Intra-cardiac transfer of fatty acids from capillary to cardiomyocyte.

Blood-borne fatty acids (Fa) are important substrates for energy conversion in the mammalian heart. After release from plasma albumin, Fa traverse the endothelium and the interstitial compartment to cross the sarcolemma prior to oxidation in the cardiomyocytal mitochondria. The aims of the present study were to elucidate the site with lowest Fa permeability (i.e., highest Fa resistance) in the overall Fa trajectory from capillary to cardiomyocyte and the relative contribution of unbound Fa (detach pathway, characterized by the dissociation time constant τAlbFa) and albumin-bound Fa (contact pathway, characterized by the membrane reaction rate parameter dAlb) in delivering Fa to the cellular membranes. In this study, an extensive set of 34 multiple indicator dilution experiments with radiolabeled albumin and palmitate on isolated rabbit hearts was analysed by means of a previously developed mathematical model of Fa transfer dynamics. In these experiments, the ratio of the concentration of palmitate to albumin was set at 0.91. The analysis shows that total cardiac Fa permeability, Ptot, is indeed related to the albumin concentration in the extracellular compartment as predicted by the mathematical model. The analysis also reveals that the lowest permeability may reside in the boundary zones containing albumin in the microvascular and interstitial compartment. However, the permeability of the endothelial cytoplasm, Pec, may influence overall Fa permeability, Ptot, as well. The model analysis predicts that the most likely value of τAlbFa ranges from about 200 to 400 ms. In case τAlbFa is fast, i.e., about 200 ms, the extracellular contact pathway appears to be of minor importance in delivering Fa to the cell membrane. If Fa dissociation from albumin is slower, e.g. τAlbFa equals 400 ms, the contribution of the contact pathway may vary from minimal (dAlb≤5 nm) to substantial (dAlb about 100 nm). In the latter case, the permeability of the endothelial cytoplasm varies from infinite (no hindrance) to low (substantial hindrance) to keep the overall Fa flux at a fixed level. Definitive estimation of the impact of endothelial permeability on Ptot and the precise contribution of the contact pathway to overall transfer of Fa in boundary zones containing albumin requires adequate physicochemical experimentation to delineate the true value of, among others, τAlbFa, under physiologically relevant circumstances. Our analysis also implies that concentration differences of unbound Fa are the driving force of intra-cardiac Fa transfer; an active, energy requiring transport mechanism is not necessarily involved. Membrane-associated proteins may facilitate Fa transfer in the boundary zones containing albumin by modulating the membrane reaction rate parameter, dAlb, and, hence, the contribution of the contact pathway to intra-cardiac Fa transfer.

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

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

Understanding the physiology of the ageing individual: computational modelling of changes in metabolism and endurance.

Ageing and lifespan are strongly affected by metabolism. The maximal possible uptake of oxygen is not only a good predictor of performance in endurance sports, but also of life expectancy. Figuratively speaking, healthy ageing is a competitive sport. Although the root cause of ageing is damage to macromolecules, it is the balance with repair processes that is decisive. Reduced or intermittent nutrition, hormones and intracellular signalling pathways that regulate metabolism have strong effects on ageing. Homeostatic regulatory processes tend to keep the environment of the cells within relatively narrow bounds. On the other hand, the body is constantly adapting to physical activity and food consumption. Spontaneous fluctuations in heart rate and other processes indicate youth and health. A (homeo)dynamic aspect of homeostasis deteriorates with age. We are now in a position to develop computational models of human metabolism and the dynamics of heart rhythm and oxygen transport that will advance our understanding of ageing. Computational modelling of the connections between dietary restriction, metabolism and protein turnover may increase insight into homeostasis of the proteins in our body. In this way, the computational reconstruction of human physiological processes, the Physiome, can help prevent frailty and age-related disease.

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.

Fractal regional myocardial blood flows pattern according to metabolism, not vascular anatomy.

Regional myocardial blood flows are markedly heterogeneous. Fractal analysis shows strong near-neighbor correlation. In experiments to distinguish control by vascular anatomy vs. local vasomotion, coronary flows were increased in open-chest dogs by stimulating myocardial metabolism (catecholamines + atropine) with and without adenosine. During control states mean left ventricular (LV) myocardial blood flows (microspheres) were 0.5-1 ml·g(-1)·min(-1) and increased to 2-3 ml·g(-1)·min(-1) with catecholamine infusion and to ∼4 ml·g(-1)·min(-1) with adenosine (Ado). Flow heterogeneity was similar in all states: relative dispersion (RD = SD/mean) was ∼25%, using LV pieces 0.1-0.2% of total. During catecholamine infusion local flows increased in proportion to the mean flows in 45% of the LV, "tracking" closely (increased proportionately to mean flow), while ∼40% trended toward the mean. Near-neighbor regional flows remained strongly spatially correlated, with fractal dimension D near 1.2 (Hurst coefficient 0.8). The spatial patterns remain similar at varied levels of metabolic stimulation inferring metabolic dominance. In contrast, adenosine vasodilation increased flows eightfold times control while destroying correlation with the control state. The Ado-induced spatial patterns differed from control but were self-consistent, inferring that with full vasodilation the relaxed arterial anatomy dominates the distribution. We conclude that vascular anatomy governs flow distributions during adenosine vasodilation but that metabolic vasoregulation dominates in normal physiological states.

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 O2­CO2 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 38:1683­1701, 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.

Modeling Fatty Acid Transfer from Artery to Cardiomyocyte.

Despite the importance of oxidation of blood-borne long-chain fatty acids (Fa) in the cardiomyocytes for contractile energy of the heart, the mechanisms underlying the transfer of Fa from the coronary plasma to the cardiomyocyte is still incompletely understood. To obtain detailed insight into this transfer process, we designed a novel model of Fa transfer dynamics from coronary plasma through the endothelial cells and interstitium to the cardiomyocyte, applying standard physicochemical principles on diffusion and on the chemical equilibrium of Fa binding to carrier proteins Cp, like albumin in plasma and interstitium and Fatty Acid-Binding Proteins within endothelium and cardiomyocytes. Applying these principles, the present model strongly suggests that in the heart, binding and release of Fa to and from Cp in the aqueous border zones on both sides of the cell membranes form the major hindrance to Fa transfer. Although often considered, the membrane itself appears not to be a significant hindrance to diffusion of Fa. Proteins, residing in the cellular membrane, may facilitate transfer of Fa between Cp and membrane. The model is suited to simulate multiple tracer dilution experiments performed on isolated rabbit hearts administrating albumin and Fa as tracer substances into the coronary arterial perfusion line. Using parameter values on myocardial ultrastructure and physicochemical properties of Fa and Cp as reported in literature, simulated washout curves appear to be similar to the experimentally determined ones. We conclude therefore that the model is realistic and, hence, can be considered as a useful tool to better understand Fa transfer by evaluation of experimentally determined tracer washout curves.

Semi-automated Modular Program Constructor for physiological modeling: Building cell and organ models.

The Modular Program Constructor (MPC) is an open-source Java based utility, built upon JSim's Mathematical Modeling Language (MML) ( http://www.physiome.org/jsim/) that uses directives embedded in model code to construct larger, more complicated models quickly and with less error than manually combining models. A major obstacle in writing complex programs for modeling physiological processes is the large amount of time it takes to code the myriad processes taking place simultaneously in cells, tissues, and organs. MPC replaces this task by code-generating algorithms that take the code from several different modules and produce model code for a new JSim model. This is particularly useful during multi-scale model development where many variants are to be configured and tested against data. MPC is implemented in Java and requires JSim to use its output. MPC source code and documentation are available at http://www.physiome.org/software/MPC/.

SBML and CellML translation in antimony and JSim.

MOTIVATION: The creation and exchange of biologically relevant models is of great interest to many researchers. When multiple standards are in use, models are more readily used and re-used if there exist robust translators between the various accepted formats. SUMMARY: Antimony 2.4 and JSim 2.10 provide translation capabilities from their own formats to SBML and CellML. All provided unique challenges, stemming from differences in each format's inherent design, in addition to differences in functionality. AVAILABILITY AND IMPLEMENTATION: Both programs are available under BSD licenses; Antimony from http://antimony.sourceforge.net/and JSim from http://physiome.org/jsim/. CONTACT: lpsmith@u.washington.edu.

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.

Reexamining Michaelis-Menten enzyme kinetics for xanthine oxidase.

Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions are violated. Here, we analyzed data of xanthine oxidase in vitro from Escribano et al. (Biochem J 254: 829, 1988) on two conversions in series, hypoxanthine to xanthine to uric acid. Analyses were done using four models: standard irreversible M-M reactions (model 1), Escribano et al.'s M-M forward reaction expressions with product inhibition (model 2), fully reversible M-M equations (model 3), and standard differential equations allowing forward and backward reactions with mass balance accounting for binding (model 4). The results showed that the need for invoking product inhibition vanishes with more complete analyses. The reactions were not quite irreversible, so the backward reaction had a small effect. Even though the enzyme concentration was only 1-2% of the initial substrate concentrations, accounting for the fraction of solutes bound to the enzyme did influence the parameter estimates, but in this case, the M-M model overestimated Michaelis constant values by only about one-third. This article also presents the research and models in a reproducible and publicly available form.

Validation of an axially distributed model for quantification of myocardial blood flow using ¹³N-ammonia PET.

BACKGROUND: Estimation of myocardial blood flow (MBF) with cardiac PET is often performed with conventional compartmental models. In this study, we developed and evaluated a physiologically and anatomically realistic axially distributed model. Unlike compartmental models, this axially distributed approach models both the temporal and the spatial gradients in uptake and retention along the capillary. METHODS: We validated PET-derived flow estimates with microsphere studies in 19 (9 rest, 10 stress) studies in five dogs. The radiotracer, (13)N-ammonia, was injected intravenously while microspheres were administered into the left atrium. A regional reduction in hyperemic flow was forced by an external occluder in five of the stress studies. The flow estimates from the axially distributed model were compared with estimates from conventional compartmental models. RESULTS: The mean difference between microspheres and the axially distributed blood flow estimates in each of the 17 segments was 0.03 mL/g/minute (95% CI [-0.05, 0.11]). The blood flow estimates were highly correlated with each regional microsphere value for the axially distributed model (y = 0.98x + 0.06 mL/g/minute; r = 0.74; P < .001), for the two-compartment (y = 0.64x + 0.34; r = 0.74; P < .001), and for three-compartment model (y = 0.69x + 0.54; r = 0.74; P < .001). The variance of the error of the estimates is higher with the axially distributed model than the compartmental models (1.7 [1.3, 2.1] times higher). CONCLUSION: The proposed axially distributed model provided accurate regional estimates of MBF. The axially distributed model estimated blood flow with more accuracy, but less precision, than the evaluated compartmental models.

JSim, an open-source modeling system for data analysis.

JSim is a simulation system for developing models, designing experiments, and evaluating hypotheses on physiological and pharmacological systems through the testing of model solutions against data. It is designed for interactive, iterative manipulation of the model code, handling of multiple data sets and parameter sets, and for making comparisons among different models running simultaneously or separately. Interactive use is supported by a large collection of graphical user interfaces for model writing and compilation diagnostics, defining input functions, model runs, selection of algorithms solving ordinary and partial differential equations, run-time multidimensional graphics, parameter optimization (8 methods), sensitivity analysis, and Monte Carlo simulation for defining confidence ranges. JSim uses Mathematical Modeling Language (MML) a declarative syntax specifying algebraic and differential equations. Imperative constructs written in other languages (MATLAB, FORTRAN, C++, etc.) are accessed through procedure calls. MML syntax is simple, basically defining the parameters and variables, then writing the equations in a straightforward, easily read and understood mathematical form. This makes JSim good for teaching modeling as well as for model analysis for research.   For high throughput applications, JSim can be run as a batch job.  JSim can automatically translate models from the repositories for Systems Biology Markup Language (SBML) and CellML models. Stochastic modeling is supported. MML supports assigning physical units to constants and variables and automates checking dimensional balance as the first step in verification testing. Automatic unit scaling follows, e.g. seconds to minutes, if needed. The JSim Project File sets a standard for reproducible modeling analysis: it includes in one file everything for analyzing a set of experiments: the data, the models, the data fitting, and evaluation of parameter confidence ranges. JSim is open source; it and about 400 human readable open source physiological/biophysical models are available at http://www.physiome.org/jsim/.

Compartmental modeling in the analysis of biological systems.

Compartmental models are composed of sets of interconnected mixing chambers or stirred tanks. Each component of the system is considered to be homogeneous, instantly mixed, with uniform concentration. The state variables are concentrations or molar amounts of chemical species. Chemical reactions, transmembrane transport, and binding processes, determined in reality by electrochemical driving forces and constrained by thermodynamic laws, are generally treated using first-order rate equations. This fundamental simplicity makes them easy to compute since ordinary differential equations (ODEs) are readily solved numerically and often analytically. While compartmental systems have a reputation for being merely descriptive they can be developed to levels providing realistic mechanistic features through refining the kinetics. Generally, one is considering multi-compartmental systems for realistic modeling. Compartments can be used as "black" box operators without explicit internal structure, but in pharmacokinetics compartments are considered as homogeneous pools of particular solutes, with inputs and outputs defined as flows or solute fluxes, and transformations expressed as rate equations.Descriptive models providing no explanation of mechanism are nevertheless useful in modeling of many systems. In pharmacokinetics (PK), compartmental models are in widespread use for describing the concentration-time curves of a drug concentration following administration. This gives a description of how long it remains available in the body, and is a guide to defining dosage regimens, method of delivery, and expectations for its effects. Pharmacodynamics (PD) requires more depth since it focuses on the physiological response to the drug or toxin, and therefore stimulates a demand to understand how the drug works on the biological system; having to understand drug response mechanisms then folds back on the delivery mechanism (the PK part) since PK and PD are going on simultaneously (PKPD).Many systems have been developed over the years to aid in modeling PKPD systems. Almost all have solved only ODEs, while allowing considerable conceptual complexity in the descriptions of chemical transformations, methods of solving the equations, displaying results, and analyzing systems behavior. Systems for compartmental analysis include Simulation and Applied Mathematics, CoPasi (enzymatic reactions), Berkeley Madonna (physiological systems), XPPaut (dynamical system behavioral analysis), and a good many others. JSim, a system allowing the use of both ODEs and partial differential equations (that describe spatial distributions), is used here. It is an open source system, meaning that it is available for free and can be modified by users. It offers a set of features unique in breadth of capability that make model verification surer and easier, and produces models that can be shared on all standard computer platforms.

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.

Multiscale modeling and data integration in the virtual physiological rat project.

It has become increasingly evident that the descriptions of many complex diseases are only possible by taking into account multiple influences at different physiological scales. To do this with computational models often requires the integration of several models that have overlapping scales (genes to molecules, molecules to cells, cells to tissues). The Virtual Physiological Rat (VPR) Project, a National Institute of General Medical Sciences (NIGMS) funded National Center of Systems Biology, is tasked with mechanistically describing several complex diseases and is therefore identifying methods to facilitate the process of model integration across physiological scales. In addition, the VPR has a considerable experimental component and the resultant data must be integrated into these composite multiscale models and made available to the research community. A perspective of the current state of the art in model integration and sharing along with archiving of experimental data will be presented here in the context of multiscale physiological models. It was found that current ontological, model and data repository resources and integrative software tools are sufficient to create composite models from separate existing models and the example composite model developed here exhibits emergent behavior not predicted by the separate models.

Multiscale modeling of metabolism, flows, and exchanges in heterogeneous organs.

Large-scale models accounting for the processes supporting metabolism and function in an organ or tissue with a marked heterogeneity of flows and metabolic rates are computationally complex and tedious to compute. Their use in the analysis of data from positron emission tomography (PET) and magnetic resonance imaging (MRI) requires model reduction since the data are composed of concentration-time curves from hundreds of regions of interest (ROI) within the organ. Within each ROI, one must account for blood flow, intracapillary gradients in concentrations, transmembrane transport, and intracellular reactions. Using modular design, we configured a whole organ model, GENTEX, to allow adaptive usage for multiple reacting molecular species while omitting computation of unused components. The temporal and spatial resolution and the number of species are adaptable and the numerical accuracy and computational speed is adjustable during optimization runs, which increases accuracy and spatial resolution as convergence approaches. An application to the interpretation of PET image sequences after intravenous injection of 13NH3 provides functional image maps of regional myocardial blood flows.

Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and temperature levels.

New mathematical model equations for O(2) and CO(2) saturations of hemoglobin (S(HbO)(2) and S(HbCO)(2) are developed here from the equilibrium binding of O(2) and CO(2) with hemoglobin inside RBCs. They are in the form of an invertible Hill-type equation with the apparent Hill coefficients KHbO(2) and KHbCO(2) in the expressions for SHbO(2) and SHbCO(2) dependent on the levels of O(2) and CO(2) partial pressures (P(O)(2) and P(CO)(2)), pH, 2,3-DPG concentration, and temperature in blood. The invertibility of these new equations allows PO(2) and PCO(2) to be computed efficiently from S(HbO)(2) and S(HbCO)(2) and vice versa. The oxyhemoglobin (HbO(2)) and carbamino-hemoglobin (HbCO(2)) dissociation curves computed from these equations are in good agreement with the published experimental and theoretical curves in the literature. The model solutions describe that, at standard physiological conditions, the hemoglobin is about 97.2% saturated by O(2) and the amino group of hemoglobin is about 13.1% saturated by CO(2). The O(2) and CO(2) content in whole blood are also calculated here from the gas solubilities, hematocrits, and the new formulas for S(HbO)(2) and S(HbCO)(2). Because of the mathematical simplicity and invertibility, these new formulas can be conveniently used in the modeling of simultaneous transport and exchange of O(2) and CO(2) in the alveoli-blood and blood-tissue exchange systems.

Quantitative imaging of coronary blood flow.

Positron emission tomography (PET) is a nuclear medicine imaging modality based on the administration of a positron-emitting radiotracer, the imaging of the distribution and kinetics of the tracer, and the interpretation of the physiological events and their meaning with respect to health and disease. PET imaging was introduced in the 1970s and numerous advances in radiotracers and detection systems have enabled this modality to address a wide variety of clinical tasks, such as the detection of cancer, staging of Alzheimer's disease, and assessment of coronary artery disease (CAD). This review provides a description of the logic and the logistics of the processes required for PET imaging and a discussion of its use in guiding the treatment of CAD. Finally, we outline prospects and limitations of nanoparticles as agents for PET imaging.