On the Effect of Flow and Degradation on Hitting Rate of Mobile Nano

Sensors in Diffusive Molecular Communication Systems

GAURAV SHARMA

Department of Electrical and Electronics Engineering

Atal Bihari Vajpayee Indian Institute of Information Technology and Management

Gwalior, Madhya Pradesh, 474015

INDIA

Abstract: In the paper, an analysis regarding the effect of drift and molecular degradation on the average

number of molecules received at the fusion center (FC) for a diffusive log-normal molecular communica-

tion (MC) system is undertaken. The effect of drift and molecular degradation simultaneously on molecular

reception has not been examined exhaustively in MC literature. Therefore, by utilizing the log-normal dis-

tribution of the number of molecules hitting FC, we calculated the closed-form expressions for the average

number of molecules received in a drift and molecular degradation-free scenario. Subsequently, we also an-

alytically calculated the closed-form expressions for the average number of molecules received at FC for a

drift-only scenario, and a drift with molecular degradation scenario, respectively. Numerical results highlight

lower average molecular receptions at FC when the transmission media neither experiences drift nor molec-

ular degradation. The drift introduction in the molecular degradation-free system signiﬁcantly increases the

average molecular receptions at FC. On the contrary, with the simultaneous introduction of molecular degra-

dation, the average number of molecular receptions at FC is signiﬁcantly higher. Finally, all the numerical

results corroborate the derived analytical ﬁndings.

Key-Words: Biomarkers, diffusive molecular communication, drift, fusion-center, log-normal molecular

channel, mobile nano-sensors, molecular degradation.

Received: April 8, 2023. Revised: November 25, 2023. Accepted: December 29, 2023. Published: February 27, 2024.

1 Introduction

Molecular communication (MC) is a nature-

inspired communication phenomenon, where the

information transfer from transmitting nanoma-

chine to receiving nanomachine is accomplished

through molecules [1]. The information transfer

between transmitter and receiver through chemical

exchange makes the MC link highly reliable in

environments where conventional electromagnetic

(EM) spectrum-based cannot provide reliable

communication [2], [3]. In the last decade, the MC

systems have experienced steady growth, wherein

numerous synthetic MC-based systems have been

proposed with the primary objective of observing,

analysing, and interpreting the communication

process at the nanoscale [4]. Unlike conventional

communication systems, where the EM spectrum

is utilized in MC modulation is accomplished by

utilizing certain physical characteristic features

such as concentration [5], type [6], or time of

release [7]. In addition to the information modu-

lation, in MC, the molecular propagation from the

source towards the destination is achieved through

pure diffusion, drift, molecular motors, etc. [8], [9].

The diffusive MC systems are widely employed

because of their practical implementation and

economical energy requirement in the shipment

of the information molecules between source and

destination. However, to facilitate the movement

of information molecules, in recent times, diffu-

sion processes along with drift mechanisms are

being utilized for information propagation from

transmitter to receiver [8].

The favoured attribute of MC lies in its instal-

lation in the biochemical and biophysical appli-

cations [8]. Therefore, many nano-scale networks

have been developed primarily to expedite the rev-

olutionary applications in health care and biomed-

ical ﬁelds [10]. Out of these approaches, some

of the most widespread entities widely employed

in biomedical applications are the Mobile Nano-

Sensors (MNSs) [11]. The rapid advancements in

nanotechnology have encouraged the deployment

of these MNSs in complex environments. One such

challenging aspect experienced in most biomed-

ical and health care scenarios is the problem of

early and timely detection of abnormalities, espe-

cially cancer inside the human cardiovascular sys-

tem [12]. Therefore, systems that can identify the

presence of an anomaly become imperative to em-

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ployment.

Nowadays, the MNSs play a pivotal role in nano-

medicine and target drug delivery systems as they

are majorly hired for shipping and dispensing imag-

ing probes, therapeutic agents and biological mate-

rials to the target locations such as speciﬁc organs,

tissue, and cells [13]. This inherent feature of the

MNSs to smartly release, move, observe and read

the anomaly inside the cardiovascular system fos-

ters the utilization of MNSs as a potential candidate

for anomaly detection. The MNSs are injected into

the human circulatory system with the help of an

injection. These MNSs navigate to the target site

with the assistance of the bloodstream (having a de-

ﬁned ﬂow) [14] and activate themselves wherever

there is a high concentration of the biomarkers. Af-

ter interaction with the biomarkers, these MNSs

are eventually transformed into secondary (Type C)

molecules, ultimately absorbed at the fusion center

(FC). The Type C molecules, on reaching the FC ex-

hibit log-normal distribution.

In MC literature, for any real-world physical pro-

cess, channel modeling is done by assuming the

Gaussian behaviour of the system. However, many

practical phenomena are analytically measured us-

ing various skewed distributions. The skewed dis-

tributions are usually employed for low average val-

ues, with higher variances, and values cannot be

negative. For example, for modeling the lengths of

latent periods of infectious diseases, the log-normal

distributions are employed as such skewed distri-

bution processes often closely ﬁt the log-normal

distribution [15]. Further, many practical case sce-

narios from the medical ﬁeld also ﬁt the log-normal

distributions [16].

Since log-normal distribution is one of the best-

suited distributions for modeling in vivo channel

behaviour, in this manuscript, we have assumed the

distribution of secondary (Type C) molecules to ex-

hibit log-normal distribution. To the best of our

knowledge, log-normal channel behaviour has not

been reported anywhere in the MC literature. The

main contributions of this manuscript are as fol-

lows:

• To calculate the average number of informa-

tion molecules reaching the FC, the expression

of the Type C (secondary biomarker) molecules

exhibiting the log-normal distribution is calcu-

lated.

• The closed-form expression of the average

number of molecules received at FC when the

information molecules experience neither drift

(ﬂow velocity) nor molecular degradation in

the media is also calculated.

• The closed-form expression for the average

number of molecules received at FC is analyt-

ically calculated for the scenario when the in-

formation molecules experience drift only.

• Lastly, we calculated the closed-form expres-

sion for the average number of molecules re-

ceived at FC in those environments where the

information molecules experience both drift

and molecular degradation simultaneously.

The rest of the paper has been organized as fol-

lows: Section II highlights the current state of the

art in MC literature. Section III illustrates the pro-

posed system model used for incorporating the de-

sign structures. Section IV depicts the performance

analysis of the system model under consideration.

Section V discusses the numerical results and the

graphical validation of the analysis, and ﬁnally, Sec-

tion VI concludes the manuscript.

2 Related Work

The dearth of relevant research laid the ground-

work for carrying out substantial research in dif-

fusive log-normal MC. In [17], the authors high-

lighted the systems’ development that would ef-

fectively perform communication at the nano-scale

level. Besides, the use of biological entities such

as pheromones, light transduction and neurons for

long-range communication over long-range nano-

networks was discussed by authors in [3]. Mean-

while, an architectural design of MC systems at a

macro-scale level was implemented in [9], wherein

static target and mobile nano-sensors were consid-

ered. Similarly, in [18], the architectural facet of

the nano-networks was discussed, while in [1], an

extensive study about the MC systems was carried

out. Furthermore, [4] proposed the mathematical

modeling for the channel in the diffusive MC sce-

nario, where log-normal distribution was employed

for the approximate modeling of the medium. Cor-

respondingly, the characterization of the MNSs in

the ﬁeld of nanochemistry was highlighted in [19]

and [11].

In [12], the technique of plasma proteome min-

ing was underlined. However, in [13], a two-

tier network for abnormality detection was empha-

sized. Authors in [20] asserted the use of MNSs

to disclose cancerous tissues by utilizing the con-

cepts of reaction-diffusion, advection-diffusion,

and degradation equations. More substantial work

on biomarkers was carried out in [21]. Alternatively,

in [14], the authors scripted the usage of multiple

biological devices known as cooperative biological

nano-machines (CN) to unveil any anomaly inside

the Internet of Bio-things (IoBT) system by assum-

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ing the mobility of the FC. Simultaneously, the co-

operation of molecules that help form a certain crit-

ical number of biological particles was highlighted

by authors in [22].

Based on the aforementioned literature, one can

say that the physical characteristics of the MC chan-

nel play a pivotal role in the modeling of MC sys-

tems. The role of molecular degradation is signiﬁ-

cant, especially in molecular biology. In molecular

biology, analyzing molecular degradation enables

understanding cellular functionality and maintain-

ing cellular hemostasis. Various cellular structures,

such as proteasomes and lysosomes, are respon-

sible for the degradation of proteins. Analyzing

molecular degradation would facilitate the early de-

tection of various cancers and neurodegenerative

diseases. Moreover, in the existing MC literature,

ﬂow velocity and molecular degradation effects are

studied separately. Further, molecular degradation

removes stray molecules from the environment to

prevent inter-symbol interference (ISI). However, in

many practical biological processes, the collective

effect of ﬂow velocity and molecular degradation

has severe implications on cellular dynamics. For

example, molecular degradation, such as proteol-

ysis, is crucial in regulating proteins’ lifetime. So,

changes in ﬂow velocity inﬂuence the activity and

distribution of proteolytic enzymes. Therefore, in

this paper, we have tried to calculate the number of

molecules received at the receiver while consider-

ing the effect of degradation and ﬂow velocity (drift)

distinctly and collectively.

3 System Model

The system model for diffusive log-normal MC

comprises the cartesian coordinate system con-

ﬁned in a semi-inﬁnite structure. The system model

characteristic features are limited to spatial and

temporal components of the aqueous environment

inside which the MNSs are injected with the help of

an injection site. These MNSs (Type A molecules)

propagate through the media at constant ﬂow ve-

locity (vf). These Type A molecules contact the

primary biomarkers secreted by the target cells,

and the healthy cells are transformed into Type

C molecules. These Type C molecules propagate

through the media and are eventually absorbed at

the FC. Fig. 1, highlights the pictorial represen-

tation of the system model, and the complete dif-

fusive molecular communication environment is

based on certain assumptions, given as:

•The whole communication environment func-

tions as spatial and temporal components with

aqueous media experiencing no temperature

and viscosity changes.

Figure 1: System Model.

•The information molecules are identical, and

the transmission time slot is large enough to

counter ISI (Inter Symbol Interference).

•The transmission starts at x=0 and t=0, with the

FC acting as a fully absorbing receiver, hyper-

sensitive to only Type C molecules.

These assumptions highlight two primary ele-

ments (molecular density and molecular ﬂux) of the

Fickian theory. The concentration density f(s,t)

represents the average number of molecules dif-

fused per unit volume for both the particles (Type A

and Type C). The molecular ﬂux (J(s,t)), being a vec-

tor component, denotes the average number of dif-

fused molecules crossing a unit cross-sectional area

per unit time. MNSs undergoing a reaction with

the Type B biomarkers yield Type C molecules. Due

to molecular degradation and ﬂow velocity (drift),

(vf), the Type C molecules are received at the FC.

Mathematically the molecular degradation as given

in [23] is expressed as:

C(t)=C0e−kdt,(1)

where C0is the initial molecular concentration and

kdis the molecular degradation rate of the envi-

ronment. In many practical environments, such

as in the blood ﬂow mechanism, the MNSs travel

by diffusion process and undergo drift and molec-

ular degradation. Therefore, the Type C molecules

reaching FC not only arrive because of the degra-

dation process but also undergo drift in the envi-

ronment. So, for accurate measurement of the av-

erage number of molecules received by the FC, it

becomes imperative to collectively analyze the ef-

fect of drift and molecular degradation in the sys-

tem. The subsequent section will provide an ana-

lytical framework for our system model.

4 Performance Analysis

The mathematical expression which gives the re-

lationship between molecular density f(s,t), and

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molecular ﬂux Φ(s,t) is given as [24]:

[f(s,t+dt)∗d xd y]−[f(s,t)∗d xd y]=

[Φx(s,t)∗d yd z ∗dt −Φx(s+~

xd x,t)∗d yd z ∗dt]

+[Φy(s,t)∗dxd z ∗d t −Φy(s+~

yd y,t)∗d xd z ∗d t ]

+[Φz(s,t)∗dxd y ∗dt −Φz(s+~

zd z,t)∗d xd y ∗dt].

(2)

The above expression derived its basis from the

fact that: "There is a sense of equality between

the average net increase in the number of diffused

molecules contained inside a diminutive volume at

a speciﬁc time and the average net inﬂux of diffused

molecules also contained inside the same diminu-

tive volume at the same time". Thus, by putting

the differential terms in the above mathematical ex-

pression equal to zero, the more generalized ver-

sion of the continuity equation is obtained as [8]:

∂f(s,t)

∂t=−µ∂Φx(s,t)

∂x+∂Φx(s,t)

∂y+∂Φz(s,t)

∂z¶(3)

Moreover, the mathematical liaison between the

concentration density and the ﬂux as represented

by Fick’s Ist diffusion law is given as [8]:

ΦS(s,t)=−D∂f(s,t)

∂s(for s=x,y,z), (4)

where Dis the diffusion coefﬁcient and the nega-

tive sign indicates the inward ﬂow of the ﬂux with

respect to (w.r.t.) concentration density f(s,t).

The value of Dis independent of the information

molecules’ temperature, viscosity, velocity and ra-

dius. By mathematical substitutions, the resultant

Fick’s IInd Diffusion Law is expressed as [1]:

∂f(s,t)

∂t=D52(f(s,t)), (5)

where 52is the Laplacian operator. The whole of

the environment is assumed to be a semi-inﬁnite

volume with reﬂecting surfaces. Therefore, there is

no transmission at x=0−instant and the expres-

sion of (5) becomes [1]:

∂f(s,t)

∂t=Dµ∂2f(x,t)

∂x2¶.(6)

The solution of (6) gives the distribution of Type A

molecules which is expressed as:

f(s,t)=2NT x

p4πDt expµ−X2

4Dt ¶for t≥0; 0 ≤X<∞,

(7)

where NT x is the number of molecules injected at

the injection site, µ=0 is the mean of the Type A

molecules and σ2=2Dt is the variance. The Type A

molecules, during the course of propagation inside

the semi-inﬁnite structure, are transformed into

Type C log-normal distributed molecules undergo-

ing reaction with the primary biomarkers. The Type

C molecules are mathematically expressed as:

f(yTr ,t)=1

2YTr

2NT x

p4πDt expµ−(lnYTr )2

4Dt ¶

for t≥0;0 <YTr <∞,

(8)

where ln(.) is the natural logarithmic function and

YTr is the transformed random variable. The mean

(µ) of Type C molecules showing log-Normal distri-

bution is 0 and Variance (σ2) is 2Dt .

The Type C molecules on reaching FC without

degradation and ﬂow velocity are collected, and the

concentration of the molecules received is given as:

Fhi t =ZT

2YTr

2NT x

p4πDt expµ−(lnYTr )2

4Dt ¶d t ,(9)

where Fhi t is the number of molecules hitting the

FC without drift (vf) and degradation (kd). Thus,

the closed-form expression of the above numerical

expression is obtained by ﬁrst substituting ln(YTr )

p4Dt =

u. The resultant expression of the average number

of molecules reaching the FC without degradation

and without drift is obtained as:

Fhi t =NT x ln(YT r )

4DYTr pπÃ−pπQ(u)+e−u2

u!,(10)

where Q(.) is the standard Q-function. By incor-

porating molecular degradation the expression (9)

gets modiﬁed as:

Fhi t ,deg =ZT

2YTr

2NT x

p4πDt

expµ−½(lnYTr )2

4Dt +kdt¾¶dt,

=ZT

YTr

NT x

p4πDt expµ−(lnYTr )2

4Dt ¶d t

+ZT

YTr

NT x

p4πDt exp(−kdt)d t , (11)

where Fhi t ,deg and kdare the average number of

molecules hitting the FC and the degradation pa-

rameter, respectively. Therefore, by utilizing inte-

gral properties, the closed-form expression of the

integral in (11) is given as:

Fhi t ,deg =NT x (YTr )µqkd

D−1¶ln(YTr )

4Dpπ

½−pπQ(u+pT kd)+e−³u+pT kd´2

u+pT kd¾,

(12)

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where kdis obtained as

kd=ln(2)

Λ(1/2),(13)

where Λ(1/2) is the half-life of the information

molecules. Furthermore, if the effect of ﬂow ve-

locity (vf) and degradation parameter (kd) is taken

into account, then the mathematical expression

of (9), used for obtaining the average number of

molecules hitting the FC, is modiﬁed into a new ex-

pression given as:

Fhi t ,f low =ZT

2NT x

2YTr p4πDt

expÃ−

(lnYTr −vft)2

4Dt −kdt!d t ,

=ZT

NT x

YTr p4πDt expÃ−

(lnYTr −vft)2

4Dt !d t

+ZT

NT x

YTr p4πDt exp(−kdt)dt, (14)

where Fhi t ,f low represents the average number

of molecules hitting the FC surface under the effect

of ﬂow and degradation. Thus, the closed-form ex-

pression of (14) is obtained as:

Fhi t ,f low =

2NT x Y(c−1)

r³v2

f+4Dkd´

erfc



qT(v2

f+4Dkd)

2pD

+ln(YTr )

2pDT ¶, (15)

where c=

vf+qv2

f+4Dkd

2D.

Remark 1: From (12), increasing degradation

kd→ ∞ causes the argument inside Q-function

and the exponential function to approach to very

high values, i.e., ³u+pT kd´→ ∞. Therefore,

with ³u+pT kd´→ ∞, the Q³u+pT kd´→0 and

exp³−u+pT kd´→0. Since the average num-

ber of molecules hitting the FC, is directly propor-

tional to the Q³u+pT kd´and exp³−u+pT kd´,

so Fhi t ,deg →0.

Remark 2: According to (15), for high ﬂow ve-

locities vfvalues, i.e., as vf→ ∞, due to exten-

sive molecular collisions, the average number of

molecules hitting the FC surface decreases such

that Fhi t ,f low →0. Simultaneously, as kd→ ∞,

the argument qT(v2

f+4Dkd)→ ∞, which leads to

erfc³qT(v2

f+4Dkd)/2pD´→0 and c→0. Since

0 0.1 0.2 0.3 0.4 0.5 0.6

Time (in sec)

100

125

150

175

200

Received molecules at fusion center (FC)

Analytical, kd = 0 sec-1

Simulation, kd = 0 sec-1

Analytical, kd = 0.01 sec-1

Simulation, kd = 0.01 sec-1

Analytical, kd = 0.1 sec-1

Simulation, kd = 0.1 sec-1

Analytical, kd = 1 sec-1

Simulation, kd = 1 sec-1

Figure 2: Number of molecules observed at Fusion

Center with different degradation parameter (kd)

values and no ﬂow velocity.

Fhi t ,f low is directly proportional to erfc(.) and c, so

for kd→∞ Fhi t ,f low →0.

Remark 3: In many practical scenarios, spe-

ciﬁc enzymes, such as acetylcholinesterase (AChE),

break down the information molecules in the en-

vironment. Therefore, the degradation process

caused by these AChE molecules inhibits the propa-

gation of molecules and hampers molecular recep-

tion. Thus, the employment of degradation (kd) in

the molecular reception process signiﬁes the sever-

ity of molecular reception at FC. Simultaneously,

ﬂow velocity in the diffusive environment facilitates

molecular motion, thereby enhancing the molecu-

lar reception process.

5 Numerical Results

Based on the mathematical analysis done in the

previous section, the plots representing the aver-

age number of molecules received at FC for differ-

ent physical environments are shown in Fig. 2, Fig.

3 and Fig. 4 respectively. The number of molecules

injected is 1,00,000, while D=79.4µm2/sec. The

distance the Type C molecules travel until FC ab-

sorbs them is 15µm. Note that for all the simula-

tion results presented in this paper, we have used

Monte Carlo simulations, where the results are av-

eraged over 60,000 independent realizations of the

system.

Fig. 2 illustrates the graphical representation

of the average number of molecules received at

the fusion center (FC) versus time duration for

different molecular degradation and no drift.

The ﬁgure shows that the average number of

molecules received at the FC in a no-drift environ-

ment ﬁrst increases with time and then decreases,

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0 0.1 0.2 0.3 0.4 0.5 0.6

Time (in sec)

500

1000

1500

2000

2500

3000

3500

4000

4500

Received molecules at fusion center (FC)

Analytical, vf = 25 m/sec

Simulation, vf = 25 m/sec

Analytical, vf = 50 m/sec

Simulation, vf = 50 m/sec

Analytical, vf = 75 m/sec

Simulation, vf = 75 m/sec

Figure 3: Number of molecules received at FC

with different ﬂow velocities and without molecu-

lar degradation.

respectively. Moreover, the effect of molecular

degradation on the molecular reception at FC also

plays an important role. With increasing kd, the

average number of molecules decreases rapidly.

Therefore, increasing kdnegatively impacts the

overall system’s efﬁciency. Moreover, increasing kd

corresponds to a scenario where the half-lifetime

of the information molecules is short. A decrease in

the half-lifetime results in a decrease in the infor-

mation molecules’ activation energy, resulting in

fewer molecular reception at FC. Further, due to the

absence of ﬂow velocity, there is a signiﬁcant drop

in the molecular absorption at FC. This can also be

observed from the plot, where for kd=1 sec−1out

of 1,00,000 molecules, around 150 molecules are

received at FC.

Fig. 3 shows the pictorial representation of the

average number of molecules received at the FC

versus time in a drift-only environment. The ﬁgure

shows that introducing drift into the MC environ-

ment facilitates the molecular reception at FC. The

drift phenomenon positively impacts the reception

probability at FC, i.e., increasing vfincreases

the reception probability of the molecules at FC.

Increasing the drift velocity enhances the overall

activation energy of the molecules. However, due to

the stochastic nature of the media, increasing the

drift velocity results in collisions among molecules.

This collision is responsible for the overall decay in

the activation energy of the molecules. Decaying in

the molecules’ activation energy due to molecular

collisions is primarily responsible for making the

molecule unrecognizable at the FC. The plot can

further validate this; increasing ﬂow velocities from

0 0.1 0.2 0.3 0.4 0.5 0.6

Time (in sec)

500

1000

1500

2000

2500

3000

3500

4000

Received molecules at fusion center (FC)

Analytical, vf = 25 m/sec

Simulation, vf = 25 m/sec

Analytical, vf = 50 m/sec

Simulation, vf = 50 m/sec

Analytical, vf = 75 m/sec

Simulation, vf = 75 m/sec

Figure 4: Number of molecules received at FC with

different ﬂow velocities and with molecular degra-

dation (kd=1sec−1).

25 µm/sec to 75 µm/sec subsequently causes a de-

cay in the average number of molecular reception

at FC from around 4500 to around 1500.

Fig. 4 gives the pictorial representation of the

average number of received molecules at FC versus

time for different values of vfand kd=1sec−1.

From the ﬁgure, it can be easily inferred that,

compared to the scenario of no degradation, the

average number of molecules reaching the FC in

the degradation case is less, subsequently decreas-

ing with the increasing values of time. The decrease

in the average number of molecules received at

FC is primarily because most molecules travelling

inside the ﬂuid die out due to molecular degra-

dation even before reaching the FC. An increase

in kdcorresponds to a decrease in the half-life

of the information molecules. A decrease in the

half-lifetime of the information molecules leads

to a simultaneous decrease in the molecular acti-

vation energy, subsequently reducing the overall

molecular reception at FC. Moreover, vfhas a pos-

itive impact on the molecular reception, whereas

kdhas a negative impact, with vfovershadowing

the effect of kd. However, for high ﬂow velocities

due to the phenomena of molecular collisions,

the average number of molecules received at FC

decreases.

From the plot, it can be concluded that there

is always a tradeoff in choosing the different val-

ues of the ﬂow velocities. Higher ﬂow velocities re-

sult in molecular collisions, subsequently reducing

the activation energy of the information molecules,

which inherently reduces the reception rate at FC.

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6 Conclusion

In this paper, we provided a detailed analysis of

the effect of drift and molecular degradation on

the reception of the average number of molecules

at FC in diffusive molecular communication. By

utilizing the log-normal distribution of the Type

C information molecules, we ﬁrst analytically cal-

culated the closed-form expression of the average

number of received molecules at FC when the in-

formation molecules experience neither molecu-

lar degradation nor any drift in the media. Subse-

quently, to analyze the effect of molecular degra-

dation in the diffusive log-normal channels, we

calculated the closed-form expression of the av-

erage number of received molecules at FC when

the information molecules experience drift without

molecular degradation in the environment. Fur-

ther, we also calculated the closed-form expres-

sion of the average number of received molecules

at FC when the information molecules simultane-

ously experience drift and molecular degradation

in the environment. Based on the mathematical

analysis, we observed that the average number of

molecules received at FC is less when there is nei-

ther drift nor molecular degradation in the environ-

ment. However, the average number of molecules

received at FC increases with the introduction of

drift (by employing ﬂow velocity) only into the me-

dia. Subsequently, for an environment where infor-

mation molecules experience both drift and molec-

ular degradation simultaneously, the average num-

ber of molecules received at FC is comparatively

less, signifying that the net effect of physical en-

vironments affects the molecular reception at FC.

Finally, the plots also highlight the dependence of

molecular reception on the time parameter. The

analysis presented in this manuscript would bridge

the gap between the analytical and practical sys-

tems, and help understand how ﬂow and molecu-

lar degradation conditions impact cellular behav-

ior. Further, the collective study of ﬂow velocity

and molecular degradation presented in this article

would pave the path for future research in the de-

sign of biomaterials.

References:

[1] N. Farsad, H. B. Yilmaz, A. Eckford, C.-B. Chae,

and W. Guo. A comprehensive survey of re-

cent advancements in molecular communica-

tion IEEE Communication Surveys & Tutorials,

Vol. 18, No. 3, pp. 18871919, 3rd Quart., 2016.

[2] G. Sharma and A. Singh. On the optimal thresh-

old for diffusion based molecular communica-

tion system. in Proceedings of 2nd European

Conference Elect. Eng. Comput. Sci. (EECS),

Bern, Switzerland, Dec. 20-22, 2018, pp. 366370.

[3] L. P. Giné and I. F. Akyildiz. Molecular commu-

nication options for long range nanonetworks.

Computer Networks, vol. 53, no. 16, pp. 2753

2766, Nov. 2009.

[4] V. Jamali, A. Ahmadzadeh, W. Wicke, A. Noel,

and R. Schober. Channel modeling for diffu-

sive molecular communication-a tutorial re-

view. Proceedings IEEE, vol. 107, no. 7, pp.

12561301, Jul. 2018.

[5] A. Ahmadzadeh, H. Arjmandi, A. Burkovski, and

R. Schober. Comprehensive reactive receiver

modeling for diffusive molecular communi-

cation systems: Reversible binding, molecule

degradation, and ﬁnite number of receptors.

IEEE Transactions on Nanobiosciences, vol. 15,

no. 7, pp. 713727, Sept. 2016.

[6] M. S. Kuran, H. B. Yilmaz, T. Tugcu, and I. F. Aky-

ildiz, Modulation techniques for communica-

tion via diffusion in nanonetworks. Proceedings

of IEEE International Conference on Communi-

cation (ICC), Kyoto, Japan, Jun. 05-09, 2011, pp.

15.

[7] G. Sharma, and A. Singh. Secrecy loss in diffu-

sive molecular timing channels. IEEE Transac-

tions on Molecular, Biological and Multi-Scale

Communication, vol. 8, no. 4, pp. 297304, Nov.

2022.

[8] T. Nakano, A. W. Eckford, and T. Haraguchi,

Molecular communication. 1st ed. Cambridge,

U.K.: Cambridge Univ. Press, 2013.

[9] H. Zhai, L. Yang, T. Nakano, Q. Liu, and

K. Yang. Bio-inspired design and implementa-

tion of mobile molecular communication sys-

tems at the macroscale. Proceedings of IEEE

Global Communications Conference (GLOBE-

COM), Abu Dhabi, UAE. IEEE, Dec. 09-13, 2018,

pp. 16.

[10] W. Wicke, A. Ahmadzadeh, V. Jamali, R.

Schober, H. Unterweger, and C. Alexiou. Molec-

ular communication using magnetic nanopar-

ticles. Proc. IEEE Wireless Communications and

Networking Conference (WCNC), Barcelona,

Spain. IEEE, Apr. 15-18, 2018, pp. 16.

[11] G. Chen, I. Roy, C. Yang, and P. N. Prasad.

Nanochemistry and nanomedicine for

nanoparticle-based diagnostics and ther-

apy. Chemical Reviews, vol. 116, no. 5, pp.

28262885, Jan. 2016.

WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE

DOI: 10.37394/23208.2024.21.8

Gaurav Sharma

E-ISSN: 2224-2902

Volume 21, 2024

[12] S. M. Hanash, S. J. Pitteri, and V. M. Faca. Min-

ing the plasma proteome for cancer biomark-

ers. Nature, vol. 452, no. 7187, p. 571, Apr. 2008.

[13] S. Ghavami, F. Lahouti, and A. Masoudi-Nejad.

Modeling and analysis of abnormality detection

in biomolecular nano-networks. Nano Commu-

nication Networks, vol. 3, no. 4, pp. 229241, Dec.

2012.

[14] N. Varshney, A. Patel, Y. Deng, W. Haselmayr,

P. K. Varshney, and A. Nallanathan. Abnormal-

ity detection inside blood vessels with mobile

nanomachines. IEEE Transactions on Molec-

ular, Biological and Multi-Scale Communica-

tions, vol. 4, no. 3, pp. 189194, Sept. 2019.

[15] E. Limpert, W. A. Stahel, and M. Abbt. Log-

normal distributions across the sciences: keys

and clues: on the charms of statistics, and how

mechanical models resembling gambling ma-

chines offer a link to a handy way to charac-

terize log-normal distributions, which can pro-

vide deeper insight into variability and proba-

bilitynormal or log-normal: that is the question.

Biosciences, vol. 51, no. 5, pp. 341352, May 2001.

[16] P. E. Sartwell. The distribution of incubation

periods of infectious diseases. American Journal

of Epidemiology, vol. 51, no. 3, pp. 31018, 1950.

[17] T. Nakano, T. Suda, M. Moore, R. Egashira,

A. Enomoto, and K. Arima. Molecular commu-

nication for nanomachines using intercellular

calcium signaling. Proceeding 5th IEEE Confer-

ence on Nanotechnology, Nagoya, Japan, Jul. 15-

15, 2005, pp. 478481.

[18] I. F. Akyildiz. Nanonetworks: A new frontier in

communications. Proceedings of 18th ACM Mo-

bile Computing Networking (MOBICOM), Istan-

bul, Turkey, Aug. 22-22, 2012, pp. 12.

[19] L. Wu, and X. Qu. Cancer biomarker detection:

recent achievements and challenges. Chemical

Society Review, vol. 44, no. 10, pp. 29632997,

May 2015.

[20] R. Mosayebi, A. Ahmadzadeh, W. Wicke, V. Ja-

mali, R. Schober, and M. Nasiri-Kenari. Early

cancer detection in blood vessels using mobile

nanosensors. IEEE Transactions on Nanobio-

sciences, Apr. 2019.

[21] N. L. Henry and D. F. Hayes. Cancer biomark-

ers. Molecular Oncology, vol. 6, no. 2, pp.

140146, Apr. 2012.

[22] T. Suda and T. Nakano. Molecular communica-

tion as a biological system. Proceedings of IEEE

International Conference Sensing, Communica-

tion and Networking (SECON Workshops), Hong

Kong, China. IEEE, Jun. 11-11, 2018, pp. 14.

[23] A. C. Heren, H. B. Yilmaz, C. Chae, and

T. Tugcu. Effect of degradation in molecular

communication: Impairment or enhancement?

IEEE Transactions on Molecular, Biological and

Multi-Scale Communication, vol. 1, no. 2, pp.

217229, Jun. 2015.

[24] D. T. Gillespie and E. Seitaridou, Simple Brow-

nian diffusion: an introduction to the standard

theoretical models. New York, NY, USA: Oxford

Univ. Press, 2013.

Please visit Contributor Roles Taxonomy (CRediT)

that contains several roles: The problem formu-

lation, numerical analysis and ﬁnal ﬁndings were

done by Gaurav Sharma.

Sources of Funding for Research Presented in a

Scientiﬁc Article or Scientiﬁc Article Itself

This work was supported in part by the Faculty Ini-

tiation Grant of ABV-IIITM, bearing project number

ABV-IIITM/DoRC/FIG/2023/2523.

Conﬂicts of Interest

The author have no conﬂict of interest.

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(Attribution 4.0 International , CC BY 4.0)

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WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE

DOI: 10.37394/23208.2024.21.8

Gaurav Sharma

E-ISSN: 2224-2902

Volume 21, 2024