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.

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.

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.

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.

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.

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.

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.

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.

Microcirculation and the physiome projects.

The Physiome projects comprise a loosely knit worldwide effort to define the Physiome through databases and theoretical models, with the goal of better understanding the integrative functions of cells, organs, and organisms. The projects involve developing and archiving models, providing centralized databases, and linking experimental information and models from many laboratories into self-consistent frameworks. Increasingly accurate and complete models that embody quantitative biological hypotheses, adhere to high standards, and are publicly available and reproducible, together with refined and curated data, will enable biological scientists to advance integrative, analytical, and predictive approaches to the study of medicine and physiology. This review discusses the rationale and history of the Physiome projects, the role of theoretical models in the development of the Physiome, and the current status of efforts in this area addressing the microcirculation.

Linking cellular energetics to local flow regulation in the heart.

A mathematical model has been developed to explain the metabolic and energetic responses induced by abnormal routes of cardiac excitation. For example, in left bundle branch block (LBBB), both glucose uptake and flow are reduced in the septal region, similar to the situation in dogs paced at the right ventricular outflow tract. In these conditions the septum is activated early, the sarcomere lengths shorten rapidly against low left ventricular (LV) pressure, and the blood flow to the interventricular septum diminishes. In contrast, the work load and the blood flow increases in the later-activated LV free wall. To provide a logical, quantitatively appropriate representation, the model links: (1) the processes of excitation-contraction coupling; (2) regional ATP utilization for force development at the cross-bridge, for ion pumping, and for cell maintenance; (3) the regulation of demands on local fatty acid and glucose metabolism for ATP generation by glycolysis and oxidative phosphorylation; and (4) feedback regulation of blood flow to supply substrate and oxygen. The heart is considered as a cylinder composed of two parts: an early-activated region and a late-activated region in tandem, but activated separately with the time delay representing the time for excitation to spread from septum to free wall. The same model equations and parameter sets are used for the two regions. The contraction of the early-activated region stretches the other region, with the result that the early-stimulated region has diminished oxygen requirements compared to those found with simultaneous stimulation. The late-activated region has increased work and increased oxygen consumption, as seen in the intact heart. Integrating the modeling of cardiac energy metabolism with local blood flow regulation and capillary-tissue substrate exchange provides a quantitative description, an hypothesis formulated to stimulate further experimentation to test its validity. The hypothesis "explains" observations of contraction and metabolism in LBBB, but whether this concept can be extended to explain the normal flow heterogeneity in the heart remains unknown.

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

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

Computational evidence for protein-mediated fatty acid transport across the sarcolemma.

Long-chain fatty acids (FAs) are important substrates used by the heart to fulfil its energy requirements. Prior to mitochondrial oxidation, blood-borne FAs must pass through the cell membrane of the cardiac myocyte (sarcolemma). The mechanism underlying the sarcolemmal transport of FAs is incompletely understood. The aim of the present study was to estimate the trans-sarcolemmal FA uptake rate using a comprehensive computer model, in which the most relevant mechanisms proposed for cardiac FA uptake were incorporated. Our in silico findings show that diffusion of FA, present in its unbound form (uFA) in close proximity to the outer leaflet of the sarcolemma and serving as sole FA source, is insufficient to account for the physiological FA uptake rate. The inclusion of a hypothetical membrane-associated FA-TFPC (FA-transport-facilitating protein complex) in the model calculations substantially increased the FA uptake rate across the sarcolemma. The model requires that the biological properties of the FA-TFPC allow for increasing the rate of absorption of FA into the outer leaflet and the 'flip-flop' rate of FA from the outer to the inner leaflet of the sarcolemma. Experimental studies have identified various sarcolemma-associated proteins promoting cardiac FA uptake. It remains to be established whether these proteins possess the properties predicted by our model. Our findings also indicate that albumin receptors located on the outer leaflet of the sarcolemma facilitate the transfer of FA across the membrane to a significant extent. The outcomes of the computer simulations were verified with physiologically relevant FA uptake rates as assessed in the intact, beating heart in experimental studies.

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.

Strategies and Tactics in Multiscale Modeling of Cell-to-Organ Systems.

Modeling is essential to integrating knowledge of human physiology. Comprehensive self-consistent descriptions expressed in quantitative mathematical form define working hypotheses in testable and reproducible form, and though such models are always "wrong" in the sense of being incomplete or partly incorrect, they provide a means of understanding a system and improving that understanding. Physiological systems, and models of them, encompass different levels of complexity. The lowest levels concern gene signaling and the regulation of transcription and translation, then biophysical and biochemical events at the protein level, and extend through the levels of cells, tissues and organs all the way to descriptions of integrated systems behavior. The highest levels of organization represent the dynamically varying interactions of billions of cells. Models of such systems are necessarily simplified to minimize computation and to emphasize the key factors defining system behavior; different model forms are thus often used to represent a system in different ways. Each simplification of lower level complicated function reduces the range of accurate operability at the higher level model, reducing robustness, the ability to respond correctly to dynamic changes in conditions. When conditions change so that the complexity reduction has resulted in the solution departing from the range of validity, detecting the deviation is critical, and requires special methods to enforce adapting the model formulation to alternative reduced-form modules or decomposing the reduced-form aggregates to the more detailed lower level modules to maintain appropriate behavior. The processes of error recognition, and of mapping between different levels of model complexity and shifting the levels of complexity of models in response to changing conditions, are essential for adaptive modeling and computer simulation of large-scale systems in reasonable time.

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.

Multiscale modeling of cardiac cellular energetics.

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

Relation between local myocardial growth and blood flow during chronic ventricular pacing.

UNLABELLED: Several studies have shown that, per unit mass, myocardial blood flow (MBF) and oxygen consumption are similar in hypertrophic and non-hypertrophic ventricles. This observation may be explained by the degree of myocardial growth matching the increase in oxygen demand. Such matching may, however, not be perfect at the local level, because substantial heterogeneity of MBF exists within the ventricular wall. We investigated to what extent local growth and MBF are matched after redistribution of workload within the left ventricular (LV) wall. Redistribution of workload was established by ventricular pacing at physiological heart rate, which induces asynchronous activation and contraction. Local wall mass (2D-echocardiography) and MBF (fluorescent microspheres) were determined in the canine LV wall before (t=0) and after 6 months of normal sinus rhythm (SHAM group, n=5) or 6 months of pacing at the LV free wall (PACE group, n=8). During acute pacing MBF (ml/min/g) increased with increasing distance to the pacing site. Local relative MBF (rMBF, local MBF normalized to mean MBF in the LV wall) varied from 0.8 adjacent to the pacing site to 1.2 in remote regions. After 6 months of pacing these regional differences had disappeared, probably due to changes in wall mass, which increased with increasing distance to the pacing site (by up to 39+/-13%). In SHAM animals rMBF at t=0 correlated well with rMBF 6 months later (r=0.71). In PACE animals, however, this correlation was poor (r=0.33), because rMBF increased in regions close to the pacing site with initial rMBF<1 and rMBF decreased in regions remote from the pacing site with initial rMBF>1. CONCLUSIONS: After redistribution of workload within the LV wall as induced by ventricular pacing, local load-regulated growth tends to equalize MBF distribution, but local adaptation of MBF also depends on initial MBF.

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/.