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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