Time-dependent density fluctuations result in periodic changes in the material’s refractive index, which in turn acts as a diffraction grating for the incoming light. Hence, the frequency shift of Brillouin peaks obtained from a combination of eqs 1– 4 is (5)From the spectral shift, relevant information on the elastic properties of the material can be obtained, specifically the longitudinal elastic modulus M at GHz frequencies (6)provided that the ratio ρ/ n 2 is independently estimated.Īs the sound wave propagates through the medium, light will undergo a change in frequency because of Doppler shift.
This simple treatment must be generalized in the case of biomedical samples, where elastic properties are structured in a complex pattern of temporal and spatial scales, which are fundamental to determine the physiological conditions of biological matter.
The various time scales of vibration and diffusion of molecules and macromolecules (i.e., the temporal heterogeneity of the material) require a viscoelastic treatment of Brillouin spectra. Moreover, the various spatial scales of organization of biological matter (i.e., its spatial heterogeneity from single cells up to tissues and organs) require 3D mapping at diffraction-limited resolution by means of a micro-Brillouin approach. The aspects of temporal and spatial heterogeneity will be treated hereafter. Viscoelastic materials are characterized by frequency-dependent elastic moduli. Here we paint a very simplified scenario, in order to comment on some very general behavior. More realistic pictures should include multiple-relaxation patterns, which are typical of complex matter structured at different temporal and spatial levels.
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