Nano-Sensor Modelling for Intra-Body Nano-Networks

Abstract

In this work, the author has evaluated the propagation of electromagnetic waves inside the human tissue such as blood, skin and fat for single-path and multi-path layers according to nano sensor transmit power calculations. In particular, the propagation characteristics of the Intra-Body Nano-Network communication channel are calculated using a theoretical approach. The analysis in this paper provides an evaluation related to the path loss, bit error rate, signal to noise ratio and the channel capacity. The model is evaluated for each single-path effect and multi-path effect. The effects of human tissue for each blood, skin and fat for single-path effect and multi-path are included in the analysis. The model frequency range is chosen from 0.01 to 1.5 THz frequencies, which are ideal for designing nano sensors antennae and using THz range for communication. This paper will also guide other researchers who are working on the electromagnetic radiation performance of Intra-Body Nano-Network and Nano sensors designed at the THz range.

Full text

Vol.:(0123456789)
Wireless Personal Communications (2021) 118:3129–3143
https://doi.org/10.1007/s11277-021-08171-2
1 3
Nano‑Sensor Modelling forIntra‑Body Nano‑Networks
MustafaAlperAkkaş1
Accepted: 28 January 2021 / Published online: 11 February 2021
© The Author(s) 2021
Abstract
In this work, the author has evaluated the propagation of electromagnetic waves inside the
human tissue such as blood, skin and fat for single-path and multi-path layers according
to nano sensor transmit power calculations. In particular, the propagation characteristics
of the Intra-Body Nano-Network communication channel are calculated using a theoreti-
cal approach. The analysis in this paper provides an evaluation related to the path loss,
bit error rate, signal to noise ratio and the channel capacity. The model is evaluated for
each single-path effect and multi-path effect. The effects of human tissue for each blood,
skin and fat for single-path effect and multi-path are included in the analysis. The model
frequency range is chosen from 0.01 to 1.5 THz frequencies, which are ideal for designing
nano sensors antennae and using THz range for communication. This paper will also guide
other researchers who are working on the electromagnetic radiation performance of Intra-
Body Nano-Network and Nano sensors designed at the THz range.
Keywords Intra-body nano-networks· Human tissue· Path loss· Nano-communication·
Terahertz· Channel analysis
1 Introduction
Next generation wearable technologies, which is also supported with Internet of Things
(IoT) and Nano-technology have to be in miniature size. Therefore, the designers need to
work on higher frequencies such as 0.1–10 THz to reduce antenna size [1]. With the help
of Nano-technology, nano-communication and THz waves, nano or micro size machines
can communicate with each other [2, 3]. Since nano-technology was put forward in 1959,
it has not only gained great attention in body-centric applications, but it has also gained
great attention in many other fields [4]. Nano-technology, nano-networks and nano-com-
munication will greatly affect human life and health. Nano-machines which are especially
designed for the human body can be placed inside the body or surface-mounted on the
body. With the help of these technologies, patient data can be sent to monitoring centers
independent of the patient location [5].
* Mustafa Alper Akkaş
alperakkas@ibu.edu.tr
1 Department ofComputer Engineering, Bolu Abant Izzet Baysal University, 14280Bolu, Turkey
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One of the most important parts to achieve nano-technology is improving nano-
machines without battery. Nano-machines are nano sized nodes which are used for commu-
nication, sensing, computation etc. [6]. In Intra-Body Nano-Networks, communication is
done by nano-machines which function like nano-nodes [1]. The communication between
nano-nodes in Intra-Body Nano-Networks is still an open issue and there are challenges to
be solved [7]. So far, two communication methods have been used for Intra-Body Nano-
Networks. These are Electromagnetic Communication (EMC) and Molecular Communi-
cation (MC). EMC communication uses EM waves for communication and transmission
of information. MC systems are different from EMC, forming a new and interdisciplinary
research area, which use the absence or presence of a selected type of molecule to digi-
tally encode messages [8]. Molecules are used as a communication carrier in MC systems.
MC is a new, open and interdisciplinary research area, and there are many challenges to
be solved. These challenges are definition of MC channel model, characterization of MC
mechanisms, development of its architectures and the networks protocols [9].
As shown in Fig.1, the magnitude of the node needs to be in the nanometer size because
the place where nano-nodes are placed is too small in biomedical applications. Nano nodes
require THz antennas for their dimensions in EM communication. In THz band communi-
cation, phase shifting effects and path loss fluctuates according to the environment. There-
fore electromagnetic (EM) waves need to communicate where phase shifting effects and
path loss fluctuates are minimum. In EMC transmission distance between nodes can be
increased by using the bandwidths where absorption and path loss is minimum.
We know that battery dependent machines are limited to use. This rule is also valid for
nano-machines. That is why alternative energy methods should be developed like changing
vibrational movement, mechanical movement or hydraulic energy into electrical energy.
Another alternative energy method is charging batteries wirelessly but it’s not easy to
implement. Whence, nano-machines transmit power is very important and is covered in
this paper [10, 11]. Part of this work was presented in [12] and an extended version of the
article is given in this study.
In this paper, the author has carried out calculations of the Path Loss, bit error rate
(BER), signal to noise ratio (SNR) and Channel Capacity effect based on the channel model
Fig. 1 A schematic network
architecture for intra-body nano-
networks with nano-sensors
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for each single-path effect and multi-path effect, shown in Fig.2. The effect of the human
tissues according to Path Loss, BER, SNR and the Channel Capacity for each blood, skin
and fat for single-path effect and multi-path effect are included in the all analysis.
This paper is organized as follows. In Sect.2, related work is investigated. In Sect.3,
models for intra-body nano-networks for single and multi-layers are given. In Sect. 4,
graphs of the theoretical model are shown. Conclusions are drawn in the last section.
2 Related Work
Akyıldız etal. [13] present an overview of two main alternatives for nano-communication,
namely Electromagnetic Communication and Molecular Communication in the THz Band.
The aim of the study is to provide a better understanding of current research topics in this
important field and pave the way for future studies in nano-networks.
Yang etal. [14] modeled the human tissue with a 3-D numerical model at the THz range
but they did not consider multi-layers according to the nano-sensor transmit power calcula-
tion. They also specify this lack in their conclusion part.
Pratap Singh etal. [8] analyzed the probability density function of radiation absorption
noise and included the properties of different tissues of the human body to demonstrate its
applicability. Also, the closed form expression of error probability for MNC under radia-
tion noise is derived. Numerical analysis is shown in different tissues of the human body:
The polarization factor of the incoming EM radiation is shown as well as the skin, brain
and blood.
Again, Pratap Singh etal. [15] proposes a more general and appropriate noise model as
the Gaussian distribution to derive a new closed form expression of the conditional error
probability for the nano communication system. They have compared their noise model
with different models in the literature. Finally, with respect to the conditional error prob-
ability, closed form statements derived for average bit error rate, the Weibull-Gamma and
Mixture Gamma were derived from fading channels.
Fig. 2 Multi-path channel model
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Hadeel Elayan etal. [16] analyzed the photo thermal effects of the THz range inside the
human body as a heat diffusion mathematical model. Shortly they have analyzed EM waves
release energy as a heat to their environment.
Zhang etal. [17] investigates the mathematical model for invivo nano networks at the
THz range including the information speed and the noise of link. In their analytical model,
they have investigated signal-to-noise ratio according to different information and power
allocation for body-centric nano-networks.
In their paper, Piro etal. [18] present the range of transmission and the channel capacity
for intra-body systems for general healthcare applications. Again, Piro etal. [19] has stud-
ied the communication capabilities of a body area nano-network by carefully taking into
account the inhomogeneous and disordered structure offered by biological tissues.
However, most of the works presented above consider the human tissue as a single level.
In this work, a multi-layer communications method has been proposed. In addition, the
reflection properties between blood, fat and skin are investigated. This work also calcu-
lates the propagation of electromagnetic waves inside the human tissue containing blood,
skin and fat for single and multi-layers according to nano-sensor transmit power calcula-
tion. Transmit power calculation is an innovative topic which has not been investigated in
detail before as it is in this paper. Hence, this work investigates Intra-Body Nano-Network
communication propagation channel characteristics which are calculated using a theoreti-
cal approach that is modeled providing an evaluation about the losses, capacity, BER and
SNR considering the multipath effect of the channel according to the nano-sensor transmit
power calculation.
3 Model forIntra‑Body Nano‑Networks forSingle andMulti‑layers
The Friis Transmission Equation is used to calculate received power from an antenna to
another antenna at some distance given a transmission frequency and antenna gains. Friis
Equation is used to find the ideal power received at an antenna from basic information
about the transmission [20]. For the propagation in human tissue, noise power (NP), ther-
mal noise and additional losses (Lmedium) at the receiver which are caused by blood, skin
and fat are added to Friis equation in formula (1). To calculate the NP, the Bandwidth (B)
and ambient temperature (T), which is taken as body temperature of 310.15K, need to be
calculated. Consequently, the received signal in the Friis equation can be updated as [21]:
Table1 shows the values in equations.
In Eq.(1) LNP calculated as 10log10(103 × kB × T × B). Lmedium equals to:
Lmedium (2) is a combination of Lβ and Lα. Lα which is 8.96αd(dB) is the transmission
loss caused by attenuation with attenuation constant α. Lβ is the attenuation loss due to the
difference of the wavelength of the signal in medium, λ, compared to the wavelength in
free space, λ0. So Lβ can be also written as 20log(λ0/ λ). Here, in this formula λ = 2π/β and
(1)
P
r
(dBm)=P
t
(dBm)+G
r
(dB)+G
t
(dB)
−LFSPL(dB)−LNP (dBm)−Lmedium(dB
)


System Loss
(2)
Lmedium(dB)=L𝛽+L𝛼
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Nano-Sensor Modelling forIntra-Body Nano-Networks
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λ0 = c/f (Here c is speed of light) then Lβ can be written as 154 − 20log(f) + 20log(β) as dB.
Then Lmedium which is our body in this work becomes:
where parameters and constants are also given in Table1. Note that Lmedium in (2) depends
on the β, α of the human body [19]. The human body’s dielectric properties in this paper
are obtained from [14].
In these analyzes, the communication channel is modeled as an independent Rayleigh
distributed random variable, Xi, i ∈ {1,2} [22, 23]. The single-path model received energy
spectral density is given by (4) and has a distribution of (5).
The received signal is modeled as the addition of two independent Rayleigh distributed
random variables.
Consequently, the composite attenuation constant, X, for the multi-path model is given
by [22, 23]:
(3)
L
medium
(dB)=6.4 +20 log(d)+20 log(𝛽)+8.69𝛼d
𝛼
=2𝜋f
√
𝜇∈�
2[
1+(∈��
∈
�)2−1
]
,𝛽=2𝜋f
√
𝜇∈�
2[
1+(∈��
∈
�)2+1
]
(4)
r=X2SNR
(5)
f(r)=1
E
[
X2
1]
SNR exp
(
E
[
X2
1
]
SNR
E
[
X2
2]
SNR
)
(6)
X
2=X
2
1+

X2⋅Γ⋅exp (−𝛼Δ(r))

2−2⋅X1⋅X2⋅Γ⋅exp (−𝛼Δ(r)) ×cos

𝜋−

𝜙−
2𝜋
𝜆
Δ(r)

Table 1 Constants and parameters
Symbol Quantity Units Symbol Quantity Units
PrReceiving antenna’s power dBm α Attenuation constant 1/m
PtTransmitting antenna’s power dBm β Phase shifting constant rad/m
GtTransmitting antenna gain dB d Distance between nano-sensors m
GrReceiving antenna gain dB PtTransmit power dBm
LFSPL Free space path loss dB LfTotal path loss dBm
c Speed of ligh m/s PnNoise energy dBm
LNP Receiver’s noise power dBm LNP Noise power dBm
B Bandwidth Hz C Capacity bits/s
k Boltzmann constant j/K Γ Amplitude of the reflection coef-
ficient
–
T Ambient temperature 310.15K ϕ Phase angle of the reflection coef-
ficient
–
LβAttenuation loss dB α Attenuation constant –
LαTransmission loss dB X1, X2Single and multi path channel model
independent Rayleigh distributed
random variables envelope
–
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The SNR is given by SNR = Pt − Lf − Pn in paper [21]. In this paper Pt assumes − 15 to 5
dBm which are low enough for nano-node [7]. LNP is given by (7) as dBm [24]:
According to paper [23] 2PSK modulation has more range when we compare with other
modulations. For this reason, in this paper 2PSK modulation is considered. The BER rate
for 2 PSK is 0.5erfc((SNR)1/2) in additive white Gaussian noise (AWGN) [23].
The multi-path channel model in blood, fat and skin is shown in Fig.2. The reflections
are the same in the other human tissue because according to the papers [25, 26] the relative
magnetic permeability is 1 in all parts of the body. The single path is the direct path, which
is shown with the red line between the two sensors in Fig.2. The medium all around the
sensor nodes can be considered homogeneous for instance the model is suitable for higher
depths.
The multi-path channel model is given by (8) [20, 21, 25]
where human tissue is the path loss due to the single path given in (4) and the second part
of the equation is the second path’s attenuation factor which is unit in dB [22, 23, 27].
Capacity is the highest data rate that can be delivered reliably over a channel. The
resulting capacity is measured in bits/s because the logarithm is taken in base 2 in Eq.(9)
[14]. The unit of the bandwidth of the channel (B) is hertz. The signal and noise powers
are S and N. The ratio between S and N is called SNR. The detailed model of the system is
shown step by step in Fig.3 to make this section more easily readable.
4 Numerical Results
In this part the proposed channel model’s path loss, BER, attenuation factor, channel
capacity and SNR values are given.
Figure 4a gives the values of path loss for blood, skin and fat. Figure4b gives a 3D
version of Fig.4a. In Fig.4a and in the following figures the red lines show the blood, the
black lines show the skin and the blue lines show the fat. The lines style at figures are the
same in the following figures that is why lines style legend is not given in some following
figures not to make them complicated. Figure4 shows that when the frequency and dis-
tance increases path loss is increased. Path loss is directly proportional to frequency and
distance. Figure4 also shows that blood has higher path loss than skin and fat. The reason
why the blood has the highest path loss is that the amount of water in blood is more than
in skin and fat. The human blood contains about 45% of erythrocytes and 54.3% of plasma
by volume. The plasma contains about 92% water, while the erythrocytes, about 64% by
weight. These papers [28–30] also prove why the water has higher absorption and path
loss.
(7)
LNP =10log10(1000 ×k×T×B)(dBm)
(8)
L
f(dB)=LHuman Tissue(dB)−10 log

A
A
=1+(Γ×exp (−𝛼Δr))2−2Γexp (−𝛼Δr)2×cos 𝜋−𝜙−2𝜋f
𝜆Δ(2)

Δr=r−d,r=r1+r2(in Fig.2)
(9)
C
=Blog
2[
1+S∕N
]
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Figure5a shows BER vs. distance for 0.5–1.5 THz. Figure 5b examines the BER for
blood in the case of − 15 to 5 dBm transmit power and frequency at 0.5 THz. The results
show that BER of the 0.5–1.5 THz operating frequencies in blood, skin and fat for the
single path channel model increases between 1 and 3mm for blood, 1–5mm for skin and
2–7mm for fat at minimum received signal power of − 5 dBm. The millimeter size com-
munication distance increments are very important for nano-nodes inside the body. Fig-
ure5 proves that the communication range depends on the value of the dielectric loss of the
human body, remaining power of the node and the operating frequency. In Fig.5b shows
that each 5 dBm increment in Pt increases the communication distance around 0.1 mm.
Figure5c, d gives the values of capacity and SNR respectively that have been calculated
from (8). Figure5c shows that path loss increments cause less capacity and Fig.5d shows
that when the frequency decreases SNR increases and when the path loss increases SNR
decreases that is why 0.5 THz fat has the highest SNR.
Figure6a, b give the values of path loss at 0.5–1.5 THz for multi-path channel accord-
ing to distance and depth respectively. When we compare Fig.6a with Fig.4a the path loss
is around 80–300dB in one-path model and the path loss is around 100–300dB in multi-
path model. Figure6a also shows that in the multi-path model, communication distance at
path loss 100dB is up to 0.8mm, 1.4 mm and 2 mm in blood, skin and fat respectively.
Also in one-path model, the range is increased by 0.2mm, 0.4mm and 0.6mm in blood,
skin and fat respectively at 0.5 THz. Added reflection component of the signals do not help
to increase the communication distance in the multi-path model because there is not much
reflection in human tissue as seen in Fig.6b. Figure6b also shows that path loss values
depend on human tissue distance and depth. Fluctuations at Fig. 6b decreases when the
depth increases and almost disappears after distance around 0.2mm. Figure6c shows path
loss, distance and depth relation in 3D dimensions at 0.5 THz. The 3D graph shows that
at depths smaller than 0.2mm there is a wave, which is too small to affect communication
distance. In Fig.6d attenuation factor is given which is the second part of the Eq.7. As
seen in the Fig.6d attenuation factor decreases at depths smaller than 0.2mm this caused
the increased path loss in multi-path model and decreased the communication distance.
Fig. 3 Detailed model of the system
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This is also one reason why the multi-path channel model has smaller communication dis-
tance than one path-channel model.
Figure7 shows BER vs. distance for 0.5–1.5 THz operating frequencies for the multi-
path channel model. BER versus depth has not been given because there is almost zero
BER at all depths. Figure7a shows that the increment in the path loss has small effect on
BER in multi-path channel model. The BER rate is directly proportional to the distance.
Figure7b examines the BER for blood in the case of − 15 to 5 dBm transmit power Pt at
frequency 0.5–1.5 THz. When we compare Figs.5b with 7b we see that there is no much
difference between one-path and multi-path channel models. Only in the multi-path chan-
nel model, the transmission distance decreases around 1mm at 0.5 THz.
Figure8 shows Capacity versus distance and depth for 0.5–1.5 THz operating frequen-
cies for the multi-path channel model. Figure8a gives capacity values according to the
distance at − 5 dBm transmit power. Figure8b gives capacity values according to depth
at − 5 dBm transmit power. Figure8c gives capacity values according to distance at − 15
Fig. 4 Path loss vs. distance for
0.5 to 1.5THz in single-path
channel model. a 2D version, b
3D version
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to 5 dBm from 0.5 to 1.5 THz. From Fig.8a we can understand that capacity and path
loss inversely proportional to each other as expected. Figure8b shows the capacity at − 5
dBm transmit power according to depth. Fluctuations at Fig.8b decreases when the depth
increases and almost disappears after distance around 0.2mm as in the Fig.6b. Figure8c
gives capacity values according to distance at − 15 to 5 dBm transmit power in the blood.
Figure8c also shows that frequency and capacity inversely proportional to each other and
transmit power increases the capacity as expected.
Figure9 shows SNR vs. distance and depth for 0.5–1.5 THz operating frequencies for
the multi-path channel model. Figure 8a gives SNR values according to distance at − 5
dBm transmit power. Figure8b gives SNR values according to depth at − 5 dBm transmit
power. Figure8c gives SNR values according to distance at − 15 to 5 dBm from 0.5 to 1.5
THz. From Fig.9a we can understand that SNR and path loss are inversely proportional to
each other as expected. Figure9b shows the SNR at − 5 dBm transmit power according to
depth. Fluctuations at Fig.8b decreases when the depth increases and almost disappears
after distance around 0.4mm but see the effect at capacity and path loss up to 0.2 mm.
Figure9c gives SNR values according to distance at − 15 to 5 dBm transmit power. Fig-
ure9c also shows that frequency and SNR inversely proportional to each other and trans-
mit power increases the capacity as expected. At Fig.9c SNR values of 1 THz and 1.5
Fig. 5 BER, capacity and SNR versus distance for 0.5 to 1.5THz in single-path channel model. a BER ver-
sus distance, b BER for blood, c capacity, d SNR
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THz frequencies are not given because they are around the zero level. SNR values can help
other researchers who are working on terahertz intra body networks. SNR is also affected
from distance, frequency depth and transmit power. Figure9 also reminds us that SNR is
indirect proportional to frequency and direct proportional to transmit power.
5 Conclusion
Due to the small communication range inside the human body EM waves do not prop-
agate easily especially in THz Bands. This paper examines the path loss, BER, channel
capacity and SNR of nano-sensors propagating THz EM waves inside the blood, skin and
fat according to transmit power and channel type. Briefly, the paper sets the theoretical
background for the propagation of THz EM waves in blood, skin and fat in the THz range
and determines the incurred path loss, BER, capacity and SNR of nano-sensors in single-
channel and multi-channel. The paper also shows the reasons for why the multi-path chan-
nel model has smaller communication distance than one path-channel model. Numerical
evaluations show that data communication is possible over the 0.01–1.5 THz band at trans-
mit power − 15 to 5 dBm but to reach more communication distance, a new communication
Fig. 6 Path loss vs. distance and depth for 0.5–1.5THz in multi-path channel model. a Path loss versus dis-
tance, b Path loss versus depth. c Path Loss, Distance and Depth Relation. d Attenuation
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Nano-Sensor Modelling forIntra-Body Nano-Networks
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model needs to be investigated. Theoretical results show that wireless nano-sensor can
communicate through the human body but thermal noise is too high to use the THz waves
inside the human body. That is why new techniques need to be develop not to harm the
body at THz range. The results in this paper also aim to guide other researchers that will
be working in the area of the intra-body nano-networks. In the future, experiments can be
done by using spectroscopy at THz range to validate the numerical findings.
Fig. 7 BER versus distance
for 0.5–1.5THz in multi-path
channel model. a BER versus
distance, b BER for blood
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Fig. 8 Capacity vs. distance and
depth for 0.5 to 1.5THz in multi-
path channel model. a Capacity
versus distance. b Capacity
versus depth. c Capacity in the
Blood
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Fig. 9 SNR versus distance
and depth for 0.5 to 1.5THz in
multi-path channel model. a SNR
versus distance. b SNR versus
depth. c SNR in the Blood
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References
1. Akyildiz, I. F., & Jornet, J. M. (2010). Electromagnetic wireless nanosensor networks. Nano Commu-
nication Networks, 1(1), 3–19.
2. Akyildiz, I. F., Brunetti, F., & Blázquez, C. (2008). Nanonetworks: A new communication paradigm.
Computer Networks, 52(12), 2260–2279.
3. Chopra, N., etal. (2014). Understanding and characterizing nanonetworks for healthcare monitor-
ing applications. In 2014 IEEE MTT-S international microwave workshop series on RF and wire-
less technologies for biomedical and healthcare applications (IMWS-Bio). IEEE.
4. Feynman, R. P. (1992). There’s plenty of room at the bottom [data storage]. Journal of Microelec-
tromechanical Systems, 1(1), 60–66.
5. Abdelaziz, A. F., etal. (2015) Terahertz signal propagation analysis inside the human skin. In 2015
IEEE 11th International Conference on Wireless and Mobile Computing, Networking and Commu-
nications (WiMob). IEEE.
6. Bush, S. F. (2010). Nanoscale Communication Networks. Norwood: Artech House.
7. Dressler, F., & Fischer, S. (2015). Connecting in-body nano communication with body area net-
works: Challenges and opportunities of the Internet of Nano Things. Nano Communication Net-
works, 6(2), 29–38.
8. Singh, S. P., Singh, S., Guo, W., Mishra, S., & Kumar, S. (2020). Radiation absorption noise for
molecular information transfer. IEEE Access, 8, 6379–6387.
9. Pierobon, M., & Akyildiz, I. F. (2010). A physical end-to-end model for molecular communication
in nanonetworks. IEEE Journal on Selected Areas in Communications, 28(4), 602–611.
10. Lee, S. J., etal. (2015). Design of wireless nanosensor networks for intrabody application. Interna-
tional Journal of Distributed Sensor Networks, 2015, 90.
11. Akkaş, M. A. (2016). A comparative review of mote size and communication method for wireless
sensor network. In Applied mechanics and materials (Vol. 850). Trans Tech Publications.
12. Akkaş, M. A. (2016). Nano-sensor capacity and SNR calculation according to transmit power esti-
mation for body-centric nano-communications. In 2016 3rd international symposium on wireless
systems within the conferences on intelligent data acquisition and advanced computing systems
(IDAACS-SWS). IEEE.
13. Akyildiz, I. F., Jornet, J. M., & Pierobon, M. (2011). Nanonetworks: A new frontier in communica-
tions. Communications of the ACM, 54(11), 84–89.
14. Yang, K., etal. (2015). Numerical analysis and characterization of THz propagation channel for
body-centric nano-communications. IEEE Transactions on Terahertz Science and Technology, 5(3),
419–426.
15. Singh, S. P., Kumar, A., & Kumar, S. (2017). Novel expressions for CEP/BEP under GGD noise for
nano communication system. International Journal of Electronics Letters, 5(4), 463–474.
16. Elayan, H., Johari, P., Shubair, R. M., & Jornet, J. M. (2017). ’Photothermal modeling and analy-
sis of intrabody terahertz nanoscale communication. IEEE Transactions on NanoBioscience, 16(8),
755–763.
17. Zhang, R., Yang, K., Abbasi, Q. H., Qaraqe, K. A., & Alomainy, A. (2018). Analytical modelling
of the effect of noise on the terahertz in-vivo communication channel for body-centric nano-net-
works. Nano Communication Networks, 15, 59–68.
18. Piro, G., etal. (2015). Terahertz communications in human tissues at the nano-scale for healthcare
applications. IEEE Transactions on Nanotechnology, 14(3), 404–406.
19. Piro, G., et al. (2016). Terahertz electromagnetic field propagation in human tissues: A study on
communication capabilities. Nano Communication Networks, 10, 51–59.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

3143
Nano-Sensor Modelling forIntra-Body Nano-Networks
1 3
20. Friis, H. T. (1946). A note on a simple transmission formula. Proceedings of IRE, 34, 254–256.
https ://doi.org/10.1109/jrpro c.
21. Akkaş, M. A. (2018). Using wireless underground sensor networks for mine and miner safety. Wire-
less Networks, 24, 1–10.
22. Vuran, M. C., & Silva, A. R. (2010) Communication through soil in wireless underground sensor
networks–theory and practice. In Sensor networks (309–347). Berlin: Springer.
23. Akyildiz, I. F., Sun, Z., & Vuran, M. C. (2009). Signal propagation techniques for wireless under-
ground communication networks. Physical Communication, 2(3), 167–183.
24. Couch, I. I., & Leon, W. (1994). Modern communication systems: Principles and applications.
Upper Saddle River: Prentice Hall.
25. Pethig, R., & Kell, D. B. (1987). The passive electrical properties of biological systems: Their
significance in physiology, biophysics and biotechnology. Physics in Medicine and Biology, 32(8),
933.
26. Collins, C. M., etal. (2002). Numerical calculations of the static magnetic field in three-dimensional
multi-tissue models of the human head. Magnetic Resonance Imaging, 20(5), 413–424.
27. Li, L., Vuran, M.C., & Akyildiz, I. F. (2007). Characteristics of underground channel for wireless
underground sensor networks. In Proceedings of Med-Hoc-Net’07.
28. Akkaş, M. A., & Sokullu, R. (2015). Channel modeling and analysis for wireless underground sen-
sor networks in water medium using electromagnetic waves in the 300–700 MHz range. Wireless
Personal Communications, 84(2), 1449–1468.
29. Akkaş, M. A., Akyildiz, I. F., & Sokullu, R. (2012). Terahertz channel modeling of underground sen-
sor networks in oil reservoirs. In Global communications conference (GLOBECOM), 2012 IEEE.
IEEE.
30. Akkaş, M. A. (2019). Terahertz wireless data communication. Wireless Networks, 25, 1–11.
Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and
institutional affiliations.
Mustafa Alper Akkaş received his B.S. degree in Electrical and Elec-
tronics Engineering from Erciyes University in 2006. He received his
Ph.D. degree in the Department of Electrical Engineering and Elec-
tronics at Ege University in 2014. Currently, he is an associate profes-
sor at the Department of Computer Engineering at Bolu Abant Izzet
Baysal University. His research interests include Wireless underground
communication networks, Terahertz-band communication networks,
Intra-body wireless nanosensor networks and Internet of Things. He
was a visiting student at Georgia Institute of Technology, in the Broad-
band Wireless Networking Lab under the supervision of Prof. Ian F.
Akyildiz from September 2011 to May 2012.
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