[Mristudio-users] The b matrix

[susumu]

Hi Darshan,

If we assume one tensor (one fiber population) in each pixel, b-value of 700
- 1,500 should provide similar results. 

If b-value is small, the image intensity is high, echo time shorter, less
motion sensitive, and less eddy current. The downside is, you have less
signal attenuation and determination of the slope (=D = proportional to
Log(S/S0)) becomes unstable. For example, if there is only 5-10% expected
signal loss while there is +/- 5% signal fluctuation by SNR, you have a
problem.

When b is higher than 1,000, you expect more than 50% of signal attenuation
in average, which is enough to determine D, but the signal goes closer to
the noise floor and have other practical issues such as longer TE (thus
lower SNR), more motion sensitive, and eddy current. 

So too small b and too high b are not good from the SNR point of view.
Empirically, the optimum b should be somewhere around 700 - 1,500.

Here, the b - SNR relationship is the center of our interest when we use the
simple tensor model.

There are some simulation-based papers that tired to theoretically determine
the optimum b, but it is not always straightforward because the impacts of
TE/motion/eddy currents are difficult to model. Danny Alexander has the most
comprehensive simulation paper in this regard. Our internal data with actual
human data didn't show much difference between b = 750 to 1,500. Start to
see problems with b-values lower than 500 and more than 2,000 .

If you are interested in more than one tensor in each pixel, there is a
totally different factor. First of all, the decay is not mono-exponential.
An interesting feature of exponential decay is, if you want to differentiate
bi-exponential and mono-exponential, you have to look at high-b range
because they behave identical in low-b range. In other words, everything
looks single-tensor if low b-values are used. This simulation can be seen in
Larry Frank's HARDI paper, showing two-crossing-fiber pixel looks like a
single pancake tensor, not "X" with a low b-value. The higher the b-value,
the higher the power to delineate the "X" shape accurately. The smaller the
crossing angle, the more difficult to resolve with smaller b. This is why
the original Van Wedeen paper used b = 30,000.

It is still under investigation by many researchers to figure out how much b
is needed. Some say 3,000 is enough, but it should be a function of crossing
angle, SNR, and the number of b-orientations. I don't know the answer.

I hope this helps.

Susumu




-----Original Message-----
From: mristudio-users-bounces at mristudio.org
[mailto:mristudio-users-bounces at mristudio.org] On Behalf Of darshan pai
Sent: Friday, July 18, 2008 4:46 PM
To: mristudio-users at mristudio.org
Subject: [Mristudio-users] The b matrix

Hello all,

I just had a question regarding the Weighting matrix . I have always seen
that the b value is usually set to be 1000 . Is there a specific reason to
do that . I have seen literature which suggest that having b value to 1000
is appropriate to at least resolve two fiber populations. Which means that
increasing the value should be advantageous for multiple orientations. Is
there an SNR issue to take care of at higher b values ?

Maybe the question is too basic and maybe a little too trivial . Just
curious to know

Regards
Darshan



      
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