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 multi-centre 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 full-width half maximum works well (i.e. 0.3pu for an MTR histogram); for tumours, which have less voxels and therefore more noisy histograms, a width of 1/20 of full-width half maximum may work better. Median smoothing can be used to smooth the histogram without removing important structure near the peak. Bin labelling should be clear (bin-centre is preferred). Appropriate y-axis scaling gives a quantity that is independent of bin width, (divide the voxel count by the total number of voxels, and the bin width, and then multiply by 100%; the histogram then has an area of 100%). Spikes at regular intervals can be caused by quantisation of signal values in the raw images used to calculate the maps (e.g. of MTR), and can be removed by adding noise to the raw images^2. 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 leave-one-out analysis^4 for best use of a limited dataset. More details are given in the book chapter^6
references
1	histogram standardisation for multi-centre studies:. Tofts PS, Steens SC, Cercignani M, Admiraal-Behloul F, Hofman PA, van Osch MJ, Teeuwisse WM, Tozer DJ, van Waesberghe JH, Yeung R, Barker GJ, van Buchem MA. Sources of variation in multi-centre brain MTR histogram studies: body-coil transmission eliminates inter-centre differences. Magn Reson Mater Phy 2006;19:209-222. download pdf
2	spike removal: Tozer DJ, Tofts PS. Removing spikes caused by quantization noise from high-resolution histograms. Magn Reson Med 2003;50:649-653. 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 whole-tumor Gd enhancement histograms predicts malignant transformation in low-grade gliomas. J Magn Reson Imaging 2007;25:208-214. 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 whole-brain histograms: application to magnetization transfer ratios and multiple sclerosis. IEEE Trans Med Imaging 2002;21:320-331. download pdf
5	T1 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;24:793-800. download pdf
6	book chapter: Tofts PS, Davies GR, Dehmeshki J. Histograms: measuring subtle diffuse disease (chapter 18). In: Paul Tofts, editor. Quantitative MRI of the brain: measuring changes caused by disease. Chichester: John Wiley, 2003: 581-610.

Paul Tofts May 12th 2009 qmri.org