CHANNEL MODELING OF MULTILAYER DIFFUSION-BASED MOLECULARNANO COMMUNICATION SYSTEM

SAIZALMURSIDI BIN MD MUSTAM

UNIVERSITI TEKNOLOGI MALAYSIA

CHANNEL MODELING OF MULTILAYER DIFFUSION-BASED MOLECULARNANO COMMUNICATION SYSTEM

SAIZALMURSIDI BIN MD MUSTAM

A thesis submitted in fulfilment of therequirements for the award of the degree of

Doctor of Philosophy (Electrical Engineering)

Faculty of Electrical EngineeringUniversiti Teknologi Malaysia

AUGUST 2016

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To my beloved father, mother, wife and sons for their endless love, encouragementand support.

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ACKNOWLEDGEMENT

I would like to express my deepest gratitude to my supervisor, AssociateProfessor Dr. Sharifah Kamilah binti Syed Yusof for giving me an opportunity to workunder her guidance, and for her trust, support and encouragement throughout the entireduration of my Ph.D study. I am also thankful for her unbounded energy and passion,which helped me to steadily advance towards the successful completion of this thesis.

I would also like to extend my appreciation to all staffs of the Faculty ofElectrical Engineering, Universiti Teknologi Malaysia (UTM) Skudai, who haveinvolved directly or indirectly throughout the period of my Ph.D study. In particular,I would like to sincerely thanks Professor Dr. Norshiela binti Fisal for her invaluablecomments, advises and motivation which have helped me to achieve a solid researchpath towards this thesis. To all my colleagues and fellow researchers in the UTM-MIMOS Telecommunication Technology Research Group, thank you for the uniqueatmosphere, constant support and true friendship we have had during my researchperiod.

I would also like to thank the Ministry of Higher Education, Malaysia, and theUniversity Tun Hussein Onn Malaysia (UTHM) for the financial support provided inthe form of a doctoral scholarship and monthly allowances.

Special thanks are due to my parents, Md Mustam bin Marzuki and Sa’emahbinti Ngadi, my wife Fazlina binti Yunus and my sons Muhammad Sadiq andMuhammad Faqih, for their understanding, patience, encouragement, support and love.

Last but not least, I would like to thank the developers of the utmthesis \LATEX\project for making the thesis writing process a lot easier for me. Thanks to them, Icould focus on the content of the thesis, and not waste time with formatting issues.Those guys are awesome.

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ABSTRACT

In nanoscale communication, diffusion-based molecular communication(DBMC) in which information is encoded into molecule patterns by a transmitternanomachine, has emerged as a promising communication system, particularly forbiomedical and healthcare applications. Although, numerous studies have beenconducted to evaluate and analyze DBMC systems, investigation on DBMC systemthrough a multilayer channel has received less attention. The aims of this research areto mathematically model a closed-form expression of mean molecular concentrationover multilayer DBMC channel, to formulate channel characteristics, and to conductperformance evaluation of multilayer DBMC channel. In the mathematical model, thepropagation of molecules over an n-layer channel is assumed to follow the Brownianmotion and subjected to Fick’s law of diffusion. The partial differential equation (PDE)of the time rate change of molecular concentration is obtained by modeling the n-layerchannel as an n-resistor in series and considering the conservation law of molecules.Fourier transform and Laplace transform were used to obtain the solution for the PDE,which represents the mean molecular concentration at a receiver nanomachine. In theformulation, channel characteristics such as impulse response, time delay, attenuationor the maximum peak, delay spread and capacity were analytically obtained from themean molecular concentration. In this stage, the multilayer channel is considered asa linear and deterministic channel. For the performance evaluation, the air-water-blood plasma medium representing the simplified multilayer diffusion model in therespiratory system was chosen. It was found that both analytical and simulation resultsof mean molecular concentration using Matlab and N3Sim were in good agreement.In addition, the findings showed that the higher the average diffusion coefficientresulted in a smaller dispersion of channel impulse response, and shortened thechannel delay spread as well as time delay. However, the channel attenuation remainsunchanged. In the performance evaluation, an increase of 100% in the transmissiondistance increased the time delay by 300% but decreased the maximum peak ofmolecular concentration by 87.5%. A high channel capacity can be achieved with widetransmission bandwidth, short transmission distance, and high average transmittedpower. These findings can be used as a guide in the development and fabricationof future artificial nanocommunication and nanonetwork systems involving multilayertransmission medium. Implication of this study is that modeling and analyzingof multilayer DBMC channel are important to support biomedical applications asdiffusion can occur through a multilayer structure inside the human body.

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ABSTRAK

Dalam komunikasi berskala nano, komunikasi berdasarkan peresapan molekul(DBMC) di mana maklumat dikodkan ke dalam pola molekul oleh pemancar mesinnano telah muncul sebagai satu sistem komunikasi berpotensi di masa hadapan,khususnya untuk aplikasi-aplikasi bio-perubatan dan penjagaan kesihatan. Walaupunbanyak kajian telah dijalankan untuk menilai dan menganalisis sistem DBMC, namunkajian ke atas sistem DBMC melalui saluran banyak lapisan masih kurang mendapatperhatian. Tujuan kajian ini adalah untuk memodelkan secara matematik ungkapantertutup bagi penumpuan purata molekul merentasi saluran DBMC banyak lapisan,pemformulaan ciri-ciri bagi saluran dan penilaian prestasi bagi saluran DBMCbanyak lapisan. Dalam permodelan matematik, pergerakan molekul merentasi n-lapisan saluran adalah diandaikan mengikuti gerakan Brownian dan tertakluk kepadahukum peresapan Fick. Persamaan pembezaan separa (PDE) bagi penumpuanpurata molekul berubah terhadap masa diperoleh dengan memodelkan n-lapisansaluran sebagai n-perintang secara sesiri dan mempertimbangkan hukum keabadianmolekul. Jelmaan Fourier dan jelmaan Laplace telah digunakan untuk mendapatkanpenyelesaian bagi PDE, yang mewakili penumpuan purata molekul di penerima mesinnano. Dalam pemformulaan, ciri-ciri bagi saluran seperti sambutan impuls, kelewatanmasa, perlemahan atau puncak maksimum, kelewatan penyebaran dan kapasiti telahdiperoleh secara analisis daripada ungkapan penumpuan purata molekul. Di peringkatini, saluran banyak lapisan dianggap sebagai satu saluran yang linear dan berketentuan.Untuk penilaian prestasi, saluran udara-air-plasma darah yang mewakili model ringkasperesapan banyak lapisan bagi sistem respirasi telah dipilih. Di dapati bahawa kedua-dua keputusan analisis menggunakan Matlab dan simulasi menggunakan N3Simbagi penumpuan purata molekul adalah selari. Selain itu, keputusan-keputusan inijuga menunjukkan bahawa semakin tinggi pekali resapan purata, mengakibatkansemakin kecil penyebaran sambutan impuls bagi saluran dan memendekkan kelewatanpenyebaran saluran dan juga kelewatan masa.Walau bagaimanapun, pelemahan saluranadalah kekal tidak berubah. Dalam penilaian prestasi saluran DBMC banyaklapisan, penambahan jarak penghantaran sebanyak 100% meningkatkan kelewatanmasa sebanyak 300% tetapi mengurangkan penumpuan puncak maksimum molekulsebanyak 87.5%. Kapasiti saluran yang tinggi boleh dicapai dengan lebar jalurpenghantaran yang besar, jarak penghantaran yang pendek dan kuasa penghantaranpurata yang tinggi. Dapatan kajian ini boleh digunakan sebagai panduan di dalampembangunan dan pembuatan sistem komunikasi nano dan rangkaian nano tiruan masadepan yang melibatkan saluran penghantaran banyak lapisan. Implikasi kajian iniadalah menerusi permodelan dan penganalisisan saluran DBMC banyak lapisan yangpenting bagi menyokong aplikasi-aplikasi bio-perubatan memandangkan peresapanmolekul boleh berlaku melalui banyak struktur lapisan di dalam tubuh manusia.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION iiDEDICATION iiiACKNOWLEDGEMENT ivABSTRACT vABSTRAK viTABLE OF CONTENTS viiLIST OF TABLES xiLIST OF FIGURES xiiLIST OF ABBREVIATIONS xviLIST OF SYMBOLS xviiLIST OF APPENDICES xxi

1 INTRODUCTION 11.1 Background 11.2 Problem Statement 31.3 Research Objectives 41.4 Research Scopes 41.5 Research Contributions 61.6 Significance of Research 81.7 Thesis Outline 8

2 LITERATURE REVIEW 102.1 Introduction 102.2 Nanocommunication and Nanonetworks 11

2.2.1 Nano-electromagnetic Communication 132.2.2 Molecular Communication 13

2.3 Overview of Diffusion-Based Molecular Communi-cation (DBMC) System 15

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2.3.1 Encoding and Transmission of Informa-tion Molecules 15

2.3.2 Propagation or Diffusion of InformationMolecules 16

2.3.3 Reception and Decoding of InformationMolecules 18

2.4 Related Research Works 182.4.1 The DBMC Channel Modeling 182.4.2 Multilayer Diffusion 21

2.5 Context of the Research 222.6 Summary 22

3 RESEARCH METHODOLOGY 243.1 Introduction 243.2 Research Procedures 25

3.2.1 Mathematical Modeling of MultilayerDBMC Channel 273.2.1.1 Derivation of mean molecular

concentration at RN 283.2.1.2 Development of Simulation

Model using N3Sim Simulator 293.2.1.3 Formulation of Multilayer

DBMC Channel ImpulseResponse, Time Delay,Attenuation and Delay Spread 30

3.2.1.4 Derivation of MultilayerDBMC Channel Capacity 31

3.2.2 Performance Evaluation of MultilayerDBMC Channel 313.2.2.1 Performance Metrics 313.2.2.2 A Multilayer Medium Under

Study 323.3 Analytical and Numerical Analysis Tools 343.4 Summary 34

4 MATHEMATICAL MODELING OF MULTILAYERDBMC CHANNEL 354.1 Introduction 35

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4.2 Multilayer DBMC Channel Modeling 364.2.1 Mean Molecular Concentration over

n−Layer Channel 374.2.2 Mean Number of Received Molecules 43

4.3 Formulation of Multilayer DBMC Channel Charac-teristics 444.3.1 Channel Impulse Response 444.3.2 Channel Time Delay 444.3.3 Channel Attenuation 454.3.4 Channel Delay Spread 46

4.3.4.1 Delay Spread of Impulse Trans-mission over Multilayer DBMCChannel 46

4.3.4.2 Spreading of a Square PulseTransmission over MultilayerDBMC Channel 49

4.3.5 Channel Capacity 534.3.5.1 The Fick’s Diffusion Mutual

Information 544.3.5.2 The Capacity of Multilayer

DBMC Channel 564.4 Summary 57

5 PERFORMANCE ANALYSIS OF MULTILAYERDBMC CHANNEL 585.1 Introduction 585.2 Channel Impulse Response, h(r, t) 615.3 Mean Molecular Concentration, c(r, t) 635.4 Mean Number of Received Molecules, s(r, t) 65

5.4.1 Effects of Layer Fraction, fi on theMaximum Mean Number of ReceivedMolecules, s(r, t)max and Time Delay, td 66

5.4.2 Effects of Transmission Distance, r onthe Maximum Mean Number of ReceivedMolecules, s(r, t)max and Time Delay, td 68

5.4.3 Effects of Total Number of Transmit-ted Molecules, Q0 on the MaximumMean Number of Received Molecules,s(r, t)max and Time Delay, td 73

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5.5 Analysis of Delay Spread in Multilayer DBMCChannel 755.5.1 Effects of Multilayer Channel on the

Channel Delay Spread, τh 755.5.2 Effects of Transmission Distance, r on the

Channel Delay Spread, τh 785.5.3 Effects of Total Number of Transmitted

Molecules, Q0 on the Channel DelaySpread, τh 80

5.5.4 Effects of Data Rate of Transmitted Bit,Rb = 1/Tb on the Pulse Spreading 82

5.6 Analysis of Capacity in Multilayer DBMC Channel 835.6.1 Transfer Function Fourier Transform of

Channel Impulse Response, h(r, f) 845.6.2 Capacity, C versus Bandwidth, W for

Different Values of Transmission Dis-tance, r 85

5.6.3 Capacity, C versus Transmission Dis-tance, r for Different Values of Band-width, W 86

5.6.4 Capacity, C versus Transmission Dis-tance, r for Different Values of LayerFraction, fi 88

5.6.5 Capacity, C versus Bandwidth, W forDifferent Values of the Average PowerTransmission, PH 89

5.7 Summary 90

6 CONCLUSIONS 916.1 Conclusions 916.2 Recommendations for Future Work 94

REFERENCES 95

Appendices A – I 104 – 137

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LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Nano-electromagnetic versus molecular communications 132.2 Summary of related works on point-to-point DBMC channel

model 235.1 Simulation parameters 595.2 Effects of doubling and halving of r = 45 µm on s(r, t)max

and td 695.3 Channel delay spread, τh and pulse spreading of a square

pulse transmission with Tb = 5 s 775.4 Numerical analysis parameters 83

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LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 An overview of nanonetworks: (a) nano-electromagneticcommunication, and (b) molecular communication 12

2.2 Molecular communication with (a) active transport, and (b)passive transport by diffusion 14

2.3 Diffusion-based molecular communication (DBMC) system 152.4 Multilayer structures: (a) an alveolar-blood capillary barrier,

and (b) the stomach-blood barrier 213.1 Flowchart of the research activities 263.2 Block diagram of the research framework 273.3 A multilayer diffusion-based molecular communication

(DBMC) system 283.4 Flowchart of simulation steps using N3Sim simulator 293.5 Multilayer DBMC channel over the air-water-blood plasma

medium (a) a physical system, and (b) the simplifiedrepresentation 33

4.1 (a) Ohm’s circuit law and (b) the equivalent relationshipbetween the radial diffusive flux and the concentrationdifference of molecules 39

4.2 Multilayer diffusion: (a) a thin interlayer between n thickdifferent mediums and (b) its equivalent circuit 40

4.3 (a) Impulse transmission sequence with symbol interval, Tsand, (b) the response of mean molecular concentration due toimpulsive transmission 47

4.4 (a) A square pulse molecules transmission with pulseduration, Tb and average amplitude of Qave and, (b) outputresponse of mean molecular concentration due to a squarepulse molecules transmission 49

4.5 Information-theoretic diagram of multilayer DBMC system 534.6 Venn diagram of the mutual information between the input

signal X and output signal Y 54

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5.1 Multilayer diffusion: (a) an alveolar-blood barrier and, (b) thesimplified multilayer representation 60

5.2 Channel impulse responses for air, water, blood plasma,water-blood plasma and air-water-blood plasma mediumswith a separation distance of r = 45 µm 61

5.3 Mean molecular concentration at the RN location, for apulse transmission of 5× 105 molecules through single layermedium with diffusion coefficient, D of 1 nm2/ns (ioniccalcium in the cytoplasm) and transmission distance of 3 µm 63

5.4 Analytical and simulation results of mean molecularconcentration at the RN sensing volume, for the transmissionof 2 × 105 molecules through water-blood plasma and air-water-blood plasma mediums with the transmission distanceof 45 µm 64

5.5 Analytical and simulation results of mean number of receivedmolecules at the RN sensing volume, for the transmission of2× 105 molecules through water-blood plasma and air-water-blood plasma propagation mediums with the transmissiondistance of 45 µm 66

5.6 Mean number of received molecules at the RN (r = 45

µm) over the water (Dwater), blood plasma (Dblood), andwater-blood plasma mediums with different fractions of layerthicknesses (Dav,1, Dav,2, and Dav,3) 67

5.7 Mean number of received molecules at the RN (r = 45 µm)over the air (Dair), blood plasma (Dblood), and air-bloodplasma mediums with different fractions of layer thicknesses(Dav,1, Dav,2, and Dav,3) 67

5.8 Mean number of received molecules at the RN over the water-blood plasma medium (f1 = f2 = 0.5) when (a) doubling theTN–RN distance from 45 µm to 90 µm and, (b) halving theTN–RN distance from 45 µm to 22.5 µm 70

5.9 Mean number of received molecules at the RN over the air-blood plasma medium (f1 = f2 = 0.5) when (a) doubling theTN–RN distance from 45 µm to 90 µm and, (b) halving theTN–RN distance from 45 µm to 22.5 µm 71

5.10 Mean number of received molecules at the RN over the air-water-blood plasma medium (f1 = f2 = f3 = 1/3) when (a)doubling the TN–RN distance from 45 µm to 90 µm and, (b)halving the TN–RN distance from 45 µm to 22.5 µm 72

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5.11 Mean number of received molecules at the RN over the water-blood plasma medium (f1 = f2 = 0.5) for 45 µm of theTN–RN distance when varying the number of transmittedmolecules from 2× 105 to 4× 105 and 8× 105 molecules 73

5.12 Mean number of received molecules at the RN over the air-blood plasma medium (f1 = f2 = 0.5) for 45 µm of theTN–RN distance when varying the number of transmittedmolecules from 2× 105 to 4× 105 and 8× 105 molecules 74

5.13 Mean number of received molecules at the RN over the air-water-blood plasma medium (f1 = f2 = f3 = 1/3) for45 µm of the TN–RN distance when varying the number oftransmitted molecules from 2 × 105 to 4 × 105 and 8 × 105

molecules 745.14 Normalized mean molecular concentration at the RN for 45

µm of the TN–RN distance, over the air-water-blood plasma(Dav,1), air-air-blood plasma (Dav,2), and air-air-water plasma(Dav,3) mediums with layer fraction of f1 = f2 = f3 = 1/3

due to (a) an impulsive transmission of molecules, and (b) asquare pulse transmission of molecules with Tb = 5 s 76

5.15 Normalized mean molecular concentration at the RN overthe air-water-blood plasma medium with equal layer fraction(f1 = f2 = f3 = 1/3) when increasing the TN–RN distancefrom 22.5 µm to 30 µm and 45 µm due to (a) an impulsivetransmission and, (b) a square pulse transmission with Tb =

5 s 795.16 Normalized mean molecular concentration at the RN for 45

µm of the TN–RN distance, over the air-water-blood plasmamedium with equal layer fraction (f1 = f2 = f3 = 1/3)

when increasing the number or transmitted molecules from2 × 105 to 4 × 105 and 8 × 105 due to (a) an impulsivetransmission and, (b) a square pulse transmission with Tb =

5 s 815.17 Normalized mean molecular concentration at the RN for 45

µm of the TN–RN distance, over the air-water-blood plasmamedium with equal layer fraction (f1 = f2 = f3 = 1/3) fora square pulse transmission with different pulse width, Tp oftransmitted bit, Tb 82

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5.18 Transfer function Fourier transform of channel impulseresponse over the air-water-blood plasma medium (f1 = f2 =

f3 = 1/3) for 30 µm, 50 µm and 100 µm of the TN–RNdistances 84

5.19 Capacity for various TN-RN distances as a function ofbandwidth over the air-water-blood plasma medium (f1 =

f2 = f3 = 1/3) 865.20 Capacity for various transmission bandwidths as a function

of TN-RN distance over the air-water-blood plasma medium(f1 = f2 = f3 = 1/3) 87

5.21 Capacity for various layer fractions as a function of TN-RNdistance over the air-water-blood plasma medium 88

5.22 Capacity for various average transmitted powers as a functionof bandwidth over the air-water-blood plasma medium (f1 =

f2 = f3 = 1/3) 89A.1 Steady-state diffusion in one dimensional 104B.1 Nonsteady-state diffusion in one dimensional 107

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LIST OF ABBREVIATIONS

BANs - Body Area Nanonetworks

dB - Decibel

C - Celcius

CSK - Concentration Shift Keying

DBMC - Diffusion-Based Molecular Communication

Hz - Hertz

IoBNT - Internet of Bio-Nano Things

ISI - Inter-Symbol Interference

MoSK - Molecule Shift Keying

OOK - On-Off Keying

ODE - Ordinary Differential Equation

PAM - Pulse Amplitude Modulation

PDE - Partial Differential Equation

RN - Receiver Nanomachine

TN - Transmitter Nanomachine

W - Watt

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LIST OF SYMBOLS

δ(r) - Dirac’s delta function of the source location

δ(t) - Dirac’s delta function of the source time

η - Dynamic viscosity of the fluidic medium

ηair - Dynamic viscosity of air

ηwater - Dynamic viscosity of water

ηblood - Dynamic viscosity of blood plasma

τh - Channel delay spread

∗ - Convolution operation

v0 − v1 - Voltage difference

∇2 - Laplacian operator

∂

∂xi+

∂

∂yj+

∂

∂zk - Three-dimensional gradient operator

∂c(r, t)

∂r- Molecular concentration gradient

∂c(r, t)

∂t- Time rate changes in molecular concentration

dc(r, t)

dt- First time derivative of mean molecular concentration

` - Total thickness of the propagation medium

`/D - Diffusive resistance of the medium

`i/Di - Diffusive resistance of the i-layer

`i/` - Fraction of the i-layer

∆c - Cocentration difference of molecules

∆r - Membrane thickness

c(x, y, z, t) - Mean molecular concentration in three dimensional

space at time t

c(r, t) - Mean molecular concentration

c(r0, t) - Concentration of molecules at the location of TN

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c(r0 + `, t) - Concentration of molecules at the location of RN

c(r, t)max - Channel attenuation, or maximum peak of mean

molecular concentration

cr(r, t) - First space derivative of mean molecular concentration

crr(r, t) - Second space derivative of mean molecular concentration

ct(r, t) - First time derivative of mean molecular concentration

ct(ω, t) - First time derivative of Laplace transforms of C(ω, t)

erfc - Complementary error function

fi - Fraction of the i-layer

fx(x) - Probability density function of all the possible transmitted

signal X

h(r, f) - Transfer function Fourier transform of the channel

impulse response

h(r, t) - Channel impulse response

i - An integer 1, 2, 3, ...

inverfc - Inverse operation of the complementary error function

k - Partition coefficient of membrane

kB - Boltzmann constant

n - Number of layers

r - Transmission distance or TN-RN distance

rm - Radius of molecules

rs - Radius of receiver sensing volume

s(r, t) - Mean number of received molecules

t - Time

td - Time delay

A - Area

C - Channel capacity

D - Diffusion coefficient

Dav - Average diffusion coefficient

Di - Diffusion coefficient of the i-layer

H(X) - Entropy per second of the transmitted signal X

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H(Y ) - Entropy per second of the received signal Y

H(Q) - Entropy of the number of transmitted molecules per time

sample of the time function signal Q(t)

H(X, Y ) - Joint entropy per second of the transmitted signal X and

the received signal Y

H(X|Y ) - Conditional entropy per second of the transmitted signal

X given the received signal Y

I - Current

I(X;Y ) - Mutual information

J - Flux or diffusion rate per unit area

J(x, t) - Net diffusion flux at x and at time t

J(x+ `, t) - Net diffusion flux at x+ ` and at time t

J(r, t) - Net radial diffusion flux

~J(x, y, z, t) - Flux vector in three dimensional space at time t

N(x, t) - Molecules at position x and time t

N(x+ δ,t) - Molecules at position x+ δ and time t

dN - Net number of particles

P - Permeability coefficient

PH - Average thermodynamic power in molecules transmission

Q - Total number of transmitted molecules

Q0 - Total number of transmitted molecules

Qave - Average number of transmitted molecules

Q(t) - Time function of molecule transmission

R - Resistance

Rb - Data rate of transmitted bits

T - Temperature

Tb - Pulse bit duration

Ts - Symbol duration or interval

V - Receiver sensing volume

dV - Differential volume

W - Bandwidth of the transmitted signal

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X - Transmitted or input signal

Y - Received or output signal

C(ω, t) - Fourier transforms of c(r, t)

F (ω) - Fourier transforms of δ(r)

C(ω, s) - Laplace transforms of C(ω, t)

F (s) - Laplace transforms of δ(t)

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LIST OF APPENDICES

APPENDIX TITLE PAGE

A The Fick’s First Law of Diffusion 104B The Fick’s Second Law of Diffusion 107C Solution of Diffusion Equation for an Impulsive Molecules

Transmission 110D Solution of Diffusion Equation for a Time-Function

Molecules Transmission 115E Solution of Multilayer Diffusion Equation for an Impulsive

Molecules Transmission 120F Solution of Multilayer Diffusion Equation for a Time-

Function Molecules Transmission 126G The Transfer Function Fourier Transform of Channel Impulse

Response 132H Conditional Entropy per Second H(X | Y ) of the Transmit-

ted Signal X Given the Mean Molecular Concentration Y 136I List of Publications 137

CHAPTER 1

INTRODUCTION

1.1 Background

Rapid development in nanotechnology has motivated nanocommunicationand nanonetworks of large numbers of nanoscale devices or nanomachines.Nanocommunication is a new research area where a communication process occursbetween nanomachines. In a nanonetwork, a group of nanomachines is interconnectedamong them and expected to share information and coordinate activities to performa specific task. With nanonetworks, the limited capabilities of a single nanomachine,such as only for computation, sensing, or actuation, can be expanded for executingmore complex tasks and a wide range of applications. Interaction among networkednanomachines will allow the implementation of collaborative and synchronous taskssuch as in-body drug delivery, disease treatments, and monitoring and controlling ofenvironmental pollution [1].

Generally, nanocommunication can be realized through four differentmechanisms, which are nanomechanical communication through mechanical contact,acoustic communication by using acoustic energy or pressure variations, nano-electromagnetic communication based on the modulation of terahertz electromagneticwaves, and molecular communication via transmission and reception of encodedinformation molecules [1]. However, both nano-electromagnetic communication andmolecular communication have been envisioned as the two main options for wirelessnanocommunication and nanonetworks [2]. Due to a small-scale, bio-compatible withthe biological environment and energy efficiency of a molecular transceiver, molecularcommunication offers the most promising approaches for nanocommunication andnanonetworks among biological nanomachines as well as with the existing biologicalsystem [1, 3–6]. Another reason is that molecular communication can be approachedthrough the observation of existing natural phenomena in biology [2, 7].

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In the past decade, research activities have shown significant interests in thearea of molecular communication to realize nanocommunication and nanonetworks.Numerous research efforts can be found in the literature to investigate the variousmodels of molecular communication. Some of the proposed models are randomwalk [8,9], flow based or random walk with drift [10–12], diffusion based [2,3,12–15],diffusion-reaction based [16], walkway or active transport based [8, 17, 18] andcollision based [19]. The performances of the proposed models are then analyzed interms of channel capacity [9, 10], modulation schemes [9], normalized gain and delay[3], probability of reaching a receiver [17], transmission rate [11,12,15,17,18], mutualinformation [10,11], noise [13], throughput and efficiency [14], signal attenuation andamplification [16], collision rate [19], and communication range [15].

Among the proposed channel models, molecular communication by diffusionor diffusion-based molecular communication (DBMC) with and without drift has beenthe focus of interest in the research community [20]. The DBMC channel modelis chosen as it represents the most basic and widespread molecular communicationarchitecture found in nature [21, 22]. The concept of congestion in the DBMCchannel for drug delivery near the targeted or disease area is introduced in [20]. Adrug delivery system model using the DBMC with drift for drug transportation overbloodstream to only unhealthy parts inside the body can be found in [23]. Recently, theconcept of body area nanonetworks (BANs) with DBMC for healthcare applicationshas been introduced in [5]. Furthermore, the concept of the Internet of Bio-NanoThings (IoBNT), involving the DBMC model for intra-body communication can befound in [24]. It is expected that from the proposed IoBNT, a healthcare provider canretrieve certain intra-body status parameters, such as glucose, sodium, and cholesterollevels, and the presence of unwanted agent through bio-nano things inside the body byusing the Internet connection. The term bio-nano things can be referred to any typeof nanosystems including liposomes [25–27], dendrimers [28], metallic nanoparticles[29], polymeric nanoparticles [30], carbon nanotubes [31] and nanowires [32, 33].

The current developments of nanotechnology in nanomedicine, tissueengineering, nanorobots, bio-sensor, bio-marker, and implant technologies haveprovided the possibilities of an intelligent system for an early disease detectionand spontaneous targeted drug delivery in the treatment of human diseases in thenear future. In these intelligent systems, a group of bio-nanomachines embeddedin the human body or implanted under the skin are expected to communicate andcooperatively share information using molecular signals among each other or with thesurrounding cells to perform a specific function such as synthesis the human health

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condition, identifying the targeted drug delivery locations, and automatically controlthe amount and time of drug release. Moreover, the molecules of the drug are expectedto be able to diffuse across a multilayer barrier or multiple environments towards thebloodstream as well as to the other parts inside the body or the infected area. Thus,a better understanding of how the drug’s molecules diffusing over the body and itsconcentration over time are utmost important for an effective disease treatment with anoptimum amount of drugs.

1.2 Problem Statement

In nanoscale communication, the DBMC has emerged as one of the mostpromising communication models, particularly for health monitoring and drug deliveryapplications. In the DBMC, a transmitter nanomachine (TN) translates a messageinto encoded molecules and transmits them to a propagation medium or channel byopening a molecular gate. The transmitted molecules are then propagated from the TNto a receiver nanomachine (RN) over the channel by a diffusion process via Brownianmotion. The RN captures the encoded molecules propagating in the channel and finallydecodes the captured molecules.

Although, numerous studies have been conducted to evaluate and analyzeDBMC system, investigation on DBMC through a multilayer channel due to variationsin the medium properties or medium temperature has had less attention. Thepropagation of molecules over various mediums and environments or more complexmedium, such as intracellular environment and the human body needs to be considered[4]. In practice, the diffusion of molecules can occur over the several layers in thehuman body, for example, diffusion of oxygen and carbon dioxide over the alveolar-blood barrier in the respiratory system [34], diffusion of digested particles, nutrientsor medicine across the stomach-blood barrier during the absorption process, anddiffusion of water, oxygen, carbon dioxide and lipid-soluble molecules through theblood-brain barrier [34]. Additionally, a tissue, particularly an arterial wall, which hasthe different material properties in each layer, is commonly modeled as a multilayermedium [35, 36].

However, no works have been reported throughout the literature thatanalytically modeled and evaluated the performance of multilayer DBMC channelfrom the perspective of communications and an information theory. It is still not

4

clear how molecules will propagate through the multilayer DBMC channel that isconsisting of different medium properties or different medium temperature. Thus,it is utmost important to develop a mathematical model to predict the concentrationprofile over time and characterize how molecules will propagate over a multilayerchannel. Modeling and analysis of molecules’ propagation over a multilayer channelwith different medium properties are important to be explored in order to supportthe future biomedical applications such as regulating the release of drugs over amultilayer structure of environment in living tissue, as well as for the BANs and IoBNTapplications. Therefore, this research work is proposed to model and evaluate theperformance of multilayer DBMC channel.

1.3 Research Objectives

The main objective of this research is to mathematically model and evaluatethe performance of multilayer DBMC channel. This research study has the followingspecific objectives:

(i) To develop a mathematical model of multilayer DBMC channel in derivinga closed-form expression of the mean molecular concentration at the RNlocation.

(ii) To formulate channel characteristics of multilayer DBMC channel.

(iii) To evaluate the performance of the multilayer DBMC channel generated fromdifferent medium properties.

1.4 Research Scopes

In order to achieve the objectives, the following scopes have been employed:

(i) The research focuses on mathematical modeling of a point to point (a pairof nanomachines) DBMC channel without any noise sources or propagationimpairments to derive the mean molecular concentration at the RN locationover a multilayer channel. Furthermore, the propagation of molecules from thepoint-source TN to the point and passive RN is governed by the Fick’s law ofdiffusion.

5

(ii) Pulse-based modulation (an impulsive transmission) with concentrationencoding scheme as well as amplitude detection technique is considered informulating the multilayer DBMC channel characteristics such as channelimpulse response, channel time delay, channel attenuation or the maximumamplitude of mean molecular concentration, channel delay spread, and channelcapacity.

(iii) The performance evaluation is done for multilayer diffusion over the air-water-blood plasma medium representing the simplified model of the alveolar-bloodcapillary barriers in the human respiration system. The interlayer between twodifferent mediums and membranes is considered thin and permeable to thetransmitted information molecules which have a radius similar to an oxygenatom.

The detailed explanations on the assumptions made in mathematical modelingof multilayer DBMC channel are given in Chapter 4. Thus, the developedmathematical model has the following limitations:

(i) The mean molecular concentration at the RN location is derived for a point-source TN and a point-source RN with an infinite boundary. For more realisticand accurate models, propagation of molecules between a spherical TN and aspherical RN in a confined medium needs to be considered in the future [37].

(ii) The propagation of molecules in the 3-D environment over a multilayerchannel is without any reaction and drift velocity. Therefore, the movement ofmolecules is subjected to a free diffusion from the higher concentration regionto the lower concentration region [7, 38], and the viscous forces within themedium dominate the propagation process [38–40]. In other words, the derivedclosed-form equation is not considered for the cases when the concentration ofmolecules is very high compared to the medium molecules, and the collisionsbetween molecules affect their movement.

(iii) The developed mathematical model is independent of any noise exists in theDBMC system such as sampling noise at the TN [13], diffusion or Browniannoise due to randomness propagation of molecules [13, 38], and reception orresidual noise at the RN [38, 41].

(iv) Modeling of the ligand-binding reception and decoding process at the RN isbeyond the scope of this research. In this work, an amplitude detection schemeis considered, where bits ’1’ and ’0’ represented by the higher and the lowerconcentration of molecules inside the RN sensing volume.

6

1.5 Research Contributions

The contributions of this research work are as follows:

(i) A derived closed-form equation of mean molecular concentration formultilayer DBMC channel.

In this work, the diffusive flux of molecules in single layer mediumis interpreted analogously to Ohm’s law. The electrical current, I in Ohm’slaw represents the diffusion flux of molecules, J(r, t), the electrical resistance,R represents the total length per unit diffusion coefficient, `/D or diffusiveresistance of the medium, and the voltage difference, (v0 − v1) represents theconcentration difference, c(r0, t) − c(r0 + `, t) of the information moleculesbetween two points [42]. Then, a multilayer channel of DBMC is modeledas an n-resistor in series where the average diffusive flux of molecules overa multilayer medium is obtained by adding the diffusive resistance of eachlayer analogous to the addition of series resistors in electrical circuit theory asproposed in [43]. By considering a conservation law of molecules, the partialdifferential equation (PDE) of time rate change at distance, r and time t ofmolecular concentration over a multilayer medium is obtained from the averagediffusive flux and the continuity equations. Finally, the closed-form equationof mean molecular concentration for multilayer DBMC channel is derived byfinding the solution of the PDE for an impulsive transmission of moleculesusing the Fourier and Laplace transforms method.

It is found that the mean molecular concentration of multilayer DBMCis dependent on the total number of transmitted molecules, transmissiondistance, and an average diffusion coefficient. In addition, the average diffusioncoefficient is inversely proportional to the summation of each layer fraction perlayer diffusion coefficient.

(ii) A formulated closed-form equation of channel characteristics of multilayerDBMC channel in terms of channel impulse response, channel time delay,channel attenuation, channel delay spread, and channel capacity.

Channel delay spread expression for multilayer DBMC channel isderived by considering 10 dB below the maximum peak of mean molecularconcentration as the minimum level using the MAPLE software. Thedelay spread is obtained by subtracting two-time instants at which the meanmolecular concentration equals one-tenth of the maximum peak of meanmolecular concentration or channel attenuation. In this work, the maximum

7

peak of mean molecular concentration is obtained by substituting time delayinto the closed-form equation of mean molecular concentration. While, thetime delay is obtained by finding the time instant at which the time derivativeof the closed-form equation of mean molecular concentration is equal to zero.

In summary, both time delay and delay spread are directly proportionalto the square of transmission distance and inversely proportional to the averagediffusion coefficient. Moreover, the channel attenuation is directly proportionalto the number of transmitted molecules and is inversely proportional to the cubeof transmission distance.

In addition, a capacity expression for multilayer DBMC channel isalso derived in this research work. The entropy of the number of transmittedmolecules per time sample of transmitted signal is obtained by modelingthe time function of the transmitted signal as a band-limited ensemblesfunction within a bandwidth, W . By performing Fourier transforms, variablesubstitution, manipulating the integration part, and simplification using deMoivre’s formula, the transfer function Fourier transform of the channelimpulse response is obtained. This equation is then used to determine theconditional entropy per second of the transmitted signal given the receivedsignal as well as the expression of mutual information of multilayer DBMCchannel. Finally, the capacity expression is obtained by maximizing the mutualinformation between the transmitted signal and the received signal with respectto the probability density function of the transmitted signal.

The capacity of multilayer DBMC is dependent on the bandwidthof transmitted signal, an average thermodynamic power spent by the TN totransmit molecules, a temperature of the system, transmission distance, andthe average diffusion coefficient. The capacity is linearly dependent on thebandwidth of transmitted signal. However, the upper and lower bound ofcapacity are affected by the transmission distance and the average diffusioncoefficient of multilayer medium.

(iii) Performance analysis of multilayer DBMC channel due to different mediumproperties.

Performance analysis of multilayer DBMC channel in terms ofchannel attenuation, channel time delay, and channel delay spread fordifferent layer fraction, transmission distance, and the number of transmittedmolecules is evaluated analytically using MATLAB software. In addition,numerical evaluation of the effects of parameter variation such as an averagethermodynamic power for molecule transmission, the bandwidth of the

8

transmitted signal, transmission distance, and layer fraction on the capacityof multilayer DBMC channel are also presented and discussed.

In general, it is found that the impulse responses of multilayer DBMCchannel rapidly increases from zero to a maximum peak and then decrease overtime, forming a long tail and approaching zero as t becomes infinity. Moreover,the higher average diffusion coefficient, the faster the rate of the mean numberof received molecules reaching its maximum peak and the shorter the channeldelay spread. The results also show that doubling the transmission distanceincreases both time delay and delay spread by four-fold, and decreases themaximum peak or channel attenuation by eight-fold. In addition, increasingthe number of molecules increases the maximum peak of mean molecularconcentration; however, the delay spread and pulses spreading as well astime delay remains unchanged. The numerical results showed that the widerthe transmission bandwidth, the higher the channel capacity, and the shortertransmission distance, the higher the channel capacity. Increasing the averagetransmitted power increases the channel capacity as well.

1.6 Significance of Research

The findings from this research work are valuable as a foundation in thedevelopment and fabrication of future artificial nanocommunication and networkssystem, which involves the propagation of molecules through a multilayer medium.Mathematical models of the molecular communication system will allow aresearcher to perform mathematical analysis, design and optimization on molecularcommunication systems. It is expected that performance evaluations of the studyprovide insight to help engineers in developing or realizing the multilayer DBMCsystem due to different medium properties.

1.7 Thesis Outline

The entire structure of the thesis is organized into six chapters. A briefoverview of research background and information related to the research work suchas problem statement, research objectives, scopes of research, research contributions,and the importance of the work are addressed in Chapter 1.

9

Chapter 2 studies the background knowledge and reviews the previous researchworks related to a molecular communication system. Firstly, this chapter outlinesthe general idea and types of nanocommunication and nanonetworks. Secondly, anoverview of the DBMC system is explained thoroughly. Next, this chapter presentsa review of important research works and finally, the direction of the research isexplained according to the identified research gaps.

Chapter 3 describes the methodology used in achieving the research objectives.The channel model under study is also described in this chapter. In addition, theperformance metrics and tools for analytical, simulation and numerical investigationsthroughout the work are also outlined and mentioned.

Chapter 4 presents a mathematical modeling of multilayer DBMC channel.First, all assumptions considered throughout the research for the proposed channelmodel are explained, followed by a derivation of mean molecular concentration atthe RN location over a multilayer channel. Afterward, multilayer DBMC channelcharacteristics such as channel impulse response, the mean number of receivedmolecules, channel time delay, channel attenuation, channel delay spread for impulsivetransmission, pulse spreading of a square pulse transmission, and channel capacity areformulated in this chapter.

Chapter 5 evaluates and discusses the performance analysis of multilayerDBMC channel due to different medium properties in terms of channel attenuation,channel time delay, channel delay spread, and channel capacity. In addition, simulationanalysis using N3Sim simulator is also provided under this chapter.

Finally, Chapter 6 concludes the entire research work with a summary andrecommendations for future work.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

In general, the field of nanocommunication and nanonetworks has gained a lotof attention among researchers in the past few years. This research area basically aimsto realize communications and networking of nanoscale devices or nanomachines.A wide range of applications can be a benefit with nanonetworks especially inbiomedical, industrial, military and environmental applications [1].

In biomedical applications, nanonetwork is important for bio-hybrid implants,drug delivery systems, and health monitoring [1, 4]. Moreover, a nanonetwork canhelp in industrial applications such as in the development of new fabrics and materialsfor better airflow, manufacturing processes, and quality control of food and water [1].In the military field, applications such as a soldier’s performance monitoring systemand a detector for aggressive chemical, biological agents, or radiological materials cantake advantage of nanonetworks [1]. In environmental applications, nanonetworks canhelp in bio-degradation process by sensing and tagging waste materials, and control ormonitor environmental pollution [1, 4]. It is believed that the communication optionsbetween nanoscale devices or nanomachines are varied depending on the specificnanoscale application domain [2].

This chapter provides a literature review of the research work. In Section 2.2,nanocommunication and nanonetworks are discussed, covering nano-electromagneticcommunication and molecular communication. In Sections 2.3 and 2.4, an overviewof diffusion-based molecular communication (DBMC) and the related works aredescribed. Finally, the contexts of research and summary are given in Sections 2.5and 2.6, respectively.

11

2.2 Nanocommunication and Nanonetworks

Basically, nanotechnology deals with the development of materials, structures,devices, systems and architectures by controlling molecules at a nanoscale. Recentbreakthroughs in nanotechnology have enabled the development and fabrication ofmachines with small size ranging from 1 to 100 nanometers [1–3, 19, 40, 44–47]. Atthis scale, nanomachine is able only to perform a simple task of computing, datastoring, sensing or actuation [2,3,19,40,46]. Nanosensor and nanoswitches are the twoexamples of nanomachines that can detect chemical compounds and perform opticalswitching through certain molecules, respectively. Nanomachines are nanoscaledevices, and can be naturally existent (i.e. biological cells) or artificially synthesized(i.e. bioengineered cells) [9]. In the literature, there are three different approaches inwhich nanomachines can be fabricated namely top-down approach (downscaling theexisting device to the nanoscale), bottom-up approach (constructed from nanoscalecomponents), and bio-hybrid approach (use the existing biological nanomachines inliving organisms) [1, 19].

In order to expand the limited capabilities of single nanomachine fromthe simple tasks to more complex tasks, implementation of networking amongnanomachines is required. Through nanonetworks, a group of nanomachines canshare information and contribute to the wide range of applications as mentionedearlier. As mentioned in the previous chapter, nano-electromagnetic and molecularcommunications are the two alternatives for communication among nanomachines.

Figure 2.1 shows the two communication options that allow the implementationof nanonetworks. In nano-electromagnetic communication networks, the exchangeof information is completed by the transmission and reception of terahertzelectromagnetic waves using a nanoscale antenna integrated at the transmitter andreceiver nanomachines or nanodevices. However, in molecular communication,information is exchanged based on the transmission and reception of encodedmolecules between bio-nanomachines (biological nanomachines).

12

TX

RX

Electromagneticwaves

Propagation speed (Light)

RX

(a)

Transmitter Nanomachine

ReceiverNanomachine

Encoder

Decoder

ReceiverNanomachine

Low propagation speed

(Random process)

Sensitive toobstacles

Noise

Molecules

Decoder

(b)

Figure 2.1: An overview of nanonetworks: (a) nano-electromagnetic communication,and (b) molecular communication [1]

Table 2.1 summarizes the main differences between nano-electromagneticcommunication and molecular communication. In nano-electromagnetic communi-cation, with high energy consumption, an electronic device (nanodevices) transmitsa message encoded in the electromagnetic or optical signals over the air or cables,and the waves signals are then propagated at the speed of light over the distanceranging from meters up to kilometers. While, in molecular communication, with lowenergy consumption, a transmitter bio-nanomachine transmits a message encoded in aphysical or chemical properties of molecules (such as type of molecules, structure,sequence, or concentration) into an aqueous medium, and then the transmittedmolecules are propagating at extremely low speed over the distance ranging fromnanometers to micrometers before reaching a receiver bio-nanomachine.

13

Table 2.1: Nano-electromagnetic versus molecular communications [1, 48]Communication Nano-electromagnetic Molecular

Carrier Terahertz electromagnetic waves Encoded molecules

Signal type Electrical or optical Chemical or physical of molecules

Propagation speed Light (3× 108 m/s) Extremely low

Propagation range m to km nm to µm

Devices Electronic devices Bio-nanomachines

Medium Air or cables Aqueous medium

Noise Electromagnetic fields and signals Particles and molecules in medium

Energy consumed High Low

2.2.1 Nano-electromagnetic Communication

In general, the transmission and reception of information among nano-devicesusing electromagnetic wave require a sensing device resonating at extremely highfrequencies [2]. In [49] both carbon nanotubes based nano-dipole antenna andgraphene nanoribbons based nano-patch antenna with length around 1 µm have beenproven can resonate in the terahertz band (0.1-10 THz). In consequences, researchworks in this area have gained a lot attention among researchers. For example, channelmodeling of nano-electromagnetic communication can be found in [50]. On chipnanonetworks for a system on chip are evaluated in [51]. In [52], the concept of carbonnanotube sensor networks is introduced. The graphene-based nano-antenna is designedand analyzed in [53]. Although, nano-electromagnetic communication has shown adrastic attention among researchers, it is however still not practically applicable formany applications such as communication inside networks of tunnels, pipelines, orsalt water environments [37].

2.2.2 Molecular Communication

In molecular communication, a message to be transmitted is encoded to anddecoded from molecules. Biological materials and process are usually involvedin molecular communication. Generally, the propagation of molecules between atransmitter nanomachine (TN) and a receiver nanomachine (RN) can be realized byusing two modes called passive transport and active transport.

14

Figure 2.2 shows a molecular communication system with active and passivetransports, respectively. In active transport, the transmission of information moleculesfrom the TN to the RN is performed by molecular motors moving along a molecularrail. On the other hand, the transmitter nanomachine transmits diffusive informationmolecules that represent a message into the environment, the information moleculesare then randomly moved (Brownian motion) in the environment and finally thereceiver nanomachine captures and decodes information molecules propagating in theenvironment, in passive transport. Brownian motion is the random motion of moleculescaused by collisions with the fluid’s molecules [54].

Transmitter

Receiver

Decoder

Encoder

De de

Molecular rail

Molecular motor

Nanomachine

NanomachineMolecule

(a)

Transmitter

Receiver

DiffusionProcessCalcium

Signaling

Encoder

Decoder

Nanomachine

Nanomachine

(b)

Figure 2.2: Molecular communication with (a) active transport, and (b) passivetransport by diffusion [1]

In this research, molecular communication by diffusion is considered becauseof it suitability in the realization of body area nanonetworks (BANs) as well as theInternet of Bio-Nano Things (IoBNT) for biomedical application such as an immunesupport system, drug delivery systems, and health monitoring system.

15

2.3 Overview of Diffusion-Based Molecular Communication (DBMC) System

In the DBMC, molecules are diffused from a region of higher concentrationto a region of lower concentration [7, 23] as shown in Figure 2.3. According to [4],the general phases of the DBMC system consist of encoding and transmission ofinformation molecules into the environment by the TN, propagation of informationmolecules through the propagation medium, reception and decoding of informationmolecules propagating in the environment by the RN. In the following section, eachphase is explained in details.

Transmitter Receiver

Nanomachine (TN) Nanomachine (RN)

Information Receiver

z molecule sensing volume Receptor

y y

x High Low

concentration concentration

Figure 2.3: Diffusion-based molecular communication (DBMC) system [55]

2.3.1 Encoding and Transmission of Information Molecules

In this phase, the TN encodes a message to transmitted into informationmolecules which can be recognized the RN [4]. Usually, the message is encodedwithin the information molecules in various forms such as in the three-dimensionalstructure of the information molecule, in the transmission order of different molecules,or in the different concentration levels of information molecules [4, 37, 56].

Then, information molecules will be diffused away into the propagationmedium or channel (such as air, water, or blood plasma mediums [57]) through a

16

molecular gate or gap junction in the cell membrane of the TN based on instantaneousor a continuous transmission scheme [58,59]. Similar to the traditional communicationtechnique, the transmission of information molecules also subjected to any modulationschemes such as pulse amplitude modulation (PAM) [39], concentration shift keying(CSK) [60,61], on-off keying (OOK) [6,15,56,62], and molecule shift keying (MoSK)[56, 60, 63].

2.3.2 Propagation or Diffusion of Information Molecules

Propagation process is the movement of information molecules from theTN through the environment to the RN. In the DBMC, information molecules arepassively diffused without chemical energy from a region of high concentration tothose of low concentration by Brownian motion [54]. In [39], the diffusion processis defined as the spontaneous spread of molecules throughout space due to a gradientin the concentration of molecules. When the transmitted information molecules areindependent of one another, the diffusion process can be modeled based accordingto the Fick’s laws of diffusion [40, 63]. According to the macroscopic theory, themovement of molecules in the fluidic medium can be explained by the Fick’s lawsof diffusion [43, 64]. The Fick’s first law relates the diffusive flux to the molecularconcentration as follows [64, 65];

J(r, t) = −D∂c(r, t)∂r

(2.1)

where J(r, t) is the net flux of particles at position r and time t, D =kBT

6πηrmis

the diffusion coefficient of spherical molecules with radius, rm within the medium

which has a viscosity η and temperature T , and∂c(r, t)

∂ris the molecular concentration

gradient. The detail derivation of Equation (2.1) by Berg [64] is given in Appendix A.

For the non-stationary environment, advective flux aids the propagation processas well as the diffusive flux given by [56, 65];

J(r, t) = −D∂c(r, t)∂r

+ v(t)c(r, t) (2.2)

where v(t) is the velocity of the propagation medium.

17

The Fick’s second law predict how molecular concentration varies with timedue to diffusion process [58]. According to the Fick’s second law of diffusion, theconcentration of molecules, c(r, t) at location r and time t is described by the followingequation [64, 66];

∂c(r, t)

∂t= D

∂2c(r, t)

∂r2(2.3)

where c(r, t) is the molecular concentration in molecules/m3, r is distance in m, t is a

time in s,∂c(r, t)

∂tis the time rate changes in molecular concentration,

∂c(r, t)

∂ris the

molecular concentration gradient and D is the diffusion coefficient. The derivation ofEquation (2.3) from Equation (2.1) according to Pica and Jantschi [66] is outlined inAppendix B.

The mean molecular concentration c(r, t) available at the receiver sensingvolume in molecules/m3 can be analytically modeled by solving Equation (2.3). Foran instantaneous transmission (impulsive transmission) scheme, the mean molecularconcentration is given by [43, 64];

c(r, t) =Q0e

− r2

4Dt

(4πDt)32

(2.4)

where r2 = x2 + y2 + z2 in the Cartesian coordinate system, Q0 is the total numberof transmitted molecules. The solution of Equation (2.4) using Fourier and Laplacetransforms is given in Appendix C.

In addition, for a continuous transmission scheme, the mean molecularconcentration is given by [43, 64];

c(r, t) =

� t

τ=0

Q(τ) exp(− r2

4D(t−τ)

)(4πD(t− τ))

32

dτ (2.5)

where c(r, t) is the molecular concentration in molecules/m3, r is transmissiondistance in m, t is time in s, τ is the variable of integration, Q(τ) is the inputtransmission signal or the transmission rate of molecules, and D is diffusioncoefficient. The solution of Equation (2.5) is provided in Appendix D.

18

2.3.3 Reception and Decoding of Information Molecules

Basically, at the surface of RN, there are uniformly distributed chemicalreceptors that permeable to information molecules. In the reception process, chemicalreceptors will detect and capture the information molecules propagating in theenvironment. Upon binding the information molecules, the RN will decode theinformation molecules into a chemical reaction such as by producing new moleculesor another signal and performing a simple task [4]. The number of bound informationmolecules is interpreted as the amplitude of the received signal [56].

2.4 Related Research Works

In nanoscale communication, the DBMC has emerged as one of the mostpromising communication models, particularly for biological applications. In thiscommunication system, molecules such as gasses (O2, CO2 and N2) and ions (K+,Mg2+, Ca2+ and Cl−) play an important role as a message carrier from the TN to theRN. The TN and RN can be a modified living cell, a biomedical implant or a nano-robot [1].

Recently, researchers have shown considerable interest in the DBMC modelfor realizing communication among nanomachines. In general, the DBMC systemconsists of three major components namely the TN, the propagation medium orchannel, and the RN [37]. However, information molecules will experience five phaseswhich are encoding, transmission, propagation, reception and decoding [1, 4]. Acomprehensive explanation of the DBMC processes is addressed by the works in [1,4].Moreover, the concept of BANs with DBMC for healthcare applications is introducedin [5]. Furthermore, the concept of the IoBNT, which involving the DBMC modelfor intra-body communication can be found in [24]. In [67], the internet of nanothings architecture for in-body nanocommunication networks integrated with BANsis proposed.

2.4.1 The DBMC Channel Modeling

Several research efforts on mathematical models of the DBMC channel inwhich the propagation of molecules is analytically modeled by solving Fick’s second

19

law of diffusion can be found in [3, 9, 38, 45, 55] as summarized in Table 2.2. In [3]a mathematical framework for a physical end-to-end model including transmission,propagation and reception modules, under a continuous diffusion of molecules in afluidic medium has been introduced. A mathematical framework for each moduleis derived. In this model, information molecules are modulated by the TN at thedifferences concentration rate. Then, it propagates by diffusion process to the RN.Finally, the RN detects the modulated molecules in terms of concentration rate anddecodes the received signal. However, the performance of the proposed modelis investigated in terms of normalized gain and delay only. Therefore, furtherextension of the work needs to be done to study the end-to-end behavior of diffusion-based molecular communication model in terms of noise, capacity, throughput andmodulation schemes.

In [38, 55], the channel impulse response of the DBMC channel is derivedby solving the diffusion equation for an impulsive transmission of molecules. Theoutput response can be obtained using the convolution operation of the channel impulseresponse with the input signal [55]. The results indicated that the propagation ofmolecules through a DBMC channel is linear and time invariant [38]. Analyticalexpressions for channel properties such as pulse delay, pulse amplitude, pulse width,pulse energy, and pulse duration of the DBMC model are derived for amplitude andfor the energy detection of pulse transmission in [45].

A time-slotted binary channel based on the naive modulation and extendedmodulation schemes in a one-dimensional environment for capacity analysis isproposed in [9]. The developed model is simple and can be used as the basis for furtherstudies on molecular communication. In extended modulation scheme, the transmittertransmits N1 molecules at the beginning of each time slot to send a ’1’ or it transmitsN0 molecules to send a ’0’ (N1 is greater than N0). But in naive modulation scheme,the transmitter transmits one molecule to send a ’1’ and no molecules to send a ’0’. Thereceiver receives a ’1’ if one or more molecules arrive in the time slot and it receivesa ’0’ if no molecule arrives (for naive modulation scheme) or the number of receivedmolecules is less than N1 (extended modulation scheme). Based on the result reportedin [9], capacity can be improved at the expense of extra molecules. Other worksrelated to modulation schemes are given in [46] which uses the transmission order ofdifferent molecules called Molecular Array-based communication (MACRO) scheme.In this model, no time synchronization between the TN and RN is required. Moreover,a multilevel amplitude modulation (M-AM) scheme and binary modulation schemehave been investigated by Mahfuz et al. [68] for concentration-encoded molecular

20

communication. The purpose of this work is to characterize intersymbol interference(ISI) in terms of communication range for these to modulation schemes.

From the information theory perspective, channel capacity is the mostimportant performance metrics which quantifies the maximum amounts of informationthat can be transferred from the TN to the RN for a given number of transmittedmolecules. The work in [58,69] studied capacity for both the diffusion channel and theligand-binding reception. In [58], the capacity expression is developed for continuoustransmission of molecules, while in [69] is for the on-off keying and time slot scheme.Moreover, the general mathematical expression of channel capacity which consideredthe Fick’s diffusion, and the molecular noise can be found in [22]. The capacity isderived for any continuous time signal of molecule transmission as a function of theaverage thermodynamic power spent by the TN. In addition, Atakan and Akan [70],developed an information theoretical approach for the capacity of the ligand-bindingreception. It is found that maximum capacity can be achieved by a proper value oftemperature, the number of emitted molecules, the TN-RN distance and duration ofmolecule emission.

Atakan and Akan [71] derived a deterministic capacity expression for threedifferent molecular channels (point-to-point, broadcast and multiple-access) for arealistic model and investigated the information rate for each channel. The transmitternanomachine emits the molecules in the medium by a diffusion process. The detectionof target molecules is based on the collision of molecules with the surface receptors ofreceiver nanomachine. Based on numerical analysis results, the researchers concludedthat high molecular communication rate could be obtained by increasing the upperbound of the channel input for both point-to-point and broadcast channels. However,in the multiple-access channel, scheduling transmissions or using different molecule,which can be distinguished by the receiver nanomachines, is needed. The researchersconcluded that increasing the number of molecules increases the channel capacity.

Based on the work done by other researchers, it can be concluded that noresearch work has been done to mathematically model the molecule transmissionover a multilayer DBMC channel. The previous works are carried out only for thepropagation of information molecules in one environment.

21

2.4.2 Multilayer Diffusion

In the human body, diffusion of molecules practically occurs through multiplemediums such as across an alveolar-blood capillary barrier in a respiratory systemand across a stomach-blood barrier during the absorption process. Figure 2.4 (a)presents the diffusion of oxygen, O2 from the alveolar air to the haemoglobin as well ascarbon dioxide, CO2 from the haemoglobin to the alveolar air across various barriers.These barriers consist of an alveolar epithelial cell, a capillary endothelial cell, andthe intervening interstitial space containing extra-cellular matrix [34]. In the stomach-blood barrier as shown in Figure 2.4 (b), digested particles, nutrients or medicine arediffused from the stomach to blood vessel also across various barriers. An arterialwall, which has different material properties in each layer, is commonly modeled as amultilayer medium [35, 36].

(a)

(b)

Figure 2.4: Multilayer structures: (a) an alveolar-blood capillary barrier, and (b) thestomach-blood barrier

22

2.5 Context of the Research

Based on the important research work presented in the previous section,although, the DBMC has been the focus of considerable attention, the existingstudies are limited to the propagation of molecules in a single channel. In practice,the diffusion process can occur through a multilayer channel, for example, in therespiratory system (across an alveolar-blood capillary barrier) and in the absorptionprocess (over the stomach-blood barrier). Modeling and analysis of moleculespropagation over multilayer channel with different medium properties are importantto be explored in order to support the future biomedical applications such as regulatingthe release of drugs over a multilayer barrier in a living tissue, as well as for the BANsand IoBNT applications. To the best of our knowledge, no works have been reportedthroughout the literature that analytically modeled and evaluated the performance ofmultilayer DBMC channel. Therefore, this work aims to model the multilayer DBMCchannel and to study the channel properties of the multilayer DBMC channel suchas channel impulse response, channel time delay, channel attenuation, channel delayspread, and channel capacity. A pulse-based modulation scheme with an amplitudedetection scheme proposed in [45] is extended for the propagation of molecules acrossa multilayer medium. Then, the channel capacity for multilayer DBMC channel isderived based on the work proposed in [22].

2.6 Summary

In this chapter, the general idea of nanocommunication and nanonetworksby using both nano-electromagnetic communication and molecular communication,explanations on molecular communication with active and passive transports, and thegeneral phases (encoding and transmission, propagation, and reception and decoding)of the DBMC system have been discussed. In addition, this chapter reviews theimportant previous research works related to the DBMC system. Finally, the directionof the research is explained according to the identified research gaps. The nextchapter presents a detailed methodology for implementing a mathematical modelingand performance analysis of multilayer DBMC channel.

23

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CHAPTER 3

RESEARCH METHODOLOGY

3.1 Introduction

The previous chapter highlighted the literature on the diffusion-basedmolecular communication (DBMC) system as a promising approach in realizing ananoscale communication and networks, particularly, for biomedical and healthcareapplications. Moreover, it has been identified that modeling and analysis of multilayerDBMC are very crucial to support the future biomedical applications such as to controland regulate the release of drugs over a multilayer barrier environment in living tissue.In this chapter, the detailed implementation of the research work to mathematicalmodel and analyze the multilayer DBMC channel are outlined. The major contributionof this research work will be on the physical layer issue regarding to a mathematicalmodeling of mean molecular concentration at the receiver nanomachine (RN) acrossa multilayer channel and the formulation of the channel properties such as channelimpulse response, channel time delay, channel attenuation, channel delay spread, andchannel capacity. Therefore, with mathematical modeling and performance analysisof multilayer DBMC channel, it is expected that performance evaluations of the studyare able to help engineers in developing or realizing the DBMC system involving amultilayer transmission medium.

The rest of this chapter is arranged as follows. The procedures of researchare described in Section 3.2. In general, it consists of three main parts; firstly,reviewing the existing DBMC system, followed by modeling of multilayer DBMCchannel, and finally, performance evaluation of multilayer DBMC channel. The stepsemployed to derive mean molecular concentration at the RN, and the formulation ofchannel characteristics are given in Section 3.2.1. Section 3.2.2 describes the evaluatedperformance metrics and channel model under study. Then, analytical and numericalevaluation tools are mentioned in Section 3.3. The chapter is concluded in Section 3.4.

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