The exchange of an inert gas within a tissue was described in 1951 using a pharmacokinetic model to extract physiologically relevant parameters from time-dependent measurements of tracer concentration (1). Many authors have since adapted this early model to the specific requirements of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) experiments to relate the enhancement pattern of a tissue to the underlying exchange between blood plasma and the extravascular extracellular space (2–5). In the clinic, DCE-MRI has shown potential as a powerful tool to characterize the microvascular environment in tissue lesions as diverse as multiple sclerosis and tumors (6, 7). Recent improvements to pharmacokinetic models accounted for additional phenomena, such as the variation in shutter speed limits associated with contrast agent (CA) concentration (8, 9). Those studies have shown that neglecting the limits of the transcytolemmal and transendothelial water exchanges can lead to erroneous estimations of standard model parameters. Recently, the tedious problem of evaluating the arterial input function (AIF) has been circumvented by the use of reference region models developed by us and others (10–14). To our knowledge, the possibility that a CA can passively diffuse from a well-perfused region to a less vascularized region has not been addressed, although diffusion is known to occur within tumors (15).
Tumor tissues show clear signs of heterogeneity in their perfusion pattern (16, 17). They are often characterized by a well perfused rim surrounding a poorly vascularized, possibly necrotic core (18, 19). In DCE-MRI experiments, this translates into a rapid and intense signal enhancement at the rim followed by a delayed enhancement of the core, which may be the result of CA diffusion from the rim to the core. A common assumption made by all current models is that DCE-MRI data can be analyzed on a voxel-by-voxel basis, which inherently neglects diffusion of low molecular weight CA. The mathematical models used with DCE-MRI experiments could potentially be improved to obtain a better representation of the underlying physiological processes. A better understanding of the microvascular environment of tumors could impact the treatment protocols using agents delivered via the blood circulation, such as chemotherapy agents. In this case, high transcapillary exchange rates commonly found in tumors are expected to result in an increased concentration of the agent. In addition, antiangiogenic treatments attempt to compromise the neovascular system (20, 21), although an effective treatment may actually require the reestablishment of a functioning microvascular system (22). Finally, a high perfusion also correlates with a larger oxygen concentration in tumor tissue (23), which increases the radiosensitivity of a tumor (24).
In this contribution, we propose a diffusion-perfusion (DP) model in which CA diffusion is explicitly taken into account and included in the standard Tofts model (6). The overall goals of this effort are: 1) to build a pharmacokinetic model that incorporates the effects of CA diffusion; 2) to test the model in simulations and to assess accuracy and precision of the model when experimental noise levels are present; and 3) to apply the model in experimental studies of mice with MC7-L1 mammary carcinomas. The comparison of the DP model with the standard model exposes limitations of the standard model.