Quantitative Estimation of Blood Velocity in T2* Susceptibility Contrast Imaging
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Quantitative Estimation of Blood Velocity in T2* Susceptibility
Contrast Imaging
N.A.Thacker, M.L.J.Scott, M.Pokric, A.Jackson.
University of Manchester, U.K.
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Net Flow
• Standard approaches for the measurement of perfusion assume no directional flow dependency.
• Can we expect this assumption to be valid?
• Can we measure net velocity and flow?
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Some Physiological Facts
1. The density of brain tissue is 1.08g/cc
2. The average brain weighs 1.4 Kg
3. Grey matter accounts for 50% of the brain
4. The total flow though the three main arteries is 750cc/min
5. Grey matter perfusion is 70cc/100g/min
6. White matter perfusion is 35cc/100g/min
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Physiological Facts
7. Fractional blood volume in grey matter is 5%
8. Fractional blood volume in white matter is 3.5%
9. Thickness of the cortex is 0.5cm.
10.Cross sectional area of the three main arteries 1sq.cm
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Relating Blood flow and volumes
• From 4 and 10 the mean velocity on the arteries must be 750/(1.0*60) = 12.5cm/s
• From 1, 5 and 7 the mean blood velocity through grey matter must be 70*1.08*20/(100*60) = 0.21 cm/s
• From 1,6 and 8 the mean blood velocity though white matter must be 35*1.08*28.6/(100*60) = 0.18 cm/s
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Contrast Velocity
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Gamma Curve
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Digital (MRI) Angiography
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New Technique
• Treats arrival of blood as a wave front.
• Arrival time estimated as time to mean within each voxel (TTM)
• Quantitative estimate of velocity.222zyx TTMTTMTTMNMTT
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Differential TTM
The net-MTT distribution peaks at a physiologically sensible value for 3mm voxels.
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Directional Velocity and Flow
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Absolute Flow vs Arterial supply for grey and white matter regions
Averaged grey matter white matter ratio 2.1.
Absolute flow estimates 30-80 ml/100g/min.
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Conclusions• There are significant directional flow processes in
the brain (>0.2cm/s).• These processes can be measured using bolus
tracking and give physiologically sensible values.• Directional flow measurement possible which is; Numerically stable. Does not require voxel input function (AIF). Independent of bolus dispersion. Statistically accurate (10%). NOT STANDARD PERFUSION.
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and Finally
• With thanks to D.Buckley, G.Parker, C.Moonen.
• Posters explaining quantitative net perfusion and TTM estimation at this conference.
• www.niac.man.ac.uk
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Statistical Model
• The effects of MTT on the observed bolus width (W) can be statistically modeled by a quadrature addition
• Question: At what resolution will MTT become un-measurable
12/)var( 22 MTTAIFw
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Statistical Imprecision in MTT• Applying error propagation and using
capillary velocities of 2mm/s , while putting SD(AIF) = 4 s and SD(W) = 0.6 s
MTT
sec 1.0 1.5 2.0 3.0 4.0 5.0
% error 2890 1280 720 320 180 120
So what are we measuring in MR perfusion?
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Cross Check on Velocity Ratios
• The blood relative velocity in arteries and the cortex should be 12.5/0.2 = 60
• From 1,2,3,7 and 9 the cross sectional area of the capillaries in the cortex must be 1400*0.5/0.5*20*1.08 = 64.8 a cross-sectional area of 1cmsq will produce relative velocities of the same ratio
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MTT vs TTP for high CBV
Flow in major vessels should be so fast that MTT is negligible !
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MTT vs TTP for all data
Perfusing tissues have the same distribution.
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MTT vs TTP for Phantom
A flow phantom constructed with physiological flow velocities shows the same distribution.
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Conclusions
• True MTT estimates from bolus broadening should be un-measurable in high resolution MR
• The range of MTT values seen is due to a dispersion process.
• A net MTT can be calculated from the spatial differential of TTP