<div dir="ltr">Hi Jan,<div><br></div><div>Just to expand a little further on what Rob said, the main reason for not normalising to the b=0 signal is essentially to preserve the apparent fibre density. Really, the problem is that normalising to the b=0 signal breaks the linearity of the DWI signal to the FOD (irrespective of the log transform), and that is something we think should be avoided if at all possible. This is an issue that I wish I'd described explicitly in my original 2004 spherical deconvolution paper (even back then, all the processing was done on the raw signal)... As Rob mentioned, we'll try to rectify this is a future paper, but for now, here's a brief description of my reasons for this.</div><div><br></div><div>This is based on a fundamental aspect of spherical deconvolution and mixture models in general: that the DWI signal scales <i>linearly</i> with the amount of tissue present. While the simulations done by Dave Rafflelt in the paper Rob mentioned do make the point very nicely, their purpose is a lot more specific than is required for this argument. Basically, If a voxel contains two fibre bundles, the signal you measure is the sum of the signals for each bundle individually (at least, it's modelled as such). This however does not necessarily hold for the signal <i>attenuation</i>, since the b=0 signal is not uniform throughout the brain. </div><div><br></div><div>Consider for example voxels containing mixtures of WM & CSF. The b=0 signal for CSF is typically very high relative to WM (due to its long T2). If half the voxel contains CSF, the other half WM, the b=0 signal for that voxel would be essentially double what it would be for pure WM (assuming CSF b=0 signal is ~3x that of WM). On the other hand, the DW signal for CSF is small, and to all intents and purposes negligible at high b-values. This means the <i>raw</i> DW signal would be what you would expect to measure for a voxel containing half the volume of WM, but the signal attenuation would be halved again (since the b=0 signal is double). So the apparent relative volume fraction (fibre density) derived using signal <i>attenuation</i> would be ~a quarter that of pure WM, while using the<i> raw</i> DW signal would give you the correct answer: half that of pure WM. If you care about being able to compare apparent fibre densities across voxels in the presence of large variations in the b=0 signal between different tissue types (i.e. as you would expect in the brain), you shouldn't normalise to the b=0 image. </div><div><br></div><div>Note this isn't just about voxel-based analysis of apparent fibre density or SIFT: this is also important for example during the tractography itself, since the termination criteria are applied on the FOD amplitude directly. It is also important for anything that involves consistent scaling of the noise (e.g. bootstrap analysis), since normalising to the b=0 will also introduce large and rapid spatial variations in the noise characteristics of the data. There are many facets to this issue, and I won't bother going into them in any more detail here - I'll leave that for the future paper Rob mentioned. But in a nutshell, this is the reason MRtrix has always operated on the raw DW signal, not its attenuated version. </div><div><br></div><div>Hope this all makes sense.</div><div>Cheers,</div><div><br></div><div>Donald.</div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On 15 December 2014 at 00:32, Robert Smith <span dir="ltr"><<a href="mailto:robert.smith@florey.edu.au" target="_blank">robert.smith@florey.edu.au</a>></span> wrote:<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Hi Jan,<div><br></div><div>This is an important point, and one that we sometimes forget that we (as in, the MRtrix dev team) think about quite differently to others in Diffusion MR.</div><div>We will draw attention to this issue in an upcoming publication, but I'll try to give a succinct explanation here.</div><div><br></div><div>Conventionally, the log-transform with respect to the b=0 image converts a signal amplitude to an apparent diffusion coefficient; nothing controversial here. However if you were to then apply a spherical deconvolution transform, the FOD amplitude along a particular direction would be proportional to the ADC of the fibre population oriented along that direction. This isn't particularly useful information; it doesn't tell us much about differences between fibre populations throughout the image, or indeed within a voxel.</div><div><br></div><div>Ideally what we actually want for a number of applications is the volume of each fibre population element, in all voxels throughout the image. Based on David Raffelt's early <a href="http://www.sciencedirect.com/science/article/pii/S1053811911012092" target="_blank">simulations</a>, it turns out that (under certain conditions) the radial component of the DWI signal amplitude is actually a pretty decent marker for intra-cellular volume. Therefore, by ignoring the b=0 images completely and just running SD on the raw DWI intensities, we get pretty useful biological information and interpretation from the FOD; we also conveniently bypass the issue of Gibbs ringing in the b=0 images. Caveat is that you need a uniform B1 field (i.e. intensity bias field correction); for applications like AFD you also need inter-subject intensity normalisation, but that's not necessarily a problem for SIFT depending on how you're using it.</div><div><br></div><div>That's all for now. Hope that clarifies why we choose to apply SD in this way; in fact, this approach dates all the way back to the original SD paper.</div><div>Rob</div></div><div class="gmail_extra"><br clear="all"><div><div><div dir="ltr"><br>--<br><br><span style="color:rgb(255,102,0)"><b>Robert Smith, Ph.D</b><br>Research Officer, Imaging Division</span><br><br>The Florey Institute of Neuroscience and Mental Health<br>Melbourne Brain Centre - Austin Campus<br>245 Burgundy Street<br>Heidelberg Vic 3084<br>Ph: +61 3 9035 7128<br>Fax: +61 3 9035 7301<br><a href="http://www.florey.edu.au/" target="_blank">www.florey.edu.au</a><br></div></div></div><div><div class="h5">
<br><div class="gmail_quote">On Sat, Dec 13, 2014 at 1:37 AM, Jan Schreiber <span dir="ltr"><<a href="mailto:schreiber@cbs.mpg.de" target="_blank">schreiber@cbs.mpg.de</a>></span> wrote:<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear MRtrix Team,<br>
<br>
thank you very much for this great software and for making it freely<br>
available!<br>
<br>
In your publication "SIFT: Spherical-deconvolution informed filtering of<br>
tractograms" you state<br>
<br>
"The diffusion signal must not be normalised to the b = 0 image<br>
intensity. This preserves the linearity of the spherical deconvolution<br>
transform between the measured DW signal and the resulting FOD."<br>
<br>
Shouldn't we preserve the linearity of the spherical deconvolution<br>
transform between the FOD and the DW _signal attenuation_ rather than<br>
the DW _signal_?<br>
<br>
Thanks,<br>
Jan<br>
<br>
</blockquote></div></div></div></div>
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<br></blockquote></div><br clear="all"><div><br></div>-- <br><div class="gmail_signature"><div dir="ltr"><b><font color="#990000">Dr J-Donald Tournier (PhD)</font></b><br><div><font color="#990000"><br></font></div><i><font color="#990000">Senior Lecturer, </font></i><i><font color="#990000">Biomedical Engineering</font></i><div><i><font color="#990000">Division of Imaging Sciences & Biomedical Engineering<br>King's College London</font></i><div><i><font color="#990000"><br></font></i></div><div><i><font color="#990000"><b style="font-family:Calibri,sans-serif;font-size:15px"><span style="font-size:10pt">A:</span></b><span style="font-family:Calibri,sans-serif;font-size:10pt"> Department of Perinatal Imaging & Health, 1<sup>st</sup> Floor South Wing, St Thomas' Hospital, London. SE1 7EH</span><br></font></i></div><div><i><font color="#990000"><b>T:</b> +44 (0)20 7188 7118 ext 53613</font></i></div></div><div><i><font color="#990000"><b>W:</b> <a href="http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering" target="_blank">http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering</a></font></i><br></div></div></div>
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