ANISOTROPIC ELASTICITY OF SOFT TISSUES - AN ACOUSTIC MICROSCOPIC APPROACH
Abstract
Many biological soft tissues are known to be structurally anisotropic. The speed of ultrasound propagation in some of these tissues has been found to be dependent on the direction of sound propagation. Most theoretical models of sound propagation which have been applied to biological soft tissues, however, have assumed tissue isotropy. The present study employs acoustic microscopy to characterize the anisotropic linear elastic properties of soft tissue specimens. The velocities of bulk wave propagation in transverse isotropic specimens, and in orthotropic specimens have been derived from the linear elastic theory, but due to the configuration of the acoustic microscope, only transverse isotropic materials could be treated experimentally. Ultrasonic velocity measurements in frog sartorius muscles and rat tail tendon fibers allowed estimation of the degree to which anisotropy affects sound propagation in these tissues, and of the values of specific elastic constants. The specimens were rotated through a sequence of sound directions, with angles of propagation relative to the fiber axis, ranging from slightly less than eight degrees, to ninety degrees. Ultrasonic velocities were calculated from measured phase values, and then, a minimum mean squared error algorithm was used to determine the best fit values for the elastic constants. The values of the elastic constants were converted to units of speed of sound, to facilitate comparison with the measured values. The four values thus obtained from the analysis were C('c)(,L), the longitudinal speed of compressional wave propagation, C('c)(,T), the tranverse compressional speed, C('i)(,LT), an interactive value, and C('s)(,LT), the longitudinal transverse shear speed of sound. A fifth value, C('c)(,80(DEGREES)L), the acoustic velocity for compressional wave propagation at an 80(DEGREES) angle with respect to the longitudinal direction, was calculated from these. Seven frog sartorius muscles and three rat tail fibers were examined. The effects of isometric tetanic contraction of the muscles were studied, but no significant differences between the passive and active states were observed. Since it is expected that the mechanisms governing sound propagation at 100 MHz may be different from those operating at frequencies five or more orders of magnitude lower, it is not surprising that these results differ from those obtained by others at the lower frequencies. For all specimens studied, it was observed that C('i)(,LT) > C('c)(,80(DEGREES)L) > C('c)(,T) > C('s)(,LT) = 0. Average values and standard deviations for the elastic constants, in meters per second, were C('c)(,T) = 1550 (+OR-) 11, C('c)(,L) = 1816 (+OR-) 897, C('i)(,LT) = 1759 (+OR-) 94, and C('c)(,80(DEGREES)L) = 1566 (+OR-) 11 for the frog muscle specimens and C('c)(,T) = 1603 (+OR-) 19, C('c)(,L) = 2083 (+OR-) 1145, C('i)(,LT) = 1970 (+OR-) 205, and C('c)(,80(DEGREES)L) = 1636 (+OR-) 23 for the rat tail fibers. As expected from the range of directions used, the values of C('c)(,L) varied widely, while the other values varied within reasonable limits. In all cases, a better fit of the data was obtained using the anisotropic model than with an isotropic one. This study represents, to the best of the author's knowledge, the first attempt to apply anisotropic linear elastic theory to characterize acoustic velocities in biological soft tissues. It is expected that further investigations in this area will lead to a better understanding of the nature of sound propagation in soft tissues, and of muscle mechanics. Other areas of biological research might also benefit from the technique.
Degree
Ph.D.
Subject Area
Biomedical research
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