Histograms –
measuring subtle
diffuse disease


Summary: Histograms are finding increasing use in characterising subtle diffuse disease, and also in summarising heterogeneous disease for example in a tumour. They enable a volume of tissue (often present in several adjacent sluices) to be characterised. Standardisation
of histogram generation usually improves multicentre agreement, and is
easy to carry out^{1}.
Several factors should be controlled. Segmentation should use a
reproducible technique. Bin width should be small enough to capture
structure, yet large enough to have enough voxels in each bin. For whole brain histograms a bin width of
about 1/100 of the fullwidth half maximum works well (i.e. 0.3pu for an Histograms of Gd enhancement in benign gliomas were able to predict malignant transformation^{3}. Multiplying the area of the tail of the histogram by tumour volume (to give an absolute volume of enhancing tissue in ml) gave improved prediction. Feature extraction from histograms can include simple ones (such as mean, median, 10^{th} or 90^{th} percentiles, and area under left or right hand tails beyond a certain threshold). PCA^{4,5} gives access to an unbiased choice of features. Optimum features can be chosen on the basis of performance, using a leaveoneout analysis^{4} for best use of a limited dataset. More details are given in the book chapter^{6} 

references 

1 
histogram standardisation for multicentre studies:. Tofts PS,
Steens SC, Cercignani M, AdmiraalBehloul
F, Hofman PA, van Osch
MJ, Teeuwisse WM, Tozer DJ, van Waesberghe JH, Yeung
R, Barker GJ, van Buchem MA. Sources of variation in multicentre brain

2 
spike removal: Tozer DJ, Tofts PS. Removing spikes caused by quantization noise from highresolution histograms. Magn Reson Med 2003;50:649653. download pdf 
3 
prediction of malignant
transformation: Tofts PS, Benton CE, Weil RS, Tozer DJ, Altmann DR,
Jager HR, Waldman AD, Rees JH.
Quantitative analysis of wholetumor Gd
enhancement histograms predicts malignant transformation in lowgrade
gliomas. J Magn Reson Imaging 2007;25:208214. download pdf 
4 
Principle Components Analysis: Dehmeshki J, Barker GJ, Tofts PS. Classification of disease subgroup and correlation with disease severity using magnetic resonance imaging wholebrain histograms: application to magnetization transfer ratios and multiple sclerosis. IEEE Trans Med Imaging 2002;21:320331. download pdf 
5 
T_{1} histogram: Tozer DJ, Davies GR, Altmann DR, Miller DH, Tofts PS. Principal component and linear discriminant analysis of T1 histograms of white and grey matter in multiple sclerosis. Magn Reson Imaging 2006;24:793800. download pdf 
6 
book chapter: Tofts PS, Davies GR, Dehmeshki J. Histograms:
measuring subtle diffuse disease (chapter 18). In: Paul Tofts, editor.
Quantitative 
Paul Tofts May 12th 2009 qmri.org