The Open Biotechnology Journal




ISSN: 1874-0707 ― Volume 14, 2020

Mathematical Model of Human Forearm Based Muscle Fiber Tissues’ Anisotropic Characteristics



Yu-Ping Qin1, , Shuang Zhang*, 1, 2, 3, 4, , Yi-he Liu*, 2
1 The Engineering & Technical College, Chengdu University of Technology, Leshan, 614000, China
2 The College of Computer Science, Neijiang Normal University, Neijiang, 641000, P.R. China
3 The State Key Laboratory of Analog & Mixed-signal VLSI, University of Macau, Macau SAR 999078, China
4 The Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Macau SAR 999078, China

Abstract

On the basis of human muscle fiber tissues' characteristics, it is first proposed to establish the analytical model of galvanic coupling intra-body communication channel. In this model, the parallel and the transverse electrical characteristics of muscular tissue are fully considered, and the model accurately presents the transmission mechanism of galvanic coupling intra-body communication signals in the channel.

Keywords: Analytical model, Fiber characteristics, Galvanic coupling, Intra-body communication.


Article Information


Identifiers and Pagination:

Year: 2016
Volume: 10
First Page: 234
Last Page: 238
Publisher Id: TOBIOTJ-10-234
DOI: 10.2174/18740707016100100234

Article History:

Received Date: 18/11/2015
Revision Received Date: 12/2/2016
Acceptance Date: 08/3/2016
Electronic publication date: 18/05/2016
Collection year: 2016

© Qin et al.; Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/legalcode), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.


* Address correspondence to these authors at the College of Computer Science, Neijiang Normal University, Neijiang, 641000, P.R. China; Emails: zhangshuanghua1@126.com, liu_yihe@163.com Authors who made equal contributions.






INTRODUCTION

The galvanic coupling intra-body communication is a newly-developing short-distance wireless communication mode, with human tissues as the signal transmission media [1Pun SH, Gao YM, Mak P, Vai MI, Du M. Quasi-static modeling of human limb for intra-body communications with experiments. IEEE Trans Inf Technol Biomed 2011; 15(6): 870-6.
[http://dx.doi.org/10.1109/TITB.2011.2161093] [PMID: 21724520]
, 2Chen XM, Mak PU, Pun SH, et al. Study of channel characteristics for galvanic-type intra-body communication based on a transfer function from a quasi-static field model. Sensors (Basel) 2012; 12(12): 16433-50.
[http://dx.doi.org/10.3390/s121216433] [PMID: 23443387]
]. Because signals are transmitted directly through these tissues, their characteristics will produce a direct effect on the attenuation characteristic of the channel. Muscular tissues are an important part of human body, which is developed from muscle fiber with the parallel and the transverse growth characteristics [3Gielen FLH, Jonge WWallinga-de, Boon KL. Electrical conductivity of skeletal muscle tissue: Experimental results from different muscles in vivo. Med Biol Eng Comput 1984; 22(6): 569-77.]. In the conventional volume conductor analytical model, the frequently-used way is to consider the muscular layer and other layers to be isotropic [1Pun SH, Gao YM, Mak P, Vai MI, Du M. Quasi-static modeling of human limb for intra-body communications with experiments. IEEE Trans Inf Technol Biomed 2011; 15(6): 870-6.
[http://dx.doi.org/10.1109/TITB.2011.2161093] [PMID: 21724520]
, 2Chen XM, Mak PU, Pun SH, et al. Study of channel characteristics for galvanic-type intra-body communication based on a transfer function from a quasi-static field model. Sensors (Basel) 2012; 12(12): 16433-50.
[http://dx.doi.org/10.3390/s121216433] [PMID: 23443387]
]. This way cannot show electrical characteristics of muscle fiber effectively, but the physical property of the model is changed, and model precision is lowered. In this paper, on the basis of the transformational relation of muscle fiber’s anisotropy and tissue’s isotropy in the cylindrical coordinate, the analytical model of the intra-body communication channel based on human forearm surface is established and verified.

METHODS

The length of human forearm is assumed to be h and equivalent to a multilayer volume conductor cylinder model comprised of skeleton, muscle, fat and skin, (r1,r2,..rn) represents circumscribed radiuses of all tissues on the tangent plane (εt1t2,..εtn), and (εl1l2,..εln) represent the transverse and the parallel permittivity’s of all tissues respectively, (δt1t2,..δtn) and (δl1l2,..δln) indicate the transverse and the parallel electric conductivity of all tissues (shown in (Fig. 1)), respectively. In the galvanic coupling intra-body communication, when the electrical signal’s frequency in the input electrode is less than 1MHz [1Pun SH, Gao YM, Mak P, Vai MI, Du M. Quasi-static modeling of human limb for intra-body communications with experiments. IEEE Trans Inf Technol Biomed 2011; 15(6): 870-6.
[http://dx.doi.org/10.1109/TITB.2011.2161093] [PMID: 21724520]
, 4Plonsey R, Heppner DB. Considerations of quasi-stationarity in electrophysiological systems. Bull Math Biophys 1967; 29(4): 657-64.
[http://dx.doi.org/10.1007/BF02476917] [PMID: 5582145]
], the propagation effect, the inductive effect and the irradiation effect from the skin to air throughout the channel may be basically ignored. As the frequency is increased, the capacitance effect of the tissue becomes more and more obvious; therefore its impact on the overall system shall be taken into account in building the tissue model. The abbreviated equation [5Geddes LA, Baker LE. The specific resistance of biological material-a compendium of data for the biomedical engineer and physiologist. Med Biol Eng 1967; 5(3): 271-93.
[http://dx.doi.org/10.1007/BF02474537] [PMID: 6068939]
] of the tissue’s potential distribution can be approximately derived in the cylindrical coordinate system by means of Maxwell’s equation under the quasi static approximation condition [1Pun SH, Gao YM, Mak P, Vai MI, Du M. Quasi-static modeling of human limb for intra-body communications with experiments. IEEE Trans Inf Technol Biomed 2011; 15(6): 870-6.
[http://dx.doi.org/10.1109/TITB.2011.2161093] [PMID: 21724520]
, 2Chen XM, Mak PU, Pun SH, et al. Study of channel characteristics for galvanic-type intra-body communication based on a transfer function from a quasi-static field model. Sensors (Basel) 2012; 12(12): 16433-50.
[http://dx.doi.org/10.3390/s121216433] [PMID: 23443387]
, 5Geddes LA, Baker LE. The specific resistance of biological material-a compendium of data for the biomedical engineer and physiologist. Med Biol Eng 1967; 5(3): 271-93.
[http://dx.doi.org/10.1007/BF02474537] [PMID: 6068939]
]:

Fig. (1)

Equivalent multi-layer cylindrical model of human arm.



(1)

Where represents the interior electric potential in the tissue of human forearm, σEQ(s)(f) indicates the combination conductivity of the tissue in the S-th layer at the frequency of f and its expression is as follows:

(2)

Where σst (f) and σsl (f) represent respectively the tangential composite electric conductivity and the lateral one of the tissue in the S-th layer at the frequency of f, they are expressed as follows:

, (3)

, (4)

where σit (f) and σil (f) indicate the transverse and the parallel conductivity of the tissue in the i-th layer at the frequency of f respectively, εrit (f) and εrit (f) indicate the transverse and the parallel relative permittivity of the tissue in the i-th layerat the frequency of f, respectively, and ε 0 represents the permittivity in the vacuum. On the basis of the cylindrical coordinate transformation relation between muscle fiber’s anisotropy and tissues' isotropy, the following can be derived [6Heringa A, Stegeman DF, Uijen GJ, de Weerd JP. Solution methods of electrical field problems in physiology. IEEE Trans Biomed Eng 1982; 29(1): 34-42.
[http://dx.doi.org/10.1109/TBME.1982.324961] [PMID: 7076267]
]:

(5)

And

(6)

Where and .

Channel Model with Muscle Fiber Characteristics

In combination with quasi-static approximation electromagnetic boundary conditions and Laplace’s equation of the anisotropic tissue in the cylindrical coordinate system, the variable separation approach is used to derive electric potential distribution of all layers of human forearm’ tissues at the frequency of f, which may be expressed as follows:

(7)

S = 1,2...N

where In(●) is the n-order modified Bessel function of the first kind, Kn(●) is the n-order modified Bessel function of the second kind; Esmn (f), Fsmn(f), Gsmn (f) and Hsmn (f) indicate constant coefficients of the electric potential equation concerning the tissue in the S-th layer at the frequency of f, respectively.

Isotropic Channel Model

When is true, it means that the tissue’ characteristics in all directions are identical at the frequency of f, so the electric potential equation of the isotropic tissue in the cylindrical coordinate system can be obtained as follows:

(8)

S= 1,2...N

Table 1

Experiment parameters.




Calculation and Verification

In order to verify reasonability of the model effectively, the preliminary confirmatory experiment is carried out. We select healthy volunteers to perform this confirmatory experiment (see Table 1) for their arm testing parameters; the experiment is performed between shoulder joint and elbow joint). In the experiment, we use AgCl electrodes with the size of 4cm*4cm as the signal electrode and the signal acquisition electrode; 1 mA current is input through the signal electrode. When human body remains stationary, averaging multiple measured values is used as the experimental result of the sample; from Reference [1Pun SH, Gao YM, Mak P, Vai MI, Du M. Quasi-static modeling of human limb for intra-body communications with experiments. IEEE Trans Inf Technol Biomed 2011; 15(6): 870-6.
[http://dx.doi.org/10.1109/TITB.2011.2161093] [PMID: 21724520]
], it can obtain electrical parameters of the isotropic model and the anisotropic model, and the electrical parameters are put in the model so as to derive the attenuation index of the channel. The experimental result and the computed result are shown in Fig. (2).

In the experiment, a network analyzer (4395A, Agilent Technologies, Santa Clara, California, USA) and a differential probe (1141A, Agilent Technologies, Santa Clara, California, USA; 1142A, Agilent Technologies, Santa Clara, California, USA) were used. The network analyzer was used to measure the signal attenuation from the implanted devices to the surface electrodes and the differential probe was used to break the common ground loop between the transmitted port and the received port of the network analyzer.

Fig. (2)

Computed result and experimental result of the model.



It can be found from Fig. (2) that, in the anisotropic channel model, when the frequency lies within the range of 1kHz to 10kHz, channel attenuation is reduced as the frequency rises; channel attenuation tendency becomes relatively steady as the frequency grows within the frequency range of 10kHz to 50kHz; while channel attenuation is increased as the frequency is raised within the frequency range of 50kHz to 1MHz; these properties are basically identical with the experimental results. For the isotropic channel model, it’s computed result conforms to the experimental result at the frequency less than 20 kHz, however, when the communication frequency exceeds 20 kHz, attenuation of the isotropic model is hardly changed, this is significantly different from the experimental result. It is important that, within the frequency range, the average error of the channel model with muscle fiber characteristics is reduced by 21% compared with that of the channel model without these characteristics. This improves the precision of the model further.

CONCLUSION

In this model, tissue characteristics of muscle fiber are adequately considered. By comparing the computed result of the channel model with muscle fiber characteristics, the computed result and the experimental result of the isotropic channel model, it is found that the computed result and the experimental result of the channel model with muscle fiber characteristics are almost the same; the maximum error of the model is 10% and the average error is 5.97% within the frequency range. Compared with the simplified isotropic model, the average error is lowered by 21%, so the model precision is greatly enhanced.

CONFLICT OF INTEREST

The authors confirm that this article content has no conflict of interest.

ACKNOWLEDGEMENTS

This work presented in this paper is supported by The Key Fund Project of Sichuan Provincial Department of Education under Grant13ZA0003, Grant 14ZB0360, Grant 14ZB0363 , Grant 14ZB0352; The Sichuan Province Department of Science and Technology under Grant 2015JY0119, the Key Fund Project of Leshan Science and Technology Bureau (15ZDYJ0177).

REFERENCES

[1] Pun SH, Gao YM, Mak P, Vai MI, Du M. Quasi-static modeling of human limb for intra-body communications with experiments. IEEE Trans Inf Technol Biomed 2011; 15(6): 870-6.
[http://dx.doi.org/10.1109/TITB.2011.2161093] [PMID: 21724520]
[2] Chen XM, Mak PU, Pun SH, et al. Study of channel characteristics for galvanic-type intra-body communication based on a transfer function from a quasi-static field model. Sensors (Basel) 2012; 12(12): 16433-50.
[http://dx.doi.org/10.3390/s121216433] [PMID: 23443387]
[3] Gielen FLH, Jonge WWallinga-de, Boon KL. Electrical conductivity of skeletal muscle tissue: Experimental results from different muscles in vivo. Med Biol Eng Comput 1984; 22(6): 569-77.
[4] Plonsey R, Heppner DB. Considerations of quasi-stationarity in electrophysiological systems. Bull Math Biophys 1967; 29(4): 657-64.
[http://dx.doi.org/10.1007/BF02476917] [PMID: 5582145]
[5] Geddes LA, Baker LE. The specific resistance of biological material-a compendium of data for the biomedical engineer and physiologist. Med Biol Eng 1967; 5(3): 271-93.
[http://dx.doi.org/10.1007/BF02474537] [PMID: 6068939]
[6] Heringa A, Stegeman DF, Uijen GJ, de Weerd JP. Solution methods of electrical field problems in physiology. IEEE Trans Biomed Eng 1982; 29(1): 34-42.
[http://dx.doi.org/10.1109/TBME.1982.324961] [PMID: 7076267]
Track Your Manuscript:


Endorsements



"Open access will revolutionize 21st century knowledge work and accelerate the diffusion of ideas and evidence that support just in time learning and the evolution of thinking in a number of disciplines."


Daniel Pesut
(Indiana University School of Nursing, USA)

"It is important that students and researchers from all over the world can have easy access to relevant, high-standard and timely scientific information. This is exactly what Open Access Journals provide and this is the reason why I support this endeavor."


Jacques Descotes
(Centre Antipoison-Centre de Pharmacovigilance, France)

"Publishing research articles is the key for future scientific progress. Open Access publishing is therefore of utmost importance for wider dissemination of information, and will help serving the best interest of the scientific community."


Patrice Talaga
(UCB S.A., Belgium)

"Open access journals are a novel concept in the medical literature. They offer accessible information to a wide variety of individuals, including physicians, medical students, clinical investigators, and the general public. They are an outstanding source of medical and scientific information."


Jeffrey M. Weinberg
(St. Luke's-Roosevelt Hospital Center, USA)

"Open access journals are extremely useful for graduate students, investigators and all other interested persons to read important scientific articles and subscribe scientific journals. Indeed, the research articles span a wide range of area and of high quality. This is specially a must for researchers belonging to institutions with limited library facility and funding to subscribe scientific journals."


Debomoy K. Lahiri
(Indiana University School of Medicine, USA)

"Open access journals represent a major break-through in publishing. They provide easy access to the latest research on a wide variety of issues. Relevant and timely articles are made available in a fraction of the time taken by more conventional publishers. Articles are of uniformly high quality and written by the world's leading authorities."


Robert Looney
(Naval Postgraduate School, USA)

"Open access journals have transformed the way scientific data is published and disseminated: particularly, whilst ensuring a high quality standard and transparency in the editorial process, they have increased the access to the scientific literature by those researchers that have limited library support or that are working on small budgets."


Richard Reithinger
(Westat, USA)

"Not only do open access journals greatly improve the access to high quality information for scientists in the developing world, it also provides extra exposure for our papers."


J. Ferwerda
(University of Oxford, UK)

"Open Access 'Chemistry' Journals allow the dissemination of knowledge at your finger tips without paying for the scientific content."


Sean L. Kitson
(Almac Sciences, Northern Ireland)

"In principle, all scientific journals should have open access, as should be science itself. Open access journals are very helpful for students, researchers and the general public including people from institutions which do not have library or cannot afford to subscribe scientific journals. The articles are high standard and cover a wide area."


Hubert Wolterbeek
(Delft University of Technology, The Netherlands)

"The widest possible diffusion of information is critical for the advancement of science. In this perspective, open access journals are instrumental in fostering researches and achievements."


Alessandro Laviano
(Sapienza - University of Rome, Italy)

"Open access journals are very useful for all scientists as they can have quick information in the different fields of science."


Philippe Hernigou
(Paris University, France)

"There are many scientists who can not afford the rather expensive subscriptions to scientific journals. Open access journals offer a good alternative for free access to good quality scientific information."


Fidel Toldrá
(Instituto de Agroquimica y Tecnologia de Alimentos, Spain)

"Open access journals have become a fundamental tool for students, researchers, patients and the general public. Many people from institutions which do not have library or cannot afford to subscribe scientific journals benefit of them on a daily basis. The articles are among the best and cover most scientific areas."


M. Bendandi
(University Clinic of Navarre, Spain)

"These journals provide researchers with a platform for rapid, open access scientific communication. The articles are of high quality and broad scope."


Peter Chiba
(University of Vienna, Austria)

"Open access journals are probably one of the most important contributions to promote and diffuse science worldwide."


Jaime Sampaio
(University of Trás-os-Montes e Alto Douro, Portugal)

"Open access journals make up a new and rather revolutionary way to scientific publication. This option opens several quite interesting possibilities to disseminate openly and freely new knowledge and even to facilitate interpersonal communication among scientists."


Eduardo A. Castro
(INIFTA, Argentina)

"Open access journals are freely available online throughout the world, for you to read, download, copy, distribute, and use. The articles published in the open access journals are high quality and cover a wide range of fields."


Kenji Hashimoto
(Chiba University, Japan)

"Open Access journals offer an innovative and efficient way of publication for academics and professionals in a wide range of disciplines. The papers published are of high quality after rigorous peer review and they are Indexed in: major international databases. I read Open Access journals to keep abreast of the recent development in my field of study."


Daniel Shek
(Chinese University of Hong Kong, Hong Kong)

"It is a modern trend for publishers to establish open access journals. Researchers, faculty members, and students will be greatly benefited by the new journals of Bentham Science Publishers Ltd. in this category."


Jih Ru Hwu
(National Central University, Taiwan)


Browse Contents




Webmaster Contact: info@benthamopen.net
Copyright © 2020 Bentham Open