Biomedical Engineering Reference
In-Depth Information
separated by a recycle delay,
d
1
, to allow the system to return to equilibrium as
dictated by the spin-lattice relaxation time T
1
(typically 1-5 s). Fitting a plot of the
maximal echo signal as a function of
yields the time constant, T
2
.
Using the spin echo sequence to measure T
2
values has two limitations. The
fi rst limitation is that any diffusion of spins during the long
d
1
delay time between
experiments can decrease the observed T
2
values. The second limitation is the long
delay time,
d
1
. Because at least fi ve datum points are necessary for a data fi t, spin
echo sequences can require over 20 s for the measurement of one T
2
value. A much
faster and more effi cient means of measuring T
2
is the CPMG pulse sequence, in
which additional 180 ° RF pulses spaced by time 2
τ
are included to provide for the
repeated refocusing of the echo signal. The amplitude of the echos measured
between the pulses decays with the time constant T
2
(Figure 1.6b). As the time
constant
τ
is typically less than a few milliseconds, a single T
2
measurement of
several hundred echos can be completed in less than 1 s. However, one must be
aware that CPMG and spin echo measurements can yield different T
2
values for
some systems. Typically, CPMG sequences are sensitive to magnetic fi eld varia-
tions that occur over periods of time less than hundreds of milliseconds, whereas
spin echoes are sensitive to variations that occur over periods of time of less than
seconds. One result of this difference is that CPMG T
2
measurements are inde-
pendent of diffusion phenomena, while spin echo T
2
measurements are heavily
dependent on diffusion, and this difference must be borne in mind when compar-
ing T
2
values obtained by the two methods. In addition, CPMG T
2
measurements
can exhibit a heavy dependence on the inter-echo delay time, 2
τ
. However, as will
be described below, this dependence may be very useful for MRSw characteriza-
tion and optimization.
τ
1.4.3
Theoretical Model for T
2
and Nanoparticle Size
Although the use of MRSw biosensors was fi rst demonstrated in 2001 [1], the
theoretical foundation for how superparamagnetic nanoparticles affect measured
T
2
relaxation rates began to take shape as early as 1991 [53]. These theory-based
investigations were made possible by the early experimental observations that
solvent relaxivity was a function of SPIO particle size [18]. In this early study, SPIO
particles of various sizes were prepared by varying the number of iron oxide cores
per particle, and the effect of ferromagnetic, paramagnetic, and superparamag-
netic iron oxide particles on the longitudinal and transverse relaxivity,
R
1
= 1/T
1
and
R
2
= 1/T
2
, respectively, was reported [18]. Subsequently, a group of theoreti-
cians in Belgium, including Robert Muller, Pierre Gillis, Rodney Brooks, and Alan
Roch, began exploring the underpinnings of magnetic, paramagnetic, and super-
paramagnetic particles that were used as contrast agents for MRI. The initial
studies demonstrated that Monte Carlo numerical simulations of a distribution
of magnetic particles surrounding by hydrogen nuclei could be used to accurately
reproduce the observed dependence of
R
2
on the size of iron oxide micro and
nanoparticles [53, 54]. Simulations and experimental data showed that both
R
2
