Scattering of SH waves in compact bone and cancellous bone
Introduction
Electromagnetic therapy has been in use since the invention of electricity. It was widely adopted in East and Western Europe [1]. Veterinarians became the first health professionals to use Pulsed Electro Magnetic Field (PEMF) therapy, usually used to treat broken legs in racehorses. In 2004, FDA approved a pulsed electromagnetic field system as an auxiliary tool for cervical fusion surgery in patients with high risk of non-fusion. Although it was reported as early as 1841 that electricity had the potential to help heal bones, it was not until the mid-1950s that scientists seriously studied the problem. During the 1970s, Bassett and his team introduced a new approach for the treatment of delayed fractures, a technique that employed a very specific biphasic low frequency signal [[2], [3], [4], [5]] to be applied for non-union/delayed fractures. The use of electrical stimulation in the lumbosacral region was the first attempt by Alan Dwyer of Australia [6,7]. In addition to using electromagnetic therapy to treat fractures, electromagnetic waves can also be used to detect osteoporosis. In the United States, it is estimated that more than 2 million people fracture due to osteoporosis each year. Meanwhile, the number of osteoporosis patients has increased year by year in the last five years in China [8,9].
Nondestructive testing (NDT) is commonly used to detect defects in material without damaging the material or making it unsuitable for use. NDT contains a variety of methods which can detect defects open to the material surface and contained within the material itself. In 2006, Petro MOILANEN and his team proposed a method to monitor bone properties using electromagnetic waves, which can be used to detect osteoporosis [10]. However, the effect of electric field on bone in electromagnetic wave has not been studied in theory.
The bone is a high-density connective tissue with a unique structure. It is mainly divided into the cortical bone and the cancellous bone, and the electromagnetic wave can scatter in the honeycomb-shaped cavities structure in the bone. The research content of this paper is of great significance for understanding bone fracture and improving the theory of osteoporosis detection.
In this paper, the influence of the cavity on the electric field in the electromagnetic wave is discussed, and the scattering problem of the electromagnetic wave in the cellular cavity unit of the reduced bone is studied by the theoretical calculation and the finite element analysis. Because the electric field in the electromagnetic wave propagates in the form of SH waves, firstly, the SH-wave scattering problem is solved by the complex function method, and the correctness and feasibility of the finite element method are verified by comparing the analytical results with the finite element results. Then the finite element method is adopted to solve the scattering problem of the SH wave to a plurality of cavities. Finally, the scattering problem of the electric field in the circular cavity of the bone is summarized and discussed.
Section snippets
Theoretical model
As shown in Fig. 1, the central position of the closed circular space contains multiple cavities of the same size, simulating the honeycomb cavity structure in cancellous bone. At the same time, there are many cavities with smaller radius at the edge position, which simulates the compact bone structure. Based on the analytical solution of single cavity and multi-cavity SH waves scattering, the influence of reflected wave at closed boundary on the cavity is considered, and the electromagnetic
Scattering theory in single and multiple cavities
The electric and magnetic fields in plane electromagnetic waves satisfy the Helmholtz equation:Where: represents the electric-field vector, represents the magnetic intensity vector, is the wave number, the expression is . is the frequency of electromagnetic wave, is the permeability and is the dielectric parameter. And in bone, the correlation parameters can be obtained from reference [[11], [12], [13]]. We can know that the
Method validation
The finite element method is verified in two steps. Firstly, because there was no previous research on the model in Fig. 1, by changing the circular region of the model into a strip-shaped region, the model becomes a strip-shaped model with cavities, the model of this paper becomes a strip-shaped model with a cavity [14]. The scattering model of SH waves in the strip-shaped domain of reference [14] is verified by the finite element method, and the comparison diagram of highly consistent results
X-rays
There is no method to measure the change curve of EFICF in bone in current clinical trials, although theoretical data and finite element data are compared, they cannot be compared with clinical trial data. The conclusion of this paper is to put forward the hypothesis and promote the relevant research. Nevertheless, we can illustrate the validity of this theory that electromagnetic wave therapy can promote fracture healing. By comparing X-ray films in the healing process of fracture patients
Conclusion
By studying the effect of honeycomb cavities in bone on the electric field in electromagnetic wave, the conclusion is as follows: compared with high frequency electromagnetic wave, the concentration effect of electric field intensity in honeycomb cavity is stronger in low frequency electromagnetic wave. The increase of the distance between the honeycomb cavities, the increase of the honeycomb cavity radius will lead to the complex change of the concentration effect of the electric field around
Fundings
This article is supported by the Fundamental Research Funds for the Central Universities, the project number is 3072019CF0205.
CRediT authorship contribution statement
Meng Xiang: Validation, Formal analysis, Visualization, Software, Resources, Writing - review & editing, Supervision, Data curation. Hui Qi: Validation, Formal analysis, Visualization, Writing - review & editing. Zhiwei Qu: Conceptualization, Methodology, Software, Investigation, Writing - original draft, Writing - review & editing. Jing Guo: Resources, Writing - review & editing, Supervision, Data curation.
Acknowledgements
Our deepest gratitude goes to the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially.
Declaration of Competing Interest
None.
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