Digital Microfluidic Biochips Online Fault Detection Route Optimization Scheme Chuan-pei XU and Tong-zhou ZHAO *

Transcription

1 2018 Iteratioal Coferece o Commuicatio, Network ad Artificial Itelligece (CNAI 2018) ISBN: Digital Microfluidic Biochips Olie Fault Detectio Route Optimizatio Scheme Chua-pei XU ad Tog-zhou ZHAO * School of Electroic Egieerig ad Automatio, Guili Uiversity of Electroic Techology Guili , Chia * Correspodig author Keywords: Digital Microfluidic Biochips (DMFBs), Pi-costraied, Fault detectio path optimizatio, Employed PSO. Abstract. Digital microfluidic biochips(dmfbs) have bee widely used i biology, medicie ad chemical experimets. These areas all have high requiremets o the reliability of experimetal results. Therefore, it is ecessary to coduct chip failure detectio durig the experimet. I this work, based o Employed particle swarm optimizatio algorithm, the fault detectio route optimizatio of direct-addressig ad pi-costraied digital microfluidic chips are respectively studied. Combiig the employed search operator of Artificial Bee Coloy algorithm ad Particle Swarm Optimizatio, the method ca improve the searchig accuracy of the algorithm while exploitig the ability of algorithm exploratio. The simulatio experimet is carried out by usig the multi-elemet biochemical test chip model. The results show that the proposed method ca shorte the fault detectio path ad improve the fault detectio efficiecy. Itroductio I recet years, with the cotiuous developmet of sciece ad techology, the microfluidic chip based o discrete fluid, also kow as digital microfluidic biochip, has replaced the traditioal experimetal equipmet ad obtaied a wide rage of applicatios i the eighborhood of cliical diagosis, drug developmet ad air quality moitorig [1]. Durig the experimet, the reliability of the experimetal results should be esured, so it is ecessary to test the DMFBs cotiuously. Accordig to differet pi cotrol methods, DMFBs are divided ito direct-addressig chip ad pi-costraied chip [2]. I direct-addressig chips, each cotrol pi cotrols a electrode to move the droplet, but will icrease the cost of productio; pi-costraied chip usig multiple pis commo oe electrode, which ca save costs. However, compared to the direct-addressig mode, the difficulty of fault detectio will be icreased. Aimed to the failure of the digital microfluidic biochip, Su F et al. first proposed dividig the fault ito parametric faults ad permaet faults, ad aalyzed the variatio of the parameters of the chip [3] ; the, Su F established the Euler circuit to cotrol the test drop traverses the chip cell, which ca detect the presece of a fault [4]. Xu Tao et al. Proposed a efficiet parallel test method that performs offlie testig for regular chips by row-ad-colum scaig, but this method is ot suitable for olie Fault detectio [5]. Zhag Lig et al. divided chip array ito multiple sub-arrays, ad used experimetal gaps i the idle module for fault detectio, which improved the test efficiecy [6]. For pi-costraied digital microfluidic chips, Xu Tao et al. Proposed a testability bioassay protocol that allows the desig of the chip to have a high level of the testability desig ad eables the chip to support drop test-related operatios, but requires the itroductio of additioal Cotrol pi [7] ; i 2010, Yag Zhao et al. proposed self-test method, which used digital logic gate circuit. Accordig to its output waveform, the circuit ca determie the existece of the fault [8]. The method is suitable for pi-costrait chips, ad the hardware overhead will be lower. Capacitace circuit aalysis of fault detectio results is o eed as well. This work maily studies the optimizatio of fault detectio paths for the two cotrol chips respectively. The paper is orgaized as follows: I sectio Ⅱ, the basic priciples of digital microfluidic biochips ad the descriptio of the test problems will be described. I sectio Ⅲ, we

2 maily describe the algorithm used to optimize the path of fault testig. I sectio experimetal results will be aalyzed. Ⅳ, the Fudametals o DMFBs DMFBs based o dielectric wettig priciple to drive discrete droplets, the structure ad drivig method are show i Figure 1, the differet cotrol voltage is applied to the electrodes o both sides of the droplets to produce a ubalaced tesio. Whe the ubalaced force o the droplet surface is greater tha the resistace for drivig the droplet, the droplet ca be moved to ay positio i the two-dimesioal array to complete the biochemical experimet [9]. (a) The structure of DMFBs (b) Drive priciple of DMFBs Figure 1. Digital Microfluidic Biochips Direct-addressig DMFBs ad Pi-costraied DMFBs The most commoly used droplet cotrol method, where each electrode is idividually addressed ad cotrolled by a cotrol pi, is called Direct-addressig DMFBs, but as icreasigly experimets are performed o a digital microfluidic platform, the productio costs would be icreased, which resulted the existece of pi-costraied DMFBs. There are several ways to reduce the umber of pis. Such as usig array ad pi assigmets, as well as broadcast addressig, which reduces the umber of cotrol pis by idetifyig ad itercoectig compatible pis so that oe cotrol sigals cotrol multiple electrodes simultaeously. Figure 2 shows the pi allocatio example of direct addressig ad broadcast addressig, through the broadcast addressig mode ca effectively reduce the cost ad umbers of cotrol pis. At preset, the pi-costraied chips are more widely used i may areas. Most of the applicatios demad high security, so the reliability requiremets of the system is very strict. Therefore, the test techology of pi-costraied DMFBs also gaied a great deal of attetio. Figure 2. Example of pi assigmet scheme Problem Formatio DMFBs fault detectio ca be regarded as a traversal problem, ad the traversal problem is trasformed ito a graph theory model [10]. Mappig the array elemet structure to a o-fully coected graph, deoted as G (V, E), V is the poit i graph G, represets each array elemet; E is the edge coectig adjacet cells. The graph G correspodig to the chip array uit would be coverted. The trasformig the edges traversed by the test droplet ito poits i the TSP problem. As show i FIGURE 3, a 3 3 array uit is take as a example for descriptio. A path coectio table is established accordig to the adjacecy relatioship betwee each edge e i ad e j i the figure, as show i Table 1. Accordig to the path adjacecy relatio table, a relatio matrix of edges ad edges is geerated, that is, the adjacecy matrix A of all edges. A ca be regarded as a o-completely coected graph

3 G '(V', E '), each edge e i is deoted by V', ad the coectivity of each edge with other edges is deoted by E '. Figure 3. Chip Model Coversio Table 1. Array uit coectivity relatioship Path Coected Paths 1 2,3,4 2 1,4,5 3 1,6,8 4 1,2,6,7,9 5 2,7,10 6 3,4,7,8,9 7 4,5,6,9,10 8 3,6,11 9 4,6,7,11, ,7, ,9, ,10,11 Accordig to the coectio path table, a adjacecy matrix A ca be established. The Floyd algorithm is used to set the shortest legth betwee ay two poits i the ocompletely coected graph G '(V', E ') represeted by A as a weight. O this basis, a fully coected graph G'' is costructed. The algorithm is proceed as follows: 1) From ay uilateral path, take the shortest distace betwee two poits as the edge weight. If there is o edge coected betwee two poits, the weight is. 2) Let each pair of vertices be represeted as u ad v, ad defie the distace as d uv. If there is a vertex w such that duw dwv duv, update the weight of u to v as duw dwv. Fially, the udirected complete graph G "is obtaied ad treated as a model of the dyamic TSP problem. Optimizatio algorithm would be used to fid the optimal fault detectio path without violatig the costraits. Objective Fuctio The test drop starts at a fixed startig poit ad traverses all sides to reach the ed poit. Due to the costat velocity of the droplet, the test efficiecy is highest at the shortest total path legth. Defie its objective fuctio as: f ( x) mi xij( i j, i, j 1,2, ) i Σ 1 j 1 (1) N idicates the umber of array elemets, x d ( i j) idicates the weight betwee elemet i to elemet j. The costraits are stated as follows: Test droplet should access at least all cells of the array oce, assumig that elemet, expressed as: i 1 ij ij X i is the array X i 1 (2)

4 Start ad ed poits ca oly be visited oce, set xsj as the startig poit, xje for the ed, expressed as: j 1 x sj 1( j 1,2,,, j s) (3) j 1 x je 1( j 1,2,,, j e) Fluid costraits are expressed as follows: Two droplets ca ot be i two adjacet array elemets at the same time, that is, there is o other droplet i the eight cells aroud a droplet. Otherwise, uexpected droplet fusio may occur, which will affect the result of fault detectio. Therefore, a certai distace should be esured betwee the k k k k droplets. Defie X 1, X 2, Y 1, Y 2 are the rows ad colums for the test droplets at the time poit k respectively. Defie static fluid costraits as follows: Two or more droplets ca ot use adjacet array elemets simultaeously, expressed as: X X Y Y k k k k or (5) Defie dyamic fluid costraits as follows: A cell to which a droplet is to be moved should ot adjacet to aother droplet, expressed as: X X Y Y k 1 k k 1 k or (6) For pi-costraied digital microfluidic chips, the electrode costraits eed to be set. This costrait is stated as follows: Let pis 1 ad 2 be cotrolled by the same electrode. If this electrode is activated, the test droplet should ot move to pi 2 whe the experimetal droplet is at pi 1. Expressed as: Nk ( t 1) Net (7) Where Nkt is the umber of the pi uit where test droplet k is located at timet, ad Net is the uit umber of test droplet e at the same time. (4) Olie Fault Detectio Route Optimizatio of DMFBs Based o Employed Particle Swarm Optimizatio I the process of biochemical experimets, fast ad effective fault detectio method should be used to esure the reliability of the experimetal results, which essetial is to search for the shortest path uder the costrait coditios. I this paper, a olie fault detectio path optimizatio scheme is proposed. By optimizig the test path, the test droplet travels the shortest path through all array elemets to improve the fault detectio efficiecy. This problem is NP-hard. Particle Swarm Optimizatio (PSO) has bee widely used i various fields i recet years due to its simple structure, easy implemetatio ad less parameters, ad achieved good results. This work applies it to the fault detectio path optimizatio of digital microfluidic chips. I 1995, ispired by the flock movemet model, James Keedy, a Ph.D. i social psychology ad Russell Eherhart, a Ph.D. i electrical egieerig, proposed Particle Swarm Optimizatio (PSO) [11]. This algorithm bases o the results of the evolutioary ad fitess fuctios o the optimizatio problem Evaluatio. The speed ad displacemet update formula of stadard PSO are as follows: vi( t 1) vi( t) c1r1( pi( t) xi( t)) c2r 2( pg( t) xi( t)) (8)

5 xi ( t 1) xi( t) vi( t 1) (9) Where represets the iertia weight, settig differet values determie the degree of ifluece for particle's historical speed to the curret speed, that is, the retaied state of the last iteratio of particle s velocity. I stadard PSO, is a radom value; c1 ad c 2 are acceleratio factors, which are two atural umbers. r 1 ad r 2 are radom umbers betwee (0,1), which role is to limit the particle velocity withi a certai rage. Combied with the characteristics of olie test problem ad the evolutioary theory of particle swarm optimizatio, as the test routig optimizatio problem is discrete, this guide formula of articles are updated as follows: 1 t t t t vi t t i i i g i v ( p x ) ( p x ) (10) t 1 t t 1 x i xi vi (11) X ( X1, X 2,..., X The -uit chip test path solutio is defied as ), which represets the order i which the droplets traverse path elemets. The solutio to the algorithm shows the order i which droplets traverse array elemets. Defiig the exchage exch ( i, j), which meas that the poiti ad poit j i the path sequece are swapped. Path solutio X ca obtai the ew path by exchagig t t t t sub-operators. I formula 10, pi xi ad pg xi are both exchage sequeces. ad deote the t t t t reservatio probabilities of the exchage orders p x ad p x, respectively. The larger the values of or, the more impact the curret best or historic best solutio respectively. Accordig to the fluidic costraits ad olie testig features of DMFBs, ad i order to avoid the algorithm fallig ito the local optimum, the stadard particle swarm optimizatio eeds to be improved to esure that the algorithm ca search shorter chip test path ad improve test efficiecy. Employed Particle Swarm Optimizatio Stadard Particle Swarm Optimizatio algorithm leads particle search trajectory with local optimal p i, ad its search accuracy is low. If pi caot jump out of a certai positio, the the particlei will be gathered i the curret optimal regio, leadig to premature pheomeo of the algorithm. I order to overcome this drawback, this work itroduces the employed bee search operator of Artificial Bee Coloy(ABC), ad uses the global optimum to lead the search path. It optimizes twice based o the previous searchig, which ca optimizes the searchig ability of particle swarm optimizatio algorithm. The artificial bee coloy algorithm is a optimizatio algorithm proposed by D Karaboga, a Turkish scholar i 2005, based o hoey bees mechaism [12]. Its ability to explore maily through the followig formula: zi, j xi, j i, j( xi, j xk, j) (12) Where x i, j is the locatio of the preset leadig particle; x k, j is the locatio of of ay particle i the eighborhood of x i, j. i, j is a radom umber i[-1,1]. z i, j is the cadidate solutio leadig by x i, j. By addig the employed bee s search operator for secodary optimizig, the ew positio ca be searched ear the preset optimal positio. There are ucertaities i the size ad directio of the differece vectors formed by the local optimal idividual vector ad the radomly selected idividual vector, which is equivalet to addig a certai rage of radom perturbatios to the base vector to icrease the populatio diversity. However, due to the small movemet rage, adjustable rage is limited, so this paper modified the search operator of the bee coloy algorithm, accordig to the characteristics of particle swarm optimizatio, the modified quadratic search operator is expressed as follows: i t t pi' pi i, j( pg xr1, r 2) (13) i g i

6 t g p is the global best for the particle, xr1, r 2 is the radom locatio i the area. The basic idea of the search operator is to search for the best local idividuals startig from a radomly geerated iitial populatio ad to adopt a oe-o-oe competitive survival method to retai the better idividuals. By meas of iteractive learig amog idividuals, the employed operator ca improve the exploratio ability of the algorithm. After PSO searchig for the first time, by usig the employed operator, the secodary search is performed aroud the preset optimal locatio, which ca improve the search accuracy ad optimizatio ability of the particle. Guided by the optimal positio of global best, the operator developmet ability ca be improved while esurig operator search ability. The distace betwee the optimal pg ad ay positio is selected as the displacemet so as to esure that the scope of quadratic search is ot restricted to the viciity of the curret local optimal positio. It icreases the radomess of the search ad explores the ew most excellet locatio possibilities. The specific operatio of particle swarm optimizatio algorithm that added the employed search operator is as follows: Firstly, the curret global optimal solutio ad preset optimal solutio positio are judged, ad the ew cadidate solutio is searched usig the formula 12 ear each local optimal solutio p i, deoted as p i'. If the fitess value of pi' is greater tha p i, the the preset optimal solutio would be updated. If the fitess of pi' is better tha p g, the curret global optimal solutio would be updated. Taboo Judgmet Strategy I order to avoid the iteractio betwee test droplet ad experimetal droplet i fault detectio process, accordig to fluid costraits ad electrode costraits, the particle eeds to calculate the locatio of the experimetal droplet i the future time ad its iteractio with the array elemet before fidig the path, which esure that the selected uit would ot iterfere with the experimet. Moreover, due to the chagig positio of the experimetal droplet, the cells will also be cotiuously updated [13]. I order to solve this problem, this work adopts the taboo judgmet method, that is, costruct the experimet taboo table, which is used to store the curret taboo path, ad save the taboo uit every time whe the experimetal droplet positio chages. If the curret test path coicides with the taboo path, it idicates that there is a coflict. Whe a coflict occurs, the coflict uit would be extracted as the exchage sequece, ad the curret path would be exchaged ad operated to obtai a ew path that does ot coicide with the curret taboo uit. Employed PSO for Olie Fault Detectio Path Optimizatio Accordig to the above, combied with the characteristics of DMFBs fault detectio ad PSO algorithm to improve the strategy, the basic steps of the test algorithm is as follows: Step 1: iitialize the basic parameters of particle swarm optimizatio, give each particle a radom iitial solutio; Step 2: Determie whether there is a coflict betwee the curret path ad the taboo uit; if there is a coflict, extract the coflict uit as the exchage sequece ad exchage the curret path to obtai a ew path; Step 3: Calculate the legth of the solutio path; Step 4: Evaluate the fitess of each particle, ad store the curret positio ad fitess value of each particle i their p i. Stores the positio ad fitess values of all the idividuals that fit the best idividuals i p g ; Step 5: Search for the cadidate solutio pi' aroud each pi accordig to Equatio 13, update the value of pi if the fitess value of pi' is greater tha p i, ad update the value of pg if the fitess value of pi' is better tha p g ; Step 6: Update the positio ad velocity of the particles accordig to Equatio 10 ad Equatio 11; Step 7: Number of iteratios NC NC 1; Step 8: Determies whether the algorithm satisfies the ed coditio or ot. If ot, the process

7 returs to step 2. If the coditio is satisfied, the search is stopped ad the result is output. The fial result is the legth of the path traveled by the droplet traversig the etire chip array. Experimetal Results ad Aalysis I this paper, as show i Figure 4, we select the glucose ad lactic acid i a multi-biochemical test i literature [4] as the experimetal model to simulate. The experimetal droplets for glucose detectio are sample S1 ad reaget R1, ad the experimetal droplets for lactate detectio are sample S2 ad reaget R2. Experimetal droplets are i the mixig pool for ezyme-catalyzed reactios. Whe the reactio is completed, the test will be started after the mixed droplets reach the optical detectio uit. Experimetal droplets would be set to the experimetal droplet pool whe the experimet is completed. Figure 4. Multi-biochemical test experimet diagram This work completes the test simulatio i the Visual Studio 2015 eviromet, usig programmig laguage of C ++. The size of the selected populatio is 500 ad the umber of iteratios is After several experimets, this paper takes the iertia weight ω = 0.9, α = 0.8, β = 0.7, ad the uit legth is defied as the weight betwee adjacet paths. The fial output is the path legth ad path sequece of the test drop traversig all the cells, ruig 30 times to average. (1) Aalysis of experimetal results:whe testig off-lie, the legth of the path traveled by test droplet usig the Employed PSO is 607 uits. Usig the stadard particle swarm algorithm, the legth of path is 629 uits. The optimizatio rate is 3.49%. I the case of olie test, whe the test object is a direct-addressig chip, the legth of the path traveled by the method i this paper is 616 uits. Compared with the stadard particle swarm algorithm (636 uits legth), the optimized path legth is 3.14%. Whe the test object is a pi-costraied chip, this article uses the broadcast addressig method for pi assigmet, as show i Figure 5, the same label pis meas that they share the same electrode. Usig the algorithm itroduced i this paper, the path legth of the test droplet is 649 uits. The stadard particle swarm optimizatio algorithm takes a legth of 672 uits. The optimizatio rate is 3.42%. It ca be see that Employed PSO algorithm ca effectively shorte the test path ad improve test efficiecy. Fault detectio route legth compariso is show i Figure 6. Figure 5. Pi assigmet Figure 6. Experimetal results

8 (2) Covergece Aalysis: The covergece of Employed PSO ad stadard PSO uder direct-addressig ad pi-costraied chips are compared respectively. The covergece curves are show i Figure 7. The direct-addressig chip test results are show i Figure 8 (a), the Employed PSO coverges at 402 geeratios, ad the covergece is 28.7% better tha the stadard PSO algorithm that bega to coverge at 689. The test results for pi-costraied chips are show i Figure 8 (b). The Employed PSO coverges o the 232th geeratio, while the stadard PSO coverges o the 572th geeratio. I cotrast, the covergece of the Leadig Particle Swarm Optimizatio algorithm is optimized by 34%. Thus, the covergece of the proposed algorithm is superior to the stadard PSO. (a) Direct-addressig chip (b) Pi-costraied chip Figure 7. Covergece curves for SPSO & Employed PSO Summary This work aims at the olie fault detetig route optimizatio for direct-addressig ad pi-costraied digital microfluidic biochips. The employed PSO algorithm is used to optimize the path of chip fault detectio. The multi-body fluid detectio model is used to simulate the experimet. The experimetal results are compared with the stadard PSO. The results show that the proposed method ca effectively shorte the test path ad improve the test efficiecy for these two kids of chips, which ca provide a referece for the fault detectio route optimizatio of digital microfluidic chips. Refereces [1] Xu T ad Chakrabarty K. Fault modelig ad fuctioal test methods for digital microfluidic biochips[j]. IEEE Trasactios o Biomedical Circuits ad Systems, 2009, 3(4): [2] XU CH P, CHEN CH Y, WANG J J. Olie Parallel Testig of Pi-costraied Digital Microfluidic Biochips[J]. Joural of Electroics & Iformatio Techology, 2015, 37(9): [3] SU F, OZEV S, CHAKRABARTY K. Cocurret Testig of Droplet-based Microfluidic Systems for Multiplexed Biomedical Assays[C]. Proc. It. Test Cof., 2004: [4] SU F, HWANG W, MUKHERJEE A, et al.testig ad diagosis of realistic defects i digital microfluidic biochips[j]. Joural of Electroic Testig: Theory ad Applicatios, 2007,23(2-3): [5] XU T, CHAKRABARTY K. Parallel sca-like testig ad fault diagosis techiques for digital microfluidic biochips[j]. IEEE Tas. Biomed. Circuits Syst., 2007,1(2): [6] ZHANG L, WANG W Z, YAN B W,Aalysis ad Optimizatio of Parallel Microfluidic Biochip [J].Microelectroics ad Computer, 2014, 31(10): [7] T. Xu, K. Chakrabarty. Desig-for-testability for digital microfluidic biochips. Proc.IEEE VLSI Test Symposium. 2009:

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