## Introduction

Dynamic susceptibility contrast (DSC) and dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) are the two most common contrast agent techniques used to probe the angiogenic character of brain neoplasms (1). With DSC-MRI, the *T*_{2}* effects of gadolinium (Gd)-chelated contrast agents are exploited. Using this approach, a concentrated bolus of Gd, confined to the intravascular space and perfusing through a tissue capillary bed, induces transient signal loss through spin dephasing caused by vascular–extravascular susceptibility gradients (2, 3). Analysis of DSC-MRI data using indicator dilution theory provides hemodynamic estimates such as relative cerebral blood volume (rCBV), cerebral blood flow (CBF), and mean transit time (4, 5). With DCE-MRI, the *T*_{1} effect of Gd contrast agents is exploited. In particular, contrast agent extravasation, arising from disruptions of the blood–brain barrier (BBB), gives rise to signal enhancement through dipolar interaction between Gd's unpaired electrons and local tissue protons (6, 7). Pharmacokinetic analysis of DCE-MRI data provides insight into the underlying tissue pathophysiology through, for example, estimation of the blood–brain volume transfer constant (K^{trans}); fractional volume of the extravascular, extracellular space (EES) (v_{e}); and the efflux rate constant from EES to plasma (k_{ep}) (8, 9).

Although DSC- and DCE-MRI approaches depend on the predominance of *T*_{2}* and *T*_{1} effects, respectively, the results of both DSC- and DCE-MRI may be confounded by the opposing relaxation effects of Gd. For example, the shift in compartmental distribution of the contrast agent from the intravascular space to the EES can result in *T*_{1} shortening effects that, although necessary for the DCE-MRI technique, compete with and confound DSC-MRI susceptibility-induced signal decreases (10–12). The most well-characterized DSC-MRI parameter affected by *T*_{1} leakage effects is rCBV, and several DSC-MRI acquisition and analysis methods have been developed and applied to mitigate the underestimation of rCBV due to the *T*_{1} leakage effects (13–16).

In this regard, it has been shown that dual-echo acquisition methods (13, 17–21) may be one of the most robust approaches for collecting DSC-MRI data in patients with brain tumor, as *T*_{1} leakage effects can be directly eliminated (17, 22–27). However, it has also been hypothesized that residual *T*_{2}/*T*_{2}* effects, attributable to recirculation and/or contrast agent leakage, may result in overestimations of DSC-MRI parameters if not taken into account.

The first goal of this paper is to introduce a novel method for DSC-MRI perfusion imaging, whereby leakage effects manifesting as either *T*_{1} or *T*_{2}/*T*_{2}* effects can be corrected. The second goal of this paper is to demonstrate that, by using the same dual-echo spiral acquisition method, DCE-MRI parameters can be derived concurrently, independent of the precontrast calibration scans (eg, *T*_{1} maps). Consequently, the complete array of DSC- and DCE-MRI parameters, corrected for confounding contrast agent effects, can be obtained simultaneously in a single acquisition with a single dose of the Gd contrast agent. The feasibility of the method is demonstrated in patients with high-grade brain tumors.

### Theory

To motivate use and ensure full understanding of the advantages of the Spiral Perfusion Imaging with Consecutive Echoes (SPICE) approach, the theory underlying conventional DSC- and DCE-MRI in comparison with SPICE is described here.

### Derivations of DSC-MRI Concentration–Time Curves

#### Conventional DSC-MRI.

The concentration–time curves in DSC-MRI are generated based on an assumed linear relationship between the Gd contrast agent concentration and the change in *apparent transverse* relaxation rate induced by the first passage of the contrast agent through the vasculature (3), and it is calculated using the following equation:

where κ is a constant dependent on transverse relaxivity, field strength, pulse sequence, and vascular morphology (

2). In conventional DSC-MRI, a rapid acquisition method is used to acquire susceptibility-weighted images, and the pulse sequences typically used are of the spoiled gradient echo (GRE) family. The generalized signal equation for conventional DSC-MRI is as follows:

where

*T*_{1}(t) and

*T*_{2}*(t) indicate that these parameters can change dynamically during acquisition. As described in detail in the online

Supplemental Appendix [equations A1 to A5], equation

2 can be used to obtain general expressions for the pre- and postcontrast

*T*_{2}* values, from which a general expression for ΔR2*(t) can be derived as follows:

where

*T*_{10} is the precontrast

*T*_{1} relaxation time and S

_{B} is the mean of the precontrast baseline signal determined by averaging S(t) over the first N

_{B} baseline points. Equation

3 shows the potential influence of dipolar

*T*_{1} effects on concentration–time curves obtained with DSC-MRI. In particular, in the absence of an intact BBB, extravasation of the contrast agent results in

*T*_{1} shortening, causing a confounding reduction in ΔR

_{2}^{*}(t) (

Figure 1A).

##### Figure 1.

Illustration of confounding leakage and recirculation effects on dynamic susceptibility contrast (DSC)-magnetic resonance imaging (MRI) concentration–time curves for representative voxels in normal brain and brain tumor. Representative ΔR_{2}^{*}(t) concentration–time curves are shown for voxels in normal brain and brain tumor after serial primary (1^{0}), 0.1 mmol/kg) (A) and secondary (2^{0}, 0.2 mmol/kg) (B) injections of Gd contrast agent in the same patient with glioma. Acquisitions were performed at 1.5 T using a gradient echo-echo planar imaging (GRE-EPI) pulse sequence with flip angle = 90°, TE = 30 milliseconds, and repetition time (TR) = 1000 milliseconds. In regions of normal brain with an intact BBB, a concentrated bolus of Gd contrast agent will remain compartmentalized to the vasculature, resulting in transient signal changes, that ultimately return to the prebolus baseline value (A). However, in regions of tumor with a disrupted blood–brain barrier (BBB), a fraction of the contrast agent will leak out of the vasculature into the extravascular extracellular space (EES), resulting in *T*_{1} shortening effects that contaminate tumor concentration–time curves. After secondary injection, the postbolus portions of both normal brain and the tumor concentration–time curves are elevated above their prebolus baseline values (B). The fact that this occurs in normal brain, with a presumably intact BBB, suggests that this is not a leakage effect, but instead may be attributable to a residual susceptibility effect caused by recirculation of an increased steady-state concentration of the contrast agent. However, the additional elevated endline in the tumor concentration–time curve suggests a dipolar *T*_{2} leakage effect or additional susceptibility effect. These curves show that both dipolar *T*_{1} and *T*_{2} and/or residual susceptibility effects may confound perfusion estimates derived by DSC-MRI.

In the presence of an intact BBB, the contrast agent remains confined to the vasculature (ie, no extravasation occurs), *T*_{1}(t) is essentially equal to *T*_{10} (ie, its precontrast value), and ΔR_{2}^{*}(t) reduces to its ubiquitous form as follows:

### Correction of DSC-MRI Time Courses for *T*_{1} Extravasation Effects

Dual-echo acquisition methods provide an effective means by which confounding dipolar *T*_{1} leakage effects can be eliminated from DSC-MRI time courses (17–21). The signal equation for the first and second echoes (TE_{i=1,2}) is as follows:

Taking the ratio of the 2 signal equations, an expression for both the baseline and postcontrast 1/*T*_{2}*(t) can be derived, which is as detailed in the online Supplemental Appendix [equations A7 to A11]. From these, the change in the transverse relaxation rate can be derived as follows:

Equation 6 is the DSC-MRI concentration–time curve that is free from the dipolar *T*_{1} leakage effects.

### Correction of DSC-MRI Time Courses for *T*_{2}/*T*_{2}* Effects

In practice, we have observed another potential confounding effect on DSC-MRI concentration–time curves characterized as elevated endlines that develop following the first pass of the contrast agent. As shown in Figure 1B, the effect appears to be exacerbated in brain tumors relative to the normal brain, which implies that there could be an additional susceptibility or *T*_{2} leakage effect in these regions beyond the effects of recirculation. The source of the elevated endlines could be dipolar *T*_{2} effects, residual susceptibility effects from the contrast agent, or some combination of both. Regardless of the source of these elevated endlines, perfusion parameters (eg, rCBV) generated using DSC-MRI may be *overestimated* if postprocessing algorithms do not account for their confounding effects (24).

One approach discussed in the literature for analyzing DSC-MRI data is voxel-wise γ-variate fitting to the concentration–time curves (10). Although fitting of a γ-variate effectively eliminates the majority of recirculation and leakage effects that occur after the first pass, it does not remove the confounding effects of leakage that occur *during* the first pass (Figure 2). A more appropriate model of a DSC-MRI time courses with elevated endlines, introduced by Johnson et al. (28), consists of a γ-variate plus its cumulative integral as follows:

##### Figure 2.

Demonstration of the time course of extravasation effects in DSC-MRI. Postcontrast *T*_{1}-weighted image of a patient with a high-grade glioma (A). Spiral Perfusion Imaging with Consecutive Echoes (SPICE) signals, obtained at short and long TE, for the representative tumor voxel depicted on the postcontrast *T*_{1}-weighted image (B). Leakage of contrast agent begins at the appearance time of the bolus and occurs during the first pass of the bolus (indicated by the shaded region). Following the first pass, leakage continues at a slower rate until back-diffusion occurs (not shown).

where

*k* is a scale factor, t

_{0} is the appearance time of the bolus, α and β are fit parameters, and h is used to scale the cumulative integral of the γ-variate (

Figure 3). Correction for elevated endlines is then performed by nonlinear least squares fitting of equation

7 to the corrupted ΔR

_{2}^{*}(t) concentration–time curves on a voxel-wise basis. After nonlinear least squares fitting, ΔR

_{2}^{*}(t) curves corrected for dipolar

*T*_{1} and

*T*_{2} and residual susceptibility effects are generated by constructing γ-variates using the parameters estimated from the full model fit as follows:

##### Figure 3.

Illustration of the proposed model of DSC-MRI concentration–time curves. The representative ΔR_{2}^{*}(t) concentration–time curve is modeled by a γ-variate plus its cumulative integral scaled by a constant. The γ-variate is used to model the first pass of the tracer, whereas the cumulative integral is used to model recirculation and/or leakage of the tracer.

In comparison with standard γ-variate fits, this two-step method, described by equations 7 and 8, results in corrected concentration–time curves that exhibit reduced peak height and bolus width, as expected in the absence of recirculation and leakage (Figure 4). Conventional algorithms can then be applied to generate estimates of DSC-MRI parameters that are free from confounding contrast agent effects.

##### Figure 4.

Illustration of the differences between methods used to correct DSC-MRI concentration–time curves for recirculation and/or leakage effects. γ-variate fit to ΔR_{2}^{*}(t) (orange) (A). Proposed full model fit to ΔR_{2}^{*}(t) (red) and corrected first pass (blue) (B). Corrected first-pass curves obtained from (A) and (B), (C). Compared to the standard γ-variate (orange), the corrected first-pass curve (blue) from the proposed method is characterized by decreased peak height and bolus width, which should be more representative of the actual first pass in the absence of recirculation and leakage effects.

### Derivation of DCE-MRI Concentration–Time Curves

#### Conventional DCE-MRI.

The concentration–time curves for DCE-MRI are generated on the basis of an assumed linear relationship between Gd concentration and the change in *spin lattice* relaxation rate, ΔR1, resulting primarily from the extravasation of the contrast agent from the vasculature to the EES, where a dipolar interaction between the unpaired electrons of the contrast agent and local tissue protons ensues (7):

where

R1 is the

*T*_{1} relaxivity of the Gd contrast agent. The DCE-MRI technique relies on the sensitivity of the pulse sequence to changes in signal intensity caused by

*T*_{1} shortening. Traditionally, conventional 2- or 3-dimensional spoiled GRE sequences are used in DCE-MRI because they provide good image quality with sufficient temporal resolution. Analogous to DSC-MRI, the generalized signal equation for DCE-MRI is then equivalent to equation

2.

Several methods have been used to convert the dynamic signal intensity time courses into tissue Gd concentration–time curves. In the method used here [which is similar to the Hittmair approach (29)], 1/*T*_{1}(t) and 1/*T*_{10} are obtained directly by solving the pre- and postcontrast signal equations as described in the online Supplemental Appendix [equations A15 and A16], and the results, along with equation 9, are used to determine ΔR_{1}(t) as follows:

Equation 10 shows the potential influence of *T*_{2}* effects on the concentration–time curves obtained with DCE-MRI. In particular, *T*_{2}* shortening may cause a confounding reduction in ΔR_{1}(t). However, because minimum echo times (TE) are typically used, it is widely assumed that an insignificant phase dispersion will occur over time scales of short TE (ie, TE ≪ *T*_{2}*). Consequently, *T*_{2}* effects are generally ignored, which results in the following approximation:

In addition, note that because *T*_{10} is determined directly from the precontrast baseline signal intensity, equation 11 does not exhibit dependence on the initial precontrast spin lattice relaxation time. Therefore, the approach eliminates the necessity of acquiring a separate precontrast *T*_{1} map. The ΔR_{1}(t) can be estimated directly from S(t), provided that an estimate of S_{0} be obtained. This is made possible by using the dual-echo SPICE sequence, as described in detail in the online Supplemental Appendix [equations A19 to A22].

### Correction of DCE-MRI Time Courses for *T*_{2}/*T*_{2}* Effects

Dual-echo acquisitions offer two significant advantages for DCE-MRI. One advantage is that, as discussed in the previous section, S_{0} can be determined from the first time point (ie, the first repetition) of a single-shot, dual-echo acquisition using the methodology described in the online Supplemental Appendix. This factor can result in significant time savings, in that no additional precontrast calibration scans are required to convert the DCE-MRI signal time courses into concentration–time curves. It may also improve the overall quality and accuracy of the computed parameter maps, since interscan patient motion is no longer an issue. Of potentially greater significance, it eliminates the confounding influence of spatial variations in B1 that result when images are acquired at multiple flip angles to determine precontrast *T*_{1} maps (30–32).

Another advantage of SPICE is that the confounding *T*_{2}* effects of the contrast agent can be eliminated from the DCE-MRI concentration–time curves. First, 1/*T*_{2}*(t) is estimated at each time point from the first and second echo signal. Second, a corrected first echo signal, S_{TE1C}(t), is obtained by extrapolating each time point of the first echo signal back to TE = 0 using the following equation:

Notice that *T*_{2}* effects have been eliminated in the corrected signal equation. Using the TE-corrected signal at baseline **(**S_{BC}) and postcontrast (S_{TE1C}(t)), the ΔR_{1C}(t), corrected for confounding *T*_{2}* effects, can be computed using the following equation:

An estimate of S_{0}, determined from the first time point of the SPICE acquisition, is then substituted into equation 13, which is then used to determine the concentration–time curves using equation 9.

## Materials and Methods

The feasibility of the SPICE method was shown in two patients with tissue-confirmed high-grade glioma exhibiting enhancement on postcontrast *T*_{1}-weighted images. Informed written consent was obtained from these patients under guidelines established by our Institution's Institutional Review Board.

### Data Acquisition

Images were acquired on a 1.5 T GE CV scanner (GE Healthcare, Milwaukee, Wisconsin), equipped with 40 mT/m gradients (150 T/m/s slew rate), using a commercial quadrature radiofrequency coil. Precontrast fluid-attenuated inversion recovery (FLAIR), diffusion-weighted imaging (DWI), *T*_{1}, and *T*_{2} images were collected as part of the standard clinical protocol. SPICE images were then acquired using a custom, multislice 2-dimensional, single-shot, dual GRE, spiral-out sequence with the following parameters: field of view: 22 cm^{2}, matrix: 96 × 96, TE_{1}: 3.1 milliseconds, TE_{2}: 41 milliseconds, TR: 1350 milliseconds, flip angle: 72°, slice thickness: 5 mm, skip: 1.5 mm, number of slices: 13, and number of samples (reps): 180. A 30-second delay was inserted between prescan and the beginning of the SPICE acquisition to allow full recovery of longitudinal magnetization. This facilitated estimation of the equilibrium magnetization from the first time point of the SPICE acquisition and eliminated the necessity of collecting a separate precontrast calibration scan, as described by equations A19 to A22 in the online Supplemental Appendix. A single dose of gadodiamide (0.1 mmol/kg, Omniscan®, GE Healthcare, Inc., Princeton, New Jersey) was injected at 3 mL/s using a power injector 60 seconds after the start of acquisition (33). Postcontrast *T*_{1}-weighted images were then acquired as part of the standard clinical protocol (TE/TR/NEX/matrix = 11/650/2/256).

As shown in Figure 5A, SPICE acquires two echoes sequentially within a free induction decay, immediately following a spatial–spectral (SPSP) excitation pulse. The SPSP excitation pulse was used to reduce the chemical shift contributions to off-resonance effects through selective excitation of water (34). The Ernst angle (72°) was chosen to maximize the signal-to-noise ratio (SNR) of the SPICE images to prevent signal saturation at the rectified noise floor during the first passage of the contrast agent. Signal saturation can result in nonlinearities in the relationship between signal changes and contrast agent concentration, introducing an error into the estimate of the arterial input function (AIF) (35). The spiral gradient waveforms were implemented using the Glover approximation (36). For a 96 × 96 matrix, the spiral waveforms consisted of 10 863 points corresponding to a readout duration of approximately 36 milliseconds. The spiral-out direction was chosen to increase the SNR and minimize the TE of the first echo, which maximized the *T*_{1} weighting for good DCE sensitivity.

##### Figure 5.

Multislice 2-dimensional single-shot, dual gradient echo (GRE), spiral-out pulse sequence (ie, SPICE) used in the present study (A). Reconstructed first (B) and second (C) echo spiral images of a patient with brain tumor acquired at 1.5 T. Images are from the first time point (ie, infinite TR) of the dual-echo acquisition. See text for acquisition parameters.

### Data Analysis

The raw SPICE data was transferred to a remote Linux workstation (quad, dual-core 2.0 GHz Opteron CPUs, 16 GB RAM, SUSE 10.2, Advanced Micro Devices, Inc., Sunnyvale, California) and reconstructed offline using custom MATLAB (Version 7.5, R2007b, The MathWorks, Inc., Natick, Massachusetts) and ANSI C software developed at our Institution. Sample-reconstructed first and second echo spiral images from the first time point of the SPICE acquisition are shown in Figure 5B–C. The reconstructed images were then postprocessed using AFNI (30) and custom software developed at our Institution.

### DSC-MRI

For comparison of SPICE with conventional methods, three versions of ΔR_{2}^{*}(t) concentration–time curves were generated and used in the DSC-MRI analysis:

ΔR_{2}^{*}(t) generated using only the second echo (ie, *T*_{2}*-weighted) signal of the dual-echo acquisition [equation 4], similar to the conventional single-echo DSC-MRI.

ΔR_{2}^{*}(t) generated using the ratio of the SPICE dual-echo signals [equation 6, similar to previous dual-echo DSC-MRI approaches.

ΔR_{2}^{*}(t) generated using the ratio of the SPICE dual-echo signals and corrected for recirculation and any additional *T*_{2}/*T*_{2}* leakage effects [equation 8].

Hemodynamic parameters were estimated from the aforementioned three concentration–time curves using conventional DSC-MRI algorithms. In particular, estimates of rCBV were obtained using the following equation:

where ρ is the density of the brain tissue (1.04 g/mL); k

_{h} is a correction factor for the difference in large versus small vessel hematocrit (HCT) (

4), and it is calculated as follows:

AIF is the arterial input function, generated by averaging ΔR_{2}^{*}(t) time courses from 3 voxels manually selected in regions of the middle cerebral arteries. Estimates of CBF were then obtained from the maximum of the residue function, determined by deconvolving the tissue ΔR_{2}^{*}(t) curves and AIF using singular value decomposition (37). The CBF estimates were then cross-calibrated to units of absolute CBF, by scaling the mean normal-appearing white matter CBF value to 22 mL/100 mL/min (38).

### DCE-MRI

For comparison of the proposed with the conventional methods, two versions of ΔR_{1}(t) concentration–time curves were generated and used in the DCE-MRI analysis:

ΔR_{1}(t) generated using only the first echo (ie, *T*_{1}-weighted) signal of the dual-echo acquisition [equation 11], similar to the conventional single-echo DCE-MRI.

ΔR_{1}(t) generated by extrapolating the first echo signal back to TE = 0 using the dual-echo signals [equation 13]. The ΔR_{1}(t) curves were then converted into tissue concentration–time curves, C_{T}(t), using equation 9, giving the following equation:

where

R1 is the longitudinal relaxivity of gadodiamide at 1.5 T (∼4.39 s

^{−1}mM

^{−1} at 37°C) (

39). A surrogate for the plasma concentration–time curve, C

_{p}(t), was determined in a 2-step process. First, the tissue concentration–time curves for three (M = 3) manually selected voxels containing arteries were averaged to determine an arterial concentration–time curve, Ca(t) as follows:

Second, the arterial concentration–time curve was adjusted for HCT to produce the plasma concentration–time curve as follows:

where an assumed value of 0.45 was used for HCT (

40). Pharmacokinetic analysis of DCE-MRI data was then performed using conventional algorithms. In particular, the volume transfer constant between blood plasma and EES, K

^{trans}, and the fractional volume of the plasma space, v

_{p}, was determined on a voxel-by-voxel basis by linear least squares fitting of the linearized Patlak model to the tissue and plasma concentration–time curves (

41) as follows:

## Results

The effect of correcting DSC-MRI concentration–time curves for confounding recirculation and leakage is shown in Figure 6. Figure 6A displays the dual-echo time series for the representative tumor voxel depicted on the first and second echo spiral images shown in Figure 6B–C. Note that the signals have been truncated to remove the first few points during which the signal approached a steady state. Extravasation of the contrast agent is apparent from the increase in signal intensity shown on both the first and second echo signals. Because the first echo signal (ie, the blue curve) is heavily *T*_{1}-weighted, the leakage effect is apparent as an immediate signal increase. However, because the second echo signal (ie, the red curve) is more strongly *T*_{2}*-weighted, a transient signal decrease is observed, with the signal increase becoming apparent after the initial transient. By comparing the dual-echo signals, note that the leakage of the contrast agent begins at the appearance time of the bolus, occurs during the first pass of the bolus, and continues after the first pass of the bolus.

##### Figure 6.

Demonstration of correction of DSC-MRI data using the proposed SPICE postprocessing method. See text for details.

Figure 6D–F displays the ΔR_{2}^{*}(t) curve (for the same tumor voxel) obtained from the second echo (ie, *T*_{2}*-weighted) signal only [equation 4], similar to conventional single-echo DSC-MRI, along with corresponding rCBV and CBF maps. Note that the curve in Figure 6D is confounded by *T*_{1} leakage effects, which causes the postbolus ΔR_{2}^{*}(t) to fall below the prebolus baseline and results in an underestimation of rCBV. This effect is apparent by a lack of blood volume (ie, regions of transparency) in Figure 6E, which is exacerbated in tumor regions.

Figure 6G–I displays the ΔR_{2}^{*}(t) curve (for the same tumor voxel) obtained from the ratio of the dual-echo signals [equation 6], similar to previous dual-echo approaches, along with corresponding rCBV and CBF maps. By using the ratio of the dual-echo signals when constructing ΔR_{2}^{*}(t), confounding *T*_{1} effects are eliminated, resulting in an increased peak height of ΔR_{2}^{*}(t) relative to that shown in Figure 6D and the unmasking of the recirculation and *T*_{2}/*T*_{2}* leakage effects (evident from the elevated endline/postbolus baseline). The elimination of *T*_{1} effects prevents underestimation of rCBV and CBF, evident by comparing Figure 6, H and I with Figure 6, E and F.

Figure 6J–L displays representative ΔR_{2}^{*}(t)' (red) and ΔR_{2}^{*}(t) (blue) curves obtained using equations 7 and 8, along with corresponding rCBV and CBF maps. Note that, after the proposed correction, the blue curve shown in Figure 6J and rCBV and CBF maps in Figure 6, K and L are no longer confounded by recirculation or by any dipolar *T*_{1} and *T*_{2} and/or residual susceptibility leakage effects. The corrected rCBV map in Figure 6K shows reduced rCBV values relative to Figure 6H (most notably in the tumor). This suggests that an overestimation of rCBV can result in the presence of recirculation and any residual susceptibility or dipolar *T*_{2} leakage effects. Although the proposed correction also reduced CBF values in Figure 6L relative to Figure 6I, the reduction is minimal compared with rCBV.

Figure 7 shows the influence of S_{0} estimates on DCE-MRI concentration–time curves constructed using equation 13. As shown in Figure 7B, failure to wait long enough for full recovery of longitudinal magnetization between prescan and the start of the acquisition results in an underestimation of S_{0} and amplified noise when the increase in signal intensity due to extravasation approaches the underestimated value of S_{0}. However, by allowing full recovery of longitudinal magnetization, noise amplification is prevented, resulting in a concentration–time curve profile (Figure 7C) that matches the signal time course (Figure 7A).

##### Figure 7.

Influence of S_{0} estimates on dynamic contrast-enhanced (DCE)-MRI tissue concentration–time curves generated with the proposed method. *T*_{1}-weighted (first-echo) signal time course for a representative voxel in tumor (A). Calculated tissue concentration–time curve for tumor voxel in (A) generated using S_{0} estimated *without* full recovery of longitudinal magnetization (B). With increasing signal enhancement (ie, as the signal approaches S_{0}), the noise in the concentration–time curve is amplified (note the scale on the ordinate). Calculated tissue concentration–time curve for tumor voxel in (A) generated using S_{0} estimated *with* full recovery of longitudinal magnetization (C). Allowing full recovery of longitudinal magnetization results in a concentration–time curve shape that closely resembles the signal in (A), prevents amplification of noise during signal enhancement, and reduces error.

Figure 8 shows the influence of *T*_{2}* effects on DCE-MRI time courses. Figure 8A displays the first, corrected first, and second echo signals for a voxel in an artery. A transient signal decrease is observed in both first echo (ie, *T*_{1}-weighted) and second echo (ie, *T*_{2}*-weighted) time series. As shown by the corrected signal (ie, green curve) in Figure 8A, the magnitude of the *T*_{2}* signal decrease is reduced using the dual-echo signals to extrapolate the first echo signal back to TE = 0 millisecond. In addition, residual susceptibility effects due to recirculation, evident from the postbolus portion of the second echo signal remaining below its prebolus baseline, are also recovered in the corrected signal. Figure 8B displays the first, corrected first, and second echo signals for a voxel in tumor. Correction for *T*_{2}* effects resulted in a slight increase in the rate of signal enhancement over the entire postbolus region.

##### Figure 8.

Demonstration of confounding *T*_{2}* effects on signals used to generate DCE-MRI concentration–time curves for representative voxels in (A) artery and (B) tumor. The dual-echo signals (blue and red curves) are used to extrapolate the first-echo signal back to TE = 0 (green curve), which eliminates the influence of *T*_{2}* effects. During the first pass of a bolus injection of a contrast agent, *T*_{2}* effects can confound *T*_{1}-weighted signals (blue curve), which can introduce error in DCE-MRI arterial input functions (AIFs). Although the majority of confounding *T*_{2}* effects are probably masked by *T*_{1} shortening, correction for *T*_{2}* effects in tumor results in an apparent increased rate of signal enhancement, which can influence heuristic DCE-MRI signal analysis (B).

The effects of correcting DCE-MRI concentration–time curves for *T*_{2}* effects are shown in Figure 9. Figure 9A–C displays a representative tissue concentration–time curve (A), along with corresponding K^{trans} (B) and v_{p} (C) maps, generated using only the first echo signal time course analogous to conventional DCE-MRI analysis [equation 13]. Figure 9D–F displays the tissue concentration–time curve (D), along with corresponding K^{trans} (E) and v_{p} (F) maps, for the same voxel as Figure 9A, but corrected for confounding *T*_{2}* effects using the dual-echo signal time courses to extrapolate the first echo signal back to TE = 0 millisecond [ie, equation 15]. In both cases, the DCE-MRI parameters were obtained following linear least squares fitting of the Patlak model fit (red line) to the tissue concentration–time curves (black lines in Figure 9, A and D). Only slight spatial differences in the K^{trans} and v_{p} maps are apparent by comparing Figure 9, E and F with Figure 9, B and C.

##### Figure 9.

Demonstration of the correction of DCE-MRI data using the proposed SPICE method. Top row: Linear least squares Patlak model fit (red line) to tissue concentration–time curve (A), and corresponding estimates of K^{trans} (B) and v_{p} (C). The concentration–time curve in (A) was constructed using a single echo signal time course analogous to conventional DCE analysis. Second row: Linear least squares Patlak model fit (red line) to tissue concentration–time curve (D), and corresponding estimates of K^{trans} (E) and v_{p} (F). The concentration–time curve in (D) was constructed using a dual-echo corrected signal time course, which facilitated correction for *T*_{2}*(t) effects.

## Discussion

We have presented the mathematical theory and feasibility of SPICE, a spiral-based perfusion imaging method by which DSC- and DCE-MRI perfusion imaging data can be derived simultaneously, with high temporal resolution using only a single dose of contrast agent. This approach has several distinct advantages over the more common approach of obtaining DSC and DCE data separately and with different imaging sequences. In particular, by using a spiral-based approach, which encodes two echoes simultaneously within an free induction decay (FID), both *T*_{1}-weighted (short TE) and *T*_{2}*-weighted (longer TE) data can be obtained with a temporal resolution of about 1 second. Although it was previously shown that a temporal resolution of close to 1 second is best to obtain the most accurate DCE parameter estimations (17, 42), such resolution cannot be achieved with the standard fast GRE methods commonly used to collect DCE-MRI data. Therefore, the dual-echo GRE spiral sequence may represent a significant step forward in achieving more robust and reproducible DCE parameters. In turn, this could translate into greater standardization across patients and sites, which has been a long-standing goal of DCE perfusion imaging.

Another important advantage of the SPICE approach is that a preload of the contrast agent is no longer necessary to diminish the contrast agent leakage effects as previously recommended when using single-echo DSC methods (11, 12, 15, 43, 44). Therefore, all data can be obtained using only a single dose of the contrast agent. This advantage is of particular importance given the recent restrictions implemented by the Food and Drug Administration on the use of Gd-based agents because of the small but real risk of nephrogenic systemic fibrosis (45) and more recent concerns regarding Gd deposition in brain (46, 47).

A further advantage of using the SPICE approach is that separate precontrast S_{0} and *T*_{1} calibration scans, traditionally required for DCE-MRI analysis (33, 48, 49), are not required. Eliminating the need for these additional scans reduces the total scan time and several potential errors associated with the collection of additional precontrast calibration scans. For example, when using multiple flip angle methods to determine the precontrast *T*_{1}, incomplete spoiling of transverse coherence can cause large errors in the determination of *T*_{1} that vary with the choice of TR and flip angle (50). In addition, the potential for errors due to interscan patient motion and B1 field inhomogeneities can be precluded by eliminating this step. Finally, with SPICE, the DSC-MRI parameters are implicitly corrected for *T*_{1} leakage effects, and both DSC- and DCE-MRI parameters can be corrected for residual susceptibility effects and *T*_{2}/*T*_{2}* effects arising from contrast agent recirculation and leakage. Consequently, this approach has the potential to provide the most accurate and comprehensive array of MRI perfusion parameters.

Despite the many demonstrated and potential advantages of this approach, there remain several aspects that need further study and optimization. For example, the 1350-millisecond TR used in this paper was chosen to obtain greater brain coverage while also maintaining a temporal resolution close to 1 second. A drawback of the longer interimage TR (relative to standard DCE TRs) is a reduction in the *T*_{1} weighting, which may not be optimal for DCE parameter estimates. Although a longer TR decreases *T*_{1} weighting, this problem diminishes at higher field strengths, which are being increasingly used. Future work will include implementation of parallel transmit capabilities to improve slice coverage while minimizing TR for improved *T*_{1} contrast (51).

Although the SPICE method does not require estimation of a precontrast *T*_{1} map, one must take into account dependence of this estimate on the SNR and a number of precontrast baseline points sampled in the DCE acquisition. Poor SNR and a small number of precontrast baseline points could affect the accuracy of the baseline signal estimate, and thus the initial *T*_{1} estimate. In the current implementation, a flip angle of 72° (the Ernst angle) and 60 baseline points were acquired to maximize SNR and thus improve the accuracy of the precontrast baseline signal intensity. Future studies to characterize these dependencies are planned.

An additional practical requirement, to ensure the collection of high-quality baseline signal intensities, is that sufficient time elapses between the performance of the prescan and the start of scanning. As shown in Figure 7, poor-quality baseline signal will result if scanning immediately follows the prescan. In this work, the scanner operator waited 30 seconds between the end of prescan and beginning acquisition, an overly conservative estimate of the time needed to allow full recovery of longitudinal magnetization. A more robust approach may be to use 30 seconds worth of discarded acquisitions (ie, disdaqs) with 0° flip angle. This would be one approach to ensure that the time between prescan and scanning is sufficient for full relaxation of the longitudinal magnetization and any potential variations in delays between scanner operators are eliminated.

The spiral-based approach has another potential option for easily determining the precontrast *T*_{1}. Theoretically, it is possible to estimate a *T*_{1} map directly from the signal transients obtained at the beginning of the perfusion-weighted imaging time series. However, the short *T*_{1} at 1.5 T and a rather coarse temporal sampling of 1350 milliseconds used in the current implementation preclude this because there are not enough points to adequately fit a curve and produce robust estimates of the initial *T*_{1}. However, this approach may find utility at higher fields or with shorter TRs.

In this study, correction for residual susceptibility effects was performed using the model introduced by Johnson et al. (28). It should be emphasized that although this model is based on the γ-variate function, the approach is not equivalent to the γ-variate fitting performed in many studies to determine rCBV from ΔR2*(t). Rather, it uses the cumulative integral of the γ-variate function to fit the recirculation effects, which are subsequently corrected. Also, in the context of fitting and correcting residual DSC baseline effects, this approach does not attempt to distinguish contributions because of recirculation from those resulting from the contrast agent leakage. Given that a residual DSC signal baseline is often apparent in a normal-appearing brain, residual DSC signal baselines observed in tumor cannot be attributed entirely to contrast agent leakage effects. Thus, there is no clear alterative at this time but to fit and correct the residual baseline with a lumped-fitting approach, as is used here.

A comparison between the proposed method and the established DCE methods is necessary, although beyond the scope of this paper. Current DCE methods use conventional spoiled GRE sequences (eg, spoiled gradient recalled echo [SPGR] or fast low angle shot magnetic resonance imaging [FLASH]) for data acquisition. The effective TR for these methods is roughly 6–15 seconds even though it has been shown that the DCE signal time course should be sampled about every 1 second for the most accurate parameter estimations (49, 52). The proposed method offers a reduced TR and should improve AIF quality. However, a direct comparison between the more accepted conventional DCE methods and the new DCE method proposed here should be undertaken.

In this work, the Patlak model was used to estimate DCE parameters, K^{trans}, and v_{p}. A more comprehensive approach would be to use the extended Tofts model to estimate K^{trans}, kep, and ve. However, only 3 minutes of SPICE data were collected such that in some voxels, the washout phase of the contrast agent was not observed, thereby precluding the use of the extended Tofts model. Future studies will extend the temporal sampling of the SPICE data from 3 to 7 minutes so that the models can be compared. Although the Patlak model was used for pharmacokinetic analysis, other DCE-MRI models could be readily applied.

The necessity for correcting DCE time courses for *T*_{2}* effects may be questioned, given the short TEs used in conventional DCE methods and in the proposed method. However, as shown in Figure 8, *T*_{2}* may also affect large vessels (eg, AIF) and tumor vasculature may contain vessels with a distribution of radii, resulting in more or less confounding effects from *T*_{2}*. Also, the differences in slopes shown in Figure 9, though seemingly small, suggest that heuristic DCE-MRI analysis methods may benefit from *T*_{2}* correction. The need for this step will be further explored with the planned DCE comparison studies described above. Nevertheless, even if *T*_{2}* effects are negligible, dual-echo acquisitions still permit conversion of signal intensity time courses into concentration–time curves without the need to acquire a precontrast *T*_{1} map.

The spiral-based approach described here offers several advantages that make it well-suited for perfusion imaging. Unlike echo planar imaging (EPI), spiral imaging does not collect data in the corners of k-space, resulting in increased time efficiency over EPI. The shorter readout durations in spiral translate into several advantages, including reduced *T*_{2}* decay during the readout, which limits the maximum achievable resolution of single-shot methods (53–55); increased temporal resolution, which is beneficial for AIF sampling in DSC and DCE imaging (52, 56–58), or increased *T*_{1}-weighting in DCE (59); increased section coverage for a given TR; and diminished vessel blooming (17). Specific to DCE-MRI, because the readout starts in the center of the k-space, spirals can achieve very short minimum TEs, producing images with good *T*_{1} weighting.

A major disadvantage of spiral is compromised image fidelity because of off-resonance-induced phase accrual over the readout. The current implementation of the proposed method does not correct for off-resonance effects. It has been well established that off-resonance effects can degrade the fidelity of spiral images. In contrast to EPI, where off-resonance effects result in a dominant one-dimensional distortion along the phase-encode direction, a two-dimensional blurring results in spiral images (60). Although an SPSP pulse was used to diminish the chemical shift contributions to off-resonance effects, off-resonant spins still arise from field inhomogeneity and tissue susceptibility differences. Although the proposed method does acquire dual echoes at each slice location, the difference in TEs is very large. The large delta TE results in phase images with multiple phase wraps, requiring unwrapping of the phase images. Methods to reduce off-resonance effects include, selectively exciting water using SPSP excitation pulses to reduce the chemical shift contribution to off-resonance effects; reducing field inhomogeneity by careful shimming; and applying off-resonance correction algorithms (51, 61, 62). Parallel imaging (eg, spiral SENSE) (63) would also provide substantial benefits for the single-shot, dual-echo spiral acquisition described here by reducing the length of the spiral readout. This would greatly improve data quality in regions of static susceptibility differences, such as resection cavities. Finally, although blurring results in a local resolution loss, it does not force the requirement to spatially remap displaced pixel data to restore its actual anatomic location (55).

The proposed SPICE method requires a single dose of the contrast agent to obtain both DSC- and DCE-MRI parameters. It should be emphasized, however, that at least a single dose (ie, 0.1 mmol/kg) must be used. Although satisfactory contrast enhancement can be obtained using only a half dose of high *T*_{1} relaxivity agents such as MultiHance (Bracco Diagnostics Inc), a half-dose does not produce appropriate susceptibility effect for DSC, regardless of the method used for acquisition (ie, single- or dual-echo, EPI, or spiral) or field strength. Contrast-to-noise is critical for adequate nonlinear least squares fitting of the model to correct for *T*_{2}/*T*_{2}* effects and least squares fitting of the Patlak model for DCE analysis. Therefore, although the proposed method reduces the total amount of contrast agent that needs to be administered, a minimum of a single dose is highly recommended.

Research Articles

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TOMOGRAPHY, December 2016, Volume 2, Issue 4: 295-307

DOI: 10.18383/j.tom.2016.00217

## Spiral Perfusion Imaging With Consecutive Echoes (SPICE™) for the Simultaneous Mapping of DSC- and DCE-MRI Parameters in Brain Tumor Patients: Theory and Initial Feasibility

Eric S. Paulson

^{1}, Douglas E. Prah^{1}, Kathleen M. Schmainda^{2}^{1}Departments of Radiation Oncology and^{2}Radiology, Medical College of Wisconsin, Milwaukee, Wisconsin## Abstract

Dynamic contrast-enhanced (DCE) and dynamic susceptibility contrast (DSC) magnetic resonance imaging (MRI) are the perfusion imaging techniques most frequently used to probe the angiogenic character of brain neoplasms. With these methods,

T_{1}- andT_{2}/T_{2}*-weighted imaging sequences are used to image the distribution of gadolinium (Gd)-based contrast agents. However, it is well known that Gd exhibits combinedT_{1},T_{2}, andT_{2}* shortening effects in tissue, and therefore, the results of both DCE- and DSC-MRI can be confounded by these opposing effects. In particular, residual susceptibility effects compete with T1 shortening, which can confound DCE-MRI parameters, whereas dipolarT_{1}andT_{2}leakage and residual susceptibility effects can confound DSC-MRI parameters. We introduce here a novel perfusion imaging acquisition and postprocessing method termed Spiral Perfusion Imaging with Consecutive Echoes (SPICE) that can be used to simultaneously acquire DCE- and DSC-MRI data, which requires only a single dose of the Gd contrast agent, does not require the collection of a precontrastT_{1}map for DCE-MRI processing, and eliminates the confounding contrast agent effects due to contrast extravasation. A detailed mathematical description of SPICE is provided here along with a demonstration of its utility in patients with high-grade glioma.## Introduction

Dynamic susceptibility contrast (DSC) and dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) are the two most common contrast agent techniques used to probe the angiogenic character of brain neoplasms (1). With DSC-MRI, the

T_{2}* effects of gadolinium (Gd)-chelated contrast agents are exploited. Using this approach, a concentrated bolus of Gd, confined to the intravascular space and perfusing through a tissue capillary bed, induces transient signal loss through spin dephasing caused by vascular–extravascular susceptibility gradients (2, 3). Analysis of DSC-MRI data using indicator dilution theory provides hemodynamic estimates such as relative cerebral blood volume (rCBV), cerebral blood flow (CBF), and mean transit time (4, 5). With DCE-MRI, theT_{1}effect of Gd contrast agents is exploited. In particular, contrast agent extravasation, arising from disruptions of the blood–brain barrier (BBB), gives rise to signal enhancement through dipolar interaction between Gd's unpaired electrons and local tissue protons (6, 7). Pharmacokinetic analysis of DCE-MRI data provides insight into the underlying tissue pathophysiology through, for example, estimation of the blood–brain volume transfer constant (K^{trans}); fractional volume of the extravascular, extracellular space (EES) (v_{e}); and the efflux rate constant from EES to plasma (k_{ep}) (8, 9).Although DSC- and DCE-MRI approaches depend on the predominance of

T_{2}* andT_{1}effects, respectively, the results of both DSC- and DCE-MRI may be confounded by the opposing relaxation effects of Gd. For example, the shift in compartmental distribution of the contrast agent from the intravascular space to the EES can result inT_{1}shortening effects that, although necessary for the DCE-MRI technique, compete with and confound DSC-MRI susceptibility-induced signal decreases (10–12). The most well-characterized DSC-MRI parameter affected byT_{1}leakage effects is rCBV, and several DSC-MRI acquisition and analysis methods have been developed and applied to mitigate the underestimation of rCBV due to theT_{1}leakage effects (13–16).In this regard, it has been shown that dual-echo acquisition methods (13, 17–21) may be one of the most robust approaches for collecting DSC-MRI data in patients with brain tumor, as

T_{1}leakage effects can be directly eliminated (17, 22–27). However, it has also been hypothesized that residualT_{2}/T_{2}* effects, attributable to recirculation and/or contrast agent leakage, may result in overestimations of DSC-MRI parameters if not taken into account.The first goal of this paper is to introduce a novel method for DSC-MRI perfusion imaging, whereby leakage effects manifesting as either

T_{1}orT_{2}/T_{2}* effects can be corrected. The second goal of this paper is to demonstrate that, by using the same dual-echo spiral acquisition method, DCE-MRI parameters can be derived concurrently, independent of the precontrast calibration scans (eg,T_{1}maps). Consequently, the complete array of DSC- and DCE-MRI parameters, corrected for confounding contrast agent effects, can be obtained simultaneously in a single acquisition with a single dose of the Gd contrast agent. The feasibility of the method is demonstrated in patients with high-grade brain tumors.## Theory

To motivate use and ensure full understanding of the advantages of the Spiral Perfusion Imaging with Consecutive Echoes (SPICE) approach, the theory underlying conventional DSC- and DCE-MRI in comparison with SPICE is described here.

## Derivations of DSC-MRI Concentration–Time Curves

## Conventional DSC-MRI.

The concentration–time curves in DSC-MRI are generated based on an assumed linear relationship between the Gd contrast agent concentration and the change in

apparent transverserelaxation rate induced by the first passage of the contrast agent through the vasculature (3), and it is calculated using the following equation:## (1)

## (2)

T_{1}(t) andT_{2}*(t) indicate that these parameters can change dynamically during acquisition. As described in detail in the online Supplemental Appendix [equations A1 to A5], equation 2 can be used to obtain general expressions for the pre- and postcontrastT_{2}* values, from which a general expression for ΔR2*(t) can be derived as follows:## (3)

T_{10}is the precontrastT_{1}relaxation time and S_{B}is the mean of the precontrast baseline signal determined by averaging S(t) over the first N_{B}baseline points. Equation 3 shows the potential influence of dipolarT_{1}effects on concentration–time curves obtained with DSC-MRI. In particular, in the absence of an intact BBB, extravasation of the contrast agent results inT_{1}shortening, causing a confounding reduction in ΔR_{2}^{*}(t) (Figure 1A).## Figure 1.

Illustration of confounding leakage and recirculation effects on dynamic susceptibility contrast (DSC)-magnetic resonance imaging (MRI) concentration–time curves for representative voxels in normal brain and brain tumor. Representative ΔR

_{2}^{*}(t) concentration–time curves are shown for voxels in normal brain and brain tumor after serial primary (1^{0}), 0.1 mmol/kg) (A) and secondary (2^{0}, 0.2 mmol/kg) (B) injections of Gd contrast agent in the same patient with glioma. Acquisitions were performed at 1.5 T using a gradient echo-echo planar imaging (GRE-EPI) pulse sequence with flip angle = 90°, TE = 30 milliseconds, and repetition time (TR) = 1000 milliseconds. In regions of normal brain with an intact BBB, a concentrated bolus of Gd contrast agent will remain compartmentalized to the vasculature, resulting in transient signal changes, that ultimately return to the prebolus baseline value (A). However, in regions of tumor with a disrupted blood–brain barrier (BBB), a fraction of the contrast agent will leak out of the vasculature into the extravascular extracellular space (EES), resulting inT_{1}shortening effects that contaminate tumor concentration–time curves. After secondary injection, the postbolus portions of both normal brain and the tumor concentration–time curves are elevated above their prebolus baseline values (B). The fact that this occurs in normal brain, with a presumably intact BBB, suggests that this is not a leakage effect, but instead may be attributable to a residual susceptibility effect caused by recirculation of an increased steady-state concentration of the contrast agent. However, the additional elevated endline in the tumor concentration–time curve suggests a dipolarT_{2}leakage effect or additional susceptibility effect. These curves show that both dipolarT_{1}andT_{2}and/or residual susceptibility effects may confound perfusion estimates derived by DSC-MRI.In the presence of an intact BBB, the contrast agent remains confined to the vasculature (ie, no extravasation occurs),

T_{1}(t) is essentially equal toT_{10}(ie, its precontrast value), and ΔR_{2}^{*}(t) reduces to its ubiquitous form as follows:## (4)

## Correction of DSC-MRI Time Courses for

T_{1}Extravasation EffectsDual-echo acquisition methods provide an effective means by which confounding dipolar

T_{1}leakage effects can be eliminated from DSC-MRI time courses (17–21). The signal equation for the first and second echoes (TE_{i=1,2}) is as follows:## (5)

Taking the ratio of the 2 signal equations, an expression for both the baseline and postcontrast 1/

T_{2}*(t) can be derived, which is as detailed in the online Supplemental Appendix [equations A7 to A11]. From these, the change in the transverse relaxation rate can be derived as follows:## (6)

Equation 6 is the DSC-MRI concentration–time curve that is free from the dipolar

T_{1}leakage effects.## Correction of DSC-MRI Time Courses for

T_{2}/T_{2}* EffectsIn practice, we have observed another potential confounding effect on DSC-MRI concentration–time curves characterized as elevated endlines that develop following the first pass of the contrast agent. As shown in Figure 1B, the effect appears to be exacerbated in brain tumors relative to the normal brain, which implies that there could be an additional susceptibility or

T_{2}leakage effect in these regions beyond the effects of recirculation. The source of the elevated endlines could be dipolarT_{2}effects, residual susceptibility effects from the contrast agent, or some combination of both. Regardless of the source of these elevated endlines, perfusion parameters (eg, rCBV) generated using DSC-MRI may beoverestimatedif postprocessing algorithms do not account for their confounding effects (24).One approach discussed in the literature for analyzing DSC-MRI data is voxel-wise γ-variate fitting to the concentration–time curves (10). Although fitting of a γ-variate effectively eliminates the majority of recirculation and leakage effects that occur after the first pass, it does not remove the confounding effects of leakage that occur

duringthe first pass (Figure 2). A more appropriate model of a DSC-MRI time courses with elevated endlines, introduced by Johnson et al. (28), consists of a γ-variate plus its cumulative integral as follows:## Figure 2.

Demonstration of the time course of extravasation effects in DSC-MRI. Postcontrast

T_{1}-weighted image of a patient with a high-grade glioma (A). Spiral Perfusion Imaging with Consecutive Echoes (SPICE) signals, obtained at short and long TE, for the representative tumor voxel depicted on the postcontrastT_{1}-weighted image (B). Leakage of contrast agent begins at the appearance time of the bolus and occurs during the first pass of the bolus (indicated by the shaded region). Following the first pass, leakage continues at a slower rate until back-diffusion occurs (not shown).## (7)

kis a scale factor, t_{0}is the appearance time of the bolus, α and β are fit parameters, and h is used to scale the cumulative integral of the γ-variate (Figure 3). Correction for elevated endlines is then performed by nonlinear least squares fitting of equation 7 to the corrupted ΔR_{2}^{*}(t) concentration–time curves on a voxel-wise basis. After nonlinear least squares fitting, ΔR_{2}^{*}(t) curves corrected for dipolarT_{1}andT_{2}and residual susceptibility effects are generated by constructing γ-variates using the parameters estimated from the full model fit as follows:## Figure 3.

Illustration of the proposed model of DSC-MRI concentration–time curves. The representative ΔR

_{2}^{*}(t) concentration–time curve is modeled by a γ-variate plus its cumulative integral scaled by a constant. The γ-variate is used to model the first pass of the tracer, whereas the cumulative integral is used to model recirculation and/or leakage of the tracer.## (8)

In comparison with standard γ-variate fits, this two-step method, described by equations 7 and 8, results in corrected concentration–time curves that exhibit reduced peak height and bolus width, as expected in the absence of recirculation and leakage (Figure 4). Conventional algorithms can then be applied to generate estimates of DSC-MRI parameters that are free from confounding contrast agent effects.

## Figure 4.

Illustration of the differences between methods used to correct DSC-MRI concentration–time curves for recirculation and/or leakage effects. γ-variate fit to ΔR

_{2}^{*}(t) (orange) (A). Proposed full model fit to ΔR_{2}^{*}(t) (red) and corrected first pass (blue) (B). Corrected first-pass curves obtained from (A) and (B), (C). Compared to the standard γ-variate (orange), the corrected first-pass curve (blue) from the proposed method is characterized by decreased peak height and bolus width, which should be more representative of the actual first pass in the absence of recirculation and leakage effects.## Derivation of DCE-MRI Concentration–Time Curves

## Conventional DCE-MRI.

The concentration–time curves for DCE-MRI are generated on the basis of an assumed linear relationship between Gd concentration and the change in

spin latticerelaxation rate, ΔR1, resulting primarily from the extravasation of the contrast agent from the vasculature to the EES, where a dipolar interaction between the unpaired electrons of the contrast agent and local tissue protons ensues (7):## (9)

T_{1}relaxivity of the Gd contrast agent. The DCE-MRI technique relies on the sensitivity of the pulse sequence to changes in signal intensity caused byT_{1}shortening. Traditionally, conventional 2- or 3-dimensional spoiled GRE sequences are used in DCE-MRI because they provide good image quality with sufficient temporal resolution. Analogous to DSC-MRI, the generalized signal equation for DCE-MRI is then equivalent to equation 2.Several methods have been used to convert the dynamic signal intensity time courses into tissue Gd concentration–time curves. In the method used here [which is similar to the Hittmair approach (29)], 1/

T_{1}(t) and 1/T_{10}are obtained directly by solving the pre- and postcontrast signal equations as described in the online Supplemental Appendix [equations A15 and A16], and the results, along with equation 9, are used to determine ΔR_{1}(t) as follows:## (10)

Equation 10 shows the potential influence of

T_{2}* effects on the concentration–time curves obtained with DCE-MRI. In particular,T_{2}* shortening may cause a confounding reduction in ΔR_{1}(t). However, because minimum echo times (TE) are typically used, it is widely assumed that an insignificant phase dispersion will occur over time scales of short TE (ie, TE ≪T_{2}*). Consequently,T_{2}* effects are generally ignored, which results in the following approximation:## (11)

In addition, note that because

T_{10}is determined directly from the precontrast baseline signal intensity, equation 11 does not exhibit dependence on the initial precontrast spin lattice relaxation time. Therefore, the approach eliminates the necessity of acquiring a separate precontrastT_{1}map. The ΔR_{1}(t) can be estimated directly from S(t), provided that an estimate of S_{0}be obtained. This is made possible by using the dual-echo SPICE sequence, as described in detail in the online Supplemental Appendix [equations A19 to A22].## Correction of DCE-MRI Time Courses for

T_{2}/T_{2}* EffectsDual-echo acquisitions offer two significant advantages for DCE-MRI. One advantage is that, as discussed in the previous section, S

_{0}can be determined from the first time point (ie, the first repetition) of a single-shot, dual-echo acquisition using the methodology described in the online Supplemental Appendix. This factor can result in significant time savings, in that no additional precontrast calibration scans are required to convert the DCE-MRI signal time courses into concentration–time curves. It may also improve the overall quality and accuracy of the computed parameter maps, since interscan patient motion is no longer an issue. Of potentially greater significance, it eliminates the confounding influence of spatial variations in B1 that result when images are acquired at multiple flip angles to determine precontrastT_{1}maps (30–32).Another advantage of SPICE is that the confounding

T_{2}* effects of the contrast agent can be eliminated from the DCE-MRI concentration–time curves. First, 1/T_{2}*(t) is estimated at each time point from the first and second echo signal. Second, a corrected first echo signal, S_{TE1C}(t), is obtained by extrapolating each time point of the first echo signal back to TE = 0 using the following equation:## (12)

Notice that

T_{2}* effects have been eliminated in the corrected signal equation. Using the TE-corrected signal at baseline(S_{BC}) and postcontrast (S_{TE1C}(t)), the ΔR_{1C}(t), corrected for confoundingT_{2}* effects, can be computed using the following equation:## (13)

An estimate of S

_{0}, determined from the first time point of the SPICE acquisition, is then substituted into equation 13, which is then used to determine the concentration–time curves using equation 9.## Materials and Methods

The feasibility of the SPICE method was shown in two patients with tissue-confirmed high-grade glioma exhibiting enhancement on postcontrast

T_{1}-weighted images. Informed written consent was obtained from these patients under guidelines established by our Institution's Institutional Review Board.## Data Acquisition

Images were acquired on a 1.5 T GE CV scanner (GE Healthcare, Milwaukee, Wisconsin), equipped with 40 mT/m gradients (150 T/m/s slew rate), using a commercial quadrature radiofrequency coil. Precontrast fluid-attenuated inversion recovery (FLAIR), diffusion-weighted imaging (DWI),

T_{1}, andT_{2}images were collected as part of the standard clinical protocol. SPICE images were then acquired using a custom, multislice 2-dimensional, single-shot, dual GRE, spiral-out sequence with the following parameters: field of view: 22 cm^{2}, matrix: 96 × 96, TE_{1}: 3.1 milliseconds, TE_{2}: 41 milliseconds, TR: 1350 milliseconds, flip angle: 72°, slice thickness: 5 mm, skip: 1.5 mm, number of slices: 13, and number of samples (reps): 180. A 30-second delay was inserted between prescan and the beginning of the SPICE acquisition to allow full recovery of longitudinal magnetization. This facilitated estimation of the equilibrium magnetization from the first time point of the SPICE acquisition and eliminated the necessity of collecting a separate precontrast calibration scan, as described by equations A19 to A22 in the online Supplemental Appendix. A single dose of gadodiamide (0.1 mmol/kg, Omniscan®, GE Healthcare, Inc., Princeton, New Jersey) was injected at 3 mL/s using a power injector 60 seconds after the start of acquisition (33). PostcontrastT_{1}-weighted images were then acquired as part of the standard clinical protocol (TE/TR/NEX/matrix = 11/650/2/256).As shown in Figure 5A, SPICE acquires two echoes sequentially within a free induction decay, immediately following a spatial–spectral (SPSP) excitation pulse. The SPSP excitation pulse was used to reduce the chemical shift contributions to off-resonance effects through selective excitation of water (34). The Ernst angle (72°) was chosen to maximize the signal-to-noise ratio (SNR) of the SPICE images to prevent signal saturation at the rectified noise floor during the first passage of the contrast agent. Signal saturation can result in nonlinearities in the relationship between signal changes and contrast agent concentration, introducing an error into the estimate of the arterial input function (AIF) (35). The spiral gradient waveforms were implemented using the Glover approximation (36). For a 96 × 96 matrix, the spiral waveforms consisted of 10 863 points corresponding to a readout duration of approximately 36 milliseconds. The spiral-out direction was chosen to increase the SNR and minimize the TE of the first echo, which maximized the

T_{1}weighting for good DCE sensitivity.## Figure 5.

Multislice 2-dimensional single-shot, dual gradient echo (GRE), spiral-out pulse sequence (ie, SPICE) used in the present study (A). Reconstructed first (B) and second (C) echo spiral images of a patient with brain tumor acquired at 1.5 T. Images are from the first time point (ie, infinite TR) of the dual-echo acquisition. See text for acquisition parameters.

## Data Analysis

The raw SPICE data was transferred to a remote Linux workstation (quad, dual-core 2.0 GHz Opteron CPUs, 16 GB RAM, SUSE 10.2, Advanced Micro Devices, Inc., Sunnyvale, California) and reconstructed offline using custom MATLAB (Version 7.5, R2007b, The MathWorks, Inc., Natick, Massachusetts) and ANSI C software developed at our Institution. Sample-reconstructed first and second echo spiral images from the first time point of the SPICE acquisition are shown in Figure 5B–C. The reconstructed images were then postprocessed using AFNI (30) and custom software developed at our Institution.

## DSC-MRI

For comparison of SPICE with conventional methods, three versions of ΔR

_{2}^{*}(t) concentration–time curves were generated and used in the DSC-MRI analysis:ΔR

_{2}^{*}(t) generated using only the second echo (ie,T_{2}*-weighted) signal of the dual-echo acquisition [equation 4], similar to the conventional single-echo DSC-MRI.ΔR

_{2}^{*}(t) generated using the ratio of the SPICE dual-echo signals [equation 6, similar to previous dual-echo DSC-MRI approaches.ΔR

_{2}^{*}(t) generated using the ratio of the SPICE dual-echo signals and corrected for recirculation and any additionalT_{2}/T_{2}* leakage effects [equation 8].Hemodynamic parameters were estimated from the aforementioned three concentration–time curves using conventional DSC-MRI algorithms. In particular, estimates of rCBV were obtained using the following equation:

## (14)

_{h}is a correction factor for the difference in large versus small vessel hematocrit (HCT) (4), and it is calculated as follows:## (15)

AIF is the arterial input function, generated by averaging ΔR

_{2}^{*}(t) time courses from 3 voxels manually selected in regions of the middle cerebral arteries. Estimates of CBF were then obtained from the maximum of the residue function, determined by deconvolving the tissue ΔR_{2}^{*}(t) curves and AIF using singular value decomposition (37). The CBF estimates were then cross-calibrated to units of absolute CBF, by scaling the mean normal-appearing white matter CBF value to 22 mL/100 mL/min (38).## DCE-MRI

For comparison of the proposed with the conventional methods, two versions of ΔR

_{1}(t) concentration–time curves were generated and used in the DCE-MRI analysis:ΔR

_{1}(t) generated using only the first echo (ie,T_{1}-weighted) signal of the dual-echo acquisition [equation 11], similar to the conventional single-echo DCE-MRI.ΔR

_{1}(t) generated by extrapolating the first echo signal back to TE = 0 using the dual-echo signals [equation 13]. The ΔR_{1}(t) curves were then converted into tissue concentration–time curves, C_{T}(t), using equation 9, giving the following equation:## (16)

^{−1}mM^{−1}at 37°C) (39). A surrogate for the plasma concentration–time curve, C_{p}(t), was determined in a 2-step process. First, the tissue concentration–time curves for three (M = 3) manually selected voxels containing arteries were averaged to determine an arterial concentration–time curve, Ca(t) as follows:## (17)

Second, the arterial concentration–time curve was adjusted for HCT to produce the plasma concentration–time curve as follows:

## (18)

^{trans}, and the fractional volume of the plasma space, v_{p}, was determined on a voxel-by-voxel basis by linear least squares fitting of the linearized Patlak model to the tissue and plasma concentration–time curves (41) as follows:## (19)

## Results

The effect of correcting DSC-MRI concentration–time curves for confounding recirculation and leakage is shown in Figure 6. Figure 6A displays the dual-echo time series for the representative tumor voxel depicted on the first and second echo spiral images shown in Figure 6B–C. Note that the signals have been truncated to remove the first few points during which the signal approached a steady state. Extravasation of the contrast agent is apparent from the increase in signal intensity shown on both the first and second echo signals. Because the first echo signal (ie, the blue curve) is heavily

T_{1}-weighted, the leakage effect is apparent as an immediate signal increase. However, because the second echo signal (ie, the red curve) is more stronglyT_{2}*-weighted, a transient signal decrease is observed, with the signal increase becoming apparent after the initial transient. By comparing the dual-echo signals, note that the leakage of the contrast agent begins at the appearance time of the bolus, occurs during the first pass of the bolus, and continues after the first pass of the bolus.## Figure 6.

Demonstration of correction of DSC-MRI data using the proposed SPICE postprocessing method. See text for details.

Figure 6D–F displays the ΔR

_{2}^{*}(t) curve (for the same tumor voxel) obtained from the second echo (ie,T_{2}*-weighted) signal only [equation 4], similar to conventional single-echo DSC-MRI, along with corresponding rCBV and CBF maps. Note that the curve in Figure 6D is confounded byT_{1}leakage effects, which causes the postbolus ΔR_{2}^{*}(t) to fall below the prebolus baseline and results in an underestimation of rCBV. This effect is apparent by a lack of blood volume (ie, regions of transparency) in Figure 6E, which is exacerbated in tumor regions.Figure 6G–I displays the ΔR

_{2}^{*}(t) curve (for the same tumor voxel) obtained from the ratio of the dual-echo signals [equation 6], similar to previous dual-echo approaches, along with corresponding rCBV and CBF maps. By using the ratio of the dual-echo signals when constructing ΔR_{2}^{*}(t), confoundingT_{1}effects are eliminated, resulting in an increased peak height of ΔR_{2}^{*}(t) relative to that shown in Figure 6D and the unmasking of the recirculation andT_{2}/T_{2}* leakage effects (evident from the elevated endline/postbolus baseline). The elimination ofT_{1}effects prevents underestimation of rCBV and CBF, evident by comparing Figure 6, H and I with Figure 6, E and F.Figure 6J–L displays representative ΔR

_{2}^{*}(t)' (red) and ΔR_{2}^{*}(t) (blue) curves obtained using equations 7 and 8, along with corresponding rCBV and CBF maps. Note that, after the proposed correction, the blue curve shown in Figure 6J and rCBV and CBF maps in Figure 6, K and L are no longer confounded by recirculation or by any dipolarT_{1}andT_{2}and/or residual susceptibility leakage effects. The corrected rCBV map in Figure 6K shows reduced rCBV values relative to Figure 6H (most notably in the tumor). This suggests that an overestimation of rCBV can result in the presence of recirculation and any residual susceptibility or dipolarT_{2}leakage effects. Although the proposed correction also reduced CBF values in Figure 6L relative to Figure 6I, the reduction is minimal compared with rCBV.Figure 7 shows the influence of S

_{0}estimates on DCE-MRI concentration–time curves constructed using equation 13. As shown in Figure 7B, failure to wait long enough for full recovery of longitudinal magnetization between prescan and the start of the acquisition results in an underestimation of S_{0}and amplified noise when the increase in signal intensity due to extravasation approaches the underestimated value of S_{0}. However, by allowing full recovery of longitudinal magnetization, noise amplification is prevented, resulting in a concentration–time curve profile (Figure 7C) that matches the signal time course (Figure 7A).## Figure 7.

Influence of S

_{0}estimates on dynamic contrast-enhanced (DCE)-MRI tissue concentration–time curves generated with the proposed method.T_{1}-weighted (first-echo) signal time course for a representative voxel in tumor (A). Calculated tissue concentration–time curve for tumor voxel in (A) generated using S_{0}estimatedwithoutfull recovery of longitudinal magnetization (B). With increasing signal enhancement (ie, as the signal approaches S_{0}), the noise in the concentration–time curve is amplified (note the scale on the ordinate). Calculated tissue concentration–time curve for tumor voxel in (A) generated using S_{0}estimatedwithfull recovery of longitudinal magnetization (C). Allowing full recovery of longitudinal magnetization results in a concentration–time curve shape that closely resembles the signal in (A), prevents amplification of noise during signal enhancement, and reduces error.Figure 8 shows the influence of

T_{2}* effects on DCE-MRI time courses. Figure 8A displays the first, corrected first, and second echo signals for a voxel in an artery. A transient signal decrease is observed in both first echo (ie,T_{1}-weighted) and second echo (ie,T_{2}*-weighted) time series. As shown by the corrected signal (ie, green curve) in Figure 8A, the magnitude of theT_{2}* signal decrease is reduced using the dual-echo signals to extrapolate the first echo signal back to TE = 0 millisecond. In addition, residual susceptibility effects due to recirculation, evident from the postbolus portion of the second echo signal remaining below its prebolus baseline, are also recovered in the corrected signal. Figure 8B displays the first, corrected first, and second echo signals for a voxel in tumor. Correction forT_{2}* effects resulted in a slight increase in the rate of signal enhancement over the entire postbolus region.## Figure 8.

Demonstration of confounding

T_{2}* effects on signals used to generate DCE-MRI concentration–time curves for representative voxels in (A) artery and (B) tumor. The dual-echo signals (blue and red curves) are used to extrapolate the first-echo signal back to TE = 0 (green curve), which eliminates the influence ofT_{2}* effects. During the first pass of a bolus injection of a contrast agent,T_{2}* effects can confoundT_{1}-weighted signals (blue curve), which can introduce error in DCE-MRI arterial input functions (AIFs). Although the majority of confoundingT_{2}* effects are probably masked byT_{1}shortening, correction forT_{2}* effects in tumor results in an apparent increased rate of signal enhancement, which can influence heuristic DCE-MRI signal analysis (B).The effects of correcting DCE-MRI concentration–time curves for

T_{2}* effects are shown in Figure 9. Figure 9A–C displays a representative tissue concentration–time curve (A), along with corresponding K^{trans}(B) and v_{p}(C) maps, generated using only the first echo signal time course analogous to conventional DCE-MRI analysis [equation 13]. Figure 9D–F displays the tissue concentration–time curve (D), along with corresponding K^{trans}(E) and v_{p}(F) maps, for the same voxel as Figure 9A, but corrected for confoundingT_{2}* effects using the dual-echo signal time courses to extrapolate the first echo signal back to TE = 0 millisecond [ie, equation 15]. In both cases, the DCE-MRI parameters were obtained following linear least squares fitting of the Patlak model fit (red line) to the tissue concentration–time curves (black lines in Figure 9, A and D). Only slight spatial differences in the K^{trans}and v_{p}maps are apparent by comparing Figure 9, E and F with Figure 9, B and C.## Figure 9.

Demonstration of the correction of DCE-MRI data using the proposed SPICE method. Top row: Linear least squares Patlak model fit (red line) to tissue concentration–time curve (A), and corresponding estimates of K

^{trans}(B) and v_{p}(C). The concentration–time curve in (A) was constructed using a single echo signal time course analogous to conventional DCE analysis. Second row: Linear least squares Patlak model fit (red line) to tissue concentration–time curve (D), and corresponding estimates of K^{trans}(E) and v_{p}(F). The concentration–time curve in (D) was constructed using a dual-echo corrected signal time course, which facilitated correction forT_{2}*(t) effects.## Discussion

We have presented the mathematical theory and feasibility of SPICE, a spiral-based perfusion imaging method by which DSC- and DCE-MRI perfusion imaging data can be derived simultaneously, with high temporal resolution using only a single dose of contrast agent. This approach has several distinct advantages over the more common approach of obtaining DSC and DCE data separately and with different imaging sequences. In particular, by using a spiral-based approach, which encodes two echoes simultaneously within an free induction decay (FID), both

T_{1}-weighted (short TE) andT_{2}*-weighted (longer TE) data can be obtained with a temporal resolution of about 1 second. Although it was previously shown that a temporal resolution of close to 1 second is best to obtain the most accurate DCE parameter estimations (17, 42), such resolution cannot be achieved with the standard fast GRE methods commonly used to collect DCE-MRI data. Therefore, the dual-echo GRE spiral sequence may represent a significant step forward in achieving more robust and reproducible DCE parameters. In turn, this could translate into greater standardization across patients and sites, which has been a long-standing goal of DCE perfusion imaging.Another important advantage of the SPICE approach is that a preload of the contrast agent is no longer necessary to diminish the contrast agent leakage effects as previously recommended when using single-echo DSC methods (11, 12, 15, 43, 44). Therefore, all data can be obtained using only a single dose of the contrast agent. This advantage is of particular importance given the recent restrictions implemented by the Food and Drug Administration on the use of Gd-based agents because of the small but real risk of nephrogenic systemic fibrosis (45) and more recent concerns regarding Gd deposition in brain (46, 47).

A further advantage of using the SPICE approach is that separate precontrast S

_{0}andT_{1}calibration scans, traditionally required for DCE-MRI analysis (33, 48, 49), are not required. Eliminating the need for these additional scans reduces the total scan time and several potential errors associated with the collection of additional precontrast calibration scans. For example, when using multiple flip angle methods to determine the precontrastT_{1}, incomplete spoiling of transverse coherence can cause large errors in the determination ofT_{1}that vary with the choice of TR and flip angle (50). In addition, the potential for errors due to interscan patient motion and B1 field inhomogeneities can be precluded by eliminating this step. Finally, with SPICE, the DSC-MRI parameters are implicitly corrected forT_{1}leakage effects, and both DSC- and DCE-MRI parameters can be corrected for residual susceptibility effects andT_{2}/T_{2}* effects arising from contrast agent recirculation and leakage. Consequently, this approach has the potential to provide the most accurate and comprehensive array of MRI perfusion parameters.Despite the many demonstrated and potential advantages of this approach, there remain several aspects that need further study and optimization. For example, the 1350-millisecond TR used in this paper was chosen to obtain greater brain coverage while also maintaining a temporal resolution close to 1 second. A drawback of the longer interimage TR (relative to standard DCE TRs) is a reduction in the

T_{1}weighting, which may not be optimal for DCE parameter estimates. Although a longer TR decreasesT_{1}weighting, this problem diminishes at higher field strengths, which are being increasingly used. Future work will include implementation of parallel transmit capabilities to improve slice coverage while minimizing TR for improvedT_{1}contrast (51).Although the SPICE method does not require estimation of a precontrast

T_{1}map, one must take into account dependence of this estimate on the SNR and a number of precontrast baseline points sampled in the DCE acquisition. Poor SNR and a small number of precontrast baseline points could affect the accuracy of the baseline signal estimate, and thus the initialT_{1}estimate. In the current implementation, a flip angle of 72° (the Ernst angle) and 60 baseline points were acquired to maximize SNR and thus improve the accuracy of the precontrast baseline signal intensity. Future studies to characterize these dependencies are planned.An additional practical requirement, to ensure the collection of high-quality baseline signal intensities, is that sufficient time elapses between the performance of the prescan and the start of scanning. As shown in Figure 7, poor-quality baseline signal will result if scanning immediately follows the prescan. In this work, the scanner operator waited 30 seconds between the end of prescan and beginning acquisition, an overly conservative estimate of the time needed to allow full recovery of longitudinal magnetization. A more robust approach may be to use 30 seconds worth of discarded acquisitions (ie, disdaqs) with 0° flip angle. This would be one approach to ensure that the time between prescan and scanning is sufficient for full relaxation of the longitudinal magnetization and any potential variations in delays between scanner operators are eliminated.

The spiral-based approach has another potential option for easily determining the precontrast

T_{1}. Theoretically, it is possible to estimate aT_{1}map directly from the signal transients obtained at the beginning of the perfusion-weighted imaging time series. However, the shortT_{1}at 1.5 T and a rather coarse temporal sampling of 1350 milliseconds used in the current implementation preclude this because there are not enough points to adequately fit a curve and produce robust estimates of the initialT_{1}. However, this approach may find utility at higher fields or with shorter TRs.In this study, correction for residual susceptibility effects was performed using the model introduced by Johnson et al. (28). It should be emphasized that although this model is based on the γ-variate function, the approach is not equivalent to the γ-variate fitting performed in many studies to determine rCBV from ΔR2*(t). Rather, it uses the cumulative integral of the γ-variate function to fit the recirculation effects, which are subsequently corrected. Also, in the context of fitting and correcting residual DSC baseline effects, this approach does not attempt to distinguish contributions because of recirculation from those resulting from the contrast agent leakage. Given that a residual DSC signal baseline is often apparent in a normal-appearing brain, residual DSC signal baselines observed in tumor cannot be attributed entirely to contrast agent leakage effects. Thus, there is no clear alterative at this time but to fit and correct the residual baseline with a lumped-fitting approach, as is used here.

A comparison between the proposed method and the established DCE methods is necessary, although beyond the scope of this paper. Current DCE methods use conventional spoiled GRE sequences (eg, spoiled gradient recalled echo [SPGR] or fast low angle shot magnetic resonance imaging [FLASH]) for data acquisition. The effective TR for these methods is roughly 6–15 seconds even though it has been shown that the DCE signal time course should be sampled about every 1 second for the most accurate parameter estimations (49, 52). The proposed method offers a reduced TR and should improve AIF quality. However, a direct comparison between the more accepted conventional DCE methods and the new DCE method proposed here should be undertaken.

In this work, the Patlak model was used to estimate DCE parameters, K

^{trans}, and v_{p}. A more comprehensive approach would be to use the extended Tofts model to estimate K^{trans}, kep, and ve. However, only 3 minutes of SPICE data were collected such that in some voxels, the washout phase of the contrast agent was not observed, thereby precluding the use of the extended Tofts model. Future studies will extend the temporal sampling of the SPICE data from 3 to 7 minutes so that the models can be compared. Although the Patlak model was used for pharmacokinetic analysis, other DCE-MRI models could be readily applied.The necessity for correcting DCE time courses for

T_{2}* effects may be questioned, given the short TEs used in conventional DCE methods and in the proposed method. However, as shown in Figure 8,T_{2}* may also affect large vessels (eg, AIF) and tumor vasculature may contain vessels with a distribution of radii, resulting in more or less confounding effects fromT_{2}*. Also, the differences in slopes shown in Figure 9, though seemingly small, suggest that heuristic DCE-MRI analysis methods may benefit fromT_{2}* correction. The need for this step will be further explored with the planned DCE comparison studies described above. Nevertheless, even ifT_{2}* effects are negligible, dual-echo acquisitions still permit conversion of signal intensity time courses into concentration–time curves without the need to acquire a precontrastT_{1}map.The spiral-based approach described here offers several advantages that make it well-suited for perfusion imaging. Unlike echo planar imaging (EPI), spiral imaging does not collect data in the corners of k-space, resulting in increased time efficiency over EPI. The shorter readout durations in spiral translate into several advantages, including reduced

T_{2}* decay during the readout, which limits the maximum achievable resolution of single-shot methods (53–55); increased temporal resolution, which is beneficial for AIF sampling in DSC and DCE imaging (52, 56–58), or increasedT_{1}-weighting in DCE (59); increased section coverage for a given TR; and diminished vessel blooming (17). Specific to DCE-MRI, because the readout starts in the center of the k-space, spirals can achieve very short minimum TEs, producing images with goodT_{1}weighting.A major disadvantage of spiral is compromised image fidelity because of off-resonance-induced phase accrual over the readout. The current implementation of the proposed method does not correct for off-resonance effects. It has been well established that off-resonance effects can degrade the fidelity of spiral images. In contrast to EPI, where off-resonance effects result in a dominant one-dimensional distortion along the phase-encode direction, a two-dimensional blurring results in spiral images (60). Although an SPSP pulse was used to diminish the chemical shift contributions to off-resonance effects, off-resonant spins still arise from field inhomogeneity and tissue susceptibility differences. Although the proposed method does acquire dual echoes at each slice location, the difference in TEs is very large. The large delta TE results in phase images with multiple phase wraps, requiring unwrapping of the phase images. Methods to reduce off-resonance effects include, selectively exciting water using SPSP excitation pulses to reduce the chemical shift contribution to off-resonance effects; reducing field inhomogeneity by careful shimming; and applying off-resonance correction algorithms (51, 61, 62). Parallel imaging (eg, spiral SENSE) (63) would also provide substantial benefits for the single-shot, dual-echo spiral acquisition described here by reducing the length of the spiral readout. This would greatly improve data quality in regions of static susceptibility differences, such as resection cavities. Finally, although blurring results in a local resolution loss, it does not force the requirement to spatially remap displaced pixel data to restore its actual anatomic location (55).

The proposed SPICE method requires a single dose of the contrast agent to obtain both DSC- and DCE-MRI parameters. It should be emphasized, however, that at least a single dose (ie, 0.1 mmol/kg) must be used. Although satisfactory contrast enhancement can be obtained using only a half dose of high

T_{1}relaxivity agents such as MultiHance (Bracco Diagnostics Inc), a half-dose does not produce appropriate susceptibility effect for DSC, regardless of the method used for acquisition (ie, single- or dual-echo, EPI, or spiral) or field strength. Contrast-to-noise is critical for adequate nonlinear least squares fitting of the model to correct forT_{2}/T_{2}* effects and least squares fitting of the Patlak model for DCE analysis. Therefore, although the proposed method reduces the total amount of contrast agent that needs to be administered, a minimum of a single dose is highly recommended.## Supplemental Materials

## Supplemental Appendix:

http://dx.doi.org/10.18383/j.tom.2016.00217.sup.01

## Notes

[1] Abbreviations:

DCE

Dynamic contrast-enhanced

DSC

dynamic susceptibility contrast

MRI

magnetic resonance imaging

Gd

gadolinium

rCBV

relative cerebral blood volume

CBF

cerebral blood flow

BBB

blood–brain barrier

EES

extravascular, extracellular space

TE

echo time

TR

repetition time

SNR

signal-to-noise ratio

AIF

arterial input function

SPSP

spatial–spectral

GRE

gradient echo

HCT

hematocrit

T_{1}spin lattice relaxation time

T_{2}spin-spin relaxation time

NEX

number of excitations

## Acknowledgments

This work was supported in part by NIH/NCI R01 CA082500, NIH/NCI U01 CA176110, NIH/NINDS R41 NS076149, NIH/NCI R44 CA134031. The authors would like to thank Eric C. Wong, PhD, MD, for the original pulse sequence upon which this work was based, and Melissa Prah and Cathy Marszalkowski, who are instrumental to all of the laboratory's imaging research. This work was presented in part at ISMRM 2007, ASNR 2007, ISMRM 2008, and ISMRM 2015.

Conflict of Interest: Kathleen M. Schmainda has ownership interest in Imaging Biometrics, LLC.

Disclosures: Imaging Biometrics LLC has been awarded a US Patent (Serial No. 12/601,241) for the SPICE technology, for which the authors of this paper are coinventors.

## References

T_{1}-weighted MRI of a diffusable tracer: standardized quantities and symbols. J Magn Reson Imaging. 1999;10(3):223–232.T_{2}*-weighted contrast-enhanced MRI. Magn Reson Med. 2004;51(5):961–968.T_{1}estimation errors in breast DCE-MRI at 3 tesla. J Magn Reson Imaging. 2013;38(2):454–459.T_{1}-weighted dynamic contrast-enhanced magnetic resonance imaging. Magn Reson Med. 2004;51(4):858–862.T_{1}andT_{2}dipolar and residual susceptibility effects in DSC-MRI using dual-echo SPIRAL. Proceedings of the International Society of Magnetic Resonance in Medicine, 15th Annual Meeting, 2007; Berlin. p 2811.T_{1}-weighted MR images: evaluation of two linear gadolinium-based contrast agents. Radiology. 2015;276(3):836–844.## Journal Information

Journal ID (nlm-ta): tom

Journal ID (publisher-id): TOMOG

Title: Tomography

Subtitle: A Journal for Imaging Research

Abbreviated Title: Tomography

ISSN (print): 2379-1381

ISSN (electronic): 2379-139X

Publisher: Grapho Publications, LLC (Ann Abor, Michigan)

## Article Information

Copyright statement: © 2016 The Authors. Published by Grapho Publications, LLC

Copyright: 2016, Grapho Publications, LLC

License (open-access, https://creativecommons.org/licenses/by/4.0/):

This is an open access article under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

Publication date (print): December 2016

Volume: 2

Issue: 4

Pages: 295-307

Publisher ID: TOM-00217-16

DOI: 10.18383/j.tom.2016.00217

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