Biomedical Engineering Reference

In-Depth Information

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
.

D

N
P
=n/, the net change of

R
2
.R
2
D

R
2

R
w
/ is given as

N
P

V
D

n

r
2

N
C

V
;

r
cell

2

R
2
D

r
2

N
c
D

(9.2)

V

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:

D

n

•

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

these accomplishments.

9.3

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

to
d

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

MNPs.