Fractal analysis of radiographic trabecular bone texture and bone mineral density: two complementary parameters related to osteoporotic fractures.

Trabecular bone microarchitecture and bone mineral density (BMD) are two main factors related to osteoporotic fractures. Currently, however, microarchitecture is not evaluated. We have developed and validated a trabecular bone texture analysis from radiographic images. The objective was to determine if the fractal analysis of texture was able to distinguish osteoporotic fracture groups from control groups, either in vertebrae, hip, or wrist fractures, and to determine if this indicator and BMD were independent and complementary. In this cross-sectional unicenter case-control population study in postmenopausal women, 107 fracture cases were enrolled and age-matched with 197 control cases. This population comprised 40 vertebral fractures (with 70 controls), 30 hip fractures (55 controls), and 37 wrist fractures (62 controls). Hip and lumbar spine BMD were measured by double-energy X-ray absorptiometry. Fractal analysis of texture was performed on calcaneus radiographs and the result was expressed as the H parameter (H = 2-fractal dimension). The H parameter showed a lower value (0.679 +/- 0.053 SD) in fracture cases versus control cases (0.696 +/- 0.030; p = 0.007), the statistical significance persisting after adjustment for age and for lumbar spine (LS) or hip BMD. This result was confirmed in vertebral fractures (p = 0.0001) and hip fractures (p = 0.003) but not wrist fractures (p = 0.07). We determined the threshold between high and low H values and then the odds ratios (OR) of fracture for low H for BMD < or = -2.5 SD in T score and for the combinations of both parameters. The OR of fracture for low H was 1.6 (95% CI, 1.1-2.6). For LS BMD < or = -2.5 SD the OR of 6.1 (3.4-10.8) shifted to 9.0 (4.0-20.4) when we added low H and for hip BMD it shifted from 5.6 (3.3-9.4) to 8.1 (4.0-16.8). In vertebral, hip, and wrist fracture cases the results were also significant. These data have shown that the fractal analysis of texture on calcaneus radiographs can distinguish osteoporotic fracture groups from control groups. This analysis and BMD provide independent and complementary information. These data suggest that we can improve the fracture risk evaluation by adding information related to microarchitecture, derived from analysis of conventional radiographic images.

Fractal organization of trabecular bone images on calcaneus radiographs.

Bone density is not the unique factor conditioning bone strength. Trabecular bone microarchitecture also plays an important role. We have developed a fractal evaluation of trabecular bone microarchitecture on calcaneus radiographs. Fractal models may provide a single numeric evaluation (the fractal dimension) of such complex structures. Our evaluation results from an analysis of images with a varying range of gray levels, without binarization of the image. It is based on the fractional brownian motion model, or more precisely on the analysis of its increment, the fractional gaussian noise (FGN). The use of this model may be considered validated if two conditions are fulfilled: the gaussian repartition and the self-similarity of our data. The gaussian repartition of intermediate lines of these images was tested on a sample of 32,800 lines from 82 images. Following a chi-square goodness-of-fit test, it was checked in 86% of these lines for alpha = 0.01. The self-similarity was tested on 20 images by two estimators, the variance method of Pentland and the spectrum method of Fourier. Self-similarity is defined by lined-up points in a log-log plot of the FGN spectrum or of the variance as a function of the lag. We found two self-similarity areas between scales of analysis ranging from 105 to 420 microns, then above 900 microns, where linear regression produced high mean correlation coefficients (r > or = 0.97). Following this validation, we studied the reproducibility of this new technique. Intra- and interobserver reproducibility, influence of transferring the region of interest, and long-term reproducibility were assessed and given CV of 0.61 +/- 0.15, 0.68 +/- 0.47, 0.53 +/- 0.16, and 2.07 +/- 0.84%, respectively. These data have allowed us to validate the use of this fractal model by checking the fractal organization of our radiographic images analyzed by the model. The good reproducibility of successive x-rays in the same subject allows us to undertake population studies and to envisage longitudinal series.

Fractal analysis of bone X-ray tomographic microscopy projections.

Fractal analysis of bone X-ray images has received much interest recently for the diagnosis of bone disease. In this paper, we propose a fractal analysis of bone X-ray tomographic microscopy (XTM) projections. The aim of the study is to establish whether or not there is a correlation between three-dimensional (3-D) trabecular changes and two-dimensional (2-D) fractal descriptors. Using a highly collimated beam, 3-D bone X-ray tomographic images were obtained. Trabecular bone loss was simulated using a mathematical morphology method. Then, 2-D projections were generated in each of the three orthogonal directions. Finally, the model of fractional Brownian motion (fBm) was used on bone XTM 2-D projections to characterize changes in bone structure that occur during disease, such a simulation of bone loss. Results indicate that fBm is a robust texture model allowing quantification of simulations of trabecular bone changes.

Fractional brownian motion: a maximum likelihood estimator and its application to image texture.

Fractals have been shown to be useful in characterizing texture in a variety of contexts. Use of this methodology normally involves measurement of a parameter H, which is directly related to fractal dimension. In this work the basic theory of fractional Brownian motion is extended to the discrete case. It is shown that the power spectral density of such a discrete process is only approximately proportional to |f|a instead of in direct proportion as in the continuous case. An asymptotic Cramer-Rao bound is derived for the variance of an estimate of H. Subsequently, a maximum likelihood estimator (MLE) is developed to estimate H. It is shown that the variance of this estimator nearly achieves the minimum bound. A generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the MLE when the discrete fractional Brownian process is contaminated with additive Gaussian noise. The results show that even at signal-to-noise ratios of 30 dB, significant errors in estimation of H can result when noise is present. The MLE is then applied to X-ray images of the human calcaneus to demonstrate how the line-to-line formulation can be applied to the two-dimensional case. These results indicate that it has strong potential for quantifying texture.

Biomechanical properties of human os calcanei: relationships with bone density and fractal evaluation of bone microarchitecture.

The relationship between bone strength and bone mass is well established. The link between trabecular microarchitecture and biomechanical properties has been less extensively explored. To address this question, we have tested the mechanical behaviour of calcaneus bone samples and investigated the correlations between mechanical properties on the one hand, bone density and fractal analysis of microarchitecture on the other hand. Mechanical properties of 43 human os calcanei were determined by uniaxial compression testing of samples from tuber calcanei. Ash density, bulk density and dual energy X-ray absorptiometry of the samples were measured. Fractal analysis of the trabecular bone on calcaneus radiographs was performed by two estimators derived from the fractional Brownian motion model. The mechanical properties of human os calcis were found to correlate with age and density measurements. Fractal parameters derived from the bone texture analysis showed weaker but significant correlations with bone strength. Fractal analysis of texture could account in part for the variations of bone strength, but in this study cannot explain better than density the mechanical properties of trabecular bone. Nevertheless, it provides a non-invasive means of assessing molecular bone microarchitecture.

Influence of catheter and arterial diameter on flow distal to an intra-aortic balloon insertion site: a theoretic examination and in vitro assessment.

Percutaneous placement of an intra-aortic balloon (IAB) through a femoral artery of a patient is associated with a risk of reduction of blood flow distal to the balloon insertion site. If this reduction is severe, it ultimately causes limb ischemia and necessitates IAB removal. Although clinicians intuitively know that larger catheters cause higher flow restrictions, very few studies have examined this situation quantitatively. The authors theoretically analyzed the insertion site geometry in relationship to the catheter diameter and other factors effecting distal flow. To verify the findings, in vitro flow tests were conducted with various IAB catheters currently available on the market, as well as their respective sheaths and hemostasis plugs. This was done using a blood analog solution in an array of polyvinyl chloride tubing sizes. Diameters of the vessel and catheter have a profound and nonlinear effect on the distal flow. For example, a 12.2 Fr catheter in a 0.187 in. vessel only allows 19.9% of normal flow, whereas a 6.1 Fr catheter in the same size vessel allows a 92.0% flow. As the catheter diameter increases, the physical resistance suddenly grows, which causes a significant drop in distal flow. These results are accurately predicted by a mathematical model that gives flow percentage results to within 15% of those measured experimentally. In general, vessels larger than 5 mm in diameter do not exhibit substantial flow reduction for most IABs with and without sheaths. In smaller vessels, however, this reduction may be significant. Sheathless insertion is extremely effective in improving distal blood flow in such a situation. Hemostasis plugs restrict the distal flow similar to respective sheaths, thus diminishing the benefits of sheathless insertion.

Successful defibrillation in water: a preliminary study.

Mild hypothermia (32-34 deg C) treatment alleviates vital organ damage after cardiac arrest. A new cooling device, the Thermosuit operates by applying of a thin layer of water directly to the body surface. Hypothermic patients may experience sequential fibrillation. Therefore, we examined whether defibrillation could be administered safely and effectively in water. A 35 kg swine was anesthetized and placed inside the Thermosuit system. This consists of a water containing surround and pumping system. Conventional AED disposable defibrillation electrodes were applied to the animal's chest. Fibrillation was created by applying a 50-volt signal to a pacing wire introduced into the heart. Following a 30-second period of fibrillation, defibrillation was attempted using Medtronic AED 1000 defibrillator. Defibrillation voltage and current were measured. There were three test cases: dry in the system, wet in the functioning system, and damp. Cooling water in the system was contaminated with saline to simulate potential conditions in clinical application. In each fibrillation-defibrillation sequence, the heart was restarted successfully; this required less than 220 joules. Only a small difference was measured in the overall defibrillation voltage and current as applied to the electrodes for the different cases. Thus, underwater defibrillation is safe and can be performed effectively.

The intraaortic balloon pump: a nonlinear digital computer model.

A computer based model for in-series cardiac assistance by intraaortic balloon pumping was developed in this study. The model, obtained from the Navier-Stokes and Continuity equations, was capable of computing pressures, volumetric flow rates and radii through the arterial system. The model was used to study the effects of a wide range of assist device timing adjustments on the benefits of ventricular assistance under conditions corresponding to those measured during animal experiments. The model was also used to study the relationship between device timing adjustments and the benefits of ventricular assistance under constant cardiovascular state conditions. Such studies are important in isolating the response of the system to assist device phasing from the response associated with system state. The results obtained in this study demonstrate that the hemodynamic response of the cardiovascular system to intraaortic balloon pumping is a sensitive function of both the state of the cardiovascular system and phasing of the assist device.

Computer analysis of external counterpulsation by use of a nonlinear mathematical model of the cardiovascular system.

A pressure system externally applied to the limbs of a patient has been proven effective in assisting circulation in animal and clinical studies. In this study a nonlinear mathematical model of the cardiovascular system is utilized to determine the effectiveness of high-frequency components in the external pressure waveform. The development of the model, the method of analysis, and the results acquired with the model are presented in this report, demonstrating its suitability for the study of external counterpulsation.

Hemodynamic effects of new intra-aortic balloon counterpulsation timing methods in patients: a multicenter evaluation.

BACKGROUND: To test whether later intra-aortic balloon pump (IABP) deflation approaching or simultaneous with left ventricular ejection would improve hemodynamics and myocardial efficiency with the use of new balloon deflation methods, 4 IABP timing techniques were evaluated in 43 patients. METHODS AND RESULTS: Later balloon deflation produced significantly greater percentage changes in mean aortic pressure (6% vs 1%), systolic pressure time index (-27% vs -20%), diastolic pressure time index (35% vs 19%), and the systolic pressure-time index/diastolic pressure-time index ratio (97% vs 51%), respectively. However, these changes increased peak systolic pressure (-15% vs -11%). Cardiac output and stroke volume indexes were not significantly altered over the 4 settings. CONCLUSIONS: These data suggest that systemic hemodynamics and myocardial efficiency may be improved by later balloon deflation approaching left ventricular ejection in comparison to conventional IABP timing.