The Permeability of Capillaries in Various Organs as Determined by Use of the ‘Indicator Diffusion’ Method
TL;DR: It is shown that the permeability of a capillary area can be expressed by three parameters: the initial extraction of test substances added in a single injection to the blood flowing to an organ, the blood flow and the surface area of the capillaries.
Abstract: Crone, C. The permeability of capillaries in various organs as deter-mined by use of the ‘Indicator Diffusion’ method. Acta physiol. scand. 1963. 58. 292—305. — The theory of a single injection technique, the ‘Indicator Diffusion’ method, for quantitative studies of capillary permeability is developed. It is shown that the permeability of a capillary area can be expressed by three parameters: the initial extraction (E) of test substances added in a single injection to the blood flowing to an organ, the blood flow (Q) and the surface area (A) of the capillaries. The equation relating these figures is: P = (=/A) × loge1/(1—E). The permeability coefficients of capillaries in kidney, liver, lung, brain and hind limb to inulin and sucrose are reported. It is found that the permeability of capillaries varies considerably from organ to organ. It is questioned whether the pore model adequately describes the functional characteristics of the capillaries in the muscles. The existence of pores should result in a pronounced deviation of the ratio between the permeability coefficients for sucrose and inulin from the ratio between the free diffusion coefficients. This was not found to be the case.
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TL;DR: A theoretical model of blood–brain exchange is developed and a procedure is derived that can be used for graphing multiple-time tissue uptake data and determining whether a unidirectional transfer process was dominant during part or all of the experimental period.
Abstract: A theoretical model of blood-brain exchange is developed and a procedure is derived that can be used for graphing multiple-time tissue uptake data and determining whether a unidirectional transfer process was dominant during part or all of the experimental period. If the graph indicates unidirectionality of uptake, then an influx constant (Ki) can be calculated. The model is general, assumes linear transfer kinetics, and consists of a blood-plasma compartment, a reversible tissue region with an arbitrary number of compartments, and one or more irreversible tissue regions. The solution of the equations for this model shows that a graph of the ratio of the total tissue solute concentration at the times of sampling to the plasma concentration at the respective times (Cp) versus the ratio of the arterial plasma concentration-time integral to Cp should be drawn. If the data are consistent with this model, then this graph will yield a curve that eventually becomes linear, with a slope of Ki and an ordinate intercept less than or equal to the vascular plus steady-state space of the reversible tissue region.
3,526 citations
Cites methods from "The Permeability of Capillaries in ..."
...lary blood flow, capillary surface area, and capillary permeability (the latter two variables are usually combined into a permeability-surface area or PS product) has been developed (Renkin, 1959; Crone, 1963) and can be used to convert the influx constant of the test solute to a P S product if blood flow is known (Patlak and Fenstermacher, 1975; Ohno et aI....
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TL;DR: A standard set of quantity names and symbols related to the estimation of kinetic parameters from dynamic contrast‐enhanced T1‐weighted magnetic resonance imaging data, using diffusable agents such as gadopentetate dimeglumine (Gd‐DTPA), are described.
Abstract: We describe a standard set of quantity names and symbols related to the estimation of kinetic parameters from dynamic contrast-enhanced T(1)-weighted magnetic resonance imaging data, using diffusable agents such as gadopentetate dimeglumine (Gd-DTPA). These include a) the volume transfer constant K(trans) (min(-1)); b) the volume of extravascular extracellular space (EES) per unit volume of tissue v(e) (0 < v(e) < 1); and c) the flux rate constant between EES and plasma k(ep) (min(-1)). The rate constant is the ratio of the transfer constant to the EES (k(ep) = K(trans)/v(e)). Under flow-limited conditions K(trans) equals the blood plasma flow per unit volume of tissue; under permeability-limited conditions K(trans) equals the permeability surface area product per unit volume of tissue. We relate these quantities to previously published work from our groups; our future publications will refer to these standardized terms, and we propose that these be adopted as international standards.
3,078 citations
Cites background from "The Permeability of Capillaries in ..."
...In the PS-limited case (PS 9 F), E 5 PS/F(1 2 Hct), and the equation reduces to Eq. [ 5 ]....
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TL;DR: General equations are derived that can be used to analyze tissue uptake data when the blood–plasma concentration of the test substance cannot be easily measured and for situations when trapping of theTest substance is incomplete and for a combination of these two conditions.
Abstract: The method of graphical analysis for the evaluation of sequential data (e.g., tissue and blood concentrations over time) in which the test substance is irreversibly trapped in the system has been expanded. A simpler derivation of the original analysis is presented. General equations are derived that can be used to analyze tissue uptake data when the blood–plasma concentration of the test substance cannot be easily measured. In addition, general equations are derived for situations when trapping of the test substance is incomplete and for a combination of these two conditions. These derivations are independent of the actual configuration of the compartmental system being analyzed and show what information can be obtained for the period when the reversible compartments are in effective steady state with the blood. This approach is also shown to result in equations with at least one less nonlinear term than those derived from direct compartmental analysis. Specific applications of these equations are illustr...
1,623 citations
Cites methods from "The Permeability of Capillaries in ..."
...lary blood flow, capillary surface area, and capillary permeability (the latter two variables are usually combined into a permeability-surface area or PS product) has been developed (Renkin, 1959; Crone, 1963) and can be used to convert the influx constant of the test solute to a P S product if blood flow is known (Patlak and Fenstermacher, 1975; Ohno et aI....
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TL;DR: Three major models for collecting and analyzing dynamic MRI gadolinium‐diethylenetriamine penta‐acetic acid (Gd‐DTPA) data are examined and the ratio kep, the efflux rate constant, is the simplest to measure.
Abstract: Three major models (from Tofts, Larsson, and Brix) for collecting and analyzing dynamic MRI gadolinium-diethylene-triamine penta-acetic acid (Gd-DTPA) data are examined. All models use compartments representing the blood plasma and the abnormal extravascular extracellular space (EES), and they are intercompatible. All measure combinations of three parameters; (1) kPSp is the influx volume transfer constant (min-1), or permeability surface area product per unit volume of tissue, between plasma and EES; (2) ve is the volume of EES space per unit volume of tissue (0 < ve < 1); and (3) K(ep), the efflux rate constant (min-1), is the ratio of the first two parameters (k(ep) = kPSp/ve). The ratio K(ep) is the simplest to measure, requiring only signal linearity with Gd tracer concentration or, alternatively, a measurement of T1 before injection of Gd (T10). To measure the physiologic parameters kPSp and ve separately requires knowledge of T10 and of the tissue relaxivity R1 (approximately in vitro value).
1,478 citations
TL;DR: In this paper, an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate non-linear regression.
Abstract: The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate nonlinear regression. The degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference, with moderate increases in computational complexity for many models. Estimation of precision from asymptotic theory and the bootstrap is discussed, and graphical methods for checking the appropriateness of the t distribution are presented.
1,336 citations
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TL;DR: The equations derived here have been applied to various permeability measurements found in the literature, such as the penetration of heavy water into animal cells, permeability of blood vessels, threshold concentration of plasmolysis and relaxation experiments with artificial membranes.
1,960 citations
TL;DR: A wealth of evidence supports the view that the exchange of materials through the walls of living capillaries takes place by physical processes which involve no expenditure of energy on the part of the capillary endothelial cells themselves.
Abstract: F ROM THE POINT OF VIEW of hemodynamics the blood is generally considered to circulate within a closed system of blood vessels. Even the smallest capillaries appear, under the microscope, as closed thin-walled vessels separating the blood from the extravascular fluid. Only occasionally are discontinuities in the capillary wall made evident by the diapedesis of one of the formed elements of the blood and even in such cases it is hard to be certain that a microscopically visible channel of egress is present. At high magnifications the blood appears to flow rapidly through individual capillaries thus forming a striking contrast to the relatively stagnant extravascular fluid and accentuating the role of the capillary membrane in providing a phase boundary separating the blood from the tissues. There are good reasons for supposing, however, that the capillary blood is in intimate contact with extravascular fluid and that the visible flow of blood through the capillaries is, in fact, very small in comparison with the intiWe flow of water and dissolved materials back and forth through the capillaxy walls. Evidence to be reviewed below suggests that this invisible component of the circulation takes place at a rate which is many times greater than that of the entire cardiac output. Indeed, it is by means of this ‘ultramicroscopic circulation’ through the capillary wall that the circulatory system as a whole fulfills its ultimate function in the transport of materials to and from the cells of the body. This review will deal with the physical properties of the ultramicroscopic circulation, its functional structure, the magnitude of flow through it and the physicochemical mechanisms regulating the flow. Direct methods for the study of ultrastructure have not as yet been applied to the capillary wall and much of what can be said must be deduced from quantitative studies of capillary permeability. A wealth of evidence supports the view that the exchange of materials through the walls of living capillaries takes place by physical processes which involve no expenditure of energy on the part of the capillary endothelial cells themselves. This evidence has been reviewed previously (20,30, 89, 162) and need not be considered here in detail. At least two types of capillary structure appear to be involved. On the one hand we have to consider the permeability characteristics of the plasma membranes which envelop the protoplasm of the capillary endothelial cells and which comprise the greater part of the visible capillary surface. On the basis of analogy with other known plasma membranes we may expect this type of structure to exhibit a relatively low order of permeability to ions and lipid insoluble molecules and a high order of permeability to oqgen, carbon dioxide and other lipid soluble substances. On the other hand, we have to consider specialized regions through or between endothelial cells which endow the capillary wall as a whole with a relatively high, degree of permeability to water, ions and large lipid insoluble molecules. This type of permeability resembles that of artificial porous membranes and has given rise to the hypothesis that the blood communicates directly with the extravascular fluid via channels or
858 citations
Additional excerpts
...PAPPENHEIMER (1953) and RENKIN and PAPPENHEIMER (1957) have published the only data comparable with those given in this paper....
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TL;DR: A method is described for studying transcapillary diffusion of K42 in isolated perfused muscles of dogs and its effects on blood flow and arteriovenous K42 differences are measured.
Abstract: A method is described for studying transcapillary diffusion of K42 in isolated perfused muscles of dogs. Blood flow and arteriovenous K42 differences are measured and blood-tissue clearance calcula...
695 citations
TL;DR: Morphological features of blood capillaries from various vertebrate forms and organs are presented and it is suggested that these varying capillary structural features may be relevant to problems relating to exchange of materials between blood plasma and parenchymal cells.
Abstract: Morphological features of blood capillaries from various vertebrate forms and organs are presented. Simple classifications are proposed, based on presence or absence of continuous basement membrane, on the nature of the endothelial cell and on the presence or absence of a complete investment of pericapillary cells. It is suggested that these varying capillary structural features may be relevant to problems relating to exchange of materials between blood plasma and parenchymal cells. Simple three-digit notation systems are presented for characterizing and designating the type of any capillary with respect to the classifications submitted.
588 citations