Dear Dr Herrmann,

Inevitably any description in a few words runs the risk of being
incomprehensible.  There is no substitute for coming to the spm short
course which is run annually, or reading the most recent course notes:
http://www.fil.ion.ucl.ac.uk/spm/course/notes.html#notes97
or getting hold of the spm book 'Human Brain Function' by Frackowiak et al.
(Academic Press, 1997), see http://www.fil.ion.ucl.ac.uk/pubs/hbf.html.

However, I can answer some of your immediate questions.  If you look at a
design matrix in its usual format, where any contrast appears along the
top, then it is simply a graphical representation of a very large matrix,
or block of numbers.  Each of these numbers is represented on a grey scale,
white representing a value of 1, mid-grey representing a value of zero and
black representing a value of -1.

Every row in the design matrix represents a single scan.  Therefore the
vertical axis could reasonably be thought of as a time axis running
downwards, with the scanning TR as the unit of time, with the start of the
experiment at the top and the end of the experiment at the bottom.  Each
column in the design matrix represents an individual 'co-variate' or effect
which you believe may be influencing the data.  (It is worth just
mentioning that in SPM96/97, the first page of spm.ps shows the design
matrix with the axes the other way round, so that a column represents a
scan.)

These columns may be constituted in any number of ways.  Just as an
example, in a block design, with two conditions 'activation' and 'rest', in
a single subject, one of the columns might be a profile of the expected
effect of the stimulation pattern on the BOLD contrast, ie. periods of
activation and rest alternating, with activations represented with ones
(ie. shown as a white vertical line) and the rest represented with zeros
(ie. shown as a grey vertical line).  Thus, in an fMRI experiment, if there
are 10 scans per block, the top bit of the column would read (downwards) 1
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1... etc.  A more accurate way of
modelling the data might be to convolve this profile in time with the
expected haemodynamic response function, but this is a refinement.  In such
an experiment, the only other column in the design matrix might be a series
of ones to enable the program to model the baseline signal.

If an event-related design is being used, then the column is designed to
model, as accurately as possible, the effect on the BOLD signal of the
series of events.  One way to do this is to assume a particular form for
the haemodynamic response to every event (spm offers a so-called 'canonical
hrf'), and to reproduce this within the column at every point when a
particular event type is known to have occurred.  These will look like a
series of blurred white dots appearing at intervals down the column.  If
there are two types of events, there may be two columns which look like
this, and another column with a series of ones as before.

In spm96/7, there was often, at the right-hand side of the design matrix, a
series of cosine functions making a rather attractive pattern.  In many
designs this took up most of the area of the graphic representation of the
design matrix, but it is in fact the least interesting part.  It simply
seeks to model low-frequency confounds which are of no interest.  Thus the
first of these columns starts 1 1 1 1 1 ... and ends ... 0 0 0 0, and
simply models a very low frequency effect with a wavelength of twice the
total duration of the experiment (eg. a downward drift in baseline
throughout the experiment).  This will no longer be seen in spm99, where
the data is simply high-pass filtered before the design matrix is applied.

I don't know if this is any help, but I wish you the best of luck.  Getting
started with understanding spm is certainly not easy, and the short course
notes can be off-putting as they immediately use quite technical language.
Perhaps someone will write a simpler 'beginners guide' some day (I seem to
remember that there were some posted comments about this on this line a few
weeks ago),

Yours sincerely,

Richard Perry.


>Dear experts,
>
>I have just started to work with SPM and  I am still dazzeled by the
>infinte possibilities of determining a design matrix. Can anyone simply
>explain me in a few words, what exactly the design matrix shows? What do
>the diferent greylevels mean and how are they calculated ?  Do any
>manuals or documentations on the functionality of SPM exist ?
>
>Thanks in advance,
>            Stefan Herrmann


from: Dr Richard Perry,
Clinical Research Fellow, Wellcome Department of Cognitive Neurology,
Darwin Building, University College London, Gower Street, London WC1E 6BT.
Tel: 0171 504 2187;  e mail: [log in to unmask]
Pager: 04325 253 566.




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