Diverse Data Sets Can Yield Reliable Information through Mechanistic Modeling: Salicylic Acid Clearance.

This is a practical example of a powerful research strategy: putting together data from studies covering a diversity of conditions can yield a scientifically sound grasp of the phenomenon when the individual observations failed to provide definitive understanding. The rationale is that defining a realistic, quantitative, explanatory hypothesis for the whole set of studies, brings about a "consilience" of the often competing hypotheses considered for individual data sets. An internally consistent conjecture linking multiple data sets simultaneously provides stronger evidence on the characteristics of a system than does analysis of individual data sets limited to narrow ranges of conditions. Our example examines three very different data sets on the clearance of salicylic acid from humans: a high concentration set from aspirin overdoses; a set with medium concentrations from a research study on the influences of the route of administration and of sex on the clearance kinetics, and a set on low dose aspirin for cardiovascular health. Three models were tested: (1) a first order reaction, (2) a Michaelis-Menten (M-M) approach, and (3) an enzyme kinetic model with forward and backward reactions. The reaction rates found from model 1 were distinctly different for the three data sets, having no commonality. The M-M model 2 fitted each of the three data sets but gave a reliable estimates of the Michaelis constant only for the medium level data (Km = 24±5.4 mg/L); analyzing the three data sets together with model 2 gave Km = 18±2.6 mg/L. (Estimating parameters using larger numbers of data points in an optimization increases the degrees of freedom, constraining the range of the estimates). Using the enzyme kinetic model (3) increased the number of free parameters but nevertheless improved the goodness of fit to the combined data sets, giving tighter constraints, and a lower estimated Km = 14.6±2.9 mg/L, demonstrating that fitting diverse data sets with a single model improves confidence in the results. This modeling effort is also an example of reproducible science available at html://www.physiome.org/jsim/models/webmodel/NSR/SalicylicAcidClearance.

Left ventricular finite element model bounded by a systemic circulation model.

A series of models were developed in which a circulatory system model was coupled to an existing series of finite element (FE) models of the left ventricle (LV). The circulatory models were used to provide realistic boundary conditions for the LV models. This was developed for the JSim analysis package and was composed of a systemic arterial, capillary, and venous system in a closed loop with a varying elastance LV and left atria to provide the driving pressures and flows matching those of the FE model. Three coupled models were developed, a normal LV under normotensive aortic loading (116/80 mm Hg), a mild hypertension (137/89 mm Hg) model, and a moderate hypertension model (165/100 mm Hg). The initial step in the modeling analysis was that the circulation was optimized to the end-diastolic pressure and volume values of the LV model. The cardiac FE models were then optimized to the systolic pressure/volume characteristics of the steady-state JSim circulatory model solution. Comparison of the stress predictions for the three models indicated that the mild hypertensive case produced a 21% increase in the average fiber stress levels, and the moderate hypertension case had a 36% increase in average stress. The circulatory work increased by 18% and 43% over that of the control for the mild and moderate hypertensive cases, respectively.

Issues of exploration: human health and wellbeing during a mission to Mars.

Today, the tools are in our hands to enable us to travel away from our home planet and become citizens of the solar system. Even now, we are seriously beginning to develop the robust infrastructure that will make the 21st century the Century of Space Travel. But this bold step must be taken with due concern for the health, safety and wellbeing of future space explorers. Our long experience with space biomedical research convinces us that, if we are to deal effectively with the medical and biomedical issues of exploration, then dramatic and bold steps are also necessary in this field. We can no longer treat the human body as if it were composed of muscles, bones, heart and brain acting independently. Instead, we must lead the effort to develop a fully integrated view of the body, with all parts connected and fully interacting in a realistic way. This paper will present the status of current (2000) plans by the National Space Biomedical Research Institute to initiate research in this area of integrative physiology and medicine. Specifically, three example projects are discussed as potential stepping stones towards the ultimate goal of producing a digital human. These projects relate to developing a functional model of the human musculoskeletal system and the heart.

The spectra and periodograms of anti-correlated discrete fractional Gaussian noise.

Discrete fractional Gaussian noise (dFGN) has been proposed as a model for interpreting a wide variety of physiological data. The form of actual spectra of dFGN for frequencies near zero varies as f(1-2H), where 0 < H < 1 is the Hurst coefficient; however, this form for the spectra need not be a good approximation at other frequencies. When H approaches zero, dFGN spectra exhibit the 1 - 2H power-law behavior only over a range of low frequencies that is vanishingly small. When dealing with a time series of finite length drawn from a dFGN process with unknown H, practitioners must deal with estimated spectra in lieu of actual spectra. The most basic spectral estimator is the periodogram. The expected value of the periodogram for dFGN with small H also exhibits non-power-law behavior. At the lowest Fourier frequencies associated with a time series of N values sampled from a dFGN process, the expected value of the periodogram for H approaching zero varies as f(0) rather than f(1-2H). For finite N and small H, the expected value of the periodogram can in fact exhibit a local power-law behavior with a spectral exponent of 1 - 2H at only two distinct frequencies.

Blood flow in small curved tubes.

Blood flow in small curved tubes is modeled by the two-fluid model where a relatively cell-free fluid layer envelops a fluid core of higher viscosity. The parameters in the model are successfully curve fitted to experimental data for straight tubes. The curved tube equations are then solved by perturbation theory. It was found that curvature in general lowers the tube resistance, but increases the shear stress near the inside wall.

Capillary supply regions.

The diffusion and consumption of substrate from capillaries are basic in human physiology. The general solution for the concentration in a region containing many parallel non-homogeneous capillaries is found. Except in very special cases, capillary supply regions cannot be approximated by Krogh's cylinder or Voronoi polygonal cylinders.

Modeling advection and diffusion of oxygen in complex vascular networks.

A realistic geometric model for the three-dimensional capillary network geometry is used as a framework for studying the transport and consumption of oxygen in cardiac tissue. The nontree-like capillary network conforms to the available morphometric statistics and is supplied by a single arterial source and drains into a pair of venular sinks. We explore steady-state oxygen transport and consumption in the tissue using a mathematical model which accounts for advection in the vascular network, nonlinear binding of dissolved oxygen to hemoglobin and myoglobin, passive diffusion of freely dissolved and protein-bound oxygen, and Michaelis-Menten consumption in the parenchymal tissue. The advection velocity field is found by solving the hemodynamic problem for flow throughout the network. The resulting system is described by a set of coupled nonlinear elliptic equations, which are solved using a finite-difference numerical approximation. We find that coupled advection and diffusion in the three-dimensional system enhance the dispersion of oxygen in the tissue compared to the predictions of simplified axially distributed models, and that no "lethal corner," or oxygen-deprived region occurs for physiologically reasonable values for flow and consumption. Concentrations of 0.5-1.0 mM myoglobin facilitate the transport of oxygen and thereby protect the tissue from hypoxia at levels near its P50, that is, when local oxygen consumption rates are close to those of delivery by flow and myoglobin-facilitated diffusion, a fairly narrow range.

The mechanical and metabolic basis of myocardial blood flow heterogeneity.

Precise measurements of regional myocardial blood flow heterogeneity had to be developed before one could seek causation for the heterogeneity. Deposition techniques (particles or molecular microspheres) are the most precise, but imaging techniques have begun to provide high enough resolution to allow in vivo studies. Assigning causation has been difficult. There is no apparent association with the regional concentrations of energy-related enzymes or substrates, but these are measures of status, not of metabolism. There is statistical correlation between flow and regional substrate uptake and utilization. Attribution of regional flow variation to vascular anatomy or to vasomotor control appears not to be causative on a long-term basis. The closest relationships appear to be with mechanical function, but one cannot say for sure whether this is related to ATP hydrolysis at the crossbridge or associated metabolic reactions such as calcium uptake by the sarcoplasmic reticulum.

Endothelial adenosine transporter characterization in perfused guinea pig hearts.

Adenosine (Ado), a smooth muscle vasodilator and modulator of cardiac function, is taken up by many cell types via a saturable transporter, blockable by dipyridamole. To quantitate the influences of endothelial cells in governing the blood-tissue exchange of Ado and its concentration in the interstitial fluid, one must define the permeability-surface area products (PS) for Ado via passive transport through interendothelial gaps [PS(g)(Ado)] and across the endothelial cell luminal membrane (PS(ecl)) in their normal in vivo setting. With the use of the multiple-indicator dilution (MID) technique in Krebs-Ringer perfused, isolated guinea pig hearts (preserving endothelial myocyte geometry) and by separating Ado metabolites by HPLC, we found permeability-surface area products for an extracellular solute, sucrose, via passive transport through interendothelial gaps [PS(g)(Suc)] to be 1.9 +/- 0.6 ml. g(-1). min(-1) (n = 16 MID curves in 4 hearts) and took PS(g)(Ado) to be 1. 2 times PS(g)(Suc). MID curves were obtained with background nontracer Ado concentrations up to 800 micrometer, partially saturating the transporter and reducing its effective PS(ecl) for Ado. The estimated maximum value for PS(ecl) in the absence of background adenosine was 1.1 +/- 0.1 ml. g(-1). min(-1) [maximum rate of transporter conformational change to move the substrate from one side of the membrane to the other (maximal velocity; V(max)) times surface area of 125 +/- 11 nmol. g(-1). min(-1)], and the Michaelis-Menten constant (K(m)) was 114 +/- 12 microM, where +/- indicates 95% confidence limits. Physiologically, only high Ado release with hypoxia or ischemia will partially saturate the transporter.

The fractal nature of myocardial blood flow emerges from a whole-organ model of arterial network.

Mammalian hearts exhibit a heterogeneous spatial distribution of blood flows, but flows in near-neighbor regions correlate strongly. Also, tracer (15)O-water washout after injection into the inflow shows a straight log-log relationship between outflow concentration and time. To uncover the role of the arterial network in governing these phenomena, morphometric data were used to construct a mathematical model of the coronary arterial network of the pig heart. The model arterial network, built in a simplified three-dimensional representation of tissue geometry, satisfies the statistical morphometric data on segment lengths, diameters and connectivities reported for real arterial networks. The model uses an avoidance algorithm to position successive vascular segments in the network. Assuming flows through the network to be steady, the calculated regional flow distributions showed (1) the degree of heterogeneity observed in normal hearts; (2) spatial self-similarity in local flows; (3) fractal spatial correlations, all with the same fractal dimension found in animal studies; (4) pressure distributions along the model arterial network comparable to those observed in nature, with maximal resistances in small vessels. In addition, the washout of intravascular tracer showed tails with power law slopes that fitted h(t) = at(-alpha-1) with the exponents alpha = 2 for the reconstructed networks compared with those from experimental outflow concentration-time curves with alpha = 2.1+/-0.3. Thus, we concluded that the fractal nature of spatial flow distribution in the heart, and of temporal intravascular washout, are explicable in terms of the morphometry of the coronary network.

A class of flow bifurcation models with lognormal distribution and fractal dispersion.

We report a quantitative analysis of a simple dichotomous branching tree model for blood flow in vascular networks. Using the method of moment-generating function and geometric Brownian motion from stochastic mathematics, our analysis shows that a vascular network with asymmetric branching and random variation at each bifurcating point gives rise to an asymptotic lognormal flow distribution with a positive skewness. The model exhibits a fractal scaling in the dispersion of the regional flow in the branches. Experimentally measurable fractal dimension of the relative dispersion in regional flow is analytically calculated in terms of the asymmetry and the variance at local bifurcation; hence the model suggests a powerful method to obtain the physiological information on local flow bifurcation in terms of flow dispersion analysis. Both the fractal behavior and the lognormal distribution are intimately related to the fact that it is the logarithm of flow, rather than flow itself, which is the natural variable in the tree models. The kinetics of tracer washout is also discussed in terms of the lognormal distribution.

Advection and diffusion of substances in biological tissues with complex vascular networks.

For highly diffusive solutes the kinetics of blood-tissue exchange is only poorly represented by a model consisting of sets of independent parallel capillary-tissue units. We constructed a more realistic multicapillary network model conforming statistically to morphometric data. Flows through the tortuous paths in the network were calculated based on constant resistance per unit length throughout the network and the resulting advective intracapillary velocity field was used as a framework for describing the extravascular diffusion of a substance for which there is no barrier or permeability limitation. Simulated impulse responses from the system, analogous to tracer water outflow dilution curves, showed flow-limited behavior over a range of flows from about 2 to 5 ml min(-1) g(-1), as is observed for water in the heart in vivo. The present model serves as a reference standard against which to evaluate computationally simpler, less physically realistic models. The simulated outflow curves from the network model, like experimental water curves, were matched to outflow curves from the commonly used axially distributed models only by setting the capillary wall permeability-surface area (PS) to a value so artifactually low that it is incompatible with the experimental observations that transport is flow limited. However, simple axially distributed models with appropriately high PSs will fit water outflow dilution curves if axial diffusion coefficients are set at high enough values to account for enhanced dispersion due to the complex geometry of the capillary network. Without incorporating this enhanced dispersion, when applied to experimental curves over a range of flows, the simpler models give a false inference that there is recruitment of capillary surface area with increasing flow. Thus distributed models must account for diffusional as well as permeation processes to provide physiologically appropriate parameter estimates.

Facilitated diffusion and membrane permeation of fatty acid in albumin solutions.

Facilitated transport is characteristic of most living systems, and usually involves a series of consecutive adjacent transfer regions, each having different transport properties. As a first step in the analysis of the multiregional problem, we consider in a single unstirred layer the facilitated diffusion of fatty acid (F) in albumin (A) solution under conditions of slow versus rapid association-dissociation, accounting for differing diffusivities of the albumin-fatty acid complex (AF). Diffusion gradients become established in an unstirred layer between a source of constant concentration of A, AF, and F in equilibrium, and a membrane permeable to F. The posited system does not reduce to a thin- or thick-layer approximation. The transient state is prolonged by slower on/off binding rates and by increasing the thickness of the unstirred layer. Solutions to transient and steady state depend upon the choice of boundary conditions, especially for thin regions. When there are two regions (each with its specific binding protein) separated by a permeable membrane, the steady-state fluxes and concentration profiles depend on the rates of association and dissociation reactions, on the diffusion coefficients, local consumption rates, and on the membrane permeability. Sensitivity analysis reveals the relative importance of these mechanisms.

Blood flow distributions by microsphere deposition methods.

The art and science of the use of deposition markers for the estimation of blood flow distributions throughout the body and within organs is reviewed. Development of diffusible tracer techniques started 50 years ago. Twenty years later, radioactive 15 micron microspheres became the standard marker. Early studies on small animals, fetal sheep in 1967 and rats in 1976, provoked much of the technical development. Needs for avoiding the use of radioactivity, for having long lasting labels, and for providing higher spatial resolution, are driving the continuing exploration of newer techniques using colored and fluorescent microspheres and molecular deposition markers. Strengths and weaknesses of the various methods are compared.

Physiological time series: distinguishing fractal noises from motions.

Many physiological signals appear fractal, in having self-similarity over a large range of their power spectral densities. They are analogous to one of two classes of discretely sampled pure fractal time signals, fractional Gaussian noise (fGn) or fractional Brownian motion (fBm). The fGn series are the successive differences between elements of a fBm series; they are stationary and are completely characterized by two parameters, sigma2, the variance, and H, the Hurst coefficient. Such efficient characterization of physiological signals is valuable since H defines the autocorrelation and the fractal dimension of the time series. Estimation of H from Fourier analysis is inaccurate, so more robust methods are needed. Dispersional analysis (Disp) is good for noise signals while bridge detrended scaled windowed variance analysis (bdSWV) is good for motion signals. Signals whose slopes of their power spectral densities lie near the border between fGn and fBm are difficult to classify. A new method using signal summation conversion (SSC), wherein an fGn is converted to an fBm or an fBm to a summed fBm and bdSWV then applied, greatly improves the classification and the reliability of H, the estimates of H, for the times series. Applying these methods to laser-Doppler blood cell perfusion signals obtained from the brain cortex of anesthetized rats gave H of 0.24+/-0.02 (SD, n=8) and defined the signal as a fractional Brownian motion. The implication is that the flow signal is the summation (motion) of a set of local velocities from neighboring vessels that are negatively correlated, as if induced by local resistance fluctuations.

Strategies for the physiome project.

The physiome is the quantitative description of the functioning organism in normal and pathophysiological states. The human physiome can be regarded as the virtual human. It is built upon the morphome, the quantitative description of anatomical structure, chemical and biochemical composition, and material properties of an intact organism, including its genome, proteome, cell, tissue, and organ structures up to those of the whole intact being. The Physiome Project is a multicentric integrated program to design, develop, implement, test and document, archive and disseminate quantitative information, and integrative models of the functional behavior of molecules, organelles, cells, tissues, organs, and intact organisms from bacteria to man. A fundamental and major feature of the project is the databasing of experimental observations for retrieval and evaluation. Technologies allowing many groups to work together are being rapidly developed. Internet II will facilitate this immensely. When problems are huge and complex, a particular working group can be expert in only a small part of the overall project. The strategies to be worked out must therefore include how to pull models composed of many submodules together even when the expertise in each is scattered amongst diverse institutions. The technologies of bioinformatics will contribute greatly to this effort. Developing and implementing code for large-scale systems has many problems. Most of the submodules are complex, requiring consideration of spatial and temporal events and processes. Submodules have to be linked to one another in a way that preserves mass balance and gives an accurate representation of variables in nonlinear complex biochemical networks with many signaling and controlling pathways. Microcompartmentalization vitiates the use of simplified model structures. The stiffness of the systems of equations is computationally costly. Faster computation is needed when using models as thinking tools and for iterative data analysis. Perhaps the most serious problem is the current lack of definitive information on kinetics and dynamics of systems, due in part to the almost total lack of databased observations, but also because, though we are nearly drowning in new information being published each day, either the information required for the modeling cannot be found or has never been obtained. "Simple" things like tissue composition, material properties, and mechanical behavior of cells and tissues are not generally available. The development of comprehensive models of biological systems is a key to pharmaceutics and drug design, for the models will become gradually better predictors of the results of interventions, both genomic and pharmaceutic. Good models will be useful in predicting the side effects and long term effects of drugs and toxins, and when the models are really good, to predict where genomic intervention will be effective and where the multiple redundancies in our biological systems will render a proposed intervention useless. The Physiome Project will provide the integrating scientific basis for the Genes to Health initiative, and make physiological genomics a reality applicable to whole organisms, from bacteria to man.

Cardiac endothelial transport and metabolism of adenosine and inosine.

The influence of transmembrane flux limitations on cellular metabolism of purine nucleosides was assessed in whole organ studies. Transcapillary transport of the purine nucleosides adenosine (Ado) and inosine (Ino) via paracellular diffusion through interendothelial clefts in parallel with carrier-mediated transendothelial fluxes was studied in isolated, Krebs-Henseleit-perfused rabbit and guinea pig hearts. After injection into coronary inflow, multiple-indicator dilution curves were obtained from coronary outflow for 90 s for 131I-labeled albumin (intravascular reference tracer), [3H]arabinofuranosyl hypoxanthine (AraH; extracellular reference tracer and nonreactive adenosine analog), and either [14C]Ado or [14C]Ino. Ado or Ino was separated from their degradative products, hypoxanthine, xanthine, and uric acid, in each outflow sample by HPLC and radioisotope counting. Ado and Ino, but not AraH, permeate the luminal membrane of endothelial cells via a saturable transporter with permeability-surface area product PS(ecl) and also diffuse passively through interendothelial clefts with the same conductance (PSg) as AraH. These parallel conductances were estimated via fitting with an axially distributed, multi-pathway, four-region blood-tissue exchange model. PSg for AraH were approximately 4 and 2.5 ml. g(-1). min(-1) in rabbits and guinea pigs, respectively. In contrast, transplasmalemmal conductances (endothelial PS(ecl)) were approximately 0.2 ml. g(-1). min(-1) for both Ado and Ino in rabbit hearts but approximately 2 ml. g(-1). min(-1) in guinea pig hearts, an order of magnitude different. Purine nucleoside metabolism also differs between guinea pig and rabbit cardiac endothelium. In guinea pig heart, 50% of the tracer Ado bolus was retained, 35% was washed out as Ado, and 15% was lost as effluent metabolites; 25% of Ino was retained, 50% washed out, and 25% was lost as metabolites. In rabbit heart, 45% of Ado was retained and 5% lost as metabolites, and 7% of Ino was retained and 3% lost as metabolites. We conclude that endothelial transport of Ado and Ino is a prime determinant of their metabolic fates: where transport rates are high, metabolic transformation is high.

Stochastic fractal behavior in concentration fluctuation and fluorescence correlation spectroscopy.

Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in two dimensions, but non-singular in three dimensions. This discovery provides one simple physical mechanism for possible long-memory fractal behavior, and its implications to various biological processes are discussed.