A Technical Perspective for Understanding Quantitative Arterial Spin-labelingMR Imaging using Q2TIPS

Tomoyuki NOGUCHI1,2*, Masashi NISHIHARA2, Yukiko HARA2, Tetsuyoshi HIRAI2,

Yoshiaki EGASHIRA2, Shinya AZAMA2, and Hiroyuki IRIE2

1Department of Radiology, National Center for Global Health and Medicine(NCGM)

1–21–1, Toyama, Shinjuku-Ku, Tokyo 162–8655, Japan2Department of Radiology, Faculty of Medicine, Saga University

(Received July 5, 2013; Accepted July 16, 2014; published online December 15, 2014)

We illustrate the fundamental theoretical principles of arterial spin-labeling (ASL) mag-netic resonance imaging (MRI) and show a system that employs the second version ofquantitative imaging of perfusion using a single subtraction (Q2TIPS) to quantify cerebralblood flow (CBF). We also discuss the effects of the parameters used in Q2TIPS on CBFvalues as measured with ASL-MRI.

Keywords: ASL, cerebral blood flow, perfusion, Q2TIPS, review

Introduction

Arterial spin labeling (ASL) is a magnetic reso-nance (MR) imaging technique that can be used toacquire brain perfusion images noninvasively with-out the use of contrast media.1 Clinical MR imagingusing 3-tesla equipment has brought ASL-MRI intothe spotlight because the increased magnetic fieldoffers longer blood T1 values as well as improvedsignal-to-noise ratios (SNR).2 In general, ASL-MRIfirst applies an inversion pulse to the cervical areathat labels the arterial blood that flows through thecervical area. Brain images (labeled images) are ac-quired after this labeled blood perfuses into thebrain tissue. Control images of the same region areacquired similarly without labeling. Finally, perfu-sion images are acquired by subtracting the labeledfrom the control images. In fact, ASL-MRI useselectromagnetically labeled arterial blood as an in-trinsic tracer, which avoids the administration ofextrinsic tracers, such as contrast media or radio-nuclides.1

ASL-MRI can be broadly divided into 2 types ac-cording to the spin-labeling technique used– pulsedASL (PASL)3–9 and continuous ASL (CASL).1,10–14

PASL consists of the single application of an inver-sion pulse over a relatively wide area (approximate-

ly 10-cm slice thickness) and labeling of all the ar-terial blood in that area at once, whereas CASLcomprises the repeated application of the pulse overa small area (approximately one- to 2-cm slicethickness) and continuous labeling of the arterialblood that flows into that area.Edelman’s group proposed the first PASL tech-

nique, echo planar imaging and signal targetingwith alternating radiofrequency (EPISTAR),4 whichapplies the inversion pulse to the area proximal tothe imaging slab in the labeling state or distal to theslab in the control state, respectively. Wong’sgroup5 described proximal inversion with controlfor off-resonance effects (PICORE), a derivativeof EPISTAR in which a control image is acquiredwith no slab-selective gradient. Both EPISTAR andPICORE provide qualitative CBF maps, but quan-titative imaging of perfusion using a single subtrac-tion (QUIPPS) and its second version, QUIPPS II,6

as well as QUIPSS II with thin-slice TI1 (elapsedtime from application of the inversion pulse untilapplication of the saturation pulse begins) periodicsaturation (Q2TIPS) can offer quantitative CBFmaps by adding saturation pulses to the areas prox-imal to the imaging slab at a given time after theinversion pulse. Kwong and associates15 developedanother PASL technique, flow-sensitive alternatinginversion recovery (FAIR), in which labeling is ap-plied using a nonselective inversion pulse to a widearea that includes the imaging slab as well as prox-

*Corresponding author, Phone: +81-3-3202-7181, Fax: +81-3-3207-1038, E-mail: tnogucci@radiol.med.kyushu-u.ac.jp

Magn Reson Med Sci, Vol. 14, No. 1, pp. 1–12, 2015©2014 Japanese Society for Magnetic Resonance in Medicine

REVIEW

doi:10.2463/mrms.2013-0064

1

imal and distal areas outside the imaging slab, andthe control is a slice-selective inversion applied tothe imaging slice. Gunther and colleagues proposedinflow turbo-sampling EPI-FAIR (ITS-FAIR), adapt-ing the Look-Locker technique16 to FAIR to acquiremultiphase perfusion images at multiple timingpoints with an interval of a few hundred millisec-onds and thereby delineate the temporal hemody-namics of the perfusion-related signal intensity. Inrecent years, the team of Peterson and Golay17 ap-plied the Look-Locker technique to Q2TIPS andaccomplished the model-free measurement of CBFwith quantitative STAR labeling of arterial regions(QUASAR).Detre’s group developed CASL, the origin of

ASL-MRI,1 and Alsop and associates refined thetechnique by setting the delay time following con-tinuous labeling to account more accurately fortransit effects in quantitative CBF.11 To achievemultislice perfusion imaging by CASL without spa-tially dependent off-resonance effects, they devel-oped the method to acquire control images by ap-plying amplitude-modulated irradiation at an equaldistance distal to the imaging slab.14 Pseudo-con-tinuous ASL (pCASL),3 a technique in which an in-termittent inversion pulse is applied at regular in-tervals, solved the problem of a highly specificabsorbed fraction (SAR) in applying a continuousinversion pulse. Recently, 3-dimensional (3D)ASL13 has become available, which combines imag-ing technologies, such as the 3D-spiral FSE methodthat acquires images of the entire volume of thehead, and the background suppression method thatsuppresses signals from the stationary tissue unre-lated to perfusion.18

PASL can measure absolute cerebral blood flow(CBF) relatively simply. Measurement of absoluteCBF enables comparison between patients or facili-ties as well as sites within the brain or changes overtime in the same patient. CASL has a high SNR,which is theoretically approximately 2.71 times(i.e., the same as Napier’s constant) that of PASL.19

However, measurement of absolute CBF ideally re-quires distribution images of T1 values (T1 maps) inaddition to the perfusion images by CASL, and theacquisition of accurate T1 maps requires the addi-tion of another imaging sequence.19

Each different ASL-MRI technique has its ownanalytical equations to quantify absolute CBF, butthe properties of these equations, with multiple spe-cific parameters and various ways to express formu-lae, are generally difficult to understand. Further-more, as authors alter those formulae, ASL-MRItechniques improve with each report. No handbookclearly summarizes these diverse ASL-MRI quanti-

tative theories. Accordingly, ignorance of the pre-requisites or limits in quantification of CBF mightlead to pitfalls.We herein explain the theoretical background of

ASL-MRI using concrete illustrations, hold upQ2TIPS, a PASL method, as a straightforward ex-ample of a system for measuring CBF, and discusscurrent issues in CBF measurement by ASL-MRI.

Basic Interpretation of ASL-MRI Methodol-ogy

Nuclear magnetic resonance (NMR) imaging iscreated by the spinning motion of the hydrogen nu-cleus. Components of organisms consisting of amixture of various hydrogen compounds can emitNMR signals, but it has been hypothesized that onlyNMR signals derived from the water molecule, orH2O, indicate blood flow when blood flow is beingmeasured in organisms with a clinical MR imagingunit.10 We have created a basic schema (Fig. 1) forunderstanding PASL that takes the above into con-sideration. This diagram shows one blood vesselpassing through one block of brain tissue. Watermolecules are present inside and outside the bloodvessel, and the magnetization vectors of each watermolecule are shown with upward-pointing arrows.The labeling slab, the space where spin labeling isconducted, is positioned under this brain tissue(Fig. 1A); an inversion pulse is applied over theentire slab (Fig. 1B), which also causes inversionof the magnetization vectors of the water moleculesinside the blood vessel in that site; the water mole-cules containing the inverted vectors flow into thebrain tissue with blood flow (Fig. 1C); the watermolecules of these inverted vectors are distributedthroughout the brain tissue; and labeled images aretaken (Fig. 1D). Though these labeled images arealready perfusion-weighted, they also contain brainparenchymal signals, so control images are taken inthe same way without application of an inversionpulse (Fig. 1E). In theory, subtracting the labeledimages from these control images should eliminatesignals of brain tissue, so images created reflect on-ly the distribution of blood flow (Fig. 1F).

Quantitative Equation of Cerebral BloodFlow by Q2TIPS

A common solution has been clearly indicated forthe quantification of CBF with ASL-MRI based onthe theory proposed by Buxton’s group,19 and thePASL imaging sequences presented by Wong’steam, QUIPPSII6 and Q2TIPS,8 have enabled thecreation of useful and highly precise CBF map im-

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ages. The commercial version of Q2TIPS was placedon the market after the group validation study byDetre’s group,20 and PASL is becoming commonlyused worldwide. Here, we provide a general expla-nation to allow the reader to understand the basic

techniques involved in PASL. The following is anequation for CBF measurement by Q2TIPS basedon a single-compartment kinetic model proposedby Wong’s team8:

Fig. 1. Schemata for explaining the fundamental principles of arterial spin-labeling magnetic resonance imaging (ASL-MRI). (A) One blood vessel passesthrough one block of brain tissue; upward-pointing arrows show the magnetiza-tion vectors of water molecules inside and outside the blood vessel. The labelingslab, the space where spin-labeling is conducted, is positioned under this braintissue. (B) When the inversion pulse is applied to the entire labeling slab, themagnetization vectors of the water molecules within the blood vessel are alsoinverted. (C) After that, water molecules containing the inverted vectors flow intothe brain tissue with blood. (D) Finally, these inverted vector water molecules aredistributed in brain tissue. Labeled images are taken after waiting for this to hap-pen. (E) Control images to which the inversion pulse has not been applied aretaken with the same timing. (F) Theoretically, brain tissue signals should be elim-inated by subtracting labeled images from these control images, creating perfusionimages that reflect only the distribution of blood flow.

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�MðTI2Þ ¼ 2�M0B � f � TI1 � e�TI2=T1B � qðTI1 < � and TI1 þ�t < TI2 < � þ�tÞ: ½1�

Here, "M is the difference in magnetization be-tween the presence and absence of spin labelingin the magnetization of one gram of brain tissue;this actually equates with the signal intensity whenthe labeled image is subtracted from the control im-age. The labeling efficiency is ¡ (%), M0B is themagnetization of one mL of arterial blood in a staticmagnetic field, and f is CBF. This is measured inseveral ways as we will describe later. The unitsused in Equation (Eq.) [1] are mL/g/s rather thanmL/100 g/min. T1B is the T1 value of arterial blood.q is a correction factor that explains the T1 pro-longed effect caused by spin exchange betweenblood and brain tissue and the effect of blood flow-

ing out from brain tissue through veins. ¸ is the timeelapsed for enough labeled arterial blood to fill thebrain tissue and show no further improvements inSNR after application of the inversion pulse; in oth-er words, ¸ represents the maximum TI1 to get themaximum difference in magnetization, "M(TI2). "trepresents arterial transit time (ATT), the prolongedtime for labeled blood to first arrive at the imagingarea after application of the inversion pulse. TI1 andTI2 are also set as optional parameters. TI1 is theelapsed time from application of the inversion pulseuntil application of the saturation pulse begins andis related to the volume of labeled arterial blood. TI2is the elapsed time from initiation of the inversionpulse in the labeled area to collection of image datain the imaging area. T1A is the T1 value of braintissue (Table).

Table. Definitions of parameters

Parameter Definition UnitAssumed valueused in Q2TIPS

f cerebral blood flow mL/g brain tissue/s —"M longitudinal magnetization difference of one g of brain

tissue between presence and absence of spin labeling

/g brain tissue —

¡ labeling efficiency % 95M0B equilibrium longitudinal magnetization

of one mL of arterial blood

/mL arterial blood —

M0 equilibrium longitudinal magnetizationof one g of brain tissue

/g brain tissue —

­ brain-blood partition coefficient for water (g water/g brain tissue) /(mL water/mL blood)

0.9

T1B T1 value of arterial blood s 1.5(3-tesla MRI)

T1A T1 value of brain tissue s —q correction factor for T1 prolonged effect caused

by spin exchange between blood and brain tissueand effect of blood flowing out from brain tissuethrough veins

(no unit) 1

¸ the time elapsed for enough labeled arterial bloodto fill the brain tissue and show no further improvementsin SNR after application of the inversion pulse

s —

"t arterial transit time, the prolonged time for labeled bloodto arrive at the imaging area after applicationof inversion pulse

s —

TI1 elapsed time from application of inversion pulseuntil initiation of saturation pulse

s 0.7

TI2 elapsed time from initiation of inversion pulse inlabeled area to collection of image data in imaging area

s 1.8

fmin minimum flow rate that can be detected by Q2TIPSwith a given TI2

mL/g brain tissue/s 0.0033(= 20mL/100 gbrain tissue/min)

fpeak maximum flow rate that can be detected by Q2TIPSwith a given TI2

mL/g brain tissue/s 0.0150(= 90mL/100 gbrain tissue/min)

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A more detailed version of the schema just out-lined will be used to explain this equation for quan-tification (Fig. 2). The block of brain tissue is one g;the magnetization of one mL of arterial blood withinthe blood vessel is M0B; and inside the blood vessel,arterial blood flows at blood flow volume f (mL/g/s) (Fig. 2A). Next, the time at which the inversionpulse is applied to the entire labeling slab is set aselapsed time 0 (s) (Fig. 2B). After that, afterelapsed time TI1 (s), the saturation pulse is appliedto the labeling slab (Fig. 2C). (Though continuoussaturation pulses are actually applied to a relativelythin slice on the distal side of the labeling pulse, thefigure shows the pulse being applied to the entirearea for convenience.) Accordingly, only the arte-rial blood that flows out from the labeling slab in theperiod from elapsed time 0 to TI1 (s) remains spinlabeling, but spin labeling is deleted from the restby the saturation pulse. Because arterial blood flowsat blood flow volume f (mL/g/s) into one g of theblock of brain tissue, the total amount of labeledblood after TI1 (s) is f0TI1(mL). Furthermore, afterlabeled blood is inverted at elapsed time 0 (s), thelongitudinal magnetization of the labeled blood isrelaxed according to T1B. Therefore, after elapsedtime of TI1 (s), the magnetization per one mL is ex-pressed as M0B0(1¹2¡e¹TI1/T1B) under ¡ (%) of thelabeling efficiency. Furthermore, after waiting untilthis labeled blood reaches and perfuses the braintissue, and after TI2 (s) has passed, labeled imagesare taken. Here, the overall volume of magnetiza-tion of all labeled blood is M0B0(1¹2¡e¹TI2/T1B)0f0TI1 (Fig. 2D). Control images taken without ap-plication of an inversion pulse are taken at thesame time (Fig. 2E). At this time, the overall vol-ume of magnetization of unlabeled arterial bloodis M0B0f0TI1. The measured signal difference,"M(TI2), is acquired by subtracting labeled imagesfrom control images. Therefore, subtraction ofM0B 0(1¹2¡e¹TI2/T1B)0f0TI1 from M0B0f0TI1 produces2¡M0B0f0TI10e¹TI2/T1B (Fig. 2F). However, becauseof the T1-prolonged effect caused by spin exchangebetween blood and brain tissue and the fact thatblood flows out from brain tissue from veins, themeasured signal difference, "M(TI2), is actuallylower than 2¡M0B0f0TI10e¹TI2/T1B. The correctionfactor, q, is included to correct this (according tothe literature, q is 0.85 to 1.0).6 Thus, Eq. [1] iscompleted.However, in practice, q is not a simple constant

value. Buxton and associates showed the followingequation that we will later describe in detail19:

q ¼ ek�TI2ðe�k��t � e�kðTI1þ�tÞÞk � TI1

and k ¼ 1

T1B� 1

T10; where

1

T 01

¼ 1

T1þ f

�: ½2�

Arterial Blood Magnetization: M0B

In theory, arterial blood magnetization, M0B, ismeasured as the signal intensity of one mL of arte-rial blood calculated from images (M0 images) tak-en with a sequence under the same conditions asthose for control images after enough time elapsesfor the full relaxation of the magnetization of thearterial blood under a static magnetic field. Howev-er, in reality, the accurate measurement of M0B isdifficult because the arterial blood does not cometo a standstill or pool in any tissue structures withinliving organisms. Therefore, M0B is calculated froma number of alternative measured values.Wong’s team used the magnetization of venous

blood inside the superior sagittal sinus instead ofarterial blood6,8 based on the hypothesis that thewater content of venous and arterial blood are al-most equal. However, it is actually difficult to set aregion of interest (ROI) in the superior sagittal sinusand make accurate measurements because M0 im-ages have low resolution. Therefore, the signal in-tensity values of venous blood and white matter arefirst measured on proton-density-weighted (PD) im-ages. Because the ratio, (R), of both signal values isalmost identical to that of proton density, the ratiosof M0B and white matter magnetization, M0WM,measured with M0 images are equal. Therefore,

M0B ¼ R �M0WM: ½3�Wong and colleagues used the EPI method to ac-

quire M0 images.6,8 With this method, repetitiontime (TR) is ¨, effective echo time (TE) is TEeff,blood signal intensity is S0B, the T2

� value of bloodis T2�B, white matter signal intensity is SWM, and theT2

� value of white matter is T2�WM. Therefore, Eq. [3]is expressed as:

S0Be�TEeff =T2�B ¼ R � SWM

e�TEeff =T2�WM$

S0B ¼ R � SWM � e 1T2�WM

� 1T2�Bð ÞTEeff : ½4�

Therefore, S0B is calculated by measuring the signalintensity of the white matter on the PD image, thatof the venous blood in the superior sagittal sinus onthe PD image, and that of the white matter on theM0 image. "M(TI2) is actually measured as the dif-ference in signal intensity, "S(TI2), between controlimages and labeled images, which are acquired us-ing EPI with the same TE. Therefore, one can apply

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Fig. 2. Schemata for explaining the quantification of blood flow by the secondversion of quantitative imaging of perfusion using a single subtraction (Q2TIPS).(A) The magnetization of one mL of intravascular arterial blood is assumed as M0B

(no unit). Intravascular arterial blood is hypothesized as flowing at a blood flowvolume of f (mL/g/s) into one g of brain tissue. (B) Time elapsed for application ofthe inversion pulse to the entire slab is set at 0. (C) After the elapsed time of TI1 s,the saturation pulse is applied. The volume of labeled blood that was not appliedwith the saturation pulse is f0TI1(mL). Furthermore, as labeled blood is defusedwith T1B, the T1 value of arterial blood, the magnetization per one mL after elapsedtime of TI1 s is expressed as M0B(1¹2¡e¹TI1/T1B) under ¡ (%) of the labelingefficiency. (D) Labeled images are taken after elapsed time of TI2 s. At this time,the total volume of the magnetization of labeled blood is M0B(1¹2¡e¹TI2/T1B)0f0TI1. (E) Next, control images to which the inversion pulse has not been appliedare taken at the same time. At this time, the total volume of the magnetization ofunlabeled arterial blood is M0B0f0TI1. For the actual signal difference "M(TI2)acquired by subtracting labeled images from control images, 2¡M0B0f0TI10e¹TI2/T1B

is acquired by subtracting M0B(1¹2¡e¹TI2/T1B)f0TI1 from M0B0f0TI1.

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"S(TI2) instead of "M(TI2) and S0B instead of M0B

to Eqs. [10] to [13] following.However, this method using additional PD im-

ages can be complicated because it requires manualmeasurement of the ROI. Wang’s group used thebrain-blood partition coefficient for water, ­,20 theunits used are (g water/g brain tissue)/(mL water/mL blood). As mentioned above, when measuringblood flow in living organisms, it is hypothesizedthat the NMR signals responsible for blood flow arederived from water molecules, H2O. Therefore, ifbrain tissue magnetization is M0, the followingequation can be established:

� ¼ tissue water content

blood water content¼ M0

M0B$ M0B ¼ M0

�: ½5�

In addition, M0B in this equation has been calcu-lated pixel by pixel from the signal intensity ofbrain tissue acquired from M0 images subdividedby ­ as a constant value, 0.9 (mL/g), based on theassumption that ­ remains unchanged at all sitesin the brain. This enables automatic creation of CBFmaps and serves as the foundation for the currentcommercially available version of Q2TIPS.

Brain-blood Partition Coefficient for Water: ­

The commercial version of Q2TIPS uses the val-ue 0.9 (mL/g) theoretically for the brain-blood par-tition coefficient for water, ­. However, the brain-blood partition coefficient for water varies withhematocrit, brain topography, age, and pathologicalchanges. Herscovitch and associates proposed thatthe water content of blood, Cbl (g/mL blood), wascalculated with hematocrit, Hct (%),21 as:

Cbl ¼ 0:948� 0:223� Hct: ½6�They used 77 (g/100 g brain tissue) of the water

content of the whole brain, so 0.9 (mL/g) of thebrain-blood partition coefficient for water is as-sumed to be less than under 42% of the Hct.22 Anerror occurs +1.7% (overestimation) to ¹0.9% (un-derestimation) in normal Hct range of 35 to 45% atTI2 = 1.8 (s) and T1B = 1.5 (s)Other values for the partition coefficient for water

are: 0.82 (white matter), 0.98 (gray matter), 0.99(cerebral cortex), 0.88 (thalamus), 0.95 (caudatenucleus), 0.83 (centrum semiovale), and 0.89 (cor-pus callosum).21,23 The partition coefficient for wa-ter in neonates is estimated as 1.10 (mL/g) becauseneonates have 45 to 65% of the normal range inHct24 and 89 (g/100 g) of the water content of theentire brain.22 On the other hand, the partition co-efficient in edematous centrum semiovale amountsto 0.96 (mL/g).21 Such variation might rather be

considered to estimate the distribution of perfusion.

T1 Value of Arterial Blood: T1B

A fixed T1 value of arterial blood, T1B, is gener-ally used for CBF measurement by ASL-MRI be-cause the true T1 value of arterial blood is similarlydifficult to measure for the same reason M0B meas-urement is difficult. In practice, T1B is typically as-sumed to be about 1.5 to 1.7 (s) on a 3T MR imag-ing unit.8,13,17,18 On the other hand, Lu and col-leagues proposed the relationship between T1B andHct as:

1=T1B ¼ ð0:52� 0:15Þ � Hct þ ð0:38� 0:06Þ: ½7�This leads to an estimated 1.664 « 0.014 (s) of T1B

at a typical human Hct of 42%.25 Equation [7] sug-gests that the normal Hct range of 35 to 45% causesan overestimation of 10 to 21% if it is used insteadof a fixed T1B of 1.5 (s), and the combination ofEqs. [5], [6], and [7] causes an overestimation of9 to 23% in Eq. [1] at TI2 = 1.8 (s). Variations ofT1B might assume more importance as the resolutionof perfusion imaging by ASL-MRI improves in thefuture.

Correction Factor: q

The model with q = 1 becomes identical to thesingle compartment model without considerationof the T1 value of brain tissue, T1A, and venous out-flow, where the labeled spin retains microvascula-ture and would not enter the tissue compartment.However, as time elapses after the spins reach thecapillary system in the brain tissue, the labeledspins move into the tissue compartment, wherethey follow T1A rather than the arterial relaxationtime, T1B. The correction factor, q, compensates forsuch consideration (See Appendix). Additionally,Buxton’s theory ignores the effect of blood flowingout from brain tissue through the veins. This effectrarely becomes significant because in practice, onan MR imaging unit of 3T or less, TI2 is usually setwithin a few seconds to gain SNR. However, itmight rather be assumed if a longer TI2 is adopted.

Arterial Transit Time: "t

"t, the biggest challenge in the accurate measure-ment of cerebral blood flow by ASL-MRI, is report-ed from 0.42 to 0.73 (s) in healthy subjects20,26–29

and can easily be affected by such factors as age,brain topography, cerebral blood flow value, and thestructural property of ASL application. Transit timelonger by approximately 0.1 (s) has been reported in

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the elderly.30 Measured delays were typically 1.0 to1.3 (s) at the occipital pole, compared to 0.5 to 0.8(s) in the parietal lobes.5 Wong’s group determinedexperimentally that this delay ranges from about 0.5to 1.5 (s) for a physical gap of one to 3 cm betweenthe labeling slab and imaging slab. Longer transittimes were estimated in the region of hypoperfusionin patients with occlusive carotid artery disease,31

whereas high-grade brain tumor had a short arterialtransit time.32

"t is determined as the smallest TI2 when"M(TI2) becomes more than zero. In practice, ac-curate measurement of "t requires several perfu-sion images with several different TI2 values, which

extends scan time. A recent study using a Look-Locker method, however, achieved measurementwithin a reasonable imaging time.33 Applicationof ASL-MRI might equip such "t correction tech-nique before long.

Errors due to Fixed Parameters of TI1 andTI2

Equation [1] only works when, as this reportstates, parameters TI1 and TI2 are TI1 < ¸ andTI1 + "t < TI2 < ¸ + "t. Under other conditions,f is represented with the following equations:

�MðTI2Þ ¼ 0 ðTI2 < �tÞ [10]

�MðTI2Þ ¼ 2�M0B � f � ðTI2 ��tÞ � e�TI2=T1B � q ð�t < TI2 < TI1 þ�tÞ ½11��MðTI2Þ ¼ 2�M0B � f � TI1 � e�TI2=T1B � q ðTI1 < �; TI1 þ�t < TI2 < � þ�tÞ ½12� ðor ½1�Þ�MðTI2Þ ¼ 2�M0B � f � � � e�TI2=T1B � q ðTI1 > �; � þ�t < TI2Þ ½13�

where

q ¼ ek�TI2ðe�k��t � e�k�TI2Þk � ðTI2 ��tÞ ð�t < TI2 < TI1 þ�tÞ

¼ ek�TI2ðe�k��t � e�kðTI1þ�tÞÞk � TI1 ðTI1 þ�t < TI2 < � þ�tÞ

¼ ek�TI2ðe�k��t � e�kð�þ�tÞÞk � � ð� þ�t < TI2Þ:

Equation [10] represents the state after applyingthe labeling pulse before the flow of labeled bloodinto the brain tissue; Eq. [11], the state after apply-ing the labeling pulse in the middle of the flow oflabeled blood into the brain tissue; Eq. [12] (or [1]),the state after labeled blood finishes flow into thebrain tissue; and Eq. [13], the state when prolonga-tion of TI1 means that all labeled blood volume fi-nally flows into the brain tissue and further TI1 pro-longation will cause no increased signal difference"M(TI2), with ¸ representing maximum TI1.8 In oth-er words, ¸ is the square bolus of duration for la-beled spin flowing in the brain tissue. However, thecommercial version of Q2TIPS20 uses the followingequation for the calculation of CBF no matter thesubject’s condition:

�MðTI2Þ ¼ 2�M0=� � f � TI1 � e�TI2=T1B: ½14�It also uses assumed values of ­ = 0.9 (mL/g),

¡ = 0.95, and T1B = 1.5 (s) on a 3T MR imagingunit and T1B = 1.2 (s) on a 1.5T unit, an acquiredM0 image, and 80 pairs of control and labeled im-ages. Compared with Eq. [1], q is set to one. Equa-tions [10] to [13] reflect changes when TI2 gradual-ly increases from zero under the fixed condition ofblood flow volume f. Furthermore, in standard clin-

ical practice, settings of TI1 and TI2 are not alteredfor the individual patient. Under these conditions,CBF values measured with ASL-MRI could differfrom true CBF values by reduced blood flow or re-duced blood flow velocity caused by such patholog-ical conditions as cerebral infarction or cerebrovas-cular stenosis. Thus far, this issue has been attrib-uted to ¦t using Eq. [11]. However, "t is subject tocerebral blood flow values as mentioned above, andit might be difficult to understand the differencebetween true CBF values and CBF values measuredwith ASL-MRI in Eqs. [10] to [13], which containboth "t and f. In this section, the imaging phantomis assumed to be a single, well-mixed compartmentwith intra- and extravascular water in perfect com-munication with penetration of a single tube, sim-ilar to the model shown in Fig. 1. Labeled waterenters and leaves with perfusion rate f . These con-ditions are specifically expressed in the followingways:

f0 ¼ 0 ð0 < f < fminÞ [A]

f0 ¼ TI2

TI1� ðf�fminÞ fmin <f<

TI2

TI2� TI1� fmin

� �

[B]

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Magnetic Resonance in Medical Sciences

f0 ¼ fTI2

TI2� TI1� fmin < f < fpeak

� �[C]

f0 ¼ fpeak ðfpeak < fÞ [D]

Here, f A expresses the flow rate measured with ASL-MRI, and f signifies the true flow rate. In Eq. [A],fmin is the minimum flow rate that can be detectedfrom the difference in signal, "M(TI2), betweencontrol images and labeled images with a givenTI2. Therefore, it follows that f A cannot be detectedwith ASL-MRI and remains 0 so long as f does notreach fmin. Moreover, when set as via, the internalvolume of the path in the tube through which la-beled blood flows until reaching the imaging slab,the equation via = fmin0TI2, is established. In Eq. [B],even if the true flow rate increases more than fmin, f Ais underestimated more than f because f A is calcu-lated using Eq. [12], though Eq. [11] should nor-mally be used. Therefore, it follows that:

2�M0B � f0 � TI1 � e�TI2=T1B

¼ 2�M0B � f � ðTI2 ��tÞ � e�TI2=T1B $f0 ¼ TI2��t

TI1� f: ½15�

At the same time, when f increases, "t grows short-er. However, labeled blood follows the same path.Therefore:

via ¼ TI2 � fmin ¼ �t � f $ �t ¼ fmin

f� TI2: ½16�

Substituting this creates Eq. [B]. When f increasesfurther, Eq. [12] is finally valid for f A. Therefore, inEq. [C], f A = f, is true. The condition for this is a

state ofTI2

TI2� TI10fmin < f. This state is explained

when f is substituted for f A in Eq. [B]. Furthermore,when "M(TI2) eventually stops changing even withincreases in f, f A becomes fixed at a specific flow rateof fpeak. This is expressed with Eq. [D]. This is be-cause labeled water volume in the labeling slab hasreached its maximum. Figure 3 demonstrates agraph showing the relationship between f A and f us-ing Eqs. [A] to [D] with fixed TI1 of 0.7 (s) andfixed TI2 of 1.8 (s). The value of fmin was assumedas 0.0033 mL/g/s (= 20 mL/100 g/min) and that offpeak, as 0.015 mL/g/s (= 90 mL/100 g/min). Previ-ously, we conducted a phantom experiment usingQ2TIPS,34 in which we created a phantom of waterflow using a pump and compared water flow, f A,measured with ASL-MRI and true water flow, f, un-der TI1 and TI2 fixed, and measured variable rates ofthe water flowing through the phantom. Thoughmeasurement units differed due to demands of thephantom structure, switching f and f A in a graph of

results creates similar results to those shown inFig. 3. In addition, the relationship between f andf A shown above changes little even if the unfixedcorrection factor, q, is used instead of q = one be-cause q approaches one as T1B approaches T1A.It is noted, however, that the formulae do not

necessarily coincide with in vivo conditions be-cause multiple vessels feed the brain in vivo, andcollaterals develop in cases of chronic cerebrovas-cular steno-occlusive disease. It should be empha-sized again that the formulae has been made to im-prove understanding of the difference between trueCBF values and CBF values measured with ASL-MRI.

Conclusions

Though equations for quantitative CBF by ASL-MRI are quite difficult to understand, physical math-ematics and schematic explanations can be helpful.Assumptions aid understanding of the optimizedconditions and serious exceptions. It is important tosee through to the truth of miscellaneous phenom-

Fig. 3. A virtual graph showing the relationship be-tween the true value of cerebral blood flow (CBF) andthe CBF value measured with arterial spin labeling(ASL) with TI1 and TI2 fixed. In this graph, f A is theCBF value measured with ASL, f is the true CBF val-ue, TI1 is 0.7 s, TI2 is 1.8 s, fmin is 20 mL/100 g/min andfpeak is 90 mL/100 g/min. Equation [A] shows that thetrue CBF value cannot be detected with ASL because itis low and f A is zero. Equation [B] shows that f A can bemeasured with ASL when f increases, but it is lowerthan the true value of blood flow. However, when fincreases further, Eq. [C], f A = f, applies. When"M(TI2) eventually stops changing even with increas-es in f, f A becomes fixed at a specific blood flow valueof fpeak. This is Eq. [D].

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Vol. 14 No. 1, 2015

ena knowing that we are dealing with a complexsystem in which events do not necessarily go ide-ally.

Acknowledgements

This work was supported in part by Grants-in-Aidfor Scientific Research from the Japan Society forthe Promotion of Science.

Appendix

Extended comment for correction factor, q(Fig. 4)Though the labeled blood in the artery decays

with the T1 value of the arterial blood, T1B, it willdecay with the T1 value of the brain tissue, T1A, afterreaching the site of capillary exchange. Buxton’stheory assumes that the spin exchange takes placejust after the elapsed time of "t (s) when the labeledblood first arrives at the imaging area after applica-

tion of the inversion pulse. The micro-volume ofarterial blood, f0dt (mL), flowing into the exchangesite has the magnetization of M0B0(1–2¡e¹"t/T1B) atthe elapsed time of "t (s) and thereafter decays ac-cording to M0B0(1–2¡e¹ "t /T1B+"t/T1A¹t/T1A) = M0B0(1–2¡e¹k"t-t/T1A) (Fig. 4A). Therefore, it has themagnetization of M0B0(1–2¡e¹k "t¹("t+dt)/T1A) at theelapsed time of "t + dt (s) (Fig. 4B). The micro-volume of arterial blood, f0dt (mL), has the magnet-ization of M0B0(1–2¡e¹("t+dt)/T1B) at the elapsedtime of "t + dt (s) and decays according to M0B0(1–2¡e¹k ("t+dt)¹t/T1A). Accordingly, it has the mag-netization of M0B0(1–2¡e¹k ("t+dt)¹("t+2dt)/T1A) at theelapsed time of "t + 2 © dt (s) (Fig. 4C). After theelapsed time of "t + TI1 (s), the inflowing of thelabeled blood is finished. At the elapsed time ofTI2 when the labeled images are taken, the overallvolume of the magnetization of all labeled bloodis:

R�tþTI1�t f �M0B � ð1� 2�e�kt�TI2=T10 Þdt (Fig. 4D).

Based on the indefinite integralRe�Axdx ¼ �e�Ax=

Aþ C, it follows that:

Fig. 4. Schemata for explaining the correction factor, q. (A) The spin-exchangestarts just after elapsed time of "t (s) when the labeled blood first arrives at theimaging area. The micro-volume of arterial blood f0dt (mL) flowing into the ex-change site has the magnetization of M0B(1¹2¡e¹"t/T1B) and thereafter decaysaccording to M0B(1¹2¡e¹k"t-t/T1A). (B) It has the magnetization ofM0B(1¹2¡e¹k "t¹("t+dt)/T1A) at elapsed time of "t+dt (s). (C) The magnetizationof the next micro-volume of arterial blood f0dt (mL) is M0B(1¹2¡e¹("t+dt)/T1B) at"t + dt (s) and becomes M0B(1¹2¡e¹k ("t+dt)¹("t+2dt)/T1A) at "t + 2 © dt (s) (D) Atelapsed time of TI2 (s), the total volume of the magnetization of all labeled bloodamounts to:

R�tþTI1�t f �M0Bð1� 2�e�kt�TI2=T10 Þdt.

10 T. Noguchi et al.

Magnetic Resonance in Medical Sciences

Z �tþTI1

�t

f �M0B � ð1� 2�e�kt�TI2=T10 Þdt ¼ f �M0B � t � � 2�e�kt�TI2=T10

k

� �� ��tþTI1

�t

¼ f �M0B � TI1 � 2 � TI1 � �e�TI2=T1B � ek�TI2ðe�k��t � e�kðTI1þ�tÞÞ

k � TI1

� �: [8]

When M0B0f0TI1 is subtracted from Eq. [8], Eqs. [1] and [2] are acquired. In addition, q can be modified as:

q ¼ ek�TI2ðe�k��t � e�kðTI1þ�tÞÞk � TI1 ¼ ekðTI2�TI1��tÞ � ðe

k�TI1 � 1Þk � TI1 : [9]

q approaches one as T1B approaches T1A based on limx!0

ex ¼ 1 and limx!0

ex � 1

x¼ 1.

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