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A Generic Defect Aware Heuristic Approach for Droplet Routing in a Digital Microfluidic Biochip with Minimal Pin Assignment Subhamita Mukherjee
Indrajit Pan
Tuhina Samanta
Techno India, Salt Lake Kolkata, India
[email protected]
Member ACM RCCIIT, Kolkata, India
[email protected]
IIEST, Shibpur Howrah, India
[email protected]
ABSTRACT Multi-tasking digital microfluidic biochip raises some challenging issues in droplet routing in presence of on-chip defects. In this work, a heuristic droplet routing algorithm is proposed that tries to perform defect aware droplet transportation on digital microfluidic biochip. The aim of the proposed algorithm is to design defect-avoiding and pin-count aware routing paths minimizing the following objective functions, (i) number or electrode usage during routing, (ii) routing completion time, and (iii) actuation pin count. The algorithm tries to find electrode fitness through a sum between, numbers of electrode elapsed in routing and an electrode count on rectilinear path between the candidate electrode and target electrode. A candidate electrode with minimum fitness value is selected for next movement in droplet route. During this routing control pins are simultaneously allocated through a comprehensive cooptimization method. This pin assignment technique helps in minimizing reuse of the resources for routing beyond sustainable level. Simulation results are compared with some exiting works and the improvement in this proposed work is quite encouraging.
Keywords Defect aware routing; Digital microfluidic biochip; Heuristics; Multi-objective optimization; Pin assignment
1. INTRODUCTION Technology associated with digital microfluidic biochip (DMFB) is rapidly advancing. DMFB is a cost effective and portable micro electro mechanical system. It is being tested for several commercial utilizations like protein crystallization, air contamination detection, on chip pathological experiments etc. [1]. DMFB consisting of two-dimensional array of electrodes is fabricated on two parallel glass plates. Each unit location of twodimensional electrode array is called unit cell [3]. The chips deal with nano or pico litre volume of sample fluids which are stored, dispensed, mixed, reacted and transported along the electrode cells.
Publication rights licensed to ACM. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only. ICTCS '16, March 04 - 05, 2016, Udaipur, India Copyright is held by the owner/author(s). Publication rights licensed to ACM. ACM 978-1-4503-3962-9/16/03 $15.00 DOI: http://dx.doi.org/10.1145/2905055.2905062
Modern DMFBs are based on microfluidic technology, which supports multiple operations in every individual deployment. Thus the use and expansion occurs at a large scale in a customized manner [2]. This rigorous use gradually affects the quality and performance of a chip. Also the lifetime of a chip decreases due to repeated use. A comparatively aged DMFB is very likely to meet defects. A range of defects occurs due to manufacturing fallacies or during execution of bioassays. These defects include dielectric breakdown, irreversible charge concentration on an electrode, misalignment of parallel plates, non-uniform dielectric layer, grounding failure, broken wire etc [3]. Reconfigurability and reusability leads to higher yield of full custom biochip to the market [1], yet reusability does not assure high performance of the chip. Multiple use of same resource, or high actuation of electrodes to increase throughput may degrade the health of a chip. General droplet routing algorithms existing in literature try to optimize electrode utilization, and routing completion time, by multiple usages of same electrodes. However, as is stated here, multiple usage of same electrode requires repetitive actuation of them, leading to device fault [10]. Failure in routing is alleviated sometimes due to the fluid traces left on the preceding phase of routing. DMFBs are mainly of two types, (i) direct addressing mode DMFB, where each electrode location is controlled through a dedicated control pin and (ii) cross referencing mode DMFB, where pins are assigned in row column addressing mode [4]. A DMFB board having N rows and M columns will require (N × M) numbers of control pins in direct addressing mode operation where as in cross referencing mode operation, these number of pins can be restricted within maximum limit of (N + M) numbers. Rigorous research on effective usage and assignment of pins has laid a path towards potential reduction in number of pins. Reduction in number of control pins curtails the design complexity of DMFB [6]. In a work of [1], the concept of pin constrained design was first proposed. Pin constrained design focuses on further reduction of control pins overcoming the drawbacks of cross-referencing mode DMFB [6]. In a pincontrolled chip design, a set of control pins can be used to provide electric bias for routing of multiple nets [1], if routing sequence of those nets comprises non-overlapping and non-conflicting electrode sequence. Control pins are further reduced on the basis of droplet routing schedules [4]. In [7], a new pin allocation technique is presented which utilizes a modified and constrained pin allocation policy. This has helped the author to design a general purpose DMFB with pins little more than the requirement of pin constrained design. These newly developed DMFBs have been tested to guarantee faster operations. A problem specific pin
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assignment method is proposed in [8]. This uses even less number of pins than cross-referencing mode.
p(Nk) is the number of pins required to route kth net
3. PROPOSED METHOD
Recent researches on DMFB put forward an avenue on analyzing defect tolerance capability of DMFB. In [5], authors have summarized different researches on pin constrained design, which attempt to reduce the cost and complexity of operations with nplex (multiplex) immune assays. A new testing technique is proposed in [9] to maintain the robustness of DMFB performance. The authors have considered the role of physical parameters like actuation voltage and actuation frequency on the distribution of electric field. A pipe-line scan procedure is adopted in this work to locate the defects. In an extensive survey reported at [10], authors have further reformulated different parameters associated with error recovery and proposed a new roadmap for designing error recovery/ fault detection technique.
Defect aware droplet routing through minimum pin assignment technique initiates with all nets (Nk) where k = 1, ..., n and each of the net is represented by their respective source (S) and target (T). The method will produce a droplet routing schedule which will comply with all three criterions mentioned above circumventing the presence of blocked regions and defective electrodes. Droplets are routed through a heuristic estimation function, which decides the next electrode to be traversed. This heuristic estimation function evaluates the fitness of neighbouring electrodes (elecfitness) on the basis of number of electrode traversed by the droplet (electrav) and rectilinear distance of the candidate electrode from the target (T) electrode of the droplet (elecrect). This is represented in following equation.
However, not many studies are found in literature that address defects on a DMFB with pin-controlled routing scheme. In this work a heuristic technique is proposed for defect aware droplet routing with minimal control pin assignment for the activated electrodes on a chip. Heuristic procedures are proven to be a robust technique to design droplet transportation driver [3]. During droplet routing, main emphasis lies on two objectivities. (i) Minimization of latest arrival time and (ii) minimization of total electrode usage are two prime objectives of droplet routing in DMFB. In addition to these two, from the previous discussion it is obvious that to reduce the production cost of DMFB, minimization of pin count is another formidable criterion for DMFB design. This work proposes a defect aware routing technique to find an optimized trade off among these three objectives as stated above. Control pins are minimized generating a reuse pattern of actuation pins that satisfy the fluidic constraints, yet delivers a minimal routing path. This method was simulated on a set of real life benchmarks like bradford protein assay, sucrose gradient analysis, qPCR etc. [10] and the results are quite encouraging. Rest of the paper is organized as in next section, problem formulation is illustrated, section III elaborates proposed method with an example and experimental results are given in section IV. Section V ends with conclusion.
elec
2. PROBLEM FORMULATION Droplet routing in DMFB needs to follow two fluidic constraints, named as, (i) static constraints and (ii) dynamic constraints [4]. Routing paths from source to the target location are represented as two-pin and three-pin nets [1]. The routing path contains the electrodes used by the droplets in order to reach respective target locations. Let, there be Nk number of two pin nets where k = 1, 2, 3, ... , n. Each of these nets is specified by their source (S) and target (T) coordinates on two dimensional board. Now the objectives are 1. Min La.Time
( N ) k = 1, 2,...., n , k
LaTime is Latest arrival time for kth net [1] 2. Min e
( N ) ∪ e ( N ) ∪ .... ∪ e ( N ) , 1
2
k
e(Nk) represents number of electrodes required to route kth net 3. Min p
( N ) ∪ p ( N ) ∪ ... ∪ p ( N ) , 1
2
k
fitness
= elec trav + elec rect
Figure 1. Regular Pin Assignment in Droplet Routing In order to make this routing conducive to avoid defective regions, the rectilinear distance (elecrect) value of defective electrodes are set to a very high value. This ensures that the defective cell will never be found fit to be a member for droplet route. After evaluation of fitness value for all neighbouring electrodes, the electrode with minimum fitness value is selected for next location on route. The process will initiate from the source coordinate of all nets and will continue till the target coordinate is reached. In parallel with this routing the method also assigns the pin. It begins to assign from a regular set of three pins, regpin = [1, 2, 3]. These three pins are bare minimum requirement to actuate the droplet movement as illustrated in Figure 1. A droplet is to be moved from electrode A to C via B. According to the principle of electrowetting of dielectric (EWOD) process [3], electrode A should be charged with high voltage while keeping B on ground voltage. This will help to move A to B. It implies the need for two separate pins for adjacent electrode A and B, accordingly P1 and P2 is assigned to A and B respectively. Now if C gets connected to P1 then upon arrival of droplet on B, it will find high actuation on its both sides. This will result in droplet degeneration. Thus C should be connected to a separate pin, P3. It also implies that the same pin can be again assigned to any other electrode which is situated at least more than two unit cells distance. This distance is henceforth referred as delta distance (∆). However, these three pins are not always sufficient to address the actuation requirements. This deficiency is explained in Figure 2. Here a crossover between two droplet paths from S1 to T1 and S2 to T2 is depicted. During crossover always it becomes conflicting to address properly with the help of three pins. Even though the individual droplet crosses the region at different timestamp still
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due to unwanted actuation it may face the trouble of degeneration. Thus the crossover region needs to be assigned with separate four pins like the shaded regions of the Figure 2.
In Figure 4 an invitro2_10 [3] bioassay analysis is illustrated through diagram, where S1, S2, S3 and S4 denote source, M denotes mixing cell and T1 and T2 are targets. Patterned cells are defective.
Figure 2. Pin Assignment in Crossover Region The overall process is summarized in an algorithmic format given in Figure 3. Algorithm: pin_defect_aware_droplet_routing() Input: Array of electrodes (M × M) with blocked electrodes (blk[]), Number of nets (k) with source (s) and target (t) locations (Nk(S, T)), Defect locations (def[]) Output: Latest arrival time (LaTime), total number of pin assigned (countp), total electrode used (electotsl[]) begin **Initialize** 1. countp = 3; LaTime = 0; electotal[] = ϕ 2. regpin = [1, 2, 3]; newpin = [] **Droplet routing & Pin assignment** 3. for all nets (Nk) | k = 1 to n 4. pick source (S) 5. if pin not allotted 6. assign from regular pin sequence, regpin 7. check compatibility on ∆ distance with other nets 8. if (∆ ≤ 2) 9. attempt alternative from regular pin set 10. while target (T) not reached 11. find number of elapsed electrodes (electrav) 12. find rectilinear distance to target (T) of neighbour electrodes (elecrect) 13. if neighbour electrode is in def[], elecrect = ∞ 14. select minimum fitness value of neighbours from (elecfitness = electrav + elecrect) of all neighbours after comparing with blk[] and def[] 15. electotal[] = electotal[] U elecfit 16. if pin not allotted 17. assign from regular pin sequence, regpin 18. check compatibility on ∆ distance with other nets 19. if (∆ < 2) 20. attempt alternative from regular pin set 21. else 22. assign a new one from newpin 23. countp++ 24. end of while 25. end of for 26. update LaTime end
Figure 3. Algorithm for Defect Aware Droplet Routing with Minimal Pin Assignment
Figure 4. Illustration of Defect Aware Pin Constrained Droplet Routing on invitro2_10
4. EXPERIMENTAL RESULTS Proposed multi-objective optimization heuristic for defect aware droplet routing algorithm and method of [10] were separately simulated in C on a PC running on Intel chip with 2 GB RAM and 2.5 GHz clock speed in Linux platform. Some of the new real life test bench suites are taken from [10] and deployed in experimentation. However, the description of test suites was modified to introduce 10% defect at random locations. These two proposed algorithms are implemented under one after another. In the first run droplet routing schedule was obtained from Algorithm 1 through minimization of latest arrival time and total electrode usage. Then in the second run, obtained routing scheduled was profiled for optimum pin assignment through simulation of Algorithm 2. In Table 1 a comparative test results is shown between proposed method and method of [10]. Experimental results of multi-objective optimization heuristic for defect aware routing shows some acceptable and notable good records in compare to existent method [10]. Thus it stands worthy in the context of importance of defect aware routing. Table 1. Comparative Results between Proposed Method and [10]
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of pin assignment and droplet routing in digital microfluidic biochip, 25th International Conference on VLSI Design (VLSID), pp. 227 – 232.
5. CONCLUSION Design automation for DMFB has evolved as a major challenge due a wide range of design constraints and design complexities. This work proposes a multi-objective optimization heuristic for high performance droplet routing method based on defect aware concept. Simulation analysis of this method displays an encouraging result and significant development over the existing methods [10]. The approaches of optimizing various parameters have worked in tune to address both reliability and cost. Notable reduction in pin count for difficult real life benchmarks ensure that production cost of this DMFB can be kept lower since the pin count aware routing performed significantly. These methods have also recorded a good clock for latest arrival time.
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