Error Recovery in a Micro-Electrode-Dot-Array DigitalMicrofluidic Biochip∗

Zipeng Li1, Kelvin Yi-Tse Lai2, Po-Hsien Yu2, Krishnendu Chakrabarty1, Miroslav Pajic1, Tsung-Yi Ho3, and Chen-Yi Lee2

1Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA2Department of Electronics Engineering, National Chiao Tung University, Hsinchu, Taiwan

3Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan

ABSTRACT

A digital microfluidic biochip (DMFB) is an attractivetechnology platform for automating laboratory proceduresin biochemistry. However, today’s DMFBs suffer fromseveral limitations: (i) constraints on droplet size andthe inability to vary droplet volume in a fine-grainedmanner; (ii) the lack of integrated sensors for real-timedetection; (iii) the need for special fabrication processes andthe associated reliability/yield concerns. To overcome theabove problems, DMFBs based on a micro-electrode-dot-array(MEDA) architecture have been proposed recently, anddroplet manipulation on these devices has been experimentallydemonstrated. Errors are likely to occur due to defects, chipdegradation, and the lack of precision inherent in biochemicalexperiments. Therefore, an efficient error-recovery strategyis essential to ensure the correctness of assays executed onMEDA biochips. By exploiting MEDA-specific advances indroplet sensing, we present a novel error-recovery techniqueto dynamically reconfigure the biochip using real-time dataprovided by on-chip sensors. Local recovery strategies basedon probabilistic-timed-automata are presented for varioustypes of errors. A control flow is also proposed to connectlocal recovery procedures with global error recovery for thecomplete bioassay. Laboratory experiments using a fabricatedMEDA chip are used to characterize the outcomes of keydroplet operations. The PRISM model checker and threeanalytical chemistry benchmarks are used for an extensive setof simulations. Our results highlight the effectiveness of theproposed error-recovery strategy.

1. INTRODUCTIONOver the past decade, microfluidic biochips, also referred

to as lab-on-a-chip, have been used for various biochemicalapplications, such as high-throughput DNA sequencing,point-of-care clinical diagnostics, and protein crystallization fordrug discovery [1–4]. While early generations of microfluidicbiochips used continuous fluid flow through permanentlyetched microchannels, more recent biochips, referred to asdigital microfluidic biochips (DMFBs), manipulate liquids asdiscrete droplets of nanoliter and picoliter volumes basedon the principle of electrowetting-on-dielectric (EWOD) [5].Compared with the conventional continuous-flow biochip, a

∗The work of K. Y.-T. Lai, P.-H. Yu, and C.-Y.Lee was sponsored in part by MOST of Taiwan under103-2221-E-009-191 and 104-2218-E-009-007.

Permission to make digital or hard copies of all or part of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor profit or commercial advantage and that copies bear this notice and the full citationon the first page. Copyrights for components of this work owned by others thanACM must be honored. Abstracting with credit is permitted. To copy otherwise, orrepublish, to post on servers or to redistribute to lists, requires prior specific permissionand/or a fee. Request permissions from permissions@acm.org.

ICCAD ’16, November 07-10, 2016, Austin, TX, USA

c© 2016 ACM. ISBN 978-1-4503-4466-1/16/11. . . $15.00

DOI: http://dx.doi.org/10.1145/2966986.2967035

DMFB offers the advantages of simple instrumentation, flexibledevice geometry, reconfigurability and easy coupling withother technologies [2, 6]. To achieve the full potential ofscalability and reconfigurability in digital microfluidics, anovel micro-electrode-dot-array (MEDA) architecture [7–10]has been proposed recently.

Unlike conventional digital microfluidics, where electrodesof equal size are arranged in a regular pattern, theMEDA architecture is based on the concept of asea-of-micro-electrodes with an array of identical basicmicrofluidic unit components called microelectrode cells

(MCs) [7]. Each MC consists of a microelectrode and acontrol/sensing circuit. A high-voltage shielding layer isinserted between the microelectrode and the control/sensingcircuit to ensure the correct operation of the MC. The MEDAarchitecture allows microelectrodes to be dynamically groupedto form a micro-component (e.g., mixer or diluter) thatcan perform different microfluidic operations on the chip.Prototypes of MEDA-based biochips have been fabricatedusing TSMC 0.35 µm CMOS technology [9], and these devicescan use a power-supply voltage of only 3.3 V for embeddedcontrol circuits [8].

However, as in the case of integrated circuits, continuedincrease in density and area of microfluidic biochips willalso result in more defects and reduce yield. In additionto defects and imperfections for fabricated MEDA-basedbiochips, faults may also arise during bioassay execution. Forexample, excessive actuation voltage may lead to electrodebreakdown and charge trapping [11, 12], and DNA foulingmay lead to the malfunction of multiple electrodes in thebiochip [13, 14]. Faults in biochips may eventually result inerrors (e.g., a splitting operation with unbalanced droplets),which can adversely impact the correctness of the entireexperiment. However, many biomedical applications (e.g.,clinical diagnostics) require high precision for each operation.Therefore, efficient error-recovery strategies are required toensure robust fluidic operations and high confidence in theoutcome of biochemical experiments.

Several error-recovery strategies for digital microfluidicshave recently been proposed in [15–19]. However, dueto the inherent differences between traditional DMFBs andMEDA, existing error-recovery solutions cannot exploit theadvantages specific to MEDA-based biochips. For example,in conventional DMFBs, droplets need to be transportedto a nearby checkpoint for error detection. However, inMEDA-based biochips, droplets can be detected anywhere onthe chip and the response time for sensing is only 10 ms [9].Moreover, previous strategies use an unified recovery procedure(e.g., roll-back [17,20]) for all types of errors; this approach canmake error recovery inefficient and result in longer recoverytime for specific types of errors. An example of roll-back isshown in Fig. 1. The initial sequencing graph correspondingto a bioassay is shown in Fig. 1(a). When an error occursat operation 9, the system will re-execute the correspondingdispensing operations and mixing operations (operations 16,

(a) (b)

Fig. 1. (a) Initial sequencing graph; (b) Updatedsequencing graph for error recovery.

17, and 18). The new sequencing graph for error recovery isshown in Fig. 1(b). However, the re-execution of operation 16,17, and 18 may not always be the most-efficient solution sincewe can recover from the error on operation 9 by redoing themixing operation. Furthermore, prior methods assume thaterror recovery is always feasible and they neglect the likehoodthat error-recovery procedures may also fail.

To overcome the above drawbacks, we propose anew probabilistic-timed-automata (PTA)-based strategy forerror recovery in MEDA-based biochips. The proposederror-recovery strategy aims to fully exploit the advancedsensing techniques offered by MEDA. The key contributionsof this paper are listed as follows:

1. We propose a classification of the outcomes of operationsinto three categories: no error, minor error, and major

error. Each outcome is treated in a different way in theproposed error-recovery strategy.

2. We carry out laboratory experiments using a fabricatedMEDA biochip to estimate these outcome probabilities.

3. Instead of utilizing the same error-recovery strategy forall types of errors (e.g., roll-back [17, 20]), we proposedifferent PTA-based error-recovery strategies for differenttypes of local errors. Discrete-time analysis and modelchecking are also used to compute the probability ofsuccess under constraints on the error-recovery time.

4. A control flow is proposed to connect the local recoveryprocedures to global error recovery for the completebioassay. We also examine the influence of local recoveryprocedures on the execution of the bioassay. Accordingly,we are able to provide users with insights about the timecost and anticipated probability of success for any givenbioassay.

5. Simulation results for three representative benchmarksare derived using the PRISM model checker. Our resultsillustrate the effectiveness of the proposed error-recoverystrategy.

The remainder of the paper is organized as follows. Section 2presents background material on digital microfluidics andthe MEDA architecture. Section 3 describes the problemformulation. Section 4 presents the PTA-based error-recoverystrategy in detail. Section 5 presents experimental results.Finally, Section 6 concludes the paper.

2. DIGITAL MICROFLUIDICS AND MEDAA DMFB utilizes electrowetting-on-dielectric (EWOD) to

manipulate and move nanoliter or picoliter droplets containingbiological samples on a two-dimensional electrode array [1].MEDA extends this basic architecture by adding moreflexibility, as described in Section 1. A comparison between aconventional DMFB and a MEDA-based biochip is presentedin Fig. 2. A typical MEDA-based biochip consists of two plates:

(a)

(b)

Fig. 2. (a) Illustration of a conventional DMFB [21]. (b)Illustration of the MEDA architecture and microelectrodecell (µ-electrode cell).

Droplet sensing

Fig. 3. Control of droplet actuation and location sensing inMEDA-based biochips [9].

a top plate, which serves as a reference electrode, and a bottomplate with patterned microelectrodes.

The size of the microelectrodes can be 10 times smaller(e.g., 100 µm [7] in length) than conventional electrodes.Each microelectrode cell (MC) consists of a microelectrode, anactivation circuit, and a sensing circuit. MEDA-based DMFBsallow the dynamic grouping of microelectrodes to form differentshapes and fluidic modules.

A dielectric layer and a hydrophobic layer are depositedabove the microelectrodes, and droplets are sandwichedbetween the two plates. Once the electrodes are actuated,the EWOD force induces droplet motion. In this way, fluidicoperations (e.g., cutting and mixing) on droplets with differentsizes can be achieved on the chip.

Fig. 3 illustrates the microfluidic processing routine inMEDA-based biochips. In the beginning, sensing circuitsdetect the initial droplet location and then the actuationpattern is shifted into registers of all MCs. A high-voltage (HV)signal is enabled for a predetermined number of clock cycles, asa results of which the droplet is moved to the expected position.If sensing circuits cannot find the droplet on the expected

location, the previous actuation pattern will be activated againuntil sensing results indicate the success of droplet movement.

3. PROBLEM FORMULATIONSensing techniques in digital microfluidics enable error

detection and error recovery [22, 23]. A number oferror-recovery strategies have been proposed for conventionalDMFBs [15]. Checkpoints must be inserted into the bioassayfor these strategies. Droplets at a checkpoint are routed toa nearby sensor/detector for error detection. If no error isdetected, the next operation is executed; otherwise, an errorrecovery graph is inserted into the original sequencing graph,and the schedule, placement, and routing plan are dynamicallycomputed and updated to enable error recovery.

In a MEDA-based biochip, droplet sensing/detection canbe accomplished anywhere within 10 ms [8, 24]. Therefore,real-time error detection is possible for any fluidic operation.Based on the available technology platform, we consider thefollowing problem formulation in this work.

Input: (1) The sequencing graph for G = {V,E} forthe bioassay, where V = {V1, V2, . . . , Vm} represents moperations and E = {(Vi, Vj) 1 ≤ i, j ≤ m} represents the datadependency between all pairs of operations i and j, i.e., theprecedence relationship. (2) The digital microfluidic library,which includes the type, size, and corresponding executiontime of on-chip fluidic functional modules. (3) The size of theMEDA-based DMFB (e.g., an m × n microelectrode array).(4) The outcome probability for each type of operation in thesequencing graph. Details about the outcome classificationand the outcome probability are described in Section 4-B andSection 4-C.

Output: (1) The error-recovery procedure for each typeof localized error (e.g., unbalanced splitting and inadequatemixing). (2) The error-recovery strategy for the completebioassay.

Constraints: We consider both a resource constraint anda time constraint : the resource constraint limits the maximumarea for chip reconfiguration; the time constraint limits themaximum time that is allowed for error recovery.

Objective: Develop an error-recovery strategy thatminimizes the impact on bioassay completion time andmaximizes the probability of successful error recovery.

4. ERROR RECOVERY STRATEGYIn this section, we first describe the errors that are being

targeted in this paper. Instead of regarding the detectionoutcome for each operation as either “success” or “failure”,we classify the outcome into three categories: “no error”,“minor error” and “major error”. These three categories canhelp to distinguish the extent of failures. A PTA-basederror-recovery approach is proposed for each type of error.The probability of success (POS) for error recovery is alsoconsidered. The outcome classification and the PTA-basedapproach distinguish this work from previous error-recoverystrategies for conventional DMFBs.

4.1 Target Errors in MEDAA DMFB is said to have an error if its operation does

not match its specified behavior. Errors are typically causedby physical defects in DMFBs [25]. Fault models can beused to represent the effect of physical defects at some levelof abstraction. As described in [26–28], faults in DMFBscan be classified as being either catastrophic or parametric.Catastrophic faults lead to a complete malfunction of thesystem, while parametric faults cause degradation in thesystem performance. Physical defects that cause parametricfaults include geometrical parameter deviations, which includes

(a)

(b)

Glucose droplet

PBS droplet

Mixed droplet

Fig. 4. Illustration of (a) two droplets before mixing andthe corresponding droplet-property sensing map, and (b)the mixed droplet and the corresponding droplet-propertysensing map.

deviation in insulator thickness, electrode length and the heightbetween parallel plates [26]. In this paper, we assume thatchips have been carefully tested using both functional testmethods [28] and structural test methods [26] before they areused for bioassay execution. For example, we assume thatdroplets will never be stuck during their transportation anddroplet dispensing can always be successfully achieved.

However, some manufacturing defects may be latent, andthey may produce errors during field operation. Moreover,harsh operational environments and biological samples (e.g.,protein) may result in particle contamination and residue onsurfaces due to adsorption, which may also result in unexpectederrors [29]. These are referred to as on-line errors, and theyoccur after a series of fluidic operations [30]. Such on-line errorscan have serious consequences on bioassay results. Therefore,to ensure robust execution of the target bioassay, we proposeefficient error-recovery approaches for these on-line errors.More specifically, we target on-line errors related to mixing,splitting, mixing, and dilution.

4.2 Outcome Classification of OperationsOutcomes of error detection can either be “success” or

“failure” in a conventional DMFB [15, 17]. However, once anerror is detected, there is no way to determine the extent ofthe error. For example, we can detect that a droplet splittingoperation produces two droplets with unbalanced volumes,but we are not able to easily determine the extent of volumeimbalance.

However, MEDA provides a practical sensing technique fordroplets on the chip, referred to as real-time droplet sizesensing [24]. This sensing technique can provide us withdetailed information about the outcomes of error detection.Accordingly, we are able to classify the outcomes of errordetection into multiple categories, and the most-efficientrecovery procedure can be utilized for each type of error.

4.2.1 Outcome Classification for Mixing

In addition to droplet-location sensing, droplet-propertysensing can also be achieved on MEDA-based biochips [24].Droplet-property sensing can be used to distinguish betweendifferent kinds of droplets based on their permittivities.Since there is a sensing circuit under each microelectrode,droplet-property sensing can be achieved anywhere on the chipin a real-time manner.

A software package can be used to map different permittivitylevels to various colors for ease of visualization [24]. An

Sensing map

Droplet 1 Droplet 2

Fig. 5. Illustration of two split droplets on a MEDA-basedchip and the corresponding droplet-sensing map.

example is shown in Fig. 4(a): the glucose droplet is visualizedin the measurement window using blue color while thephosphate-buffered saline (PBS) droplet is orange. Basedon the detected permittivity levels, we are able to determinewhether two droplets are uniformly mixed. If two dropletsare uniformly mixed, there is only one detected permittivitylevel. Accordingly, there is only one color, defined as final color,in the visualization of the mixed droplet in the measurementwindow. Otherwise, there are multiple color associated withthe visualization of the mixed droplet; see Fig. 4(b). We nextquantify the error factor (Fmix) for mixing operation:

Fmix =NP

NT

(1)

where NP denotes the number of microelectrodes visualized bythe final color in the measurement window, and NT representsthe total number of microelectrodes occupied by the droplet.

After we calculate Fmix, two user-defined thresholds, Tm1

and Tm2 (Tm1 < Tm2), can be used to distinguish betweendifferent outcomes. The outcome of a mixing operation ischaracterized as (i) major error if Fmix ≤ Tm1, (ii) minor

error if Tm1 < Fmix ≤ Tm2, or (iii) no error if Fmix > Tm2.

4.2.2 Outcome Classification for Splitting

The outcome classification for splitting is based on the sizedifference between two split droplets. The computation of theerror factor for the splitting operation (Fsplit) is describedby (2), where N1 is the number of microelectrodes occupiedby one split droplet, and N2 is the number of microelectrodesoccupied by the other split droplet.

Fsplit = 1−|N1 −N2|

max{N1, N2}(2)

An example is shown in Fig. 5. After splitting, Droplet1 occupies 17 microelectrodes (N1 = 17) and Droplet 2occupies 25 microelectrodes (N2 = 25). Therefore, the errorfactor for the splitting operation in Fig. 5 is calculated to be

1− |17−25|max{17,25}

= 0.68.

Similar to mixing operations, two user-defined parametersTs1 and Ts2, are used to distinguish between the outcomes ofno error, minor error, and major error for splitting operations.Accordingly, the outcome of any splitting operation can beclassified into either of these categories.

4.2.3 Outcome Classification for Dilution

A dilution operation can be regarded as a mixing operationfollowed by a splitting operation [18, 31]. Therefore, theoutcome classification for any dilution operation is determinedby the outcome classifications of the corresponding mixing andsplitting operations. The outcome of the dilution operation canbe characterized as no error if and only if outcomes of both themixing and splitting operations are characterized as no error.If the outcome of either mixing or splitting is characterizedas a major error, the outcome of the dilution operation ischaracterized as a major error. In other cases, the outcomeof the dilution operation is characterized as a minor error.The outcome classification for dilution operations is shown inTable 1.

Table 1. Outcome Classification of Dilution Operations.

Outcome (Dilution) Outcome (Mixing) Outcome (Splitting)No error No error No error

Minor error No error Minor errorMinor error Minor error No errorMinor error Minor error Minor errorMajor error No error Major errorMajor error Minor error Major errorMajor error Major error No errorMajor error Major error Minor errorMajor error Major error Major error

(a) (b)

Fig. 6. (a) Chip micro-photo and (b) experimental setup.

(a) (b)

Nu

mb

er o

f m

ixin

g

op

era

tio

ns

Nu

mb

er o

f sp

litt

ing

op

era

tio

ns

Fig. 7. Experimental results for (a) mixing operations, and(b) splitting operations.

4.3 Outcome ProbabilityNote that Tm1, Tm2, Ts1, and Ts2 are user-defined

parameters. Higher values of these parameters indicate higherprecision requirements on the bioassay outcomes. In thispaper, without any loss of generality, we set Tm1, Tm2, Ts1

and Ts2 to be 0.70 and 0.90, 0.50, and 0.80, respectively.The outcome probability of an operation is defined as the

probability that the outcome of the operation belongs to thatparticular category. We estimated the outcome probabilitiesfor mixing and splitting using experiments on a fabricatedMEDA-based biochip. The micro-photo of the fabricated chipand the experimental setup are shown in Fig. 6. The splittingoperation was performed using a 7 × 7 deionized (DI) waterdroplet. The mixing operation was performed using a 10× 10PBS droplet and a 10× 10 glucose droplet.

We repeated experiments involving the mixing and splittingoperations 100 times. Each mixing (splitting) operationtakes two seconds (one second) to complete. Based on theclassification method described in Section 4-B, the outcomeof each operation is placed in one of the three categories: no

error, minor error, and major error. The experimental resultsare presented in Fig. 7.

The outcome probability of mixing/splitting/dilutionoperations can be calculated based on the experimental results.Experimentally characterized outcome probabilities are shownin Table 2. We observed that the outcome probability of oneoperation does not depend on the outcome of the previousoperation. Therefore, the outcome probabilities in Table 2 arestatic. However, the outcome probabilities may be differentfor different types of droplets. More studies are needed to

Table 2. Experimentally Characterized OutcomeProbability.

OutcomeProbability

Mixing Splitting Dilution

No error 0.82 0.68 0.56Minor error 0.13 0.23 0.30Major error 0.05 0.09 0.14

explore the relationship between the outcome probability andthe type of droplet. For the sake of simplicity and due tothen lack of significant experimental results to the contrary,we assume here that the outcome probability is the same forall types of droplets. According to Table 2, if we detect amixing error, the probability that the error is a minor erroror a major error is calculated to be 0.13/(0.13 + 0.05) ≈ 0.77or 0.05/(0.13 + 0.05) ≈ 0.23, respectively. Similarly, theprobability that the splitting error is a minor (major) erroris calculated to be 0.72 or 0.28, respectively.

4.4 Local Recovery ApproachesWe have developed PTA-based methods for local recovery in

the case of mixing, splitting, and dilution errors, respectively.The state-transition diagram of the PTA for mixing errors(PTAm) is shown in Fig. 8(a). There are two thresholds inPTAm: the time threshold tth and the location threshold lth.Time threshold tth limits the maximum time for local recoveryand location threshold lth limits the largest number of mixersthat can be used for error recovery. The parameters t, try, andloc are used to record the time cost, the number of recoveryoperations on one mixer, and the number of mixers that havebeen used for local recovery, respectively.

In PTAm, we first carry out error detection and thenclassify the corresponding detection outcome; an error-recoveryapproach is then selected based on the correspondingclassification. For example, a mixing operation with a minorerror can be simply recovered by redoing the mixing on thecurrent mixer, while a mixing operation with a major error hasto be routed to a nearby mixer to redo the mixing operation.

hen a mixing error is detected, PTAm enters theFaulty Check state. Based on the classification results, thenext state can either be Minor Error or Major Error; thecorresponding transition probabilities are calculated using theexperimental results discussed in Section 4-C and highlightedin Fig. 8(a). If the PTAm moves to Minor Error, the nextstate can be Reroute1, Mix, Call Backup or Final Fail. Inthe state of Reroute1, the droplet will be moved to a nearbyavailable mixer to redo the mixing. In the Mix state, thedroplet will be mixed one more time on the same mixer; InCall Back state, PTAm will search for backup droplets torecover from the mixing error (here we use the same methodas in [15] to find backup droplets); In Final Fail, because thetime-cost execeeds tth, the local recovery is deemed to havefailed. Similarly, if PTAm moves to the Major Error state,the next state can be Reroute1, Call Backup or Final Fail.Whenever PTAm transitions to Mix, the next state is alwaysCheck. Based on the results of error detection, PTAm canmove to Minor Error, Major Error or Final Success. Thecorresponding transition probabilities are also highlighted inFig. 8(a). The Final Success state indicates that local recoveryhas been successful, while the Minor Error and Major Errorstates will continue to lead to other states until PTAm moveseither to Final Success or Final Fail. In PTAm, the timecost associated with the Mix state is 2 s; other states are notassociated with any time cost.

The PTA for dilution errors (PTAd) is shown in Fig. 9. Sincea dilution operation can be regarded as a mixing operationfollowed by a splitting, here we divide the dilution intotwo stages: mixing stage and splitting stage. Accordingly,

(a) PTAm (PTA for mixing errors)

(b) PTAs (PTA for splitting errors)

Fig. 8. Illustration of PTAs for recovery from (a) mixingerrors, and (b) splitting errors. Orange (green) outlineindicates that the corresponding state is a start (end) statein the state transition diagram.

Mixing_PTA Splitting_PTA

Final_Success Final_Fail

try:=0

loc:=0

t:=0

try:=0

t:=0 Detect_Split

mix_s = 1

mix_s = 0

split_s = 0

split_s = 1

detect = 1

detect = 0

Fig. 9. Illustration of PTAd (PTA for error recovery ofdilution errors).

the proposed PTAd is a combination of PTAm and PTAs

(see Fig. 9). Parameters try, loc and t in PTAd have thesame meaning as the corresponding parameters in PTAm andPTAs. If an error is detected in the mixing stage, PTAd entersthe Mixing PTA state. The parameter mixs (splits) is usedto indicate whether recovery has been made from the mixing(splitting) error. The parameter detect is used to indicatewhether a splitting error is detected. If mixs = 1, PTAd

moves to the Detect Split state; otherwise, PTAd transitionsto the Final Fail state. In the Detect Split state, parameterstry and t are reset to 0. If an error is detected in the splittingstage, then PTAd moves to Splitting PTA; otherwise, PTAd

Specify Bioassay

High-Level Synthesis

Store Operations in Queue Qt

Select Front Operation

Faulty

Operations?

Select Next

Operation in Qt

Apply Proposed Error

Recovery Approach

Partial re-

synthesis

possible?

Fail

Re-Synthesis

Update Qt

Finished?

Success

Local Recovery

Yes

No Yes

No

Success

Fail

Yes No

Fig. 10. Control flow for error recovery.

transitions to the Final Fail state. Note that PTAd will finallytransition to either the Final Fail or Final Success state basedon whether recovery can be made from the splitting error.

In the proposed PTAs for local recovery, i.e., PTAs, PTAm,and PTAd, a transition to the next state depends only on thecurrent state; this is referred to as the Markov property [32].Therefore, we map these PTAs to discrete-time Markov chains(DTMCs). Here, we assume that the computation time fordroplet routing and droplet-transportation time are negligiblecompared to microfluidic operation times in local recoveryprocedures [33]. However, the transition times from the initialstate to the Final Success state in PTAm, PTAs, or PTAd

may be different. Therefore, we divide the Final Successstate into different sub-states, referred to as Final Successsub-states, in each of the above DTMCs. For example,it can take 2, 4, 6, 8, or 10 s to transition from theFaulty Check (initial state) to the Final Success state inPTAm. We divide the Final Success state into the followingsub-states: (i) Final Success 2, (ii) Final Success 4, (iii)Final Success 6, (iv) Final Success 8, and (v) Final Success 10in the DTMC corresponding to PTAm. The utilization ofFinal Success sub-states eliminates the need for cumbersometime calculations, hence we can focus exclusively on thestate-occupancy probability calculations.

We use the probabilistic model checker, PRISM version4.0.3 [34], to verify and analyze the DTMCs. We first developa model for each DTMC using PRISM and check whetherlocal recovery will eventually enter either the Final Fail stateor the Final Success sub-states. We then apply discrete-timesimulation to calculate the probabilities that the DTMC caneventually transition to different Final Success states. Thesummation of these probabilities is the probability of successfulrecovery.

4.5 Error Recovery for the Complete BioassayNext we propose a control flow (Fig. 10) to connect the

local recovery procedures with global error recovery for thecomplete bioassay. When a bioassay is specified for executionon the biochip, high-level synthesis techniques are first utilizedto derive the results of operation scheduling, module placementand droplet routing [33, 35]. Then all operations are storedin the queue Qt based on their assigned starting time in anascending order. Operations are executed based on their orderin Qt. Once an operation is found to have an error, the localerror-recovery approach is invoked. If the bioassay can recoverfrom that error, local error-recovery returns global control tothe controller and the next operation in Qt is executed. Ifrecovery cannot be made from the error, the controller checkswhether partial re-synthesis (PRS) [17] is available. If PRS

is available, new synthesis results are generated and Qt isupdated; otherwise, the error recovery fails and we need toexecute the bioassay from the beginning.

For the complete bioassay, the probability of successfulrecovery and the completion time depend on the numberof detected errors and the local recovery approaches. Letn denote the number of detected errors in the bioassay.Suppose the probability of successful local recovery for errori (i = 1, 2, . . . , n) is Pi. Under the assumption that localerror recoveries are mutually independent, the correspondingprobability of successful recovery (Pb) can be computed as Pb =n∏

i=1

Pi. We use the method described in [18] to dynamically

generate synthesis results when errors are detected and tocalculate the bioassay completion time.

5. EXPERIMENTAL RESULTSWe first examine the relationship between the probability

of success for error recovery and the error-recovery time foreach type of local error. The evaluation is carried out forboth scenarios—with the presence and absence of backupdroplets. We then present simulation results for three real-lifebenchmarks to evaluate the proposed error-recovery strategy.

5.1 Results for Local FaultsProbability computation in PTAs can be carried using a

recursive procedure [36]; therefore, as discussed in SectionIV, we utilize the PRISM model checker to calculate theprobability of success (POS) for each type of local error.

Some types of samples, e.g., fibronectin, are known todegrade within 10 s [37]. Therefore, the time threshold tthis set to be 10, 5, and 10 s in the PTAs for mixing, splitting,and dilution errors, respectively. The location threshold lth isset to be 2 in both PTAs for mixing errors and dilution errors.This is because if recovery cannot be made from the error afterusing two mixers (diluters), the error-recovery time has alreadyexceeded the time threshold.

Lines 1-2 in Table 3 present the relationship between thePOS (Pmix) and the time cost (Tmix) for mixing errors. Wenote that, as expected, the more the time spent on errorrecovery, the higher is the value of Pmix. When Tmix is largerthan 8 s, Pmix for the scenario of “with backup droplets” islarger than the corresponding Pmix for the scenario of“withoutbackup droplets”. However, the difference is almost negligible;thus the backup droplets do not significantly influence Pmix

for mixing errors.The relationship between the POS (Psplit) and the time cost

(Tsplit) for splitting errors is shown in line 3 in Table 3. Asexplained in Section 4-E, no backup droplet is utilized by thePTA for splitting errors. Therefore, here we only consider thescenario of “without backup droplet”. Note that Psplit alsoincreases with the increase in Tsplit.

Lines 4-5 in Table 3 present the relationship between thePOS (Pdilute) and the time cost Tdilute for dilution errors.Similar to local recovery for mixing and splitting errors,Pdilute increases with the increase in Tdilute. Based on thesesimulation results, we conclude that Pdilute for the scenario of“with backup droplet” is larger than the corresponding Pdilute

for the scenario “without backup droplet”when Tdilute is largerthan 15 s. However, since we have set tth to be 10 s for dilutionerrors, there is no difference between the values of Pdilute inlines 4-5 in Table 3.

5.2 Results for BioassaysWe next present simulation results for three real-life

benchmarks, namely PCR [38], in-vitro diagnostics [39], andprotein dilution [40], to evaluate the proposed method. Allsimulations are carried out on an Intel Core i7 platform with

Table 3. Probability of Success for Different Local Strategies∗.

Local RecoveryProbability of Success with Different Time Cost Constraint t

t = 1 s t = 2 s t = 3 s t = 4 s t = 5 s t = 6 s t = 7 s t = 8 s t = 9 s t = 10 s

Mixing (without backup droplets) N/A 0.820 0.820 0.968 0.968 0.994 0.994 0.997 0.997 0.998Mixing (with backup droplets) N/A 0.820 0.820 0.968 0.968 0.994 0.994 0.998 0.998 0.999

Splitting 0.680 0.880 0.966 0.985 0.992 0.992 0.992 0.992 0.992 0.992Dilution (without backup droplets) N/A N/A 0.557 0.721 0.792 0.851 0.934 0.952 0.960 0.978Dilution (with backup droplets) N/A N/A 0.557 0.721 0.792 0.851 0.934 0.952 0.960 0.978

∗N/A denotes the fact that the local recovery cannot be completed with the corresponding time constraint.

Table 4. Experimentally characterized MEDA modulelibrary for synthesis.

Operation Resource Time

Dispensing Reservoir 3 sMixing 2 × 2-array mixer 2 sDiluting 2 × 2-array diluter 3 sSensing sensing circuit 0.01 s

a 2.67 GHz CPU and 8 GB of RAM. The experimentallycharacterized module library for MEDA is shown in Table 4.Without any loss of generality, we first set the size of oneelectrode in conventional DMFBs to be equal to a 4 × 4microelectrode array in MEDA-based biochips; therefore, a2×2 array in Table 4 actually represents an 8×8 microelectrodearray. We then set the chip size to be 10× 10.

The error-recovery capability of MEDA-based biochips canbe evaluated on the basis of the bioassay completion time andthe POS when errors are detected. Here we use Ppcr, Pinvitro,and Pprotein to present the POS for bioassays of PCR, in-vitrodiagnostics, and protein dilution, respectively. Likewise, Tpcr,Tinvitro, and Tprotein refer to the completion time for bioassaysof PCR, in-vitro diagnostics, and protein dilution, respectively.

In our simulation, we randomly inject up to four errors intoeach benchmark 30 times, and then calculate the correspondingcompletion time and POS for different time limits on localrecovery (TLLR). TLLR is defined as the maximum time thatis allowed for local recovery. Here we utilize a single value ofTLLR for all local errors. For example, if TLLR is set to 5 s,the time limits for all types of errors are also 5 s. Based on thesimulation results, the variance in the completion time and thePOS is negligible for all benchmarks; therefore, we only presentthe mean values in Fig. 11 to Fig. 13.

As shown in Fig. 11-13, larger TLLR and a smaller numberof inserted errors result in higher POS for all three bioassays.However, larger TLLR leads a significant increase in thecompletion time. Therefore, there is a trade-off between thePOS and the completion time. More studies on this trade-offare needed to select an optimal TLLR for the given bioassay.

In order to compare the proposed method with priorwork [15], we randomly injected errors into the threebenchmarks 30 times and calculated the mean value of boththe POS and the completion time. For both methods, alloperations that did not have injected errors were assumed tocomplete successfully with probability of one.

For the proposed method, when an error is detected, thecorresponding local recovery procedure is invoked. If localrecovery fails, no additional recovery approaches are utilized.For [15], when an error is detected, we must repeat all necessaryoperations since there is no specific local recovery procedure.We used the same probabilities that were presented in Section 4for the computation. The results of this comparison arepresented in Table 5 and Table 6. We use Ne to denote thenumber of injected errors in these two tables. As the numberof errors increases, the POS of the proposed method fallsslowly while the POS for [15] falls rapidly for all benchmarks.Moreover, the proposed method also takes less completion timefor most cases compared to [15].

6. CONCLUSIONWe have presented the first error-recovery strategy for

(a) (b)

Probability of Success Completion Time (s)

Fig. 11. Illustration of (a) the probability of success and(b) the completion time as the TLLR and the number ofinserted errors are varied for the PCR benchmark.

(a) (b)

Probability of Success Completion Time (s)

Fig. 12. Illustration of (a) the probability of success and(b) the completion time as the TLLR and the numberof inserted errors are varied for the in-vitro diagnosticbenchmark.

(a) (b)

Probability of Success Completion Time (s)

Fig. 13. Illustration of (a) the probability of success and(b) the completion time as the TLLR and the numberof inserted errors are varied for the protein dilutionbenchmark.

MEDA-based biochips. We first described a classificationof the outcomes of operations into different categories.Laboratory experiments using a fabricated MEDAbiochip were used to estimate outcome probabilitiesfor various operations. We then presented differentprobabilistic-timed-automata (PTA)-based error-recoverystrategies for various types of local errors. A control flow wasalso proposed to connect the local recovery procedures withglobal error recovery for the complete bioassay. Simulation

Table 5. Comparison between the proposed method and [15] with respect to Probability of Success.

Recovery StrategyPCR benchmark In-vitro benchmark Protein benchmark

Ne = 1 Ne = 2 Ne = 3 Ne = 4 Ne = 1 Ne = 2 Ne = 3 Ne = 4 Ne = 1 Ne = 2 Ne = 3 Ne = 4

[15] 0.820 0.551 0.409 0.304 0.669 0.327 0.186 0.106 0.582 0.218 0.102 0.048TLLR = 3 s 0.820 0.672 0.551 0.452 0.689 0.474 0.327 0.225 0.602 0.363 0.218 0.132TLLR = 4 s 0.968 0.936 0.906 0.877 0.844 0.713 0.602 0.508 0.763 0.582 0.445 0.339TLLR = 6 s 0.994 0.987 0.981 0.975 0.922 0.851 0.785 0.724 0.875 0.766 0.671 0.587TLLR = 8 s 0.998 0.995 0.993 0.991 0.975 0.950 0.926 0.903 0.960 0.921 0.884 0.848TLLR = 10 s 0.998 0.996 0.994 0.992 0.988 0.976 0.964 0.952 0.981 0.962 0.944 0.926

Table 6. Comparison between the proposed method and [15] with respect to completion time.

Recovery StrategyPCR benchmark In-vitro benchmark Protein benchmark

Ne = 1 Ne = 2 Ne = 3 Ne = 4 Ne = 1 Ne = 2 Ne = 3 Ne = 4 Ne = 1 Ne = 2 Ne = 3 Ne = 4

[15] 16.80 s 24.20 s 29.23 s 34.40 s 22.17 s 28.63 s 32.07 s 35.93 s 194.30 s 234.37 s 287.33 s 351.23 sTLLR = 3 s 12.00 s 16.50 s 17.43 s 18.37 s 16.70 s 16.90 s 17.73 s 17.93 s 170.43 s 171.53 s 174.83 s 176.53 sTLLR = 4 s 13.00 s 19.30 s 20.63 s 21.97 s 17.70 s 17.90 s 18.73 s 18.93 s 171.38 s 172.17 s 176.17 s 178.13 sTLLR = 6 s 15.00 s 20.27 s 21.63 s 23.47 s 19.10 s 22.53 s 23.57 s 24.13 s 173.43 s 175.73 s 178.33 s 180.13 sTLLR = 8 s 17.00 s 25.23 s 25.97 s 28.63 s 20.93 s 26.53 s 27.63 s 28.37 s 175.43 s 178.37 s 182.13 s 183.37 sTLLR = 10 s 19.00 s 26.30 s 27.43 s 29.13 s 23.17 s 27.37 s 32.37 s 33.07 s 177.43 s 179.37 s 185.43 s 187.17 s

results for three benchmarks and comparison with [15]highlight the effectiveness of the proposed error-recoverystrategy.

7. ACKNOWLEDGEMENTSThe authors thank John McCrone from Duke University for

valuable comments and discussions.

8. REFERENCES[1] R. Fair, “Digital microfluidics: is a true lab-on-a-chip possible?,”

Microfluidics and Nanofluidics, vol. 3, pp. 245–281, 2007.

[2] K. Choi et al., “Digital microfluidics,” Annual Review ofAnalytical Chemistry, vol. 5, pp. 413–440, 2012.

[3] M. Ibrahim et al., “Advances in design automation techniques fordigital-microfluidic biochips,” in Formal Modeling andVerification of Cyber-Physical Systems, pp. 190–223, 2015.

[4] Z. Li et al., “Optimization of 3D digital microfluidic biochips forthe multiplexed polymerase chain reaction,” ACM TODAES,vol. 21, pp. 25:1–27, 2016.

[5] M. Pollack et al., “Electrowetting-based actuation of liquiddroplets for microfluidic applications,” Applied Physics Letters,vol. 77, pp. 1725–1726, 2000.

[6] Z. Li et al., “Optimization of heaters in a digital microfluidicbiochip for the polymerase chain reaction,” in Proc. of IEEETHERMINIC, pp. 1–5, 2014.

[7] G. Wang et al., “Digital microfluidic operations on micro-electrodedot array architecture,” IET Nanobiotechnology, vol. 5,pp. 152–160, 2011.

[8] G. Wang et al., “Field-programmable lab-on-a-chip based onmicroelectrode dot array architecture,” IET Nanobiotechnology,vol. 8, pp. 163–171, 2013.

[9] K. Lai et al., “An intelligent digital microfluidic processor forbiomedical detection,” Journal of Signal Processing Systems,vol. 78, pp. 85–93, 2015.

[10] Z. Li et al., “High-level synthesis for micro-electrode-dot-arraydigital microfluidic biochips,” in Proc. of ACM/IEEE DAC,pp. 146–151, 2016.

[11] H. Verheijen et al., “Reversible electrowetting and trapping ofcharge: model and experiments,” Langmuir, vol. 15,pp. 6616–6620, 1999.

[12] A. Drygiannakis et al., “On the connection between dielectricbreakdown strength, trapping of charge, and contact anglesaturation in electrowetting,” Langmuir, vol. 25, pp. 147–152,2008.

[13] J.-Y. Yoon et al., “Preventing biomolecular adsorption inelectrowetting-based biofluidic chips,” Analytical Chemistry,vol. 75, pp. 5097–5102, 2003.

[14] Z. Li et al., “Design and optimization of 3D digital microfluidicbiochips for the polymerase chain reaction,” in Proc. ofIEEE/ACM ASP-DAC, pp. 184–189, 2015.

[15] Y. Luo et al., “Error recovery in cyberphysical digital microfluidicbiochips,” IEEE TCAD, vol. 32, pp. 59–72, 2013.

[16] K. Hu et al., “Experimental demonstration of error recovery in anintegrated cyberphysical digital-microfluidic platform,” in Proc. ofIEEE BioCAS, pp. 1–4, 2015.

[17] Y. Zhao et al., “Integrated control-path design and error recoveryin the synthesis of digital microfluidic lab-on-chip,” ACM JETC,vol. 6, pp. 1–11, 2010.

[18] M. Alistar et al., “Online synthesis for error recovery in digitalmicrofluidic biochips with operation variability,” in Proc. IEEEDTIP, pp. 53–58, 2012.

[19] M. Ibrahim and K. Chakrabarty, “Efficient error recovery incyberphysical digital-microfluidic biochips,” IEEE TMSCS, vol. 1,pp. 46–58, 2015.

[20] C. Jaress et al., “Rapid online fault recovery for cyber-physicaldigital microfluidic biochips,” in Proc. of IEEE VTS, pp. 1–6,2015.

[21] T. Xu et al., “A droplet-manipulation method for achievinghigh-throughput in cross-referencing-based digital microfluidicbiochips,” IEEE TCAD, vol. 27, pp. 1905–1917, 2008.

[22] S. Shih et al., “Digital microfluidics with impedance sensing forintegrated cell culture andanalysis,” Biosensors andBioelectronics, vol. 42, pp. 314–320, 2013.

[23] L. Luan et al., “Integrated optical sensor in a digital microfluidicplatform,” IEEE Sensors Journal, vol. 8, pp. 628–635, 2008.

[24] K. Lai et al., “A field-programmable lab-on-a-chip with built-inself-test circuit and low-power sensor-fusion solution in 0.35µmstandard CMOS process,” in Proc. IEEE A-SSCC, pp. 1–4, 2015.

[25] T.-Y. Ho et al., “Digital microfluidic biochips: recent research andemerging challenges,” in ACM/IEEE CODES+ISSS, pp. 335–343,2011.

[26] F. Su et al., “Testing of droplet-based microelectrofluidic systems,”in Proc. IEEE ITC, pp. 1192–1200, 2003.

[27] F. Su et al., “Microfluidics-based biochips: technology issues,implementation platforms, and design-automation challenges,”IEEE TCAD, vol. 25, pp. 211–223, 2006.

[28] T. Xu et al., “Functional testing of digital microfluidic biochips,”in Proc. of IEEE ITC, pp. 1–10, 2007.

[29] R. Fair et al., “Chemical and biological applications ofdigital-microfluidic devices,” IEEE Design & Test of Computers,vol. 24, pp. 10–24, 2007.

[30] Y. Zhao et al., “On-line testing of lab-on-chip using reconfigurabledigital-microfluidic compactors,” International Journal ofParallel Programming, vol. 37, pp. 370–388, 2009.

[31] R. Fair et al., “Electrowetting-based on-chip sample processing forintegrated microfluidics,” in IEEE IEDM, pp. 32–35, 2003.

[32] P. Bremaud, Markov Chains: Gibbs Fields, Monte CarloSimulation, and Queues. Springer Science & Business Media,2013.

[33] F. Su et al., “High-level synthesis of digital microfluidic biochips,”ACM JETC, vol. 3, p. 1, 2008.

[34] M. Kwiatkowska et al., “PRISM 4.0: Verification of probabilisticreal-time systems,” in Proc. CAV, pp. 585–591, 2011.

[35] Y. Luo et al., “A cyberphysical synthesis approach for errorrecovery in digital microfluidic biochips,” in Proc. of IEEEDATE, pp. 1239–1244, 2012.

[36] K. S. Trivedi, Probability and Statistics with Reliability,Queueing, and Computer Science Applications. John Wiley &Sons, 2008.

[37] A. Gefen, Bioengineering Research of Chronic Wounds: AMultidisciplinary Study Approach. Springer Science & BusinessMedia, 2009.

[38] F. Su et al., “Module placement for fault-tolerantmicrofluidics-based biochips,” vol. 11, pp. 682–710, 2004.

[39] F. Su et al., “Droplet routing in the synthesis of digitalmicrofluidic biochips,” in Proc. of IEEE/ACM DATE, pp. 1–6,2006.

[40] F. Su et al., “Unified high-level synthesis and module placementfor defect-tolerant microfluidic biochips,” in Proc. of ACM/IEEEDAC, pp. 825–830, 2005.