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Experimental Studies |
1 From the Mallinckrodt Institute of Radiology, Washington University School of Medicine, 510 S Kingshighway Blvd, St Louis, MO 63110. Received August 19, 1999; revision requested October 14; revision received November 16; accepted December 7. Supported by Mallinckrodt Medical, St Louis, Mo. Address correspondence to K.T.B. (e-mail: baet@mir.wustl.edu).
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIXREFERENCES |
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MATERIALS AND METHODS: With a computer-based, compartmental model of the cardiovascular system, theoretic analysis was performed to estimate an injection algorithm for uniform, prolonged vascular enhancement. For algorithm validation, four pigs were scanned after intravenous injection of 50 or 70 mL of contrast medium (282 mg of iodine per milliliter). Uni-, bi-, and multiphasic injection schemes were tested. In most cases, the initial injection rate was 2 mL/sec. In each CT study, 27 dynamic images were acquired every 2 seconds at a fixed mid–abdominal aortic level. Time-enhancement curves were calculated. Injection duration, peak aortic enhancement, and enhancement uniformity (duration of enhancement achieved within 90% of the peak [90% DCE]) were evaluated.
RESULTS: Theoretic and experimental results agreed well. Compared with uniphasic injection, biphasic injection resulted in more prolonged enhancement but generated two enhancement peaks with a valley between, and multiphasic injection yielded more uniform and prolonged enhancement. With 50- and 70-mL multiphasic injections, respectively, injection duration increased by 32% and 51%, peak enhancement decreased by 19% and 18%, and 90% DCE increased by 81% and 94%.
CONCLUSION: Uniform, prolonged vascular enhancement, which is desirable for CT angiography and essential for steady-state quantification of blood volume in organs, can be achieved with multiphasic injection.
Index terms: Animals • Aorta, CT, 981.12912, 981.12913, 981.12915, 981.12916, 981.12918 • Computed tomography (CT), contrast enhancement, 981.12912, 981.12913 • Computed tomography (CT), helical technology, 981.12915 • Computers, simulation • Model, mathematical
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIXREFERENCES |
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Uniform vascular enhancement through the entire period of image acquisition is highly desirable for the purpose of image processing and display in which three-dimensional postprocessing is frequently based on a threshold CT attenuation value. In addition, achieving uniform vascular enhancement is crucial in some quantitative physiologic studies in which steady-state methods are used to map regional blood volume in the brain (2,3). Accurate measurement of changes in regional cerebral blood volume can provide important information for the assessment of various neuropathologic states.
Uniform enhancement can also contribute to more efficient use of contrast medium. For a given volume of contrast medium, uniform enhancement with a magnitude lower than the peak enhancement generated by a uniphasic injection would provide a longer temporal window of adequate vascular enhancement, resulting in a longer optimal scanning interval. Conversely, for a given scanning duration, uniform vascular enhancement would require the use of a smaller volume of contrast medium.
Achieving uniform, prolonged vascular contrast enhancement requires an injection method that is more sophisticated than the standard uniphasic or biphasic injection. A typical biphasic injection consists of two phases, a short rapid-injection phase, followed by a longer slow-injection phase (4). A biphasic injection yields more prolonged enhancement than a uniphasic injection, but it generates two enhancement peaks with a valley of enhancement in between. The enhancement peaks occur shortly after the completion of each injection phase. We postulated that a well-designed, multiphasic injection method could provide uniform, prolonged vascular contrast enhancement that is optimal for CT angiography and that is essential for steady-state quantification of blood volume.
The objectives of this study were (a) to develop a mathematic algorithm for a multiphasic injection method that would provide uniform, prolonged vascular contrast enhancement for spiral CT angiography and (b) to validate this algorithm by using a porcine model.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIXREFERENCES |
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Figure 1 shows a compartmental model designed to simulate early contrast enhancement in the aorta. In this model, contrast medium is injected into an antecubital vein and distributed to the right heart, pulmonary compartment, left heart, and aorta. It then recirculates to the right heart via the systemic circulation. This transport scheme is simplified to focus on the early pharmacokinetics of aortic enhancement, reducing the complexity of our analysis. For example, the elimination of contrast medium from the central blood compartment by means of renal excretion (transport to urine) is substantial in only late pharmacokinetics and, thus, is not considered in this simplified compartmental model.
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Simulation of Aortic Enhancement
The aortic enhancement curves were computer simulated by numerically solving Equations (A1)–(A5). The physiologic parameters used in the model for humans included 40 mL for Vv (peripheral vein), 250 mL each for Vr (right heart) and Vl (left heart), 600 mL for Vp (pulmonary circulation), and 10 L for Vs (systemic circulation). Associated volumetric blood flow rates were 250 mL/min or 4.2 mL/sec for Qv and 6.5 L/min for the cardiac output. These values were estimated on the basis of published human physiologic data for a standard adult (5,7). To mimic channels of blood vessels, the peripheral venous and pulmonary compartments were further divided into multiple smaller compartments in series (five and 30 subcompartments, respectively).
Because, to our knowledge, detailed cardiovascular physiologic data for pigs are lacking compared with those available for humans, we rescaled the previous human physiologic parameters to determine those appropriate for use in the porcine model. The compartmental volumes of the porcine model were estimated by multiplying the compartmental volumes of a typical 70-kg human by the body weight ratio (eg, 25:70 for a 25-kg pig). It is known that the mean cardiac output per body weight of pigs is twice that of humans (8). Therefore, the cardiac output for a 25-kg pig corresponds to that of a 50-kg human. Although our selection of model parameters was somewhat subjective, the parameters were estimated from available physiologic data and simply represent a set of reference values for simulation to compare with experimental data.
A total of 38 ordinary differential equations were used to describe the model in Figure 1. These equations were solved by using numerical integration programs with the fifth-order Runge-Kutta method (9). The model was programmed on a personal computer and required a fraction of a second to compute. The contrast medium concentration curve over time was calculated for each region by solving these differential equations for a given contrast medium injection protocol. The computed concentration of contrast medium in each compartment was translated into a CT enhancement value (5).
Solving the Inverse Problem and Verifying the Solution
For a given input injection protocol, the mathematic model described previously can be used to predict the output contrast enhancement curve in the aorta. Conversely, the model can be used to solve the inverse problem, that is, to predict an input function for a given output contrast-enhancement profile. In this study, our specific goal was to use the model to solve for an input contrast medium injection algorithm that would generate uniform, prolonged vascular contrast enhancement.
For a given desired constant aortic enhancement and for given initial conditions, the input contrast medium injection algorithm can be predicted by solving the inverse problem by using the Laplace transform of governing equations in the model. The mathematic manipulations for this solution are detailed in the Appendix. The solution, that is, the desired contrast injection profile, was in turn applied as an input to the mathematic model to verify that it would result in uniform aortic contrast enhancement. Simulations were performed with both porcine and human mathematic models by adjusting the physiologic input values. Different injection profiles were tested to study their effect on aortic contrast enhancement. In addition, the effect of reduced cardiac output on aortic enhancement was investigated by decreasing the cardiac output in the model by 20% (1.3 L/min) and 40% (2.6 L/min). Simulations were performed by using the input injection profile that, when used in a subject with normal cardiac output, would produce uniform aortic enhancement. The enhancement curves from these simulations were compared with those from simulations with normal cardiac output in the model.
Experimental Porcine Model
All animal care and procedures performed in this study were approved by the institutional animal study committee. Four pigs (A, B, C, D) initially weighing 24–26 kg underwent scanning in two or three sessions. Each session was separated by at least 2 days. In two pigs, all sessions were completed within 10 days, whereas, in the other two pigs, the first two and last sessions were 4–5 weeks apart, which resulted in an increase in their weights to 36.3 kg (pig B) and 40.6 kg (pig D) at the last session.
In each experimental session, a pig was anesthetized and intubated and underwent scanning for the acquisition of three or four sets of images. During scanning, each pig was ventilated with oxygen and low tidal volume to minimize breathing motion artifact. Each set of images consisted of 27 dynamic CT images (5-mm collimation) acquired at a fixed mid–abdominal aortic level after the intravenous injection of contrast medium into a peripheral vein. The acquisition of sets of images were separated by 45–60 minutes to minimize the effect of prior administrations of contrast medium. All CT scanning was performed with a Somatom Plus-S scanner (Siemens Medical Systems, Iselin, NJ) by using a 1-second scanning time and a 1-second interscan delay.
The following three types of injection schemes were tested: uni-, bi-, and multiphasic. Biphasic injections were performed by means of a power injector used in routine clinical CT scanning (Medrad microprocessor CT injector system; Medrad, Pittsburgh, Pa), whereas uni- and multiphasic injections were performed by means of an investigational power injector (Liebel-Flarsheim, Cincinnati, Ohio). This power injector was capable of delivering contrast medium by using either uni- (ie, zero exponential decay coefficient) or multiphasic injection algorithms (ie, various nonzero exponential decay coefficients). A biphasic injection algorithm was not implemented in this version of the investigational injector to simplify its operation mode. The multiphasic injection rate was determined by the initial injection rate and an exponential decay coefficient, as shown in Figure 2. Total injected volume of contrast medium corresponds to the integrated sum of the multiphasic injection over the injection duration.
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The most extensively tested injections consisted of 50 mL of contrast medium injected uniphasically (2 mL/sec) or multiphasically (initial rate of 2 mL/sec, with an exponential decay coefficient of 0.017). The same injection methods were repeated with an increased volume of contrast medium (70 mL) and with both increased injection rate (3 mL/sec) and increased volume (90 mL). Other injection studies included the use of biphasic injections of 50 (2 mL/sec for 12 seconds, then 1.4 mL/sec for 18 seconds) and 70 mL (2 mL/sec for 17 seconds, then 1.0 mL/sec for 36 seconds) of contrast medium. Approximately half of the total volume of contrast medium was injected in each phase of the biphasic injections. The first and second injection rates of the biphasic injections were determined by the initial and final injection rates of the multiphasic injections, with an exponential decay coefficient of 0.017.
Attenuation values in the aorta were measured on scans obtained after contrast enhancement (at the same level as the scans obtained before enhancement) by using a circular region of interest placed by a radiologist (K.T.B.) at the center of the aorta. Each region of interest had an area of 40–50 mm2 and occupied more than 90% of the aortic cross-sectional area. Contrast enhancement was calculated as the absolute difference in attenuation value between the scans obtained before and after contrast enhancement. For the data analysis, the injection duration, the magnitude of peak aortic enhancement, and the uniformity of enhancement (duration of the enhancement achieved within 90% of the peak [90% DCE]) were evaluated. Means and SDs were computed.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIXREFERENCES |
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Figure 5a shows the exponential injection profiles for three decay coefficients (0.01, 0.02, and 0.03) applied to an injection duration of 120 seconds with an initial injection rate of 2 mL/sec. The total amount of contrast medium in each injection is represented by the area under each curve. A lower exponential decay resulted in a higher total amount of contrast medium and a higher final injection rate at the completion of the injection. Aortic contrast enhancement curves corresponding to these exponential injection profiles were simulated from the mathematic model (with porcine physiologic parameters) by solving Equations (A1)–(A5); these curves are demonstrated in Figure 5b. Uniform (plateau) aortic enhancement was observed, with an exponential decay constant of 0.02 (Q/Vs = 77/3,571 = 0.021). Contrast enhancement steadily increases above this plateau level, with a decay coefficient of 0.01, while it decreases below the plateau level after reaching a peak, with a decay coefficient of 0.03.
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Figure 8 demonstrates the empiric porcine aortic enhancement curves obtained in two pigs by using multiphasic exponential injections with three exponential decay coefficients (0.007, 0.017, 0.026). The contrast medium injection profiles are depicted in Figure 2. The multiphasic injection with a decay coefficient of 0.017 produced aortic enhancement that was more uniform than that of the other injections. This result was consistent with the prediction of the theoretic model that a multiphasic injection with an exponential decay constant of 0.02 provides uniform aortic enhancement. Injections with lower (0.007) or higher (0.026) decay coefficients resulted in aortic enhancement curves that steadily increased or decreased, respectively, after a peak, as predicted by the theoretic model. Although the magnitude of aortic enhancement for the two pigs differed substantially, reflecting their difference in body weight (24.8 kg vs 40.6 kg), the patterns of aortic enhancement resulting from the three different exponential decay coefficients were consistent.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIXREFERENCES |
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The results of this study show that uniform, prolonged aortic contrast enhancement can be achieved by using a multiphasic injection with an appropriate exponential decay coefficient. Our multiphasic injection method was mathematically derived from a physiologically based pharmacokinetic model. A porcine model was then used to confirm the findings predicted in our theoretic analyses and computer simulations. Although further clinical studies are warranted to validate our findings, our experience with previous comparative pharmacokinetic studies suggests that a human model should behave similarly to the porcine model.
We have demonstrated that a biphasic injection method is not adequate to achieve uniform vascular contrast enhancement. However, if one chooses to use a biphasic injection for this purpose, it is not certain what the best biphasic injection method is. For a biphasic injection of a given volume of contrast medium, three of four parameters (rate 1, rate 2, duration 1, duration 2) must be determined. Although the biphasic protocol used in our experiment was chosen arbitrarily, we believe that it was a reasonable choice to provide evenly distributed contrast enhancement during the injection period.
Recently, Fleishmann and Hittmair (10) investigated a modified biphasic injection method to generate uniform aortic enhancement. Assuming a time-invariant linear system, they calculated the transfer function of the system with a test bolus using the Fourier transform and then computed a theoretic bolus geometry that would provide uniform enhancement. This nonlinear bolus geometry was simplified to generate a biphasic injection that was subsequently applied in five patients. Their results confirmed that the bolus geometry of injection could be modified to provide enhancement that is more uniform than that of a uniphasic injection and that a biphasic injection tends to generate two enhancement peaks with a valley in between.
Our method differed from theirs in that we used physiologically based pharmacokinetic model rather than a "black box" concept with a linear and time-variant assumption to calculate an optimal bolus geometry. We have demonstrated that a multiphasic injection with exponential decay is the desired bolus geometry, which was subsequently validated in a controlled animal experiment.
In this study, we used a simplified pharmacokinetic model with a limited number of compartments instead of a more complex whole-body model (5). This simplified model was specifically designed to determine the contrast medium injection profile that would generate uniform, prolonged vascular enhancement. Although the model does not provide a complete description of enhancement characteristics in each organ, it can adequately describe the underlying pharmacokinetic process of interest, that is, the first-pass enhancement characteristics of the aorta. In this respect, our simulated results correlated well with the experimental results from our porcine model.
The fact that a multiphasic injection with an exponentially decaying injection rate generates uniform vascular enhancement can be explained conceptually as follows. Contrast enhancement in a system is proportional to the net amount of contrast medium present, that is, the inflow of contrast medium minus the outflow. Aortic enhancement reflects the accumulation of contrast medium in the central blood volume (ie, the volume of contrast medium injected and recirculated minus the volume of contrast medium lost from the vessel by diffusion into the interstitium). Thus, vascular enhancement increases when the rate of contrast medium infusion into the central blood volume exceeds the rate at which it exits the central blood volume by means of diffusion. This physiologic phenomenon explains why aortic enhancement peaks shortly after the termination of a uniphasic injection, reflecting the maximal accumulation of contrast medium. The rate at which contrast medium diffuses from the central blood compartment to the interstitial compartment is related to the concentration gradient between the two compartments, which is an exponential function of time because the contrast medium transport phenomenon is governed by passive diffusion and permeability. Thus, when the contrast medium outflow rate is balanced by the infusion rate, a condition that is achieved with a multiphasic injection and an exponentially decaying rate, uniform vascular enhancement occurs.
Our results show that proper selection of a decay coefficient is crucial to generate uniform vascular enhancement with a multiphasic injection. The decay coefficient is proportional to the cardiac output per body weight. Because the cardiac output per body weight in humans is approximately half that of pigs, a decay coefficient of 0.01 is appropriate in humans. This value is independent of body weight because it is already normalized for body weight. For example, in pigs that gained 15–20 kg from their baseline weight of 25 kg, a multiphasic injection with a decay coefficient of 0.017 resulted in a uniform vascular enhancement pattern that was similar, but with a decrease in magnitude, to that of the same pigs at their baseline weight.
The decay coefficient designed to generate uniform enhancement in subjects with normal cardiac output resulted in a more dome-shaped enhancement curve with increased magnitude when cardiac output was reduced in simulations. In theory, if the degree of cardiac output reduction is known, the same uniform vascular enhancement can be reproduced in patients with reduced cardiac output, although this may be difficult to do in practice. This uniform enhancement can be achieved by lowering the initial injection rate and decay coefficient calculated for patients with normal cardiac output, in proportion to the reduction in cardiac output. However, it is apparent that a multiphasic injection designed to achieve a certain level of vascular enhancement in patients with normal cardiac output will not result in inadequate enhancement in patients with reduced cardiac output.
Although our theoretic analysis indicated that a multiphasic injection should follow an exponential decay to generate uniform, prolonged vascular enhancement, other functional patterns may be used to approximate an exponential decay. For example, a short segment of an exponential curve can be replaced by a linear function without much disparity. This implies that, in practice, multiphasic linear injection may be used instead of multiphasic exponential injection when the injection duration is not too long and when the decay coefficient is relatively small (eg, the exponential curve with a decay coefficient of 0.007 in Figure 2). In addition, a subtle discrepancy in enhancement from a slightly different approximation of exponential function may be indiscernible because of intrinsic physiologic fluctuations in enhancement caused by vascular pulsation and respiratory motion.
The number and interval of temporal steps required for a multiphasic injection depends on the injection duration and the exponential decay coefficient. The biphasic injections used in our study were not sufficient to generate uniform vascular enhancement. Our multiphasic injections were generated with subsecond temporal resolution by using an investigational injector. However, this degree of high temporal resolution may not be necessary. Although we have not investigated the effect of temporal resolution on vascular enhancement with multiphasic injections, a multiphasic temporal resolution of 2–3 seconds appears to be sufficient to generate uniform enhancement because of intrinsic physiologic fluctuations in vascular enhancement.Practical application: In summary, uniform prolonged vascular contrast enhancement, which is desirable for CT angiography and essential for steady-state quantification of blood volume, can be achieved by using a multiphasic exponential decay injection method. This technique, which was developed mathematically and is based on cardiovascular physiology and pharmacokinetics, is a good example of how a contrast medium injection algorithm can be modified to achieve a desired application-specific contrast enhancement profile. We are currently evaluating this multiphasic injection method in a clinical trial of CT angiography.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIXREFERENCES |
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Equations (A1)–(A5) and the initial conditions for C at time t = 0 can be numerically solved to predict and simulate an aortic enhancement curve for a given contrast injection condition. An example in a porcine model with a 2 mL/sec uniphasic injection is shown in Figure 3.
Conversely, these differential equations can be used to estimate an input contrast injection algorithm that generates a uniform, prolonged vascular enhancement (ie, solving an inverse problem, as shown later). Because the initial contrast concentrations in the body compartments equal 0, taking the Laplace transform of Equations (A1)–(A5) yields
is a scaling constant and H(s) is the Laplace transform of the Heaviside step-function H(t), where
The inverse Laplace transform of Equation (A13) gives the desired result:
Equation (A14) can be approximated by eliminating the terms involving the Dirac delta function 
(t) and its derivatives, since these terms contribute only to the impulse rise in contrast concentration immediately following t = 0 and not to the steady-state behavior. Without these terms, Equation (A14) simplifies to
, to set as the initial injection rate. |
ACKNOWLEDGMENTS |
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FOOTNOTES |
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K.T.B. and H.Q.T. have filed a U.S. patent application on the multiphasic injection method described in this manuscript; are currently collaborating with Libel-Flarsheim, Cincinnati, Ohio, and Mallinckrodt Medical, St Louis, Mo, on a clinical trial of this method; and plan to develop, for use in clinical practice, an injector capable of providing multiphasic contrast medium injections.
Author contributions: Guarantor of integrity of entire study, K.T.B.; study concepts, K.T.B.; study design, K.T.B., J.P.H.; definition of intellectual content, K.T.B., H.Q.T.; literature research, K.T.B.; experimental studies, K.T.B.; data acquisition and analysis, K.T.B.; statistical analysis, K.T.B.; manuscript preparation, K.T.B., H.Q.T.; manuscript editing and review, K.T.B., J.P.H.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIXREFERENCES |
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), and 0.026 (
). (Injection profiles depicted in 
