Geoffrey Dougherty

Measurement of thickness and density of thin structures by computed tomography: A simulation study

The limited spatial resolution of clinical CT systems causes difficulties in the measurement of the density and thickness of thin structures such as the vertebral cortical shell. We simulated the imaging process by convolving experimentally determined point spread functions with rectangular and Gaussian profiles, for various fields of view or pixel sizes and reconstruction kernels. The simulations successfully explained the reported overestimation of thickness and underestimation of density when imaging thin structures. Both effects are larger for Gaussian profiles. For the rectangular profiles, experimental estimates of thickness and density will only be accurate when the true thickness is greater than about 1.5 times (for the bone reconstruction kernel) or 2.0 times (for the standard kernel) the full width at half maximum of the point spread function (PSF) of the imaging system. For Gaussian profiles imaged by a system with a Gaussian PSF, there are straightforward analytical expressions for the overestimation of thickness and underestimation of density: and these are useful approximations to the simulations of Gaussian profiles with experimental (pseudo-Gaussian) PSFs. We have demonstrated that thresholding of the vertebral image cannot provide accurate estimates of cortical thickness and density because the appropriate threshold level requires foreknowledge of the cortical thickness. To circumvent such difficulties we suggest that the average value of the peak CT numbers measured along the medial axis of the cortical shell be adopted as an index of cortical shell strength, since its value depends on both the density and the thickness of the shell.

Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images

Fractal analysis is a method of characterizing complex shapes such as the trabecular structure of bone. Numerous algorithms for estimating fractal dimension have been described, but the Fourier power spectrum method is particularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided accurate estimates of fractal dimension for synthesized fractal images. For natural texture images fractality is limited to a range of scales, and the fractal dimension as a function of spatial frequency presents as a fractal signature. We found that the fractal signature was more successful at discriminating between these textures than either the global fractal dimension or other metrics such as the mean width and root-mean-square width of the spectral density plots. Different natural textures were also readily distinguishable using lacunarity plots, which explicitly characterize the average size and spatial organization of structural sub-units within an image. The fractal signatures of small regions of interest (32x32 pixels), computed in the frequency domain after corrections for imaging system noise and MTF, were able to characterize the texture of vertebral trabecular bone in CT images. Even small differences in texture due to acquisition slice thickness resulted in measurably different fractal signatures. These differences were also readily apparent in lacunarity plots, which indicated that a slice thickness of 1 mm or less is necessary if essential architectural information is not to be lost. Since lacunarity measures gap size and is not predicated on fractality, it may be particularly useful for characterizing the texture of trabecular bone.

A quantitative index for the measurement of the tortuosity of blood vessels

We propose a novel index for quantitating arterial tortuosity, based on second differences of the coordinates of the vessel midline. The index is independent of the magnification of the image and of sampling frequency. We have demonstrated its validity as an indicator of changes in morphology using simulated shapes. It is superior to two other putative indices based on vessel elongation and the variance of differences in the vessel midline coordinates, presented previously in the literature. The proposed index is easily generalised to three dimensions, allowing a true three-dimensional tortuosity index to be calculated from biplane angiograms or serial tomographic slices. It has a number of clinical applications. Preliminary data, using 82 aortograms from radiographic archives, showed a significant correlation between the tortuosity of the abdominal aorta and subject age (r=0.684, P<0.001). For this group, increased tortuosity was especially evident for subjects above 40 yr of age.

Quantitative CT in the measurement of bone quantity and bone quality for assessing osteoporosis

The biomechanical strength of the skeleton, and hence the risk of future fractures, depends on both the bone quantity (assessed in terms of bone mineral density) and bone quality (assessed in terms of the integrity of its internal architecture). Precise methods of measuring the calcium-equivalent density of both the trabecular and cortical components of vertebral bone using quantitative computed tomography are presented. For a group of post-menopausal Kuwaiti females, we have shown that the trabecular and cortical components are highly correlated with each other at both the L3 and L4 lumbar vertebral levels, with correlation coefficients of 0.78 and 0.74 (P < 0.0001) respectively. We have explored the anisotropic distribution of trabecular bone and considered the use of the standard deviation and the coefficient of variation of trabecular CT numbers as texture indicators and surrogate measures of bone quality. The coefficient of variation was the better texture indicator: used with bone mineral density values it successfully discriminated between two classes of patients (those with fractures and those without) with high sensitivity (> or = 89%) and specificity (> or = 82%).

Lacunarity analysis of spatial pattern in CT images of vertebral trabecular bone for assessing osteoporosis

The structural integrity of vertebral trabecular bone is determined by the continuity of its trabecular network and the size of the holes comprising its marrow space, both of which determine the apparent size of the marrow spaces in a transaxial CT image. A model-independent assessment of the trabeculation pattern was determined from the lacunarity of thresholded CT images. Using test images of lumbar vertebrae from human cadavers, acquired at different slice thicknesses, we determined that both median thresholding and local adaptive thresholding (using a 7 x 7 window) successfully segmented the grey-scale images. Lacunarity analysis indicated a multifractal nature to the images, and a range of marrow space sizes with significant structure around 14-18 mm(2). Preliminary studies of in vivo images from a clinical CT scanner indicate that lacunarity analysis can follow the pattern of bone loss in osteoporosis by monitoring the homogeneity of the marrow spaces, which is related to the connectivity of the trabecular bone network and the marrow space sizes. Although the patient sample was small, derived parameters such as the maximum deviation of the lacunarity from a neutral (fractal) model, and the maximum derivative of this deviation, seem to be sufficiently sensitive to distinguish a range of bone conditions. Our results suggest that these parameters, used with bone mineral density values, may have diagnostic value in characterizing osteoporosis and predicting fracture risk.

A comparison of the texture of computed tomography and projection radiography images of vertebral trabecular bone using fractal signature and lacunarity

The structural integrity of trabecular bone is an important factor characterizing the biomechanical strength of the vertebra, and is determined by the connectivity of the bone network and the trabeculation pattern. These can be assessed using texture measures such as the fractal signature and lacunarity from a high resolution projection radiograph. Using central sections of lumbar vertebrae we compared the results obtained from high-resolution transverse projection images with those obtained from spatially registered low-resolution images from a conventional clinical CT scanner to determine whether clinical CT data can provide useful structural information. Provided the power spectra of the CT images are corrected for image system blurring, the resulting fractal signature is similar for both modalities. Although the CT images are blurred relative to the projection images, with a consequent reduction in lacunarity, the estimated trabecular separation obtained from the lacunarity plots is similar for both modalities. This suggests that these texture measures contain essential information on trabecular microarchitecture, which is present even in low resolution CT images. Such quantitative texture measurements from CT or MRI images are potentially useful in monitoring bone strength and predicting future fracture risk.

Computerized evaluation of mammographic image quality using phantom images

A simple, quick and computerized method for quantitatively evaluating the image quality of mammography phantom images has been developed. Images of the American College of Radiology (ACR) mammographic accreditation phantoms were acquired under different X-ray techniques, scored and ranked subjectively by five expert readers, and digitized for quantitative analysis. The contrast and signal-to-noise (contrast-to-noise) ratios of the main nodule and microcalcification group were obtained accurately and reproducibly using an image processing protocol. The contrast values were successful at discriminating differences in image quality due to variations in scatter conditions (as a result of different kVps, and the presence or absence of an acrylic scatterer and/or a moving Bucky grid). They were more precise, reproducible and sensitive than the ACR score. In particular, the contrast of the main nodule was highly correlated (r(s) = 0.988: p<0.001) with the ranking of image quality by our panel of expert readers.

Effect of sub-pixel misregistration on the determination of the point spread function of a CT imaging system

The point spread function (PSF) of an imaging system provides a complete, quantitative description of its resolution. In computed tomography (CT) it can be obtained conveniently and directly from the image of a thin metal wire. However, the shape of the observed PSF is affected by arbitrary sub-pixel shifts in alignment between the wire object and the imaging raster, causing partial volume averaging. We investigated the loss of symmetry of the PSF due to this misregistration, using a thin wire at a small angle to the axis of the CT scanner. We were able to identify the optimal registration, and hence the best estimate of the PSF, from the minimum skewness of a series of images. Determination of an exact PSF is important in the imaging of structures of sub-pixel size, such as small blood vessels or trabeculae in spongy bone. The method is particularly useful for modalities with coarse rasters such as magnetic resonance imaging and nuclear medicine.

Spectral analysis of laser Doppler signals in real time using digital processing

A versatile spectrum analyser was developed to generate and display laser Doppler shift signals, and derived parameters, continuously in real time using a digital signal processing chip. A major attraction of the system is that it is entirely programmable, so that both the algorithms and the attributes of the system, such as window function and frame overlap, can be easily altered. It was used to investigate the relative merits of a variety of algorithms using a blood-flow phantom. An index based on the first moment of the Doppler power spectrum was found to be the most reliable flow indicator, with linearity extending towards a velocity of 5 mm s-1 for a blood haematocrit of 5%. The system is not limited to analysis based on the fast Fourier transform (FFT), and is suitable for non-linear techniques such as maximum entropy spectral estimation (MESE).

Quantitative indices for ranking the severity of hepatocellular carcinoma.

A method for quantifying the severity of tumour burden based on fractional affected areas, weighted by their mean attenuation values relative to normal tissue, is presented. The procedure was applied retrospectively to routine computerized tomography (CT) scans of patients with hepatocellular carcinoma, and produced severity indices that reliably followed the ranking of an expert panel.