Optical diffraction by well-ordered muscle fibres

Abstract

We have studied the diffraction of a focussed laser beam by single fibres of glycerinated rabbit psoas muscle as a function of the angle of incidence. Diffraction efficiencies as high as 34% were observed at the first-order Bragg angle, indicative of well-ordered striated fibres with a strong periodic modulation of the refractive index. A theory is presented to account for our observations based upon the coupled-wave model developed by Kogelnik (1967) and Magnusson and Gaylord (1977) for the description of thick phase gratings in holography. We have solved the coupled-wave equations on a computer using a realistic index modulation taken from the measurements of Huxley and Hanson (1957). Comparison of theory with experiment shows that coupled-wave effects are indeed present in well-ordered muscle fibres, and the observed diffraction efficiency is in quite good agreement with what would be expected theoretically. Most importantly, the computer model allows us to calculate the diffraction efficiency for curved striations, which are observed for real muscle fibres under a microscope. The sensitivity of the diffraction efficiency to curvature of the striations may have implications for the interpretation of other optical experiments on muscle. We also consider the effects on our measurements of the focussing lens and refraction by the cylindrical fibre.

Polarization-sensitive reflectance imaging in skeletal muscle

“…7), by using a three dimensional coupled wave theory [5,25]. A physical sarcomere structure model and properties proposed by Thornhill et al [5,26] was used in the calculation. The sarcomere length used was 2.8 μm.…”

Imaging 2D optical diffuse reflectance in skeletal muscle

“…In order to test this, we applied a three dimensional coupled wave theory [27] in a semi-infinite Monte Carlo model. The sarcomere structure model and properties proposed by Thornhill et al [28] was used in the calculation. Each sarcomere was taken as a single grating with following geometrical parameters: sarcomere length = 3.1μm, length of A band =1.5μm, and length of I band = 2.0μm.…”

“…Each sarcomere was taken as a single grating with following geometrical parameters: sarcomere length = 3.1μm, length of A band =1.5μm, and length of I band = 2.0μm. A photon packet experienced regular scattering events as in the conventional Monte Carlo model [28] with Henyey-Greenstein phase function. However, in between two consecutive scatterings, the photon had a probability to be diffracted instead of following a ballistic trajectory.…”

Effects of inhomogeneous myofibril morphology on optical diffraction in single muscle fibers

“…However, his model was not capable of analyzing muscle fibers with different striation patterns. On the basis of the work of Huxley and Hanson's work [11] on refractive index modulation in sarcomeres, Thornhill et al [12] described a much improved sarcomere model and applied the first-order coupled wave theory developed by Kogelnik [13]. Sidick et al [14] further introduced rigorous coupled wave analysis for planar diffraction (2DCW) [15] to analyze light diffraction in muscle fibers for TE polarization.…”

“…We hypothesized that such apparent inconsistencies can be explained if the inhomogeneous nature of the muscle fibers was taken into consideration. Most of the previous theoretical studies assumed that muscle fiber had a uniform and wellorganized myofibril arrangement featuring straight, skewed, or sinusoidal ripple striations [7,12,[17][18][19]. On the other hand, microscopic studies have shown that morphological and optical parameters do not remain constant throughout a myofibril [20][21][22][23].…”