Key Point: Ultrasound waves cause shear stress and strain.

Treatise on New Physical Mechanism of Medical Diagnostic Ultrasound (MDU) for Bio-effects from Shear Stress/Strain Resolved from Longitudinal and Extensional Wave

Harold M. Frost, PhD (HMF), P.O. Box 162, Sheffield, VT 05866 USA.
Contact: halfrost@charter.net. 802-626-3508

Abstract:  Over 2005-2020 pro bono research was carried out on the evidently overlooked but simple origins, action and implications of resolved shear stress and shear strain predicted to occur in biological tissue and human patients in clinical settings via exposure to MDU as MHz longitudinal plane waves and focused beams, either emitted by medical devices like ultrasound scanners and imaging machines. Termed (purely) solid state mechanical shear strain and stress (SSMSSS), discovery of this effect – first observed and measured photoviscoelastically in soft solids in the 1970’s by Frost – resulted from insight gained from analyzing a cause-and-effect chain beginning with emission at time t=0 of elastodynamic radiation from a point or line source on the plane surface of a solid half-space or solid half-plate, with waves or particles observed at t>0 at a field point in the far field.  Much math analysis of this type “is concerned with an initially undisturbed body which in its interior, and at a specified time, say t = 0, is subjected to external disturbances” which “give rise to wave motions propagating away from the disturbed region.”[1]  With relatively simple math, Part 1 sets up this treatise plus the tensor calculus and analysis of Part 2 whose own math climaxes in Addendum A for calculating critical values of observables related to possible tissue damage thresholds from MDU.  Both Parts move a rational argument towards a tensor-based continuum mechanics and dynamics model for critical resolved time-averaged principal shear stress or strain for calculating damage thresholds for exposure of biological tissue to plane waves of MDU under conditions of mechanical creep and wave absorption without cavitation or strong heating.  Featured are simple models of uniaxial stress (extensional waves) and uniaxial strain (longitudinal waves) in a half-space or a half-plate of a dry isotropic homogeneous viscoelastic solid with small amplitude-attenuation coefficients based on a relaxation or retardation process.  The Postscript of Addendum E indicates how this analysis is pertinent to searches for causes of ASD and other early-in-life neurocognitive developmental disorders, taking account of special vulnerability to damage of the CNS from MDU including the prenatal & neonatal brain and blood brain barrier even in adults.

LIST OF CONTENTS:

PART 1:  SIMPLE NONCAVITATIONAL NONTHERMAL PHYSICS MODEL FOR ULTRASONIC SSMSSS BIOEFFECTS):

– General

– On the status of dose-bioeffect laws

– Sensing/measuring usually hidden variable of orientational dependence of rank-2 strain tensor vs. pressure’s orientation-invariant scalar effects

– Need for ‘time-longitudinal’ studies of medical diagnostic ultrasound (MDU) bioeffects and experiments on purely solid-state MUBEM’s

PART 2:  TENSOR PARADIGM OF ENTROPY PRODUCTION, HOOKE’S LAWS AND EQUATIONS OF MOTION NEEDED TO REFORM MATH FRAMEWORK USED TO ASSESS MEDICAL DIAGNOSTIC ULTRASOUND (MDU) RISK-V.-BENEFIT:

– Summary, Scope and Perspective

– Linear rate-independent Hooke’s law as constitutive equation in absence of relaxation

– Use of linear Hooke’s law to distinguish scalar-invariance from tensor-invariance concepts used in descriptions of action of MDU

– Linear Hooke’s law as constitutive equation in the presence of a rate process

– Frame-invariant octahedral shear stress

– Nonlinear Hooke’s law as the constitutive equation in presence of a rate process, and equation of motion (EOM) as balance of linear momentum

– Discussion including co-alignment facilitated by entropic and other thermodynamic matters, with frame-dependent effects

– Practical example of the Blood Brain Barrier (BBB) in which co-alignment-related damage effects may multiply in presence of ultrasound

– Spatial averages of tensor quantities of increasing rank number

– Context of emerging trends and gaps and the future of possible research on a purely solid-state bioeffect mechanism or MUBEM like SSMSSS

– Context of national health policy, policy analysis and epidemiology on assessing and managing uncertainty of risk of harm from ultrasonic SSMSSS

– Going forward from here – Simple steps to take to start process of uncovering overlooked evidence for SSMSSS bioeffects of ultrasound

            * Preliminary Matters

            * Pertinent Background for Preliminary Matters

            * Suggested New in Situ and Ex Situ Experiments with Quantitative Exposimetry of Induced Localized Stress and Strain, With Some Theoretical Considerations

            * Considerations Directly Related to Medical Diagnostic Ultrasound (MDU) with Plane Longitudinal Waves, with Comments on Attenuation and Intensity

– Advisory Notice

– Acknowledgements

– Dedication

– Addendum A – Math Framework of Complex Numbers Including Conventions for Elastodynamic Waves

– Addendum B – Chart for Information Flow on Ultrasound’s Action on Biological Tissue 

– Addendum C – 2002 Classification Scheme for Known Physical Mechanisms for Changes Produced by Ultrasound in Biological Systems

– Addendum D – Snapshot of Formal Derivation of Equation of Motion (EOM) for Wave Propagation in Elastic Solids (incomplete)

– Addendum E – Postscript

BIBLIOGRAPHY:  ANNOTATED EXAMPLES OF PERTINENT PUBLICATIONS OF HM FROST

SELECTED ACRONYMS, ABBREVIATIONS AND SYMBOLS USED

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