A numerical method to optimize presaturation sequences
on multiexponential samples

POSTER by ^{a}Mirko Gombia, ^{b}Stanislav Sykora, ^{c}Villiam Bortolotti, ^{a}Elisa Vacchelli, and ^{a}Paola Fantazzini
^{a} Department of Physics, University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy,
^{b} Extra Byte, Castano Primo, Italy, and
^{c} DICMA, University of Bologna, Via Terracini 28, 40131 Bologna, Italy
presented at
9th International Bologna Conference on Magnetic Resonance Applications to Porous Media,
MRPM9, July 1317, 2008, Cambridge MA, USA.

Abstract
We have developed a mathematical model to simulate the effects of pulse sequences on
composite samples and coded it in Matlab. The objectoriented code accommodates pulse
sequences and samples of any complexity, including ones with any distribution of relaxation
rates and offsets. Of equal importance is the fact that the most common instrumental artifacts (B0
and B1 inhomogeneity) can be easily taken into account. The package permits to simulate the
magnetization of a composite sample during the whole sequence by using Bloch equations to
track the magnetization of each sample component. The software allows one to obtain three
quality factors related to: the highest residual magnetization among all components (Q_{1}); the
square mean of all the residual magnetization components (Q_{2}); the modulus of the total
magnetization vector of the sample (Q_{3}). Low values of Q_{i} (i=1,2,3) indicate good zeroings of
the sample residual magnetization. In particular, a low value of Q_{1} indicates good zeroing of all
the sample residual magnetization components.
This approach has been applied to the problem of fast and efficient presaturation by a
suitable Sample Magnetization Suppression pulse sequence (SMS) in the presence of a wide
spread of offsets, relaxation rates, and magnetic field imperfections. This led us to the
Logarithmicallydistributed APeriodic Saturation Recovery sequence (LAPSR) which comes as
close as possible to suppressing the absolute magnetization of all sample components and is, in
this respect, much better than the classical sequences Saturation Recovery (SR) and APeriodic
Saturation Recovery (APSR). LAPSR is characterized by the following pulse sequence:
P(α)  D  P(α)  D.q  P(α)  D.q^{2}  ...  P(α)  D.q^{n2}  P(α)  D.q^{n1}  P(α)  t  P(90°),
where D is the delay between the first two presaturating pulses and a the nutation angle of the
magnetization vector for each pulse. We notice that delays between presaturating pulses decrease
logarithmically by a factor q<1 to reach the value D.q^{n1} between the last two pulses of the
presaturating sequence. The code was also used both to optimize LAPSR parameters, i.e. the
delay D, the angle a, the number n of presaturating pulses, the qvalue, and to show the effects of
field inhomogeneities.
The performance of LAPSR has been verified on a composite largevolume phantom.

