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Magnetic Susceptometry
( Liver Iron Measurement )
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Liver Iron Measurement
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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
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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
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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
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aB
v
x
y
z
r
r
r - r
Field point
Source point
05 3V
3M(r ) r - rμ M(r )B(r) = dv -4π r - r r - r
0 aμ M(r ) = (r)B (r)
a a5 3V
3B (r ) r - r B (r )1B(r) = dv (r ) -4π r - r r - r
Magnetic susceptibility :
Theory of Magnetic Susceptometry
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Theory of Magnetic Susceptometry
Flux : c
= d l B(r) C
B(r)
Reciprocity Theorem :
a RV0
1= (r )B (r ) B (r )R
dvI
:orR ReciprocalB (r) BMagnetic flux density that the pickup coil generate in the element if energized with a current
Δv
RI
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j a j R j0
1= (r )B (r ) B (r )jR
vI
aB
v
x y
z
r
r
r - r
Pickup coil
a RV0
1= (r )B (r ) B (r )R
dvI
Theory of Magnetic Susceptometry
RI
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Theory of Magnetic Susceptometry
Fe ,(r) c m Fe Fe
36,
c
1.6 10m Femkg
Iron Concentration
mass susceptibility of Iron
Fe , RaV
0
c B (r )B (r )m Fe
R
dvI
Ra
B (r )B (r )R
SSF spatial sensitivity functionI
Susceptometry is an INVERSE problem
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Liver Iron Measurement
1- Liver ≈ 1530 cm3
2- Lung
3- Other tissues
Liver Lungs
6 60.36 10 9.032 10lung air tissue
Modeling the human body
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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
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Liver Iron Measurement
Torso Modeling
~ 17 mm
~ 50 mm
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Liver Iron Measurement
Water bag
Liver Lung
1- Homogeneous magnetizing field
2- Localized magnetizing field
Magnetizing Field
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Liver Iron Measurement
Water bag
Liver Lung
1- Homogeneous magnetizing field (Rubins coil)
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Liver Iron Measurement
Water bag
Liver Lung
2- Localized magnetizing field(Small ring coil)
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Liver Iron Measurement
Water bag
Liver Lung
1- Second order axial gradiometer
2- First order planar gradiometer
Pickup coil
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Liver Iron Measurement
Water bag
Liver Lung
1- Second order axial gradiometer
2z2
Δ BΔz
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Liver Iron Measurement
Water bag
Liver Lung
2- First order planar gradiometer
zΔBΔx
x
z
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Liver Iron Measurement
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