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Magn Reson Imaging. Author manuscript; available in PMC 2010 November 1.

Published in final edited form as:

Published online 2009 June 25. doi: 10.1016/j.mri.2009.05.015

PMCID: PMC2763042

NIHMSID: NIHMS119957

The publisher's final edited version of this article is available at Magn Reson Imaging

See other articles in PMC that cite the published article.

A baseline T_{10} value is typically needed for dynamic contrast-enhanced (DCE-) MRI studies. However, an assumed baseline T_{10} has to be used when T_{10} measurements for patients are not available. In this work, we systematically investigate the dependence on T_{10} of the commonly used DCE-MRI parameters (*K ^{trans}*,

Dynamic contrast-enhanced- (DCE-) MRI is a technique by which images are acquired during intravenous injection of a gadolinium contrast agent to assess the vascular characteristics of tissues. DCE-MRI is commonly used in cancer diagnosis, in which DCE-MRI-based measures correlate well with tumor angiogenesis [1–6]. DCE-MRI is also used to assess cancer drug efficacy by comparing findings from imaging acquired before and after therapy [7, 8]. DCE-MRI has also been applied in assessing cerebral [9] and cardiac [10] ischemia.

Although DCE-MRI is growing in importance in many clinical applications, repeatability is a major limiting factor preventing it from being used in wider applications and clinical trials [11–13]. One factor that drastically limits repeatability is the intrinsic baseline T_{10}. A T_{10} is generally required for quantitative [14] and semi-quantitative analyses [15] to determine DCE-MRI kinetic parameters, and any error in T_{10} measurement can be magnified in the resulting parameters.

There are several techniques available for assessing T_{10}. One accurate method is the inversion recovery (IR) technique, but IR methods for T_{10} assessment often require long scan times, particularly when large volume coverage is desired [16]. A more efficient technique is the variable flip angle method, which uses a set of gradient recalled-echo images with different flip angles [17–19]. However, errors caused by radiofrequency field inhomogeneity or uncertainty can be significant when using this method [19]. Even though the actual flip angle could be measured to correct for field inhomogeneity to some extent [20], T_{10} measurement is still problematic due to other factors, such as imperfect slice profile. In large clinical studies, T_{10} measurements for some patients may also not be reliable or available due to either motion or other factors. An assumed T_{10} value has to be used in DCE-MRI analyses when a measured T_{10} is not available.

Given the difficulty of assessing the baseline T_{10}, Haacke et al. [13] recently presented a parameter, NR50, which is independent of T_{10}. NR50 represents the relative change in the median of the initial area under the signal-time curve (IAUC) for assessing drug effectiveness by comparing pre- and post-treatment findings. T_{10} independence of NR50 assumes that T_{10}s are unchanged pre- and post-treatment. But this assumption may not be generally true when treatment is involved.

DCE-MRI kinetic parameters (*K ^{trans}*,

In this paper, we have also defined several new characteristic parameters, the normalized ratios (NR) of *K ^{trans}*,

In DCE-MRI, the tracer concentration in the tissue, *C _{t}*, also called tissue enhancement curve (TEC), can be described by Tofts' model [28], one of the modified Kety models [29].

$$\begin{array}{c}\hfill {C}_{t}\left(t\right)={\upsilon}_{p}{C}_{p}\left(t\right)+{K}^{\mathit{trans}}{C}_{p}\left(t\right){e}^{-\frac{{K}^{\mathit{trans}}t}{{\upsilon}_{e}}}\hfill & \hfill ={\upsilon}_{p}{C}_{p}\left(t\right)+{K}^{\mathit{trans}}{C}_{p}\left(t\right){e}^{-{k}_{\mathit{ep}}t}\hfill \end{array}$$

(1)

where *C _{p}* is the tracer concentration in the blood plasma,

While absolute values of the above DCE-MRI kinetic parameters may be of some interest in cross-sectional studies, the relative change in these parameters subsequent to therapy may be an additional pertinent measure of treatment effects in serial studies. For this purpose, analogous to the definition of NR50 [13], which is the normalized ratio of IAUC, three new parameters, the normalized ratios (NR) of *k _{ep}*,

$$\mathit{NR}=\frac{{P}^{\mathit{pre}}-{P}^{\mathit{post}}}{{P}^{\mathit{pre}}}$$

(2)

where *P* represents perfusion parameters (*k _{ep}*,

A series of simulations were performed to investigate how the parameters (*k _{ep}*,

An AIF was generated according to the experimentally derived functional form [30], which is based on a population-averaged high-temporal-resolution AIF measurement:

$${C}_{b}\left(t\right)=\frac{\alpha {e}^{-\beta t}}{1+{e}^{-s(t-\tau )}}+\sum _{n=1}^{2}\frac{{A}_{n}}{\sqrt{2\pi}}{e}^{-\frac{{(t-{\tau}_{n})}^{2}}{2{\sigma}_{n}^{2}}}$$

(3)

where α is 1.05 mmol; β is 0.1685 min^{−1}; s is 38.078 min^{−1}; τ is 0.483 min; A_{1} is 14.3694 mmol; A_{2} is 2.5 mmol; τ_{1} is 0.17046 min; τ_{2} is 0.365 min; σ_{1} is 0.0563 min; and σ_{2} is 0.132 min [30]. TECs were generated according to Eq. (1) using various *K ^{trans}* and

The tracer concentration in the tissue, *C _{t}*, was then generated using this AIF and given kinetic parameters (

$$S\left(t\right)=\frac{{M}_{0}\phantom{\rule{thinmathspace}{0ex}}\mathrm{sin}\phantom{\rule{thinmathspace}{0ex}}\theta (1-{e}^{-\mathit{TR}({R}_{10}+\Delta {R}_{1}\left(t\right))})}{1-\mathrm{cos}\phantom{\rule{thinmathspace}{0ex}}\theta {e}^{-\mathit{TR}({R}_{10}+\Delta {R}_{1}\left(t\right))}}$$

(4)

where *R _{10}* =

In our simulation, T_{10} independence of *K ^{trans}*,

For in vivo studies, DCE-MRI data from six pediatric patients aged from 11 to 16 with osteosarcoma treated on a phase II trial of multi-agent chemotherapy acquired previously from 1999 to 2008 were utilized. Prior institutional review board approval and informed consent were obtained. DCE-MRI images were acquired on a 1.5 T Siemens Symphony scanner at presentation (before chemotherapy, week 0) and at week 12. After selection of the single slice that best showed the tumor, images were acquired before, during, and after bolus injection into a central line of a 0.1 mmol/kg dose of Gd-DTPA, followed by a saline flush. Thirty sequential FLASH images (TR[TE=23/10 ms, 40°flip angle, xres/yres = 256/256, 10 mm thickness, 40–50 cm FOV, 2 acquisitions) were collected over a 6.5 minute period. Tumor regions of interest (ROIs) for all patients were drawn by an experienced radiologist. A measured AIF was not available for these patients and AIF shown in Eq. (3) was used for the computation of *K ^{trans}* and

The baseline T_{10} was measured prior to the DCE-MRI scan using the optimized IR method [16]. A turbo inversion recovery (TIR) pulse sequence was used to acquire four images with different TIs, 100, 500, 900 and 2400 ms. The TIR protocol was as follows: single slice with 10 mm thickness; TR/TE = 2500/60 ms; xres/yres = 256/192; 40–50 cm FOV the same as DCE-MRI images; echo train length was 11; ~45 seconds for each acquisition. Occasionally, IR images were corrupted by large patient movements which caused the slice position to shift dramatically and T_{10} could not be computed.

Figure 1 shows the simulation results of the baseline T_{10} dependence of *K ^{trans}*,

Plots of *K*^{trans} (a), IAUC (b) and *k*_{ep} (c) vs. assumed baseline T_{10} when the true T_{10}=800 ms. The y-axis represents the computed *K*^{trans} (or IAUC or *k*_{ep}) values when an assumed T_{10} (x-axis) is used. For each plot, the three curves represent results for **...**

The nonlinear relationship between the signal and the change of the relaxivity rate (ΔR_{1}) (i.e. the concentration) for different flip angles using a spoiled gradient echo pulse sequence is shown in Fig. 2. The results in Fig. 2a show that there existed strong nonlinearity between the signal and ΔR_{1} for small flip angles; however, the relationship became more linear as the flip angle increased. When the signal is linearly proportional to the concentration, *k _{ep}* is independent of T

Nonlinearity changes as flip angle. (a) The relationship between the signal amplitude and ΔR_{1} becomes more linear as flip angle becomes larger; (b) *k*_{ep} is less dependent on T_{10} at larger flip angles. TR of 4 ms was assumed.

Fig. 3 shows that the normalized ratios (NRs) of *k _{ep}*,

Plots of the normalized ratios of IAUC, *k*_{ep}, *K*^{trans} and *v*_{e}. True NRs are 0.77, 0.6, 0.5 and 0.125, respectively (dotted lines). The same true T_{10} (800 ms) was assumed for both pre- and post-treatment.

T_{10} independence of the normalized ratios could vary with the true T_{10}. Fig. 4a shows the independence of the normalized ratio of *K ^{trans}* for four different true T

Plots of the normalized ratios of *K*^{trans} for the different true T_{10} values (a) and flip angles (b). The true NR of *K*^{trans} is 0.5. The same true T_{10}s were assumed for both pre- and post-treatment. The large dots are the true NRs for the different true **...**

Baseline T_{10}s for pre- and post-treatment were often assumed to be the same when T_{10} measurements were not available. However, this assumption may generally not be valid. Table 1 shows average T_{10} values within whole tumor ROIs from the six osteosarcoma patients without motion. According to the table, chemotherapy treatment can lead to substantial changes in T_{10}, e.g. over 300 ms change between pre- and post-treatment in some cases. Effects of T_{10} changes on the normalized ratios were investigated using simulations and the results are shown in Fig. 5. The normalized ratio of *k _{ep}* was insensitive to this T

Effects of changes in baseline T_{10} following treatment. Plots of the normalized ratios of *k*_{ep} (a), *K*^{trans} (b), *v*_{e} (c) and IAUC (d) with different pre- and post-treatment baseline T_{10} values. True NRs are 0.0.429, 0.5, 0.125 and 0.36, respectively. A change **...**

Plots of the error of normalized ratios vs. percentage change of T_{10}. The true T_{10}_pre is fixed to 800 ms. The percentage change of T_{10} is equal to (T_{10}_pre-T_{10}_post)/T_{10}_pre.

Results from one of the osteosarcoma patients without motion are demonstrated in Fig. 7. Fig. 7a shows the pre- and post-treatment post-contrast images near the knee with tumor ROIs outside the bone. Even though the shape of tumor outside the bone has slightly changed, two similar ROIs were selected in a relative homogeneous region. Average T_{10} and kinetic parameters (*k _{ep}*,

Baseline T_{10} is necessary to obtain accurate lesion kinetic parameters in DCE-MRI studies. However, physiologic or voluntary motion can often cause large errors or even corrupt T_{10} measurements, especially for 3D volume measurements. Errors in the flip angle and imperfect slice profiles can yield large uncertainties in T_{10} measurements as well when using the variable flip angle (VFA) method. *K ^{trans}*,

Normalized ratios of *k _{ep}*,

The actual T_{10} value and flip angle affected the T_{10}-independent property of normalized ratios of *k _{ep}*,

When the relationship between Gd concentration (and thus ΔR_{1}) and signal is approximately linear, *k _{ep}* could be determined without any T

In conclusion, we have demonstrated with simulations and in vivo experiments that DCE-MRI parameters *k _{ep}* and the normalized ratio of

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