General Questions Regarding Distribution of B Values for Grid scheme Converted to q Space

[William McCuddy]

Hello Frank, 

The Philips research team put together a DTI sequence based on your 256-grid scheme converted to q space. A summary of the b value sampling in the sequence they provided is below. I understand that there is no need to oversample at the low b-values, but was curious about the outliers b=2560, b=1920, and b=1280 with so few samples. Is this problematic?

A summary of the primary (abs) vector orientations:
Left: 0, Right: 108, Up: 53, Down: 30, Front: 35, Back: 30

Assuming my python script is correct, I suppose the lack of left pointing vectors is due to the bipolar acquisition scheme needed to correct for eddy current distortions at the sequence level  because post-processing correction requires a higher number of samples per b-value. 

So really, the actual directions would be:
Left: 54, Right: 54, Up: 53, Down: 30, Front: 35, Back: 30

Is this correct?

I might be oversimplifying things too much, but with these assumptions it seems that the acquisition should be left to right and not anterior to to posterior; however I know that is not the case.  

Am I missing something?

python script:

import numpy as np

# List of vectors [excluding B0]

vectors = np.array([

[0.8, -0.6, 0],

[0.8, 0, 0],

#...other vectors

[0.8, 0, -0.6],

])

# Initialize counters for each direction

left = right = up = down = front = back = 0

# Loop through the list of vectors

for vec in vectors:

    x, y, z = vec

    # Check the primary direction of the vector

    primary_direction = np.argmax(np.abs(vec))

    if primary_direction == 0:  # x-axis

        if x > 0:

            right += 1

        elif x < 0:

            left += 1

    elif primary_direction == 1:  # y-axis

        if y > 0:

            up += 1

        elif y < 0:

            down += 1

    elif primary_direction == 2:  # z-axis

        if z > 0:

            front += 1

        elif z < 0:

            back += 1

# Display the results

print(f"Left: {left}, Right: {right}, Up: {up}, Down: {down}, Front: {front}, Back: {back}")

[Frank Yeh]

The Philips research team put together a DTI sequence based on your 256-grid scheme converted to q space. A summary of the b value sampling in the sequence they provided is below. I understand that there is no need to oversample at the low b-values, but was curious about the outliers b=2560, b=1920, and b=1280 with so few samples. Is this problematic?

The grid points distribution is very different from shell-based. The low samplings at certain b values are entirely okay.

 

So really, the actual directions would be:
Left: 54, Right: 54, Up: 53, Down: 30, Front: 35, Back: 30

Is this correct?

It is hard to tell based on these numbers. I would plot the q-space sampling points in a 3D view to see if there is any potential issue. 

I might be oversimplifying things too much, but with these assumptions it seems that the acquisition should be left to right and not anterior to to posterior; however I know that is not the case.  

It does not matter, because the q-space signals are assumed to be symmetric w.r.t. the origin.

 

[William McCuddy]

Thanks for your response. 3D plots below. Many more L-R directions (green lines) and no -x values. 

The reason I'm looking into this is because I will likely need to shorten the scan time by removing some directions and/or B values and/or n number of samples for particular B values and I want to keep results as similar to the 258 dir acquisition as possible.

I noticed provide a 101 dir table here but it does not contain the b-values. So I'm trying to work out the best way to assign specific B-values to each of the 101 directions. I assume it is not random?

Travis

[Frank Yeh]

This is half sphere acquisition. Here needs to plot its corresponding full sphere:

For each sample 'q', the plot needs to duplicate another point at -q

This is because the DWI signal at q is assumed to be the same as -q.

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