Modeling of sectionally continuous communication channel with inhomogeneously distributed tissues

Abstract

BACKGROUND:

This study aimed to investigate effects on the transmission channel caused by heterogeneous distribution in tissues and joint characteristics.

METHOD:

Human arm section scans were taken using CT technology, and zoned, following which, a circumference measurement experiment was performed to analyze the effect of inhomogeneous distribution of tissues. In order to analyze the arm joint’s effect on channel transmission, we proposed a piecewise modeling method in combination with connection conditions.

CONCLUSIONS:

It can be seen from the experiment that, in the quasi-static mode, the communication channel error caused by the inhomogeneous distribution of tissues is small enough to be negligible. The error between calculated and experimental results is reduced by 3.93 dB in this experiment relative to models that did not include joint characteristics, and the average error is lowered by 0.73 dB. The variation curve fit to experimental data is also improved in this method. As such, it can be quantitatively determined that a channel model with joint characteristics is superior to models excluding joint characteristics.

Keywords

Inhomogeneous distribution quasi-static communication channel joint

1. Introduction

Scientific and technological improvements in recent years, paired with the rapid development of the microelectronics industry, have begun introducing miniaturized personal and medical apparatuses for daily use. One such device, the handheld electrocardiogram (ECG) monitor, is able to analyze human health conditions by monitoring the ECG signal on the body surface – specifically, the palms [1]. ECG monitoring has been of rising importance to the medical community during recent years in part due to its potential for real-time monitoring and evaluation of cardiac function, thereby improving the prevention and treatment of cardiovascular diseases [2]. This is of special importance, as cardiovascular diseases have become one of the leading causes of death in the modern era [3]. This shows a strong relation with the rapid development of agricultural modernization, and associated increase in pesticides, fertilizers, antistaling agents, and food additives, which have become widely used in agricultural products. A great deal of industrial residue enters our food, resulting in a proportional number of hazardous substances entering the human body.

Application of ECG monitoring to alleviate these rising medical issues, however, requires a greater understanding of internal electrical signals. During transmission, ECG signals arrive at the palm via one of many available routes through the arm, elbow, shoulder, and other locations; and the signal is certain to be influenced by the changing factors in this transmission process.

Experimental and modeling methods have both frequently been used to analyze the effects of these factors. In current modeling methods, including the electric circuit method, finite element method, and mathematical method, the human arm is assumed to be a cylindrical volume conductor with four distinct but homogeneous layers (skin, fat, muscle, and bone). Unfortunately, this model is an enormous oversimplification of the tissue distribution characteristics seen in a human arm. Although the tissue characteristics of muscular fiber are developed to full complexity in the modeling method in Reference [4], this model’s accuracy and fit compared to experimental data still show obvious room for improvement, which may be helped by a more accurate representation of the inhomogeneous distribution of the other three tissues and joints.

This study addressed the above problems using multi-angle experiments to analyze inhomogeneously distributed tissue in these channels. A novel piecewise modeling method along the Z axis is proposed to describe the effect of human joints on ECG signal transmission through the communication channel.

Figure 1.

Sectional view of human arm (CT).

2. Circumference measurement experiment

To obtain arm section information, we selected Siemens SOMATOMDefinitionAS $+$ 128-layer 4D spiral CT system to continuously scan the arms of a healthy person. A total of 848 arm section pictures were taken with this method (see Fig. 1). The data points of the pictures were used to present the size (1 pt $=$ 0.35146 mm, diameter: 0.35146 $\times$ 140 $=$ 49.2044 mm) and tissue distribution characteristics of the arm.

In Fig. 1, the arm in the CT image was divided into quadrants (A, B, C, and D). It is apparent from this image that the muscular tissues, which have the most effect on electric current signal transmission, differ in distribution between the four zones. In order to analyze the effect of the distribution on channel transmission, we carried out the following circumference measurement experiment.

A network analyzer (4395A, Agilent Technologies, Santa Clara, CA, USA) and differential probe (1141A and 1142A, Agilent Technologies, Santa Clara, CA, USA) were used to gather data. The network analyzer was used to measure the signal attenuation from the transmitter (signal source) and receiver, while the differential probe was used to break the common ground loop between the transmitted port and received port of the network analyzer.

In the intra-body communication experiment, the attenuation noise caused by human body was approximately $\pm$ 1.5 dB, and phase noise was approximately $\pm$ 5 ${}^{\circ}$ [4, 5, 6, 7, 8, 9]. In order to reduce the effect of noise on the channel characteristics, the noise with the phase difference was assumed to be negligible.

Figure 2.

Circumference measurement experiment result.

In the experiment, a measurement was performed once every 45 ${}^{\circ}$ on each evaluated circumference, the results of which are shown in Fig. 2. These data points show that neither the path attenuation nor phase of the channel displayed major changes with angular variation. In the quasi-static mode ( $f<$ 200 kHz), the maximum path attenuation error caused by tissue distribution was 0.95 dB, and the maximum phase error was 9 ${}^{\circ}$ . These values are considered negligible in channel modeling. In the high-frequency mode (1 MHz), the maximum path attenuation error was 2 dB and the maximum phase error was 17 ${}^{\circ}$ ; caused by the more obvious capacitance effect in the channel in this mode. For the purposes of this study, we mainly consider the galvanic coupling channel in the quasi-static mode.

3. Modeling of joint characteristics

Figure 3.

Arm structure diagram.

The human arm consists of the upper arm, joint, and forearm (see Fig. 3) [5, 6, 7]. The joint represents a discontinuity in the skeleton, functionally creating a piecewise structure to increase freedom of bending and movement in the limb. Given this structure, the conventional modeling method [4, 8, 9] is an imperfect fit for the real system. To handle the discontinuous property of skeletal system, a novel communication channel model was built using the piecewise modeling method.

As a first course of action, the arm was simplified and standardized to a multi-layer cylinder [4]. In the tangential direction, it comprised the traditional four layers: skin, fat, muscle, and skeleton [4]. As electrical characteristics of muscular tissue differ greatly in the parallel and the tangential directions [10, 11, 12, 13], the potential distribution seen in galvanic coupling for intra-body communication may be given as follows (based on [4]).

3.1 Fiber characteristics channel model

$\displaystyle\varphi_{i}(f,r,\theta,z)=\sum\limits_{m=1}^{\infty}{\sum\limits_% {n=0}^{\infty}{\left[{E_{\textit{imn}}(f)I_{n}\bigg{(}\frac{m\pi r}{h}\sqrt{{% \sigma_{\textit{Eq}\left(i\right)}(f)}/{\hat{{\sigma}}_{it}(f)}}\bigg{)}\cos(n% \theta)∼{}+}\right.}}$ $\displaystyle\quad∼{}F_{\textit{imn}}(f)I_{n}\bigg{(}\frac{m\pi r}{h}\sqrt{{% \sigma_{\textit{Eq}\left(i\right)}(f)}/{\hat{{\sigma}}_{it}(f)}}\bigg{)}\sin(n% \theta)∼{}+$ $\displaystyle\quad∼{}G_{\textit{imn}}(f)K_{n}\bigg{(}\frac{m\pi r}{h}\sqrt{{% \sigma_{\textit{Eq}\left(i\right)}(f)}/{\hat{{\sigma}}_{it}(f)}}\bigg{)}\cos(n% \theta)∼{}+$ $\displaystyle\quad\left.{H_{\textit{imn}}(f)K_{n}\bigg{(}\frac{m\pi r}{h}\sqrt% {{\sigma_{\textit{Eq}\left(i\right)}(f)}/{\hat{{\sigma}}_{it}(f)}}\bigg{)}\sin% (n\theta)}\right]\sin\bigg{(}\frac{m\pi{\rm z}}{h}\sqrt{{\sigma_{\textit{Eq}% \left(i\right)}(f)}/{\hat{{\sigma}}_{il}(f)}}\bigg{)},$ (1)

$i=1,2,\ldots N,$

where $I_{n}(\cdot)$ is the n-order modified Bessel function of the first kind; $K_{n}(\cdot)$ is the n-order modified Bessel function of the second kind (In numerical calculation, $n$ indicates the order of the Bessel function; the larger $n$ is, the more precise the model calculation is; however, the relevant calculation needs more resources. In this paper, $n=$ 30); and $E_{\textit{imn}}(f)$ , $F_{\textit{imn}}(f)$ , $G_{\textit{imn}}(f)$ , and $H_{\textit{imn}}(f)$ indicate constant coefficients of the electric potential equation corresponding to the tissue in the $i$ -th layer at frequency $f$ ; $h$ is the length of human forearm, $\hat{{\sigma}}_{it}(f)$ and $\hat{{\sigma}}_{il}(f)$ represent respectively the tangential composite electric conductivity and the lateral one of the tissue in the $i$ -th layer at the frequency of $f$ , and $\sigma_{\textit{Eq}(i)}(f)=\sqrt{\hat{{\sigma}}_{it}(f)\hat{{\sigma}}_{il}(f)}$ .

The three sections of the human arm are independent of each other, while being connected by muscle, skin, and other flexible tissues. From Fig. 3, it can be seen that signals traveling transversely across the arm will be transmitted from A1 (TX) to A2 (RX), with a total transmission distance of $d$ . In the transmission channel, the joint length is supposed to be $z_{2}$ ; and the two points connecting the joint to the upper arm and forearm are $b$ and $c$ , respectively. The current continuity boundary conditions (2-b) and the potential continuity boundary conditions (2-c) can be derived in accordance with the continuous property of the volume conductor.

3.2 Electrical continuity condition at the joint

$\displaystyle\begin{cases}\vspace{6pt}\>d=z_{1}+z_{2}+z_{3}&\qquad({\rm a})\\ \vspace{6pt}\left.\begin{array}[]{@{} l @{}}\vspace{6pt}\left.{\tilde{{\sigma}% }_{i1}{\displaystyle\frac{\partial\varphi_{i}(f,r_{i},\theta,z_{1})}{\partial z% }}}\right|_{z=b}=\left.{\tilde{{\sigma}}_{i2}{\displaystyle\frac{\partial% \varphi_{i}(f,r_{i},\theta,z_{2})}{\partial z}}}\right|_{z=b}\\ \left.{\tilde{{\sigma}}_{i2}{\displaystyle\frac{\partial\varphi_{i}(f,r_{i},% \theta,z_{2})}{\partial z}}}\right|_{z=c}=\left.{\tilde{{\sigma}}_{i1}{% \displaystyle\frac{\partial\varphi_{i}(f,r_{i},\theta,z_{3})}{\partial z}}}% \right|_{z=c}\end{array}\right\}&\qquad({\rm b})\\ \left.\begin{array}[]{l @{}}\varphi_{i}(f,r,\theta,z_{1}=b)=\varphi_{i}(f,r,% \theta,z_{2}=b)\\ \varphi_{i}(f,r,\theta,z_{2}=c)=\varphi_{i}(f,r,\theta,z_{3}=c)\end{array}% \right\}&\qquad({\rm c})\end{cases},$ (2)

where $\tilde{{\sigma}}_{ik}=\sigma_{ik}+j\omega\varepsilon_{0}\varepsilon_{ik}$ , $i=1,2,\ldots,N-1,N$ , $k=\begin{cases}1&\text{others}\\ 2&\text{bone}\\ \end{cases}$ .

Table 1

Human arm’s circumference channel characteristics

	Circumference (mm)
Position	Source (TX)	Joint	Detection (RX)
Size	225	233	228

3.3 Sectionally continuous communication channel model

In terms of the fiber characteristics, channel model Eq. (3.1), and joint continuity Eq. (2), an arm channel model with joint characteristics may be expressed as follows.

$\varphi_{i}(f,r,\theta,z)=\varphi_{i}(f,r,\theta,z_{1})+\varphi_{i}(f,r,\theta% ,z_{2})+\varphi_{i}(f,r,\theta,z_{3}),$ (3)

where $\varphi_{i}(f,r,\theta,z_{1})$ is the coupling potential from the transmitting terminal ( $A_{1}$ ) to the connection ( $b$ ) between the upper arm and joint; $\varphi_{i}(f,r,\theta,z_{2})$ is the entire critical coupling potential from the connection ( $b$ ) between the upper arm and joint to the connection ( $c$ ) between the joint and forearm; $\varphi_{i}(f,r,\theta,z_{3})$ is the coupling potential from the connection ( $c$ ) between the joint and forearm to the receiving terminal ( $A_{2}$ ); and $\varphi_{i}(f,r,\theta,z)$ is the coupling potential from the transmitting to receiving terminal evaluated as the cumulative sum of all potentials from the transmitting to receiving terminal.

3.4 Geometric property of the joint

To verify model performance and applicability, we gathered experimental data from a healthy adult male. Measurements of his arm’s geometric properties are displayed in Table 1. According to Reference [6], the average length of an adult male’s joint is approximately 2.5 mm, and the main connection tissue is periosteum. In light of this, our model replaced bone tissue with periosteum at the joint.

Table 2
Channel model tissue parameters

	Frequency (HZ)	Conductivity $\sigma$ (S/m)	Relative permittivity $\epsilon$
Bone	1 k	2.00e-2	2.70e3
	10 k	2.00e-2	5.20e2
	100 k	2.10e-2	2.30e2
	1 M	2.40e-2	1.40e2
Muscle	1 k	3.20e-1	4.30e5
	10 k	3.40e-1	2.60e4
	100 k	3.60e-1	8.10e3
	1 M	5.00e-1	1.80e3
Fat	1 k	2.24e-2	2.41e4
	10 k	2.38e-2	1.09e3
	100 k	2.44e-2	9.29e1
	1 M	2.51e-2	2.72e1
Bone cortical	1 k	2.02e-3	2.70e3
	10 k	2.04e-2	5.22e2
	100 k	2.08e-3	2.27e2
	1 M	2.44e-3	1.45e2
Dry skin	1 k	2.00e-4	1.14e3
	10 k	2.04e-4	1.13e3
	100 k	4.51e-4	1.12e3
	1 M	1.32e-2	9.91e2

To reduce experimental error, all dead skin on the arm’s surface was first removed with an alcohol-soaked cotton swab before the experiment. Two pairs of ECG electrodes were placed on A1 and A2, respectively, with positive and the negative electrodes opposite each other. The experimental apparatus was the same as that used in the circumference measurement experiment.

In model calculation, we used the tissue parameters [14] in Table 2 as the electrical parameters of the model solution. From associated research findings [5, 6, 7], we learnt that the tissue at human joints is mainly comprised of bone cortex, namely $\tilde{{\sigma}}_{12}=\tilde{{\sigma}}_{\textit{BoneCortical}}$ . The electrical parameters of tissues (Table 2) are substituted into Models (1) and (3) to derive the arithmetic solution (Fig. 4) of the human forearm communication model in the frequency domain. In the accuracy evaluation of the model, the error between the model calculation and experimental result is one of the important indicators used to judge a model’s accuracy. In this paper, we used the calculation results and experimental results from two models to implement the subtraction used to obtain the error; the absolute value was used to evaluate the modeling error. The smaller the absolute value, the less the error, and the more accurate the model.

It can be seen from Fig. 4 that the channel model calculation results with and without joint characteristics have almost same variation curve as the experimental result. Without a joint section, the maximum error between the channel model calculation and experimental results is 6.86 dB, with an average error of 2.18 dB. However, when joint characteristics are considered, the maximum deviation between modeling and experimental results is 2.93 dB, and the average error is 1.45 dB. It is thus quantitatively shown that the latter model’s calculation result reduced the maximum error by 3.93 dB, additionally reducing the average error by 0.73 dB. Furthermore, the variation curve including joint characteristics exhibits an improved fit with experimental results, as clearly seen in Fig. 4. For this reason, we may draw the conclusion that the channel model with joint characteristics shows improved performance relative to the model without joint characteristics.

Figure 4.

Model calculation result and experiment result.

In the experiment, the geometrical parameters of a model exhibit distinct differences because of the difference between individuals. We used CT slices to assess sectional tissue to better estimate the geometrical distribution parameters of tissues belonging to different individuals.

4. Conclusions

In order to study the effect of heterogeneous distribution of tissues on the transmission channel, we designed a circumference measurement experiment and an accurate experimental model. The circumference measurement experiment demonstrated that neither path attenuation nor channel phase showed major dependence upon angular variation. In the quasi-static mode (f $<$ 200 kHz), the maximum path attenuation error caused by tissue distribution was 0.95 dB and the maximum phase error was 90 ${}^{\circ}$ . In channel modeling, both the errors were negligible. To analyze the effect of the joint on the communication channel, we established a sectionally continuous communication channel model. By comparing the obtained model calculation and experimental results with the model calculation result without joint characteristics, a visible improvement in the variation curve fit between the two was obtained. In summary, the channel model with joint characteristics was found to be quantitatively superior to that without joint characteristics.

Conflict of interest

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

Footnotes

Acknowledgments

This work presented in this paper is supported by the Sichuan Province Department of Science and Technology under Grant 2015JY0119, the Key Fund Project of Sichuan Provincial Department of Education under Grants (17CZ0005, 17ZA0047), the Engineering and Technical College of Chengdu University of Technology under Grants (C122015005, C122016030), the Leading Talent Training Project of Neijiang Normal University (2016 [Liu Yi-He]), the Foundation of Ph.D. Scientific Research of Neijiang Normal University.

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