yes, that&#39;s what I&#39;m saying, you&#39;re really, really, really small numbers are basically 0&#39;s to FSL. <br><br>Statistically it should be fine to multiply the numbers by a common number.  The interpretation of the p-values should be the same, but the interpretation of the copes will be adjusted by your value of 100000.  For example, if I run this regression<br>
<br>Y=X*beta<br><br>and find that beta-hat=0.33 and then I run this regression<br><br>Y=X2*beta2<br><br>where X2=10,000*X, then beta2=3.3*10^(-6).  The p-values for both models will be equivalent.  Fire up your favorite stats program and play with the linear regression to see for yourself.  Whether or not your really small number are interpretable, is another story and that&#39;s for you to decide.  <br>
<br>Hope that helps,<br>Jeanette<br><br><div class="gmail_quote">On Wed, Oct 26, 2011 at 9:16 AM, Amandine Pelletier <span dir="ltr">&lt;<a href="mailto:[log in to unmask]"><a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind1110%26L%3DFSL%26E%3Dquoted-printable%26P%3D2749396%26B%3D--001517473782a2168004b034d17a%26T%3Dtext%252Fhtml%3B%2520charset%3DISO-8859-1%26pending%3D" target="_parent" >[log in to unmask]</a></a>&gt;</span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">Hi Jeanette,<br><br>Thanks for your answer,<br><br>Indeed, in my design, the 5th regressor corresponds to a column of 0&#39;s. But in reality, the MD values inputs are certainly very low but are not equivalent to 0. It means that, when the design is created, the values will be round off 0 ?<br>

<br>I&#39;m not sure that I understand, when I multiply my MD values by a common factor, from a statistical point of view, do you think that it&#39;s correct or not ?<br><br>Thank you very much for your time and help,<br>

<br>Amandine<br><br>But in reality, the values are not equal to 0,<div><div></div><div class="h5"><br><div class="gmail_quote">2011/10/26 Jeanette Mumford <span dir="ltr">&lt;<a href="mailto:[log in to unmask]" target="_blank"><a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind1110%26L%3DFSL%26E%3Dquoted-printable%26P%3D2749396%26B%3D--001517473782a2168004b034d17a%26T%3Dtext%252Fhtml%3B%2520charset%3DISO-8859-1%26pending%3D" target="_parent" >[log in to unmask]</a></a>&gt;</span><br>


<blockquote class="gmail_quote" style="margin:0pt 0pt 0pt 0.8ex;border-left:1px solid rgb(204, 204, 204);padding-left:1ex">Hi,<br><br>The error message you initially reported means you have a rank deficient design matrix and if you look at the design matrix you sent you&#39;ll see that FSL reads your design input for the 5th regressor as a column of 0&#39;s which clearly cannot be modeled in a linear regression.  When you multiply by 100000  the number is now large enough that it doesn&#39;t look like a column of 0&#39;s to FSL and hence the model works.  <br>



<br>I highly recommend reviewing an intro stats book for what makes designs rank deficient, as it is an easy thing to do in these fMRI models and if you get good at spotting rank deficient matrices before you go to the trouble of putting them into the FSL gui you can save yourself some time and increase your understanding of your model.<br>



<br>So, that&#39;s the explanation on the modeling side of things.  <br><font color="#888888"><br>Jeanette</font><div><div></div><div><br><br><br><div class="gmail_quote">On Wed, Oct 26, 2011 at 7:15 AM, Amandine Pelletier <span dir="ltr">&lt;<a href="mailto:[log in to unmask]" target="_blank"><a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind1110%26L%3DFSL%26E%3Dquoted-printable%26P%3D2749396%26B%3D--001517473782a2168004b034d17a%26T%3Dtext%252Fhtml%3B%2520charset%3DISO-8859-1%26pending%3D" target="_parent" >[log in to unmask]</a></a>&gt;</span> wrote:<br>



<blockquote class="gmail_quote" style="margin:0pt 0pt 0pt 0.8ex;border-left:1px solid rgb(204, 204, 204);padding-left:1ex">Hi Stephen,<br><br>Thanks for your answer.<br><br>Below, more details concerning the model used:<br>


<br><b>Design.con</b><br>
/ContrastName1     MD_values_LHippo_positive_correlation<br>/ContrastName2     MD_values_LHippo_negative_correlation<br>
/NumWaves    5<br>/NumContrasts    2<br>/PPheights        0.000000e+00    0.000000e+00<br>/RequiredEffect        -nan    -nan<br><br>/Matrix<br>0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00 <br>0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 -1.000000e+00 <br>




<br><b>Design.mat</b> <b>(column 1=group ; 2=age demeaned ; 3=gender ; 4=level of education ; 5=MD values demeaned)</b><br>/NumWaves    5<br>/NumPoints    154<br>/PPheights        1.000000e+00    1.900000e+01    1.000000e+00    2.000000e+00    0.000000e+00<br>




<br>/Matrix<br>1.000000e+00    -1.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    -4.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>




1.000000e+00    -0.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    -3.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    1.000000e+01    0.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    -0.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -4.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    -6.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    3.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    -1.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    -7.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -7.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    -1.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    -0.000000e+00    1.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    -6.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    6.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    4.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    5.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>




1.000000e+00    6.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    -6.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    -6.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    9.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    5.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    4.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -0.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -3.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>




1.000000e+00    -6.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    3.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    -1.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    7.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -7.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    6.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>




1.000000e+00    -3.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    -0.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    -7.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    -4.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    -4.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    -1.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>




1.000000e+00    -2.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    6.000000e+00    1.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    -5.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    -1.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -2.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    -5.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>




1.000000e+00    -6.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    6.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    -2.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    0.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    -3.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    -5.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    -4.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    -1.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -5.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    1.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    -1.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    -7.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>




1.000000e+00    -3.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    -2.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    -3.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    -7.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    1.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    -4.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -2.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    -6.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    1.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    -5.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    -6.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    2.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -2.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    1.200000e+01    1.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    -0.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    2.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    3.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    -6.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    -2.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    -2.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    -1.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    8.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    2.000000e+00    1.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    -3.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    1.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    7.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>




1.000000e+00    -2.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    7.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>




1.000000e+00    -5.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    -0.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    1.000000e+01    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -2.000000e+00    1.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    3.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>




1.000000e+00    -4.000000e+00    1.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    -3.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    5.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    2.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    1.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    3.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>




1.000000e+00    7.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    4.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    1.000000e+01    1.000000e+00    0.000000e+00    -0.000000e+00    <br>




1.000000e+00    8.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -0.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    -3.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    -3.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    -1.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    9.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    -3.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    1.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    3.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>




1.000000e+00    3.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    -4.000000e+00    0.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    -1.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    -3.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    3.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    -4.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>




1.000000e+00    1.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    1.000000e+01    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -2.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    -2.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    0.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    -0.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>




1.000000e+00    -5.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    7.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    8.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    -3.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    5.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    -3.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>




1.000000e+00    7.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -1.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -2.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    -5.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    -4.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>




1.000000e+00    -4.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>1.000000e+00    3.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    1.000000e+00    1.000000e+00    1.000000e+00    -0.000000e+00    <br>




1.000000e+00    -3.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    2.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    -0.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    4.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    <br>1.000000e+00    1.100000e+01    0.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    2.000000e+00    0.000000e+00    2.000000e+00    -0.000000e+00    <br>




1.000000e+00    -2.000000e+00    1.000000e+00    2.000000e+00    -0.000000e+00    <br>1.000000e+00    1.100000e+01    1.000000e+00    1.000000e+00    -0.000000e+00    <br>1.000000e+00    4.000000e+00    0.000000e+00    0.000000e+00    -0.000000e+00    <br>




1.000000e+00    -1.000000e+00    1.000000e+00    0.000000e+00    -0.000000e+00    <br>1.000000e+00    0.000000e+00    1.000000e+00    1.000000e+00    0.000000e+00    <br>1.000000e+00    -5.000000e+00    0.000000e+00    2.000000e+00    0.000000e+00    <br>




1.000000e+00    0.000000e+00    1.000000e+00    0.000000e+00    0.000000e+00    <br><br>Moreover, in a second time, I ran the same model but I have multiplied the MD values by a common factor (by 100000) in order to obtain values less lower. In this model, I didn&#39;t obtain an error message. Do you think that it&#39;s correct to process that ?<br>




<br>Thank you very much for your help,<br><font color="#888888"><br>Amandine</font><div><div></div><div><br><br><div class="gmail_quote">2011/10/26 Stephen Smith <span dir="ltr">&lt;<a href="mailto:[log in to unmask]" target="_blank"><a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind1110%26L%3DFSL%26E%3Dquoted-printable%26P%3D2749396%26B%3D--001517473782a2168004b034d17a%26T%3Dtext%252Fhtml%3B%2520charset%3DISO-8859-1%26pending%3D" target="_parent" >[log in to unmask]</a></a>&gt;</span><br>



<blockquote class="gmail_quote" style="margin:0pt 0pt 0pt 0.8ex;border-left:1px solid rgb(204, 204, 204);padding-left:1ex">
<div style="word-wrap:break-word">Hi - we would need to know more specifics about the models you used, to comment on this error message.<div>Please see Jeanette Mumford&#39;s web page for advice on modelling and demeaning.</div>




<div>Cheers.</div><div><div><div></div><div><br><div><div>On 24 Oct 2011, at 14:08, Amandine Pelletier wrote:</div><br><blockquote type="cite"><div>Dear FSL experts,<br><br>I&#39;m working on a cohort of 154 subjects, two types of scans were acquired : anatomical MRI and DTI scans.<br>




<br>I performed two TBSS analyses (with randomise=5000 permutations) :<br>1/ First analysis: MD values measured in hippocampus (values were extracted to mask of segmented hippocampus created with FIRST tool) were adjusted for age, sex, level of education in a general linear model.<br>




2/ Second analysis: Volumes of hippocampus (in the same manner, the values were extracted to mask of segmented hippocampus created with FIRST tool) were adjusted age, sex, level of education and total intracranial volume (TIV) in a general linear model.<br>




<br>However for the first analysis, when I created the design, I obtain the following error message:<br>&quot;Problem with processing the model: Warning: at least one EV is (to close to) a linear combination of the others. You probably need to alter your design. (Design matrix is rank deficient - ratio of min:max eigenvalues in SVD of matric is 0).&quot; Nevertheless, the GLM design is created. For the second analysis, I didn&#39;t obtain this following message.<br>




Has knowledge that, Age, TIV, Volumes of hippocampus and MD values of hippocampus are demeaned.<br><br>I don&#39;t understand this error message, Is it that MD values are too lower ? Can anyone help with interpreting the reason for this error message ?<br>




Is it can have consequences on my results ?<br><br>Moreover, I would like to understand why is it recommended to demean the continuous variables ?<br><br>Any suggestions or tips would be very appreciated,<br>Thanks for your time and your help.<br>




<br>Amandine<br><br></div></blockquote></div><br></div></div><div>
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<br>---------------------------------------------------------------------------<br>Stephen M. Smith, Professor of Biomedical Engineering<br>Associate Director,  Oxford University FMRIB Centre<br><br>FMRIB, JR Hospital, Headington, Oxford  OX3 9DU, UK<br>




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