This document discusses magnetic susceptometry for measuring liver iron concentration. It describes how magnetic susceptometry works by measuring the induced paramagnetic response of iron in the liver to an external magnetic field. It discusses modeling of the human torso, including using a water bag to cancel out background tissue signals. Different types of magnetizing fields and pickup coil configurations are presented for localized measurement of liver iron.
3. 3
Liver Iron Measurement
Total iron content in a normal adult body = 4 g
Iron content residing in liver = 1 g
Normal iron concentration = Cfe = 200 μg /g of liver tissue
4. 4
Liver Iron Measurement
1- Liver Biopsy ( painful, highly invasive, fatal )
2- Nuclear Resonant Scattering of X-rays ( Requires high radiation dose from a
short lived isotope)
3- Computed Tomography (CT)
4- Magnetic Resonance Imaging (MRI)
5- Magnetic Susceptometry
Diagnosis methods
They may be able to detect iron
overload but do not extend to
lower levels
5. 5
Liver Iron Measurement
This technique measures the induced paramagnetic
response from iron stored in the liver to a weak
external magnetic field in the region of the abdomen.
Liver
External
magnetic Field
M
SQUID Detector
∆B ~ 10-9
to 10-12
Tesla
6. 6
aB
∆v
x
y
z
r
r
′
r
r
′
r r
r - r
Field point
Source point
( )0
5 3V
3M(r ) r - rμ M(r )
B(r) = dv -
4π r - r r - r
′ ′ ′
′
′ ′
∫
g
0 aμM(r) = (r)B (r)χ
( )a a
5 3V
3B (r ) r - r B (r )1
B(r) = dv (r ) -
4π r - r r - r
χ
′ ′ ′
′ ′
′ ′
∫
g
Magnetic susceptibility :
Theory of Magnetic Susceptometry
7. 7
Theory of Magnetic Susceptometry
Flux :
c
= dl B(r)φ ∫ g C
B(r)
Reciprocity
Theorem :
a RV
0
1
= (r )B (r ) B (r )
R
dv
I
φ χ
µ
′ ′ ′ ′∫ g
:orR ReciprocalB (r) B
Magnetic flux density that the pickup coil
generate in the element if energized
Δv
RI
8. 8
j a j R j
0
1
= (r )B (r) B (r)
jR
v
I
φ χ
µ
∆∑ g
aB
∆v
x y
z
r
r
′
r
r
′
r r
r - r
Pickup coil
a RV
0
1
= (r )B (r ) B (r )
R
dv
I
φ χ
µ
′ ′ ′ ′∫ g
Theory of Magnetic Susceptometry
RI
9. 9
Theory of Magnetic Susceptometry
Fe ,(r) c m Feχ χ=
( )
Fe
36
,
c
1.6 10m Fe
m
kg
χ −
→
→ = ×
Iron Concentration
mass susceptibility of Iron
Fe , R
aV
0
c B (r )
B (r )m Fe
R
dv
I
χ
φ
µ
′
′ ′= ÷
∫
R
a
B (r )
B (r )
R
SSF spatial sensitivity function
I
′
′ = → ÷
Susceptometry is an INVERSE problem
10. 10
Liver Iron Measurement
1- Liver ≈ 1530 cm3
2- Lung
3- Other tissues
Liver
Lungs
6 6
0.36 10 9.032 10lung air tissueχ χ χ − −
= + = × − ×
Modeling the human body
11. 11
Liver Iron Measurement
In the absence of Liver iron and air into the Lungs the flux change should be
due to presence of tissue.
It can be cancelled out by using a water bag between the pickup coil and the
torso
Torso Modeling
Water bag
Liver Lung
