Quantitative Magnetization Transfer Imaging Using
M. Gloor,*K. Scheffler, and O. Bieri
It is generally accepted that signal formation in balanced
steady-state free precession (bSSFP) is a simple function of
relaxation times and flip angle only. This can be confirmed for
fluids, but for more complex substances, magnetization trans-
fer (MT) can lead to a considerable loss of steady-state signal.
Thus, especially in tissues, the analytical description of bSSFP
requires a revision to fully take observed effects into ac-
count. In the first part of this work, an extended bSSFP signal
equation is derived based on a binary spin-bath model. Based
on this new model of bSSFP signal formation, quantitative MT
parameters such as the fractional pool size, corresponding
magnetization exchange rates, and relaxation times can be
explored. In the second part of this work, model parameters
are derived in normal appearing human brain. Factors that
may influence the quality of the model, such as B1 field
inhomogeneities or off-resonances, are discussed. Overall,
good correspondence between parameters derived from
two-pool bSSFP and common quantitative MT models is ob-
served. Short repetition times in combination with high sig-
nal-to-noise ratios make bSSFP an ideal candidate for the
acquisition of high resolution isotropic quantitative MT maps,
as for the human brain, within clinically feasible acquisition
times. Magn Reson Med 60:691–700, 2008. © 2008 Wiley-
Key words: balanced SSFP; magnetization transfer; quantitative
Balanced steady-state free precession (bSSFP; also known
as TrueFISP, FIESTA, and balanced FFE) (1,2) has become
a valuable and indispensable tool in diagnostic imaging
over the last several years, especially for cardiac and car-
diovascular applications (3–5). It is generally accepted that
signal formation in bSSFP can be derived from the Free-
man-Hill formula (6), being proportional to the ?T2/T1for
repetition times TR ?? T1,T2(7). However, only recently
subtle signal deviations (8–10) from the Freeman-Hill for-
mula indicated further contrast mechanisms, especially
the steady-state of bSSFP in tissues may be reduced up to
a factor of two from magnetization transfer (MT) effects
(11). Here, short TRs in combination with large flip angles
(?) saturate the magnetization of protons associated with
macromolecules and membranes in biological tissues (re-
stricted pool protons). As a result, subsequent exchange of
these protons with mobile ones (liquid pool protons) con-
stituting the steady-state leads to an overall signal reduc-
tion, if compared to a situation in absence of exchange. For
bSSFP, on-resonant excitation thus not only generates the
steady-state but also acts directly as MT sensitizing radio-
frequency (RF) pulse. From this, a new method for MT
imaging with bSSFP was proposed (12), which in contrast
to common MT methods (13–15) circumvents the need for
additional MT sensitizing prepulses.
MT was first demonstrated by Wolff and Balaban in the
late 1980s (16). Not only has it become a standard tool for
suppression of background signals from tissues in MR
angiography (14), but it was also realized that MT shows
great promise in the field of multiple sclerosis offering
tissue characterization beyond conventional T1, T2, and
T2* (16). In its simplest and common form of quantifica-
tion, MT effects are often condensed within the so-called
magnetization transfer ratio (MTR) (17). MTR has become
popular not only for characterizing subtle diseases in the
brain (15) but also for the assessment of breast, knee and
cartilage (14). Although great effort has been undertaken to
ensure reproducibility in MTR measurements (18), the
phenomenological breakdown of a complex tissue system
to a single parameter may be inappropriate simply by its
virtue of oversimplification, and thus may overlook useful
diagnostic information. Indeed, there has been given evi-
dence that MTR has only limited pathological specificity
(19), making MTR results incomplete and controversial.
As a result, binary spin-bath models have been investi-
gated in detail over the last several years by many research
groups, capable of gaining intrinsic MT model parameters
(19–21). Quantitative MT imaging (qMTI) yields the frac-
tion (F) of restricted pool protons, the magnetization ex-
change rate (kf), as well as the pool relaxation properties
(T1, T2). Recent studies indicate that especially F may be of
great diagnostic potential, because it correlates with the
myelin content in brain white matter (22). Quantitative
MT, in contrast to MTR, has the potential to yield ex-
tended and unquestionable diagnostic information; how-
ever, measurement protocols lack clinically applicable ac-
So far, quantitative MT parameters are commonly de-
rived from associated MT dispersion curves. Sampling of
these curves is time consuming because different MT-
weighted spin-echo or gradient-echo measurements have
to be acquired based on a set of MT pulses that differ in
power and off-resonance frequency (19,20). In contrast, the
overall MT sensitivity of bSSFP in combination with its
excellent SNR and the short acquisition time makes it an
ideal candidate to meet the clinical requirements for fast
and reliable high resolution qMTI. In the first part of this
work, an extended bSSFP signal equation is derived based
on a binary spin-bath model to take MT exchange effects
into account. Assuming that relaxation and exchange can
be separated into two independent processes within any
Division of Radiological Physics, Department of Radiology, University Hospi-
tal Basel, Basel, Switzerland.
Grant sponsor: Schweizerischen Nationalfonds; Grant number: SNF PP0B-
68783; Grant sponsor: Novartis Pharma AG.
*Correspondence to: Monika Gloor, Division of Radiological Physics, Depart-
ment of Radiology, University Hospital Basel, Petersgraben 4, CH-4031
Basel, Switzerland. E-mail: email@example.com
Received 1 November 2007; revised 10 March 2008; accepted 25 April 2008.
Published online in Wiley InterScience (www.interscience.wiley.com).
Magnetic Resonance in Medicine 60:691–700 (2008)
© 2008 Wiley-Liss, Inc.
TR, partial integration of the coupled Bloch equations
yields an extended steady-state eigenvector equation for
bSSFP that can be solved analytically. Numerical simula-
tions confirm the validity of the derived two-pool bSSFP
signal equation and thereby justify the conceptual separa-
tion of exchange and relaxation processes. In the second
part of this work, the extended two-pool bSSFP signal
equation is used to derive qMTI parameters from human
brain, such as the fractional pool size and corresponding
exchange rates. It will be demonstrated that the fitted
parameter values are in good correspondence with litera-
ture values. Possible issues and differences with respect to
common qMTI methods are discussed and analyzed. Fi-
nally, it will be shown that qMTI with bSSFP offers great
potential for generating qualitative high resolution MT
parameter maps within clinically feasible acquisition
times. In summary, this work introduces a novel fast and
quantitative MTI method that is based on bSSFP.
Single-Pool bSSFP Signal Equation
For a centered echo (TE ? TR/2) between alternating ex-
citations (??), the steady-state of bSSFP is calculated from
the Bloch equations using partial integration, yielding:
1 ? E1
1 ? E1E2? ?E1? E2?cos?, 
where E1,2? exp(–TR/T1,2) and M0is the equilibrium mag-
netization (6,7). This formal description has been con-
firmed for simple probes consisting of a single aqueous
phase (11). However, considerable deviations (up to a fac-
tor of two) were detected in tissues, and the molecular
origin of this apparent signal reduction was found to be
MT (11). Thus, at least for tissues the ordinary description
of the steady-state according to Eq.  is inappropriate and
demands for an extended bSSFP signal equation including
MT effects. In the following, signal formation in bSSFP is
analyzed based on a standard binary spin-bath MT model
(19,23) similar to the two compartment model for blood
oxygen saturation (24).
Two-Pool bSSFP MT Model
The minimal model for MT based signal analysis is com-
posed of two pools: a liquid pool of “free” protons (sub-
script f) and a semisolid pool of protons that are restricted
in motion (subscript r). The formal description of this
binary spin-bath model leads to a set of coupled differen-
tial equations, as described in any detail elsewhere (19,23).
Saturation of restricted pool protons is typically achieved
by off-resonance irradiation (frequency offset ?), that ide-
ally leaves the magnetization of free pool protons unaf-
fected. The effect of pulsed irradiation (25) on the longi-
tudinal magnetization of the restricted pool protons can be
described by a time-dependent mean saturation rate:
where G(?) is the absorption line shape, and where ?W????
depends on the shape ?1(t) ? ? |B1(t)| and on the duration
TRFof the RF pulse.
On-resonance RF pulses are applied for MT bSSFP, that
is, ? 3 0 (11), and the system of differential equations (19)
? ? R2,fMx,f,[3a]
? ? R2,fMy,f? ?1?t?Mz,f,[3b]
? R1,f?M0,f? Mz,f? ? kfMz,f? krMz,r? ?1?t?My,f,
? R1,r?M0,r? Mz,r? ? kfMz,f? krMz,r
? W?? 3 0,t?Mz,r, [3d]
where the subscripts x, y, z denote the various spatial
components of the magnetization vector M, R1,f(R1,r) refers
to the longitudinal relaxation rate, and R2,f(R2,r) to the
transverse relaxation rate of the pools (R1,2? 1/T1,2). Mag-
netization exchange is given by the pseudo-first-order rate
constants kf? RM0,rand kr? RM0,f, where R is the funda-
mental rate constant between the two pools and M0,f(M0,r)
denotes the equilibrium magnetization of the free (re-
stricted) pool. The fractional size of the restricted pool
amounts to F ? M0,r/ M0,f, and by definition kr? kf/ F.
Idealized Two-Pool bSSFP Signal Equation
The restricted pool in an idealized MT bSSFP experiment
is fully saturated, that is, Mz,r? 0. This leads to a decou-
pling of Equations [3c] and [3d] similar to the idealized
MT spoiled GRE case (26). Equation [3c] can be rewritten
? ?R1,f? kf??
R1,f? kfM0,f? Mz,f?? ?1?t?My,f, 
being formally analogous to a single-pool situation, but
with modified longitudinal relaxation and equilibrium
magnetization. Therefore, Equation  can be used to de-
scribe the idealized two-pool bSSFP signal using the sub-
R1,f3 R1,f? kf and M0,f3
R1,f? kfM0,f. 
However, it can be readily deduced that especially in the
range of low to moderate flip angles the Mz,r? 0 condition
is inapplicable leading to a substantial overestimation of
MT effects at low saturation levels. Thus, although the
idealized bSSFP MT model is only of limited experimental
interest, it represents the theoretical upper bound in the
overall achievable MT effects.
692Gloor et al.
2. Oppelt A, Graumann R, Barfuss H, Fischer H, Hartl W, Schajor W. FISP:
eine neue schnelle Pulssequenz fu ¨r die Kernspintomographie. Electro-
3. Scheffler K, Lehnhardt S. Principles and applications of balanced SSFP
techniques. Eur Radiol 2003;13:2409–2418.
4. Deshpande VS, Li D. Contrast-enhanced coronary artery imaging using
3D trueFISP. Magn Reson Med 2003;50:570–577.
5. Thiele H, Nagel E, Paetsch I, Schnackenburg B, Bornstedt A, Kouwen-
hoven M, Wahl A, Schuler G, Fleck E. Functional cardiac MR imaging
with steady-state free precession (SSFP) significantly improves endo-
cardial border delineation without contrast agents. J Magn Reson Im-
6. Freeman R, Hill H. Phase and intensity anomalies in fourier transform
NMR. J Magn Reson 1971;4:366–383.
7. Haacke E, Brown R, Thompson M, Venkatesan R. Magnetic resonance
imaging: physical principles and sequence design. New York: Wiley;
8. Schmitt P, Griswold MA, Jakob PM, Kotas M, Gulani V, Flentje M,
Haase A. Inversion recovery TrueFISP: quantification of T(1), T(2), and
spin density. Magn Reson Med 2004;51:661–667.
9. Huang TY, Huang IJ, Chen CY, Scheffler K, Chung HW, Cheng HC. Are
TrueFISP images T2/T1-weighted? Magn Reson Med 2002;48:684–688.
10. Scheffler K, Hennig J. T(1) quantification with inversion recovery True-
FISP. Magn Reson Med 2001;45:720–723.
11. Bieri O, Scheffler K. On the origin of apparent low tissue signals in
balanced SSFP. Magn Reson Med 2006;56:1067–1074.
12. Bieri O, Scheffler K. Optimized balanced steady-state free precession
magnetization transfer imaging. Magn Reson Med 2007;58:511–518.
13. Wolff SD, Balaban RS. Magnetization transfer imaging: practical as-
pects and clinical applications. Radiology 1994;192:593–599.
14. Henkelman RM, Stanisz GJ, Graham SJ. Magnetization transfer in MRI:
a review. NMR Biomed 2001;14:57–64.
15. Tofts P. Quantitative MRI of the brain. New York: Wiley; 2003.
16. Wolff SD, Balaban RS. Magnetization transfer contrast (MTC) and tis-
sue water proton relaxation in vivo. Magn Reson Med 1989;10:135–
17. Dousset V, Grossman RI, Ramer KN, Schnall MD, Young LH, Gonzalez-
Scarano F, Lavi E, Cohen JA. Experimental allergic encephalomyelitis
and multiple sclerosis: lesion characterization with magnetization
transfer imaging. Radiology 1992;182:483–491.
18. Tofts PS, Steens SC, Cercignani M, Admiraal-Behloul F, Hofman PA,
van Osch MJ, Teeuwisse WM, Tozer DJ, van Waesberghe JH, Yeung R,
Barker GJ, van Buchem MA. Sources of variation in multi-centre brain
MTR histogram studies: body-coil transmission eliminates inter-centre
differences. Magma 2006;19:209–222.
19. Sled JG, Pike GB. Quantitative imaging of magnetization transfer ex-
change and relaxation properties in vivo using MRI. Magn Reson Med
20. Ramani A, Dalton C, Miller DH, Tofts PS, Barker GJ. Precise estimate of
fundamental in-vivo MT parameters in human brain in clinically fea-
sible times. Magn Reson Imaging 2002;20:721–731.
21. Morrison C, Henkelman RM. A model for magnetization transfer in
tissues. Magn Reson Med 1995;33:475–482.
22. Davies GR, Ramani A, Dalton CM, Tozer DJ, Wheeler-Kingshott CA,
Barker GJ, Thompson AJ, Miller DH, Tofts PS. Preliminary magnetic
resonance study of the macromolecular proton fraction in white matter:
a potential marker of myelin? Mult Scler 2003;9:246–249.
23. Henkelman RM, Huang X, Xiang QS, Stanisz GJ, Swanson SD, Bronskill
MJ. Quantitative interpretation of magnetization transfer. Magn Reson
24. Dharmakumar R, Hong J, Brittain JH, Plewes DB, Wright GA. Oxygen-
sensitive contrast in blood for steady-state free precession imaging.
Magn Reson Med 2005;53:574–583.
25. Graham SJ, Henkelman RM. Understanding pulsed magnetization
transfer. J Magn Reson Imaging 1997;7:903–912.
26. Pike GB. Pulsed magnetization transfer contrast in gradient echo
imaging: a two-pool analytic description of signal response. Magn
Reson Med 1996;36:95–103.
27. Deoni SC, Peters TM, Rutt BK. High-resolution T1 and T2 mapping of
the brain in a clinically acceptable time with DESPOT1 and DESPOT2.
Magn Reson Med 2005;53:237–241.
28. Homer J, Roberts JK. Conditions for the Driven Equilibrium Single
Pulse Observation of Spin-Lattice Relaxation Times. J Magn Reson
29. Akoka S, Franconi F, Seguin F, Le Pape A. Radiofrequency map of an
NMR coil by imaging. Magn Reson Imaging 1993;11:437–441.
30. Smith SM, Jenkinson M, Woolrich MW, Beckmann CF, Behrens TE,
Johansen-Berg H, Bannister PR, De Luca M, Drobnjak I, Flitney DE,
Niazy RK, Saunders J, Vickers J, Zhang Y, De Stefano N, Brady JM,
Matthews PM. Advances in functional and structural MR image anal-
ysis and implementation as FSL. Neuroimage 2004;23(Suppl 1):S208–
31. Cox RW. AFNI: software for analysis and visualization of functional
magnetic resonance neuroimages. Comput Biomed Res 1996;29:162–
32. Cercignani M, Symms MR, Schmierer K, Boulby PA, Tozer DJ, Ron M,
Tofts PS, Barker GJ. Three-dimensional quantitative magnetisation
transfer imaging of the human brain. Neuroimage 2005;27:436–441.
33. Scheffler K, Heid O, Hennig J. Magnetization preparation during the
steady state: fat-saturated 3D TrueFISP. Magn Reson Med 2001;45:
700 Gloor et al.