The influence of noninstantaneous mixing on the measurement of fluxes of solute and water across a biological membrane

The usual method of tracer analysis for calculating the flow across a biological membrance is based on the assumption that the compartments on either side are well-stirred. Thus, the validity of the rate of flow determination is questionable for cases where the distribution of tracer is not homogeneous. In this study, a mathematical model is developed for the purpose of estimating the effect of slow mixing on the calculation of the flow rate. The model is applied to the measurement of the rate of flow of aqueous humor through the living eye by use of a fluorescent dye as a tracer. A transit time of several minutes for the passage of fluorescein through the posterior chamber and an extended period of nonuniform distribution of fluorescein in the anterior chamber was observed. The effect of slow mixing on the calculated flow rate is compared to rates derived from equations based on the assumption of rapid mixing. Aqueous flow rates determined by the two methods were found to agree to within ≈20%.     

Field Evaluation of Alternative Earthen Final Covers

Five methods to assess percolation rate from alternative earthen final covers (AEFCs) are described in the context of the precision with which the percolation rate can be estimated: trend analysis, tracer methods, water balance method, Darcy's Law calculations, and lysimetry. Trend evaluation of water content data is the least precise method because it cannot be used alone to assess the percolation rate. The precision of percolation rates estimated using tracer methods depends on the tracer concentration, percolation rate, and the sensitivity of the chemical extraction and analysis methods. Percolation rates determined using the water balance method have a precision of approximately 100 mm/yr in humid climates and 50 mm/yr in semiarid and drier climates, which is too large to demonstrate that an AEFC is meeting typical equivalency criterion (30 mm/yr or less). In most cases, the precision will be much poorer. Percolation rates computed using Darcy's Law with measured profiles of water content and matric suction typically have a precision that is about two orders of magnitude (or more) greater than the computed percolation rate. The Darcy's Law method can only be used for performance assessment if the estimated percolation rate is much smaller than the equivalency criterion and preferential flow is not present. Lysimetry provides the most precise estimates of percolation rate, but the precision depends on the method used to measure the collected water. The lysimeter used in the Alternative Cover Assessment Program (ACAP), which is described in this paper, can be used to estimate percolation rates with a precision between 0.00004 to 0.5 mm/yr, depending on the measurement method and the flow rates.     

Some notes on the theory of reaction rates: Enzymatic reactions

A generalized model of an enzymatic reaction in a biological system is used for the construction of a possible model of the “concentrating mechanism” after the introduction of a tracer, and for the formulation of an excretion rate of substances reabsorbed or actively secreted into the urine by the kidneys. In considering this generalized model of the enzymatic reaction, the term “tracer” is used in a limited sense, and it is concluded that a linear system is suitable for the study of the kinetics of the tracer—even in the case when the transport of the tracer between compartments is due to an enzymatic reaction. The rate coefficients of the linear differential systems, which are dependent on the state of the enzymatic system, are functions of the amount of the substrates, as well as of the amounts of activators and inhibitors of the enzymatic reaction and of the amount of the substances, which are responsible for the enzyme production.     

A flow immunoassay for studies of human exposure and toxicity in biological samples

This paper describes a heterogeneous competitive flow immunoassay with a high sample throughput which can be used for the screening of smaller analytes in various samples. The method is based on off-line incubation of the analyte (Ag), a fluorescent labelled tracer (Ag*) and the corresponding antibody (Ab). The separation of bound (Ab-Ag*) and free tracer (Ag*) is based on a size exclusion and reversed phase mechanism utilizing a restricted access (RA) column. The column traps the free unbound tracer (Ag*) in its hydrophobic (C18) inner cavity but excludes the large Ab-Ag* complex, which is passed on and measured by the fluorescence detector. The flow immunoassay was developed using the triazine herbicide atrazine as a model compound owing to its human toxicity and widespread use. A sample throughput of 80 samples per hour and a detection limit of 300 pg ml-1 in water were obtained. Urine samples were successfully applied for direct injections into the flow system, while for human plasma samples an additional clean-up step using solid phase extraction was efficiently included where pure extract is obtained with the highly stable and biocompatible extracting column material. The resulting detection limits for atrazine in plasma and water samples using this clean-up and trace enrichment procedure were found to be 2 ng ml-1 and 20 pg ml-1 respectively.     

Rate of incorporation of CO2 carbon into glucose and other body constituents in vivo.

Specific activity curves of respired CO2 and of body glucose after intravenous NaH14CO3 as tracer and, in separate experiments, after [U-14C]glucose as tracer were employed to assess rate of interchange of carbon between HCO3 and glucose, and to calculate other rates of input and output for each of these substances. Solution for six rates attending the model was by integrals rather than by curve analysis. Fasting caused a twofold increase in rate of transport of CO2 carbon to glucose. Whereas in fed animals this rate was only 7% of the forward flow from glucose to CO2, it rose to 31% during fasting. Glucose carbon derived from CO2 rose from 3.7 to 20%. As expected, the rates of entry of new glucose to blood, and the conversion rate of glucose to products in body depots and to CO2 were reduced by fasting, whereas, the non-glucose input to CO2 was increased. Fasting was attended by a 20-fold increase in rate of conversion of CO2-derived carbon to hepatic glycogen and a fourfold increase to non-hepatic glycogen. Protein exceeded all whole-body depots for rate of acceptance of such carbon, and total lipids received an appreciable amount, but fasting caused no overall increase for either.     

COMPARISON OF TWO SIMPLE METHODS FOR THE MEASUREMENT OF DETECTION THRESHOLDS FOR BASIC, UMAMI AND METALLIC TASTES

Two simple methods were followed to determine detection thresholds for the taste of substances in aqueous solution. The methods applied were: a modification of the ascending method of limits and a method based on the use of scales. Detection thresholds were calculated for the four basic tastes (sweet, salty, acid, and bitterness), umami and metallic. Reference substances for each taste were sucrose, sodium chloride, citric acid, caffeine, monosodium glutamate and iron (II) sulfate heptahydrate and the results of the two methods were compared. We found that the threshold values calculated by method ASTM-679 was within the range of concentrations identified with the scales method.     

A model for measurement of lactate disappearance with isotopic tracers in the steady state.

1. The irreversible disappearance of lactate carbon from the body (RdL) is commonly calculated from data obtained with a continuous infusion of isotopically labelled lactate tracer. The tracer infusion rate divided by the steady-state lactate specific radioactivity in blood is taken to give the rate of lactate disappearance. 2. Measurement of lactate disappearance is complicated by the fact that it is reversibly converted into pyruvate as well as being irreversibly removed from the system. 3. We analysed a four-compartment model of lactate metabolism, representing blood lactate, tissue lactate and pyruvate carbon pools. 4. The standard method of calculating RdL from the lactate tracer infusion rate divided by the specific radioactivity of lactate was not validated. 5. We found that RdL can be calculated from the infusion rate and the pyruvate specific radioactivity, multiplied by the fraction of the total carbon flow out of pyruvate that goes to lactate. 6. Therefore, if almost all of the pyruvate carbon flows back to lactate, then RdL approaches the tracer infusion rate divided by the pyruvate specific radioactivity. On the other hand, if the rate of oxidation is large in relation to the rate of pyruvate conversion into lactate, than RdL is overestimated when calculated from the pyruvate specific radioactivity. 7. Calculation of RdL with the arterial lactate specific radioactivity results in an underestimate of the true RdL.     

Estimation of glucose production during exercise with a one-compartment variable-volume model.

A variable-volume one-compartment model of glucose kinetics and step increases in the rate of tracer infusion were examined for estimation of endogenous glucose production (Ra) during moderate exercise in dogs. A primed infusion of D-[3-3H]glucose was left constant or increased 1.5-, 2-, 3-, 4-, or 5-fold at the onset of a 60-min period of exercise. Application of a regression method, in which Ra and the effective distribution volume were estimated over time, revealed dynamic changes in Ra that were not evident during the constant tracer infusion with a fixed-volume model. Application of the fixed-volume model to studies performed with a two- or three-fold step increase in tracer resulted in the lowest sum-of-squares difference from the regression method. Our results demonstrate that application of a variable-volume model can be achieved during exercise by enrichment of the plasma specific activity through step increases in the rate of tracer infusion and application of a regression method. Alternately, estimates of Ra with a fixed-volume model can be improved by enrichment of the plasma specific activity through a single step increase in the rate of tracer infusion. Our results suggest that when endogenous Ra is changing rapidly, such as at the onset of exercise, these methods will provide a more accurate estimate of Ra than the standard fixed-volume model and constant tracer infusion.     

A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone

Interstitial fluid flow through the lacunocanalicular cavities of mechanically loaded bone provides the biophysical basis for a number of postulates regarding mechanotransduction in bone. Recently, the existence of load-induced fluid flow and its influence on molecular transport through bone has been confirmed using tracer methods to visualize fluid flow induced by in vivo four-point-bending of rat tibiae. In this paper, we present a theoretical two-stage approach for the calculation of load-induced flow fields and for the evaluation of their influence on molecular transport in bone loaded in four-point bending, analogous to the aforementioned experimental model. In the first stage, the fluid velocities are calculated using a three-dimensional, poroelastic finite element model. In the second stage, mass transport analysis, this calculated fluid flow serves as a forced convection flow and its contribution to the total transport potential is determined. Based on this combined approach, the overall tracer concentration in the loaded bone is significantly higher than that in the unloaded bone. Furthermore, augmentation of mass transport through convective flow is more pronounced in the tension band of the tissue, as compared to the compression band. In general, augmentation of tracer concentration via convective mechanisms is most pronounced in areas corresponding to lowest fluid velocities, which is indicative of fluid flow direction and areas of increased "dwell time" or accumulation during the loading cycle. This theoretical model, in combination with the corresponding experimental model, provides unique insight into the role of mechanical loads in modulating local flow distributions and concentration gradients within bone tissue.     

Acute responses of muscle protein metabolism to reduced blood flow reflect metabolic priorities for homeostasis

The present experiment was designed to measure the synthetic and breakdown rates of muscle protein in the hindlimb of rabbits with or without clamping the femoral artery. l-[ring-(13)C(6)]phenylalanine was infused as a tracer for measurement of muscle protein kinetics by means of an arteriovenous model, tracer incorporation, and tracee release methods. The ultrasonic flowmeter, dye dilution, and microsphere methods were used to determine the flow rates in the femoral artery, in the leg, and in muscle capillary, respectively. The femoral artery flow accounted for 65% of leg flow. A 50% reduction in the femoral artery flow reduced leg flow by 28% and nutritive flow by 26%, which did not change protein synthetic or breakdown rate in leg muscle. Full clamp of the femoral artery reduced leg flow by 42% and nutritive flow by 59%, which decreased (P < 0.05) both the fractional synthetic rate from 0.19 +/- 0.05 to 0.14 +/- 0.03%/day and fractional breakdown rate from 0.28 +/- 0.07 to 0.23 +/- 0.09%/day of muscle protein. Neither the partial nor full clamp reduced (P = 0.27-0.39) the intracellular phenylalanine concentration or net protein balance in leg muscle. We conclude that the flow threshold to cause a fall of protein turnover rate in leg muscle was a reduction of 30-40% of the leg flow. The acute responses of muscle protein kinetics to the reductions in blood flow reflected the metabolic priorities to maintain muscle homeostasis. These findings cannot be extrapolated to more chronic conditions without experimental validation.     

Translational and rotational motions of proteins in a protein crowded environment

Fluorescence correlation spectroscopy (FCS) was used to measure the translational diffusion of labeled apomyoglobin (tracer) in concentrated solutions of ribonuclease A and human serum albumin (crowders), as a quantitative model system of protein diffusive motions in crowded physiological environments. The ratio of the diffusion coefficient of the tracer protein in the protein crowded solutions and its diffusion coefficient in aqueous solution has been interpreted in terms of local apparent viscosities, a molecular parameter characteristic for each tracer-crowder system. In all protein solutions studied in this work, local translational viscosity values were larger than the solution bulk viscosity, and larger than rotational viscosities estimated for apomyoglobin in the same crowding solutions. Here we propose a method to estimate local apparent viscosities for the tracer translational and rotational diffusion directly from the bulk viscosity of the concentrated protein solutions. As a result of this study, the identification of protein species and the study of hydrodynamic changes and interactions in model crowded protein solutions by means of FCS and time-resolved fluorescence depolarization techniques may be expected to be greatly simplified.     

Solution-flow in the Phloem: I. Theoretical considerations

A mathematical model for the reversible exchange of THO between the sieve tube lumen and its surrounding phloem tissue is used to explain the difference between the apparent velocities of THO and ¹⁴C-sucrose transport observed when both are supplied simultaneously. Theoretically predicted results show a close correlation with those obtained experimentally. This model may be used in evaluating previous work in which THO was used as a tracer. The calculations support the existence of a mass flow of sugars in aqueous solution along the path.     

Instabilities,bifurcations and fluctuations in chemical systems : L. E. Reichl and W. C. Schieve University of Texas Press, 1982, xi+427 pp, $35.00

The occupancy principle and the mean-transit-time theorem are derived for the passage of a tracer through a system that can be described by a general pool model. It is proved, using matrix theory, that if (and only if) tracer entering the system labels equally all tracee fluxes into the system, then the integral of the tracer concentration is the same in all the pools. It is also proved that if, in addition, all flow out of the system is through the observation point, the first moment of the tracer concentration at the observation point can be used to calculate the total amount of trace in the system. The necessity of this condition is analyzed. Examples are given of models in which the occupancy principle and the mean-transit-time theorem hold or do not hold.     

Robust nonlinear parameter estimation in tracer kinetic analysis using infinity norm regularization and particle swarm optimization

In positron emission tomography (PET) studies, the voxel-wise calculation of individual rate constants describing the tracer kinetics is quite challenging because of the nonlinear relationship between the rate constants and PET data and the high noise level in voxel data. Based on preliminary simulations using a standard two-tissue compartment model, we can hypothesize that it is possible to reduce errors in the rate constant estimates when constraining the overestimation of the larger of two exponents in the model equation. We thus propose a novel approach based on infinity-norm regularization for limiting this exponent. Owing to the non-smooth cost function of this regularization scheme, which prevents the use of conventional Jacobian-based optimization methods, we examined a proximal gradient algorithm and the particle swarm optimization (PSO) through a simulation study. Because it exploits multiple initial values, the PSO method shows much better convergence than the proximal gradient algorithm, which is susceptible to the initial values. In the implementation of PSO, the use of a Gamma distribution to govern random movements was shown to improve the convergence rate and stability compared to a uniform distribution. Consequently, Gamma-based PSO with regularization was shown to outperform all other methods tested, including the conventional basis function method and Levenberg–Marquardt algorithm, in terms of its statistical properties.     

PET脑血流量测量方法和临床应用进展

脑血流量测量对于脑血管疾病、脑肿瘤诊断和疗效评估具有重要的临床价值。PET是基于正电子示剂技术无创性、精确测量脑血流量的方法,正日益广泛地应用于临床。按照PET测量脑血流量的方法和使用的正电子示踪剂不同,其测量方法分为平衡法、放射自显影法和动力学方法三种。18O-H2O示踪剂PET测量脑血流量被认为测量脑血流方法的"金标准"。随着PET设备分辨率提高、新的图像重建方法使用和PET与MRI图像融合技术不断成熟,18F-FDG首次通过、采用图像衍生动脉输入函数(imagederived arterial input function,IDAIF)替代动脉抽血样精确测量脑血量方法受到广泛重视,有可能逐步取代高成本的18O-H2O测量脑血流量。PET无创、方便和精确测量脑血流量的方法在临床应使用有助于脑血管性疾病、脑肿瘤和脑退行性病变早期诊断、鉴别诊断和个性化医疗。本文介绍PET脑血流量测量原理、方法和临床应用进展。     

Applications of a Serratia marcescens bacteriophage as a new microbial tracer of aqueous environments

A bacteriophage of Serratia marcescens was evaluated as a tracer in three appropriate aqueous environments and compared with an accepted tracer in two cases. The phage compared favourably with lithium chloride in demonstrating flow characteristics and retention times of various stages in the sewage treatment process. The phage exhibited virtually identical distribution in a marine harbour to spores of Bacillus subtilis var. niger (' B. globigii ') 36–48 h after their addition to a sewage works' final effluent which entered an adjacent bay. Transit times of river water were accurately measured between two points under various flow conditions.     

Synthesis, turnover and compartment analysis of the free fatty acids in the placenta of rats.

The in vivo tracer method and in vitro acetate incorporation experiments were used to investigate the metabolism of placental free fatty acids. Analysis of data revealed that free fatty acids pass into the fetus from maternal plasma through a small placental compartment, which accounts for only 5 percent of all of the placental free fatty acids. The turnover time of this compartment is 0.57 min. The rate of placental fatty acid synthesis evaluated by both methods is very small and amounts to 0.003 mumols fatty acids/min/all placentas of one litter.     

A Comparison of the Heat Pulse Method and Deuterium Tracing Method for Measuring Transpiration from Eucalyptus grandis Trees

Estimates of transpiration obtained with the heat pulse velocity(HPV) method and the deuterium tracing method were comparedin two Eucalyptus grandis Hill ex Maiden trees aged 18 monthsand 4 years, respectively. The HPV estimate of weighted meandaily flow rate differed from the deuterium mean by 7% in theolder tree, and 35% in the younger tree. An analysis of possiblesources of error revealed that the discrepancy in the youngertree may have arisen as a result of inadequate probe espacementradially through the sapwood, or from sapwood disruption causedwhen holes were drilled to release the tracer. We conclude thatthe two methods can provide very similar estimates of mean weightedtranspiration rate in E. grandis trees if due precautions aretaken to minimize known sources of error. The relative meritsof the two techniques, which in many respects are complementary,are discussed. Key words: Eucalyptus grandis, heat pulse velocity, deuterium, tracer, transpiration     

Body weight,metabolic rate,and trace substance turnover in animals

Summary Consequences of size-dependent metabolic rate on the turnover of trace substances in animals are investigated. At steady state, the biological half-life, body burden, and whole body concentration of a trace substance are shown to be proportional to body weight raised to (1-b), 1, and 0, respectively, where b is the exponent relating body weight to standard metabolic rate. The condition is that the trace substance is turned over in proportion to the standard metabolic rate; the derived equations can accordingly be used to test whether a given substance is feasible as a tracer of energy flow in ecologic systems.     

Binding and distribution of three prototype calcium channel blockers in perfused rat liver

This work represents a study of the binding and distribution of three different calcium channel blockers in the Sprague-Dawley rat liver, using an in situ perfusion technique. For this purpose, [3H] desmethoxyverapamil, [3H] PN200-110 (isradipine) and [3H] azidopine were used as binding probes interacting with calcium channels. The perfusion steps of the liver involved both portal vein and thoracic inferior vena cava cannulations as inlet and outlet respectively. The subhepatic inferior vena cava was ligated to prevent leakage of the perfusate. Buffer, containing the tracer drug, was administered via the portal vein at a rate of l mL/min and perfusate collected at the same rate within specified time intervals during 50 min. The concentration of the tracer solutes in the perfusate's outlet increased with time, and steady state was observed for all tracers at 40 min. The effect of adding cold isradipine to tracer desmethoxyverapamil, or cold verapamil to tracer PN200-110 were also assessed. First order rate constants for hepatocellular influx, efflux and calcium channel binding of the tracer substances were obtained using a simplified model from Goresky et al. [25]. These constants were mathematically manipulated and changed into permeability constants, second order binding constants, and residency times.Tracer solute influx across hepatocellular membranes is solubility-diffusion controlled, is inversely related to the molecular weights and is different in value from the efflux constants. Cold isradipine reduced the binding constant of desmethoxyverapamil by 36%, while cold verapamil reduced the binding constant of PN200-110 by 23%. Azidopine cellular distribution was low, however, binding to its receptor was analogous to desmethoxyverapamil and PN200-110. Moreover, PN200-110 had the highest residency time with no effect of cold verapamil on its receptor binding, while desmethoxyverapamil had the lowest residency time which significantly increased in the presence of cold isradipine.