Jonathan J. Kaufman

Computational methods for ultrasonic bone assessment

Ultrasound has been proposed as a means to noninvasively assess bone and, particularly, bone strength and fracture risk. Although there has been some success in this application, there is still much that is unknown regarding the propagation of ultrasound through bone. Because strength and fracture risk are a function of both bone mineral density and architectural structure, this study was carried out to examine how architecture and density interact in ultrasound propagation. Due to the difficulties inherent in obtaining fresh bone specimens and associated architectural and density features, simulation methods were used to explore the interactions of ultrasound with bone. A sample of calcaneal trabecular bone was scanned with micro-CT and subjected to morphological image processing (erosions and dilations) operations to obtain a total of 15 three-dimensional (3-D) data sets. Fifteen two-dimensional (2-D) slices obtained from the 3-D data sets were then analyzed to evaluate their respective architectures and densities. The architecture was characterized through the fabric feature, and the density was represented in terms of the bone volume fraction. Computer simulations of ultrasonic propagation through each of the 15 2-D bone slices were carried out, and the ultrasonic velocity and mean frequency of the received waveforms were evaluated. Results demonstrate that ultrasound propagation is affected by both density and architecture, although there was not a simple linear correlation between the relative degree of structural anisotropy with the ultrasound measurements. This study elucidates further aspects of propagation of ultrasound through bone, and demonstrates as well as the power of computational methods for ultrasound research in general and tissue and bone characterization in particular.

Relationship between plain radiographic patterns and three- dimensional trabecular architecture in the human calcaneus.

Abstract: The purpose of this study was to determine the relationship between three-dimensional (3D) trabecular structure and two-dimensional plain radiographic patterns. An in vitro cylinder of human calcaneal trabecular bone was three-dimensionally imaged by micro-CT using synchrotron radiation, at 33.4 μm resolution. The original 3D image was processed using 14 distinct sequences of morphologic operations, i.e., of dilations and erosions, to obtain a total of 15 3D models or images of calcaneal trabecular bone. These 15 models had distinct densities (volume fractions) and architectures. The 3D structure of each calcaneal model was assessed using mean intercept length (fabric), by averaging individual fabric measurements associated with each medial-lateral image slice, and determining the relative anisotropy, R3D, of the structure. A summated pattern or plain radiograph was also computed from the 3D image data for each calcaneal model. Each summated pattern was then locally thresholded, and the resulting two-dimensional (2D) binary image analyzed using the same fabric analysis as used for the 3D data. The anisotropy of the 2D summated pattern was denoted by Rx-ray. The volume fractions of the 15 models ranged from 0.08 to 0.19 with a mean of 0.14. The medial-lateral anisotropies, R3D, ranged from 1.38 to 2.54 with a mean of 1.88. The anisotropy of the 2D summated patterns, Rx-ray, ranged from 1.35 to 2.18 with a mean of 1.71. The linear correlation of the 3D trabecular architecture, R3D, with the radiographic trabecular architecture, Rx-ray, was 0.99 (p<0.0001). This study shows that the plain radiograph contains architectural information directly related to the underlying 3D structure. A well-controlled sequential reproducible plain radiograph may prove useful for monitoring changes in trabecular architecture in vivo and in identifying those individuals at increased risk of osteoporotic fracture.

Dynamic relationships of trabecular bone density, architecture, and strength in a computational model of osteopenia

A computational model was developed to study the effects of short- and long-term periods of disuse osteopenia and repair to elucidate the interrelationships between bone mass, architecture, and strength. The model is one in which the sequence of structural change events is followed in time. This temporal feature contrasts with studies of real trabecular tissue which are necessarily cross-sectional in nature and do not lend themselves to insights into the dynamic nature of the structural changes with time. In the model it was assumed that the stimulus for bone adaptation to mechanical load is the local mechanical strain rate, according to which the trabecular surfaces are differentially formed and resorbed. The effects of mechanical loading and unloading (disuse) on the cancelous bone properties were studied. The bone mass, architecture, and elastic stiffness were shown to be strongly dependent upon the period of the unloading phase, as well as the period of the reloading phase. Mechanical stiffness is demonstrated computationally to be a multivalued function of bone mass, if architecture is not accounted for. The model shows how the same value of trabecular bone mass can be associated with two or more distinct values of biomechanical stiffness. This result is the first explicit demonstration of how bone mass, architecture, and strength are related under dynamical load-bearing conditions. The results explain the empirical observation that bone mass can account for about 65% of the observed variation in bone strength, but that by incorporating measures of bony architecture into the analysis, the predictability is increased to 94%. The computational model may be used to explore the effects of different loading regimes on mass, architecture, and strength, and potentially for assistance in designing both animal and clinical bone loss studies.

Diffraction correction methods for insertion ultrasound attenuation estimation

Diffraction effects in acoustic ultrasound attenuation coefficient estimation using an insertion technique are described. The estimation error produced by diffraction is characterized as a function of distance and nominal attenuation values. Two methods for correcting for the diffraction effect, termed the theoretical diffraction correction and experimental diffraction correction techniques, respectively, are presented. Experimental validation of the two techniques, using two different sets of ultrasound measurements obtained with 1-MHz and 500-kHz transducer pairs, respectively, is also presented. Significant improvement in the accuracy of the acoustic attenuation coefficient is demonstrated for both techniques.<<ETX>>

Influence of Marrow on Ultrasonic Velocity and Attenuation in Bovine Trabecular Bone

Measurements of ultrasonic velocity and specific differential attenuation (SDA) were obtained on 24 bovine trabecular bone specimens from the femoral condyles. The measurements were obtained using two pairs of ultrasonic transducers, one with a low nominal center frequency (500 kHz) and the other pair with a high nominal center frequency (1 MHz). The ultrasonic velocity and specific differential attenuation associated with the bone samples were determined both with and without marrow, i.e., replacing the marrow with water in the pores of the trabecular bone. Significant increases (2.1% and 2.9%) in the velocity of ultrasound were observed after removal of the marrow, for the low and high frequency transducer pairs, respectively. In contrast, significant decreases (−6.5% and −8.8%) in SDA were observed after removal of the marrow, for the low and high frequency transducer pairs, respectively. The bone densities (BD) of the samples were also determined using single photon absorptiometry (SPA). Correlations between ultrasonic parameters and bone densities for samples both with and without marrow were found to be similar. For example, for the 1 MHz transducer pair, the correlation between BD and velocity was r=0.86 with marrow, and r=0.89 without marrow. This study also compared the results obtained using a contact (no water bath) technique and an insertion (with a water bath) technique of ultrasonic measurements. For the high frequency transducer pair, the correlation coefficients between the two methods were r=0.99 and r=0.93, for the velocity and specific differential attenuation, respectively. Similar results were found for the low frequency transducer pair as well. In addition, approximately equal correlations between BD and ultrasonic velocity and SDA were also found, indicating that contact and insertion measurements provide essentially equivalent information.

Gap junction impedance, tissue dielectrics and thermal noise limits for electromagnetic field bioeffects

Abstract The model presented in this study quantitatively examines the effect of gap junctions and gap junction impedance on electromagnetic field (EMF) dosimetry in a tissue target. A simple linear distributed-parameter electrical model evaluates the effect of tissue structure on the thermal threshold (signal-to-thermal-noise ratio) for detectable induced transmembrane voltage. Analysis of the angular frequency response of the array model, using a membrane impedance which includes ion binding and coupled surface chemical reaction kinetics, suggests that the frequency range, over which maximum detectable induced transmembrane voltage could be achieved, is orders of magnitude lower than that for a single cell. Gap junction impedance has negligible effect on both the frequency response and the increased transmembrane voltage due to a cell array unless its value becomes as high as that of an artificial bilayer lipid membrane. This results in a threshold for induced electric field bioeffects of approximately 10 μV cm−1 at the target site for a 1–10 mm cell array. Physiological variations in gap junction impedance appear to have little effect on this threshold. Thus, cells in gap junction contact in developing, repairing or resting state tissue structures would be expected to be able to detect significantly weaker EMF signals than isolated single cells. The lowered frequency response of a cell array reinforces the suggestion that the spectral density of the input signal should be adjusted to the bandpass of the detector pathway for dose-efficient and selective EMF bioeffects.

Diffraction effects in insertion mode estimation of ultrasonic group velocity

We describe diffraction effects in ultrasonic group velocity estimation using an insertion technique. We characterize the estimation error produced by diffraction as a function of distance and nominal velocity values. A new method termed Group Velocity Diffraction Correction (GVDC) which corrects for the diffraction effect is presented. Experimental validation of the technique is also presented using measurements made with both 1 MHz and 500 kHz ultrasonic transducer pairs. The results demonstrate that diffraction effects on ultrasonic group velocity estimation are usually small, and may often be neglected. Significant improvement, up to about 50%, in the accuracy of the group velocity estimate can however be obtained using the method described here in those cases in which higher degrees of accuracy are required.<<ETX>>

Extremely Weak AC and DC Magnetic Fields Significantly Affect Myosin Phosphorylation

Recent studies show that extremely low level electromagnetic fields (EMF) are capable of producing significant bioeffects. These effects have most often been related to the induced electric field, while the role of the magnetic component remains ambiguous. Most of the effects of weak magnetic fields have been studied by assuming that the cell membrane is the EMF target (Markov and Blank, 1988; Marino, 1988). In fact, the actual biophysical pathways involved in the coupling of weak electromagnetic fields to biological systems still remains unclear. The physical mechanisms which allow extremely low frequency and DC magnetic fields of milli- and microtesla intensity to interact with cells and to produce physiological and/or biochemical reactions is difficult to model. Nevertheless, a number of studies have recently been reported concerning the effects of weak magnetic and electromagnetic fields on calcium dependent processes and reactions. Several resonance mechanisms have been proposed by Chiabrera et al., 1985; Liboff,1985; Lednev, 1991; and Chiabrera et al., 1991. They are related to the Lorentz force effects on ion transport (cyclotron resonance) or on ion/ligand binding kinetics. Recently, a quantum approach was taken which suggests that the ion movement in a binding site is quantitized, leading to parametric resonance. It has been reported that weak AC/DC fields tuned to calcium frequencies can significantly affect Ca2+/calmodulin dependent myosin phosphorylation (Shuvalova et al., 1991). Myosin light chains are known to be capable of binding divalent cations and are phosphorylated by myosin light-chain kinase, which requires calmodulin, a calcium binding protein, to function.

A neural network approach for bone fracture healing assessment

An approach based on auscultatory percussion, a technique used by some orthopedists both for bone fracture detection and bone fracture healing assessment, is described. Low-frequency, low-intensity mechanical power, very much like the finger tap of orthopedists, is used to evaluate the vibrational response of the bone. The novel element is the data processing, which incorporates specialized preprocessing and a neural network for estimating fractured bone strength. In addition, a new mathematical model for the vibrational response of a fractured limb, which provides data to design and test the neural network processing scheme, is presented. An experimental procedure is described for acquiring real data from animal and human fractures in a form necessary for neural network input.<<ETX>>

On the sensitivity of cells and tissues to therapeutic and environmental electromagnetic fields

Abstract The question of the thermal noise threshold at biological membranes for electromagnetic field (EMF) effects is addressed. It is shown that increased EMF sensitivity occurs when cells are connected by gap junctions (short circuits) in a tissue, as compared with isolated cells. A distributed parameter (transmission line) model representing a cell array allowed the transmembrane voltage to thermal noise ratio to be evaluated. The results show that this ratio increases by a maximum factor of 103 at the ends of the cell array as array length progresses from 10 μm (single cell) to 1 mm, a physiologically relevant length for tissues other than nerves insulated with a myelin sheath. The frequency response of the cell array is always at much lower frequencies than isolated cells with significantly higher spatial amplification. This study provides a physical basis, using simple linear modelling, for demonstrating how real cells and tissues can be significantly more sensitive to weak EMF signals than commonly realized.