Let me add little more history.<div><br></div><div>Suppose you do diffusion constant measurement using X, Y, and Z gradient individually. You get three results, diffusion along X (Dx), Y (Dy), and Z (Dz).</div><div><br></div>
<div>When you image an anisotropic sample like brain, Dx, Dy, Dz are not equal.</div><div>Each of these is called "Apparent diffusion constant". They are "apparent" because depending on the gradient axis you use or the orientation of the sample, they vary.</div>
<div><br></div><div>Then people found that Dx+Dy+Dz is invariant, meaning it stays the same regardless of the sample orientation.</div><div>Dx is rotation-variant because if you use X-gradient and measure the same sample (e.g. a chunk of meat) three times with different orientations, you get different Dx values.</div>
<div><br></div><div>So, Dx+Dy+Dz is a convenient value because you don't have to worry about consistency of sample orientations. </div><div>Dx+Dy+Dz is called "Trace". In DtiStudio, we use this "Trace".</div>
<div><br></div><div>(Dx+Dy+Dz)/3 is called "Mean diffusivity"</div><div><br></div><div>Confusion arises when we start to use "Averaged diffusion constant", which also is (Dx+Dy+Dz)/3 and the same as "Mean diffusivity".</div>
<div><br></div><div>When we use the abbreviation, "ADC", it is not clear if it means "apparent diffusion constant" or "averaged diffusion constant".</div><div><br></div><div>So, you have to read the context carefully. MD is, in this sense, a better term.<br>
<br><div class="gmail_quote">On Thu, Feb 14, 2013 at 2:46 PM, Abhijit Das <span dir="ltr"><<a href="mailto:adas@kesslerfoundation.org" target="_blank">adas@kesslerfoundation.org</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div style="direction:ltr;font-size:10pt;font-family:Tahoma">Dear Venkatesh and Hangyi,<br>
You clarified a big confusion for me today. <br>
Thanks,<br>
Abhijit<br>
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<hr>
<div style="direction:ltr"><font color="#000000" face="Tahoma"><b>From:</b> <a href="mailto:mristudio-users-bounces@mristudio.org" target="_blank">mristudio-users-bounces@mristudio.org</a> [<a href="mailto:mristudio-users-bounces@mristudio.org" target="_blank">mristudio-users-bounces@mristudio.org</a>] on behalf of Hangyi Jiang [<a href="mailto:hjiang@jhmi.edu" target="_blank">hjiang@jhmi.edu</a>]<br>
<b>Sent:</b> Thursday, February 14, 2013 2:44 PM<div><div class="h5"><br>
<b>To:</b> DTI Studio, ROI Editor, DiffeoMap Questions/Support<br>
<b>Subject:</b> Re: [Mristudio-users] difference between ADC and MD<br>
</div></div></font><br>
</div><div><div class="h5">
<div></div>
<div>
<div style="direction:ltr;font-size:10pt;font-family:Tahoma"><br>
some papers may use ADC for Averaging Diffusion Coefficient (<span style="color:#1f497d">synonymously with MD</span>). We don't use it in this way, it is so easy to get confused.<br>
<br>
I cannot say it is not right to use ADC as a synonymous term of MD (language changes all the time, :) ). but in the very beginning, ADC means
<span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">apparent diffusion coefficient.<br>
<br>
best,<br>
<br>
hangyi<br>
<br>
</span><br>
<br>
<br>
<br>
<div style="font-size:16px;font-family:Times New Roman">
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<div style="direction:ltr"><font color="#000000" face="Tahoma"><b>From:</b> <a href="mailto:mristudio-users-bounces@mristudio.org" target="_blank">mristudio-users-bounces@mristudio.org</a> [<a href="mailto:mristudio-users-bounces@mristudio.org" target="_blank">mristudio-users-bounces@mristudio.org</a>] on behalf of Venkatesh Rajagopalan [<a href="mailto:VRajagopalan@kesslerfoundation.org" target="_blank">VRajagopalan@kesslerfoundation.org</a>]<br>
<b>Sent:</b> Thursday, February 14, 2013 2:27 PM<br>
<b>To:</b> 'DTI Studio, ROI Editor, DiffeoMap Questions/Support'<br>
<b>Subject:</b> Re: [Mristudio-users] difference between ADC and MD<br>
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<div></div>
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<div>
<p class="MsoNormal"><span style="color:#1f497d">Hangyi,</span></p>
<p class="MsoNormal"><span style="color:#1f497d"> </span></p>
<p class="MsoNormal"><span style="color:#1f497d">Sorry again though. In some manuscripts ADC is used synonymously with MD, so this is wrong, right?.</span></p>
<p class="MsoNormal"><span style="color:#1f497d"> </span></p>
<p class="MsoNormal"><span style="color:#1f497d">Thanks</span></p>
<p class="MsoNormal"><span style="color:#1f497d">Venkat</span></p>
<p class="MsoNormal"><span style="color:#1f497d"> </span></p>
<div>
<div style="border:none;border-top:solid #b5c4df 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> <a href="mailto:mristudio-users-bounces@mristudio.org" target="_blank">mristudio-users-bounces@mristudio.org</a> [mailto:<a href="mailto:mristudio-users-bounces@mristudio.org" target="_blank">mristudio-users-bounces@mristudio.org</a>]
<b>On Behalf Of </b>Hangyi Jiang<br>
<b>Sent:</b> Thursday, February 14, 2013 2:12 PM<br>
<b>To:</b> DTI Studio, ROI Editor, DiffeoMap Questions/Support<br>
<b>Subject:</b> Re: [Mristudio-users] difference between ADC and MD</span></p>
</div>
</div>
<p class="MsoNormal"> </p>
<div>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">hi,<br>
<br>
apparent diffusion coefficient (ADC) is a measurement for a diffusion weighted image in a specific gradient. its definition is:<br>
<br>
ADC = ln(S/S0) / (-b)<br>
here, S is the gradient weighted image, S0 is the B0 image, b is the b value.<br>
<br>
so, if a data set has 30 gradient orientations, there will be 30 ADCs. for each gradient, there will be a ADC map for this particular DW-image.<br>
<br>
<br>
mean- diffusivity is defined as the mean value of eigen values (Lamda 1-3) of the tensor ellipsoid:<br>
Mean_Diffusivity = (Lamda_1 + Lamda_2 + Lamda_3) / 3;<br>
<br>
mathematically, this is equal to the average of the diagonal elements of the tensor matrix:<br>
Mean_Diffusivity = (Dxx + Dyy + Dzz) / 3;<br>
<br>
in noise-free situation (practically, it is impossible), mean-diffusivity is also equal to the mean value of ADCs of the DWI data set.<br>
e.g. given a data set with 30 orientations, then Mean_Diffusivity = (ADC1 + ADC2 + .. ADC30) / 30;<br>
<br>
BTW: the sum of eigen-values or the sum of the diagonal elements of the tensor matrix is called TRACE:<br>
TRACE = (Lamda_1 + Lamda_2 + Lamda_3) = (Dxx + Dyy + Dzz);<br>
<br>
so, Mean_Diffusivity = TRACE/3;<br>
<br>
<br>
best,<br>
<br>
hangyi<br>
<br>
<br>
<br>
</span></p>
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<hr align="center" size="2" width="100%">
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">
<a href="mailto:mristudio-users-bounces@mristudio.org" target="_blank">mristudio-users-bounces@mristudio.org</a> [<a href="mailto:mristudio-users-bounces@mristudio.org" target="_blank">mristudio-users-bounces@mristudio.org</a>] on behalf of Venkatesh Rajagopalan [<a href="mailto:VRajagopalan@kesslerfoundation.org" target="_blank">VRajagopalan@kesslerfoundation.org</a>]<br>
<b>Sent:</b> Thursday, February 14, 2013 1:40 PM<br>
<b>To:</b> 'DTI Studio, ROI Editor, DiffeoMap Questions/Support'<br>
<b>Subject:</b> [Mristudio-users] difference between ADC and MD</span><span style="font-size:12.0pt;font-family:"Times New Roman","serif""></span></p>
</div>
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<p class="MsoNormal"><span style>Hi All,</span></p>
<p class="MsoNormal"><span style> </span></p>
<p class="MsoNormal"><span style>I very often come across apparent diffusion coefficient and mean diffusivity being measured in studies. I am wondering what is the difference between these two measures in terms of the formula used.</span></p>
<p class="MsoNormal"><span style> </span></p>
<p class="MsoNormal"><span style>Thanks</span></p>
<p class="MsoNormal"><span style>Venkat</span></p>
</div>
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