Dynamic contrast-enhanced (DCE)-MRI is emerging as a cancer imaging tool for diagnosis, monitoring of treatment effect, and evaluation of anticancer drugs (1–3). In DCE-MRI, *T*_{1}-weighted signals are repeatedly acquired after the injection of a contrast agent (CA), typically a low-molecular-weight gadolinium (Gd) chelate. By evaluating tissue enhancement, which is the imaging correlate of CA transfer between plasma and the tissue extravascular extracellular space (EES), one can infer clinically useful physiologic information, including tumor perfusion and/or permeability.

Although both semiquantitative and quantitative approaches to DCE-MRI kinetic analysis have been utilized, quantitative parameters, such as the CA transfer rate between the blood plasma and the EES, *K*^{trans}, are generally believed to the most useful as DCE-MRI endpoints, such as in Ref.4 and the DCE-MRI group consensus recommendations from the NCI CIP MR Workshop on Translational Research in Cancer—Tumor Response, Bethesda, MD, USA, Nov. 22–23, 2004 (http://imaging.cancer.gov/reportsandpublications/ReportsandPresentations/MagneticResonance). To accurately extract quantitative kinetic parameters, DCE-MRI kinetic models must be constructed. These models require a precise measurement of CA concentration in the arterial blood plasma as a function of time, *C*_{p}(*t*), also referred to as the arterial input function (AIF). The most commonly used kinetic model, which has been recognized by consensus as the recommended model for DCE-MRI analysis, is the Tofts model (5). It assumes that the water exchange system between the different compartments of a tissue, including intra-/extracellular space and the blood, are in the fast exchange limit (FXL) so that the CA concentration vs. time curve, *C*_{t}(*t*), can be calculated using a linear relationship between *C*_{t}(*t*) and the apparent longitudinal relaxation rate constant *R*_{1}(*t*):

where *R*_{10}(≡1*/T*_{10}) is the longitudinal relaxation rate constant in the absence of CA, and *r*_{1} is the relaxivity coefficient. With inclusion of the blood plasma volume, *v*_{p}, *C*_{t}(*t*) in the Tofts model is written as:

where *v*_{e} is the EES volume, *k*_{ep} ≡ *K*^{trans}/*v*_{e} represents the rate constant of CA backflux from the EES to the blood plasma, *C*_{p}(*t*) is the AIF. The *v*_{p} term in Eq. [2] is often neglected in what has been termed the “simple Tofts model.” As the CA concentration in the tissue increases, the water exchange system between the tissue compartments will deviate from the FXL, and the simple linear relation in Eq. [1] will no longer hold (6, 7). Recently, unified kinetic models, the so-called “shutter-speed models,” have been proposed to address the nonlinear effect caused by incomplete exchange averaging (8, 9).

Obtaining accurate measurements of the AIF by directly imaging the arteries or heart is a well known challenge in DCE-MRI that is complicated by *T*_{2}* effects, high CA concentration (10), partial volume effects (11), low signal-to-noise ratio (SNR) when only small arteries are in the FOV, and errors due to the rapid blood flow in the artery (12). Alternative approaches that use the measured data from the tissues themselves to inversely determine the AIF are thus being used more frequently. These approaches are often referred to as “reference tissue/region-based methods.” The initial applications of reference tissue/region-based approaches either assume that the kinetic parameters of the tissues are known or have small variability, such that literature values can be utilized (13, 14), or that the functional form of the AIF is known (15, 16).

More recently, reference tissue/region-based approaches called “pure blind identification methods” have been proposed (17–19). These approaches use multiple reference tissues/regions to estimate the AIF without assuming a specific functional form of the AIF, or the kinetic parameters of the reference issues. By assuming that the multiple reference tissues used have the same AIF, iterative estimations can be utilized to both calculate the kinetic parameters and construct an AIF that fits the observed data. However, the existing pure blind identification approaches have important limitations. For example, Riabkov and Di Bella (17) assume that the bolus arrival times for all tissues is the same, which is unrealistic and can introduce large errors (20). Furthermore, the constructed AIF is noisy and has values only at the original measurement time points, which limits its temporal resolution and the ability to adequately resolve its shape. More importantly, the computational time for their approach is prohibitive. They utilize an iterative quadratic maximum-likelihood algorithm (IQML) that involves hundreds of iterations, with each iteration requiring the solution of a large matrix-sized linear equation. Finally, the IQML algorithm can only be used in linear system models, which means the algorithm cannot be used in the shutter-speed models or any models that require nonlinear terms. The double reference tissue method (DRTM) previously proposed by Yang et al. (19) allows a difference in bolus arrival times in the two reference tissues, is computationally efficient, and gives a robust, smooth, and continuous estimate of the AIF. However, only one tissue is used to construct the AIF, and only tissues that are adequately described by a two-compartment model can be used in the algorithm. Therefore, it also cannot be used with shutter-speed models and often cannot be used in tumors, for which multicompartment models are typically required to describe CA kinetics (21).

Here we present a novel pure blind identification method termed the “multiple reference tissue method” (MRTM). As in other approaches, the MRTM utilizes two or more reference tissues to estimate the AIF, but in this case assumes only that the AIFs in the reference tissues have the same shape, with a possible difference in bolus arrival time. Importantly, the MRTM is a mathematical framework equipped with efficient algorithms that can be applied to any kinetic model, including nonlinear models, and to any CE imaging modality. The constructed AIF is smooth and has high temporal resolution. Because there is no limitation on the kinetic models that can be utilized, the tumors themselves can be used as a source of reference tissues. In fact, the inherent heterogeneity of tumors can be exploited by utilizing individual subregions with different properties as “reference tissues.” This ability avoids the necessity of including multiple normal reference tissues in the FOV.

In this paper we describe the theoretical framework of the MRTM and use Monte Carlo simulations to investigate its performance as a function of measurement noise and temporal resolution. We also provide an example of its application to clinical DCE-MRI data, including how the multiple reference tissues can be obtained from a tumor region of interest (ROI).