MR perfusion imaging by alternate slab width inversion recovery arterial spin labeling (AIRASL): a technique with higher signal-to-noise ratio at 3.0 T

Abstract

Object

To propose a new arterial spin labeling (ASL) perfusion-imaging method (alternate slab width inversion recovery ASL: AIRASL) that takes advantage of the qualities of 3.0 T.

Materials and methods

AIRASL utilizes alternate slab width IR pulses for labeling blood to obtain a higher signal-to-noise ratio (SNR). Numerical simulations were used to evaluate perfusion signals. In vivo studies were performed to show the feasibility of AIRASL on five healthy subjects. We performed a statistical analysis of the differences in perfusion SNR measurements between flow-sensitive alternating inversion recovery (FAIR) and AIRASL.

Results

In signal simulation, the signal obtained by AIRASL at 3.0 and 1.5 T was 1.14 and 0.85%, respectively, whereas the signal obtained by FAIR at 3.0 and 1.5 T was 0.57 and 0.47%, respectively. In an in vivo study, the SNR of FAIR (3.0 T) and FAIR (1.5 T) were 1.73 ± 0.49 and 1.02 ± 0.20, respectively, whereas the SNRs of AIRASL (3.0 T) and AIRASL (1.5 T) were 3.93 ± 1.65 and 1.34 ± 0.31, respectively. SNR in AIRASL at 3.0 T was significantly greater than that in FAIR at 3.0 T.

Conclusion

The most significant potential advantage of AIRASL is its high SNR, which takes advantage of the qualities of 3.0 T. This sequence can be easily applied in the clinical setting and will enable ASL to become more relevant for clinical application.

Appendix

To derive an expression for the signal difference between control and labeled spins, we begin with the Bloch equation for longitudinal magnetization of brain tissue water corrected for the effects of arterial and venous flow:

$$ \frac{{{\text{d}}M(t)}}{{{\text{d}}t}} = - \frac{{M_{0} - M(t)}}{{T_{1} }} + fM_{a} \left( t \right) - \frac{f}{\lambda }M\left( t \right) . $$

(5)

Because the perfusion signal is obtained by subtracting two images acquired with arterial spin tagging states but with identical blood flow, the signal from each compartment is defined as the difference in magnetization in i-th interval between the labeled and control scans:

$$ {\text{ASL signal}}: \Updelta S_{i} (t) = M^{\text{control}} \left( t \right) - M^{\text{label}} \left( t \right). $$

(6)

The difference in magnetization of arterial blood between control and labeled states can be expressed as follows:

$$ \frac{{(M^{\text{control}} \left( t \right) - M^{\text{label}} \left( t \right))}}{{{\text{d}}t}} = - \frac{{\left( {M^{\text{control}} \left( t \right) - M^{\text{label}} \left( t \right)} \right)}}{{T_{1} }} + f\left( {M_{a}^{\text{control}} \left( t \right) - M_{a}^{\text{label}} \left( t \right)} \right) - \frac{f}{\lambda }\left( {M^{\text{control}} \left( t \right) - M^{\text{label}} \left( t \right)} \right). $$

(7)

First, z-magnetization of the 1st period is considered as:

$$ \frac{{\Updelta {\text{S}}_{1} \left( t \right)}}{{{\text{d}}t}} = - \frac{{\Updelta S_{1} \left( t \right)}}{{T_{1} }} + f\left( {M_{a}^{\text{control}} \left( t \right) - M_{a}^{\text{label}} \left( t \right)} \right) - \frac{f}{\lambda }\Updelta S_{1} \left( t \right), $$

(8)

where T _1app is given by

$$ \frac{1}{{T_{{1{\text{app}}}} }} = \frac{1}{{T_{1} }} + \frac{f}{\lambda } , $$

(9)

and the inflowing spins in acquisition of the 1st interval are written as follows:

$$ M_{a}^{\text{control}} \left( t \right) = M_{a,1}^{0} , $$

(10)

$$ M_{a}^{\text{label}} \left( t \right) = M_{a,1}^{0} \left( {1 - 2\alpha e^{{ - (\frac{t}{{T_{1a} }} + \frac{{\delta_{a} }}{{T_{1a} }})}} } \right)\quad (\delta_{a} \le t < {\text{IT}}), $$

(11)

where δ _a represents transit time (delay time), and we assume that the label duration (labeling slab width/flow velocity) equals IT. Then, by substituting Eqs. 9, 10, 11 into Eq. 8, we obtain the following:

$$ \frac{{\Updelta S_{1} \left( t \right)}}{{{\text{d}}t}} + \frac{{\Updelta S_{1} \left( t \right)}}{{T_{{1{\text{app}}}} }} = {\text{f}}\left( {M_{a}^{0} - M_{a,1}^{0} \left( {1 - 2\alpha {\text{e}}^{{ - \left( {\frac{\text{t}}{{{\text{T}}_{1a} }} + \frac{{\delta_{a} }}{{{\text{T}}_{1a} }}} \right)}} } \right)} \right), $$

(12)

where $M_{a}^{0} = \frac{{M_{0} }}{\lambda }$ by substituting this equation into Eq. 12, we obtain the following:

$$ \frac{{\Updelta S_{1} \left( t \right)}}{{{\text{d}}t}} + \frac{{\Updelta S_{1} \left( t \right)}}{{T_{{1{\text{app}}}} }} = \frac{{2\alpha fM_{0} }}{\lambda } \cdot {\text{e}}^{{ - \left( {\frac{\text{t}}{{T_{1a} }} + \frac{{\delta_{a} }}{{T_{1a} }}} \right)}} \quad ( \delta_{a} < t). $$

(13)

Then, the general solution is as follows:

$$ \Updelta S_{1} (t) = {\text{e}}^{{ - \frac{{{\text{t}} - \delta_{a} }}{{T_{{1{\text{app}}}} }}}} \left[ {\frac{{2\alpha fM_{0} }}{\lambda } \cdot {\text{e}}^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} \cdot {\text{e}}^{{\left( {\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}} \right)\left( {{\text{t}} - \delta_{a} } \right)}} + M + C_{1} } \right], $$

(14)

where M and C ₁ represent initial value of z-magnetization and arbitrary constant in the 1st period, respectively.

where S ₁(t = 0) equal 0, then:

$$ C_{1} = - \frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} $$

(15)

when we substitute C ₁ into the general solution, we obtain the following:

$$ \Updelta S_{1} (t) = e^{{ - \frac{{{\text{t}} - \delta_{a} }}{{T_{{1{\text{app}}}} }}}} \left[ {\frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} \cdot {\text{e}}^{{\left( {\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}} \right)\left( {{\text{t}} - \delta_{a} } \right)}} - \frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}}} \right]\quad (\delta_{a} < t \le {\text{IT)}} . $$

(16)

Next, we consider the signal change of z-magnetization in the 2nd interval. If we define the ASL signal with the following equation:

$$ {\text{ASL}}\; {\text{signal}}: \Updelta S_{2} (t) = M_{a}^{\text{label}} \left( t \right) - M_{a}^{\text{control}} \left( t \right) $$

(17)

we have to note that the signal is obtained from the opposite subtraction between control and labeled states. Then, we can derive the following equation:

$$ \frac{{\Updelta S_{2} \left( t \right)}}{{{\text{d}}t}} + \frac{{\Updelta S_{2} \left( t \right)}}{{T_{{1{\text{app}}}} }} = {\text{f}}\left( {M_{a,2}^{0} - M_{a,2}^{0} \left( {1 - 2\alpha {\text{e}}^{{ - \left( {\frac{\text{t}}{{{\text{T}}_{1a} }} + \frac{{\delta_{a} }}{{{\text{T}}_{1a} }}} \right)}} } \right)} \right). $$

(18)

This formula is identical to the Eq. 12. The arterial inflow spins are also inverted in the 2nd period after 180 pulse as follows:

$$ M^{\text{control}} \left( t \right) = M_{a,2}^{0} \left( {1 - 2\alpha e^{{ - \frac{{t + {\text{IT}}}}{{T_{1a} }}}} } \right), M^{\text{label}} \left( t \right) = M_{a,2}^{0} \quad ({\text{IT}} < t \le 2{\text{IT}}). $$

(19)

Therefore, from the Eqs. 18 and 19, we can obtain the same differential equation as that seen for the 1st period.

$$ \frac{{\Updelta S_{2} \left( t \right)}}{{{\text{d}}t}} + \frac{{\Updelta S_{2} \left( t \right)}}{{T_{{1{\text{app}}}} }} = \frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \left( {\frac{t}{{T_{1a} }} + \frac{{\delta_{a} }}{{T_{1a} }}} \right)}} \quad ({\text{IT}} < t \le 2{\text{IT}}). $$

(20)

Since the signal of end of the 1st period should be same as the initial signal of the 2nd period, the relationship: S ₂(t = IT) = S ₁(t = IT) is used.

$$ \Updelta S_{2} \left( {t - {\text{IT}}} \right) = \left[ {\frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} + S_{1} ({\text{IT}}) + C_{2} } \right] = S_{1} ({\text{IT}}) , $$

(21)

where C ₂ represents the arbitrary constant in the 2nd period.

$$ C_{2} = - \frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}}. $$

(22)

Therefore,

$$ \Updelta S_{2} (t) = e^{{ - \frac{{t - \delta_{a} }}{{T_{1app} }}}} \left[ {\frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} \cdot e^{{\left( {\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}} \right)\left( {t - \delta_{a} } \right)}} + S_{1} ({\text{IT}}) - \frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}}} \right]. $$

(23)

The signal of the 3rd period can be considered with the same equation used the first period, but with a different start signal, where S ₃(t = 2*IT) = S ₂(t = 2*IT). Therefore,

$$ \Updelta S_{3} \left( {t - 2*{\text{IT}}} \right)|_{{t = 2*{\text{IT}}}} = \left[ {\frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} + S_{2} (2{\text{IT}}) + C_{3} } \right] = S_{2} (2{\text{IT}}), $$

(24)

where C₃ represents the arbitrary constant in the 3rd period.

$$ C_{3} = - \frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} $$

(25)

$$ \Updelta S_{3} \left( t \right) = e^{{ - \frac{{t - \delta_{a} }}{{T_{{1{\text{app}}}} }}}} \left[ {\frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} \cdot e^{{\left( {\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}} \right)\left( {t - \delta_{a} } \right)}} + S_{2} \left( {2{\text{IT}}} \right) - \frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}}} \right] \quad (2{\text{IT}} < t \le 3{\text{IT}}). $$

(26)

Finally, we obtained the general solution of the AIRASL signal for i-th period as follows:

$$ \Updelta S_{i} \left( t \right) = e^{{ - \frac{{\left( {t - \delta_{a} - \left( {i - 1} \right)*{\text{IT}}} \right)}}{{T_{{1{\text{app}}}} }}}} \left[ {\frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}} \cdot e^{{\left( {\frac{1}{{T_{{ 1 {\text{app}}}} }} - \frac{1}{{T_{1a} }}} \right)\left( {t - \delta_{a} - \left( {i - 1} \right)*{\text{IT}}} \right)}} + S_{i - 1} \left( {\left( {i - 1} \right)*{\text{IT}} + \delta_{a} } \right) - \frac{{2\alpha fM_{0} }}{\lambda } \cdot e^{{ - \frac{{\delta_{a} }}{{T_{1a} }}}} \cdot \frac{1}{{\frac{1}{{T_{{1{\text{app}}}} }} - \frac{1}{{T_{1a} }}}}} \right] \quad (\delta_{a} < t). $$

(27)

If $\delta_{a}$ = 0 and i = 1, this Eq. 27 is in agreement with the general solution of FAIR in a previous report [18].