Brent K. Hoffmeister

ULTRASONIC DETERMINATION OF THE ANISOTROPY OF YOUNG'S MODULUS OF FIXED TENDON AND FIXED MYOCARDIUM

The linear elastic properties of a soft tissue exhibiting a unidirectional arrangement of reinforcing fibers may be described in terms of the five independent elastic stiffness coefficients C11, C13, C33, C44, and C66. In previous studies, ultrasonic measurements of these coefficients for formalin fixed specimens of bovine Achilles tendon and normal human myocardium were reported. In the present study these results are used to analyze the anisotropy of Youngs modulus of these tissues. For formalin fixed tendon a value of 1.37 GPa is obtained for Youngs modulus along the fiber axis of the tissue, and a value of 0.0706 GPa is obtained perpendicular to the fibers. For formalin fixed myocardium, values of 0.101 and 0.0311 GPa parallel and perpendicular to the fibers, respectively, are obtained. Based on the results for the angular dependence of Youngs modulus from unidirectional specimens of myocardium, a model is introduced to estimate these features for the more complicated fiber architecture of the left ventricular wall.

Effect of collagen and mineral content on the high-frequency ultrasonic properties of human cancellous bone.

Abstract: The technology surrounding ultrasonic bone assessment is evolving rapidly as investigators explore the utility of new ultrasonic parameters and different ultrasonic frequencies. This study had three main goals. The first was to perform in vitro measurements of the speed of sound (SOS) and normalized broadband ultrasonic attenuation (nBUA) in specimens of normal human cancellous bone using a 2.25 MHz broadband measurement system. The second was to explore the utility of a backscatter-based parameter called apparent integrated backscatter (AIB). The third goal was to investigate the roles that collagen and mineral content play in affecting each of these three ultrasonic parameters. This was accomplished by chemically treating the specimens to remove one or the other of these two important constituents of bone. Our results showed that in most cases SOS and nBUA correlated well (p<0.05) with bone mineral density (BMD) as measured by quantitative computed tomography (QCT). In contrast, AIB did not correlate strongly with BMD. When the specimens were demineralized, decreases were produced in SOS (19–39%) and nBUA (44–58%). Changes produced in AIB were not significant except along the superoinferior direction, in which a 12% decrease was measured. When the specimens were decollagenized, decreases were produced in SOS (10–12%). In contrast, increases were produced in both nBUA (35–77%) and AIB (14–15%). From this study we conclude that high-frequency ultrasonic measurements may yield useful information about the content and organization of both collagen and mineral in cancellous bone.

Anisotropy of Young's modulus of human tibial cortical bone

The anisotropy of Youngs modulus in human cortical bone was determined for all spatial directions by performing coordinate rotations of a 6 by 6 elastic stiffness matrix. The elastic stiffness coefficients were determined experimentally from ultrasonic velocity measurements on 96 samples of normal cortical bone removed from the right tibia of eight human cadavers. The following measured values were used for our analysis: c11=19.5 GPa, c22=20.1 GPa, c33=30.9 GPa, c44=5.72 GPa, c55=5.17 GPa, c66=4.05 GPa, c23=12.5 GPa. The remaining coefficients were determined by assuming that the specimens possessed at least an orthorhombic elastic symmetry, and further assuming that c13=c23, c12=c11–2c66. Our analysis revealed a substantial anisotropy in Youngs modulus in the plane containing the long axis of the tibia, with maxima of 20.9 GPa parallel to the long axis, and minima of 11.8 GPa perpendicular to this axis. A less pronounced anisotropy was observed in the plane perpendicular to the long axis of the tibia. To display our results for the full three-dimensional anisotropy of cortical bone, a closed surface was used to represent Youngs modulus in all spatial directions.

Comparison of the anisotropy of apparent integrated ultrasonic backscatter from fixed human tendon and fixed human myocardium

The content and organization of collagen in the cardiac interstitium may represent significant determinants of the ultrasonic scattering properties of myocardium. This study was designed to investigate the anisotropic backscattering properties of a fibrous soft tissue exhibiting an ordered arrangement of fibers similar to myocardium, but possessing a substantially greater content of collagen. Human Achilles tendon was chosen for this study because it possesses a simple unidirectional arrangement of fibers and a high content of collagen compared to normal myocardium. Integrated (frequency-averaged) backscatter was measured from ten formalin fixed samples of tendon as a function of insonifying angle relative to the fiber axis of the tissue. The samples were insonified in a water bath using a 5-MHz center frequency piezoelectric transducer. Maximum backscatter occurred for insonification perpendicular to the fibers, and minimum backscatter occurred for insonification parallel to the fibers. The mean peak to nadir variation, or magnitude of anisotropy, of integrated backscatter for the ten formalin fixed samples of tendon was 36.3 dB. This compares to 14.5 dB for formalin fixed human myocardium measured in an earlier study by our laboratory.

Effect of collagen on the anisotropy of quasi‐longitudinal mode ultrasonic velocity in fibrous soft tissues: A comparison of fixed tendon and fixed myocardium

The widespread use of echocardiography has generated considerable interest in the ultrasonic properties of myocardial collagen. This study was designed to investigate the effect of collagen on the propagation of ultrasound by measuring the anisotropy of ultrasonic velocity through formalin fixed specimens of bovine Achilles tendon. Tendon was chosen for this study because it possesses a high content of collagen and a well-defined unidirectional arrangement of fibers. Ultrasonic velocity data were acquired from nine samples of fixed tendon that were each insonified at multiple angles relative to the fibers in 2 degrees increments for a full 360 degrees. Analysis of the data revealed a substantial angular dependence of velocity qualitatively similar to that reported for formalin fixed specimens of normal human myocardium, but approximately 17 times larger in magnitude. Together with measured values of density, these results were used to compute the elastic stiffness coefficients C11 (corresponding to propagation perpendicular to the fibers) and C33 (corresponding to propagation parallel to the fibers) of fixed tendon, yielding 3.08 and 4.51 GPa, respectively.

Anisotropy of the slope of ultrasonic attenuation in formalin fixed human myocardium

Clinical implementation of quantitative ultrasonic tissue characterization is likely to require imaging the heart with sound propagating at varying angles relative to the fibers of the heart. Under these circumstances, the variation of the ultrasonic properties of myocardium with the angle of propagation relative to the myofibers may represent a significant source of potential misinterpretation. In the present study, the systematic approach of assessing the impact of anisotropy on quantitative myocardial tissue characterization is extended by reporting results of a recent in vitro study to measure the anisotropy of the slope of ultrasonic attenuation in specimens of formalin fixed human myocardium. Data obtained from regions of remote infarct are presented and compared to data acquired from regions identified to be free of infarct. The slope of attenuation for both regions exhibit a sinusoid-like dependence on angle that is approximately doubled for propagation parallel to the fibers as compared to perpendicular. These results are, in turn, compared to an earlier study from the laboratory that examined the effects of myocardial infarction on ultrasonic attenuation and interstitial collagen content in freshly excised canine hearts. Discussion regarding the analysis and interpretation of measurements of slope of attenuation is presented as well as a discussion of the possible influence of formalin fixation on our results.

Ultrasonic characterization of the curing process of hydroxyapatite-modified bone cement.

Ultrasonic parameters such as velocity of sound and broad-band ultrasonic attenuation (BUA) are sensitive to changes in the viscoelastic properties of a material. Bone cement undergoes changes is these properties as it cures. By monitoring the propagation of ultrasonic pulses through a sample of curing bone cement, the curing reaction of polymethylmethacrylate-based (PMMA) bone cement was investigated for hydroxyapatite (HA) concentrations of 0, 10, and 30% (by weight). As the material hardens, the velocity of sound increases by 70%. BUA shows a large peak at the midpoint of the velocity transition. These data are used to compare the cure time and cure duration for PMMA bone cement mixed with hydroxyapatite particles. Measurements of the final sound velocity and BUA were also performed to investigate the mechanical properties of the fully cured cement, and to compare to compression testing data. This is the first time the curing process of bone cement has been investigated as a function of hydroxyapatite concentration. Results indicate that the cure time is not significantly affected by the addition of HA particles, and that both velocity of sound and BUA are sensitive to the curing process.

Kramers-Kronig analysis of attenuation and dispersion in trabecular bone.

A restricted-bandwidth form of the Kramers-Kronig dispersion relations is applied to in vitro measurements of ultrasonic attenuation and dispersion properties of trabecular bone specimens from bovine tibia. The Kramers-Kronig analysis utilizes only experimentally measured properties and avoids extrapolation of ultrasonic properties beyond the known bandwidth. Compensation for the portions of the Kramers-Kronig integrals over the unknown bandwidth is partially achieved by the method of subtractions, where a subtraction frequency acts as an adjustable parameter. Good agreement is found between experimentally measured and Kramers-Kronig reconstructed dispersions. The restricted-bandwidth approach improves upon other forms of the Kramers-Kronig relations and may provide further insight into how ultrasound interacts with trabecular bone.

Ultrasonic characterization of cancellous bone using apparent integrated backscatter.

Apparent integrated backscatter (AIB) is a measure of the frequency-averaged (integrated) backscattered power contained in some portion of a backscattered ultrasonic signal. AIB has been used extensively to study soft tissues, but its usefulness as a tissue characterization technique for cancellous bone has not been demonstrated. To address this, we performed measurements on 17 specimens of cancellous bone over two different frequency ranges using a 1 MHz and 5 MHz broadband ultrasonic transducer. Specimens were obtained from bovine tibiae and prepared in the shape of cubes (15 mm side length) with faces oriented along transverse (anterior, posterior, medial and lateral) and longitudinal (superior and inferior) principal anatomic directions. A mechanical scanning system was used to acquire multiple backscatter signals from each direction for each cube. AIB demonstrated highly significant linear correlations with bone mineral density (BMD) for both the transverse (R2 = 0.817) and longitudinal (R2 = 0.488) directions using the 5 MHz transducer. In contrast, the correlations with density were much weaker for the 1 MHz transducer (R2 = 0.007 transverse, R2 = 0.228 longitudinal). In all cases where a significant correlation was observed, AIB was found to decrease with increasing BMD.

Effect of marrow on the high frequency ultrasonic properties of cancellous bone.

A number of investigators have performed in vitro measurements of cancellous bone to determine how various ultrasonic parameters depend on bone density and trabecular orientation. To facilitate handling and storage of bone specimens, the marrow is often removed prior to ultrasonic measurements. However, the assumption that marrow does not affect ultrasonic measurements at high frequencies (>1 MHz) has not been tested. The goal of this study is to determine the effect of marrow on the ultrasonic properties of bovine cancellous bone at frequencies greater than 1 MHz. Twelve specimens of cancellous bone were obtained from the proximal end of four bovine tibia. Ultrasonic measurements consisting of normalized broadband ultrasonic attenuation (nBUA), speed of sound (SOS) and apparent integrated backscatter (AIB) were measured in each specimen using 2.25 MHz (centre frequency) broadband ultrasonic pulses. These measurements were performed before and after marrow removal either along the superoinferior (SI) or mediolateral (ML) direction. SOS and nBUA showed no significant difference (p > 0.05) for either direction of propagation after marrow removal. AIB showed no significant difference in the SI direction. For the ML direction, a small but statistically significant difference (p = 0.044) was observed after marrow removal.