Myocardial blood flow (MBF) is an important indicator of cardiac tissue health, which can be measured using arterial spin labeling. This study aimed to develop a new method of MBF quantification with blood pool magnetization measurement (“bpMBF quantification”) that allows multislice cardiac arterial spin labeling.
Theory and Methods
A multislice segmented ECG-gated Look-Locker T1 mapping sequence was validated. Quantification of multislice arterial spin labeling is not straightforward due to the large volume of blood inverted following slice-selective inversion. For bpMBF quantification, a direct measurement of the left-ventricle blood pool magnetization was used to approximate the blood input function into the Bloch equations. Simulations and in vivo measurements in the mouse heart were performed to evaluate the bpMBF method.
Measurements indicated that blood pool magnetization requires ∼3 s to return to equilibrium following slice-selective inversion. Simulation and in vivo results show that bpMBF quantification is robust to variations in slice-selective thickness and therefore applicable to multislice acquisition, whereas traditional methods are likely to underestimate multislice perfusion. In vivo, single and multislice perfusion values matched well when quantified using bpMBF.
Noninvasive preclinical imaging offers unparalleled opportunities to study cardiac structure and function in vivo, and as such has become essential in the study of experimental models of cardiovascular disease [1, 2]. Emphasis has been placed on developing fast, specific, and sensitive MRI methods for these studies. Perfusion, or capillary level blood flow, is an important tissue parameter, which can be measured noninvasively using arterial spin labeling (ASL) . Currently, ASL data can only be acquired in a single slice when applied to the heart. The ability to measure myocardial blood flow (MBF) in multiple slices would be greatly advantageous in characterizing disease models. However, quantifying perfusion in the multislice case is not straightforward.
A single slice pulsed ASL technique (flow alternating inversion recovery) comparing T1 recovery following global and slice-selective inversion has been implemented in the mouse and rat heart, and applied in many preclinical cardiovascular studies [4-22]. When moving to the multislice scenario, a wider slice-selective inversion is required to measure T1 in all slices. This results in the inversion of a large volume of blood in the heart and lungs and therefore changes the input function of the blood magnetization into the myocardium.
In this study, we present a multislice segmented ECG-gated Look-Locker T1 mapping sequence, which generates multislice data in the same scan time as the single slice acquisition. We develop a new method of quantifying perfusion using a measurement of the blood magnetization from the blood pool. This method will be referred to as the blood pool MBF (bpMBF) quantification method. Simulation studies (guided by in vivo data acquired in the mouse heart) are used to investigate the effects of the blood magnetization input function on MBF measurements and to investigate the sensitivity of the quantification method. Our simulation and in vivo results imply that the bpMBF quantification is robust to variations in slice-selective inversion thickness and is therefore applicable to multislice ASL perfusion mapping. We note that that perfusion is likely to be underestimated using traditional quantification methods if the model assumptions are not carefully obeyed, especially when moving to thicker slice-selective inversions for the multislice case. This study presents the first multislice perfusion measurements in the mouse heart using MRI.
Myocardial perfusion measurements with ASL are based on the difference between T1 recovery under two different conditions: following a global inversion pulse (tagged condition) and following a slice-selective inversion pulse (control condition) . Following the slice-selective inversion, the blood perfusing into the tissue of interest is “fresh” (i.e., fully relaxed) and therefore causes an apparent acceleration of T1 recovery. Bauer et al.,  modeled the effect of perfusion on myocardial T1 recovery and Belle et al.,  extended this model to estimate perfusion under the assumption that all inflowing blood is fresh in the slice-selective case and recovering with the T1 of blood (T1blood) in the global inversion case. Using this model, the T1 values derived from curve fitting are directly compared to generate an estimate of perfusion (Eq. (1)) :
where λ (the blood-tissue partition coefficient of water) = 0.95 mL/g , myocardial T1 measurements following global and slice-selective inversion are indicated by subscripts and T1blood is taken from the left-ventricle blood pool. T1 is typically measured in the mouse heart using a Look-Locker acquisition where a segment of k-space is acquired for each heart beat after the inversion throughout T1 recovery [9, 12, 22]. T1 can be quantified from the signal recovery data using a three parameter exponential fit with Look-Locker correction factor .
However, the assumption of Eq.  that all inflowing blood is fresh after the slice-selective inversion is not always valid. When applying a slice-selective inversion slab to invert the myocardial tissue, a large volume of blood contained within the right ventricle, left ventricle, capillary bed of the lung and vessels is inverted simultaneously, particularly in the multislice case (Fig. 1a,b). The inverted blood from the right ventricle and lungs is then recirculated through the left ventricle before being pumped through the coronary arteries to perfuse the myocardial tissue [transit time from right to left heart is ∼0.83 s in mice ] (Fig. 1). In addition, the fraction of left-ventricle blood ejected in a single heart beat (the ejection fraction) is <1. Therefore, for many heartbeats following inversion, some fraction of blood delivered to the myocardium will be labeled (due to circulation of inverted blood and ejection fraction<1).
To account for the blood magnetization input function in the slice-selective case, we used the modified Bloch equations presented by Detre et al.,  describing the longitudinal magnetization with the effects of perfusion (Eq. (2)). Sufficiently fast exchange of spins between intravascular and extracellular compartments has been demonstrated by Bauer et al.,  in rats and Wacker et al.,  in humans, meeting the assumptions of this model. This model has been used previously to estimate cerebral perfusion in cases where the Mblood(t) input is not straightforward .
Mtissue(t) myocardial T1 recovery curves are measured, λ is known, and Mblood(t) curves can be approximated from the blood pool magnetization. The remaining three parameters, MBF, T1tissue and M0tissue, can be determined through curve fitting to the inversion recovery Look-Locker data. Equation (2) can also be solved in the general case for any function Mblood(t) by:
For this study, we used a numerical integration of Eq. (2) for the estimation of MBF, however, Eq. (3) could also be used.
Data were acquired on a 9.4T Agilent scanner (Agilent Technologies, Santa Clara) with volume resonator RF coil (diameter 35 mm, length 60 mm, RAPID Biomed, Rimpar, Germany). The segmented ECG-gated Look-Locker T1 mapping sequence  was extended to have multislice capabilities (Fig. 2). Four lines of k-space are acquired per heart beat for each slice (requiring 12 ms per slice acquisition), meaning each slice is acquired at a slightly different cardiac phase. Using this sequence slice-selective and global recovery curves for multiple slices can be acquired in a total acquisition time of ∼15 min. We acquired three slices per acquisition at the beginning of systole in these studies (5 ms delay after R-wave trigger before acquisition). Slice-selective inversion thickness was wide enough to include all slices (at least 6 mm for three 1.5 mm slices) and global inversion thickness was set to 150 mm to cover the entire mouse. Inversion and excitation were performed using an adiabatic full passage (sech pulse, length = 4 ms, and bandwidth = 20 kHz) and gaussian pulses (length = 500 μs), respectively. A data logger (Cambridge Electronic Design, Cambridge, UK) was used to record ECG, respiration and RF events for the retrospective rejection of images deemed to be corrupted by respiration based on the central two lines of k-space. In addition, the data logger trace was used to trigger the scanner at each ECG event recorded as well as interpolate overdue RF triggers (activated after [mean +1 standard deviation RR interval] has elapsed since previous trigger), as described previously .
Multislice T1 mapping was compared with single slice segmented ECG-gated Look-Locker acquisition in phantoms of 0, 0.3, 0.6, and 1.3 mM Ni2+ in agarose and in vivo (n =3 CD1 mice). The T1 of three slices acquired separately was compared with the T1 of the same slices acquired using the multislice acquisition for slice-selective and global inversion. Scan parameters were set as follows: TE/TR(inv)/TR(RF) = 1.18 ms/13.5 s/3 ms, 4 lines of k-space per heart beat, flip angle = 5°, FOV = 40 × 40 mm2 (phantom) or 25.6 × 25.6 mm2 (in vivo), matrix = 128 × 128, slice thickness = 1.5 mm, inversion thickness = 7.5 mm (slice-selective) or 150 mm (global), number of slices = 1 or 3, slice gap = 0 mm, number of points in recovery curve= 50, slice acquisition order = centric, short-axis view (in vivo).
bpMBF Quantification Method
The blood magnetization input in Eq. (2) was estimated from a measurement of left ventricle blood pool magnetization at the previous heart beat with 1 RR-interval's T1 recovery (modeled), for both slice-selective and global inversion. This blood pool is already present in the cardiac images, and therefore no extra data acquisition is necessary. We assume that the spins are well mixed and the net magnetization is measured (from hand-drawn regions of interest including entire visible blood pool). The time-varying blood magnetization curve throughout inversion recovery was compared for multiple slice-selective thicknesses and different short axis positions in vivo in six CD1 mice (not all positions/thicknesses acquired in all subjects).
Numerical integration of Eq. (2) was performed to generate Mtissue(t) curves for given Mblood(t) data input and the mean-squared difference between the experimental data and the synthesized Mtissue(t) curves was minimized for slice-selective and global data simultaneously to fit for MBF, T1tissue and M0tissue. Because a 5° flip angle was used, it was assumed that the effect of the Look-Locker RF train on the Mtissue(t) curve was negligible compared with other effects. To initialize the MBF parameter value, a linear fit was used (as described in Appendix 1).
Simulations of Mtissue(t) and bpMBF Quantification
Modeling of Mblood(t)
For the purposes of simulation, Mblood(t) after slice-selective inversion was modeled to a first approximation by a three parameter exponential fit Eq. (4), as informed by experimental results (see Results):
where Tb,ss is the time constant describing the recovery to equilibrium of the left ventricle blood after slice-selective inversion (related to pulmonary circulation, T1blood and ejection fraction), and ε is an indication of the initial fraction of inverted blood in the left ventricle. To model the variations in Mblood(t) with slice-selective inversion thickness, ε was varied from ε = 0 (all inflowing blood is fresh) to ε = 2 (all blood in left-ventricle is inverted), while Tb,ss and M0blood were kept constant. For global inversion, Mblood(t) was assumed to be an exponential recovery:
MBF and ε were varied in simulations and other parameters were fixed based on observed values as follows: M0tissue = 0.07 au, T1tissue = 1.7 s, λ = 0.95 mL/g, M0blood = 0.08 au, Tb,ss = 1.4 s, and T1blood = 2 s. For the purposes of our simulation, the numerical integration of Eq. (2) was used to mimic the in vivo quantification method. As an alternative method, Eq. (3) can be solved explicitly for simulated Mblood(t), which gives identical Mtissue(t) curves to numerical integration of Eq. (2) using the simulated parameters (data not shown).
Three simulation experiments were performed. Experiment 1: Using the numerical integration of Eq. (2), Mtissue(t) curves were generated for a variety of Mblood(t) curves to simulate the relationship observed in vivo. Experiment 2: The mean-squared difference between synthetic Mtissue(t) curves generated with perturbations in MBF (MBF ± 5 mL/g/min) was used to assess the sensitivity of the mean-squared difference objective function and the ability to correctly estimate MBF. Experiment 3: To test the quantification methods, global and slice-selective Mtissue(t) curves were generated for a given MBF at a range of ε values and noise was added to the curves (100 repetitions). We compare MBF quantified using fit T1global and T1slice-selective in the standard method (Eq. (1)) to the multiparameter bpMBF quantification method. For figures, MBF = 5, 10, and 15 mL/g/min are shown, as well as MBF = 0 mL/g/min for the model comparison.
In Vivo Validation
Animal experiments were completed according to the UK Animal (Scientific Procedures) Act 1986 and local guidelines. For technique development and validation, CD1 mice were used. Anesthesia was induced with 4% isoflourane in 2 L/min O2 and maintained at 1.5–2% isoflurane in 1 L/min O2. A small animal physiological monitoring device (SA Instruments, Stony Brook, NY) was used to monitor respiration using a neonatal apnea pad, temperature using a rectal probe and ECG using two electrodes inserted subcutaneously.
Perfusion was estimated using standard quantification (Eq. (1)) and bpMBF quantification for the same midventricle single slice with a variety of slice-selective inversion thicknesses (n = 5). To compare single to multislice perfusion estimates, the mean perfusion estimates from the centre slice of a multislice acquisition were compared with single slice perfusion estimates in the same slice using bpMBF in n = 8 data sets. A combination of apical and midventricle positions were used, and slice-selective inversion thickness = 6 or 7.5 mm (multislice) and 4.5 mm (single slice). Multislice MBF maps are shown from one animal to demonstrate sensitivity to experimental manipulation with isoflurane varied from 1.25 to 2% (previously shown to produce a ∼2.5 fold increase in perfusion [10, 22]) and for comparison to single slice ASL acquisition.
T1 measurements generated using the single and multislice acquisitions compared well (Fig. 3). In phantoms, T1multi = 1.00·T1single − 0.03 s, and in vivo, T1multi = 0.77·T1single + 0.37 s. The additional variation in vivo was due to physiological noise, range of physiological T1 values (T1,slice-selective = 1.31–1.50 s and T1global = 1.78–1.92 s for single slice acquisition) or subtle differences in cardiac cycle. A small bias is observed in phantom T1 quantification where the multislice sequence overestimates T1 by a small margin. This overestimation is a small effect compared with physiological noise in vivo.
Measurements of Blood Magnetization
In Vivo Mblood(t) and Mtissue(t) Curves
For a range of inversion thicknesses, we observed that the blood pool magnetization requires ∼3 s to return to equilibrium in the left ventricle (Fig. 4). The amount of blood inverted increases with slice-selective inversion thickness, as expected, and with midventricle positioning. Slice-selective tissue magnetization recovery curves become closer to global recovery curves as the amount of inverted blood increases.
Modeling Parameters of Mblood(t)
Parameter ε (Eq. (3)) demonstrated a clear positive relationship with the slice-selective thickness (Fig. 5). However, Tb,ss and M0blood are not strongly related to slice-selective thickness. The relationship (slope and R2) between the parameters and slice-selective thickness are given in Table 1. This justified our choice to vary ε and keep M0blood and Tb,ss constant for the purpose of Mblood(t) simulation. ε takes a lower value when slices are positioned closer to the apex because less blood is inverted in this case. Mblood(t) parameters were found to be independent of isoflourane levels (data in Supporting Information). Typical values of ε for a midventricle slice are 0.75−1 for single-slice inversion thicknesses (blue curve in Fig. 4) and 1.25–1.5 for multislice inversion thicknesses (red curve in Fig. 4).
Table 1. Relationship Between Mblood(t) Parameters and Slice-Selective Thickness (Fig. 5) Given by Slope and R2
Mean slope (95% confidence interval)
There is a clear positive relationship between ε and slice-selective inversion thickness, whereas, Tb,ss and M0blood are constant (95% confidence interval of slope surrounds zero).
Simulations of Mtissue(t) and bpMBF Quantification
Experiment 1: Varying the simulated shape of Mblood(t) confirmed a relationship with Mtissue(t) (Fig. 6), which was analogous to the in vivo data shown in Figure 4. Experiment 2: For larger values of ε (and thus wider slice-selective thickness) or for higher MBF, the mean-squared difference curve is flatter and the minimum is more difficult to detect, meaning MBF values are more difficult to estimate correctly (Fig. 7). For example, when ε = 2 the slice-selective inversion recovery curves are very similar to the global inversion recovery curves, making the estimation of MBF challenging. This is an important observation relevant to planning the position of slices and inversion thickness used.
Experiment 3: Simulations show that when the assumptions of Eq. (1) are satisfied (ε = 0) or if MBF = 0 mL/g/min, the MBF is correctly estimated, otherwise, the standard quantification method (Eq. (1)) underestimates MBF, particularly if ε > 0.5 (Fig. 8a). However, using bpMBF quantification, MBF is well estimated regardless of ε (Fig. 8b). As ε increases, the uncertainty of the bpMBF estimation increases, as predicted above. This simulation indicates that the bpMBF quantification method is better suited to the estimation of myocardial perfusion under realistic circumstances, recalling the typical values of ε from the in vivo data were 0.75−1 for single slice inversion thickness and 1.25−1.5 for multislice inversion thickness.
In Vivo Validation
Mean MBF estimates from the standard quantification method (Eq. (1)) show a negative trend with slice-selective inversion thickness (Fig. 9a) for the same midventricle slice. The mean [95% confidence interval] slope of this relationship was −1.17 mL/g/min/mm (−1.95 mL/g/min/mm − 0.39 mL/g/min/mm) and R2 = 0.72. Importantly, the bpMBF quantification generates more consistent MBF estimates for the same data sets (Fig. 9b), with a group mean [95% confidence interval] slope of 0.02 mL/g/min/mm (−1.13 mL/g/min/mm, 1.16 mL/g/min/mm) and R2 = 0.37. This matches the simulation predictions well. The mean coefficient of variation  of the MBF estimates is 21%, which is within the expected range of within-session variability of the single slice technique found previously .
Comparing myocardial perfusion estimates from the central slice of multislice acquisitions to single slice acquisition of the same slice using bpMBF quantification gave a mean coefficient of variation of 16% (n =8 measurements). This is within the expected range of the within-session variability found previously , indicating the good correspondence between measurements. Figure 10 shows MBF maps (generated using bpMBF quantification) of three contiguous midventricle slices acquired using multislice ASL demonstrating increased perfusion with increased isoflurane levels. In addition, multislice MBF maps show good correspondence to single slice MBF maps acquired of the same three slices.
DISCUSSION AND CONCLUSIONS
To summarize, we have developed a multislice ECG-gated Look-Locker T1 mapping pulse sequence together with a new method for quantifying MBF by ASL. We demonstrated that the bpMBF quantification method is more robust to variations in the slice-selective inversion thickness than standard quantification methods, and is ideally suited to multislice ASL data. This new methodology has been used to generate multislice perfusion maps in vivo in the mouse heart.
The multislice T1 mapping pulse sequence presented here is an extension of the single slice sequence demonstrated previously  and was confirmed to generate accurate T1 measurements in phantoms and in vivo. A small bias was observed in the T1 quantification in phantoms, where multislice T1 values were longer than single slice measurements. The magnitude of the bias depends on the acquisition order, such that the bias increases for slices acquired later in the multislice acquisition. This is likely because the slice gap is set to 0 mm and therefore the excitation pulses will affect the magnetization of the neighboring slices. In vivo, the mean difference in T1 is approximately zero (combining global and slice-selective inversion data sets); however, a slight negative bias still appears to be present in the slice-selective case. The magnitude of this bias is very small (compared with physiological variation) and should not significantly affect results.
We chose to acquire four lines of k-space per heart beat per slice in order to ensure limited cardiac motion during the acquisition for each slice. Each k-space segment requires a 12 ms acquisition, and therefore the three slices will be acquired at slightly different cardiac phases. Although full heart coverage is ideal, three slices is advantageous over a single slice, particularly in regional conditions such as myocardial infarction. A different number of slices could be acquired with the same sequence depending on the needs of the study; however, decreased fitting sensitivity with larger volumes of inverted blood after slice-selective inversion must be considered. If full heart coverage is required, we would recommend two acquisitions of three 1.5 mm slices (30 min acquisition time, 9 mm coverage). It is also important to note that perfusion will change throughout the cardiac cycle, as coronary blood flow is highest during diastole, and this may introduce a small slice differences to perfusion values .
Alternatively, the same temporal resolution for the acquisition of three slices could be achieved by acquiring 12 lines of k-space per cardiac cycle and performing three separate single slice acquisitions. This may introduce blurring due to myocardial motion as the segment of k-space is acquired over 36 ms. Therefore, there is a trade-off between thicker slice-selective inversions or myocardial blurring. We believe that acquiring a limited number of slices per acquisition with a restricted slice-selective inversion thickness is better than introducing myocardial blurring.
bpMBF Quantification Method
This study has demonstrated that perfusion can be underestimated when making incorrect assumptions about the blood magnetization input function, particularly in the multislice case. This effect has not previously been investigated in detail in the heart. Our in vivo blood pool magnetization plots (Fig. 4) show that even for the thinnest slice-selective thickness (3 mm), the blood magnetization is not at equilibrium at short inflow times, indicating that perfusion could potentially be misestimated even in the single slice case. The slice-selective inversion thickness must be wider than the imaging slice to compensate for slice profile effects. Particularly when investigating a midventricle slice, the slice-selective inversion thickness necessary for multislice acquisition (at least 6 mm for 3 contiguous 1.5 mm slices) results in a large fraction of inverted blood. These effects are much less of a concern in other organs where the volume of inverted blood is much lower.
The novelty of this MBF quantification method comes from the direct measurement of the blood magnetization from the left-ventricle blood pool at each time point of the Look-Locker T1 acquisition in vivo. This method makes no assumptions about the blood magnetization at any point in the MBF quantification. Here we have focused on slice-selective inversion thickness, however other factors, such as impaired cardiac function, may also change the blood magnetization input function. This should not affect MBF quantification because blood magnetization is directly measured for each case. In addition, this method is not reliant on assumptions of blood T1, which reduces the sensitivity of perfusion measurements to blood oxygenation. In the future, a more comprehensive model of the blood magnetization, such as recently presented by Kampf et al. , may be useful.
It was assumed for the bpMBF quantification method that the Look-Locker saturation (using a flip angle of 5°) had a minimal effect on the T1 curves compared to the blood magnetization and perfusion. If, however, a different implementation requires this effect to be considered, an iterative updated fitting process could be used at the cost of extra computation time.
T1tissue was a fitted parameter, rather than assumed to be equal to T1global, because this assumption is not valid at the high perfusion rates present in the mouse heart (as validated by simulation, not shown) and will lead to a misestimation of perfusion. Therefore, we chose to perform a fit with three free parameters: M0tissue, T1tissue, and MBF. The linear fit used to initialize the MBF parameter, shown in Appendix 1, was an original approach to estimating MBF. It is, however, not as sensitive as the three parameter fit.
Simulations of Mtissue(t) and bpMBF Quantification
Simulations calculating the difference between tissue magnetization curves for small perturbations in MBF (Experiment 2) showed the importance of minimizing ε to enable accurate identification of the minimum of the objective function. Maximizing the difference between the slice-selective and global recovery curves improves the ability to fit the data and correctly estimate MBF. In order to do this, one must minimize the amount of blood inverted in the slice-selective case by: acquiring a fewer number of slices and doing extra acquisitions to cover the area of interest, if necessary; minimizing the inversion thickness; positioning the slices near the apex; or, choosing an inversion plane different to imaging plane, as long as myocardial tissue is included. It is important to be aware that errors may be introduced into perfusion for wider slice-selective thicknesses and high perfusion rates.
Simulations estimating MBF using the standard method (Eq. (1)) and bpMBF showed the underestimation of perfusion using Eq. (1) under certain conditions (Experiment 3). Parameters for this simulation were chosen based on myocardial tissue parameters, but the MBF estimates of Eq.  may vary from the choice of different tissue parameters. Belle et al.,  clearly states that the model assumes that all inflowing blood is at equilibrium in the slice-selective case, and there is the potential to underestimate perfusion if this assumption is not met. One must be careful to use this model only when appropriate, and otherwise, particularly in the multislice acquisition case, move to a model compensated for time-varying blood magnetization such as the bpMBF method.
In Vivo Validation
In vivo experiments show the robust nature of the bpMBF quantification method to changes in slice-selective inversion thickness. In contrast, the perfusion estimate generated using the standard method (Eq. (1)) decreased with increasing inversion thickness (as the assumptions of the model were increasingly invalid). The average coefficient of variation of the bpMBF perfusion estimations was slightly higher than the average within-session variability, although still within the range reported for normal animals previously . The increased variability could be caused by the difficulty of fitting data sets with wider slice-selective thicknesses. Importantly, the mean myocardial perfusion was found to compare well for the same slice acquired using single and multislice acquisition. The MBF maps demonstrated the sensitivity of the multislice technique to changes in perfusion. In addition, the MBF maps demonstrated the good correspondence between maps generated using single and multislice acquisitions, with small differences caused by inherent technique variability and differences in cardiac cycle.
The perfusion values generated in vivo using bpMBF quantification were of similar magnitude to those generated using Eq. (1) with the narrowest slice-selective inversion thickness within this study. Although, these values were slightly higher than those previously reported [4–7 mL/g/min [9, 10, 21]], which could be due to previous underestimated perfusion with Eq. (1). In addition, anesthetic can strongly influence myocardial perfusion and therefore, it is difficult to directly compare quantitative values between studies using different anesthetic protocols.
In this study, we have presented a multislice segmented ECG-gated Look-Locker T1 mapping sequence for application to multislice ASL perfusion measurements. We have presented a new quantification method, bpMBF, needed to accurately quantify the multislice ASL signal, which uses an estimation of the blood magnetization from the left ventricle blood pool. We demonstrated though simulation that perfusion estimation using this method is robust to changes in slice-selective thickness, and furthermore suggest that the bpMBF quantification method may be more applicable under realistic conditions, particularly for multislice acquisition. The ability to acquire multislice perfusion data in a single acquisition will be of great benefit to the study of cardiac disease and the techniques presented here will be of much use in future cardiac MRI studies.
In this study, a multiparameter fit was used to generate MBF estimates. The MBF parameter of this fit was initialized using the linear fit described here. The Bloch equations modified to including perfusion give:
Following the structure of the Look-Locker acquisition, Eq. (A1) can be considered at time points, ti, one RR-interval apart:
The notation is used for the temporal derivative. For n points on Look-Locker recovery curve, ti takes values t1 to tn.
The magnetization of the blood perfusing into the myocardium is best modeled as the left-ventricle blood pool magnetization during the previous heart beat having one RR-interval (length of time defined as RR) of T1 magnetization recovery. From the general solution to the Bloch equations, T1 recovery can be described by: M(t) = M0 + [M(0) − M0] exp(−t/T1). Therefore, Mblood(ti) can be re-written as follows:
where Mbloodpool(ti − 1) is a measured value. Substituting Eq. (A3) into Eq. (A2) for Mblood(ti) gives:
Numerical coefficients of Eq. (A4) can be grouped to simplify notation to:
For ASL measurement, magnetization is measured after a global and a slice-selective inversion, we therefore have two equations both satisfied by the same coefficients
This linear system can be solved for using measured magnetization vectors Mtissue(ti) and Mbloodpool(ti−1), and M′tissue(ti) estimated as follows, considering each of these vectors to contain both slice-selective and global inversion recovery data.
M′tissue(ti) could be calculated using numerical finite differences in Mtissue(ti); however, we found that using the Mtissue(t) fit parameters as follows provided a more stable solution. The tissue magnetization experimental data from the global and slice-selective inversion recoveries are typically modeled as a three parameter exponential:
where T1* is the effective T1 before Look-Locker correction and α is the inversion efficiency. Therefore, M′tissue(ti) can be calculated from slice-selective and global inversion recovery curves using the curve fit parameters:
The numerical coefficients of can be computed by solving the linear system of Eq. (A5) with the given vectors Mtissue(ti), Mbloodpool(ti−1) and M′tissue(ti) from slice-selective and global inversion measurements. Eq. [A5] can be redefined as:
Equation (A6) is solvable for numerical coefficients (1 × 3) using the following matrix solution:
To adapt for the measurement of Mbloodpool at ti−1 and Mtissue at ti, only (n − 1) points of the Look-Locker curve are used. Mtissue(ti), Mbloodpool(ti−1) and M′tissue(ti) vectors contain both slice-selective and global Look-Locker data and have dimensions [1 × 2 (n − 1)]. Therefore, is a [1 × 2 (n − 1)] vector and X is a [3 × 2 (n − 1)] matrix.
Each of the coefficients in can be rearranged algebraically to estimate MBF assuming values for the other parameters (T1tissue, T1blood, M0tissue, or M0blood). Because, we can estimate T1blood more accurately than M0tissue or T1tissue, we chose to use β2to generate an estimate of MBF. Blood pool estimation of T1blood from the global Look-Locker curve was used to estimate MBF from the following relationship:
This MBF estimation was used as the starting value for the multiparameter fit.