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.

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?

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

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

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

Contrast Velocity

Gamma Curve

Digital (MRI) Angiography

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

Differential TTM

The net-MTT distribution peaks at a physiologically sensible value for 3mm voxels.

Directional Velocity and Flow

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.

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.

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

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

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?

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

MTT vs TTP for high CBV

Flow in major vessels should be so fast that MTT is negligible !

MTT vs TTP for all data

Perfusing tissues have the same distribution.

MTT vs TTP for Phantom

A flow phantom constructed with physiological flow velocities shows the same distribution.

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