Radiology
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published online before print July 9, 2004, 10.1148/radiol.2323031198
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
2323031198v1
232/3/921    most recent
Right arrow Submit a response
Right arrow Alert me when this article is cited
Right arrow Alert me when eLetters are posted
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Dennis Cheong, L. H.
Right arrow Articles by Koh, T. S.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Dennis Cheong, L. H.
Right arrow Articles by Koh, T. S.
(Radiology 2004;232:921-930.)
© RSNA, 2004

Technical Developments

Dynamic Contrast-enhanced CT of Intracranial Meningioma: Comparison of Distributed and Compartmental Tracer Kinetic Models—Initial Results1

L. H. Dennis Cheong, BSc, C. C. Tchoyoson Lim, MBBS, MMed, FRCR and Tong San Koh, PhD

1 From the Center for Modeling and Control of Complex Systems and Center for Signal Processing (L.H.D.C., T.S.K.), School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Ave, Block S2.1 B4-02, Singapore 639798; and Department of Neuroradiology, National Neuroscience Institute, Singapore (C.C.T.L.). Received July 28, 2003; revision requested October 9; revision received November 13; accepted January 13, 2004. Supported by National Healthcare Group of Singapore grant NHG-RPR-01058. Address correspondence to L.H.D.C. (e-mail: dennis_lhcheong@pmail.ntu.edu.sg).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Materials and Methods
Results
 Discussion
 APPENDIX
 REFERENCES
 
Dynamic contrast material–enhanced computed tomographic images of intracranial meningioma were analyzed by using both distributed-parameter and conventional compartmental tracer kinetic models. The distributed-parameter models were found to yield consistently better fitting of data sets than were conventional compartmental models. Although linear correlations were found between the kinetic parameters of the two models, some of these parameters (such as perfusion and mean transit time) did not correspond quantitatively. For all models, the kinetic parameters associated with the extravasation of tracer were found to be distinctly higher in meningiomas than in normal white- and gray-matter tissues.

© RSNA, 2004

Index terms: Brain, perfusion • Brain neoplasms, CT, 10.12113, 10.12115 • Computed tomography (CT), contrast enhancement • Computed tomography (CT), functional imaging, 10.12113, 10.12115 • Meninges, neoplasms, 10.366 • Model, mathematical


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Materials and Methods
Results
 Discussion
 APPENDIX
 REFERENCES
 
Dynamic contrast material–enhanced imaging with computed tomography (CT) or magnetic resonance (MR) has recently gained widespread interest (1–26) because these techniques allow noninvasive in vivo assessment of tissue hemodynamics and could provide important functional information about the tissue microvasculature. Evidence has shown that microcirculatory parameters (eg, perfusion, blood volume, mean transit time, and vessel permeability) derived from dynamic contrast-enhanced imaging may be useful for the diagnosis of tumors and the monitoring of cancer therapy outcome (1–14).

Tracer kinetic models used for estimating microcirculatory parameters at dynamic contrast-enhanced imaging are usually linear compartmental models, which can be broadly categorized as conventional compartmental (CC) or distributed-parameter (DP) models (27–30). Comprehensive reviews (31,32) by experts in dynamic contrast-enhanced imaging have indicated that DP models could allow a more complete analysis of the various kinetic parameters. Also, as explained by Larson et al (28), the assumptions on which CC models are based may not possess sufficient realism, because tracer concentration gradients within compartments are assumed to be zero at all times, and, consequently, the tracer is assumed to distribute instantaneously on arrival in each compartment. In contrast, DP models attempt to account for concentration gradients in the vascular compartment by defining tracer concentration as a function of both time and space. A DP model that accounted for two compartments (one vascular and one interstitial) was first proposed by Johnson and Wilson (27), who published their solution in a power series. St Lawrence and Lee (29) achieved a simplified solution with an adiabatic approximation of the bicompartmental DP model, which we refer to as the adiabatic tissue homogeneity (ATH) model. Larson et al (28) also derived solutions for both two- and three-compartment catenary DP models. More recently, Koh et al (30) reported a generalized solution for the multiple-compartment mammillary DP model.

Although DP models are more realistic in describing the kinetics of capillary-tissue transfer, CC models are more commonly used in the analysis of dynamic contrast-enhanced imaging data. The greater frequency of use of CC models is probably due to the numeric complexity of DP models, which makes computation with the latter less efficient. Nevertheless, the compelling question among researchers is whether the simplicity of the CC model is justified or, in other words, whether the parameters derived from CC and DP models differ significantly. A theoretic comparison of DP and CC models for positron emission tomography (PET) receptors was recently reported by Muzic and Saidel (33), whose study was designed to investigate how well the output of the CC model emulated that of the DP model. Muzic and Saidel concluded that the DP model had no advantage, given the typical temporal resolution (approximately 10 seconds) available with PET. Larson et al (28), however, found that DP models provided better data fitting than did CC models for high-temporal-resolution experimental data of radiolabeled water in brains of rhesus monkeys.

Since modern CT and MR imagers offer image acquisition time of about 1 second or less, it would be of interest to compare CC and DP models for dynamic contrast-enhanced imaging with these modalities. However, to date, studies of dynamic contrast-enhanced imaging with CT or MR have been few. Thus, the purpose of our study was to compare DP and CC kinetic models used to estimate tumor microcirculatory parameters at dynamic contrast-enhanced CT.


   Materials and Methods
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
Results
 Discussion
 APPENDIX
 REFERENCES
 
Tracer Kinetic Models
The technique of dynamic contrast-enhanced imaging involves the intravenous bolus injection of contrast medium (tracer) and subsequent sequential imaging to simultaneously monitor the changes in tracer concentration as a function of time t both in the tissue of interest, Ctiss(t), and in the feeding artery, Ca(t). The operational equation that expresses the relationship between Ctiss(t) and Ca(t) can be given as a convolution integral (29–32):

{r04se04e01}
where F is the blood perfusion, Hct is the fractional hematocrit (approximately 0.45 in major vessels) (31), and {rho} is the tissue density (often assumed to be 1 g/mL). The impulse residue function R(t) indicates the fraction of an impulse input of tracer remaining in the tissue region over time. One may consider the incoming bolus of tracer as a sequence of impulses entering the tissue region, and the total amount of tracer remaining in the tissue region at a given time, Ctiss(t), is hence the superposition of the corresponding residue functions of the incoming impulses, which can be represented by using a convolution integral. Thus, R(t) is characteristic of the tissue and tracer used, and can be modeled by considering the tracer kinetics for capillary-tissue exchange.

In this study, we compared bicompartmental versions of the CC, ATH, and DP models for R(t). Each model represented R(t) in two compartments: intravascular space and extravascular extracellular space. Table 1 lists the definitions of the physical terms discussed here. A constant flow (or perfusion) F is assumed to supply the intravascular space, and the mean time taken by the tracer to traverse the intravascular space is called the mean vascular transit time, t1. The tracer could also diffuse between the two compartments at a rate that depends on the transfer constants K21 and K12, which denote the rates of influx and efflux (backflux), respectively. For all three models, the transfer constants have been assumed to be equal to the permeability–surface area product PS, given an assumed nonpreferential diffusion of tracer between compartments (29,30). The impulse residue functions R(t) for CC, DP, and ATH models are expressed according to the conventions proposed by Tofts et al (31). The impulse residue functions for the CC and DP models (Eqq [A2], [A4], [A5]) depend explicitly on the ratio of the transfer constant and its associated fractional volume, which is called the rate constant, k12 = K12/v2, where v1 and v2 are the fractional volume of compartments 1 and 2, respectively (31). In the CC and DP models, the four fundamental kinetic parameters that can be estimated directly through parametric fitting of Equation (1) with dynamic contrast-enhanced imaging data are F, t1, k12, and k21. Other physiologic parameters, such as the fractional vascular volume v1, first-pass extraction ratio E, permeability–surface area product PS, and fractional volume of extravascular extracellular space v2, can be derived from these fundamental kinetic parameters with the CC and DP models by using appropriate approximations and assumptions (Appendix). In the ATH model, the four fundamental parameters that can be obtained with parametric fitting are F, t1, k12, and E; estimates of v1, v2, and PS can be derived from these measurements on the basis of further assumptions (Appendix).


View this table:
[in this window]
[in a new window]

  		TABLE 1. Definition of Terms for Microcirculatory Parameters

 
Patients and Dynamic Contrast-enhanced CT Protocol
Our study was approved by the local ethics committee. Informed consent was obtained from six consecutive patients with intracranial meningioma who were studied over a 10-month period (two women and four men with a mean age of 59.3 years ± 9.27 [standard deviation]). All patients underwent CT for evaluation of perfusion in intracranial mass lesions. Final diagnosis was based on the results of histologic analysis (four patients) and follow-up imaging (two patients). A slip-ring helical CT scanner (HiSpeed CT/i; GE Medical Systems, Milwaukee, Wis) that allows for cine mode scanning was used in the imaging studies. Dynamic CT images were obtained of a single section at the level of the largest tumor diameter identified on nonenhanced CT scans. Fifty contrast-enhanced images were acquired with a scanning time of 1 second per image and with intravenous injection of 50 mL of nonionic iodinated contrast medium containing 300 mg of iodine per milliliter (Omnipaque; Nycomed, Oslo, Norway) at a rate of 4 mL/sec by using an automatic injector. Parameters for contrast-enhanced CT were 80 kVP, 190 mAs, 512 x 512 matrix, 20–25-cm field of view, and 10-mm (five patients) or 5-mm (one patient) collimation. None of the patients experienced any complications directly related to this study.

Image Analysis
The CT image data were transferred for analysis to a personal computer with a Pentium IV processor. With the use of specially developed software (SPM; University College, London, England) and with the first image used as a template, image registration was corrected for any patient movement during scanning. To derive the arterial input function Ca(t) for each patient, a region of interest (ROI) was manually drawn (L.H.D.C., C.C.T.L.) over an artery that clearly occupied at least one voxel along the plane of the CT image and that showed an early bolus arrival time. To obtain the tissue curves {r04se04e02} for tumor and normal tissues, ROIs were drawn (L.H.D.C., C.C.T.L.) over the meningioma and in areas of normal white matter and gray matter on the contralateral side. The areas of the ROIs for arteries, meningiomas, white matter, and gray matter were 0.175 mm2 ± 0.020, 76.327 mm2 ± 31.468, 92.511 mm2 ± 40.146, and 107.687 mm2 ± 47.576, respectively. The degree of attenuation that resulted from the concentration of contrast material within the ROI (32) was estimated by one of the authors (L.H.D.C.) computing the mean attenuation value (in Hounsfield units) of all pixels within the ROI. Before commencing this study, we validated the linear relationship between attenuation values and tracer concentration for our CT imager in a calibration experiment by using phantoms of various tracer concentrations.

Arteries in the brain are usually small, and a single artery may not fully occupy a voxel in a section. The effect of partial-volume averaging could result in a decreased value of Ca(t) (32). This underestimation of Ca(t) would, in turn, lead to overestimation of perfusion F, as can be deduced from Equation (1). Using Monte Carlo simulation (29,30), we can obtain estimates of a 25% increase in F even if the sampled artery occupies only about 80% of a voxel. To reduce the effect of partial-volume averaging, one approach is to sample a venous concentration curve to correct for the height of the reduced Ca(t) curve. A suitable vein should clearly occupy at least one voxel in the image plane and should be larger than the arteries (hence, less affected by partial-volume averaging). An ROI is manually drawn (L.H.D.C., T.S.K.) over such a vein to derive the vein concentration-time curve Cv(t). The height of Ca(t) is then scaled upward by equating the areas under the curves of Ca(t) and Cv(t). Implicit is the assumption that an equal amount of tracer enters and eventually leaves the tissue, as represented by Ca(t) and Cv(t), respectively.

Statistical Analysis
A cost function commonly used for quantifying the goodness of fit between model and data is given by the {chi}2 statistic,

{r04se04e03}
where p denotes the array of parameters to be fitted for each model, and vark is the noise variance in the experimental data. Since the {chi}2 statistic gives the sum of squares of deviation between the experimental data and model fittings, a higher {chi}2 value corresponds to greater discrepancy (worse fit) between the data and the model.

A test statistic to compare the goodness of fit of two models with respective {chi}2 values such that {r04se04e04} is greater than {r04se04e05} can be given by

{r04se04e06}
which follows the F distribution (34). We (L.H.D.C., T.S.K.) implemented a one-tailed F test such that, if f( {r04se04e04} , {r04se04e05} ) ≥ f{alpha},ß1,ß2, which is the (1–{alpha}) quantile of the F distribution with degrees of freedom ß1 = ß2 = (n – 1) – 4 = n – 5, and n is the number of data points, then model 2 fits better than model 1 at the 95% confidence level ({alpha} = .05).

The tracer kinetic parameters in p were estimated with least-squares fitting of the theoretical model {r04se04e07} (given in Eq [1]) with the image data set {r04se04e08} by one of the authors (L.H.D.C.), by using software (Matlab version 6.5; Mathworks, Natick, Mass) with a constrained nonlinear optimization algorithm. Linear regression analysis was performed (L.H.D.C., T.S.K.) to assess for correlations between parameter estimates among the various tracer kinetic models. Since we expected the more elaborate DP model to correspond more closely to physiologic reality, the parameter estimates obtained with the CC and ATH models were compared with those obtained with the DP model, by using an approach similar to that of Muzic and Saidel (33). The quantitative measures of interest are the coefficient of determination (r2), P value for correlation, gradient (m), and y intercept (c) of the linear regression. An r2 value close to unity and a P value less than .05 were considered to indicate strong correlation and significant difference, respectively, between the estimates obtained with the two models; and a gradient m close to unity with near-zero intercept c was considered to indicate quantitative equivalence. The one-tailed paired Student t test was used (L.H.D.C., T.S.K.) to compare the parameter estimates in the tumor with those in normal gray matter and white matter.


   Results
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
Results
Discussion
 APPENDIX
 REFERENCES
 
A representative case of intracranial meningioma is shown in Figure 1. Concentration-time curves for meningioma were typically much higher than those for normal white matter and gray matter (Fig 1b). The impulse residue function in the CC model (Fig 1c) differs from those in the ATH and DP models in the first few (approximately 10) seconds, after which the three converge and indicate a closely similar amount of tracer remaining in the ROI and a substantial amount of tracer slowly leaving the ROI. On the other hand, the impulse residue functions for white matter (Fig 1d) and gray matter (Fig 1e) decrease more rapidly than does that for meningioma, which indicates that almost all of the tracer has left the ROI within a short period of time (approximately 3 seconds with the ATH and DP models, and approximately 8 seconds with the CC model).



View larger version (88K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 1a. Intracranial meningioma. (a) Transverse contrast-enhanced CT image shows ROIs for which tracer concentration-time curves were derived. Ca = artery, GM = gray matter, WM = white matter. (b) Plot shows corresponding concentration-time curves for the artery (triangles), meningioma (black circles), and normal white matter (white circles) and gray matter (gray circles). (c-e) Plots show F-scaled curves for impulse residue function over time, F · R(t), obtained for (c) meningioma, (d) white matter, and (e) gray matter by using CC (dotted line), DP (solid line), and ATH (dashed line) models. Curves for ATH and DP models show similar features, related to vascular and parenchymal phases, that may indicate pathologic conditions of brain tissue.

 


View larger version (29K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 1b. Intracranial meningioma. (a) Transverse contrast-enhanced CT image shows ROIs for which tracer concentration-time curves were derived. Ca = artery, GM = gray matter, WM = white matter. (b) Plot shows corresponding concentration-time curves for the artery (triangles), meningioma (black circles), and normal white matter (white circles) and gray matter (gray circles). (c-e) Plots show F-scaled curves for impulse residue function over time, F · R(t), obtained for (c) meningioma, (d) white matter, and (e) gray matter by using CC (dotted line), DP (solid line), and ATH (dashed line) models. Curves for ATH and DP models show similar features, related to vascular and parenchymal phases, that may indicate pathologic conditions of brain tissue.

 


View larger version (20K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 1c. Intracranial meningioma. (a) Transverse contrast-enhanced CT image shows ROIs for which tracer concentration-time curves were derived. Ca = artery, GM = gray matter, WM = white matter. (b) Plot shows corresponding concentration-time curves for the artery (triangles), meningioma (black circles), and normal white matter (white circles) and gray matter (gray circles). (c-e) Plots show F-scaled curves for impulse residue function over time, F · R(t), obtained for (c) meningioma, (d) white matter, and (e) gray matter by using CC (dotted line), DP (solid line), and ATH (dashed line) models. Curves for ATH and DP models show similar features, related to vascular and parenchymal phases, that may indicate pathologic conditions of brain tissue.

 


View larger version (18K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 1d. Intracranial meningioma. (a) Transverse contrast-enhanced CT image shows ROIs for which tracer concentration-time curves were derived. Ca = artery, GM = gray matter, WM = white matter. (b) Plot shows corresponding concentration-time curves for the artery (triangles), meningioma (black circles), and normal white matter (white circles) and gray matter (gray circles). (c-e) Plots show F-scaled curves for impulse residue function over time, F · R(t), obtained for (c) meningioma, (d) white matter, and (e) gray matter by using CC (dotted line), DP (solid line), and ATH (dashed line) models. Curves for ATH and DP models show similar features, related to vascular and parenchymal phases, that may indicate pathologic conditions of brain tissue.

 


View larger version (20K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 1e. Intracranial meningioma. (a) Transverse contrast-enhanced CT image shows ROIs for which tracer concentration-time curves were derived. Ca = artery, GM = gray matter, WM = white matter. (b) Plot shows corresponding concentration-time curves for the artery (triangles), meningioma (black circles), and normal white matter (white circles) and gray matter (gray circles). (c-e) Plots show F-scaled curves for impulse residue function over time, F · R(t), obtained for (c) meningioma, (d) white matter, and (e) gray matter by using CC (dotted line), DP (solid line), and ATH (dashed line) models. Curves for ATH and DP models show similar features, related to vascular and parenchymal phases, that may indicate pathologic conditions of brain tissue.

 
The goodness of fit achieved with the CC and ATH models is compared with that achieved with the DP model in Figure 2. Although there are only two cases in which the DP model performed significantly better (P ≤ .05, 95% confidence level) than the CC model, we noted that the DP model achieved a better fit of the data set than did the CC model in most cases (Fig 2a). The single exception occurred in gray matter in the case that contained the greatest amount of image noise. The ATH model achieved a very similar goodness of fit (Fig 2b).



View larger version (20K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 2a. Graphs show results of {chi}2 goodness-of-fit test for concentration-time curves obtained with the (a) CC and (b) ATH models, plotted against those obtained with the DP model, for meningioma, white matter (WM), and gray matter (GM). Straight dotted lines indicate equal goodness of fit. Points above dotted lines denote cases in which DP model gave better fit; circled points indicate significantly better fit with DP model at 95% confidence level. Insets show magnification of areas inside dotted rectangles.

 


View larger version (16K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 2b. Graphs show results of {chi}2 goodness-of-fit test for concentration-time curves obtained with the (a) CC and (b) ATH models, plotted against those obtained with the DP model, for meningioma, white matter (WM), and gray matter (GM). Straight dotted lines indicate equal goodness of fit. Points above dotted lines denote cases in which DP model gave better fit; circled points indicate significantly better fit with DP model at 95% confidence level. Insets show magnification of areas inside dotted rectangles.

 
Results of regression analysis show excellent correspondence in parameter estimates between the ATH and DP models, with values for r2 and gradient m closely approaching unity (except with regard to the clearance rate constant k12 [r2 = 0.9531, m = 0.69]), as well as near-zero values for intercept c and P for all parameters (Fig 3). There was a strong association between parameter estimates obtained with the CC model and those obtained with the DP model, with r2 close to unity (0.8827 < r2 < 0.9979) and near-zero P values. However, quantitative differences were found between estimates with the CC and DP models, which resulted in various m values for F (m = 1.70), t1 (m = 0.65), k21 (m = 0.82), and v1 (m = 1.25).



View larger version (28K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 3a. Scatterplots show correlation of estimates obtained for microcirculatory parameters (a) F, (b) t1, (c) k12, and (d) k21 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for parameters F, t1, and k21. Scatterplots show correlation of estimates obtained for microcirculatory parameters (e) v1, (f) E, (g) PS, and (h) v2 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for v1.

 


View larger version (27K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 3b. Scatterplots show correlation of estimates obtained for microcirculatory parameters (a) F, (b) t1, (c) k12, and (d) k21 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for parameters F, t1, and k21. Scatterplots show correlation of estimates obtained for microcirculatory parameters (e) v1, (f) E, (g) PS, and (h) v2 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for v1.

 


View larger version (27K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 3c. Scatterplots show correlation of estimates obtained for microcirculatory parameters (a) F, (b) t1, (c) k12, and (d) k21 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for parameters F, t1, and k21. Scatterplots show correlation of estimates obtained for microcirculatory parameters (e) v1, (f) E, (g) PS, and (h) v2 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for v1.

 


View larger version (19K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 3d. Scatterplots show correlation of estimates obtained for microcirculatory parameters (a) F, (b) t1, (c) k12, and (d) k21 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for parameters F, t1, and k21. Scatterplots show correlation of estimates obtained for microcirculatory parameters (e) v1, (f) E, (g) PS, and (h) v2 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for v1.

 


View larger version (26K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 3e. Scatterplots show correlation of estimates obtained for microcirculatory parameters (a) F, (b) t1, (c) k12, and (d) k21 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for parameters F, t1, and k21. Scatterplots show correlation of estimates obtained for microcirculatory parameters (e) v1, (f) E, (g) PS, and (h) v2 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for v1.

 


View larger version (21K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 3f. Scatterplots show correlation of estimates obtained for microcirculatory parameters (a) F, (b) t1, (c) k12, and (d) k21 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for parameters F, t1, and k21. Scatterplots show correlation of estimates obtained for microcirculatory parameters (e) v1, (f) E, (g) PS, and (h) v2 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for v1.

 


View larger version (32K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 3g. Scatterplots show correlation of estimates obtained for microcirculatory parameters (a) F, (b) t1, (c) k12, and (d) k21 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for parameters F, t1, and k21. Scatterplots show correlation of estimates obtained for microcirculatory parameters (e) v1, (f) E, (g) PS, and (h) v2 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for v1.

 


View larger version (34K):
[in this window]
[in a new window]
[Download PPT slide]
  		Figure 3h. Scatterplots show correlation of estimates obtained for microcirculatory parameters (a) F, (b) t1, (c) k12, and (d) k21 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for parameters F, t1, and k21. Scatterplots show correlation of estimates obtained for microcirculatory parameters (e) v1, (f) E, (g) PS, and (h) v2 with CC (circles) and ATH (triangles) models, plotted against those obtained with DP model (squares), for meningioma (black symbols), white matter (white symbols), and gray matter (gray symbols). Linear regression equations are given beside regression lines for CC (dotted line) and ATH (dashed line) models, and corresponding coefficient of determination r2 and P values are stated in legends. Excellent agreement was found between ATH and DP models. Quantitative differences were found between CC and DP models for v1.

 
The parameters k12, k21, E, and PS, which are related to the extravasation of tracer into the extravascular extracellular space, have value ranges that are distinctly separable, without overlap, between meningioma and normal tissues (white matter and gray matter) (Figs 3c, 3d, 3f, 3g). For these extravasation parameters, normal tissues yielded values close to zero because the blood-brain barrier was intact, whereas the values in meningioma were substantially higher. The fractional vascular volume v1 also was generally higher for meningioma than for normal white matter and gray matter, except in one case (Fig 3e).

With all three models, the mean values of all estimated parameters in meningioma were clearly higher than those in normal white matter and gray matter (Table 2). The results of paired Student t tests performed for each tracer kinetic model revealed that the mean values of all parameters in meningioma were significantly (P < .05) higher than those in the normal white matter and gray matter (Table 3).


View this table:
[in this window]
[in a new window]

  		TABLE 2. Estimates of Microcirculatory Parameters with the CC, ATH, and DP Models

 

View this table:
[in this window]
[in a new window]

  		TABLE 3. Results of Comparison of Microcirculatory Parameter Estimates in Meningioma with Those in Normal Tissues

 

   Discussion
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
Results
 Discussion
APPENDIX
 REFERENCES
 
To the best of our knowledge, this is the first application of the DP model to dynamic contrast-enhanced CT of intracranial meningioma and brain tissues. Nevertheless, we can compare our parameter estimates for the DP, ATH, and CC models with those reported in the literature. The F values of 19.93 mL ± 7.25 and 19.95 mL ± 7.23 per 100 g·min, which we obtained for normal white matter by using the DP and ATH models, respectively, are in good agreement with the value of 22.9 mL per 100 g · min, reported by Nabavi et al (35). For gray matter, the F values of 29.71 mL ± 9.65 and 29.69 mL ± 9.64 per 100 g · min, estimated by using the DP and ATH models, respectively, are lower than the value reported by Nabavi et al (44.3 mL per 100 g · min). The F values that we estimated by using the CC model are generally higher: 38.83 mL ± 15.51 and 58.44 mL ± 12.45 per 100 g·min, for white matter and gray matter, respectively. The relatively large standard deviations for these estimates may be attributable to the small sample size in this initial study.

The present t1 values for normal white matter and gray matter are 2.95 seconds ± 0.86 and 3.23 seconds ± 2.06, respectively, for both the DP and the ATH models. These values are in good agreement with those reported by Eastwood et al (3.4 seconds ± 0.6) (36) and obtained by Ostergaard et al (white matter, 3.19 seconds ± 0.93; gray matter, 2.62 seconds ± 0.6) with their numeric deconvolution method (37). The t1 values obtained with the CC model in the present study are slightly lower: 1.78 seconds ± 0.44 and 1.82 seconds ± 0.60 for white matter and gray matter, respectively.

The estimated PS values for meningioma were 51.18 mL ± 48.15, 51.52 mL ± 48.86, and 52.40 mL ± 59.30 per 100 g·min, for the DP, ATH, and CC models, respectively. These are comparable with the values of 57.5 to 462 mL per 100 g·min, reported by Yeung et al (26), and 14.3 mL ± 10.9 per 100 g · min, reported by Andersen and Jensen (13) for an analysis performed with the CC model in data sets obtained with dynamic MR imaging with gadopentetate dimeglumine in six patients.

The behavior of the impulse residue function R(t) as estimated with the ATH and DP models can be described as consisting of two phases: a vascular phase and a parenchymal phase (28–30). During the vascular phase, R(t) remains constant for a time t1, which is determined by the average time needed for the tracer to traverse the intravascular space. If there are highly permeable blood vessels in the tumor, or if there is disruption of the blood-brain barrier, a portion of the tracer could diffuse into the extravascular extracellular space (28–30). The proportion of tracer that leaks into the extravascular extracellular space can be estimated by the first-pass extraction ratio E. After t1, the tracer that was not extracted and that remains in the intravascular space, exits through outflowing blood, which results in a sudden decrease in R(t). The vascular phase is then followed by a parenchymal phase, during which a more gradual decrease in R(t) occurs as the extracted portion diffuses back into the intravascular space and is cleared by means of blood outflow.

Hence, the behavior of the impulse residue function R(t) as estimated with the ATH or DP models should differ between meningioma and normal brain tissue. Since the normal white matter and gray matter have an intact blood-brain barrier, R(t) exhibits only the vascular phase, during which R(t) remains constant, followed by a rapid decrease to zero during the parenchymal phase. In meningiomas with leaky blood vessels, however, a portion of the tracer might escape, and the parenchymal phase would ensue. This difference in behavior of the impulse residue functions was seen in all of our cases, and it can be observed by comparing the trends of the impulse residue functions. On the other hand, the CC model, because of its strictly biexponential form, yields monotonically decreasing impulse residue functions for both normal tissues and meningioma, with a more rapidly decreasing trend for normal tissues.

Hence, apart from the extravasation parameters, the ATH and DP impulse residue functions can also display features related to the parenchymal phase that reveal possible pathologic conditions of the brain tissue. We note that ATH and DP impulse residue functions for meningioma also exhibit a longer vascular phase than do those for normal white matter and gray matter. This finding suggests longer path lengths and transit times between the feeding and draining vessels in the tumor. This phenomenon may be important in neoangiogenesis, especially in primary malignant tumors, in which denser and more irregular vasculature causes the tracer to traverse long and circuitous paths within the tumor.

The good agreement of most parameter estimates obtained by using the ATH model with those obtained by using the DP model indicates that the adiabatic approximation is appropriate for use in estimating these parameters. The only parameter for which estimates with the ATH model deviated appreciably from those with the DP model is the efflux rate constant, k12. With the ATH model, k12 is given by kadb = EF/v2 (Appendix). The deviation becomes more obvious as k12 increases. Given that a higher rate constant may be associated with higher vessel permeability, this development indicates the potential difficulty of using the adiabatic efflux rate constant to approximate the actual rate constant in a regime of high permeability. When vessel permeability is high, a more rapid exchange of substances between the intravascular space and extravascular extracellular space is expected, and the tracer concentration in the extravascular extracellular space varies more closely with the concentration in the intravascular space. Because the adiabatic approximation assumes a much slower rate of exchange of tracer concentration in the extravascular extracellular space compared with that in the intravascular space (29), the adiabatic efflux rate constant kadb might deviate from the actual rate constant. Nevertheless, a linear correlation between kadb and k12 was observed.

On the basis of our present data sets, the parameter estimates obtained with the CC model were linearly correlated with those of the DP model, but some parameters did not correspond quantitatively. The implication is that, although some parameter estimates obtained with the CC model did not agree quantitatively with those obtained with the ATH and DP models, all three models might yield similar results qualitatively, in classification and correlation studies, because of good linear correlation. Generally, on the basis of the present goodness-of-fit results for estimates obtained with the three models in the various tissues, we believe that the ATH and DP models better describe the dynamic contrast-enhanced image data sets and the underlying kinetic processes than does the CC model. This conclusion is consistent with the results of a study by Larson et al (28), who found that the DP model yielded a better fit of their experimental data sets than did the CC model.

Although only the parameters related to extravasation could give distinct parameter ranges between meningioma and normal white matter and gray matter, the results of the paired t tests reveal that all of the parameters show a significant increase for meningioma compared with normal tissue. The increase in F, v1, and t1 suggests a denser vasculature that is more perfused, and the increase in rate constants, E, and PS indicates that the vessels are leaky. Hence, enhancement of meningioma on dynamic contrast-enhanced images could be based on a combination of increased extravasation, high perfusion, and dense vasculature.

Here, we should also indicate the limitations of the present study. Because of the lack of existing reference standards (32) for in vivo quantification of the various blood flow parameters, the question of which model is more accurate for estimating such parameters in situations in which the parameters differ among models can only be discussed from the standpoint of theoretical accuracy or realism in the derivation of the impulse residue models and the comparison of model fittings of the data sets. It is hoped that, in the near future, more case studies can be carried out to add statistical strength to such analysis, as the medical imaging community awaits the development of reference standards. In addition, in this study only a single tumor type (meningioma) was studied. Because meningiomas are known to be much more permeable than other brain tumor types, they could be more easily distinguished from normal brain tissues; hence, the present findings may not be representative of brain tumors in general. Similar studies with other brain tumor types should be encouraged.

In summary, we found excellent agreement between parameter estimates obtained with the ATH and DP models, except for the ATH efflux rate constant, which may be underestimated in comparison with the corresponding DP rate constant in the regime of high permeability. Although a significant linear correlation was found between estimates obtained with the CC model and those obtained with the DP model, some parameters (F, t1, v1, k21) did not correspond quantitatively. The DP model not only possesses more realism theoretically, it was found to consistently give better fittings than the CC model. Another advantage of the ATH and DP models is that their impulse residue functions might reveal features indicative of pathologic conditions in brain tissue. Although all parameter estimates in all three models showed significant increases for meningioma compared with normal tissues, only the parameters related to extravasation exhibited nonoverlapping ranges. These parameters may be useful for differentiating between normal and abnormal tissues.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
Results
 Discussion
 APPENDIX
REFERENCES
 
In this study, each of the three tracer kinetic models (CC, ATH, and DP) is a bicompartmental system that can be described by a pair of linear differential equations, with consideration for the conservation of tracer mass. The CC and DP models differ in the formulation of these differential equations, because of the different assumptions on which the system is based. The formal solution of the impulse residue function for each model can be obtained by simultaneously solving the paired differential equations.

The CC model assumes instantaneously well-mixed (homogeneous) compartments, and a pair of differential equations for the two interacting compartments can be given by

{r04se04e09}
and

{r04se04e10}
where {delta}t(t) is the unit impulse at t = 0, and v1, v2, {rho}, C1, and C2 are defined as in Table 1.

The solution for the impulse residue function of the CC model is

{r04se04e11}
which is a biexponential function with

{r04se04e12}
and

{r04se04e13}

The DP model does not assume a homogeneous intravascular space; it defines the tracer concentration within the intravascular space as a function of both time and position along the length L of the capillary. Because of the small radial dimension of a capillary, however, radial concentration gradients can be ignored, and concentration is assumed to be homogeneous in the radial direction. Therefore, as pointed out by Larson et al (28), the DP model encompasses a combination of CC and DP assumptions, expressed in the following set of differential equations:

{r04se04e14}
and

{r04se04e15}
where z is the distance from the arterial end, {delta}t(t){delta}z(z) is the unit impulse at t = 0 and z = 0, and other terms are defined as in Table 1.

The corresponding impulse residue function for the DP model (30) is

{r04se04e16}
where

{r04se04e17}
and I1 is the modified Bessel function. The first-pass extraction ratio for the DP model can be formally evaluated as E = 1 – exp(–k21t1).

For both the CC and DP models, the four fundamental kinetic parameters, which can be directly estimated with parametric fitting of Equation (1), are F, t1, k12, and k21. Additional parameters of physiologic importance can be deduced from the four fundamental kinetic parameters. Using the central volume principle (32), we may calculate the fractional vascular volume v1 by

{r04se04e18}
When there is no preferential extraction for the diffusible tracer (ie, when nonselective distribution takes place through passive diffusion), the transfer constants in opposite directions may be assumed to be equal (ie, Ki1 = K1i) and may be associated with the permeability–surface area product PS. We may then estimate PS as

{r04se04e19}
The fractional extravascular extracellular space volume v2 can then be estimated as

{r04se04e20}
The ATH model has a formulation similar to that of the DP model but differs in the use of the adiabatic approximation to solve for the impulse residue function. The resultant solution for the impulse residue function with the ATH model is

{r04se04e21}
where kadb = EF/v2 is the adiabatic version of the efflux (clearance) rate constant k12. RATH(t) is much simpler (and hence more efficiently calculated) than RDP(t). The parameters that can be directly estimated by parametric fitting of Equation (1), are F, t1, kadb, and E. We may again use Equation (A7) to estimate v1, and PS may be estimated by using the following equation developed by Renkin (38) and Crone (39):

{r04se04e22}


   FOOTNOTES
 
See also Science to Practice in this issue.

Authors stated no financial relationship to disclose.

Abbreviations: ATH = adiabatic tissue homogeneity, CC = conventional compartmental, DP = distributed parameter, ROI = region of interest

Author contributions: Guarantors of integrity of entire study, C.C.T.L., T.S.K.; study concepts and design, L.H.D.C., C.C.T.L., T.S.K.; literature research, L.H.D.C., C.C.T.L., T.S.K.; clinical studies, C.C.T.L.; data acquisition, C.C.T.L.; data analysis/interpretation, L.H.D.C., C.C.T.L., T.S.K.; statistical analysis, T.S.K., L.H.D.C.; manuscript preparation, L.H.D.C.; manuscript definition of intellectual content, editing, revision/review, and final version approval, L.H.D.C., C.C.T.L., T.S.K.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
Results
 Discussion
 APPENDIX
 REFERENCES
 

  1. Turetschek K, Huber S, Floyd E, et al. MR imaging characterization of microvessels in experimental breast tumors by using a particulate contrast agent with histopathologic correlation. Radiology 2001; 218:562-569.[Abstract/Free Full Text]
  2. Ludemann L, Grieger W, Wurm R, Budzisch M, Hamm B, Zimmer C. Comparison of dynamic contrast-enhanced MRI with WHO tumor grading for gliomas. Eur Radiol 2001; 11:1231-1241.[CrossRef][Medline]
  3. Padhani AR, Husband JE. Dynamic contrast-enhanced MRI studies in oncology with an emphasis on quantification, validation and human studies. Clin Radiol 2001; 56:607-620.[CrossRef][Medline]
  4. DeVries AF, Griebel J, Kremser C, et al. Tumor microcirculation evaluated by dynamic magnetic resonance imaging predicts therapy outcome for primary rectal carcinoma. Cancer Res 2001; 61:2513- 2516.[Abstract/Free Full Text]
  5. Lyng H, Vorren AO, Sundfor K, et al. Assessment of tumor oxygenation in human cervical carcinoma by use of dynamic Gd-DTPA-enhanced MR imaging. J Magn Reson Imaging 2001; 14:750-756.[CrossRef][Medline]
  6. Yamashita Y, Baba T, Baba Y, et al. Dynamic contrast-enhanced MR imaging of uterine cervical cancer: pharmacokinetic analysis with histopathologic correlation and its importance in predicting the outcome of radiation therapy. Radiology 2000; 216:803-809.[Abstract/Free Full Text]
  7. Uematsu H, Maeda M, Sadato N, et al. Vascular permeability: quantitative measurement with double-echo dynamic MR imaging—theory and clinical application. Radiology 2000; 214:912-927.[Abstract/Free Full Text]
  8. Cooper RA, Carrington BM, Loncaster JA, et al. Tumour oxygenation levels correlate with dynamic contrast-enhanced magnetic resonance imaging parameters in carcinoma of the cervix. Radiother Oncol 2000; 57:53-59.[CrossRef][Medline]
  9. Gong QY, Brunt JN, Romaniuk CS, et al. Contrast enhanced dynamic MRI of cervical carcinoma during radiotherapy: early prediction of tumour regression rate. Br J Radiol 1999; 72:1177-1184.[Abstract]
  10. Hoskin PJ, Saunders MI, Goodchild K, Powell ME, Taylor NJ, Baddeley H. Dynamic contrast enhanced magnetic resonance scanning as a predictor of response to accelerated radiotherapy for advanced head and neck cancer. Br J Radiol 1999; 72:1093-1098.[Abstract]
  11. Mayr NA, Hawighorst H, Yuh WT, Essig M, Magnotta VA, Knopp MV. MR microcirculation assessment in cervical cancer: correlations with histomorphological tumor markers and clinical outcome. J Magn Reson Imaging 1999; 10:267-276.[CrossRef][Medline]
  12. Taylor JS, Tofts PS, Port R, et al. MR imaging of tumor microcirculation: promise for the new millennium. J Magn Reson Imaging 1999; 10:903-907.[CrossRef][Medline]
  13. Andersen C, Jensen FT. Differences in blood-tumour-barrier leakage of human intracranial tumours: quantitative monitoring of vasogenic oedema and its response to glucocorticoid treatment. Acta Neurochir (Vienna) 1998; 140:919-924.[CrossRef]
  14. Griebel J, Mayr NA, De Vries A, et al. Assessment of tumor microcirculation: a new role of dynamic contrast MR imaging. J Magn Reson Imaging 1997; 7:111-119.[Medline]
  15. Rijpkema M, Kaanders JH, Joosten FB, Kogel AJ, Heerschap A. Method for quantitative mapping of dynamic MRI contrast agent uptake in human tumors. J Magn Reson Imaging 2001; 14:457-463.[CrossRef][Medline]
  16. Koh TS, Zeman V, Darko J, et al. The inclusion of capillary distribution in the adiabatic tissue homogeneity model of blood flow. Phys Med Biol 2001; 46:1519-1538.[CrossRef][Medline]
  17. Kuhl CK, Mielcareck P, Klaschik S, et al. Dynamic breast MR imaging: are signal intensity time course data useful for differential diagnosis of enhancing lesions? Radiology 1999; 211:101-110.[Abstract/Free Full Text]
  18. Brix G, Bahner ML, Hoffmann U, Horvath A, Schreiber W. Regional blood flow, capillary permeability, and compartmental volumes: measurement with dynamic CT—initial experience. Radiology 1999; 210:269-276.[Abstract/Free Full Text]
  19. Knopp MV, Weiss E, Sinn HP, et al. Pathophysiologic basis of contrast enhancement in breast tumors. J Magn Reson Imaging 1999; 10:260-266.[CrossRef][Medline]
  20. Port RE, Knopp MV, Hoffmann U, Milker-Zabel S, Brix G. Multicomparmental analysis of gadolinium chelate kinetics: blood-tissue exchange in mammary tumors as monitored by dynamic MR imaging. J Magn Reson Imaging 1999; 10:233-241.[CrossRef][Medline]
  21. Barbier EL, Den Boer JA, Peters AR, Rozeboom AR, Sau J, Bonmartin A. A model of the dual effect of gadopentetate dimeglumine on dynamic brain MR images. J Magn Reson Imaging 1999; 10:242-253.[CrossRef][Medline]
  22. Hulka CA, Edmister WB, Smith BL, et al. Dynamic echo-planar imaging of the breast: experience in diagnosing breast carcinoma and correlation with tumor angiogenesis. Radiology 1997; 205:837-842.[Abstract/Free Full Text]
  23. Buadu LD, Murakami J, Murayama S, et al. Breast lesions: correlation of contrast medium enhancement patterns on MR images with histopathologic findings and tumor angiogenesis. Radiology 1996; 200:639-649.[Abstract/Free Full Text]
  24. Tofts PS, Berkowitz B, Schnall MD. Quantitative analysis of dynamic Gd-DTPA enhancement in breast tumors using a permeability model. Magn Reson Med 1995; 33:564-568.[Medline]
  25. Hulka CA, Smith BL, Sgroi DC, et al. Benign and malignant breast lesions: differentiation with echo-planar MR imaging. Radiology 1995; 197:33-38.[Abstract/Free Full Text]
  26. Yeung WT, Lee TY, Del Maestro RF, Kozak R, Bennett JD. Effect of steroids on iopamidol blood-brain transfer constant and plasma volume in brain tumors measured with x-ray computed tomography. J Neurooncol 1994; 18:53-60.[CrossRef][Medline]
  27. Johnson JA, Wilson TA. A model for capillary exchange. Am J Physiol 1966; 210:1299-1303.[Free Full Text]
  28. Larson KB, Markham J, Raichle ME. Tracer-kinetic models for measuring cerebral blood flow using externally detected radiotracers. J Cereb Blood Flow Metab 1987; 7:443-463.[Medline]
  29. St Lawrence KS, Lee T. An adiabatic approximation to the tissue homogeneity model for water exchange in the brain. I. Theoretical derivation. J Cereb Blood Flow Metab 1998; 18:1365-1377.
  30. Koh TS, Cheong LH, Hou Z, Soh YC. A physiologic model of capillary-tissue exchange for dynamic contrast-enhanced imaging of tumor microcirculation. IEEE Trans Biomed Eng 2003; 50:159-167.[CrossRef][Medline]
  31. Tofts PS, Brix G, Buckley DL, et al. Estimating kinetic parameters from dynamic contrast-enhanced T1-weighted MRI of a diffusible tracer: standardized quantities and symbols. J Magn Reson Imaging 1999; 10:223-232.[CrossRef][Medline]
  32. Lee TY. Functional CT: physiological models. Trends Biotechnol 2002; 20 (suppl 8):S3-S10.
  33. Muzic RF, Jr, Saidel GM. Distributed versus compartment models for PET receptor studies. IEEE Trans Med Imaging 2003; 22:11-21.[CrossRef][Medline]
  34. Bevington PR. Data reduction and error analysis for the physical sciences New York, NY: McGraw-Hill, 1969.
  35. Nabavi DG, Cenic A, Craen RA, et al. CT assessment of cerebral perfusion: experimental validation and initial clinical experience. Radiology 1999; 213:141-149.[Abstract/Free Full Text]
  36. Eastwood JD, Lev MH, Azhari T, et al. CT perfusion scanning with deconvolution analysis: pilot study in patients with acute middle cerebral artery stroke. Radiology 2002; 222:227-236.[Abstract/Free Full Text]
  37. Ostergaard L, Sorensen AG, Kwong KK, Weisskoff RM, Gyldensted C, Rosen BR. High resolution measurement of cerebral blood flow using intravascular tracer bolus passages. II. Experimental comparison and preliminary results. Magn Reson Med 1996; 36:726-736.
  38. Renkin EM. Transport of potassium-42 from blood to tissue in isolated mammalian skeletal muscles. Am J Physiol 1959; 197:1205-1210.[Abstract/Free Full Text]
  39. Crone C. The permeability of capillaries in various organs as determined by use of the indicator-dilution method. Acta Physiol Scand 1963; 58:292-305.[Medline]



This article has been cited by other articles:


Home page
 RadiologyHome page
W. T. Sobol and J. K. Cure
Can in Vivo Assessment of Tissue Hemodynamics with Dynamic Contrast-enhanced CT Be Used in the Diagnosis of Tumors and Monitoring of Cancer Therapy Outcomes?
Radiology, September 1, 2004; 232(3): 631 - 632.
[Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
2323031198v1
232/3/921    most recent
Right arrow Submit a response
Right arrow Alert me when this article is cited
Right arrow Alert me when eLetters are posted
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Dennis Cheong, L. H.
Right arrow Articles by Koh, T. S.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Dennis Cheong, L. H.
Right arrow Articles by Koh, T. S.

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
RADIOLOGY RADIOGRAPHICS RSNA JOURNALS ONLINE