Theoretical Calculation of Resonant Frequencies of the Human Alveolar Wall and Its Implications in Ultrasound Induced Lung Hemorrhage

Abstract

Abstract-The human alveolar wall was modeled here as membranes and its resonant frequency was determined in order to analyze the mechanism of alveolar resonance of the ultrasound induced lung hemorrhage. The resonant frequency of the membrane models of the human alveolar wall was determined to be within the range of the frequency of diagnostic ultrasound used in the thoracic and abdominal regions; which is > 2.5 MHz. Thus, the alveolar resonance is proved to occur during the diagnostic ultrasound imaging of humans. However the possibility of alveolar wall damage at resonance was not analyzed here. Nevertheless according to the resonant frequency equations derived here, the resonance of the alveolar wall by diagnostic ultrasound waves can be eliminated from occurring when total lung capacity is ~ 20% (at maximal expiration).

Theoretical Modelling of Alveolar Resonance Mechanism of Ultrasound-Induced Lung Haemorrhage

“…The fundamental frequency of the square membrane model occurs when mode is n x = n y = 1. The transverse wave velocity on alveolar wall is determined to range from 0 to 489 m/s [23]. The diameters of the alveolus for the adult mouse and human are 40 -80 μm and 200 -400 μm, respectively [24].…”

Effect of Stress and Temperature on the Optical Properties of Silicon Nitride Membranes at 1,550 nm

“…in which n x and n y are integer numbers to define the modes which have (n x − 1) and (n y − 1) nodes in the x and y directions, L is the length of the sides of a square membrane, S is the membrane stress, and ρ is the material density (Jabaraj and Jaadar, 2013). This shows that the resonance frequencies of the membrane are proportional to the square root of the membrane stress S. (For the membranes of side length L = 5 mm, ρ = 3,100 kg/m 3 , and S ≤ 250 MPa 1 used in this experiment, the resonance frequency of the first mode is f 1,1 ≤40 kHz.…”