How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.     

Information content of the multibreath nitrogen washout: effects of experimental error

Methods that recover a continuous distribution of specific ventilation (ventilation-to-volume ratio, VA/V) from the multibreath N2 washout curve theoretically can resolve up to four modes of ventilation and reveal the major characteristics of the underlying distribution if experimental error is absent. This paper quantitatively assesses the effects of experimental error on resolution. The washout curves from five typical distributions were studied using linear programming and Monte Carlo methods. A measurement error of 0.1% was assumed in the mixed-expired N2 signal. Only 7 of the first 17 breaths contribute independent information about the underlying distribution, and only rough resolution of the underlying distribution is possible in the presence of error. Only two modes of ventilation plus an estimate of dead space can be confidently resolved. It is not possible to separate VA/V greater than 10 from dead space. A 10-fold reduction in experimental error will not greatly improve resolution. Experimental error, by reducing the linear independence of the defining kernels, significantly limits the information content and resolution of the multibreath N2 washout.     

A heterogeneous tissue model for measurement of regional blood perfusion in the myocardium using inert gas isotopes

Inert gas isotopes are finding increasing application in the measurement of blood perfusion in the capillary beds of muscle, especially the myocardium. When measuring blood perfusion of the myocardium, washout curves are first produced by precordial monitoring of isotope activity following intracoronary artery injection of an inert gas isotope dissolved in saline. The washout curve data are then applied to a mathematical model to yield blood perfusion rate. Present models for this purpose either ignore any diffusive effects of gas movement (Kety-Schmidt model), or diffusive effects are accounted for by weighting the calculated perfusion value (Zierler's height-over-area technique). A new model is described here for convective and diffusive movement of an inert, nonpolar gas in myocardial tissue. A digital computer simulation of the model equations is used both to simply the model and to show agreement between the model response and experimental ¹³³Xe washout curves from normal and infracted canine hearts. The model assumes that the tail of the washout curves (portion after roughly 1.5 minutes) is caused by a heterogeneous, diffusion-limited tissue structure. The model provides two parameters which can be adjusted to washout curve data using model-matching techniques. These are perfusion rate, and a parameter which is an index of the diffusive nature of the particular myocardial area under study.     

Simulation of regional lung emptying during slow and forced expirations.

Regional lung emptying was simulated by means of a bialveolar lung model. The influence of bronchial asymmetry and the vertical pleural pressure gradient was evaluated. The model suggests that 1) in vivo the influence of the pleural pressure gradient prevails over that of the bronchial asymmetry; 2) in the presence of this gradient, the shape of phases III and IV of the single-breath washout curves obtained following inspiration of a tracer gas bolus at residual volume is determined by the recoil pressure-volume curve of the lung, by the vertical displacements of the alveoli, and,, at higher flow rates, by the elastic characteristics of the airways; 3) if the pleural pressure gradient is independent of lung volume and of flow rate, the factors mentioned in 2 suffice to produce single-breath washout curves (phases III and IV) and regional vs. overall lung volume relationships corresponding to those observed in vivo; 4) the configuration of the maximal expiratory flow-volume curve is relatively insensitive to pulmonary and bronchial asymmetry, at least in healthy individuals.     

Contributions of diffusion jet flow and cardiac activity to regional ventilation in CFV.

The magnitude and regional distribution of local gas transport during constant-flow ventilation (CFV) were quantified by imaging the washout of nitrogen 13 (13NN) from anesthetized and paralyzed mongrel dogs with positron emission tomography. Equal jet flows, through two 2-mm-ID bronchial catheters 1 cm distal to the carina, were adjusted to provide eucapnic CFV (total flow = 57.6 ml.s-1.kg-1). Basal, midheart, and apical transverse sections were studied in supine and prone anesthetized dogs. The ventilation per unit volume (sV) of selected areas was computed from local 13NN concentration vs. time curves during washout. To separate the regional contributions of CFV and cardiogenic oscillation to enhanced molecular diffusion, additional supine dogs were also studied during unilateral CFV. In this protocol the CFV jet flow was delivered to a single lung while the contralateral lung was left apneic. For each lung, washout data were obtained under CFV and apnea both living and postmortem animals. The local contributions of diffusion, CFV jet effects, and cardiac activity to gas transport were evaluated and tested for additive and multiplicative synergistic interactions. The regional distribution of gas transport during CFV was found to be highly nonuniform and characterized by higher ventilation to regions located close to the main bronchi and those located in the direction in which the CFV jet pointed. No major differences were observed between supine and prone positions. This regional pattern of ventilation distribution was found to be the result of complementary and nearly multiplicative interaction between the regional effects of the CFV jet, concentrated in the central airways, and the preferential cardiogenic gas transport enhancement in ventral regions close to the heart. The data were also analyzed with a model that divides the regional diffusive gas transport resistance into a central component, affected by the CFV jet, and a peripheral component, affected only by cardiac activity. This analysis showed substantial regional heterogeneities in the effects of the different gas transport mechanisms, which are consistent with the geometry of the bronchial tree and the location of the heart in the dog. The results indicate that regional nonuniformities must be considered when modeling gas transport in CFV.     

A statistical model of the VA/Q distribution

A "blocks model" is proposed to model the distribution of the ventilation-perfusion ratio (VA/Q distribution). This model is developed from statistical principles and enables the estimated VA/Q distribution to be interpreted in a straightforward and intuitive manner. Estimation of parameters of the blocks model uses a constrained weighted least-squares procedure. Although developed initially to estimate VA/Q distributions from data generated by the multiple inert gas elimination technique (P. D. Wagner, H. A. Saltzman, and J. B. West, J. Appl. Physiol. 36: 588-599, 1974), the blocks method is applicable to any problem in which the unknown distribution is related to the data through an ill-posed integral equation and is particularly suited for problems in which the data are scarce. The method is illustrated with several examples--hypothetical data representing a wide range of VA/Q distributions as well as some real data.     

Linear programming analysis of VA/Q distributions: average distribution

The defining equations of the multiple inert gas elimination technique are underdetermined, and an infinite number of VA/Q ratio distributions exists that fit the same inert gas data. Conventional least-squares analysis with enforced smoothing chooses a single member of this infinite family whose features are assumed to be representative of the family as a whole. To test this assumption, the average of all ventilation-perfusion ratio (VA/Q) distributions that are compatible with given data was calculated using a linear program. The average distribution so obtained was then compared with that recovered using enforced smoothing. Six typical sets of inert gas data were studied. In all sets but one, the distribution recovered with conventional enforced smoothing closely matched the structure of the average distribution. The single exception was associated with the broad log-normal VA/Q distribution, which is rarely observed using the technique. We conclude that the VA/Q distribution conventionally recovered approximates a simple average of all compatible distributions. It therefore displays average features and only that degree of fine structural detail that is typical of the family as a whole.     

Analysis of factors that influence rates of carbon monoxide uptake, distribution, and washout from blood and extravascular tissues using a multicompartment model.

To better understand factors that influence carbon monoxide (CO) washout rates, we utilized a multicompartment mathematical model to predict rates of CO uptake, distribution in vascular and extravascular (muscle vs. other soft tissue) compartments, and washout over a range of exposure and washout conditions with varied subject-specific parameters. We fitted this model to experimental data from 15 human subjects, for whom subject-specific parameters were known, multiple washout carboxyhemoglobin (COHb) levels were available, and CO exposure conditions were identical, to investigate the contributions of exposure conditions and individual variability to CO washout from blood. We found that CO washout from venous blood was biphasic and that postexposure times at which COHb samples were obtained significantly influenced the calculated CO half times (P < 0.0001). The first, more rapid, phase of CO washout from the blood reflected the loss of CO to the expired air and to a slow uptake by the muscle compartment, whereas the second, slower washout phase was attributable to CO flow from the muscle compartment back to the blood and removal from blood via the expired air. When the model was used to predict the effects of varying exposure conditions for these subjects, the CO exposure duration, concentration, peak COHb levels, and subject-specific parameters each influenced washout half times. Blood volume divided by ventilation correlated better with half-time predictions than did cardiac output, muscle mass, or ventilation, but it explained only approximately 50% of half-time variability. Thus exposure conditions, COHb sampling times, and individual parameters should be considered when estimating CO washout rates for poisoning victims.     

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scale-up.     

The pressure-flow relation for plasma in whole organ skeletal muscle and its experimental verification.

The whole-organ pressure-flow relation in resting rat skeletal muscle is examined for the flow of plasma. Due to the small size of the blood vessels in this organ, inertia and convective forces in the blood are negligible and viscous forces dominate. Direct measurements in the past have shown that skeletal muscle blood vessels are distensible. Theoretical formulations based on these measurements lead to a third order polynomial model for the pressure-flow relation. The purpose of the current study is to examine this relation experimentally in an isolated muscle organ. A high precision feedback controlled pump is used to perfuse artificial plasma into the vasodilated rat gracilis muscle. The results indicate that the pressure-flow curve in this tissue is nonlinear in the low flow region and almost linear at physiological flow rates, following closely the third order polynomial function. Vessel fixation with glutaraldehyde causes the curves to become linear at all pressures, indicating that vessel distention is the primary mechanism causing the nonlinearity. Furthermore, the resistance of the post-fixed tissue is determined by the pressure at which the fixative is perfused. At fixation pressures below 10 mmHg, the resistance is three times higher than in vessels fixed at normal physiological pressures. Dextran (229,000 Dalton) is used to obtain Newtonian perfusates at different viscosities. The pressure-flow relation is found to be linearly dependent on viscosity for all flow rates.(ABSTRACT TRUNCATED AT 250 WORDS)     

Metabolic adaptations to repeated periods of contraction with reduced blood flow in canine skeletal muscle

Background  

Patients suffering from Intermittent Claudication (IC) experience repeated periods of muscle contraction with low blood flow, throughout the day and this may contribute to the hypothesised skeletal muscle abnormalities. However, no study has evaluated the consequences of intermittent contraction with low blood flow on skeletal muscle tissue. Our aim was to generate this basic physiological data, determining the 'normal' response of healthy skeletal muscle tissue. We specifically proposed that the metabolic responses to contraction would be modified under such circumstances, revealing endogenous strategies engaged to protect the muscle adenine nucleotide pool. Utilizing a canine gracilis model (n = 9), the muscle was stimulated to contract (5 Hz) for three 10 min periods (separated by 10 min rest) under low blood flow conditions (80% reduced), followed by 1 hr recovery and then a fourth period of 10 min stimulation. Muscle biopsies were obtained prior to and following the first and fourth contraction periods. Direct arterio-venous sampling allowed for the calculation of muscle metabolite efflux and oxygen consumption.     

A flexible estimating equations approach for mapping function-valued traits

In genetic studies, many interesting traits, including growth curves and skeletal shape, have temporal or spatial structure. They are better treated as curves or function-valued traits. Identification of genetic loci contributing to such traits is facilitated by specialized methods that explicitly address the function-valued nature of the data. Current methods for mapping function-valued traits are mostly likelihood-based, requiring specification of the distribution and error structure. However, such specification is difficult or impractical in many scenarios. We propose a general functional regression approach based on estimating equations that is robust to misspecification of the covariance structure. Estimation is based on a two-step least-squares algorithm, which is fast and applicable even when the number of time points exceeds the number of samples. It is also flexible due to a general linear functional model; changing the number of covariates does not necessitate a new set of formulas and programs. In addition, many meaningful extensions are straightforward. For example, we can accommodate incomplete genotype data, and the algorithm can be trivially parallelized. The framework is an attractive alternative to likelihood-based methods when the covariance structure of the data is not known. It provides a good compromise between model simplicity, statistical efficiency, and computational speed. We illustrate our method and its advantages using circadian mouse behavioral data.     

Arteriolar and systemic autoregulatory responses during the development of hypertension in the spontaneously hypertensive rat

Pressure-flow curves were constructed to determine whether acute autoregulation in rat skeletal muscle was altered during the development of hypertension in the spontaneously hypertensive rat (SHR). Under chloralose:urethane anesthesia, hindlimb blood flow and pressure, plus diameter changes of gracilis muscle arterioles, were simultaneously measured in the 6- and 9-week Wistar-Kyoto (WKY) and SHR. Femoral blood flow was measured by electromagnetic flowmetry and hindlimb pressure controlled with an hydraulic occluder. Arteriolar diameters were measured using image shearing techniques. Acute autoregulatory capacity was assessed by comparing the closed-loop gain and the regression lines over the regulated and passive pressure ranges of the pressure-flow curves. The lower pressure limit of autoregulation (LPLAR) shifted upward as the blood pressure increased in the SHR with age; it did not shift in the WKY. Resting hindlimb flow, elevated in the SHR at 6 weeks, was also elevated at the LPLAR. At 9 weeks hindlimb blood flow was comparable in the WKY and SHR. As blood pressure was increased autoregulation was accompanied by vasoconstriction of gracilis arterioles. However, neither the gain of the autoregulatory system nor the regression lines describing the pressure-flow curves were different between the hypertensive and normotensive animals at either age. These results indicate that the acute autoregulatory response mechanism was not affected by the developing hypertension in the SHR, and is consistent with a structural basis for the chronic maintenance of the elevated peripheral vascular resistance.     

A novel Bayesian functional spatial partitioning method with application to prostate cancer lesion detection using MRI

Spatial partitioning methods correct for nonstationarity in spatially related data by partitioning the space into regions of local stationarity. Existing spatial partitioning methods can only estimate linear partitioning boundaries. This is inadequate for detecting an arbitrarily shaped anomalous spatial region within a larger area. We propose a novel Bayesian functional spatial partitioning (BFSP) algorithm, which estimates closed curves that act as partitioning boundaries around anomalous regions of data with a distinct distribution or spatial process. Our method utilizes transitions between a fixed Cartesian and moving polar coordinate system to model the smooth boundary curves using functional estimation tools. Using adaptive Metropolis-Hastings, the BFSP algorithm simultaneously estimates the partitioning boundary and the parameters of the spatial distributions within each region. Through simulation we show that our method is robust to shape of the target zone and region-specific spatial processes. We illustrate our method through the detection of prostate cancer lesions using magnetic resonance imaging.     

Atrial natriuretic peptide (ANP) does not inhibit the basal vascular tone present in the in situ blood-perfused dog gracilis muscle

This study evaluated the effects of rat ANP(5-28) infusion into the blood-perfused dog gracilis muscle at concentrations ranging from 30 to 10,000 pg/ml. The vasculature of gracilis muscles from anesthetized beagle dogs was isolated and pump-perfused at constant flow with blood utilizing an extracorporeal circuit. Maximal vasodilatory capacity was determined by adenosine injection. ANP was infused into the arterial circuit to produce increasing arterial blood concentrations. Each infusion lasted 10 min. Systemic arterial pressure, central venous pressure, cardiac output and heart rate did not change during ANP infusion into the gracilis vasculature. ANP at arterial blood concentrations up to 10,000 pg/ml did not produce significant vasodilation although the vasculature showed pronounced vasodilation in response to adenosine. In vitro experiments showed that ANP had much less vasorelaxant activity in dog femoral artery and saphenous vein than in rabbit aorta. Therefore, rat ANP(5-28) at concentrations within and well above physiological and pharmacological ranges does not inhibit the basal vascular tone present in the innervated, blood-perfused dog gracilis muscle in situ.     

Model Testing in Radioligand/Receptor Interaction by Monte Carlo Simulation

Abstract

Monte Carlo simulations have been applied for evaluating the reliability of parameter estimates as well as for testing models in radioligand saturation binding experiments. Scatchard analysis was compared to the nonlinear least-square curve fitting method for one-site saturation binding curves. It was found that linear regression analysis from the transformed data in the Scatchard plot yielded generally less accurate parameter estimates than nonlinear regression analysis of untransformed data. The advantage of the nonlinear least-squares curve fitting method was especially pronounced in cases where the scatter and number of data points, as well as the radioligand concentration range, were chosen similar to less optimal experimental conditions. Under such circumstances, several K_D and B_max values derived by Scatchard analysis led to physically impossible negative values whereas the same data analyzed by nonlinear regression yielded reasonable parameter estimates. Furthermore, it was found that for both means of analysis, K_D and B_max correlated positively. In another set of Monte Carlo experiments, saturation binding curves involving two receptor sites were generated and subsequently analyzed according to both a one-site and a two-site model. The confidence with which one is able to distinguish the two-site model from nonlinear least-squares curve fitting was then estimated for optimal, as well as for, less ideal experimental condigions.     

Timing of microcirculatory injury from ischemia reperfusion

The low flow state that results from ischemia and reperfusion injury is a potentially reversible process that is important in numerous clinical situations. However, the point in time during the course of reperfusion where tissue injury becomes irreversible is unknown. This experiment evaluated the continuum of tissue damage in skeletal muscle after ischemic insult by quantifying the number of flowing capillaries and percentage muscle necrosis in a male Wistar rat skeletal muscle model. A gracilis muscle flap was raised on the vascular pedicle of 39 male Wistar rats and examined at 832x using intravital videomicroscopy. The numbers of flowing capillaries in five consecutive high-power fields were counted for baseline values. The flap was then subjected to 4 hours of global ischemia (except in sham animals, n = 7) by placing a microvascular clamp on the pedicle artery and vein. Upon reperfusion, flowing capillaries were counted in the same five high-power fields at intervals of 5, 15, 30, and 60 minutes, then at 2 to 8 (1-hour intervals), 24, and 48 hours. The gracilis muscle was then harvested at these intervals during reperfusion and assessed for viability. Compared with baseline, flowing capillaries from the ischemia and reperfusion group (mean +/- SEM) decreased significantly in the first 8 hours of reperfusion (7.7 +/- 0.2 to 3.2 +/- 0.3, p < 0.001) with minimal change noted from 8 to 48 hours. Percentage muscle necrosis increased progressively in ischemia and reperfusion preparations from 1 to 7 hours of reperfusion (16.5 +/- 2.6 percent to 38.9 +/- 1.2 percent, p < 0.001). No significant change in muscle necrosis in the ischemia and reperfusion group was noted between 7 and 48 hours. Sham preparations showed no change in the number of flowing capillaries through 3 hours of reperfusion, with a slight decrease at 24 hours. This rat gracilis microcirculation skeletal muscle model demonstrates a heterogeneous reperfusion injury. The decrease in flowing capillaries correlated with the increase in percentage necrosis and appeared to stabilize at the 7- to 8-hour interval. This finding may have important implications for the timing of interventions aimed at minimizing tissue damage from ischemia-reperfusion.     

Xenon kinetics in muscle are not explained by a model of parallel perfusion-limited compartments

Experimental tissue gas kinetics do not follow the prediction for a single stirred perfusion-limited compartment. One hypothesis proposes that the kinetics might be explained by considering the tissue as a collection of parallel compartments, each with its own flow, reflecting the tissue microcirculatory flow heterogeneity. In this study, observed tissue gas kinetics were compared with the kinetics predicted by a model of multiple parallel compartments. Gas exchange curves were generated by recording the time course of tissue radioactivity in the intact calf muscles of anesthetized ventilated dogs exposed to step function changes of 133Xe in the inspired air for 5-h periods. Microcirculatory flow heterogeneity in the same tissue was determined by the radioactive microsphere method. Observed mean tissue transit times were on average longer than predicted by a factor of 6.7. Observed means averaged 52.1 min compared with 8.3 min predicted by the perfusion-limited model. Relative dispersions of tissue transit times were also uniformly larger than predicted. We conclude that Xe gas kinetics in intact canine skeletal muscle are not explained by a model of multiple parallel perfusion-limited compartments. Countercurrent exchange of gas between vessels is a possible explanation.     

Skin blood flow in sheep: comparison of xenon-133 washout and radioactive microsphere techniques

Blood flow was measured in leg and torso skin of conscious or anesthetized sheep by using 15-micron radioactive microspheres (Qm) and the 133Xe washout method (QXe). There was a good relationship between Qm in the cutaneous compartment and QXe calculated from the fast component of the biexponential washout curves (QXe = 0.40.Qm + 6.2, r = 0.90, P less than 0.001) with QXe values substantially below those determined with microspheres. Only at low blood flow levels was there a tendency for QXe to overestimate capillary blood flow as assessed with microspheres, but at higher blood flow levels the 133Xe washout method resulted in values substantially below those determined with microspheres. The slope of the slow component of the washout curves was inversely related to the tissue-blood partition coefficient in the subcutaneous tissue (r = 0.52, P less than 0.001), indicating an influence of the amount of subcutaneous fat on the washout rate. QXe calculated from the slow component of the washout curves was not significantly correlated with Qm in the subcutaneous compartment (r = 0.19, P greater than 0.10). In leg skin with dilated arteriovenous anastomoses, QXe was generally higher than in torso skin and leg skin with constricted arteriovenous anastomoses, indicating that shunt blood flow increases the washout of 133Xe.