reliability and delay analysis of multihop virus-based nanonetworks

674 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 12, NO. 5, SEPTEMBER 2013

Reliability and Delay Analysis of MultihopVirus-Based Nanonetworks

Frank Walsh and Sasitharan Balasubramaniam, Member, IEEE

Abstract—Molecular communication is a new communicationparadigm that allows nanomachines to communicate using biolog-ical mechanisms and/or components to transfer information (e.g.,molecular diffusion, molecular motors). One possible approachfor molecular communication is through the use of virus particlesthat act as carriers for nucleic acid-based information. This pa-per analyzes multihop molecular nanonetworks that utilize virusparticles as information carrier. The analysis examines the phys-iochemical and biological characteristics of virus particles such asdiffusion, absorption, and decay, and how they affect the reliabil-ity of multihop communication in molecular nanonetworks. Thepaper also analyzes the use of a simple implicit acknowledgementprotocol for a single-path topology, and compare its performance todefined and random multipath topologies that do not use acknowl-edgments. Numerical results show that commensurate reliabilityis achievable for single-path with implicit acknowledgement andmultipath topologies. However, the single-path topology exhibitsincreased communication delay and more uncertain end-to-endcommunication time.

Index Terms—Nano and molecular communication, nanonet-works, virus-based nanonetworks.

I. INTRODUCTION

THE advancement of nanotechnology has led to the de-velopment of miniature devices, which has brought new

opportunities for various applications. One particular applica-tion domain that has benefited immensely from nanotechnologyis the health care domain. Example contributions of nanotech-nology in health care include accurate analysis and detectionof harmful diseases and drug transportation (e.g., through nanoparticles) to accurate locations within the tissues to terminateharmful diseases. These applications have been enabled by theminiature devices which can be placed in hard to access ar-eas. The term nanodevice or nanomachine refers to a devicethat is composed of nanometer scale components (10−9 m) thatpossesses the ability to perform simple tasks [5]. While recentadvancements have illustrated the potential of biological-basednanomachines [36], nanomachines have numerous limitations.

Manuscript received January 2, 2013; accepted May 11, 2013. Date of publi-cation June 12, 2013; date of current version September 4, 2013. This work wassupported by the Academy of Finland FiDiPro program Nano CommunicationNetworks, 2012–2016. The review of this paper was arranged by AssociateEditor D. Strukov.

F. Walsh is with the Telecommunication Software and Systems Group, Wa-terford Institute of Technology, Waterford, Ireland (e-mail: [email protected]).

S. Balasubramaniam is with the Department of Electronic and Communica-tion Engineering, Tampere University of Technology, Tampere 33720, Finland(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TNANO.2013.2268389

For example, the limited processing capabilities of these de-vices lead to limited functionalities. However, these function-alities can be expanded when communication capabilities areintegrated into nanomachines. In particular, communication be-tween the devices can further extend the application base of nan-otechnology. The field of molecular communication [9] aims toenable communication between nanomachines in a biologicalenvironment. In this new paradigm, information is transformedinto molecules that propagate within biological environmentsto transport information. The examples of molecular commu-nication solutions that have been investigated include calciumsignaling [10], molecular diffusion [1] [3], and bacteria commu-nication [4] [11]. These solutions are now being used to investi-gate molecular communication nanonetworks using moleculararrays [2] and body area nanonetworks [6].

However, developing molecular communication nanonet-works between nanomachines poses a number of challenges[7], [8]. First and foremost, molecular communication betweenthe devices is highly unreliable and suffers from long delay. Thisrequires that communication protocols developed for nanoma-chines must consider these properties, and at the same time, thedesign of such protocols must fit and suit the biological process.Molecular communication network topology has a significanteffect on several important factors such as reliability and effi-ciency. An acceptable level of robustness and redundancy mustbe present in the network to ensure that it can support criticalservices and continue to perform when parts of the networkare temporarily down. These issues are not dissimilar to thosefaced in conventional sensor networks. However, nanonetworksmust also take into account domain specific factors such as in-creased delay, particle decay, and the computational constraintsof nanomachines.

In this paper, we propose the use of virus particles as informa-tion carriers for molecular communication. We consider virusparticles as organic nanoparticles consisting of the followingparts: a nucleic acid-based payload of either DNA or RNA (De-oxyribonucleic Acid and Ribonucleic Acid, respectively) infor-mation molecules, a protein coat that protects the informationmolecules, and a lipid envelope that encapsulates the proteincoat. In particular our focus is on the capability of using virusparticles to transport nucleic acid-based messages through a net-work topology. Viruses have a number of appealing propertiesthat make them suitable for use in nanonetworks. These prop-erties include the ability to encapsulate nucleic acid moleculesand carry them to other distant cells. By latching onto cells, thevirus can release the encapsulated message. This mechanismhas made viruses useful for gene therapy applications and basedon these characteristics we apply them as information carriersfor molecular communication. A particular functionality that

1536-125X © 2013 IEEE

WALSH AND BALASUBRAMANIAM: RELIABILITY AND DELAY ANALYSIS OF MULTIHOP VIRUS-BASED NANONETWORKS 675

we intend to investigate is multihop networking that could beachieved through virus-based nanonetworks. Since virus parti-cles can only propagate to a certain distance, a relaying mech-anism will be required for a network of nanomachines. Weinvestigate multihop routing and how this is impacted by differ-ent topology shapes. In this paper, we design and compare twoapproaches to topology design for virus-based nanonetworks.The first is a single-path topology with implicit acknowledge-ment. The second is redundant multipath topology inspired bynatural virus propagation mechanisms. We evaluate both topol-ogy design approaches in the context of transmission delay andreliability.

This paper is organized as follows. Section II presents therelated work in molecular communication, in particular focus-ing on nanonetworks. Section III describes the key propertiesof viruses that are relevant to our proposed networking mecha-nisms between nanomachines. Section IV presents an overviewof virus-based nanonetworks. Section V describes the analyticalmodel for network links, single-path and multipath topology invirus-based nanonetworks. Section VI presents and comparesthe performance for single-path and multipath topologies. Fi-nally, Section VII presents our conclusion.

II. RELATED WORK

Since the introduction of molecular communication, a num-ber of different solutions have been explored and developed.In this section, we will present some works that have investi-gated molecular communication from both a wireless and wiredperspective.

A. Wireless Paradigm of Molecular Communication

Wireless devices communicate typically using radio wavesthat propagate through space. From a molecular communicationperspective, a number of approaches have been investigated thatmimic the propagation of radio waves using molecules. A goodexample is the diffusion process, which occurs in biologicalsystems, where a node emits molecules that diffuse throughthe medium and slowly approach the receiver. In [10], Nakanoand Liu investigated calcium signaling as a mode for molecularcommunication from an information theory perspective. Thisincluded the information transfer rate and its dependence onthe concentration as well as distance of propagation. In [18]and [32], Pierobon and Akyildiz investigated the achievableend-to-end capacity using molecular diffusion. This includedinvestigating the impact of noise and how this could affect thechannel capacity. In [17], Gregori and Akyildiz proposed the useof bacteria as a carrier for molecular communication. Similarlyto viruses, bacteria are able to carry genetic contents in theform of DNA, and are able to mobilize themselves toward adestination point. In [11], Balasubramaniam and Lioproposed amultihop routing mechanism that utilizes bacteria as a carrier fora network of nanomachines. The process mimics the mechanismof delay tolerant networks (DTN) found in mobile networks,where devices opportunistically encounter each other to passmessages. While bacteria provide the ability to carry DNA-based messages, the use of viruses has one significant benefit:viruses can latch naturally onto cells to unload their nucleic acid

payload, which is beneficial for cell-based nanomachines (e.g.,cells that are programmed to act as nanomachines).

B. Wired Paradigm of Molecular Communication

While wireless paradigms have gained the most popularityfor molecular communication, there have also been approachesproposed for wired paradigms. In [20], Enomoto et al. pro-posed creating artificial microtubules to connect between dif-ferent nanomachines, which in turn mimic the wired intercon-nection found in conventional communication networks. Thetransportation process is conducted through molecular motorsthat walk on the microtubules. In [22], Moritani et al. proposedvesicle-based nanotubes to interconnect devices. These nan-otubes could in turn allow various types of molecules to glidebetween different nanomachines. The use of neurons has alsobeen proposed for molecular communication. In [21], Balasub-ramaniam et al. designed an interface between nanomachine andneurons that could initiate signaling. The design also included atransmission scheduler between multiple devices connected toa neuronal network which ensured successful transmission withminimum interference.

Results contained in these related works often highlight thephysiochemical and biological constraints of building molecu-lar nanonetworks. For example, in [21] the refractory time forneurons places an upper limit on the signal throughput in aneuronal link. Similarly, Nakano and Liu [10] pointed out theeffects of delay in replenishing intracellular calcium stores onthe production of calcium signals. We now examine biologicaland physiochemical mechanisms of virus dynamics that bothenable and constrain our design of virus-based nanonetworks.

III. VIRUS CHARACTERISTICS

This section outlines key characteristics and properties ofviruses used for multihop routing. As with all molecular com-munication networks, a protocol stack is required that providesthe following layers: an application interface, a network layerproviding logical addressing, and a physical layer to providea transmission mechanism for the biological channel. Manydifferent virus types exist in biology, each adapted to a par-ticular environment. However, all viruses share the followingcharacteristics: a DNA or RNA core which contains the geneticinformation such as virus replication instructions for target cellsand a protein coat (capsid) that encapsulates and protects thecore. Furthermore, some virus types such as lentivirus have anouter lipid membrane or envelope that coats the capsid withligands designed to attach the virus to target cell receptors. Asimple illustration of a lentivirus lifecycle is shown in Fig. 1. Weaim to use viruses as information carriers, reusing existing viruscharacteristics, and mapping them to corresponding functionsin a molecular communication protocol stack. Our proposedapproach is a communication system that transports the infor-mation between different biological-based nanomachines. Theintermediary nodes are synthetic cells that have been engineeredto forward messages to the next hop address in a similar wayto intermediary nodes in wireless sensor networks. As we cansee in Fig. 1, the destination does not continue to produce viralparticles to take messages onto the next node, but instead goes


Fig. 1. Diagram showing stages of virus-based multihop nanonetwork. (i) Transduction of an extracellular event (e.g., from a nanomachine via applicationinterface) inhibits the action of interfering RNA pathway and allows proviral gene expression. (ii) Source cell is programmed to produce a genetic circuit. Thecell transcribes proviral messenger RNA(mRNA) species. Simultaneously, the cell also transcribes shRNA that combines with DICER to silence proviral genesvia siRNA pathway. (iii) Payload gene produces an encoded mRNA payloads which are packaged into the lentivirus and transmitted to extracellular space.(iv) Extracellular lentivirus envelope exposes ligands and either decays or bonds to the receptors on the target cell (i.e., next hop address). (v) Upon binding, thevirus releases an encoded mRNA into the destination cell’s cytoplasm, where the mRNA is processed by the cell. (vi) Translation of the mRNA in the intermediarynode results in expression of new lentivirus for the next hop and also copies of the received mRNA payload molecule. (vii) Lentivirus is embedded with ligandsfor next hop destination and packs the duplicated mRNA payload. (viii) Lentivirus releases the mRNA payload for the destination cell, where the mRNA will betranslated in the destination to actuate a response.

through a reverse transcription to produce proteins that will berecognized by the attached bionanomachine or sink.

A. Viral-Based Molecular Communication

Our research uses the ability of viruses to transport andtransduce genetic information between biological cells. Thisapproach is similar to emerging therapies in the treatment ofseveral human diseases where viral vectors are used to deliveran artificially engineered payload such as a DNA plasmid intospecifically targeted biological cells [29]. While several types ofviral vectors are currently used in biological research and med-ical science, this research focuses on lentiviral vectors due totheir ability to target nondividing cells and their current preva-lence in biomedical research. Fig. 1 illustrates the routing ofvirus particles from source nanomachine to destination nanoma-chine via intermediary relay cells. We use the term cell and nodeinterchangeably in the following sections since we are mappingthe functions of a network node to biological cells. We focus onthe network layer and physical layer aspects of these networksand do not consider DNA message encoding mechanisms. Thereason for not considering the DNA message encoding mech-anisms is because we assume that the nanomachine will havemolecular computing capabilities, and can produce the DNAmessages. Therefore, the output from the molecular computingprocess will be transported by our proposed approach to thereceiving nanomachine.

B. Virus Transmission

In our previous work [25], we proposed artificially engineeredcells as communication platforms for nanomachines, allowingdevices and sensors to interface to nanonetworks via biologicalcells, thus offloading the network and physical communicationlayers to the cell. We assume the application layer is containedin the nanomachine while an application interface with the cellis implemented using a short interfering RNA (siRNA) mediatedgenetic circuit. The use of siRNAs is a relatively new tech-

nique for gene expression control and can be used to silencespecific aspects of viral gene expression and allow the concep-tual design of a biological communication circuit in the sourcecell, and this is illustrated in Fig. 2. This approach is used tocontrol proviral genes that are responsible for payload selec-tion, packing, and addressing of virus in the cell. A modularapproach described in [25] and [26] uses aptamer fused shorthairpin RNAs (shRNA) that have high affinity to chemical signalsfrom interfacing nanomachines to control expression of provi-ral packing and addressing genes in the cell. The payload genetranscribes mRNA containing a packing nucleotide sequencewhich marks it for packing into a lentivirus for transmission.The packed mRNA can have an address region and a messageregion in its nucleotide sequence. The address region of themRNA molecule is analogous to the destination address fieldof an IP packet indicating the logical address of the destination.This can be reverse translated into a physical layer address in thereceiving cell which produces a virus that packs the replicatedmRNA message molecule. The virus surface, in turn, is encodedwith ligands/proteins that bind with receptors on the next hopcell in the network.

Our proposed virus-based nanonetwork is illustrated in Fig. 1,where we have a nanomachine that can interface to a cell anduse the cell as a transmitting platform. The nanonetwork alsocontains intermediate nanomachines that relay the viral particlesfrom one nanomachine to the next. In this particular case, theintermediate nanomachines are synthetically engineered cells.Similar to the source nanomachine, the destination nanomachineis also interfaced to a cell, where the viral particles received bythe cells will be passed onto the destination nanomachine. InFig. 1, the source cell is engineered to contain the followingproviral genes that translate to the biological components of avirus: a packing and envelope gene responsible for wrapping theDNA message in a protein coat that reflects the address, and apayload gene which produces genomic DNA/RNA payload (inthis case the message molecule to be transmitted). As describedpreviously, the interfacing nanomachine controls the proviral


Fig. 2. Application interface using shRNA circuit taken from [25]. (i) Interfacing device interacts with the shRNA pathway via the aptamer portion of theshRNA. (ii) This leads to a disruption of the siRNA pathway, which prevents the formation of RISC/viral mRNA complex). (iii) This will then lead to virus particleproduction.

genes in the source cell. Furthermore, as shown in [23] and [24],it is possible for the source cell to contain several envelope andpayload genes which would give the ability to send multiplepayloads to multiple destinations using a single-source cell. Inthis paper, we confine our study to one payload and envelopegene per cell. Once the required genes are unblocked, the virusparticles are created and emitted into the extracellular space.

C. Virus Forwarding and Reception

Transmitted virus particles are received and processed bynodes with complimentary receptors with respect to their sur-face binding ligands. When a virus binds to a host it introducesan mRNA payload into the hosts cytoplasm, where it is pro-cessed by the cell’s internal machinery. As stated previously,the payload mRNA can have both addressing and data sectionwhich are processed separately: processing the address sectionresults in the activation of gene that produces lentivirus for nexthop transmission (i.e., encoded with surface ligands for nexthop node). Processing the payload activates gene expressionwhich is responsible for creating multiple copies of the mRNAmessage molecule complete with packing instructions for newlycreated lentivirus. Finally, virus particles are extruded out of thecell, essentially forwarding the mRNA payload to the next hop.

When the mRNA finally reaches the destination node, mRNAexpression at the destination or sink results in the activation ofupper layer functions to process the payload section. This upperlayer function could in turn be a molecular computing processthat recognizes and interprets the address and the message fromthe payload. For experimental purposes, this could be activationof a gene that produces photoluminous proteins which indicatesuccessful transmission. As we can see in Fig. 1, the destinationdoes not have the necessary proviral genes to forward viral par-ticles but instead goes through a reverse transcription to produceproteins that will be recognized by the attached nanomachines.

D. Virus Cell Dynamics

Pearson et al. [30] proposed the following simple dynamicmodel for the absorption and release of virus particles from hostcells:

IQ→V + I (1a)

Vka b Y→ I (1b)

Iδ→φ (1c)

Vkd→φ (1d)

where V is the virus particle concentration, I is the infectedcell concentration, Y is the target cell concentration, Q is virusextrusion rate from infected cells, kab is the absorption rate ofvirus particles by target cells, δ is the death rate of infected cells,and kd is the decay rate of virus particles. We use this model as abasis to design and simulate nodes in our multihop nanonetworktopologies, where viruses are used as information carriers. Theaforementioned reactions can be used to model the messagetransmission (1a), message reception (1b), receiver loss (1c),and virus particle loss (1d). We assume that the virus infectionsdo not cause the cell death described in 1c and that virus releaseis based on the continuous model as described in [30].

E. Virus Diffusion

Viruses are not living organism; they offer no form of selfpropulsion and require the internal genomic machinery of ahost cell to replicate and propagate. We consider extracellularmovement of virus particles over a single hop as a pure diffusionprocess [19] from the sender to the receiver. If virus particlesare released in sufficient quantity, this process can be describedusing the standard diffusion equation

δV

δt= D

δ2V

δr2 − kdV (2)


Fig. 3. Multipath virus-based nanonetwork. Communication between thesource and sink device (Tx and Rx, respectively) is routed via several inter-mediary nodes. Each network link involves: (a) emission of virus particles,(b) transmission of virus particles across links via diffusion, and (c) adsorptionat the receiver device.

TABLE IVIRUS DIFFUSION PARAMETERS

where D is the environment diffusion coefficient, V is the virusconcentration at location r, and kd is the virus particle decay rate.For simplicity, we model transmission in a 2-D environment asillustrated in Fig. 3, which approximates an infinite plane. Thesender encodes messages in the form of mRNA that are encap-sulated into virus particles whose emission is described by thefunction Q(t) at the emitter. For simplicity, this is modeled as apoint source. During an emission event, all virus particles en-capsulate the same encoded mRNA message. The concentrationof particles at location j at time t from a source at location i isgiven by integrating the solution to the diffusion equation for aninstantaneous point source as follows [13]:

c(rij , t) =1

4πD

∫ t

0

Q(t)t − t′

exp

(−r2

ij

4D(t − t′)− kd(t − t′)

)dt′

(3)where rij is the distance between the locations i and j, D is thediffusion coefficient for the virus particle in two dimensions,and t is the time. This allows us to calculate the concentration ofvirus particles at a receiver location for a transmission describedby the function Q(t). Typical values for lentivirus parameters in(3) are shown in Table I.

IV. VIRUS COMMUNICATION NANONETWORKS

Virus particles have limited spatial range, depending on theenvironment characteristics and virus concentration within theenvironment. To address this, intermediate nanomachines act asrelay nodes that can receive certain virus particles and replicatethem in much the same way as they do in nature. Our studyfocuses on reliability and delay in communication between dis-tant nanomachines. In this section, we introduce two types of

Fig. 4. Single-path (SP) topology. The message originates from Tx, and ispassed along the relay nodes (A and B), before finally arriving at the destinationnode Rx.

topologies that we have considered in our study: a single-pathtopology, and a redundant multipath topology.

A. Single-Path Topology

A single-path topology selects a set of intermediate nodesthat have good link qualities and are used in sequence to for-ward particles to a destination nanomachine. An example of asingle path is illustrated in Fig. 4. Transmission failure acrosseach link could be handled using a simple implicit acknowledge-ment process as follows: consider transmission of one particlebetween nodes Tx and B via node A. During a transmission slotTx releases a quantity of virus particles, all containing the samemessage payload. When A successfully receives one particlefrom Tx, it proceeds to forward the particle to node B. Duringthis period, Tx also listens for this forwarded particle from Aand if it is not received within a time-out interval it is assumedthat the transmission Tx to A has failed and Tx proceeds toretransmit the same quantity of virus particles. Each link failurewill increase the overall communication delay by at least thetime-out interval.

B. Multipath Topology

Natural virus propagation through a medium is analogous toconnectionless transmission in sensor networks. For example,virus emitting cells rely on the availability of suitable hostswithin their communication range and the probability of suc-cessful virus propagation through a medium increases with thenumber of viable paths. We classify a viable path as having twohosts within the effective communication distance for each hopon that path. As seen in Fig. 1, in order for a virus to infecta target cell, the cell must expose complementary receptors onits surface. This gives two options for multipath design 1) de-fined multipathwhereby explicit paths are defined through thetopology by using specific receptor and addressing pairs or 2)random multipath whereby virus particles can be received andabsorbed by all the nodes in the network.

V. ANALYTICAL MODEL

We now develop a deterministic model for reliability andtransmission delay for virus-based nanonetworks based on thecharacteristics discussed in the previous sections. We developinitially a model for reliability and transmission delay over asingle link between two nodes in a virus-based nanonetwork,and then extend this analysis to develop models for single-path,defined multi-path and random multipath topology.

A. Network Link Analysis

We approximate the transmission channel as a set of discretesquare locations, and assume all events occur at some discrete


Fig. 5. Illustration of single-network link. The transmitter releases virus quan-tity at τ0 , and graph illustrates the resulting concentration gradient at timesτa , τb , and τc , (τa < τb < τc ). The virus particles begin to reach the receivingcell at τ = τb .

time τη = ητdiff , where η ∈ N, 0 ≤ η ≤ T, τT is the maximumtime an event can occur and τdiff = d2

c /4D, which is the averagetime it takes for a virus to diffuse a distance dc in two dimensions.We can now express (3) as

cij (η)=1

4πD

η∑x=0

Q(τx)τη −τx

exp

(−r2

ij

4D(τη −τx)−kd(τη − τx)

)

(4)where cij (η) is the concentration at the location containing nodej at event time τη due to a release event from node i at time τ0 ,and rij is the distance between node i and receiver locationcontaining node j. Thus, the virus particle concentration foreach location can be calculated as a function of spatial locationand discrete time events. Solving (4) for several event times isshown in Fig. 5.

We model our receiver on (1b) and envision the receivernanomachine as an artificially engineered cell, for example amodified human T cell of diameter 10 μm [16]. If we examinethe location containing node j and assume that the virus particleconcentration is homogeneous in this location, then at someevent time τη the expected number of absorbed virus particlesfor a transmission between nodes i and j can be approximatedby

Iij (η) ≈ kabYj cij (η)τdiff (5)

where Yj is the quantity of nanomachines at location j (this isfor both the relay and receiver nanomachine) and kab is therate of virus absorption. The cell absorption of virus particles ismodeled typically as a Poisson counting process [19], wherebythe probability of α absorption events occurring at event timeτη at location i is given by

pij (α, η) =Iαij (η) exp(−Iij (η))

α!. (6)

It follows that the probability of no absorption events (α = 0)occurring at τη is therefore

pij (0, η) = pij (η) = exp(−Iij (η)). (7)

If virus emission begins at event time τ0 , then it follows thatthe reliability of a single link βij is

βij = 1 −T∏

η=0

pij (η) = 1 − exp

(−τdiff kabYj

T∑η=0

cij (η)

)

(8)where T is the sample size. We are interested in the first receptionevent and assume that the first virus absorbed is successfullyprocessed by the receiving node. We define a reception eventas the first virus absorption at the receiver and this will initiateforwarding of the virus particles in the intermediary nodes. Fora single hop, the probability of the first virus reception to occurat some event time τη is given by

Pij (η) = (1 − pij (η))η−1∏x=0

pij (x). (9)

where pij (η) is the transmission failure probability during eventtime τη given in (7). We can also calculate the median transmis-sion time for a link ij as the time τMED ,ij for the cumulativeprobability of first received particle to reach 0.5 of the overalllink reliability

τMED ,ij = min

{τx :

1β ij

x∑η=0

Pij (η) ≥ 0.5, x ≤ T

}. (10)

It is apparent from the summation component of (8) thatmaintaining a high virus concentration at the receiver locationover time increases the probability of a virus absorption event(i.e., link reliability). Our expression for link reliability is alsoa function of distance and time. It is also evident that reliabilitydecreases with the link distance and takes longer to achieve max-imum reliability for distant nodes as illustrated in Fig. 5. In theevent where a link must maintain a critical reliability, βc , then thenext hop must be within an effective radius re of the sender suchthat βij >= βc for all rij <= re . The effective radius could beused as a weight in routing algorithms whereby a nanomachinecalculates the distance between its neighboring nodes and onlyconsiders transmission to those within the effective communica-tion distance. This is used to calculate possible paths in randommultipath topologies in Section V-C. Techniques to determinethe distance between nodes in molecular communication-basednanonetworks are explored in [12]. However, calculating thedistance would require an additional computational capabilityin each node.

B. Single-Path Topology With Implicit Acknowledgment

We now expand the network link model to examine a sim-ple single-path topology shown in Fig. 4. We define a path sconnecting source and destination nodes as a set of M nodesstarting with source node and ending with the receiver node.For example, s = [1, 3, 4, 6] represents a path from node 1 tonode 6 via node 3 and node 4. We also define a set of corre-sponding link reliabilities, Bs = [β1,3 , β3,4 , β4,6 ] and link de-lays Ts = [τMED ,1,3 , τMED ,3,4 , τMED ,4,6 ].

As in (4), we assume all events occur at some discrete timeτη = ητdiff . At each stage of particle transmission, we assume


the next hop and previous hop are within the effective communi-cation distance of each intermediary device. Each intermediarynode replicates the original molecular communication after acell propagation delay τl (i.e., releases the same number of par-ticles at the same rate). Thus, the path reliability (βs) and thethe sum of the median transmission delay times (τs) for a singlepath from source to receiver with no link failures is

βs =∏

β∈Bs

β (11)

τs = (M − 1)τl +∑τ ∈T s

τ. (12)

The single-path topology uses an implicit acknowledgementprotocol as described in Section IV-A. The time for a successfulimplicit acknowledgement over a link ij is (τl + 2τMED ,ij ) andthe probability of receiving a successful acknowledgement isβ2

ij . We also wish to estimate a suitable time-out value for theacknowledgement protocol. The probability of the sender deviceto receive an acknowledgement at time τη over one hop withcell propagation delay τl is

PACK(η)ij =η−l∑x=0

Pij (x)Pij (η − l − x) (13)

where η ≥ l. Using (13), we can also estimate a realistic re-transmission time-out value τACK ,ij for a link such that theprobability of acknowledgement failure for the link exceeds anacceptable threshold, pACK ,c .

τACK ,ij = min

{τx : 1 −

x∑η=0

PACK(η) ≥ pACK ,c , x ≤ T

}.

(14)Obviously single-path transmission delay increases with eachlink failure. For each link failure, the delay will increase atleast by the corresponding link time-out value τACK ,ij . An ap-proach to implementing a time-out function could be based onthe solutions proposed in [35] and [12], where an engineeredchemical process in can act as a clock. The mechanism oper-ates as follows: a source nanomachine will release a quantity ofvirus particles and simultaneously start a chemical timer processwhich accumulates timer molecules. If no acknowledgement isdetected and the source nanomachine detects a concentrationof timer molecules greater than some predetermined thresholdconcentration, then the source bionanomachine will retransmitthe message. The threshold concentration for the timer processwould be calculated using the timeout value, τACK ,ij . This im-plementation would also require a suitable biomolecular com-puting solution similar to those already referenced in [25] thatwould use the acknowledgement signal and the timer processconcentration as inputs.

In a path s, we define fij as the number of retransmissionsrequired to successfully transmit across link ij. The set of re-transmissions for path s is Fs = [fij , fj l . . . .], and the totalnumber of retransmissions is fs =

∑f∈Fs

f . The probability ofFs retransmissions occurring during a transmission from source

Fig. 6. Illustration of multipath paths. The independent paths are illustratedby solid lines, while the dotted link indicates possible random paths. Distancesare in μm and are used for numerical results in Section VI.

device to receiver is given by

Ps,Fs=

∏βi j ∈Bs

(1 − βij )fi j βij (15)

And the associated delay for path s and the link failure set Fs

is

τs,Fs= τs +

∑fi j ∈Fs

τACK ,ij fij (16)

We now can calculate analytically the reliability and delayfor a single-path virus network with implicit acknowledgement.

C. Multipath Topology

We initially consider an explicitly defined multipath topol-ogy consisting of independent paths such that, for each hop, areleased virus can only attach to the next hop node for forwardtransmission and the previous node for acknowledgement. Thiscan be achieved by addressing transmitted virus through the en-velope gene as described in Section III-A and illustrated by thesolid path lines in Fig. 6.

1) Defined Multipath Topology With Independent Paths: Wenow define S as the set of all paths in the network and eachpath sk in S has Msk

hops. As in the single-path model, wedefine an set of corresponding link reliabilities for each path,Bsk

= [βij , βjl , βlm . . .], where βjl is the reliability betweennodes j and l.

In the case where all paths are disjoint, then the overall net-work reliability (i.e., successful transmission over at least onepath) is

βM P = 1 −∏

sk ∈S

(1 − βsk) (17)

where βsiis calculated of each path in S using (11). Finally,

the transmission delay is the sum of the individual path delayscalculated using (12) multiplied by the respective path reliabilityfrom (11) and divided by the sum of all path reliabilities asfollows:

τmp =1∑

sk ∈S βsk

∑sk ∈S

βskτsk

(18)


2) Random Multi-path Topology With Dependent Paths: Inthe random multipath topology, the virus particles operate asthey would typically in nature. The characteristics of this ap-proach have, as expected, a close resemblance to Gossip orEpidemic protocols [33] in conventional networks since bothprotocols are inspired by the characteristics of viral epidemics,albeit at an organism level (it is a case of coming full circle!). Ifwe assume broadcast communication, where each virus-basedmessage can be received by any node (i.e., all intermediarynodes have complementary receptors and can receive once theyare within the effective communication distance of a trans-mitting node), then the virus can also have several dependentpaths through the environment. For example Fig. 6 illustratestwo dependent path Tx → a → b → Rx and Tx → a → Rx,whereby both have link Tx → a in common.

For comparison, we focus on a source and destination devicein defined locations as in Fig. 3. However, the intermediarynodes are distributed randomly in the 2-D environment. Thereliability and transmission delay are calculated as follows usingMATLAB [34]:

1) Calculate all possible node links, ij, using an effectivecommunication radius described in Section V-A and cal-culate the corresponding link reliability βij for each nodepair using (8).

2) Create a set of all possible paths, S, from source node toend node using the path finding algorithm from [27] andsort in ascending order based on the hop count.

3) Calculate the conditional reliability of each path in S andthen the end-to-end reliability using an implementation ofthe SYREL algorithm [28].

4) Create a subset of “effective paths” from S such that theircombined reliability exceeds a predetermined reliabilitythreshold. In this case we used .99 of the overall reliabiltycalulated in step 3. This minimizes probability mass func-tion (pmf) calculations in the next step and removes longpaths that make an insignificant contribution to overallreliability.

5) The pmf for the first virus reception event is calculated foreach path from step 4 as follows:

a) Using (9), the pmf for each path is calculated bysuccessive convolutions of the pmf of each link(PPMF,ij = Pij /βij) in the path.

b) Via the principle of superposition, the path pmfs arecombined to calculate the overall pmf for first virusreception event at the receiver.

This analysis can be used to calculate the pmf of the first virusparticle received at the receiver and is used in the next section(see Fig. 11) to illustrate the predictability of the first receptionevent.

VI. NUMERICAL RESULTS

We now analyze reliability and communication delay for asingle link by varying the link distance and diffusion coeffi-cient. We then extend this to obtain the reliability and trans-mission delay for multihop routing between a source and desti-nation device using single-path, defined multipath, and randommultipath virus-based nanonetworks. For all multihop analyses,

Fig. 7. Link reliability and virus particle concentration (virus particles/μm2 )as a function of time for a 400 μm link and transmission of 3 × 104 virusparticles. Note that this is the cumulative reliability calculated using (8). Thereliability continues to increase as long as a significant virus concentration existsat the receiver.

we examine communication between a source and destinationdevice with fixed location 1200μm apart using each topology.

A. Single Link

The calculation of virus particle concentration and associatedlink failure for a location set at 400 μm from a sender is shownin Fig. 7.

It is possible to visualize the virus particle propagation as adecaying wave front moving away from the transmission sourceresulting in the virus concentration profile illustrated in Fig. 7.Assuming the virus quantity released at the sender is fixed,then the virus dynamics as it moves away from a sender andencounters a receiver is constrained by the following physicaland biological parameters: diffusion coefficient, distance fromthe sender, and virus decay. As already stated, the virus de-cay combined with the diffusion coefficient creates a theoreticalmaximum communication distance and can be calculated basedon diffusion. From a communication network perspective, weare particularly interested in the reliability and transmission de-lay associated with a given link. Using (10), we calculate theeffective link distance and the associated transmission delay fora link using a reliability threshold. The reliability threshold isthe lowest average reliability permitted for a link. We illustratethis by plotting the transmission delay and maximum link dis-tance as a function of threshold reliability for a link. Analysis ofFig. 8 shows significant increase in transmission delay to achievereliability greater than 0.7. Also, the gap in transmission delaybetween different link distances for the same threshold becomeswider as the reliability threshold goes toward 1. This is causedby the relatively longer time virus particles take to diffuse tooutlying locations and also the dilution effect of the virus quan-tity as it spreads out from its source. For example, the differencein transmission delay to achieve reliability greater than 0.5 fora 100 and 300μm link is 1.3 h. The difference to achieve re-liability greater than 0.9 for the same distances is 3.9 h. Thissuggests that to create multihop networks with low delay andhigh reliability a redundant multipath approach would increasethe throughput time.

The effect of the diffusion coefficient on link distance is il-lustrated in Fig. 8(b). The behavior of single links in environ-ments with a large diffusion coefficient shows interesting results.Intuitively one would expect that faster diffusion would result


Fig. 8. Transmission delay (a) and Effective Link Distance (b) versus Relia-bility Threshold for a single link. The quantity of virus Q(0) = 30 000 and thelink distance ri = 400 μm is used in (b). Other parameters are from Table I.

in less transmission delay times and increased effective linkdistances for a given reliability threshold. However, calculatingthe effective communication distance for several diffusion co-efficients suggests the opposite: that environments with higherdiffusion coefficients have shorter effective communication dis-tances. For example, effective link distance to achieve reliabilitygreater than 0.9 is approximately 600 and 500 μm for diffusioncoefficients of 3.6 and 10 μm2 s−1 , respectively. The larger dif-fusion coefficient does result in faster and further virus propa-gation, but with less concentrated molecules being maintainedover time at the receiver and consequently lower probability ofabsorption. Thus, the reliability performance of multihop net-work topologies is affected significantly by the physiochemicaldiffusion properties of the deployed environment. We now an-alyze the design of single-path, defined multipath and randommultipath topology models using the single link model as abasis.

B. Multihop Topologies

We now compare the performance of the multipath and single-path analytical models presented in Section IV. For single-pathtopology, we use the design shown in Fig. 4 with each linkdistance set at 400 μm. For the defined multipath topology, weuse the paths and link distances shown by the solid lines inFig. 6.

Applications that will use this type of network will not havean indefinite time period to propagate molecules. Therefore, fora single path with acknowledgement, we set a maximum numberof single-path retransmissions. We also wish to compare accu-rately both single and multipath approaches. Therefore, we seta maximum number of retransmissions, r, such that the numberof transmissions that can occur in the single-path topology isequal to the expected number of transmissions in the definedmultipath scenario as follows:

r = 1 − Ms +∑sk ∈S

∑βi j ∈βs k

βij (hij − 1). (19)

where βskis the set of link reliabilities in path sk ,Ms is the

number of hops in the single-path topology, and hij is the hop

Fig. 9. Reliability (a) and Average Delay (b) versus Virus Quantity releasedduring transmission events. The plot is annotated with corresponding maximumnumber of retransmissions (r) used in single-path(Ack) calculations required tomatch the expected number of transmission in the defined multipath.

Fig. 10. Reliability (a) and average delay (b) for successful transmission oversingle path of 1200μm with 1, 2, and 3 intermediary nodes. All nodes areequidistant and only communicate with the nearest neighbors.

index for link i − j in path sk . For example, in path sk = [1 2 34], hsk ,12 = 1 (first hop), hsk ,23 = 2 (second hop). Our numer-ical study focuses on multihop transmission between a sourceand destination device 1200 μm apart in a channel with diffu-sion coefficient of 3.6 μm2s−1 . We also impose a constraint thatcommunication is between neighbors and, initially, all paths inthe network are independent. Successful particle delivery withrespect to released virus quantity for single-path, multipath, andsingle-path with implicit acknowledgement and number of re-tries r calculated using (19) is shown in Fig. 9. The single pathwithout acknowledgement is also shown for comparison pur-poses. The Fig. 9 plot annotations indicate changes to single-path maximum retransmissions, r, required to match the numberof transmissions that occur in the multipath topology. It is appar-ent from Fig. 9 that the reliability of multipath topology is im-proved by increasing the virus quantity, assuming other physicalfactors are fixed. Single-path reliability can also be improved byincreasing the number of retransmissions allowed per message.However, as indicated in (13), the retransmissions significantlyincrease the delay in transmission and this is illustrated in Figs.9(b) and 10. This is due predominantly to the delay associated


Fig. 11. Probability mass function for single path, defined multipath, andrandom multipath topologies. The random topology uses an identical number ofintermediary nodes as defined multipath. The random nodes are distributed in asimulation area of 1200 μm × 1200 μm. Each node releases 3 × 104 particlesper release event.

with each retransmission. Fig. 10(a) shows superior delay for a 2hop single path compared to 3 hop and 4 hop. However, this is atthe expense of inferior reliability. Reliability is improved by in-creasing the maximum number of retransmissions, but this alsoincreases the delay time [Fig. 10(b)]. We base our estimation ofpropagation delay, τl , on time it takes an infected cell to emitreplicated virus. It is substantially larger than the correspondinghop transmission delay, τx,ij calculated in Section IV. The cor-responding approach in multipath topologies is to create morepaths to the receiver. Doing so does not exhibit such dramaticdifferences in delay times and any delay time changes would bedue to diffusion-based transmission delay already discussed inthe single-path model.

We also include results for a random multipath solution. Inthis case, source and destination nodes are in the same fixedlocations, and we distribute the intermediary nodes randomlyin a 1200 μm × 1200 μm area and do not impose any routingrestrictions as described in Section V-C1. The results indicatethat this topology provides improved transmission delay com-pared to other topologies. This is due to the predominance ofshort two hop paths through the environment. However, reli-ability performance is less than the multipath and single pathwith acknowledgement topologies, particularly for higher virusquantity emissions.

Finally, we examine the predictability of a successful messagereception event at the destination device. Fig. 11 shows thepmf of time taken for the first message reception event at thedestination. The pmf for the single-path approach with implicitacknowledgement is spread over a longer time compared toour multipath approach. This is due to the high probability ofretransmissions being required to attain the threshold reliability.The spikes in the plot for single-path correspond to messagereception after zero, one, and two retransmissions, respectively,as time increases. The defined multipath topology, where eachpath has an identical number of hops as illustrated in Fig. 6,exhibits a tighter pmf profile and, therefore, exhibits a morepredictable performance for message delivery.

Clearly, the defined multipath solution appears to be moredesirable in terms of minimizing delay and maximizing pre-

dictability. Also, it may be the case that the multipath solutionmight be a simpler solution to realize physically as it does notrequire the computational mechanisms to implement the im-plicit acknowledgement protocol. On the other hand, the single-path topology requires fewer relay nodes and the implicit ac-knowledgement solution does provide a best of both worlds inallowing reliability to be tailored by adjusting the maximumallowed number of retransmissions. For example, as discussedin Section IV, changes in the diffusion coefficient can signif-icantly affect reliability. Implicit acknowledgement allows thesource to destination reliability to be reprogrammed through thecommunication protocol by adjusting the maximum number ofretransmissions. This would be of benefit, particularly, if thevirus quantity released during a transmission event is a biologi-cal constant that cannot be modulated apart from on/off processdescribed in Section III.

C. Comparison to Other Molecular Communication Solutions

The virus-based nanonetwork proposed in this paper isdiffusion-based similar to those proposed in [1] and [3]. The dif-ference is that we have selected one specific biological compo-nent for the diffusion (viruses) and these works do not cover thespecific scenarios that we use in this paper (multipath and sin-gle path with acknowledgement). However, the bacteria modelproposed in [4] and [11] can be compared with the virus modelproposed in this paper. Based on the delay of the single link inFig. 8, for a distance of 200 μm, the virus propagation takes ap-proximately 5 h. This is slightly faster than the bacteria commu-nication model of [11], where a single link took approximately4.9 h for 180 μm (however, in the case of bacteria communica-tion only 30 bacteria were emitted, which is much lower than thequantity of virus emitted in this paper). Based on the delay andreliability pattern, we can observe that a similar delay patternto multihop bacteria nanonetworks is observed [11]. The reasonfor this similarity is due to the infection process of virus on cellswhich increases the delay, and this is similar to the conjugationprocess in bacteria.

VII. CONCLUSION

The physiochemical and biological characteristics of virus-based nanonetworks combined with heterogeneous deploymentenvironments pose challenges to the development of commu-nication networks to transport data from the source to destina-tion. Our analysis of a single link in virus-based nanonetworksshows that particle dilution and diffusion speed of virus parti-cles can have a significant and in some cases counter-intuitiveeffect on transmission delay and reliability. Our numerical re-sults show that equivalent reliability is possible in single pathwith implicit acknowledgement and defined multipath topolo-gies for virus-based nanonetworks. However, the large replica-tion delay relative to channel transmission delay means that sin-gle path with implicit acknowledgement and random multipathtopologies introduce more uncertainty for source to destinationcommunication time compared to defined multipath topologies.Furthermore, the analysis indicates that replication delay inintermediary nodes dominates overall transmission delay inmultihop virus-based nanonetworks. However, this inherent de-lay can be offset by the ability to encode large amounts of


information in DNA payload molecules [31]. Our future workwill examine how different parameters such as the number ofpaths and channel encoding techniques can be used to improvethe efficiency and reliability of virus-based nanonetworks.

REFERENCES

[1] A. Guney, B. Atakan, and O. B. Akan, “Mobile ad hoc nanonetworks withcollision-based molecular communication,” IEEE Trans. Mobile Comput.,vol. 11, no. 3, pp. 353–266, Mar. 2012.

[2] B. Atakan, S. Galmes, and O. B. Akan, “Nanoscale communication withmolecular arrays in nanonetworks,” IEEE Trans. NanoBiosci., vol. 11,no. 2, pp. 149–160, Jun. 2012.

[3] I. Llatser, A. Cabellos-Aparicio, and E. Alarcon, “Networking challengesand principles in diffusion-based molecular communication,” IEEE Wire-less Commun. Mag., vol. 19, no. 5, pp. 36–41, Oct. 2012.

[4] M. Gregori, I. Llatser, A. Cabellos-Aparicio, and E. Alarcon, “Physicalchannel characterization for medium-range nano-networks using flagel-lated bacteria,” Comput. Netw., vol. 55, no. 3, pp. 779–791, Feb. 2011.

[5] I. F. Akylidiz, F. Brunetti, and C. Blazquez, “NanoNetworking: A com-munication paradigm,” Comput. Netw., vol. 52, no. 120, pp. 2260–2279,Jun. 2008.

[6] B. Atakan, O. Akan, and S. Balasubramaniam, “Body area nanonetworkswith molecular communications in nanomedicine,” IEEE Commun. Mag.,vol. 50, no. 1, pp. 28–34, Jan. 2012.

[7] C. Teuscher, C. Grecu, T. Lu, and R. Weiss, “Challenges and promisesof nano and bio communication networks,” in Proc. 5th ACM/IEEE Int.Symp. Netw.-on-Chip 0), New York, NY, USA, 2011, pp. 247–254.

[8] M. Anghel, C. Teuscher, and H. -L. Wang, “Adaptive learning in ran-dom linear nanoscale networks,” in Proc. 11th Int. Conf. Nanotechnol.,Cincinnati, OH, USA, 2011, pp. 445–450.

[9] T. Nakano, M. Moore, F. Wei, A. T. Vasilakos, and J. W. Shuai, “Molecularcommunication and networking: Opportunities and challenges,” IEEETrans. NanoBiosci., vol. 11, no. 2, pp. 135–148, Jun. 2012.

[10] T. Nakano and J. Q. Liu, “Design and analysis of molecular relay channels:An information theoretic approach,” IEEE Trans. NanoBiosci., vol. 9,no. 3, pp. 213–221, Sep. 2010.

[11] S. Balasubramaniam and P. Lio, “Multi-hop conjugation based bacteriananonetworks,” IEEE Trans. NanoBiosci., vol. 12, no. 1, pp. 47–59, Mar.2013.

[12] M. J. Moore, T. Nakano, A. Enomoto, and T. Suda, “Measuring distancefrom single spike feedback signals in molecular communication,” IEEETrans. Signal Process., vol. 60, no. 7, pp. 3576–3587, Jul. 2012.

[13] H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed.New York, NY, USA: Oxford Univ. Press, 1959.

[14] B. E. Lai, M. H. Henderson, J. J. Peters, D. K. Walmer, and D. F. Katz,“Transport theory for HIV diffusion through in vivo distributions of topicalmicrobicide gels,” Biophys J., vol. 97, no. 9, pp. 2379–2387, 2009.

[15] A. R. Sedaghat, J. B. Dinoso, L. Shen, C. O. Wilke, and R. F. Siliciano,“Decay dynamics of HIV-1 depend on the inhibited stages of the viral lifecycle,” PNAS, vol. 105, no. 12, pp. 4832–4837, 2008.

[16] A. K. Abbas and A. H. Lichtman, Cellular and Molecular Immunology,5th ed. New York, NY, USA: Elsevier Science Health Science Division,2005.

[17] M. Gregori and I. F. Akyildiz, “A new nanonetwork architecture usingflagellated bacteria and catalytic nanomotors,” IEEE J. Sel. Areas Com-mun., vol. 28, no. 4, pp. 612–619, May 2010.

[18] M. Pierobon and I. F. Akyildiz, “Noise analysis in ligand-binding recep-tion for molecular communication in nanonetworks,” IEEE Trans. SignalProcess., vol. 59, no. 9, pp. 4168–4182, Sep. 2011.

[19] H. C. Tuckwell, P. D. Shipman, and A. S. Perelson, “The probability ofHIV infection in a new host and its reduction with microbicides,” Math.Biosci., vol. 214, no. 1–2, pp. 81–86, 2008.

[20] A. Enomoto, M. J. Moore, T. Suda, and K. Oiwa, “Design of self-organizing microtubule networks for molecular communication,” NanoCommun. Netw., vol. 2, no. 1, pp. 16–24, 2011.

[21] S. Balasubramaniam, N. T. Boyle, A. Della-Chiesa, F. Walsh,A. Mardinoglu, D. Botvich, and A. Prina-Mello, “Development of ar-tificial neuronal networks for molecular communication nano communi-cation networks,” Nano Commun. Netw., vol. 2, no. 2–3, pp. 150–160,2011.

[22] Y. Moritani, S. Hiyama, and T. Suda, “Molecular communication amongnanomachines using vesicles,” in Proc. NSTI Nanotechnol., 2006, pp. 705–708.

[23] K. Frimpong and S. A. Spector, “Cotransduction of nondividing cellsusing lentiviral vectors,” Gene Therapy, vol. 7, no. 18, pp. 1562–1569,2000.

[24] S. F. Johnson and A. Telesnitsky, “Retroviral RNA dimerization and pack-aging: The what, how, when, where, and why,” PLoS Pathog., vol. 6,no. 10, p. e1001007, 2010.

[25] F. Walsh, S. Balasubramaniam, D. Botvich, and W. Donnelly, “Syntheticprotocols for nano sensor transmitting platforms using enzyme and DNAbased computing,” Nano Commun. Netw., vol. 1, no. 1, pp. 50–62, 2010.

[26] A. Avihoo, I. Gabdank, M. Shapira, and D. Barash, “In silico design ofsmall RNA switches,” IEEE Trans. NanoBioSci., vol. 6, no. 1, pp. 4–11,Mar. 2007.

[27] J. R. Evans and E. Minieka, Optimization Algorithms for Networks andGraphs, 2nd ed. New York, NY, USA: Marcel Dekker, 1992.

[28] S. Hariri and C. S. Raghavendra, “SYREL: A symbolic reliability algo-rithm based on path and cutset methods,” IEEE Trans. Comput., vol. 36,no. 10, pp. 1224–1232, Oct. 1987.

[29] R. Waehler, S. Russell, and D. T. Curiel, “Engineering targeted viral vec-tors for gene therapy,” Nature Rev. Genet., vol. 8, no. 8, pp. 573–587,2007.

[30] J. E. Pearson, P. Krapivsky, and A. S. Perelson, “Stochastic theory ofearly viral infection: Continuous versus burst production of virions,” PLoSComput. Biol., vol. 7, no. 2, p. e1001058, 2011.

[31] G. M. Church, Y. Gao, and S. Kosuri, “Next-Generation Digital Informa-tion Storage in DNA,” Science, vol. 337, no. 6102, p. 1628, 2012.

[32] M. Pierobon and I. F. Akyildiz, “Diffusion-based noise analysis for molec-ular communication in nanonetworks,” IEEE Trans. Signal Process.,vol. 59, no. 6, pp. 2532–2547, Jun. 2011.

[33] E. Riviere and S. Voulgaris, “Gossip-based networking for internet-scaledistributed systems,” in E-Technologies: Transformation in a ConnectedWorld. Berlin, Germany: Springer-Verlag, 2011, pp. 253–284.

[34] MATLAB version 7.11.0., The MathWorks, Inc., Natick, MA, USA, 2010.[35] A. Hjelmfeltt, E. D. Weinberger, and J. Ross, “Chemical implementation

of finite-state machines,” in Proc. Nat. Acad. Sci. USA, 1992, vol. 89,pp. 383–387.

[36] B. Yurke, A. J. Turberfield, A. P. Mills, F. C. Simmel, and J. L. Neumann,“A DNA-fuelled molecular machine made of DNA,” Nature, vol. 406,no. 6796, pp. 605–608, 2000.

Frank Walsh received the Bachelor’s degree in elec-trical engineering from Trinity College, Dublin, Ire-land, in 1994, the Master’s degree in physics fromQueens University, Belfast, U.K., in 1996, and is cur-rently working toward the Ph.D. degree in protocolsfor molecular cCommunications.

He is currently a Lecturer in computing withthe Department of Computing, Mathematics, andPhysics, Waterford Institute of Technology, Water-ford, Ireland. Previously, he was a Research Assis-tant at the Telecommunication Software and Systems

Group, Waterford Institute of Technology, where he worked on a number ofEuropean Commission funded projects. His research interests include nanocommunication networks, biomolecular computation, and autonomic servicesusing bioinspired approaches.

Sasitharan Balasubramaniam (M’05) received theBachelor’s degree in electrical and electronic engi-neering from the University of Queensland, St Lucia,Qld, Australia, in 1998, the Masters’ degree in com-puter and communication engineering from Queens-land University of Technology, Brisbane, Qld, in1999, and the Ph.D. degree from the University ofQueensland in 2005.

He is currently a Senior Research Fellow at theNano Communication Centre, Department of Elec-tronic and Communication Engineering, Tampere

University of Technology, Tampere, Finland. Previously, he was a ResearchFellow at the Telecommunication Software and Systems Group, Waterford In-stitute of Technology, Waterford, Ireland, where he worked on a number ofScience Foundation Ireland projects. He has published more than 70 papers,and actively participates in a number of technical programme committee forvarious conferences. His current research interests include bioinspired futureInternet, as well as molecular communications.

Dr. Balasubramaniam is currently an Editor for Elsevier Nano Communica-tion Networks.

reliability and delay analysis of multihop virus-based nanonetworks

Documents