Paul S. Tofts

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.

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).

Leakage of Gd-DTPA through a defective blood-brain barrier is measured quantitatively using dynamic MRI scanning, in which repeated scans are made after a bolus injection. Image registration artifacts are minimized; a dose of 0.1 mM/kg and an IR sequence enable enhancement to be measured quantitatively. The triexponential enhancement curve is fitted to a theoretical model based on compartmental analysis. The transfer constant, or permeability surface area product per unit volume of tissue (k), and leakage space per unit volume of tissue (v1) are measured. Estimates for a quickly enhancing multiple sclerosis lesion are k = 0.050 min-1, v1 = 21%; for a slow one k = 0.013 min-1, v1 = 49%. This implies permeability in the range 4-17 x 10(-6) cm s-1, in broad agreement with other physiological methods. The method is noninvasive and can be used to make serial measurements in patients and in experimental animal models. The time course of pathological aspects of diseases with blood-brain barrier breakdown, such as multiple sclerosis, tumors, and infections (e.g., HIV) can be studied, along with their response to therapy. The measurements are of physiological variables and are therefore independent of imaging equipment and field.

Recent MRI studies in multiple sclerosis have highlighted the potential importance of spinal cord atrophy (implicating axonal loss) in the development of disability. However, the techniques applied in these initial studies have poor reproducibility which limits their application in the serial monitoring of patients. The aim of this study was to develop a highly reproducible and accurate method for the quantification of atrophy. The technique we describe demonstrates an intra-observer coefficient of variation (scan-rescan) of only 0.8%. When applied to 60 patients with clinically definite multiple sclerosis there was a strong correlation between spinal cord area and disability measured by Kurtzke's Expanded Disability Status Scale (EDSS) (r = -0.7, P < 0.001). The correlation was graded providing evidence for a causal connection. At levels 3 and 8 of the EDSS we observed a reduction in average cord area of 12 and 35%, respectively. Given its reproducibility, the magnitude of the change detected and the strong correlation with disability, this new technique should prove to be a sensitive measure of progressive neurological deterioration and could be readily incorporated into imaging protocols aimed at monitoring therapy.