Channel Modeling for In-Body Optical Wireless Communications

Abstract

Next generation in-to-out-of body biomedical applications have adopted optical wireless communications (OWCs). However, by delving into the published literature, a gap is recognized in modeling the in-to-out-of channel, since most published contributions neglect the particularities of different types of tissues. In this paper, we present a novel pathloss and scattering models for in-to-out-of OWC links. Specifically, we derive extract analytical expressions that accurately describe the absorption of the five main tissues’ constituents, namely fat, water, melanin, and oxygenated and de-oxygenated blood. Moreover, we formulate a model for the calculation of the absorption coefficient of any generic biological tissue. Next, by incorporating the impact of scattering in the aforementioned model, we formulate the complete pathloss model. The developed model is verified by means of comparisons between the estimated pathloss and experimental measurements from independent research works. Finally, we illustrate the accuracy of the proposed model in estimating the optical properties of any generic tissue based on its constitution. The extracted channel model is expected to enable link budget analysis, performance analysis, and theoretical framework development, which will boost the design of optimized communication protocols for a plethora of biomedical applications.

Full text

Article
Channel Modeling for In-Body Optical Wireless Communications †
Stylianos E. Trevlakis 1,* , Alexandros-Apostolos A. Boulogeorgos 2, Nestor D. Chatzidiamantis 1
and George K. Karagiannidis 1


Citation: Trevlakis, S.E.;
Boulogeorgos, A.-A.A.;
Chatzidiamantis, N.D.; Karagiannidis,
G.K. Channel Modeling for In-Body
Optical Wireless Communications.
Telecom 2022,3, 136–149. https://
doi.org/10.3390/telecom3010009
Academic Editor: Thomas Newe
Received: 3 November 2021
Accepted: 27 January 2022
Published: 4 February 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
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iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki,
54124 Thessaloniki, Greece; nestoras@auth.gr (N.D.C.); geokarag@auth.gr (G.K.K.)
2Department of Digital Systems, University of Piraeus, 18534 Piraeus, Greece; al.boulogeorgos@ieee.org
*Correspondence: trevlakis@auth.gr
† This paper is an extended version of our paper published in part at the 10th International Conference on
Modern Circuits and Systems Technologies (MOCAST), Thessaloniki, Greece, 5–7 July 2021.
Abstract:
Next generation in-to-out-of body biomedical applications have adopted optical wireless
communications (OWCs). However, by delving into the published literature, a gap is recognized in
modeling the in-to-out-of channel, since most published contributions neglect the particularities of
different types of tissues. In this paper, we present a novel pathloss and scattering models for in-to-
out-of OWC links. Specifically, we derive extract analytical expressions that accurately describe the
absorption of the five main tissues’ constituents, namely fat, water, melanin, and oxygenated and de-
oxygenated blood. Moreover, we formulate a model for the calculation of the absorption coefficient
of any generic biological tissue. Next, by incorporating the impact of scattering in the aforementioned
model, we formulate the complete pathloss model. The developed model is verified by means of
comparisons between the estimated pathloss and experimental measurements from independent
research works. Finally, we illustrate the accuracy of the proposed model in estimating the optical
properties of any generic tissue based on its constitution. The extracted channel model is expected to
enable link budget analysis, performance analysis, and theoretical framework development, which
will boost the design of optimized communication protocols for a plethora of biomedical applications.
Keywords:
absorption coefficient; biomedical engineering; fitting; machine learning; optical properties;
pathloss; scattering coefficient
1. Introduction
The dawn of the sixth generation (6G) wireless communication era comes with the
promise of enabling revolutionary multi-scale applications [
1
]. An indicative example is
in-to-out-of-body biomedical applications [
2
]. Beyond the technical requirements, such as
high reliability and energy efficiency and low power consumption and latency, they need
to invest in wireless technologies that, on the one hand allow compact deployments, while
on the other soothe possible safety concerns.
The reliability, speed, energy efficiency, and latency of optical wireless communications
(OWCs) in biomedical applications have been accurately quantified and experimentally
verified over the last decade, and a great amount of research effort has been devoted
towards optimising in-body OWC systems [
3
–
7
]. The current state-of-the-art system would
greatly benefit from an accurate pathloss model capable of incorporating any generic
tissue’s characteristics.
Motivated by this, several researchers turned their eyes to OWCs for biomedical
applications. Specifically, [
8
–
10
] investigated the optical properties of human brain tissue
at various ages in the visible spectrum. Additionally, in [11,12], the optical characteristics,
as well as the mineral density of the bone tissue, was measured in the range from 800 to
2000
nm
. Moreover, the authors in [
13
–
15
] performed experiments in order to measure
the optical properties of human female breast tissues in multiple wavelengths and over
different distances, while, in [16–18], the optical properties of both healthy and cancerous
Telecom 2022,3, 136–149. https://doi.org/10.3390/telecom3010009 https://www.mdpi.com/journal/telecom

Telecom 2022,3137
skin were studied in the visible and near-infrared spectral range. From the aforementioned
works, it is observed that the majority of published works have focused on quantifying
the optical characteristics of specific tissues at certain wavelengths [
8
–
18
]. Despite the
significance of these results, they cannot always be exploited from future researchers due to
the fact that they may not include all the necessary wavelengths, while even if the desired
wavelength is available, the constitution of a tissue is different enough between distinct
individuals that the results cannot be regarded as confident.
A method that estimates the optical properties of any generic tissue based on its
constitution is required in order to aid the development of novel biomedical applications
that utilise the optical spectrum for communication. As a result, specific formulas have
been reported for the pathloss evaluation of a generic tissue that take into account the
variable amounts of its constituents (i.e., blood, water, fat, melanin) but require their
optical properties at the exact transmission wavelength, which hinders the use of these
formulas [
19
,
20
]. The development of such a method will open the road towards not
only the theoretical analysis of in-to-out-of body OWC links but also the design of novel
transmission and reception schemes, as well as scheduling and routing techniques for
next generation networks. Motivated by this, this work derives a novel mathematical
model, which requires no experimental measurements for the calculation of the pathloss
for in-body OWCs. In more detail, the technical contribution of this work is summarized
as follows:
•
The utilization of an ML-enabled mathematical framework for the extraction of ana-
lytical expressions for the absorption coefficients of the main constituents of tissues,
namely oxygenated and de-oxygenated blood, water, fat, and melanin.
•
Based on these expressions, we drew a general model that enabled the estimation of
the absorption coefficient of any generic tissue (i.e., skin, muscle, etc.) based only on
its constitution.
•
The usability of this model was extended by incorporating the phenomenon of scatter-
ing in the analysis and, therefore, increasing the estimation accuracy of the attenuation
due to the existence of generic tissues. This model is expected to have a great impact
in the design and optimization of future medical devices that require the transmission
of optical radiation inside the human body.
•
We validated the extracted expression twofold. On the one hand, we fed experimental
data into the ML algorithm to extract the mathematical expressions of the aforemen-
tioned coefficients and we drew the numerical results to visualize their performance.
On the other hand, we compared the extracted numerical results against experimental
data taken from different published papers and provided proof that they coincide.
This twofold comparison illustrates the validity of the presented channel model.
•
We provided the design with insightful discussions based on the pathloss varia-
tions, with regard to variable transmission wavelength, complex tissue types, and
tissue thickness.
The organisation of this paper and a list of variables alongside their names are pre-
sented in Figure 1and Table 1, respectively. In more detail, Section 2is devoted to presenting
the pathloss model based on the absorption and scattering properties of the constituents
of any generic tissue. Section 3presents respective numerical results that verify the math-
ematical framework and insightful discussions, which highlight design guidelines for
communication protocols. Finally, future research directions are highlighted in Section 4,
while closing remarks are summarized in Section 5.

Telecom 2022,3138
1. Introduction
2. Pathloss Model
2.1 Absorption
2.2 Scattering
3. Results
3.1 Verification
3.2 Pathloss
4. Conclusions
References
Figure 1. The structure of this paper.
Table 1. Table of variables.
Variable Name
BBlood volume fraction
cos(·)Cosine function
δTissue thickness
exp(·)Exponential function
FFat volume fraction
fRay Rayleigh scattering factor
gAnisotropy factor
LPathloss
MMelanin volume fraction
µaAbsorption coefficient
µsScattering coefficient
µ0
sReduced scattering coefficient
sin(·)Sine function
WWater volume fraction
2. Channel Model
The losses due the propagation of optical radiation through any biological tissue can
be expressed based on classic OWC theory, as in [21].
L=exp((µa+µs)δ), (1)
where
µs
and
µa
represent the scattering and absorption coefficient, respectively, while
δ
is the propagation distance that is in the range of some mm in real world applications,
such as cochlear, cortical, and retinal implants [
22
]. In addition, the TX and RX are placed
at fixed positions and are characterized by high directivity. Therefore, the link under
investigation can be regarded as line-of-sight (LoS). However, as discussed in Section 4, we
aim to extend the current research to incorporate non-LoS scenarios, where diffusion plays
an important role.
2.1. Absorption
The absorption coefficient can be modeled as
µa=−1
T
dT
dδ, (2)

Telecom 2022,3139
with
T
denoting the fraction of residual optical radiation at distance
δ
from the origin of
the radiation. Thus, the fractional change of the incident light’s intensity can be written as
in [23].
T=exp(−µaδ). (3)
As a result,
µa
can be expressed as the sum of all of the tissue’s constituents, namely water,
melanin, fat, and oxygenated and de-oxygenated blood. Thus,
(2)
can be analytically
expressed as in [19].
µa=BSµa(oBl)+B(1−S)µa(dBl)+Wµa(w)+Fµa(f)+Mµa(m), (4)
where
µa(i)
represents the absorption coefficient of the
i
-th constituent, while
B
,
W
,
F
,
and
M
represent the blood, water, fat, and melanin volume fractions, respectively. Finally,
Sdenotes the oxygen saturation of hemoglobin.
From
(4)
, we observe that the absorption coefficients and volume fractions of each
constituent are required in order to calculate the complete absorption coefficient of any
tissue. At this point, it is essential to highlight the dependence of any tissue’s optical prop-
erties on the type of tissue, person, and even the procedure of collecting the sample, which
hinders their mathematical modeling, despite the recent advances in optical measurement
techniques. Although such variations are inherent characteristics of each individual and
are subject to tissue preparation protocols, it has been proven in various past publications
that they are mainly dependent on the wavelength of the transmitted optical radiation.
Based on the aforementioned, we utilised the non-linear regression-based machine
learning algorithm presented in Algorithm 1to derive analytical expressions for the absorp-
tion coefficients based on experimental datasets for each of the constituents [
24
]. In more
detail, the experimental data of the absorption coefficient of water in [
25
–
27
] were used to
extract a Fourier series that accurately describes the absorption coefficient as a function of
the transmission wavelength, which can be written as:
µa(w)(λ)=a0(w)+
7
∑
i=1
ai(w)cos(iwλ)+bi(w)sin(iwλ). (5)
Moreover, the analytical expressions of the absorption coefficients of oxygenated and
de-oxygenated blood were fitted on the experimental results presented in [
28
–
31
] by using
the sum of Gaussian functions and can be expressed as:
µa(oBl )(λ)=
5
∑
i=1
ai(oBl )exp
− λ−bi(oBl )
ci(oBl )!2
, (6)
and
µa(dBl)(λ)=
4
∑
i=1
ai(dBl)exp
− λ−bi(dBl)
ci(dBl)!2
. (7)
Furthermore, special attention is required for the appropriate preparation of fat tissue,
which requires proper purification and dehydration before measuring its optical properties.
As mentioned in [
32
], this necessary procedure can result in inconsistencies between
different published works. To limit this phenomenon, we selected the measurements in [
32
]
as they coincide with multiple published works in the visible spectrum. The extracted

Telecom 2022,3140
analytical expression of the absorption coefficient of fat can be written as a sum of Gaussian
functions, as follows:
µa(f)(λ)=
5
∑
i=1
ai(f)exp
− λ−bi(f)
ci(f)!2
. (8)
Note that the parameters of the aforementioned expressions are presented in Table 2.
Finally, the absorption coefficient of melanin is highly consistent throughout various
experimental measurements in the visible spectrum [
19
,
33
,
34
], based on which we write its
analytical expression as:
µa(m)(λ)=µa(m)(λ0)λ
550 −3
, (9)
with
µa(m)(λ0)
denoting the absorption coefficient of melanin at
λ0=
550
nm
, which is
equal to 519 cm−1[34].
Table 2. Fitting parameters for the constituent’s absorption coefficient.
dBlood oBlood Water Fat
a0- - 324.1 -
a138.63 14 102.2 33.53
a260.18 13.75 −568 50.09
a325.11 29.69 −126.6 3.66
a42.988 4.317 ×1015 236.8 2.5
a5-−34.3 73 19.86
a6- - −40.53 -
a7- - −12.92 -
b1423.9 419.7 697.9 411.5
b231.57 581.5 121.7 968.7
b3559.3 559.9 −395.3 742.9
b4664.7 −25,880 −107.1 671.2
b5- 642.6 115.6 513.8
b6- - 35.46 -
b7- - −8.373 -
c133.06 16.97 - 38.38
c2660.8 11.68 - 525.9
c359.08 46.71 - 80.22
c428.53 4668 - 32.97
c5- 162.5 - 119.2
w- - 0.006663 -

Telecom 2022,3141
Algorithm 1 ML-based fitting mechanism
1: procedure ({µa(i),X}i∈{oBl, bBl, w, f}, NMSE, λ,{aj,bj,cj,wj}j∈[0,ki])
2: for i∈ {oBl, bBl, w, f}do
3: ki←degrees of freedom
4: for j∈[1, ki]do
5: aj←0, bj←0, cj←1, wj←0, λ←400 nm.
6: while {aj,bj,cj,wj} ∈ R,λ∈[400, 1000]nm do
7: Normalized Mean Square Error (NMSE)0←kX−µa(i)k2
2
kXk2
2
8: if NMSE0<NMSE then
9: break
10: end if
11: end while
12: end for
13: end for
14: end procedure
2.2. Scattering
The analysis so far neglects the effects of scattering on the propagation of the optical
radiation through the human tissue. So far, the transmission distance,
δ
, was regarded as
a single linear path through the material. However, when taking into account the optical
scattering, it became the sum of all the paths between scattering events. The analytical
evaluation of scattering is not well defined in the literature due to its stochastic nature,
especially in diffuse reflectance geometries, such as the majority of tissues found inside
the human body. In more detail, the scattering phenomenon can be decomposed into
two factors, namely mean free path and phase function. The former represents the mean
distance between two scattering instances, while the latter quantifies the stochastic change
in direction of a photon when scattering occurs. Throughout the literature, the mean
free path is represented as the inverted scattering coefficient, i.e.,
1
µs
, which represents
the probability of scattering as a function of the transmission distance. Furthermore,
the scattering coefficient can be expressed in terms of the more tractable reduced scattering
coefficient as
µ0
s=(1−g)µs, (10)
where
g
represents the anisotropy factor of the generic tissue. On the other hand, the stochas-
tic behavior of the phase function can be mathematically defined based on Mie scatter-
ing theory.
Unlike absorption, there is no well-defined analytical relationship that can be used
to define the spectral dependence of volume scattering. However, based on experimental
observations and simplifying analysis of Mie scattering theory, there is a consensus that the
reduced scattering coefficient can be modeled using a power law relationship, as in [19].
µ0
s=µ0
s(δ0)δ
δ0−β
, (11)
where
µ0
s(δ0)
denotes the reduced scattering coefficient at distance
δ0
and
β
is a dimension-
less variable that provides an estimation of the average size of particles in the medium,
for instance, if the tissue is composed of small sized particles,
β≈
4, which can be modeled
as Rayleigh scattering. On the contrary, if larger particles exist in the tissue,
β
approaches

Telecom 2022,3142
0.37 [
35
,
36
]. However, when a generic tissue is comprised of variable size particles, which is
the most common case, the reduced scattering coefficient can be expressed, as in [
21
,
32
,
37
].
µ0
s=µ0
s(δ0) fRayδ
δ0−4
+1−fRayδ
δ0−β!, (12)
which corresponds to the combination of the two limiting cases, namely Rayleigh and Mie
scattering, with
fRay
denoting the fraction of Rayleigh scattering due to the existence of
small sized particles.
3. Results
This section illustrates the performance of the model presented in Section 2. Initially,
the extracted expressions for the absorption and scattering coefficients are verified by
comparison with experimentally verified results from previously published works. Next,
the accuracy of the extracted mathematical framework for estimating the optical properties
of any generic tissue is validated against experimental measurements of complex biological
tissues, such as skin, bone, breast, and brain tissue. Lastly, the complete pathloss for
each of the aforementioned tissues is evaluated, and important design guidelines for
communication protocols are derived through insightful discussions.
3.1. Verification
In this subsection, we verify the validity of the extracted analytical expressions pre-
sented in Section 2by comparing them with experimentally verified data from published
works. In the following figures, the analytical expressions and the experimental results are
depicted as continuous lines and geometric symbols, respectively. Starting with
Figure 2a
,
experimental data for the absorption coefficient of each constituent are plotted against the
analytical results extracted from
(6)
through
(9)
. In particular, the experimental data for the
oxygenated and de-oxygenated blood, water, melanin, and fat are represented by square,
circle, star, triangle, and cross symbols, respectively, while the corresponding analytical
expressions are drawn in black, red, green, blue, and purple colors. The validity of the
proposed framework is proven based on the fact that the analytical and experimental
results coincide. Moreover, the absorption coefficient of blood is not only higher than the
rest of the constituents, between 400 and 600
nm
, but is also among the most influential
constituents regardless of the wavelength. Therefore, even with relatively low volume
fraction, blood plays an important role in the total absorption coefficient of any generic
tissue. Furthermore, it is evident that, as
λ
increases, the absorption coefficient increases as
well, which highlights the importance of carefully selecting the transmission wavelength
for tissues that are rich in water. In addition, the absorption of melanin is among the highest
between the generic tissue constituents, as well as the most consistent. This illustrates
the significance of the concentration of melanin in the tissue under investigation and,
at the same time, the negligible effect of the transmission wavelength on the absorption
due to melanin. Lastly, the absorption coefficient of fat has a somewhat stable impact
throughout the visible spectrum due to the fact that it receives values around 1
cm−1
, with
very small variations.
It should be highlighted that the volume fraction of any of the constituents plays a very
important role in the final form of the absorption coefficient. For instance, if a tissue has a
high concentration in water, the impact of its absorption coefficient after it is multiplied
by the water volume fraction can affect the total absorption coefficient significantly, even
if the absorption coefficient of water seems insignificant on its own. On the other hand,
the impact of a constituent with high absorption coefficient, such as melanin, can be
diminished if it has a low volume fraction. Thus, although the absorption coefficients
presented in Figure 2a play an important role in determining which of them affect the
total absorption coefficient of the generic tissue, it is not an absolute metric. The rest of
this subsection illustrates the performance of the proposed mathematical framework by

Telecom 2022,3143
comparing the estimation of the absorption and scattering coefficients of complex human
tissues with experimental results from the open literature.
400 500 600 700 800 900 1000
10- 4
10- 3
10- 2
10- 1
100
101
102
103
104
μ
a ( c m - 1 )
λ (n m )
A n a l y t i c a l E x p e r i m e n t a l
o B lo o d
d B lo o d
M e la nin
W a te r
F a t
(a)
400 500 600 700 800 900 1000
10- 2
10- 1
100
101
102
μ
a ( c m - 1 )
λ (n m )
A n a l y t i c a l E x p e r i m e n t a l
S k in
B r e a st
B r a in
B o n e
(b)
400 500 600 700 800 900 1000
101
102
μ
's ( c m - 1 )
λ (n m )
A n a l y t i c a l E x p e r i m e n t a l
S k in
B r e a s t
B r a in
B o n e
(c)
Figure 2.
Attenuation coefficients of complex tissues and their constituents as a function of
λ
.
(
a
) Absorption coefficient of tissue constituents. (
b
) Absorption coefficient of complex tissues.
(c) Reduced scattering coefficient of complex tissues.
Next, Figure 2b presents the absorption coefficients of complex tissues, such as skin,
bone, brain, and breast, as a function of the transmission wavelength. The parameters that
characterise the constitution of each tissue are provided in Table 3, alongside their sources.
From Figure 2b, it can be observed that the analytical expression for the total absorption
coefficient provide a very close fit to the experimental data, which not only verifies the
extracted expressions but also complements the accuracy of the presented mathematical
framework in describing the optical absorption in generic tissues. Moreover, the absorption
coefficient of the skin has the most linear behavior out of all of the plotted tissues. This
happens due to the increased concentration of melanin in the skin, which leads to increased
absorption in higher wavelengths. In addition, the absorption coefficients of other tissues
that are rich in blood and water bare a strong resemblance to the blood absorption coefficient
in the region between 400 and 600
nm
, while the impact of water becomes visible after
900
nm
. The higher concentration of blood and water results in increased attenuation in
the wavelengths, where each of them has relatively high absorption.
Figure 2c depicts the experimental data for the reduced scattering coefficient of each
of the complex tissues, namely skin, bone, brain, and breast, against the analytical results
extracted from
(12)
. The experimental parameters for each of the tissues are available
in Table 3, alongside their sources. This figure verifies the validity and accuracy of the
extracted expressions for the reduced scattering coefficient due to the proved fact that they
provide a very close fit to the experimental data. Furthermore, all of the reduced scattering

Telecom 2022,3144
coefficients not only exhibit a more linear behavior than the corresponding absorption
coefficients, but also hold significantly higher values. This highlights the detrimental
effect that scattering plays in the propagation of optical radiation through the human body.
Moreover, it is evident that, as
λ
increases, the reduced scattering coefficient decreases,
which suggests that, as we increase the transmission wavelength, the impact of scattering
could prove to diminish. For example, for skin tissue, as
δ
rises from 400
nm
to 1000
nm
,
the reduced scattering coefficient decreases by 87.5%. Finally, we observed that skin caused
almost half an order of magnitude higher attenuation than the rest of the tissues under
investigation, while brain tissue exhibited the lowest.
Table 3.
Tissue parameters related to optical absorption and scattering for skin, bone, brain, and
breast tissue.
Tissue B S W F M fRay β µ0
s(δ0)gSource
Skin 0.41 99.2 26.1 22.5 1.15 0.409 0.702 48 0.92 [13,16–18]
Breast 0.5 52 50 13 0 0.288 0.685 18.7 0.96 [13–15]
Bone 0.15 30 30 7 0 0.174 0.447 19.3 0.93 [11–13]
Brain 1.71 58.7 50 20 0 0.32 1.09 12.72 0.9 [8–10]
3.2. Pathloss
Based on the extracted accurate expressions for the reduced scattering and absorption
coefficients of various complex tissues that take into account the particularities of the
channel, we can estimate the pathloss. Therefore, Figure 3a depicts the pathloss as a
function of the wavelength due to absorption and scattering in skin tissues with different
values of thickness. In order to ensure a fair comparison between the plotted tissues, it
is necessary to use the same tissue thickness, with the determining tissue being the skin,
whose average thickness varies between 0.5 and 4 mm [
22
]. Thus, we selected a slightly
wider range of thickness for the analysis, i.e., 1–5 mm. Additionally, it is highlighted that,
in order to increase the readability of Figure 3, the area below each line is depicted in
a specific color that corresponds to a specific skin thickness value. From this figure, it
is evident that the complete pathloss (continuous line) decreased with the wavelength
and increased with the skin thickness, while the pathloss due to absorption (dashed line)
had more fluctuations throughout the visible spectrum. In more detail, we observed
that the optimal wavelength was 1000
nm
. Furthermore, in the following, we assumed a
transmission window to be the spectrum region where the pathloss did not exceed 6
dB
(red
dotted line), i.e., the residual optical signal was at least a quarter of the transmitted signal.
Thus, for
δ=
1
mm
, a transmission window existed for wavelength values higher than
450
nm
, which shrank as the transmission distance increased. For instance, for
δ=
3
mm
it reduced to wavelengths higher than 650
nm
, while for
δ>
3
mm
, it became even
smaller. On the other hand, when taking into consideration the scattering coefficient,
the complete pathloss exhibited a more linear behavior. Specifically, the impact of scattering
in the propagation of light through biological tissues was approximately two orders of
magnitude higher than that of the absorption, which constitutes the dominant phenomenon
concerning the optical transmission. For example, if we assume
δ=
5
mm
and
λ=
600
nm
,
the scattering coefficient exceeds
µa
100 times, while for
λ=
600
nm
,
µs
is 125 times higher.
As a result, it is obvious that the absorption coefficient decreases with an increased rate
compared to µs.
Figure 3b illustrates the pathloss due to the existence of brain tissue as a function of
the wavelength for different values of
δ
. As expected, for higher values of
δ
, the pathloss
was also higher, while the behavior of pathloss for wavelength variations was not linear.
For example, as
λ
increased from 500 to 550
nm
the pathloss increased, and while for
the same increased from 550 to 600
nm
, pathloss decreased. Additionally, the optimal
transmission wavelength was 700
nm
. In addition, two transmission windows existed for

Telecom 2022,3145
δ=
4
mm
. The first was between 450 and 550
nm
, while the second was after 600
nm
.
However, as the transmission distance increased, only the second window was valid.
Furthermore, when taking into consideration the effect of scattering, the complete pathloss
took much higher values and the fluctuations of the absorption became almost obsolete,
with its impact being visible only in the 400 to 500
nm
range. By observing Figure 3b, it
became evident that the impact of
µa
varied greatly with the wavelength, which resulted in
fluctuations of the relation between
µs
and
µa
. For instance, for
δ=
1
mm
, as
λ
increased
from 400 to 700
nm
, the relation between the scattering and absorption coefficient increased
from 10xto 400x.
400 500 600 700 800 900 1000
10- 2
10- 1
100
101
102
103
104
P a t h l o s s ( d B )
λ (n m )
δ = 5 m m
δ = 4 m m
δ = 3 m m
δ = 2 m m
δ = 1 m m
(a)
400 500 600 700 800 900 1000
10- 2
10- 1
100
101
102
103
104
P a t h l o s s ( d B )
λ (n m )
δ = 5 m m
δ = 4 m m
δ = 3 m m
δ = 2 m m
δ = 1 m m
(b)
400 500 600 700 800 900 1000
10- 2
10- 1
100
101
102
103
104
P a t h l o s s ( d B )
λ (n m )
δ = 5 m m
δ = 4 m m
δ = 3 m m
δ = 2 m m
δ = 1 m m
(c)
400 500 600 700 800 900 1000
10- 2
10- 1
100
101
102
103
104
P a t h l o s s ( d B )
λ (n m )
δ = 5 m m
δ = 4 m m
δ = 3 m m
δ = 2 m m
δ = 1 m m
(d)
Figure 3.
Pathloss due to absorption and scattering of various tissues as a function of the transmission
wavelength for different values of tissue thickness. Continuous and dashed lines denote the complete
pathloss and the pathloss only due to the absorption coefficient. (
a
) Skin tissue. (
b
) Brain tissue.
(c) Breast tissue. (d) Bone tissue.
In Figure 3c, the pathloss for transmission through breast tissue is presented with
regard to the transmission wavelength for various values of tissue thickness. When taking
into account only the absorption phenomenon, it was evident that, as the
δ
increased,
the pathloss increased as well. On the contrary, the wavelength influenced the pathloss in
a non-linear manner. Additionally, a single transmission window was observed for all the
plotted values of
δ
for wavelengths higher than 450
nm
. Although the optimal transmission
wavelength for breast tissue with regard to the absorption was 700
nm
, after introducing
the scattering coefficient into the analysis, the complete pathloss exhibited an almost linear
behavior and the optimal wavelength shifted to 1000
nm
. The increased impact of
µs
varied between 1 and 3 orders of magnitude more than the absorption coefficient’s impact.
Specifically, for
δ=
1
mm
and
λ=
400
nm
,
µs
was approximately 33 times higher than
µa
,
while for λ=650 nm, it was 600 times higher.
Finally, Figure 3d depicts the pathloss through bone tissue as a function of the trans-
mission wavelength for various transmission distance values. Yet again, pathloss increases

Telecom 2022,3146
with tissue thickness, while its behavior, with regard to
λ
, depends. The optimal
λ
for
transmission through bone tissue is 700
nm
. For the plotted
δ
values, only one transmission
window exists for
λ
higher than 425
nm
, while for higher values, two transmission win-
dows can be formed. For example, the first window was between 475 and 525
nm
, while
the second was in the range of 600–950 nm. However, the complete pathloss appeared to
be the most detrimental between the studied tissues, which was expected due to the more
compact constitution of the bone tissue. This effect was highlighted by the fact that after
adding the scattering phenomenon in our simulations, the complete pathloss increased by
almost three orders of magnitude. In more detail, for a specific value of
δ
equal to 5
mm
,
as the transmission wavelength increased from 400 to 950
nm
, the relation between the
µs
and µaincreased from 200xto 2000x.
4. Future Research Directions
The objective of this work was to build the basic pillar towards an accurate, tractable,
easily-used, and general channel model for an optical wireless in-body and transdermal
channel. To achieve this, as a first step, the basic propagation mechanisms in such a medium,
namely (i) spreading loss and (ii) scattering, were identified. Next, low-complexity models
that account the propagation medium particularities, i.e., the different tissue compositions,
were introduced. The aforementioned models can open the door to a number of important
studies, ranging from ray-tracing-based channel modeling to theoretical assessment of
point-to-point to point-to-multi-point links and systems, as well as systems, transmission,
and reception schemes and policies designed to optimize. In more detail, the following
future research directions can be identified:
•
Stochastic channel modeling: As discussed in [
2
], transdermal and in-body optical
wireless links suffer from wavelength-dependent particulate scattering. Within the
skin, the main source of scattering is filamentous proteins (e.g., keratin in epider-
mis and collagen in dermis). Note that, since these particles are comparable to or
larger than the wavelength, scattering can be approximated as a Mie solution to
Maxwell’s equations. On the other hand, in in-body applications, tissues, such as
membranes, striations in collagen fibrils, macromolecules, lysosomes, vesicles, mito-
chondria, and nuclei are the main scatterers. Note that membranes are usually lower
than 1/10 of the wavelength, while all the other structures are comparable to the
wavelength. Thus, scattering in tissues can be modeled as a mixture of Rayleigh and
Mie processes. By taking into consideration the inhomogeneities in the body content
in light-absorbing and scattering, which lead to a variation of the reflective index
along the transmission path, it becomes evident that the received power is expected to
randomly fluctuate. To model this phenomenon, experimentally verified ray-tracing
investigations that capitalize the models presented in the current contribution need to
be conducted. Furthermore, except for line-of-sight links, non-line-of-sights scenarios,
where diffusion may be the key player, also need to be investigated.
•
Theoretical investigation: Several different use cases, such as cochlear, gastric, cortical,
retinal, foot drop implants, etc., have been identified [
2
]. However, only for a small
number of them, a link budget analysis that supports their feasibility and reveals the
architectural requirements that need to be accounted for has been conducted [
6
,
7
].
This motivates the use of the presented contribution as a building block towards the
performance assessment of existing and envisioned designs and system models, as
well as networks. In particular, for low-distance links, in the orders of some cm, where
the strength of line-of-sight components are expected to be considerably larger than
the one of non-line-of-sight, due to the high directionality of the links, the channel
variation from its expected values will be relatively low. As a result, the presented
channel model will provide a very accurate estimation of the received signal strength.
•
Design and development of communication, energy harvesting, and neural stimula-
tion modules: In order to select the optimal transmission and reception parameters
and equipment, design energy and spectral efficient transmission waveforms, and

Telecom 2022,3147
reception filters and processes, develop low-complexity channel and error correction
codes, devise suitable energy harvesting modules, and utilize energy transfer and
harvesting policies, a low-complexity channel model that captures the inherent char-
acteristics of the propagation medium is required. In more detail, and as illustrated in
Section 3, the presented channel model can aid in identifying optimal transmission
wavelengths, as well as transmission windows for different applications. This identi-
fication provides guidelines for the architecture designer concerning the LS and PD
that should be used, as well as to the industry concerning the characteristics of the
aforementioned units that need to be developed. By taking into account the channel
characteristics, which in general are wavelength- and distance-dependent, suitable
transmission waveform, codes, constellation, reception filters and detection processes
that contribute to the maximization of the system’s energy efficiency can be developed
and theoretically studied. Additionally, wavelength splitting strategies that ensure
uninterrupted and reliable operation can be designed and optimized. Finally, com-
bining the presented channel model with optogenetic stimulation, a highly efficient
cell stimulation technique that offers improved spectral coding of sound information
due to its higher temporal confinement, aspires great promise for the development of
novel architectures capable of achieving unprecedented performance.
5. Conclusions
This paper introduces a novel mathematical framework that models the optical signal’s
attenuation as it travels through any generic biological tissue. Initially, we extract analytical
expressions for the absorption coefficient of the major generic tissue constituents based
on published experimental measurements, which enable the estimation of not only the
absorption coefficient of each constituent at any given wavelength but also the absorption
coefficient of any generic tissue. Moreover, the phenomenon of scattering is incorporated
into the proposed framework as a complex stochastic process comprised of a Rayleigh and
Mie scattering component in order to model the impact due to the existence of smaller and
larger particles, respectively, in the generic tissue. Next, the phenomena of absorption and
scattering are incorporated into a unified framework, which is validated by comparing the
analytical results with experimental data from the open literature. Moreover, we illustrate
the pathloss as a function of the transmission wavelength for different complex tissues
and tissue thickness and provide insightful discussions, as well as design guidelines, for
future in-body OWC applications. Finally, the importance of scattering is highlighted in
the results of this contribution, and, therefore, future research should further investigate
novel techniques to mitigate its impact.
Author Contributions:
Conceptualization, S.E.T.; methodology, S.E.T.; software, S.E.T.; validation,
S.E.T., A.-A.A.B., N.D.C. and G.K.K.; writing—original draft preparation, S.E.T.; writing—review
and editing, A.-A.A.B., N.D.C. and G.K.K.; visualization, S.E.T.; supervision, A.-A.A.B.; project ad-
ministration, N.D.C.; funding acquisition, N.D.C. All authors have read and agreed to the published
version of the manuscript.
Funding:
This research is co-financed by Greece and the European Union (European Social Fund-
ESF) through the Operational Programme “Human Resources Development, Education and Lifelong
Learning 2014–2020” in the context of the project “IRIDA-Optical wireless communications for
in-body and transdermal biomedical applications” (MIS 5047929).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.

Telecom 2022,3148
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