Kinetics of glucose transport and sequestration in lactating bovine mammary glands measured in vivo with a paired indicator/nutrient dilution technique.

To quantify kinetics of mammary glucose utilization in vivo, 24 paired glucose and extracellular indicator (p-aminohippuric acid) dilution curves across intact bovine mammary glands were obtained after bolus injections into the external iliac artery. Dilution curves were analyzed using a compartmental capillary, convolution integration model. Four candidate submodels of glucose transport and metabolism in capillary supply zones were fit to the glucose dilution curves and evaluated. Model I, with one extracellular compartment for glucose and first-order unidirectional uptake, failed, indicating that efflux of glucose from the intracellular space could not be ignored. Model II, with first-order exchanges between extracellular and intracellular compartments and sequestration from the latter, was overdefined because unidirectional clearance of glucose was at least five times the blood flow rate and 20 times the net clearance rate. Model III, combining extracellular and intracellular space into one compartment, was superior in its goodness-of-fit to curves and identifiability of parameters. Michaelis-Menten parameters of sequestration were not identifiable. Parameters of the optimal compartmental capillary, convolution integration model were applicable to both the dynamics of injected glucose dilution and the steady-state background arteriovenous difference of glucose. Glucose sequestration followed first-order kinetics between 0 and 7 mM extracellular glucose with an average rate constant of 0.006 s(-1) or a clearance of 44 ml/s. The ratio of intracellular to extracellular glucose distribution space was 0.34, which is considerably lower than the expected intracellular volume and suggests an intracellular occlusion compartment with which extracellular glucose rapidly exchanges.     

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.     

Transit time dispersion in pulmonary and systemic circulation: effects of cardiac output and solute diffusivity

We present an in vivo method for analyzing the distribution kinetics of physiological markers into their respective distribution volumes utilizing information provided by the relative dispersion of transit times. Arterial concentration-time curves of markers of the vascular space [indocyanine green (ICG)], extracellular fluid (inulin), and total body water (antipyrine) measured in awake dogs under control conditions and during phenylephrine or isoproterenol infusion were analyzed by a recirculatory model to estimate the relative dispersions of transit times across the systemic and pulmonary circulation. The transit time dispersion in the systemic circulation was used to calculate the whole body distribution clearance, and an interpretation is given in terms of a lumped organ model of blood-tissue exchange. As predicted by theory, this relative dispersion increased linearly with cardiac output, with a slope that was inversely related to solute diffusivity. The relative dispersion of the flow-limited indicator antipyrine exceeded that of ICG (as a measure of intravascular mixing) only slightly and was consistent with a diffusional equilibration time in the extravascular space of approximately 10 min, except during phenylephrine infusion, which led to an anomalously high relative dispersion. A change in cardiac output did not alter the heterogeneity of capillary transit times of ICG. The results support the view that the relative dispersions of transit times in the systemic and pulmonary circulation estimated from solute disposition data in vivo are useful measures of whole body distribution kinetics of indicators and endogenous substances. This is the first model that explains the effect of flow and capillary permeability on whole body distribution of solutes without assuming well-mixed compartments.     

Extension of the theory of the multiple-indicator dilution technique to metabolic systems with an arbitrary number of rate constants

The multiple indicator dilution technique consists in the instantaneous injection of a mixture of tracers into the arterial perfusate flow of a catheterized or isolated perfused organ, followed by the analysis of the effluent perfusate. The theory of this technique, which has hitherto been developed for cases where metabolism of a tracer is confined to sequestration described by a single rate constant, is extended in this paper to include an arbitrary number of metabolic rate constants. Partial differential equations with constant coefficients describing the events in a single capillary are derived by applying conventional compartmental analysis to infinitesimally small sections of the capillary. Methods for solving such systems in the time as well as in the frequency domain are developed. From the solutions, the impulse response of the whole organ is evaluated assuming variable capillary and uniform large-vessel transit times. In addition, an efficient method using much less computer time was developed, based on the approximation of the distribution of the capillary transit times by a sum of exponentials. Evaluation of moments (recoveries and mean transit times) is also treated. The results are applied to an example from hepatic lactate metabolism.     

Mathematical analysis of circulatory mixing process

The circulatory mixing process was analyzed as the time course of the dispersion of indicator after its injection into the heart. In simplified models, which had one or two lumped mixing chambers and circulatory pathways connected with them, it was suggested that the extent of dispersion could be evaluated by the variance of indicator distribution in the total circulating blood when the circulation time distributions between the chambers and the concentration curves in the chambers were known. The method of determining the circulation time distributions through the pulmonary, systemic and total circulations was derived and the actual distributions were obtained in dogs by indicator dilution techniques. With the use of these distributions, the time course of the circulatory mixing process was numerically calculated. The results showed that there was considerable difference in velocities of the process between the case of the right heart injection and the left heart injection of the indicator.     

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.     

The identification of transport parameters from truncated physiological tracer curves

The primary data curves from the injection of tracers into the circulation are often obscured by the appearance of a recirculation hump. Previous techniques for parameter identification in the presence of such a complication have been extended from compartmental models to include circulatory models consisting of partial differential equations of the Taylor dispersion and Turner capacitance types. A comparative analysis of the efficiency of parameter identification by several computational strategies is presented.     

Indicator dilution measurements of extravascular lung water: basic assumptions and observations

Since they were introduced more than five decades ago, a variety of single-pass indicator, thermal, and osmotic dilution approaches have been developed for detecting and measuring excess fluid in the lungs. This brief review discusses why studies of the extravascular lung water (EVLW) continue to intrigue physiologists and clinicians and the likelihood that they will become sufficiently reliable for more widespread use. Emphasis is placed on the basic assumptions that underlie these measurements and limitations imposed by the nature of the data that are collected. A distinction is made between approaches that are based on compartmental models of solute and water exchange and those that represent extensions of more conventional washout procedures, which have been utilized extensively for measurements of gas volumes in the lungs. Although the compartmental approach has been used to simplify indicator dilution studies by eliminating the need for a vascular indicator, it is based on assumptions that may not be realistic. Early recirculation inevitably limits the period in which observations can be made and impairs detection of those portions of the lungs with decreased perfusion. These general principles are also used to develop a new method of analyzing osmotic transient studies. A short account is given of EVLW observations that have been made in animals and humans. Both the sensitivity and specificity of EVLW measurements in humans are uncertain, and the normal clinical range of EVLW remains in doubt.     

Understanding respirometry chambers: what goes in must come out

An examination of the compartmental dilution washout in metabolic chambers was conducted and new equations for the calculation of "instantaneous" VO2 were derived. Using appropriate compartmental models, an evaluation was carried out on systems used in previous estimates of this parameter. Effects of chamber mixing and sampling times on calculated VO2 values were also examined. Alternatives to resolving "instantaneous" VO2 are presented with emphasis on system design rather than on mathematical manipulation.     

Model of gas transport during high-frequency ventilation

We analyze gas exchange during high-frequency ventilation (HFV) by a stochastic model that divides the dead space into N compartments in series where each compartment has a volume equal to tidal volume (V). We then divide each of these compartments into alpha subcompartments in series, where each subcompartment receives a well-mixed concentration from one compartment and passes a well-mixed concentration to another in the direction of flow. The number of subcompartments is chosen on the basis that 1/alpha = (sigma t/-t)2, where -t is mean transit time across a compartment of volume, and sigma t is standard deviation of transit times. If (sigma t/-t)D applies to the transit times of the entire dead space, the magnitude of gas exchange is proportional to (sigma t/-t)D, frequency, and V raised to some power greater than unity in the range where V is close to VD. When V is very small in relation to VD, gas exchange is proportional to (sigma t/-t)2D, frequency, and V raised to a power equal to either one or two depending on whether the flow is turbulent or streamline, respectively. (sigma t/-t)D can be determined by the relation between the concentration of alveolar gas at the air outlet and volume expired as in a Fowler measurement of the volume of the dead space.     

Fluid volumes in rainbow trout, Salmo gairdneri: application of compartmental analysis

1. The measurement of fluid volumes by the indicator dilution technique and compartmental analysis was re-evaluated in free-swimming, undisturbed rainbow trout. 2. Plasma (33.5 ml/kg body wt) and blood (41.3 ml/kg body wt) volumes estimated by compartmental analysis from blood samples taken early (less than 5 min) after dye injection were 40% lower than volumes calculated by sampling late (greater than or equal to 80 min). 3. The rate of exchange of dye between plasma and interstitial fluid was high (48%/hr) compared to mammals (5%/hr) which supports the hypothesis that teleost capillaries have high protein permeability. 4. Total extracellular volume estimated using a single pool model (210.5 ml/kg body wt) of inulin kinetics was 20% higher than that calculated by a three pool model (172.8 ml/kg body wt).     

A mathematical model of indicator extraction by the pulmonary endothelium via saturation kinetics

When a bolus containing a nonpermeating indicator and an indicator which permeates the endothelial cell membrane by a saturable process is injected into the blood flowing into the lung, the instantaneous extraction ratio curves measured in the pulmonary venous outflow are asymmetric with respect to the nonpermeating indicator curve. If the bolus contains a sufficient quantity of the permeating indicator that the capillary concentration begins to saturate the transfort mechanism, the extraction ratio curves are concave upward as well. The purpose of this study was to determine whether a mathematical model which represents endothelial extraction by Michaelis-Menten kinetics could explain the time variation in the instantaneous extraction ratio curves. The venous concentration curves were assumed to be the result of the endothelial transfort and distributed capillary input and transit times. In addition, we evaluated a method for estimating the kinetic parameters (K_m and V_max) of the saturable transfort process in such an organ. The results of simulations indicate that the important features of the data can be reproduced by the model, and that useful estimates of the kinetic parameters will be obtained from linear multiple regression analysis of the venous concentration curves if the standard deviation of the capillary input time distribution is not less than that of the capillary transit time distribution.     

Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling

We consider plankton-nutrient interaction models consisting of phytoplankton, herbivorous zooplankton and dissolved limiting nutrient with general nutrient uptake functions and instantaneous nutrient recycling. For the model with constant nutrient input and different constant washout rates, conditions for boundedness of the solutions, existence and stability of non-negative equilibria, as well as persistence are given. We also consider the zooplankton-phytoplankton-nutrient interaction models with a fluctuating nutrient input and with a periodic washout rate, respectively. It is shown that coexistence of the zooplankton and phytoplankton may arise due to positive bifurcating periodic solutions.Research has been supported in part by a University of Alberta Ph.D. Scholarship and is in part based on the author's Ph.D. thesis under the supervision of Professor H. 1. Freedman, to whom the author owes a debt of appreciation and gratitude for his kind advice, helpful comments and continuous encouragement     

The dispersion of indicator in the cardio-pulmonary system

This paper presents a three-parameter model of the mechanism of dispersion of an indicator in the cardio-pulmonary system, based on the postulates that this dispersion can be described by the one-dimensional diffusion equation and that dispersion continues past the sampling site. The model is tested using indicator dilution curves obtained from dogs, and the coefficient of diffusion is thus measured. It is found that this coefficient increases in magnitude non-linearly with increasing blood speed.     

Increased expression of MDM2, cyclin D1, and p27Kip1 in carcinogen-induced rat mammary tumors

It is thought that environmental pollutants, such as polycyclic aromatic hydrocarbons (PAH), contribute to human breast tumorigenesis, yet their roles remain incompletely elucidated. The prototypical PAH 7,12-dimethylbenz(alpha)anthracene (DMBA) specifically and effectively induces mammary tumor formation in rodent models. In an attempt to explore the molecular mechanisms by which PAH initiates and promotes mammary tumorigenesis, we examined the expression of several cell cycle regulators in rat mammary tumors induced by DMBA. Expression of cyclin D1, murine double minute-2 (MDM2), and Akt was up-regulated in tumors in comparison to normal mammary glands, as indicated by RT-PCR, Western blot analysis, and immunohistochemical staining. Expression of p27Kip1 protein was also elevated in the tumors with increased cytoplasmic localization. However, RB protein remained hyperphosphorylated. To directly test the effects of DMBA, the MCF-7 human breast cancer cells were treated. DMBA induced MDM2 expression in a dose- and time-dependent fashion in the MCF-7 cells, and this activation appeared to be p53 dependent. These data suggest that activation of cyclin D1, MDM2, and AKT as well as increased expression and cytoplasmic localization of p27Kip1 may play a role in this model of environmental pollutant-induced mammary tumorigenesis.     

Effects of Age and Parity on Mammary Gland Lesions and Progenitor Cells in the FVB/N-RC Mice

The FVB/N mouse strain is extensively used in the development of animal models for breast cancer research. Recently it has been reported that the aging FVB/N mice develop spontaneous mammary lesions and tumors accompanied with abnormalities in the pituitary glands. These observations have a great impact on the mouse models of human breast cancer. We have developed a population of inbred FVB/N mice (designated FVB/N-RC) that have been genetically isolated for 20 years. To study the effects of age and parity on abnormalities of the mammary glands of FVB/N-RC mice, twenty-five nulliparous and multiparous (3-4 pregnancies) females were euthanized at 16-22 months of age. Examination of the mammary glands did not reveal macroscopic evidence of mammary gland tumors in either aged-nulliparous or multiparous FVB/N-RC mice (0/25). However, histological analysis of the mammary glands showed rare focal nodules of squamous changes in 2 of the aged multiparous mice. Mammary gland hyperplasia was detected in 8% and 71% of the aged-nulliparous and aged-multiparous mice, respectively. Epithelial contents and serum levels of triiodothyronine were significantly higher in the experimental groups than the 14-wk-old control mice. Immuno-histochemical staining of the pituitary gland pars distalis showed no difference in prolactin staining between the control and the aged mice. Tissue transplant and dilution studies showed no effect of age and/or parity on the ability of putative progenitor cells present among the injected mammary cells to repopulate a cleared fat pad and develop a full mammary gland outgrowth. This FVB/N-RC mouse substrain is suitable to develop mouse models for breast cancer.     

Transit time dispersion in the pulmonary arterial tree

Knowledge of the contributions of arterialand venous transit time dispersion to the pulmonary vascular transittime distribution is important for understanding lung function and forinterpreting various kinds of data containing information aboutpulmonary function. Thus, to determine the dispersion of blood transittimes occurring within the pulmonary arterial and venous trees, imagesof a bolus of contrast medium passing through the vasculature ofpump-perfused dog lung lobes were acquired by using an X-ray microfocalangiography system. Time-absorbance curves from the lobar artery andvein and from selected locations within the intrapulmonary arterial tree were measured from the images. Overall dispersion within the lunglobe was determined from the difference in the first and second moments(mean transit time and variance, respectively) of the inlet arterialand outlet venous time-absorbance curves. Moments at selected locationswithin the arterial tree were also calculated and compared with thoseof the lobar artery curve. Transit times for the arterial pathwaysupstream from the smallest measured arteries (200-µm diameter) wereless than ~20% of the total lung lobe mean transit time. Transittime variance among these arterial pathways (interpathway dispersion)was less than ~5% of the total variance imparted on the bolus as itpassed through the lung lobe. On average, the dispersion that occurredalong a given pathway (intrapathway dispersion) was negligible. Similar results were obtained for the venous tree. Taken together, the resultssuggest that most of the variation in transit time in theintrapulmonary vasculature occurs within the pulmonary capillary bedrather than in conducting arteries or veins.

     

Kinetic measurements of gas exchange in the intact pulmonary microcirculation.

The kinetics of gas exchange are monitored in an isolated perfused lung preparation contained within a plethysmograph. The lungs are perfused with buffer, and there is no gas exchange until a 2.0-ml bolus of reactant is injected into the perfusion system. Subsequent gas exchange produces a pressure transient that is related to the corresponding volume of exchanged gas. The observed rate of volume change is the result of two separate processes: 1) the rate of gas exchange during transit through the capillary bed and 2) the distribution of vascular transit times between the point of injection and the capillary bed. The latter is assessed by a control injection containing a dissolved inert gas that is liberated in the alveoli as the bolus enters the capillary bed. Analysis of the experimental curves permits the separation of these two processes. A model of exchange kinetics indicates that this method has the capability of measuring kinetic events occurring during gas exchange in the microcirculation under physiological conditions.     

Effects of lung inflation and blood flow on capillary transit time in isolated rabbit lungs.

In a previous study, direct measurements of pulmonary capillary transit time by fluorescence video microscopy in anesthetized rabbits showed that chest inflation increased capillary transit time and decreased cardiac output. In isolated perfused rabbit lungs we measured the effect of lung volume, left atrial pressure (Pla), and blood flow on capillary transit time. At constant blood flow and constant transpulmonary pressure, a bolus of fluorescent dye was injected into the pulmonary artery and the passage of the dye through the subpleural microcirculation was recorded via the video microscope on videotape. During playback of the video signals, the light emitted from an arteriole and adjacent venule was measured using a video photoanalyzer. Capillary transit time was the difference between the mean time values of the arteriolar and venular dye dilution curves. We measured capillary transit time in three groups of lungs. In group 1, with airway pressure (Paw) at 5 cmH2O, transit time was measured at blood flow of approximately 80, approximately 40, and approximately 20 ml.min-1.kg-1. At each blood flow level, Pla was varied from 0 (Pla less than Paw, zone 2) to 11 cmH2O (Pla greater than Paw, zone 3). In group 2, at constant Paw of 15 cmH2O, Pla was varied from 0 (zone 2) to 22 cmH2O (zone 3) at the same three blood flow levels. In group 3, at each of the three blood flow levels, Paw was varied from 5 to 15 cmH2O while Pla was maintained at 0 cmH2O (zone 2).(ABSTRACT TRUNCATED AT 250 WORDS)