Precision of magnetic resonance velocity and acceleration measurements: theoretical issues and phantom experiments.

Magnetic resonance (MR) sequences have been developed for acquiring multiple components of velocity and/or acceleration in a reasonable time and with a single acquisition. They have many parameters that influence the precision of measurements: NS, the number of flow-encoding steps; NEX, the number of signal accumulations; and ND, the number of dimensions. Our aims were to establish a general relationship revealing the precision of these measurements as a function of NS, ND, and NEX and to validate it by experiments using phantoms. Previous work on precision has been restricted to two-step (NS = 2) or 1D (ND = 1) MR velocity measurements. We describe a comprehensive approach that encompasses both multistep and multidimensional strategies. Our theoretical formula gives the precision of velocity and acceleration measurements. It was validated experimentally with measurements on a rotating disk phantom. This phantom was much easier to handle than fluid-based phantoms. It could be used to assess both velocity and acceleration sequences and provided accurate and precise assessments over a wide, adjustable range of values within a single experiment. Increasing each of the three parameters, NS, ND, and NEX, improves the precision but makes the acquisition time longer. However, if only one parameter is to be assessed, maximizing the number of steps (NS) is the most efficient way of improving the precision of measurements; if several parameters are of interest, they should be measured simultaneously. By contrast, increasing the number of signals accumulated (NEX) is the least efficient strategy.

High-contrast resolution of CT images for bone structure analysis.

The modulation transfer function (MTF) of an imaging system may be used as a figure of merit to assess its geometrical resolution. As such it is often derived from the point spread function (PSF) through a Fourier transformation, or through a FFT in case of digital images. Using the special features of the convolution-backprojection algorithm and making some simplifying assumptions about the number of rays, it is shown that the desired MTF is also obtainable without a Fourier transformation of the PSF, different shapes and sizes of the beam-profile are then analyzed, and finally it is shown that calculated and measured MTF functions are in good agreement. The effects of aliasing on the cutoff frequency are also discussed.

Differential effects of aging and disease on trabecular and compact bone density of the radius.

We constructed a special purpose CT system to get a spatial resolution of 0.2 mm and developed a procedure for the precise determination of trabecular and compact bone density (TBD and CBD) in the radius. Seven groups of healthy females and patients were measured to explore differential effects on compact and trabecular bone. In healthy females CBD remains constant within 0.2% from age 20 to 70. TBD measured in the same individuals is reduced by 50%. The scatter of the individual CBD values is 1.5% only, that of TBD 20%. Longitudinal examinations of corticosteroid treated asthmatics during one year showed a loss of TBD of 4.8%. During the same period CBD remained completely stable. In other diseases such as hyperparathyroidism CBD is reduced as well. This study showed the feasibility of a noninvasive determination of the density of compact bone and demonstrated that density loss of compact and trabecular bone is considerably different.

Cancellous bone structure: analysis of high-resolution CT images with the run-length method.

Quantitative computed tomography is extensively used to assess bone density; its potential to quantify bone structure, however, remains to be explored. In this work we present the modifications of the run-length method necessary to enable an analysis of the trabecular bone structure at the distal radius and the distal tibia. Furthermore, the close relationship between histomorphometric values and the run-length parameters is shown. The procedure may be regarded as a noninvasive, reproducible biopsy. For an adequate analysis, high resolution CT images are required. To obtain such images, we modified a special purpose CT system and achieved a high contrast resolution of 0.25 mm. The procedure was applied to groups of normal volunteers and osteoporotic patients, and the results are interpreted with the help of simple two- and three-dimensional models of the trabecular architecture.