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.

/pdf/graphical-evaluation-of-blood-to-brain-transfer-constants-2e29v1hms2.pdf

Graphical Evaluation of Blood-to-Brain Transfer Constants from Multiple-Time Uptake Data:

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.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/%28SICI%291522-2586%28199909%2910%3A3%3C223%3A%3AAID-JMRI2%3E3.0.CO%3B2-S

Estimating kinetic parameters from dynamic contrast-enhanced T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols.

The gross composition of the body.

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...

https://journals.sagepub.com/doi/pdf/10.1038/jcbfm.1985.87

Graphical Evaluation of Blood-to-Brain Transfer Constants from Multiple-Time Uptake Data. Generalizations:

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).

Modeling tracer kinetics in dynamic Gd-DTPA MR imaging

Effects of blood flow on diffusion kinetics in isolated, perfused hindlegs of cats; a double circulation hypothesis.

Capillary Permeability to Lipid-Soluble Molecules

The quantity of "rapidly exchanging" K+ in isolated, skeletal muscles of dogs was determined by measuring the back-diffusion of K42 during perfusion with blood containing this isotopic tracer. This...

Exchangeability of tissue potassium in skeletal muscle

Effects of adrenal hormones on capillary permeability in perfused rat tissues.

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...

Transport of potassium-42 from blood to tissue in isolated mammalian skeletal muscles.

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