Susceptibility-based magnetic resonance imaging
Viktor Vegh
Centre for Advanced Imaging (v.vegh@uq.edu.au)
It is now easy to see how ingenious engineering has allowed the creation of an instrument capable of imaging the human body, but how knowledge of electromagnetism can be applied to sample characterisation may be difficult to perceive.
Introduction
• Development of ultra-high field MRI instruments is enabling for the study of biological processes involved in a number of diseases and disorders affecting humans.
• We know that SNR of acquired images approximately scales with the magnetic field strength of the scanner (B0). Therefore, increased field strength scanners provide higher resolution images and/or shorter acquisition times.
Partial brain images acquired using standard sequences at 3T and 7T (Tallantyre, 2010)
• New contrast mechanisms come into play at ultra-high magnetic fields.
• Slightly magnetic materials, such as tissue, have little impact on the magnetic field at 1.5T, but at 7T produce exquisite contrast due to permeability differences across structures.
• It has been shown that around 10-fold increase in contrast between grey and white matter can be achieved by studying susceptibility variations across samples.
Frequency maps derived from susceptibility variations of the human mid-brain acquired at various fields strengths (Yao, 2009)
Introduction
Frequency maps derived from susceptibility variations of the human brain at 7T compared to magnitude images (Duyn, 2009)
Magnetic susceptibility
• Magnetic susceptibility, or simply susceptibility, is a magnetic property of materials defined through
μm =μ0μr μ0(1= χm), +
where μ is permeability and Ӽ is susceptibility (0 – free space, r – relative, m – material) and μ0 = 1.2566 x 10-6 WbA-1m-1. Materials can be classified as diamagnetic, paramagnetic and ferromagnetic. In MRI diamagnetic and paramagnetic materials are of interest, defined by having negative or positive susceptibilities corresponding to diamagnetic or paramagnetic, respectively. Therefore, the above equation states that diamagnetic materials have a smaller permeability in comparison to paramagnetic materials. Mapping of susceptibility instead of permeability allows materials to be classified in a straightforward manner by looking at the sign.
permeability:
Magnetic susceptibility
• Biologically relevant susceptibilities are small, as can be seen in the table.
• Question: Why do we care about mapping susceptibility in humans?
• An answer: MRI contrast due to proton density, longitudinal and transverse relaxation time weightings result in qualitative images. Measure of a physical parameter such as susceptibility provides a platform for quantitative analysis. Furthermore, tissue state may correlate with amount of susceptibility.
Susceptibility and magnetic field
• A magnetically susceptible object changes the magnetic field in which it is immersed
B = μm H
B = μ0 μr H
B=μ0(1 χm)+H
B=μH μχ+H 00m
B=B χ+B 0m0
B−B0 =χmB0 ∆B = χm B0
Susceptibility and T2* relaxation
• Susceptibilityvariationspersistasmagneticfield changes in an MRI experiment
• Adirectrelationshipbetweenfieldchangeand T2* exists: 1 1 γ∆B
*=+ TT2
22
• Thisequationstatesthatthedifferencebetween T2 and T2* is explained by the susceptibility effect
• In other words, T2 and T2*-weighted data are sensitive to field change and therefore susceptibility
• Question: Which of T2 or T2* is more sensitive to field change?
Susceptibility in MRI
• Field changes can be due to a number of sources: interference between grey and white matter, brain tissue and air-containing bone structures such as sinuses, auditory canals and mastoid cells.
• Effectively, magnetic susceptibility of materials results in distortion or perturbation of the static magnetic field in which imaging takes place. Because materials imaged are a heterogeneous collection of susceptibilities, the variations in susceptibility contain detail about the structure or micro- architecture of, for example, tissue. In the brain this can be seen as contrast between grey and white matter, however blood and iron implicated in many neurodegenerative diseases have distinct susceptibilities.
• Question: How does a point source of strong susceptibility (iron) creating a B0 field distortion present in the image?
(Haacke, 2009)
Local susceptibilities in MRI
• Answer: Can lead to very short T2* to the extent that signal is lost, and local distortions can occur as well.
Illustrations of gradient echo sequence acquired image weighted by susceptibility (left) and as acquired (right).
Iron in the blood
• Temporal variation in susceptibility in blood has led to the ability to map stimulated brain activity through functional MRI (fMRI). In fMRI, iron (Fe) is the source of contrast, which has large susceptibility.
• The effect is so large that standard gradient echo (T2*-weighted) sequences can be used to acquire data and magnitude signals can be analysed for susceptibility variations.
• The magnitude of the signal has not been able to adequately detail small scale spatial variations in susceptibility.
• For this purpose, mapping of field change has been important. Recall:
∆B = χm B0
Figure shows the relative signal change in the image with respect to level of blood oxygenation (Ogawa, 1990)
Susceptibility: Good or bad?
• Spatial distribution of susceptibility produces two types of signal variations:
– Macroscopic (larger than image voxels): introduced by large boundary effects such as tissue/air boundaries, and by movements such as the heart. The effect increases with an increase in echo time in the T2*-weighted acquisition
– Microscopic: (smaller or same scale as image voxels): introduced by heterogeneous magnetic susceptibility of tissue, and also by deposits of iron (Parkinson’s disease and normal ageing) and plaque (Alzheimer’s disease)
(Yang, 2006)
Macroscopic susceptibility effects
• Models have been developed for airways and sinuses (top)
• FEM-based studies have shown that air-material interfaces cause large field variations across the human head (middle)
• MRI-based field mapping measurements have confirmed simulation results
• Macroscopic field effects hinder image signals, often to the extent that large distortions and signal loss occurs near boundaries
• MRI data acquisition sequences are continually being developed to try and reduce the impact of air-material interfaces on image signals
Microscopic susceptibility effects
• Susceptibility variations induced by structures other than air-material interfaces are important to the understanding of brain structure and function
• These measurable variations can also help to provide a quantitative platform for assessing diseases and disorders
• Ideally, measures of susceptibility changes in both space and time can be insightful in the monitoring of disease progression (e.g. multiple sclerosis and Alzheimer’s disease)
Image acquired at 7T showing cortical contrast between grey and white matter due to spatial variations in susceptibility (Zhong, 2008)
A break from susceptibility
• To understand the information contained in magnetic resonance images, we need to understand signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR)
High (sharp) and low (smooth) spatial
frequencies
1.5 1 0.5 0 -0.5 -1
-1.50 1 2 3 4 5 6 Time (ms)
1.5 1 0.5 0 -0.5 -1
-1.50 1 2 3 4 5 6 Time (ms)
1.5 1 0.5 0 -0.5 -1
-1.50 1 2 3 4 5 6 Time (ms)
• Signal:
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
SNR = 37.5
• Noise:
00 2 4 6 8 10 Space (mm)
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
00 2 4 6 8 10 Space (mm)
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
00 2 4 6 8 10 Space (mm)
SNR = 7.5
• Contrast:
Amount
Amount Amount
Amount Amount Amount
Reconstruction via FT • Fourier transform and noise:
1.5 1 0.5 0 -0.5 -1
-1.50
1.5 1 0.5 0 -0.5 -1
-1.50
50 45 40 35 30
2
4
6
8
10
FT
iFT 25
20 15 10
5 00
0.01
0.02 0.03 0.04 0.05 Space
2
4
Time
6
8
10
20 15 10
5 00
0.01
0.02 0.03 0.04 0.05 Spac e
Time
FT
iFT 25
50 45 40 35 30
16/167
Amplitude
Amplitude
Magnitude
Magnitude
MRI relevance
• Gradient echo (GE) magnitude signal:
−TR−TE S=ρ 1 e −e*
TT 012
• GE contrast between voxels (A) and (B):
S −S =ρ A B
−TR −TE −TR −TE 0,A 1,A 2,A 0,B 1,B 2,B
1 eT− eT* ρ− 1 eT− eT*
SA −SB =CAB
17/167
MRI relevance • Gradient echo (GE) signal:
−TR−TE S=ρ 1 e −e*
TT 012
• GE contrast between voxels (A) and (B):
S −S =ρ A B
−TR −TE −TR −TE 0,A 1,A 2,A 0,B 1,B 2,B
1 eT− eT* ρ− 1 eT− eT*
SA −SB =CAB
18/167
MRI relevance • Gradient echo (GE) signal:
−TR−TE S=ρ 1 e −e*
TT 012
• GE contrast between voxels (A) and (B):
S −S =ρ A B
−TR −TE −TR −TE 0,A 1,A 2,A 0,B 1,B 2,B
1 eT− eT* ρ− 1 eT− eT*
SA −SB =CAB
19/167
MRI relevance
• Also, we can show that:
SNR(CAB ) = SNR(SA ) SNR(SB )−
• which means:
SNR CNR
Motivation
• B0 increase implies an increase in SNR:
B0 ∝SNR
• It does not follow that:
B0 ∝CNR
• This is because relaxation time differences
between tissue A and B decrease with an
increase in B0, and recall:
−TR −TE S −S =ρ 1 eT− eT*
−TR −TE 0,B 1,B 2,B
ρ− 1 eT− eT*
A B 0,A 1,A 2,A
SA −SB =CAB
Implications at high field
−TR −TE −TR −TE S −S =ρ 1 eT− eT* ρ− 1 eT− eT*
A B 0,A 1,A 2,A 0,B 1,B 2,B
• Question: What happens when proton densities and longitudinal relaxation times are approximately the same for two tissues?
• Answer: CNR dominated by contrast due to T2*
• Interestingly, the level of T2* contrast can be
manipulated by changing TE (see equation above) • However, T2* is a function of field (recall):
1 1 γ∆B *=+
TT2 22
What happens at high field?
• A new contrast mechanism becomes active:
B = μH
B = μ0μr H B=μ0(1 χ)H+ B=μ0H μ0χ+H B = B 0 χ +B 0 B−B0 =χB0
∆B = χB0
• Hence, increase B0 and the induced field change (∆B) will increase also
23/167
χ is susceptibility μ is permeability
B0
B0 ↑
Effect on field
24/167
Magnitude and phase
• Let S(x,y) be a signal of any image voxel:
S(x, y) = Sreal (x, y) i Simag (x,+y) = S(x,y)eiφ(x,y)
S= S2 (x+,y) S2 (x.y),=φ tan−1Simag(x,y)
real imag
( x , y )
MAGNITUDE
S
real PHASE
(Duyn, 2007)
Phase relationship
• The GE-MRI signal has magnitude and phase
• The phase has a direct relationship with the field change:
• which implies that the field change in independent of TE
(G – constant defined by local geometry, CS – chemical shift, geometry – macroscopic effect, main field – inherent impurities)
(Barnes, 2012)
Relationships
• Phase-based measurements can be expressed in one of many ways:
∆φ=−γ∆BT → ∆B=− ∆φ (T)
ω = γ B , ω = γ B → ∆ ω = ∆γ B ( r a d / s ) 00
ω = 2π f → ∆f = − ∆φ (Hz)
E
γT E
2πT E
Purpose of filtering
• Phase filtering is the common method of removing macroscopic variations
• Question: How to depict variations due to susceptibility?
Susceptibility Weighted Imaging (SWI)
(Haacke, 2005)
(Gilbert, 2012)
30/167
Ex vivo mouse brain images
(Vegh, 2012)
Ex vivo mouse brain images
Phase evaluation issues
• Steps:
– Phase calculation – Unwrap or not?
– Image space or Fourier space filtering?
Example: Process of enhancing veins Magnitude Phase SWI
(Haacke, 2009)
New contrast (T1, SWI, HP-phase)
Haacke et al., AJNR, 2009
35/167
Vein enhancement
36/167
Traumatic brain injury (CT, T1, T2, SWI)
37/167
Traumatic brain injury (CT, SWI)
38/167
Hemorrhage (CT, SWI)
39/167
Microbleeds (T1, T2, MRA, SWI)
40/167
Acute stroke (ADC, SWI)
41/167
Multiple sclerosis (MS-SWI, cont-SWI)
42/167
MS – ringlike (T2, T1, SWI, HP-phase)
43/167
Sturge-Weber Syndrome (T1, SWI)
44/167
Calcification (SWI, CT, HP-phase)
45/167
Contrast enhanced (T1-no, T1-yes, SWI-no)
46/167
Contrast enhanced (T1-yes, SWI-no, SWI-yes)
47/167
Susceptibility relationship
• Thus far we have considered susceptibility contrast qualitatively based on phase:
• However, the induced field change can be considered as dipole sources (in k-space a multiplication is used instead of convolution):
• where C is the dipole kernel and k
defines location (Wharton,,2010)
Quantitative susceptibility mapping (QSM)
• Question: Why is it important to have quantitative values?
• QSM is a method under development
• Full potential of QSM is yet to be realized, nonetheless it is clear that it can provide valuable information in the context of clinical diagnosis and monitoring of disease progression
QSM
• Quantitative susceptibility mapping requires the solution of the inverse problem using the susceptibility dipole approximation
• Effectively, can be thought of as a method of projecting onto a dipole field
• Inherently ill-posed, requires regularization (Tikhonov) or use of priors (Bayesian statistical methods)
(Bowtell, 2010)
Bulk susceptibility versus tensor
• Tothispointwehaveconsideredsusceptibilityas a bulk measure, however it can be formulated as a tensor with 6 components:
χ11 χ12 χ13 χ=χχχ
12 22 χχχ
23 13 23 33
• wherethemeansusceptibility(MS)is: MS = χ11 + χ22 + χ33
• However,toresolvethe6unknownsofthe tensor, additional measurements are required
STI limitations • Current technology is limited by:
– directionality of the MRI scanner field, requiring that more than 10 sample rotations and associated data acquisitions are performed
– impractical imaging times
– co-registration of frames after all data has been acquired
52/91
Susceptibility tensor imaging (STI)
(Liu, 2010)
∆B
53/167
What may the future hold?
• It is clear that QSM-based methods will find utility in the study and evaluation of neurodegenerative disorders by being able to define levels of, for example, myelination
• Diffusion tensor imaging (DTI) is an existing method highly informative in studies of structural brain connectivity
– Susceptibility tensor imaging (STI) may provide information about integrity of connections
• Also, in functional MRI the use of phase may inform about partial oxygenation state and tissue viability
• Many applications of quantitative susceptibility mapping are yet to be uncovered
• A few examples are provided over the next few slides
DTI and STI fibre tracking
(Wharton, 2012)
55/91
fMRI – magnitude or phase or both?
• fMRI is normally a method based on magnitude data, however phase may provide additional detail
• Figure illustrates differences between magnitude (M) and phase (P) based analyses
(Rowe, 2005)
Feng et al., Neuroimage, 2009
57/167
Arja et al., Neuroimage, 2010
58/167