Method for Rapid Calculation of Quantitative Cerebral Perfusion

Abstract

Purpose

To evaluate an algorithm based on algebraic estimation of T₁ values (three-point estimation) in comparison with computational curve-fitting for the postprocessing of quantitative cerebral perfusion scans.

Materials and Methods

Computer simulations were performed to quantify the magnitude of the expected error on T₁ and consequently cerebral perfusion using the three-point estimation technique on a Look-Locker (LL) EPI scan. In 50 patients, quantitative cerebral perfusion was calculated using the bookend method with three-point estimation and curve-fitting. The bookend method, a novel approach for calculating quantitative cerebral perfusion based on changes in T₁ values after a contrast injection, is currently being validated. The number of computations was used as a measure of computation speed for each method. Student’s paired t-test, Bland-Altman, and correlation analyses were performed to evaluate the accuracy of estimation.

Results

There was a 99.65% reduction in the number of computations with three-point estimation. Student’s t-test showed no significant difference in cerebral perfusion (P = 0.80, 0.49, paired t-test N = 50, quantitative cerebral blood flow-white matter [qCBF-WM], qCBF-gray matter [qCBF-GM]) when compared to curve-fitting. The results of the two techniques were strongly correlated in patients (slope = 0.99, intercept = 1.58 mL/(100 g/minute), r = 0.86) with a small systemic bias of -0.97 mL/(100 g/minute) in Bland-Altman analysis.

Conclusion

The three-point estimation technique is adequate for rapid calculation of qCBF. The estimation scheme drastically reduces processing time, thus making the method feasible for clinical use.

THE IMAGING OF PHYSIOLOGIC PARAMETERS related to cerebral perfusion, such as mean transit time (MTT), cerebral blood volume (CBV), and cerebral blood flow (CBF), is possible with MRI (1-5). In its current clinical implementation, MR-based perfusion images report relative, rather than quantitative perfusion. The ease of use and widespread availability of MRI based cerebral perfusion is becoming increasingly important in determining the underlying pathophysiology of several diseases (6-8). A method for obtaining quantitative CBF (qCBF), called the “bookend technique,” which is based on T₁ changes after injection of gadolinium-based contrast, has been reported (9-11). The bookend approach has not been fully validated to the reference standard, [¹⁵O]-H₂ positron emission tomography (PET); however, the bookend approach has produced values that are consistent with historical reference values and has been shown to be highly reproducible in a clinical setting (9-11). A major impediment to the dissemination and more widespread evaluation of this technology is the need for specialized software for image postprocessing.

The goal of this report is to evaluate an algorithm for the postprocessing of bookend perfusion scans. We present an approach to approximate T₁ values using three-point estimation fitting. We propose that this three-point estimation approach is adequate for the purpose of quantifying cerebral perfusion.

MATERIALS AND METHODS

This Health Insurance Portability and Accountability Act (HIPAA)-compliant study was approved by the institutional review board at our institute. Our approach is a modification to the postprocessing used in the bookend method, which has been proved to be accurate, reliable, and reproducible (9-11). All image post-processing and analyses were performed using commercially available software (MATLAB R2006a; The MathWorks, Inc., Natick, MA, USA). Currently, post-processing of bookend perfusion images can take over an hour, hindering the adaptation of MR cerebral perfusion into the diagnostic algorithm. The rate-limiting step for quantitative MR perfusion using the bookend technique is currently the mapping of longitudinal relaxation (T₁) values. Obtaining the quantitative CBV (qCBV) is the first step in obtaining the qCBF, based on the ratio of differences in inverse T₁ in blood and tissue after a gadolinium injection as shown by Eq. [1]. The bookend equation takes into account intravascular water exchange correction (WCF), the brain density (ρ), and the hematocrit levels (Hct) in large and small vessels (LV and SV) (9,10,12):

$$qCBV={100}^{\ast }WC{F}^{\ast }\frac{1}{rho}\ast \frac{1-Hc{t}_{LV}}{1-Hc{t}_{SV}}\ast \frac{{(1∕T_1^{\text{Post}}-1∕T_1^{\text{Pre}})}_{\text{Tissue}}}{{(1∕T_1^{\text{Post}}-1∕T_1^{\text{Pre}})}_{\text{Blood}}}.$$ [1]

To calculate qCBF, relative CBV and CBF (rCBV and rCBF) have to be determined next. rCBV is determined from a ratio of integrals of tissue concentration (C) and arterial input function (AIF) as shown in Eq. [2], taking into account the brain density (ρ) and Hct in LV and SV (9,10):

$$rCBV=\frac{1}{rho}\ast \frac{1-Hc{t}_{LV}}{1-Hc{t}_{SV}}\ast \frac{{\int }_{C\left(t\right)dt}}{{\int }_{AIF\left(t\right)dt}}.$$ [2]

rCBF is found by deconvolution of the tissue concentration and AIF by singular value decomposition of a reformulation of Eq. [3], where R(t) is the residue function (9).

$$C\left(t\right)=rCBF\times (AIF\otimes R(t\left)\right).$$ [3]

Since the ratio qCBV/rCBV is the same as the ratio qCBF/rCBF, qCBF is determined by Eq. [4] (9):

$$qCBF=rCB{F}^{\ast }\frac{qCBV}{rCBV}.$$ [4]

The T₁ maps for qCBV determination are derived from signal data acquired with a Look-Locker echo-planar imaging (LL-EPI) sequence by fitting the signal data to a relaxation curve for each voxel using a Levenberg-Marquardt (L-M) least-squares approach (13). L-M curve fitting is a well-established iterative technique for curve-fitting that has been proven to have high accuracy and convergence properties but can be prohibitively slow.

THEORY

Our analysis is based on the LL signal relaxation equation (Eq. [5]), where M₀ is the initial magnetization, InvF is the inversion factor, and T₁* is the apparent T₁. T₁* is used to determine longitudinal T₁ relaxation values using Eq. [6] (10,13):

$$M(t=\text{time})=\mid M_0(1-InvF\exp (-t∕T_1^{\ast }\left)\right)\mid ,$$ [5]

$$T_1=T_1^{\ast }(InvF-1).$$ [6]

We simplified the signal equation using three parameters to characterize the signal as shown in Eq. [7], where X₁ is equal to M₀, X₂ is equal to InvF times M₀, and X₃ is equal to T₁*, similar to Deichmann et al (14):

$$S(t=\text{time})=\mid X_1-X_2\exp (-t∕X_3)\mid .$$ [7]

In the L-M fit, X₁, X₂, and X₃ are free parameters and are used in determining T₁:

$$T_1=X_3(X_2∕X_1-1).$$ [8]

To mitigate the time-intensive least-squares fit to determine the parameters X₁, X₂, and X₃ of the signal relaxation equation, we implemented a three-point estimate of T₁, obtained from three points of the signal curve: 1) the initial magnetization point (M₀) where we approximate S(t = 0) in Eq. [6], 2) the null point (t_null) (S(t) = 0), and 3) the signal at t > T₁, called “infinity point” (t_∞):

$$X_1=S\left(t_{\infty }\right),$$ [9]

$$X_2=X_1+S(t=0),$$ [10]

$$X_3=\frac{-t_{\text{null}}}{\ln (X_1∕X_2)}.$$ [11]

Figure 1 shows a plot of a short and long T₁ relaxation curves and the points used for determining the fit parameters. For the purposes of this study, we approximated the infinity point (X₁) as t_∞ = 2520 msec, which corresponds to the last image acquired in the LL scan, that is, the last time point sampled on the regrowth curve. We calculated X₂ by using the initial magnetization point since at time zero the exponential term is equal to one and thus initial magnetization is the absolute difference between X₁ and X₂. The initial magnetization point was estimated as the signal from the first sampled time point. Lastly, X₃ is calculated from X₁ and X₂ using the fact that at the null point (t_null) the signal value is zero as shown in Eq. [11]. We estimated the null point as the point of minimum signal intensity in the T₁ regrowth curve. Once the parameters had been estimated, T₁ values were calculated using Eq. [8].

Figure 1.

T₁ relaxation curves shows the three-point estimation parameters used for estimating the fit of the longitudinal relaxation signal equation. Note that for long T₁ species, the approximation that the last acquired data point corresponds to t = ∞ breaks down.

Simulations

Computer simulations were performed in MATLAB to quantify the magnitude of the expected error on T₁ from the three-point estimation technique. This simulation was designed to determine the range of T₁ values over which the three-point estimation would be valid for the calculation of CBF. A signal was simulated using the Bloch equation with parameters for the existing scanning sequence (LL-EPI) (13). Noise was generated using Eq. [12], where M is the magnetization without noise, normalized so M₀ = 1, n_1,2 are random numbers from a Gaussian distribution with zero mean and unit variance. The value of the signal-to-noise ratio (SNR) was set to 110, based on measurement of signal and noise regions of interest (ROIs) from an LL image at the first time point (15). In the simulations, we set a T₁ value (true T₁ value), and then generated a signal with noise using that T₁ value. We then used both the curve-fitting technique and our three-point estimation technique to measure experimental T₁:

$$\sqrt{{(M+\frac{n_1}{SNR})}^2+\left(\frac{{n_2}^2}{SNR}\right)}.$$ [12]

Data Analysis

Simulation results were used in a correlation analysis to determine the relative error introduced in the quantification of cerebral perfusion. Because there is a linear dependence between qCBV measurement in white matter (WM) and the global qCBF values (9-11, 16-18), we determined the resulting error on qCBF analytically as the relative error in qCBV in WM. We assume a 2% blood volume, for WM, a single dose (0.1 mmol/kg body weight) gadolinium injection and an initial WM T₁ of 650 msec. Under these assumptions: T₁ WM pre = 650 msec, T₁ WM post = 625 msec, T₁ blood precontrast = 1200 msec, T₁ blood postcontrast = 250 msec. These values yield a qCBV_TRUTH value of 1.94 mL/100 g. This was compared with the same value calculated from the T₁ values calculated from the three-point estimate. To get an estimate of the error calculated as:

$$\text{Error}=(\text{truth}-\text{reconstructed})∕{\text{truth}}^{\ast }100\%.$$ [13]

Patient Study

The MRI perfusion examinations of 50 consecutive patients (male: 23, female: 27, ages 54 ± 17 years) with a wide range of pathologies: stroke (N = 9), tumor (N = 21), or intracranial arteriovenous malformation (AVM) (N = 10) were retrospectively reviewed. Patients were excluded if there was severe motion during the perfusion scans or if they had undergone contrast-enhanced MRI within 24 hours of the perfusion scan.

MRI

All 50 patients were scanned in a 1.5T scanner (Avanto: N = 19, Espree: N = 3, Sonata: N = 6, Symphony: N = 22; Siemens Medical Solutions, Erlangen, Germany). In the bookend perfusion protocol, three scans are required. First, a segmented inversion-recovery (IR) LL-EPI (nonselective inversion pulse, 20° excitation flip angle, TR = 21 msec, TE = 9.9 msec, TI = 15 msec, 128 × 128 matrix, 220 mm field of view (FOV), 21 lines in k-space per an acquisition, 5 mm thickness, 120 time points) scan was performed. A delay time between the data acquisition at the last time point and another inversion pulse is 2 seconds, leading to a total scan time of 45 seconds. This sequence was designed with 4400 msec between inversion pulses to allow full regrowth. This LL-EPI scan was used to estimate the initial T₁ values. The LL-EPI sequence was designed without regard to scanner-specific parameters and falls within specifications of all of the scanners used in the data accrual. Next, a perfusion-weighted imaging (PWI; gradient echo, TR/TE = 1500 msec/40 msec, matrix size = 128 × 128, FOV = 220 mm, slice thickness = 5 mm, slices = 13, 50 measurements on each slice) scan consisting of single-shot EPI acquisitions was performed. A single-dose injection of a gadolinium-based contrast agent (0.1 mmol/kg; Magnevist; Berlex, Princeton, NJ, USA) was injected during PWI at a rate of 5 mL/second by a power injector. The last scan is another segmented IR LL-EPI scan with same specifications as the first scan. This LL-EPI scan was used to estimate the final T₁ values, shortened by contrast injection. The slice for LL-EPI is usually one of the 13 slices of the PWI containing a major WM region. In the event that the slices did not match between LL-EPI and PWI, coregistration was performed using Statistical Parametric Mapping (SPM) software package (SPM5; Wellcome Department of Cognitive Neurology, London, England).

Image Postprocessing

qCBF values were calculated according to the bookend method (Eqs. [1]-[4]) using the three-point estimation approach for determining T₁ values. As Eq. [1] shows, qCBV calculation is based on the ratio of differences in inverse T₁ values in WM (tissue) and blood before and after gadolinium-based contrast (9-11). WM was automatically chosen from the estimated T₁ distribution by selecting the full width of half the maximum of T₁ distribution (9,10). Thus, T₁ of WM results directly from WM segmentation (10). The sagittal sinus was used for obtaining blood T₁ values and was chosen by an automatic algorithm without user input (9,10). First, a ΔR₁ map was obtained from the difference of inverse T₁ values before and after gadolinium-based contrast injection as shown by Eq. [14]:

$$\Delta R_1=(1∕T_1^{\text{Post}}-1∕T_1^{\text{Pre}}).$$ [14]

Maximum ΔR₁ occurs in blood, specifically the sagittal sinus (9,10). To create a mask of the sagittal sinus, we empirically determined that raising ΔR₁ to the sixth power creates a large enough separation between blood and tissue ΔR₁ values to allow for efficient segmentation of the sagittal sinus. After filtering out values for which ΔR₁ < 0.80 × (ΔR₁)⁶, the only values left corresponded to voxels for the sagittal sinus. We found the cutoff by finding a ratio between an ROI of the sagittal sinus and the rest of the brain. Contrast acts as a T₁ shortening agent, and thus T₁ of blood before contrast injection is much higher (about 1200 msec at 1.5T) than T₁ of blood after contrast (about 250 msec at 1.5T) for a signal dose injection (9,10). Since qCBV calculation involves the inverse of these T₁ values (i.e., R₁), the R₁ of blood precontrast is very close to zero; hence, we approximated 1/T₁ blood precontrast to be zero. This step reduced the systematic error on qCBV from the poor performance of our estimation for long T₁ species. The T₁ of blood postcontrast value was calculated from the average T₁ value from all voxels covering the sagittal sinus.

Data Analysis

The three-point estimation technique was evaluated based on its computational efficiency, accuracy in determining T₁ values, and accuracy in quantifying CBF. A simple computation of time measurement between the three-point estimation and fitting methods was not sufficient because processing time varies depending on the computer, processor, and background processes running. Even when the background processes are controlled by disconnecting the computer from the network, operating system processes can change between trials; hence, a better measure of processing time is a record of the number of computational operations each method utilizes. This was measured by using a built-in MATLAB function. All measurements were performed on the same computer (Lenovo T60, Intel Core2 Duo T5500, 1.66 GHz, 1.00 GB RAM). A paired t-test for difference in number of operations for all 50 patients was performed to determine whether observed differences were statistically significant.

A comparison of the three-point estimation and the fitting methods was performed using paired Student’s t-tests for qCBF in WM and gray matter (GM). WM and GM regions were chosen by drawing ROIs in qCBF images calculated by the fitting method, and same ROIs were used for comparison of qCBF values calculated using the three-point estimation method. A Bland-Altman analysis of the L-M fitting and three-point estimated qCBF values was performed to elucidate any trends that depend on the value of perfusion.

RESULTS

Simulations

Figure 2 shows the correlation between T₁ determined from the three-point estimate and the L-M fitting of the full regrowth curve. The unity line shows that the L-M fitting method correlates well with true T₁ values, but the three-point estimation correlates only for values less than 1000 msec. Based on these simulations, we determined that the percentage error of 10.5% was present in the three-point estimate of qCBF. For WM this corresponds to 2.2 mL/(100 g/minute).

Figure 2.

Simulation results of three-point estimation and fitting compared to true T₁ values. The fitting method shows a good correlation and three-point estimation correlates for T₁ values less than 1000 msec.

Patient Study

Examinations and postprocessing were performed successfully in all 50 patients. Figure 3 shows a direct comparison between images in a stroke patient reconstructed with the L-M fitting and three-point estimation methods. The parametric images show quantitative perfusion on a scale from 0 to 120 mL/(100 g/minute), with the red-green-blue (RGB) scaling that is used clinically at our institution. Quantitatively, the two approaches to image reconstruction are identical, and qualitatively right hemispheric hypoperfusion is evident in both images.

Figure 3.

Parametric images from a stroke patient of CBF reconstructed using the bookend technique with (a) L-M fitting and (b) the three-point estimation. Note the areas of hypoperfusion in the right hemisphere that are equally represented by both approaches to image reconstruction.

Results of the ROI analysis of measured T₁ values are shown in Fig. 4. These plots show that linearity exists for T₁ values less than 1000 msec and nonlinearity increases for higher T₁ values because of higher variability. The results of the correlation analysis for T₁ values up to 2400 msec (twice the expected T₁ of unenhanced blood) yield a slope of 1.11, intercept of 177 msec and r-value of 0.991. The Bland-Altman analysis shows good agreement between the L-M fitted and estimated T₁ with a mean bias of 85.34 msec.

Figure 4.

a: Voxel-by-voxel comparison of T₁ values measure in patients (N = 50) between the three-point estimation and L-M fitting methods. The line of unity shows correlation between the methods at low values of longitudinal relaxation (T₁ < 1000 ms). b: Bland-Altman analysis of voxel-by-voxel comparison of the same data.

We found the mean qCBF-WM, and qCBF-GM values for the fitting method are 26.03 ± 11.46 mL/(100 g/minute), and 69.68 ± 27.30 mL/(100 g/minute), respectively. The mean qCBF-WM and qCBF-GM values for the three-point estimation method are 25.69 ± 11.90 mL/(100 g/minute) and 71.96 ± 34.64 mL/(100 g/minute), respectively. Paired t-tests for qCBF show no significant difference between the fitting and three-point estimation methods (P = 0.80, 0.49, paired t-test N = 50, qCBF-WM, qCBF-GM, respectively). Figure 5a shows a correlation plot of qCBF values in both WM and GM between the three-point estimation and fitting methods. A good correlation (slope = 0.99, intercept = 1.58 mL/(100 g/minute), r = 0.86) is observed. A Bland-Altman analysis (shown in Fig. 5b) yielded a systematic bias of -0.97 mL/(100 g/minute) in the determination of qCBF.

Figure 5.

a: Correlation of qCBF values between the three-point estimation and fitting methods. Good correlation is seen with slope = 0.99, intercept = 1.58 mL/100 g/minute, and correlation coefficient of r = 0.86. b: Bland-Altman analysis of qCBF values shows no systematic bias.

The number of computational operations for T₁ mapping did not change at different times of day or with/without network activity. The average number of operations was 6,934,582 ± 697,661 operations for the fitting method, and 24,284 ± 1914 operations for the three-point estimation technique.

DISCUSSION

We have found that using the three-point T₁ estimation method in the calculation can reduce the postprocessing of quantitative perfusion images by two orders of magnitude. Despite systematic errors on our three-point estimation at long T₁s, the error on the quantification of cerebral perfusion is negligible. The results indicate the analytical and curve-fitting approaches are comparable. This novel approach to accelerating perfusion quantification has the potential to reduce the complexity of image processing of quantitative perfusion images, a recognized limitation in the bookend technique. The bookend method has been shown to produce accurate and reproducible results (11), but has not been fully validated. We are currently focusing on validating the bookend technique to the reference standard [¹⁵O]-H₂ PET.

Several MR approaches toward absolute quantification of CBF exist. Arterial spin labeling (ASL) consists of inverting the magnetization of flowing blood upstream of the desired region for perfusion measurement. The inverting magnetization is transferred to tissue as blood flows into imaging regions, altering local magnetization in proportion to CBF. Consequently, CBF can be calculated by measuring change in local magnetization (19). The accuracy of CBF depends on the time it takes for blood to flow from the labeling region to the readout slice. Some ASL techniques can minimize this dependence when transit times are in the normal range, but in patients with severely altered hemodynamics, the transit time can confound accurate CBF determination (20). Accordingly, the utility of ASL has not been established, since label-to-tissue transit times cannot be predicted.

The strongest correlation between MRI and the reference standard, radiolabeled [¹⁵O]-H₂ PET, was found in an MR approach that applies a scale factor to rCBF images, accounting for errors in AIF (16). However, in this approach the correction factor relies on population-based, average venous efflux. Similarly, Ostergaard et al (18) have shown that it is possible to accurately determine qCBF by applying an empirically determined scale factor from a concurrent PET measurement. These population-based methods, nevertheless, do not account for the observed age-dependent reductions in qCBF (21,22) or vasoreactive hemodynamic responses seen in a disease state such as stroke that can alter the value of CBF in presumably normal tissue (17). The bookend method is a patient-based approach for determining the scale factor.

The three-point estimation technique for the bookend method introduces errors at three stages. First, as shown in Fig. 1, for a longer relaxation time, the signal curve does not reach steady state as fast as the signal for a short relaxation time. When we estimate the infinity point at t = 2520 msec, we assume the signal has reached steady state, but this assumption is a limitation at higher relaxation times. The next error is introduced when estimating M₀. The first measured point of the signal is not the true initial magnetization point because of delay between signal readout and start of the scan, TI (initial time-point). The last source of error in estimation results from measurement of t_null. Since the LL-EPI signal is not continuous and is measured at 120 discrete time points, the true null point could possibly occur between the measured time points. Thus an error is introduced when using the minimum of LL-EPI signal as the null point. Because relatively short TR and TI (TR = 21 msec, TI = 15 msec) are used in our protocol, the error in null point estimations is minimized, and most error probably results mainly from infinity point estimation at higher true T₁ values. Simulation and in vivo results (Figs. 2 and 4) support the conclusion that three-point estimation is adequate at T₁ values less than 1000 msec.

Since WM T₁ values are in the range of 500-700 msec, three-point estimation is valid for WM segmentation. The higher T₁ values occur in cerebrospinal fluid and unenhanced blood. Thus we can only apply the same reasoning for T₁ blood postcontrast, since contrast is a T₁ shortening agent. However, the estimation scheme is not valid for T₁ blood precontrast, as those values typically exceed 1200 msec. Since qCBV calculation involves the inverse of these T₁ values (Eq. [1]), the R₁ blood precontrast is very close to zero; hence, we approximate 1/T₁ blood precontrast to be zero by setting T₁ blood precontrast to infinity. For the purpose of whole-brain T₁ mapping, we may be able to extend LL-EPI scanning to include more time points to allow longer relaxation signals to reach steady state, consequently improving the range for which estimation is adequate.

No difference occurs in the number of computational operations throughout the day, whereas network traffic fluctuates, and thus the number of computations is a better measure of reconstruction efficiency than absolute reconstruction time. A significant difference in speed exists between the methods (reduction by 99.65% in operations used). The average computationaloperations were 6,934,582 ± 697,661 operations for the fitting method and 24,284 ± 1,914 operations for the three-point estimation technique. In addition, MATLAB functions are compiled right before being used and remain in memory for the duration of the program. Thus, when a program calls a function numerous times, the function is executed faster after the first call. This is a major disadvantage for using MATLAB in the clinical setting. The final algorithm will be coded in C/C++, in which the code is precompiled; as a result, the speed of these programs is much faster. Thus, by coding our quantification analysis in C/C++ for use on the MRI console, we anticipate a further reduction in postprocessing time. We can also expect to see a decrease in time for curve-fitting, but curve-fitting will always be slower due to the iterative process, even if fully optimized.

As shown by paired t-tests, no significant difference exists between the fitting and three-point estimation methods (P = 0.80, 0.49, paired t-test N = 50, qCBF-WM, qCBF-GM, respectively) in patients. This means that our three-point estimation technique was adequate for qCBF calculation. Figure 3 yields visual evidence of the similarity of the two methods, showing that both perfusion images have the same voxel-to-voxel perfusion values. This agreement between the results demonstrates that there are no systematic shifts (up or down) in the parameters related to quantification of perfusion. Figure 5a supports the results by showing a good correlation (slope = 0.99, intercept = 1.58 mL/(100 g/minute), r = 0.86) in qCBF values in both GM and WM between the three-point estimation and fitting methods. This means that in a clinical setting, in cases where qCBF scans would be advantageous (e.g., stroke, AVM, and tumors), qCBF can be quickly and adequately determined using the three-point T₁ estimation scheme. Using LL for T₁ measurement in flowing blood has the potential confounding effect that the blood is flowing. This could result in differences in signal saturation, which depends on the velocity of the flowing blood. We did not find this effect to be a problem in these exams due to the fact that T₁ measurement enters the quantification analysis as differences and ratios of T₁. Therefore, the error introduced by systematic effects, such as signal saturation, is small. Figure 5b shows the Bland-Altman analysis of qCBF values between the fitting and three-point estimation methods. Higher variation is seen at higher qCBF values of 50-100 mL/(100 g/minute). This is due to blood-vessel blooming and partial volume averaging effects in qCBF images. These errors can potentially be minimized in the future by using spin-echo sequences instead of gradient-echo sequences (23).

This approach to qCBF quantification is not without limitations. Of primary concern is the lack of agreement for T₁ values exceeding 1000 msec. This poor agreement results from insufficient regrowth of the magnetization within the echo train of the LL scan. Although these effects do not adversely affect our results when scanning at 1.5T, we anticipate that 3.0T scans, where T₁ values are 30% longer, may be affected. This would require a retuning of the pulse sequence. Requiring a longer delay time between inversion pulses has the potential to mitigate these effects, at the expense of prolonged scan times. A second limitation is that the L-M fitting routines were not fully optimized prior to the comparison with the three-point method. However, it is unlikely that software optimization of an iterative fitting algorithm will ever be more efficient than simply extracting single data points from a vector. Last, the LL pulse sequence is a sequence we developed in-house, which can hinder clinical availability. We hope that if there is a need for widespread dissemination of the technology, productization would include a vendor-supplied pulse sequence.

In conclusion, we have found that our three-point estimation technique is adequate for rapid calculation of qCBF. However, the T₁ estimation technique does not meet the need for rapid T₁ measurement because estimation variability increases at high T₁ relaxation times. Our estimation scheme drastically reduces processing time, thus making the method feasible for clinical use.