title: Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion.
abstract: Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5  μm in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.
authors.affiliation: Centre de Recherche sur l'Inflammation (CRI), UMR 1149 Inserm-Université Paris Diderot, Paris 7, France.|King's College London, BHF Centre of Excellence, Division of Imaging Sciences and Biomedical Engineering, St. Thomas' Hospital, London SE1 7EH, United Kingdom.
authors.forename: Simon A
authors.initials: SA
authors.lastname: Lambert
authors.affiliation: NORSAR, P.O. Box 53, N-2027, Kjeller, Norway.
authors.forename: Sven Peter
authors.initials: SP
authors.lastname: Näsholm
authors.affiliation: King's College London, BHF Centre of Excellence, Division of Imaging Sciences and Biomedical Engineering, St. Thomas' Hospital, London SE1 7EH, United Kingdom.
authors.forename: David
authors.initials: D
authors.lastname: Nordsletten
authors.affiliation: King's College London, BHF Centre of Excellence, Division of Imaging Sciences and Biomedical Engineering, St. Thomas' Hospital, London SE1 7EH, United Kingdom.
authors.forename: Christian
authors.initials: C
authors.lastname: Michler
authors.affiliation: Neuroscience Research Australia, Randwick, Sydney, NSW 2031, Australia.|School of Medical Sciences, University of New South Wales, Sydney, NSW 2052, Australia.
authors.forename: Lauriane
authors.initials: L
authors.lastname: Juge
authors.affiliation: CHU Xavier Bichat, Université Paris Diderot, APHP, U698 INSERM, CEFI, Paris 7, France.
authors.forename: Jean-Michel
authors.initials: JM
authors.lastname: Serfaty
authors.affiliation: Neuroscience Research Australia, Randwick, Sydney, NSW 2031, Australia.|Prince of Wales Clinical School, University of New South Wales, Sydney, NSW 2052, Australia.
authors.forename: Lynne
authors.initials: L
authors.lastname: Bilston
authors.affiliation: Department of Civil, Environmental & Geo-Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA.
authors.forename: Bojan
authors.initials: B
authors.lastname: Guzina
authors.affiliation: Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, N-0316 Oslo, Norway.
authors.forename: Sverre
authors.initials: S
authors.lastname: Holm
authors.affiliation: King's College London, BHF Centre of Excellence, Division of Imaging Sciences and Biomedical Engineering, St. Thomas' Hospital, London SE1 7EH, United Kingdom.
authors.forename: Ralph
authors.initials: R
authors.lastname: Sinkus
mesh_terms: D003198:Computer Simulation; D017709:Fractals; D008962:Models, Theoretical; D013016:Sound