) exhibit a relatively chaotic mitochondrial pattern. Neighboring mitochondria can be found in any direction relative to each other. Thus, two potential subpopulations of mitochondria in trout are not distinguishable by their pattern. The developed method required minor interaction in the filtering of the mitochondrial centers. It is therefore a practical approach to describe intracellular organization and may also be used for analysis of time-dependent organizational changes. The obtained quantitative description of mitochondrial organization is a requisite for accurate mathematical analysis of mitochondrial systems biology.

A computational model of oxygen transport in skeletal muscle for sprouting and splitting modes of angiogenesis

Oxygen transport from capillary networks in muscle at a high oxygen consumption rate was simulated using a computational model to assess the relative efficacies of sprouting and splitting modes of angiogenesis. Efficacy was characterized by the volumetric fraction of hypoxic tissue and overall heterogeneity of oxygen distribution at steady state. Oxygen transport was simulated for a three-dimensional vascular network using parameters for rat extensor digitorum longus (EDL) muscle when oxygen consumption by tissue reached 6, 12, and 18 times basal consumption. First, a control network was generated by using straight non-anastomosed capillaries to establish baseline capillarity. Two networks were then constructed simulating either abluminal lateral sprouting or intraluminal splitting angiogenesis such that capillary surface area was equal in both networks. The sprouting network was constructed by placing anastomosed capillaries between straight capillaries of the control network with a higher probability of placement near hypoxic tissue. The splitting network was constructed by splitting capillaries from the control network into two branches at randomly chosen branching points. Under conditions of moderate oxygen consumption (6 times basal), only minor differences in oxygen delivery resulted between the sprouting and splitting networks. At higher consumption levels (12 and 18 times basal), the splitting network had the lowest volume of hypoxic tissue of the three networks. However, when total blood flow in all three networks was made equal, the sprouting network had the lowest volume of hypoxic tissue. This study also shows that under the steady-state conditions the effect of myoglobin (Mb) on oxygen transport was small.

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.

A biophysical model of the mitochondrial respiratory system and oxidative phosphorylation

A computational model for the mitochondrial respiratory chain that appropriately balances mass, charge, and free energy transduction is introduced and analyzed based on a previously published set of data measured on isolated cardiac mitochondria. The basic components included in the model are the reactions at complexes I, III, and IV of the electron transport system, ATP synthesis at F₁F₀ ATPase, substrate transporters including adenine nucleotide translocase and the phosphate–hydrogen co-transporter, and cation fluxes across the inner membrane including fluxes through the K⁺/H⁺ antiporter and passive H⁺ and K⁺ permeation. Estimation of 16 adjustable parameter values is based on fitting model simulations to nine independent data curves. The identified model is further validated by comparison to additional datasets measured from mitochondria isolated from rat heart and liver and observed at low oxygen concentration. To obtain reasonable fits to the available data, it is necessary to incorporate inorganic-phosphate-dependent activation of the dehydrogenase activity and the electron transport system. Specifically, it is shown that a model incorporating phosphate-dependent activation of complex III is able to reasonably reproduce the observed data. The resulting validated and verified model provides a foundation for building larger and more complex systems models and investigating complex physiological and pathophysiological interactions in cardiac energetics.

Cells are able to perform tasks that consume energy (such as producing mechanical force in muscle contraction) by using chemical energy delivered in the form of a chemical compound called adenosine triphosphate, or ATP. Two Nobel Prizes were awarded (in 1978 to Peter D. Mitchell and in 1997 to Paul D. Boyer and John E. Walker) for the determination of how ATP is synthesized from the components adenosine diphosphate (ADP) and inorganic phosphate in a subcellular body called the mitochondrion. The operating theory, called the chemiosmotic theory, describes how a driving force called the proton motive force, which arises from the sum of contributions from the electrical potential and the hydrogen ion concentration difference across the mitochondrial inner membrane, is developed by reactions catalyzed by certain enzymes and consumed in generating ATP. Yet, to date, no computer model has successfully described the development and consumption of both the chemical and electrical components of the proton motive force in a thermodynamically balanced simulation. Beard introduces such a model, which is extensively validated based on previously published sets of data obtained on isolated mitochondria. The model is used to test hypotheses about how intracellular respiration is regulated; this model could serve as a foundation for investigating the control of mitochondrial function and for developing larger integrated simulations of cellular metabolism.

Reduced oxygen supply explains the negative force-frequency relation and the positive inotropic effect of adenosine in buffer-perfused hearts

In isolated rat hearts perfused with HEPES and red blood cell-enriched buffers, we examined changes in left ventricular pressure induced by increases in heart rate or infusion of adenosine to investigate whether the negative force-frequency relation and the positive inotropic effect of adenosine are related to an inadequate oxygen supply provided by crystalloid perfusates. Hearts perfused with HEPES buffer at a constant flow demonstrated a negative force-frequency relation, whereas hearts perfused with red blood cell-enriched buffer exhibited a positive force-frequency relation. In contrast, HEPES buffer-perfused hearts showed a concentration-dependent increase in left ventricular systolic pressure [EC50 = 7.0 ± 1.2 nM, maximal effect (Emax) = 104 ± 2 and 84 ± 2 mmHg at 0.1 μM and baseline, respectively] in response to adenosine, whereas hearts perfused with red blood cell-enriched buffer showed no change in left ventricular pressure. The positive inotropic effect of adenosine correlated with the simultaneous reduction in heart rate ( r = 0.67, P < 0.01; EC50 = 3.8 ± 1.4 nM, baseline 228 ± 21 beats/min to a minimum of 183 ± 22 beats/min at 0.1 μM) and was abolished in isolated hearts paced to suppress the adenosine-induced bradycardia. In conclusion, these results indicate that the negative force-frequency relation and the positive inotropic effect of adenosine in the isolated rat heart are related to myocardial hypoxia, rather than functional peculiarities of the rat heart.

Myocardial oxygenation and adenosine release in isolated guinea pig hearts during changes in contractility

Previous work from this laboratory using near-infrared optical spectroscopy of myoglobin has shown that ∼20% of the myocardium is hypoxic in buffer-perfused hearts that are perfused with fully oxygenated buffer at 37°C. The present study was undertaken to determine cardiac myoglobin saturation in buffer-perfused hearts when cardiac contractility was increased with epinephrine and decreased during cardiac arrest with KCl. Infusion of epinephrine to achieve a doubling of contractility, as measured by left ventricular maximum pressure change over time (dP/d t), resulted in a decrease in mean myoglobin saturation from 79% at baseline to 65% and a decrease in coronary venous oxygen tension from 155 mmHg at baseline to 85 mmHg. Cardiac arrest with KCl increased mean myoglobin saturation to 100% and coronary venous oxygen tension to 390 mmHg. A previously developed computer model of oxygen transport in the myocardium was used to calculate the probability distribution of intracellular oxygen tension and the hypoxic fraction of the myocardium with an oxygen tension below 0.5 mmHg. The hypoxic fraction of the myocardium was ∼15% at baseline, increased to ∼30% during epinephrine infusion, and fell to ∼0% during cardiac arrest. The coronary venous adenosine concentration changed in parallel with the hypoxic fraction of the myocardium during epinephrine and KCl. It is concluded that catecholamine stimulation of buffer-perfused hearts increases hypoxia in the myocardium and that the increase in venous adenosine concentration is a reflection of the larger hypoxic fraction of myocardium that is releasing adenosine.

Thermodynamic-based computational profiling of cellular regulatory control in hepatocyte metabolism

Thermodynamic-based constraints on biochemical fluxes and concentrations are applied in concert with mass balance of fluxes in glycogenesis and glycogenolysis in a model of hepatic cell metabolism. Constraint-based modeling methods that facilitate predictions of reactant concentrations, reaction potentials, and enzyme activities are introduced to identify putative regulatory and control sites in biological networks by computing the minimal control scheme necessary to switch between metabolic modes. Computational predictions of control sites in glycogenic and glycogenolytic operational modes in the hepatocyte network compare favorably with known regulatory mechanisms. The developed hepatic metabolic model is used to computationally analyze the impairment of glucose production in von Gierke's and Hers' diseases, two metabolic diseases impacting glycogen metabolism. The computational methodology introduced here can be generalized to identify downstream targets of agonists, to systematically probe possible drug targets, and to predict the effects of specific inhibitors (or activators) on integrated network function.

Intracoronary administration of FGF-2: a computational model of myocardial deposition and retention

This study uses a computational model to characterize the myocardial deposition and retention of basic fibroblast growth factor (FGF-2) at the cellular level after intracoronary (IC) administration of exogenous FGF-2. The model is applied to the in situ conditions present within the myocardium of a dog for which the plasma pharmacokinetics resulting from IC injection of FGF-2 were recorded. Our estimates show that the processes involved in FGF-2 signaling are not diffusion limited; rather, the response time is determined by the reaction time of FGF-2 binding to cell surface receptors. Additionally, the processes of receptor secretion and internalization are found to play crucial roles in the FGF-2 dynamics; future experiments are required to quantify these processes. The model predictions obtained in this study suggest that IC administration of FGF-2 via either a single bolus or repetitive injections causes a transient increase (time scale of hours) in myocardial FGF-2 concentration if the endogenous level of free interstitial FGF-2 is low enough to allow permeation of FGF-2 molecules from the microvascular to the interstitial spaces. The model shows that the majority (64%) of the extracellular FGF-2 ligands are located within the interstitium, and similar fractions are found in the basement membrane and extracellular matrix. Among the FGF-2 molecules found within the interstitium, 2% are free and 98% are bound to interstitial heparan sulfate proteoglycans. These results support the theory of extracellular control of the bioavailability of FGF-2 via dynamic storage of FGF-2 within the basement membrane and extracellular matrix.

Pattern differences between distributions of microregional myocardial flows in crystalloid- and blood-perfused rat hearts

Regional myocardial flow distributions in Langendorff rat hearts under Tyrode and blood perfusion were assessed by tracer digital radiography (100-μm resolution). Flow distributions during baseline and maximal hyperemia following a 60-s flow cessation were evaluated by the coefficient of variation of regional flows (CV; related to global flow heterogeneity) and the correlation between adjacent regional flows (CA; inversely related to local flow randomness). These values were obtained for the original images (642 pixels) and for coarse-grained images (322, 162, and 82 blocks of nearby pixels). At a given point in time during baseline, both CV and CA were higher in blood ( n = 7) than in Tyrode perfusion ( n = 7) over all pixel aggregates ( P < 0.05, two-way ANOVA). During the maximal hyperemia, CV and CA were still significantly higher in blood ( n = 7) than in Tyrode perfusion ( n = 7); however, these values decreased substantially in blood perfusion and the CV and CA differences became smaller than those at baseline accordingly. During basal blood perfusion, the 60-s average flow distribution ( n = 7) showed a smaller CV and CA than those at a given point in time ( P < 0.05, two-way ANOVA). Coronary flow reserve was significantly higher in blood than in Tyrode perfusion. In conclusion, the flow heterogeneity and the local flow similarity are both higher in blood than in Tyrode perfusion, probably due to the different degree of coronary tone preservation and the presence or absence of blood corpuscles. Under blood perfusion, temporal flow fluctuations over 60-s order are largely involved in shaping microregional flow distributions.

Comparison of buffer and red blood cell perfusion of guinea pig heart oxygenation

Myocardial mean myoglobin oxygen saturation was determined spectroscopically from isolated guinea pig hearts perfused with red blood cells during increasing hypoxia. These experiments were undertaken to compare intracellular myoglobin oxygen saturation in isolated hearts perfused with a modest concentration of red blood cells (5% hematocrit) with intracellular myoglobin saturation previously reported from traditional buffer-perfused hearts. Studies were performed at 37 degrees C with hearts paced at 240 beats/min and a constant perfusion pressure of 80 cmH2O. It was found that during perfusion with a hematocrit of 5%, baseline mean myoglobin saturation was 93% compared with 72% during buffer perfusion. Mean myoglobin saturation, ventricular function, and oxygen consumption remained fairly constant for arterial perfusate oxygen tensions above 100 mmHg and then decreased precipitously below 100 mmHg. In contrast, mean myoglobin saturation, ventricular function, and oxygen consumption began to decrease even at high oxygen tension with buffer perfusion. The present results demonstrate that perfusion with 5% red blood cells in the perfusate increases the baseline mean myoglobin saturation and better preserves cardiac function at low oxygen tension relative to buffer perfusion. These results suggest that caution should be used in extrapolating intracellular oxygen dynamics from buffer-perfused to blood-perfused hearts.