Magnetic Resonance in Medicine 000:000–000 (2012) A Unified Impulse Response Model for DCE-MRI Matthias C. Schabel 1,2 * We describe the gamma capillary transit time model, a gen- eralized impulse response model for DCE-MRI that mathe- matically unifies the Tofts-Kety, extended Tofts-Kety, adiabatic tissue homogeneity, and two-compartment exchange models. By including a parameter (α -1 ) representing the width of the distribution of capillary transit times within a tissue voxel, the GCTT model discriminates tissues having relatively monodis- perse transit time distributions from those having a large degree of heterogeneity. All five models were compared using in vivo data acquired in three brain tumors (one glioblastoma multi- forme, one pleomorphic xanthoastrocytoma, and one anaplastic meningioma) and Monte Carlo simulations. Our principal find- ings are : (1) The four most commonly used models for dynamic contrast-enhanced magnetic resonance imaging can be unified within a single formalism. (2) Application of the GCTT model to in vivo data incurs only modest penalties in parameter uncertainty and computational cost. (3) Measured nonparametric impulse response functions in human brain tumors are well described by the GCTT model. (4) Estimation of α -1 is feasible but achiev- ing statistical significance requires higher SNR than is typically obtained in single voxel dynamic contrast-enhanced magnetic resonance imaging data. These results suggest that the GCTT model may be useful for extraction of information about tumor physiology beyond what is obtained using current modeling methodologies. Magn Reson Med 000:000–000, 2012. © 2012 Wiley Periodicals, Inc. Key words: DCE-MRI; pharmacokinetic modeling; perfusion imaging; brain tumor An anomalous and highly heterogeneous vascular bed is one of the hallmarks of malignant tumors, resulting in increased permeability and consequent uptake of injected contrast molecules within the tumor tissue. With the advent of antiangiogenic and antineovascular cancer ther- apies, there is growing interest in noninvasive methods of characterizing changes in the tumor vasculature. A number of models extending the standard Tofts-Kety (TK) compart- mental approach (1) have been proposed for the analysis of dynamic contrast-enhanced magnetic resonance imag- ing (DCE-MRI) data, primarily motivated by the desire to more accurately model the tumor vascular bed and separately discriminate blood flow and vascular permeabil- ity. These models include the extended Tofts-Kety (ETK) model (2,3), the adiabatic tissue homogeneity (ATH) model 1 Advanced Imaging Research Center, Oregon Health & Science University, Portland, Oregon USA 2 Department of Radiology, Utah Center for Advanced Imaging Research, University of Utah Health Sciences Center, Salt Lake City, Utah, USA *Correspondence to: Matthias C. Schabel, Ph.D., Advanced Imaging Research Center, Oregon Health & Science University, Portland, OR 97239. E-mail: schabelm@ohsu.edu Received 11 July 2011; revised 15 December 2011; accepted 21 December 2011. DOI 10.1002/mrm.24162 Published online in Wiley Online Library (wileyonlinelibrary.com). (4–6), the two-compartment exchange (2CX) model (7–12), and the distributed capillary adiabatic tissue homogeneity (DCATH) model (13,14). All of these models can be described within the impulse response formalism by the following set of equations (7): C v (t ) = FR v (t ) ⋆ C a (t ) C p (t ) = FR p (t ) ⋆ C a (t ) C t (t ) = F (R v (t ) + R p (t )) ⋆ C a (t ), [1] where C v (t ) is the contrast concentration in the capillary (vascular) bed, C p (t ) is the contrast concentration in the parenchyma, C t (t ) is the (measured) total tissue contrast concentration, C a (t ) is the contrast concentration in arte- rial blood (also known as the arterial input function or AIF), R v (t ) is the vascular impulse response function (IRF), R p (t ) is the parenchymal IRF, F is the blood flow to the tissue of interest, and the asterisk represents convolution. Func- tional forms for the IRFs of these five models are given in Table 1. The TK model is effectively a single compartment model in which contrast molecules from an external vascular space are transported into a well-mixed compartment rep- resenting the accessible tissue space. The arterial blood acts as an inexhaustible reservoir but does not contribute to the measured tissue concentration. The ETK model attempts to address the missing vascular signal by adding a direct arte- rial term that represents a separate reservoir contributing to the total concentration within the voxel. The blood pool term in the ETK model does not represent a true second compartment because its concentration remains indepen- dent of extraction into the tissue compartment. In contrast, the 2CX model is a true two compartment formulation that incorporates the blood pool as a separate, well-mixed com- partment that is supplied with contrast molecules from the arterial circulation and exchanges contrast with the tissue compartment (7,9). A recent article by Sourbron and Buck- ley thoroughly analyzes the relationships between these three models (12). The ATH model proposed by St. Lawrence and Lee takes an alternative approach beginning from a 1D space-time distributed parameter model formulation that represents the capillary and surrounding tissue as a pair of concentric cylinders (6). Arterial blood enters the central (capillary) cylinder, then transits the capillary in a finite amount of time while exchanging contrast molecules with the outer (tissue) cylinder. By assuming that the time rate of change in the tissue compartment is small relative to that of the capillary compartment (the adiabatic approxima- tion, which is essentially equivalent to assuming that the tissue compartment is well-mixed), the partial differen- tial equations governing this model may be reduced to a compartment model form. © 2012 Wiley Periodicals, Inc. 1