A multivessel model describing replenishment kinetics of ultrasound contrast agent for quantification of tissue perfusion

Abstract

To improve the quantification of tissue perfusion using intermittent sonography, a new model describing replenishment kinetics of microbubbles is proposed. The new approach takes into account the variability of blood flow velocities found in vivo, especially in tumors, and consistently describes the refilling process of microbubbles. Based upon this model, blood volume, blood velocity, blood flow and perfusion in 17 experimental tumors were calculated, and compared with the results obtained with the established, phenomenologically derived exponential kinetic model. In contrast to the existing model, our approach describes tissue vascularization more physiologically and allows deduction of a consistent new hyperbolic model for quantification of intermittent sonography. Blood volume and mean blood velocity did significantly correlate between both the new and the established model (k = 0.99; k = 0.94, both p < 0.001). However, mean tumor blood velocity was lower (−19%, p < 0.01) with the established model compared to the newly developed model. In addition, the range and distribution of blood flow velocities found in vivo can be estimated with the new model. Furthermore, it uses simpler mathematical fitting routines and allows easier data acquisition, which may allow a more practicable clinical application of intermittent sonography. In conclusion, a more valid, detailed and accurate calculation of perfusion parameters, especially of tumors, can be derived in vivo with the new multivessel model of intermittent sonography. (E-mail: [email protected])

Introduction

The visualization of vasculature, in particular of the capillary blood flow, as well as the quantification of perfusion in vivo are highly desirable for various experimental and clinical applications, in organs (heart, brain, etc.) as well as in tumors. In malignant tumors, vascularization correlates with their invasive potential (Folkman 1995), and the mean vessel density is a prognostic factor of malignant disease (Weidner et al. 1991). As a consequence, different strategies to modulate tumor vascularization by antiangiogenic therapies are the subjects of current research (Fox et al. 2001). However, monitoring functional changes of the microvascularization caused by those therapies requires measurement of perfusion (i.e., the blood flow per tissue unit) noninvasively, but this is a difficult task considering the slow blood flow velocity and irregular nature of vessels, particularly in tumor vasculature. Unfortunately, all modern diagnostic methods including magnetic resonance imaging (MRI) (Newman 2000) have notable limitations in this regard.

Although ultrasound (US) provides promising methods to evaluate tissue vascularization (Ferrara et al. 2000), even contrast-enhanced conventional US methods are not capable of visualizing blood flow in the smallest vessels (Delorme et al. 2001).

An approach to assess perfusion indirectly is intermittent sonography (Wei et al. 1998). This novel US method quantifies replenishment kinetics of US contrast agent (microbubbles) in a region-of-interest (ROI) after their destruction by high US energy pulses. Subsequently, the microbubbles refill from outside the ROI as long as they are delivered by the systemic circulation. The kinetics of this replenishment allow calculattion of blood flow by quantifying blood volume and mean blood velocity within the ROI. Because high US signals can be measured even from stationary microbubbles, capillary blood flow can be visualized when microbubbles are given enough time to fill the small vessels. Therefore, the baseline revised US signal intensity derived at the maximum replenishment (late phase of refilling) describes the blood volume in the ROI, whereas the initial phase of replenishment primarily reflects the blood velocity.

In cardiology, intermittent sonography has proven useful to evaluate myocardial perfusion Wei et al., 1998, Linka et al., 1998, Koster et al., 2001. Also, renal or cerebral blood flow has been examined using this new approach Schlosser et al., 2001, Seidel et al., 2001. Recently, effects of antiangiogenic therapy on tumor perfusion have been monitored (Krix et al. 2002) using intermittent US imaging after just a single bolus injection of microbubbles (Krix et al. 2003). In these previous studies, blood volume in tumors determined by intermittent US was significantly correlated with microvessel density and with corresponding dynamic MRI parameters Kiessling et al., 2002, Krix et al., 2002a. Thus, intermittent sonography using replenishment kinetics of microbubbles is a promising tool to quantitatively assess therapy-related changes of tumor vascularization, and may even further our understanding of tumor angiogenesis.

The model described by Wei et al. (1998) has been used to quantify the microbubble replenishment. This established model predicts an exponential increase of the US signal intensity followed by a saturation behavior. The parameter A describes the plateau (maximum replenishment), and the exponential coefficient β indicates the initial increase. However, the model has to be inconsistently transferred into a linear replenishment, noncontinuously reaching the plateau. This switch from the exponential to the linear, noncontinuous model enables the calculation of the mean blood velocity and, thereby, of blood flow, but it may not always lead to valid results. Furthermore, the exponential model assumes a constant blood velocity in the ROI and, therefore, does not correctly reflect the process of replenishment, especially when considering tissue that has an irregular distribution of blood flow like tumors. It is rather a phenomenological description of the experimental findings obtained in confined settings of phantoms or organs with regular architecture Wei et al., 1998, Tiemann et al., 2000, Veltmann et al., 2002. Because blood velocity and blood volume are essential for quantifying tissue perfusion, a model that provides these parameters needs to be more than just a phenomenological and inconsistent description of experimental findings that may, moreover, not reflect perfusion, especially of irregular tumor vessels.

In this study, we present a new hyperbolic model for quantifying the replenishment of microbubbles. This model relies on a physiological and consistent description of refilling, and takes into account the distribution of blood velocities in a given volume of tissue in vivo.

The newly developed model was compared with the established model by calculating the vascularization parameters in experimental tumors, which were examined in vivo by intermittent bolus-contrast sonography.