1. Why magnetic nano-particles (MNP) ? Typical dimensions in biomedicine
pollen
Human hair
Bacteria
Gene (width)
0.1 nm
1 nm
10 nm
100 nm
1 m
10 m
100 m
DNA
Cells
Aspirin molecule
Proteins
Virus

2. Sensing lymphnodes (FDA approved)
Sentimag for sentinel lymphnodes approach + NP
For surgery of
breast tumour.
Used SP in place of
radio-isotopes

3. MFH treatment of tumours
Magnetic Fluid Hyperthermia (MFH) or Magnetothermia
Heating through application of AC magnetic field via activation of 12 nm amino-silane coated Fe3O4 MNP directly implanted in the tumour mass at high doses (ca. 50 mg/cm3)
Typically :  ~ 100 kHz, amplitude 10 kA/m
Minor side effects
Typical values of the reported specific loss of power, SLP or SAR (the energy converted into heat per mass unit) are : 10200 W/g
Exceptions :
- 35 nm bacterial magnetosomes (960 W/g at
410 KHz and 10 kA/m)
- 16 nm γ-Fe2O3 N P ( 1650 W/g
at 700 kHz and 24.8 kA/m, 300 W/g at 11 kA/m)

4. Magnetic Resonance Imaging (MRI)
MRI Timeline
1946 MR phenomenon - Bloch & Purcell
1952 Nobel Prize - Bloch & Purcell
NMR developed as analytical tool
1972 Computerized Tomography
1973 Backprojection MRI - Lauterbur
1975 Fourier Imaging - Ernst
1977 Echo-planar imaging - Mansfield
1980 FT MRI demonstrated - Edelstein
1986 Gradient Echo Imaging - NMR Microscope
1987 MR Angiography - Dumoulin
1991 Nobel Prize - Ernst
1992 Functional MRI
1994 Hyperpolarized 129Xe Imaging
2003 Nobel Prize - Lauterbur & Mansfield
Typical MRI apparatus for
clinical use, magnetic field
H = 1.5 Tesla

5. The ideal (not realistic ??) task : a single theranostic nano-object
Diagnostics : MRI CA, fluorescence
Therapy : Magnetothermia, drug release 5

6. Why Magnetic Nanoparticles are appealing for
Biological and Medical Applications
They can be manipulated by a external magnetic field
In MRI, they provide an important decrease of the T1 and/or T2 nuclear relaxation per unit of metal
They may interact with time-varying field and convert the electromagnetic energy in local heat (MFH) 6

7. Mechanisms and magnetism (MRI, Sentimag, MEG-SQUID,…)
Sensing
(MRI, Sentimag, MEG-SQUID,…)
Moving
(navigation)
Heating
(Magnetic
Hyperthermia)

8. Liver tumour detection by “negative” SP-CA
Generally the negative CA are based on superparamagnetic nanoparticles
Example : liver tumour
without CA with CA

9. MRI angiography by “positive” CA
(contrast agents=CA
can be considered MNP)
Evaluate blood vessels non-invasively  MR angiography (MRA). 
head and neck vessel narrowing (stenosis), blood vessel blockage, cerebral aneurysm, arteriovenous malformation (AVM) and blood vessel dissection.   
Contrast enhanced MRA utilizes an intravenous injection of MRI contrast media (Gd-DTPA). 

10. Why MRI ? MRI: Optical Imaging: Poor spatial resolution Non-invasive
Good spatial resolution
Good temporal resolution
Low sensitivity
Optical Imaging:
Poor spatial resolution
Poor temporal resolution
high sensitivity
Reporters: luminescent probes
X-Ray (CT):
Good spatial resolution
Good temporal resolution
Low sensitivity
Nuclear Medicine:
Poor spatial resolution
Poor temporal resolution
High sensitivity
Reporters: radionuclides

11. The MRI image intensity (the contrast) thus depends on :
Why MRI with CA ?
MRI signal is s(t)  N(H) e-TE/T2 (1-e-TR/T1)
The MRI image intensity (the contrast) thus depends on :
Intrinsic Parameters
Local proton density N(H) (water, fat)
Nuclear Relaxation times T1 and T2
Magnetic susceptibility differences
Diffusion processes
Extrinsic Parameters
Magnetic field
Timing of the pulse sequence
Contrast Agents (CA)
with contrast agents
the nuclear relaxation times change
(much better idea than protons’ density) 
better image contrast and pathology evidence

12. MRI contrast agents: features
TWO KINDS OF CA, BASICALLY
NON-SPECIFIC CA SPECIFIC CA FOR BIO-DISTRIBUTION
(Gd-based systems, ferrites-based systems)
MAGNETIC PROPERTIES
Paramagnetic CA Superparamagnetic CA
(i.e. paramagnetic core) (i.e.superparamagnetic core)
(Gd-based CA)
Extracellular CA (Gd-DTPA)
Blood-Pool CA
Organ-Specific CA (tissutal targeting)
Molecular Imaging CA (cell targeting)
EFFECT ON THE IMAGES
Positive CA (signal increase) Negative CA (signal decrease)

13. Main missing scientific investigations/results on SP-CA
Molecular Imaging. Examples of MI-MRI : stem cells targeting, specific tumoral cells targeting , macrophages, etc.
Higher relaxivities optimization compounds (both T1 and T2)
Understanding the mechanism of nuclear relaxation
All the above depend on the control of dimensions, shape, bulk anisotropy, kind of magnetic ion, coating in SP NP

14. Alessandro Lascialfari - NMR in solids
H = Hz + HD + HCS + HQ + Hhyp + HJ + Hce
HZ = Zeeman interaction , path 1 ( B0 10 9)
HD = Dipolar interactions among nuclear spins, path 2,3 ( ISr -3 10 3-5)
HCS = Chemical shielding interaction, path 6 and 3 (1 – 10 5)
HQ = Quadrupolar interaction (nuclei I>1/2) with surrounding E), path 3 (10 3 – 10 7)
Hhyp (paramagnetic shift) = hyperfine e-n dipolar (pseudocontact) and contact interactions,
path 3 (influenced by 5)
HJ = J-coupling, path 2 via path 3
Hce= interaction of nuclei with conduction electrons (e.g. nuclei, Knight shift), path 3
NMR for dummies - Mons - April 2015

15. Going toward fundamental physics: few words on NMR TECHNIQUE
3 main NMR experimEntal parameters: spectrum, nuclear spin-spin relaxation time T2, nuclear spin-lattice relaxation time T1
Nuclei
(T2n)
Electrons
(T2e)
phonons
T1n
T1e
Nuclei are LOCAL PROBES  sensitive to hyperfine interactions
LOCAL MAGNETIC FIELDS AND DYNAMICS can be studied
In MRI and NMRrelaxometry, sensitivity to
magnetic properties, spin dynamics
and molecular “motion”

16. Efficiency of MRI Contrast Agents
Efficacy of a contrast agent in reducing T1 and T2 is evaluated by measuring the nuclear relaxivity ri (i=1,2), that represents the relaxation rate of hydrogen nuclei in presence of 1mM of magnetic center
The nuclear relaxation rate is the sum of the diamagnetic contribution (absence of CA) and the paramagnetic one (presence of CA)
c = concentration of CA expressed in mM/L
T1-relaxing systems : R2/R1 < 2 (generally paramagnetic).
POSITIVE CA (brilliant spots)
T2-relaxing systems (generally superparamagnetic) :
r2 must be maximum  NEGATIVE CA (dark zones)

17. Nuclear Relaxation Mechanisms
Several correlation times within the game :
Chemical exchange time of coordinated water tM
rotational time (brownian) tR
electronic relaxation time (also Neel reversal) tSi
diffusion time tD
Two main
contributions
Inner Sphere (IS)
Outer Sphere (OS)

18. Relaxation rate : Weak-collision theory
H = Hn + He + Hze + Hzn + Hen
Hen = perturbazione

19. Relaxation rate : Weak-collision theory

20. Relaxation rate : Weak-collision theory

21. Relaxation rate : Weak-collision theory
In termini di variabili collettive :

22. Teoria BPP

23. Teoria BPP

25. Inner-sphere mechanism
Chemical exchange time of coordinated water tM
rotational time (brownian) tR
electronic relaxation time (also Neel reversal) tSi

28. based on
BPP or SBM
equation

29. Dephasing - T2 shortening due to SP-CA Susceptibility effect

30. Outer-sphere mechanism
electronic relaxation time (also Neel reversal) tSi
diffusion time tD

32. MRI contrast agents : paramagnetic CA

33. Inner-sphere mechanism generally mainly contributes
to Gd-based paramagnetic CA

34. Relaxomety profile of nuclear longitudinal
relaxivity for paramagnetic CA
1H NMR
This profile reports the longitudinal relaxivity r1
as a function of the frequency (i.e. the applied magnetic field).
The red arrows are indicating the clinical typical fields).
r1 measures the efficiency of the CA.

35. Inner-sphere : influence of molecular size
NMR-Dispersion
profiles

36. MRI contrast agents : superparamagnetic MNPs

37. For SP CAs, outer-sphere mechanism dominates
Simplest form : magnetic core (often simple ferrites) + organic coating
TEM
High monodispersity
* Natural NPs (magnetosomes)
* Hollow / different shape

38. Nanomagnetism: basic concepts
Below a critical temperature, TC, some materials exhibit spontaneous magnetization (ferro- and ferrimagnetism). Demagnetizing field induces domain formation (i.e. uniformly magnetizated regions of different shape and size are formed).
E = Eex + Ek + Eλ + ED
Eex exchange energy, Ek magnetocrystalline anisotropy energy, Eλ magnetoelastic energy, ED magneto-static energy
remnant M
coercivity
Bloch wall
The width of the domain wall depends on the anisotropy and exchange coupling and
 =pA/K
A = exchange energy density (J/m2) K = magnetic anisotropy energy density (J/m2)
Typical values of domain wall width are in the nm range.

39. Single Domain Nanoparticles
Total wall energy per area unit: Es=2(AK)1/2
Reducing the dimensions of the crystal: competition among Es and the magnetostatic energy, Eλ . But Eλ scales with the volume, Es with the surfaces
There exists a lower limit in size, D, corresponding to the single domain state.
D=18 Es / m0MS2
Typical D values:
Fe nm
Co nm
Ni nm
NdFeB nm
Fe3O4 128 nm
g-Fe2O3 166 nm =
100 nm
When D< all the spins are coupled (Exchange Energy is constant). The inversion of M occurs through a coherent movement of all the spins of the particle.
SUPERPARAMAGNETISM

40. Single Domain Nanoparticles If NPs interact : Vogel-Fulcher model=
100 nm
Stoner-Wolhfarth model: q
The inversion of M occurs through a coherent movement of all the spins of the particle DE
Energy barrier DE=kAV
kA= anisotropy constant, V= particle volume
tN = t0 exp(DE/kBT)
H0f ≤ Am-1s-1 (*)
50 kHz ≤ n ≤ 1 MHz
Neel correlation time
(*) Depending on the radius of the
exposed region
If NPs interact : Vogel-Fulcher model
tN = t0 exp[DE/kB(T-T0)]

41. Mechanisms of relaxation in superparamagnetic CA (i)
TYPICAL RELAXOMETRY CURVES
“dispersion”
absence of
“dispersion”
Low magnetic anisotropy
High magnetic anisotropy
Dominating correlation times
Diffusion time at “high” freq.
Neel time at “low” freq.
tN = t0 exp (D/kBT)

42. Mechanisms of relaxation in superparamagnetic CA (ii) : beyond the outer-sphere model
ANALYTICAL EXACT
MODEL MISSING for
d>2-3 nm
CURIE RELAX.
ANISOTROPY
Very complicate HEURISTIC
“approximate” expressions
for nuclear relaxation rates
(a combination of -anisotropy, P=0&Q=1,
and zero-anisotropy terms, P=1&Q=0)

43. Longitudinal relaxivity
Varying
anisotropy
Varying total spin value
Varying NPs
diameter
Roch, Muller, Gillis,
J. Chem. Phys. 110, 5403 (1999)

44. Transverse relaxivity (the one really important for SP-CA)
r1-r2 comparison
Varying NPs
diameter
Roch, Muller, Gillis, J. Chem. Phys. 110, 5403 (1999)

45. r1 heuristic fit model works …

46. ….but the same model for r2 does not work Motional Averaging Regime
However, simplifying :
Motional Averaging Regime
MAR
SDR
But the refined model is needed ! Study in progress, thanks to the possibility of measuring T2 with Smartracer