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Imaging Science and Biomedical Engineering, University of Manchester, Stopford Medical School, Oxford Road, Manchester M13 9PT, UK
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Abstract |
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Introduction |
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Many approaches to the segmentation of MR brain images have been taken. Generally these techniques aim either at classifying each pixel as a particular tissue type or at estimating the proportion of each tissue in the voxel. Since the work of Vannier et al [6], extraction of grey and white matter tissues from single images [7] has been largely superceded by the use of multispectral approaches. Use of multispectral data has the advantage of providing greater information content for the classification of individual voxels. Production of a multidimensional feature space from this multispectral data allows the application of a wide variety of cluster recognition techniques, either alone or in conjunction with physical connectivity data [8–13]. Multidimensional feature space can also be divided by automatic or manual thresholding techniques in the original or transformed feature space [14–16]. Estimates of the percentage of different tissues within a single voxel using these techniques are based on probability calculations or estimates of the distance of a pixel from the cluster centers in feature space.
Rusinek et al [17] described a method for tissue quantification in MR image analysis that has the advantage of great simplicity whilst, at the same time, taking into account partial volume effects. This technique makes use of two imaging sequences to provide three linearly independent linear equations, which relate the quantities of cerebral spinal fluid (CSF), grey matter and white matter (pc, pg and pw, respectively) for each pixel grey level g such that:
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The method used by Rusinek et al [17] relied on the use of an inversion recovery image with a long echo time (TE), chosen to minimize the signal from grey and white matter. The inversion time (TI) was chosen to place signal from grey and white matter pixels equidistant from zero so that the average proportion of tissue P within a volume generates a contribution to the average grey level PgG1g+PwG1w, which averages out to zero. The average value of G1 within the volume can then be used directly to estimate Pc.
Given this value and the other two equations, it is simple to estimate Pc and Pw within the volume of V voxels v:
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This mathematical approach to segmentation has several potential advantages. First, it is methodologically simple to implement and, since calculations can be performed on whole regions of interest (ROIs) rather than single pixels, it can be used to estimate tissue volumes from any standard clinical image display console. Second, it does not rely on accurate classification of the tissue type within the region but actually calculates the partial volume of each tissue included. However, the technique also has a number of potential disadvantages. First, the use of linear equations to provide a segmentation solution assumes the presence of three pure tissue types. The presence of a significant volume of tissue with other characteristics, such as diffuse signal abnormality in the white matter, will lead to unavoidable errors in the volume estimates. Second, the original method was described using two standard inversion recovery sequences, which constrained the number of images that could be generated in a clinically acceptable time. This resulted in the use of thick, 10 mm axial slices to enable coverage of the whole brain. Although the technique specifically allows for partial voluming effects between brain tissues, use of thick slices introduces the risk of partial volume effects from other cranial tissues, which will introduce inaccuracy. More importantly, use of thick slices restricts the accuracy with which small ROIs can be defined.
In current practice, typical studies of brain morphology exploit the developments in gradient performance and fast image acquisition techniques to generate high spatial resolution data sets. A typical brain image will consist of at least 50, 3 mm thick images with an inplane resolution of less than 1 mm. Volume acquisition techniques can result in even higher spatial resolution and we routinely obtain T1 weighted volume data with isotropic voxels less than 1 mm in size. Although these images improve the accuracy with which anatomical structures can be identified in the data block, they result in significant changes in the properties of the image both in terms of signal-to-noise ratio (SNR) and also as a result of the fast image acquisition techniques employed.
This study is designed to examine the problems associated with the use of a mathematical segmentation technique when applied to high resolution data sets. The study has three main aims. First, to examine the implications of using fast spin echo techniques in place of the original standard inversion recovery images. Second, to determine whether the method can be applied to other pairs of images. And third, to determine the level of statistical accuracy that can be expected from different image combinations.
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Methods |
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and N(H) is the number of protons.
When this is plotted as a function of T1 there is a point at which the signal for grey and white matter have equal and opposite values. This is the point selected by Rusinek et al [17] for their first imaging sequence. The expression for brain tissue signal intensity in an inversion recovery fast spin echo sequence (IR-FSE) is:
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MR scanning
Scans were performed in three normal male volunteers. All scanning was performed on a 1.5 T Philips Gyroscan ACS NT scanner (Philips, Reigate, UK) using a birdcage head coil. In two volunteers the effects of variations in TI on the mean signal intensity of grey matter, white matter and CSF were examined using an IR-FSE sequence (TR 6650 ms; TE 100 ms; TI 450–550 ms; echo train length 6).
In the remaining volunteer, imaging data were acquired using a range of scanning techniques. Scan parameters are shown in Table 1
. All scans were acquired using the same geometric parameters (field of view 230 mm2; matrix 256x256; slice thickness 2.7 mm, interslice gap 0.3 mm; number of slices 40). The scanning sequence consisted of (A) IR-FSE sequence designed to produce cancellation of grey and white matter signal as described above; (B) IR-FSE with similar grey white matter contrast characteristics to image 2 in the original Rusinek technique [17]; (C) IR-FSE with increased SNR and grey/white matter contrast; (D) a variable echo (VE) sequence producing proton density (PD); (E) T2 weighted images such as commonly used in clinical practice; (F) a FLAIR-FSE sequence designed to null CSF signal but using an intermediate TR to minimize flow artefacts; and (G) a FSE sequence with a long TR and TE designed to maximize signal from CSF and minimize signal from brain.
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These equations revert to the original solution if we make the assumption that G1g=G1w=0. Once again these equations are based on the property of linear additivity of tissue to the image signal, which follows from the Bloch equations for a wide variety of imaging sequences. As this solution takes no account of the noise process during image formation, it is possible for these solutions to take non-physical values, i.e. Pi<0 or Pi>1. These numbers cannot therefore be interpreted directly as probabilities, although they are unbiased estimates of tissue proportion. This is the correct solution for any pair of MR images for which the grey levels are linearly independent and can be used on any pair of images that fulfil this constraint. This is true of all MR images so that we are free to select any pair of images to maximize the statistical accuracy of partial volume estimations.
Measurement of pure tissue signal intensities
Mathematical segmentation requires estimates of mean grey matter, white matter and CSF grey level values. The approach suggested in the original work was the manual identification of ROIs. However, this technique can give systematic differences across the brain depending on which specific region is chosen. These effects were investigated by measuring interobserver and intraobserver repeatability on a series of standard images obtained using scanning sequences A, B and C (Table 1
). Idealized measures of grey and white matter mean values were made by three observers using two techniques. The first technique was to identify the mean intensity based on a manually defined ROI placed in the cortical grey or deep white matter, performed on each image type of each case. The second technique consisted of interactively windowing the image to identify narrow grey scale windows, which isolated the cortical grey and deep white matter, respectively. The mean greyscale value for the tissue was then taken as the window level, performed on each image type of each case.
In addition, we have developed an automatic technique that estimates an average result for one slice. The method is based on the observation that the three tissues we wish to label produce a characteristic histogram of image values, composed of pure tissue and mixed tissue contributions. The pure tissue contribution appears to be well modelled by Gaussian peaks, with a width determined by the random noise present in the image. The mixed tissues are due to partial volume effects within a voxel. On average, the particular placement of a partial volume boundary must be a random process, as the boundaries of the voxels do not relate to the positioning of a patient under the scanner or to the structure of the brain. If we make the assumption that there is a uniform probability of producing a particular partial volume owing to the random placement of a tissue boundary within a voxel, the linear dependency of the measured grey levels on tissue volume predicts a rectangular distribution of grey levels between pure tissue peaks. This distribution must be convolved with the same measurement error as the pure tissue peaks. In practice, this distribution seems to be correct to within 10% of the mean value. On this basis, we can define a simple composite model for the expected distribution of grey levels from any region containing only the three tissues of interest. This can then be fitted to the data to extract mean values for pure tissue values and a direct estimate of image noise. When applied to a rectangular region enclosing the majority of the brain, we have found these estimates to be very reliable, with a root-mean-square (rms) repeatability of 10% and 40% of the estimated image noise for white matter and grey matter, respectively.
Predictions of statistical accuracy
The process of MR image formation contains several factors that can be modelled in a series of stages. The Bloch equations establish mean grey level values for particular tissues. Partial volume effects are modelled linearly, as in the assumptions for the derivation of the method described above. Finally, there is the process of noise that perturbs the grey level values away from their nominal values. For the purpose of the following analysis, we assume that the noise source can be modelled as the expected linearly weighted means plus a uniform measurement noise. This can be observed to be generally true for a wide range of MR image sequences. Thus, the grey level that we observe in an image i is given by:
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i We can compute the expected accuracy on the calculation of Pcv using these numbers. Assuming that the mean grey level values are much more accurate than individual pixel measurements, it is possible to estimate the expected accuracy 
of per-pixel partial volume measurements using the established methods for covariance propagation described and validated by Haralick [18, 19].
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To allow predictions of segmentation accuracy, estimates of image noise were extracted directly from the histogram fitting procedure described above. Calculation of expected values for gv and wv were performed for all possible image combinations from Volunteer 3.
Calculation of segmentation accuracy from images
The predictions of segmentation accuracy were tested using two image pairs (Table 1, scans A–D). The first pair conformed to the technique as originally described and consisted of two IR-FSE sequences (Figures 1A, B). The first of these was designed to minimize the contribution to signal from grey and white matter and to place them on the image intensity scale so that they are equal in magnitude but of opposite sign. The second image was designed to produce high contrast between grey and white matter. The second pair of images was chosen on the basis of calculations of statistical accuracy described above.
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cv, gv and wv (Equations 14–16) shows that the best noise performance will be obtained when the numerator is as large as possible. Whilst the choice of signal intensities in the original technique reduces the negative term to zero, we can actually improve on this by inverting the order of Gw and Gg. One image type that fulfils this requirement is produced by the FLAIR sequence. The suppression of CSF signal in FLAIR images means that CSF has the lowest signal intensity and grey matter has the highest. The second pair of images therefore consisted of a FLAIR-FSE and IR-FSE pair (Figures 1C, D; scans C and F in Table 1).
Nominal tissue values were obtained by curve fitting the histograms of pixel intensity as described above. The image data were processed on a pixel-by-pixel basis using the new segmentation equations (Equations 11–13). Pixel-level probability maps were then produced masked in the area of the brain (Figure 2). Using these images, the effects of accuracy improvements were visualized by direct comparison of the probability images. Quantification of the segmentation bias in the original solution was calculated by setting the assumed intensity values for grey and white matter equal to the average value.
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Results |
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; Table 2).
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0.966) or interobserver (0.952) differences. Greyscale levels for individual tissues showed no significant differences within individual imaging sequences. Grey level values for grey matter were consistently higher on thresholding estimations for all observers by approximately 1.5% of the mean greyscale value, although this failed to reach significance.
Estimates of grey level values for the three tissues as well as the estimate of rms noise are shown in Table 2. Calculated estimates of the per-pixel partial volume measurements for grey and white matter are shown in Table 3. The lowest predicted error values for grey matter (gv=0.11) and white matter (wv=0.10) resulted from a combination of FLAIR-FSE with an IR-FSE sequence (images F and C, Table 1). These errors compared with gv=0.26 and wv=0.23 when using scans A and B, which have the original image properties described above.
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3) demonstrated bias that was bimodal due to the systematic dependency on tissue type, which has a typical value of 4% (Figure 3).
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) with those calculated from images C and F (Figure 2) clearly demonstrates the improvement in stability of the tissue density estimation with the second image pair. A subtraction of corresponding tissue density maps from these two data sets shows that these estimates are consistent except for the improvement in statistical noise. |
Discussion |
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The mathematical segmentation technique represents a generic approach to multispectral segmentation that has significant differences from the various cluster analysis techniques. The method relies on the concept that pure tissues contribute to signal intensity in a linear manner and that these contributions are additive where partial volume effects occur. This approach has a number of significant advantages. First, the calculation of partial volume contributions is made directly rather than as an estimation on the basis of cluster distributions. This means that the technique can be applied to any ROI without the requirement to produce pixel-by-pixel estimates of pure tissue content. This in turn makes the technique so computationally simple that the grey matter, white matter and CSF content of any region can be calculated from any clinical imaging workstation using a pocket calculator. Second, the statistical behaviour of the MR data and, in particular, the contribution made to the segmentation by image noise, means that the accuracy of the tissue volume estimates will increase with the square root of the number of pixels.
The mathematical segmentation technique as originally described was restricted in a number of significant ways [17]. First, the reliance on an imaging sequence that provides cancellation of grey and white matter signal was highly restrictive in the design of imaging studies. The use of an inversion recovery sequence with a long TR and TI produced the required imaging features at the expense of increased imaging noise and long image acquisition times. Indeed, the acquisition time required was reduced in the original study by the use of an image with a lower inplane spatial resolution than the image with which it was paired for analysis. In addition, the assumption of cancellation is of course a simplification and gives rise to systematic bias in the estimates of grey and white matter components, as shown in Figure 3. Fortunately, we have shown the requirement for a sequence that provides grey/white matter signal cancellation is removed if the full solution of the linear equations is used. This removes the measurement bias in the estimation of grey and white matter volumes and has the considerable advantage of allowing the technique to be used with any co-registered pair of MR images. The form of the equations for proportional tissue content (Equations 11–13) shows that the greatest accuracy would be predicted if the order of grey level signal intensities for pure tissues in the two images were reversed. This is supported in both calculated predictions and in measurements of segmentation accuracy (Table 2; Figure 2) using a FLAIR-FSE image compared with standard sequences. Indeed, we have shown that the segmentation accuracy achieved using images with the characteristics described by Rusinek et al [17] (gv=0.26, wv=0.23) can almost be matched by a conventional VE pair (gv=0.35, wv=0.29) and can be significantly improved by the use of other specifically chosen images. The combination of an IR-FSE sequence (image C) with high grey/white matter contrast and good signal-to-noise characteristics with either a FLAIR-FSE (gv=0.11, wv=0.10) or long TR, long TE, gradient echo sequence (image G, gv=0.14, wv=0.14) produces an effective doubling of segmentation accuracy. The contribution of region volume to segmentation accuracy further improves estimates of gv and wv in a predictable way (Equation 17). This sample size effect means that a 10x10x1 pixel ROI (sample volume <0.25 cm3) from a pair of images using sequences C and F (Table 1) would produce gv and wv = 0.01, representing a segmentation accuracy of 1% for both grey and white matter.
The technique can be used to produce true segmentation maps in which the pixel signal intensity directly represents the proportion of the voxel composed of a specific tissue. These segmentation images differ from those generated by probabilistic techniques, since the partial volume estimate represents a directly calculated tissue fraction rather than a regional probability estimate (Figure 2).
The modified mathematical segmentation technique we have described offers a computationally simple alternative to cluster identification techniques for tissue classification based on multispectral data sets. The benefits of the technique make it applicable to studies of aging and atrophic brain disease and for the calculation of segmentation maps to provide partial volume corrections for images from other modalities such as PET or SPECT. There are, however, a number of significant limitations that must be appreciated if the technique is to be employed. First, the presence of more than three tissues will invalidate the technique. This is a particular problem in the presence of widespread areas of signal change such as are seen in leukoiarosis or demyelination. Second, the accuracy of the technique is dependent on the measurement of signal intensities for pure tissue. This can be particularly problematic in grey matter, where the proportion of pixels around the thin cortical mantle that contain significant proportions of white matter or CSF will be high. Furthermore, the proportion of grey matter pixels containing white matter or CSF will increase as grey matter atrophy progresses. In the current study, and in the original study of Rusinek et al [17], use of ROI measurements was shown to provide repeatable measures of pure tissue values. ROI measures and use of interactive windowing as a method for identifying mean tissue values are simple and quick to perform on most standard clinical workstations. Use of a windowing method allows visualization of the selected grey level across the entire image, thus avoiding errors due to ROI placement or small sample size. The histogram fitting technique that we have used in our estimation of segmentation accuracy offers an automated and reproducible method for the estimation of mean tissue values but does require that images be transferred to an independent workstation for analysis.
In conclusion, we have described a mathematical segmentation technique for use with paired MR images. The technique allows accurate measurement of grey matter, white matter and CSF volumes within a ROI. Although the technique can be used on any image pair, the predicted accuracy will be highest when one image has a high grey/white matter contrast and the other has a minimal difference between grey and white matter intensity or has the order of pure tissue intensities reversed. The technique can be used to calculate directly the volume of tissues within the ROI or can be applied on a pixel-by-pixel basis to produce maps of tissue distribution, which include a directly calculated estimate of partial volume contributions.
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Acknowledgments |
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Received for publication June 20, 2000. Revision received October 16, 2000. Accepted for publication October 20, 2000.
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This article has been cited by other articles:
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  N A Thacker, D C Williamson, and M Pokric Voxel based analysis of tissue volume from MRI data Br. J. Radiol., December 1, 2004; 77(suppl_2): S114 - S125. [Abstract] [Full Text] [PDF]
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