Biomedical Engineering Reference
where R w is the relaxation rate of the background (usually water), V is the NMR
detection volume, and N P is the total number of MNPs in V . If each biological
cell has n MNPs and the total number of cells is N C .
N P =n/, the net change of
R 2 .R 2 D
R w / is given as
R 2 D
N c D
where r cel 2 .
r 2 / is defined as the cellular relaxivity (transverse relaxivity per
given cell concentration). Note that r cel 2 is indicative of the abundance of relevant
surface biomarkers. NMR thus can be used effectively for molecular profiling of
target cells [ 27 , 28 ]. Equation 9.2 provides valuable insights into how to increase the
sensitivity and specificity of NMR-based sensors:
MNPs with high r 2 relaxivity . Pronounced R 2 changes will occur when cells are
labeled with MNPs of high r 2 relaxivity [ 23 ]. Because r 2 is proportional to the
magnetic moment ( p ) of particles [ 32 , 33 ], making magnetically stronger MNPs
will benefit the measurements.
Maximal MNP labeling on cell. The R 2 changes are also directly proportional to
the number of MNPs loaded onto cells. In addition to increasing the r 2 potency
of individual MNPs, it is equivalently important to establish a labeling protocol
to maximize and/or amplify MNP loading on cells.
Miniaturized NMR probes. Higher sensitivity can be achieved on the device level
by decreasing the NMR detection volume (V/. This approach can effectively
increase the analyte concentration (N C =V), leading to large R 2 .Furthermore,
smaller NMR probes assume higher SNR (signal-to-noise) ratio due to the
increased sample filling factor. It can be shown that the sensitivity of NMR coils
(with a typical dimension of d) scales as d 1=2 [ 34 ].
These recognitions motivated us to explore three major activities in DMR
development: synthesis of new MNPs, optimization of such MNPs for cellular
labeling, and miniaturization of NMR systems. The following sections will describe
New Magnetic Nanoparticles
We have developed many different types of MNPs (Table 9.1 ) and engineered the
particle size and composition to enhance the transverse relaxivity. According to the
outer-sphere model of transverse relaxation, the r 2 value of an MNP is proportional
M 2 ,where d is the residence time of water molecules around the particle
and M is the particle magnetization [ 35 ]. The efforts to enhance r 2 were thus
focused on synthesizing larger MNPs using magnetically stronger material. We
herein introduce two types of such particles: metal-doped ferrite and iron (Fe)-based