Hierarchical structure of bone and micro-computed tomography.

Bone is highly complex, with multiple hierarchical levels of structure. Micro-CT has been able to provide much information about the properties of bone at several of these levels at the mid-range of bone's hierarchical structure, and it will continue to provide a valuable tool for further characterizing bone in various conditions and explaining mechanisms of bone failure.

The relationship between the structural and orthogonal compressive properties of trabecular bone.

In this study, cubes of trabecular bone with a wide range of structural properties were scanned on a micro-computed tomography system to produce complete three-dimensional digitizations from which morphological and architectural parameters could be measured in a nondestructive manner. The cubes were then mechanically tested in uniaxial compression in three orthogonal directions and to failure in one direction to find the orthogonal tangent elastic moduli and ultimate strengths. After testing, the cubes were weighed and ashed to determine the apparent and ash densities. A high correlation between the basic stereologic measurements was found, indicating that there is a relationship between the amount of bone and number of trabeculae in cancellous bone. Regression analysis was used to estimate the modulus and ultimate strength; these regressions accounted for 68-90% of the variance in these measures. These relationships were dependent on the metaphyseal type and donor, with the modulus also dependent on the direction of testing. This indicates that the properties of the individual trabeculae, as well as their amount and organization, may be important in predicting the mechanical properties of cancellous bone.

Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks.

Although the potential of the powerful mapping and representational capabilities of recurrent network architectures is generally recognized by the neural network research community, recurrent neural networks have not been widely used for the control of nonlinear dynamical systems, possibly due to the relative ineffectiveness of simple gradient descent training algorithms. Developments in the use of parameter-based extended Kalman filter algorithms for training recurrent networks may provide a mechanism by which these architectures will prove to be of practical value. This paper presents a decoupled extended Kalman filter (DEKF) algorithm for training of recurrent networks with special emphasis on application to control problems. We demonstrate in simulation the application of the DEKF algorithm to a series of example control problems ranging from the well-known cart-pole and bioreactor benchmark problems to an automotive subsystem, engine idle speed control. These simulations suggest that recurrent controller networks trained by Kalman filter methods can combine the traditional features of state-space controllers and observers in a homogeneous architecture for nonlinear dynamical systems, while simultaneously exhibiting less sensitivity than do purely feedforward controller networks to changes in plant parameters and measurement noise.

Evaluation of a microcomputed tomography system to study trabecular bone structure.

A new microcomputed tomography (micro-CT) system and thresholding procedure was evaluated as a tool for nondestructive analysis of trabecular bone. Images of 6-mm trabecular bone cubes acquired from the micro-CT system were compared with optical images of corresponding histologic sections to determine the accuracy of representation. The stereologic measures of bone volume fraction (PP) and trabecular plate density (PL) were used to quantify the comparisons. The results showed that the micro-CT measures of PP were not significantly different from those measured from histologic sections and therefore were very accurate. Measures of PL were different by approximately 14%, which translated into discrepancies in trabecular plate thicknesses of about 19 microns. This difference was significantly correlated to the microstructural characteristics of the specific specimen scanned. The precision of both measurements was excellent.

The direct examination of three-dimensional bone architecture in vitro by computed tomography.

We describe a new method for the direct examination of three-dimensional bone structure in vitro based on high-resolution computed tomography (CT). Unlike clinical CT, a three-dimensional reconstruction array is created directly, rather than a series of two-dimensional slices. All structural indices commonly determined from two-dimensional histologic sections can be obtained nondestructively from a large number of slices in each of three orthogonal directions. This permits a comprehensive description of structural variation within a specimen and greatly facilitates the study of structural anisotropy. A measure of three-dimensional connectivity (Euler number/tissue volume) has been determined for the first time in human cancellous bone and shown to correlate with several two-dimensional histomorphometric indices. The method has the potential for overcoming many of the limitations of current approaches to the study of bone architecture at the microscopic level.

Comparison of the trabecular and cortical tissue moduli from human iliac crests.

The purpose of this study was to design a method to produce and test mechanically microspecimens of trabecular and cortical tissue from human iliac crests, and compare their measured moduli. Rectangular beam specimens were prepared on a low-speed diamond blade saw and a miniature milling machine. The final specimen dimensions ranged from approximately 50-200 microns for base and height. The modulus of each specimen was measured using three-point bending tests across a span length of 1.04 mm and performed at a constant rate of displacement. A subset of specimens was recovered for a radiographic estimation of degree of mineralization. The results showed the mean trabecular tissue modulus of all iliac crest specimens to be 3.81 GPa, whereas cortical tissue specimens averaged 4.89 GPa. This was a significant difference according to a two-way analysis of variance that controlled for differences between donors. No strong correlations were found between modulus and mineral density. Future investigations that consider other microstructural characteristics and their contributions to modulus, and specimen size effects, are indicated.

Examination of subchondral bone architecture in experimental osteoarthritis by microscopic computed axial tomography.

Subchondral bone changes have been proposed as an early event in the pathogenesis of osteoarthritis. In this study, microscopic computed axial tomography was used to evaluate the subchondral bone structure in femoral heads from a guinea pig model of osteoarthritis. Examination of trabecular bone within the femoral head showed a highly significant increase in bone fraction in the experimental animals. This was due to the development of trabeculae that were thicker and closer together. We conclude that trabecular remodeling may be an early event in this model of osteoarthritis.

Comments, with reply, on ;Tomographic reconstruction from experimentally obtained cone-beam projections' by S. Webb, et al.

The above paper (ibid., vol.MI-6, p.67-73, 1987) purports to propose an algorithm and implementation formulas for cone-beam reconstruction. The commenters point out that the exposition of the paper is little more than a paraphrase of their own earlier work (J. Opt. Soc. Amer. A, vol.1, no.6, p.612-19, 1984). All the benefits claimed are intrinsic to the algorithm proposed and were pointed out in the commenters paper. Webb et al. also suggest the use of a modified convolution scheme previously proposed for fan-beam reconstruction. Use of this scheme does not alter the basic premise of the commenters' work and does not entitle Webb et al. to claim to have developed a new algorithm. The authors reply that their paper presents experimental results that are based on the commenters' theoretical results, which were cited in the formers' paper.

Motion of mitochondria in cultured cells quantified by analysis of digitized images.

Translational movements of mitochondria in cultured rat liver cells were characterized quantitatively by using a video camera to detect and a video digitizer-computer system to analyze fluorescent images of mitochondria stained with rhodamine 123. The centroids of the images of individual mitochondria were determined at selected time intervals and the paths followed by the mitochondria were defined by the paths of the centroids. The predominant translation motion of the mitochondria satisfied the formal conditions of a Brownian random walk for a free particle, although in several cases there was a slow drift superimposed on the random motion. The apparent diffusion coefficients were approximately 5 X 10(-12) cm2 s-1, and the drift speeds approximately 2 X 10(-3) micron s-1.