Extracting data from messy text file

It's just a repetitive application of textscan...

fmt1='Time       [T] %f';
fmt2='Area    [V] %f %f %f Volume  [V] %f %f %f';
fid=fopen('Data.txt');
% read first set as has unique number header lines
time=cell2mat(textscan(fid, fmt1,'headerlines',10));  % 1st time value
data=cell2mat(textscan(fid, fmt2, ...
              'headerlines',3,'collectoutput',true,'delimiter','\n'))
% and second also has unique number to skip...
time=[time; cell2mat(textscan(fid, fmt1,'headerlines',5))];
data=[data; cell2mat(textscan(fid, fmt2, 'headerlines',3, ...
                     'collectoutput',true,'delimiter','\n'))];
while ~feof(fid)
  time=[time; cell2mat(textscan(fid, fmt1,'headerlines',7))];
  data=[data; cell2mat(textscan(fid, fmt2, 'headerlines',3, ...
                        'collectoutput',true,'delimiter','\n'))];
end
fid=fclose(fid);

At the end you'll have a Nx1 vector of time and Nx6 of volumes and areas. You could either concatenate time and data into one array or separate out A and V based on the columns in data; your choice.

At the command line the above gives me

>> [time data]
ans =
 1.0e+04 *
       0    1.7221    1.6475    0.0746    0.0995    0.0987    0.0009
  0.1054    1.7221    1.6475    0.0746    0.1089    0.1081    0.0008
  0.2108    1.7221    1.6475    0.0746    0.1102    0.1093    0.0008
  0.3162    1.7221    1.6475    0.0746    0.1111    0.1103    0.0008
  0.4216    1.7221    1.6475    0.0746    0.1118    0.1110    0.0008
  0.5270    1.7221    1.6475    0.0746    0.1124    0.1116    0.0008
  0.6324    1.7221    1.6475    0.0746    0.1129    0.1120    0.0008
  0.7379    1.7221    1.6475    0.0746    0.1134    0.1126    0.0008
  0.8433    1.7221    1.6475    0.0746    0.1139    0.1130    0.0008
  ...