Kenneth Zierler

Theoretical Basis of Indicator-Dilution Methods For Measuring Flow and Volume

• The purpose here is to inquire into the justification of the use of the indicator-dilution principle for measurement of fluid flow and volume. What is the validity of the formal expressions? Upon what assumptions are they based? What are the effects of specified violations of these assumptions? An indicator, in the sense used here, is a substance that permits observations of some element of volume of the fluid under study. The indicator shows the position of the element of volume in space and with respect to time, and distinguishes the indicated element from all other elements of volume. In practice, a known quantity of indicator is introduced into a fluid flowing at unknown rate through a system of unknown volume. Fluid is sampled or monitored at one or more points downstream from the plane of introduction and the concentration of indicator, diluted by the parent fluid, is measured as a function of time. Indicator may be introduced into the system in any of a number of ways, usually either only once as rapidly as possible (sudden injection) or continuously at constant rate (constant injection). It is claimed that from a knowledge only of the quantity of indicator injected (or of the rate of its injection for the case of constant injection) and of the observed concentration of diluted indicator at the sampling site, over appropriate time intervals, both flow and volume can be calculated. The validity of this statement has been argued effectively by Stewart,Hamilton and his colleagues, StephenDepartment of Medicine, The Johns Hopkins University School of Medicine, Baltimore, Maryland. Original studies described here have been aided by a contract between the Office of Naval Research, Department of the Navy, and The Johns Hopkins University (NE 101-241), and by a grant from the National Institute of Arthritis and Metabolic Disease (A-750). Reproduction in whole or in part is permitted for any purpose of the United States Government. son, Sheppard, Meier and Zierler, and Burger and colleagues. The argument that follows is adapted from one given previously 8, 10, 11

Whole body glucose metabolism

This review describes major factors that, singly or together, influence the concentration and distribution of D-glucose in mammals, particularly in humans, with emphasis on rest, physical activity, and alimentation. It identifies areas of uncertainty: distribution and concentrations of glucose in interstitial fluid, kinetics and mechanism of transcapillary glucose transport, kinetics and mechanism of glucose transport via its transporters into cells, detailed mechanisms by which hormones, exercise, and hypoxia affect glucose movement across cell membranes, whether translocation of glucose transporters to the cell membrane accounts completely, or even mainly, for insulin-stimulated glucose uptake, whether exercise stimulates release of a circulating insulinomimetic factor, and the relation between muscle glucose uptake and muscle blood flow. The review points out that there is no compartment of glucose in the body at which all glucose is at the same concentration, and that models of glucose metabolism, including effects of insulin on glucose metabolism based on assumptions of concentration homogeneity, cannot be entirely correct. A fresh approach to modeling is needed.

Indicator Dilution Methods for Measuring Blood Flow, Volume, and Other Properties of Biological Systems: A Brief History and Memoir

In 1824 Hering introduced an indicator-dilution method for measuring blood velocity. Not until 1897 was the method extended by Stewart to measure blood (volume) flow. For more than two decades, beginning in 1928, Hamilton and colleagues measured blood flow, including cardiac output. They proposed that the first-passsage indicator concentration-time curve could be recovered from observed curves that included recirculation by semilogarithmic extrapolation of the early downslope. Others followed with attempts to fit the complete first-passage curve by various forms, such as by the sum of three exponential terms (three well-stirred compartments in series). Stephenson (1948) thought of looking at indicator-dilution curves as convolutions of indicator input with a probability density function of traversal times through the system. Meier and I reached a similar conclusion, and extended it. The fundamental notion is that there exists a probability density function of transit times, h(t), through the system. We proved that mean transit time t=V/F, where V is volume in which the indicator is distributed. Thus, V, F, and t might all be calculated, or t alone might suffice if one wanted only to know relative blood flow. I extended the analysis to include residue detection of indicator remaining in the system, so that V, F, and t could be calculated by external monitoring. Chinard demonstrated the value of simultaneous multiple indicator-dilution curves with various volumes of distribution. Goresky extended the technique to study cell uptake and metabolism. He also found a transform of indicator-dilution output curves (equivalent to multiplying the ordinate by t and dividing the time by t) which made congruent the family of unalike curves obtained by simultaneous injection of indicators with different volumes of distribution. Bassingthwaighte showed the same congruency with the transform of outputs of a single indicator introduced into a system with experimentally varied blood flows. We showed the same congruency for the pulmonary circulation, adding a correction for delays. Success of these transforms suggests that the architecture of the vascular network is a major determinant of the shape of density functions of transit times through the system, and that there is in this architecture, a high degree of self-similarity, implying that the fractal power function is a component in shaping the observed density of transit times. I proposed that the distribution of capillary critical opening pressures, which describes recruitment of vascular paths, may be important in shaping indicator-dilution curves, and that h(t) may be derived from flow-pressure and volume-pressure curves under some circumstances.

Misuse of nonlinear scatchard plots

Scatchard plots--plots of bound/free ligand vs bound ligand--are a common graphical presentation of binding data. They are often nonlinear. Despite examples of correct usage and several articles calling attention to incorrect treatment of Scatchard plots, erroneous interpretations of nonlinear Scatchard plots remain frequent; plots are resolved incorrectly into two or more linear components which have no relation to an acceptable binding model. Correct analysis requires determination, usually by computer, of numerical values of the binding parameters that give the best nonlinear fit to an appropriate model, examples of which are specified.

β-adrenergic effect on Na+-K+ transport in rat skeletal muscle

1. Intact rat extensor digitorum longus muscles soaked in L-isoproterenol plus 10(-5) M ouabain gained less sarcoplasmic Na+ than did muscles soaked in ouabain alone. Half maximal effect was produced by 10(-8) M L-isoproterenol. 2. D-Isoproterenol and oxidized L-isoproterenol were only 3 and 1%, respectively, as potent as L-isoproterenol. Other catechols tested had no effect. 3. The effect of L-isoproterenol on sarcoplasmic Na+ content appears to be a beta-adrenergic function in that it was blocked by propranolol, but not by phentolamine, and could be mimicked by dibutyryl cyclic AMP or by caffeine. 4. Reduced gain in sarcoplasmic Na+ was accompanied by reduced loss of sarcoplasmic K+. 5. L-Isoproterenol increased loss of sarcoplasmic Na+ in the absence of ouabain, in muscles recovering from cold treatment. 6. Results suggest that the beta-adrenergic system stimulates a coupled Na-K+ pump. 7. A model is proposed in which stimulation of the Na+-K+ pump in response to beta-adrenergic agents involves a number of intermediate steps, identified tentatively.

MEASUREMENT OF MUSCLE BLOOD FLOW IN THE HUMAN FOREARM WITH RADIOACTIVE KRYPTON AND XENON

IN 1949 Kety proposed that if the rate of removal from the site of injection of an intramuscularly injected radioactive isotope was limited principally by flow, then the clearance of the tracer from the injection site could be used to measure local blood flow. In the past, sodium-24 or iodine-131 has been used for this purpose, but with considerable variability in the results obtained in serial studies of the same persons.2 The chemically inert gases krypton-85 and xenon-133 have certain advantages over Na24 and I 131. They are chemically and physiologically inert; they are not normally present in the body; and they are rapidly excreted from the body via the lungs.3 The long physical half-life of Kr 85 ( 10.3 years) and the half-life of Xe33 (5.27 days) make the use of these nuclides more convenient than Na 24 (15 hours). Finally, the lower gamma ray energies of Kr85 (0.513 mev) and Xe33 (0.081 mev) are more suitable for external radiation detection than the high energy of Na24 (1.368 mev), which is difficult to localize accurately in the body. Accordingly, blood flow to forearm muscle was estimated by external monitoring of the rate of disappearance of radioactivity following intramuscular injection of an aqueous solution of Kr85 or Xe 33

Catechol, a structural requirement for (Na+ + K+)-ATPase stimulation in rat skeletal muscle membrane.

1. Catecholamines can nearly double (Na+ + K+)-ATPase acts effect is not mediated by cyclic AMP and is not beta-adrenergic. 3. Orthodihydroxybenzene compounds and their orthoquinone derivatives enhance (Na+ + K+)-ATPase activity. 4. Enhancement of (Na+ + K+)-ATPase activity by catechols is not due to increased availability of ATP. 5. It is suggested that catechols and their orthoquinones somehow alter or protect the configuration of the enzyme so that it becomes more active or so protect the configuration of the enzyme so that it becomes more active or so that its activity is maintained under conditions in which its activity is otherwise diminished.

Rapid hyperpolarization of rat skeletal muscle induced by insulin

It has been proposed that the increase produced by insulin in electrical potential differences across membranes of target cells may be a mechanism by which the cell surface insulin-receptor complex causes at least some of the metabolic effects of insulin. If insulin-induced hyperpolarization is a transducer of common effector responses it must precede those responses. The problem has not been addressed previously, so that rapid responses to insulin have not been sought. Two methods were used. In one method, the bathing solution was changed rapidly so as to include insulin in supramaximal concentrations, and a series of measurements of membrane potentials. Er, were made. Insulin hyperpolarized by 9.4 mV within 1 min. In the other method, nanoliter amounts of highly concentrated insulin solution were ejected from a micropipette onto the surface of an impaled muscle fiber. In 21 out of 32 insulin injections, hyperpolarization occurred with 1 s; in 11 control injections there was no change. This is the most rapid response to insulin yet reported, and is consistent with the hypothesis that insulin-induced hyperpolarization may transduce effector responses.

Specific d-glucose transport in sarcolemma vesicles

The sarcolemmal fraction prepared from rat skeletal muscle consists of osmotically active vesicles that accumulate D-glucose in preference to L-glucose, apparently by facilitated diffusion into intravesicular space. Stereospecific D-glucose uptake by these vesicles is a saturable rpocess, inhibited by phloridzin, by cytochalasin B, and by certain sugars, and enhanced by counterflow. An additional leak pathway permits entry of both D- and L-glucose into the vesicles. Stereospecific D-glucose transport by sarcolemmal vesicles is enhanced to a small extent by insulin, provided the hormone is administered prior to cell disruption. In membranes prepared from insulin-pretreated muscle, Ca2+ produces a small further enhancement. Local anesthetics preferentially inhibit stereospecific D-glucose transport. Apparent uptake of both D- and L-glucose is greater when vesicles are suspended in salt solutions rather than sucrose, an effect attributed to increased functional vesicular volume.

An error in interpretation of double-reciprocal plots and Scatchard plots in studies of binding of fluorescent probes to proteins, and alternative proposals for determining binding parameters

One of the objects of experiments in which a fluorochrome is added to suspensions of cell membranes is to determine the parameters n and KD, the capacity of unit mass of protein to bind fluorochrome and the dissociation constant, respectively. Currently, these are estimated from Scatchard plots, construction of which first requires that observed fluorescence intensity be converted to moles of bound fluorochrome. This in turn is said to be possible by analysis of the intercept of a plot of reciprocal fluorescence intensity against reciprocal protein concentration. However, analysis of the classical mass action equilibrium equation, upon which the foregoing procedures are said to be based, reveals that the intercept of the double-reciprocal plot always underestimates the desired value. The error is formalized and shown to increase without bound with fluorochrome concentration. The error in turn leads to erroneous assessment of n and KD. Alternative methods for calculating the desired parameters are proposed, based on direct plots of fluorescence intensity.