Propagation of Acoustic Waves Caused by the Accelerations of Vibrating Hand-Held Tools in Viscoelastic Soft Tissues of Human Hands and a Mechanobiological Picture for the Related Injuries

As is well known, hand-arm vibration syndrome (HAVS), or vibration-induced white finger (VWF), which is a secondary form of Raynaud’s syndrome, is an industrial injury triggered by regular use of vibrating hand-held tools. According to the related biopsy tests, the main vibration-caused lesion is an increase in the thickness of the artery walls of the small arteries and arterioles resulted from enlarged vascular smooth muscle cells (VSMCs) in the wall layer known as tunica media. The present work developed a mechanobiological picture for the cell enlargement.

In the study, the authors analyzed the propagation along the thickness of an infinite planar layer of a soft living tissue (SLT). The work considered acoustic modeling. As a general viscoelastic acoustic model, the work suggested linear non-stationary partial integro-differential equation (PIDE) for the weakly non-equilibrium component of the average normal stress (ANS) or briefly, the acoustic ANS. The PIDE was, in the exponential approximation for the normalized stress-relaxation function (NSRF), reduced to the third-order linear non-stationary partial differential equation (PDE), which was of the Zener type. The one-spatial-coordinate version of this PDE in the planar SLT layer with the corresponding boundary conditions was considered. The relevance of these settings was motivated by a conclusion of other authors, which was based on the results of the frequency-domain simulation in three spatial coordinates.

The boundary-value problem at arbitrary value of the stress-relaxation time (SRT) and arbitrary but sufficiently regular shape of the external acceleration was analytically solved by means of the Fourier method. The obtained solution was the steady-state acoustic ANS and allowed calculation of the corresponding steady-state acoustic pressure as well. The derived analytical representations were computationally implemented. Propagation of the pressure waves in the SLT layer at zero and different nonzero values of the SRT, and the single-pulse external acceleration was presented. They complemented the zero-SRT and zero-SRT-asymptote results with the results for various values of the SRT. The obtained pressure values were, at all of the space-time points under consideration, meeting the condition for the adequateness of the linear model. In the case where the SRT was zero, the results well agreed with the ones obtained by using the simulation software package LS-DYNA. The dependence of the damping of acoustic variables in an SLT on the SRT in the present third-order case significantly generalized the one in the second-order linear systems. The related resonance effect in the waves of the acoustic pressure propagating in an SLT was also discussed. The effects of the NSRF-originated memory function provided by the present third-order PDE model were necessary for proper simulation of the pressure, which was of special importance in the aforementioned mechanoboiological picture.

 The results obtained in the work presented a viscoelastic acoustic framework for SLTs. These results opened a way to quantitatively specific evaluation of technological strategies for reduction of the vibration-caused injuries or, loosely speaking, achieving “zero’’ injury.

Article by Eugen Mamontov and Viktor Berbyuk, from Sweden.

Full access: http://mrw.so/3fzeWw

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