紙基微流體生物晶片（Paper-Based Digital Microfluidic Biochips）是一種兼具安全、低成本及高效率的生物實驗（Bioassay）平台，通過電濕潤技術在紙張上執行流體操作以完成實驗。為了實現電潤濕技術，在電極擺放完成後，須將其繞線至紙張兩側的控制板，藉以控制電極上的電壓。混合式紙基微流體生物晶片（Active Paper-Based Hybridized Chips）有別於傳統的紙基微流體生物晶片，可以容許紙張上存在無玻璃遮蓋的區域，藉以省下維護此層玻璃遮蓋的成本。然而這也導致流體與紙張間的接觸面積變小，電極排列得更為緊密。這使得現有的電極繞線演算法無法對混合式紙基微流體生物晶片產生成功的繞線結果。本文針對此種晶片提出了一種基於多物網絡流的繞線演算法，能夠考慮電極之間的引腳共享，提高可繞線性並且最小化繞線線長。實驗結果則證實提出的方法在現實的混合式紙基微流體生物晶片設計上實現了100％的成功繞線率。

Paper-based digital microfluidic biochips (P-DMFBs) have emerged as a safe, low-cost, and fast-responsive platform for biochemical assays. In P-DMFB, droplet manipulations are executed by the electrowetting technology. In order to enable the electrowetting technology, pattern arrays of electrodes and control lines are coated on paper with a hydrophobic Teflon film and dielectric parylene-C film. Different from traditional DMFBs, the manufacturing of P-DMFBs is efficient and inexpensive since the electrodes and control lines are printed on photo paper with an inkjet printer. Active paper-based hybridized chip (APHC) is a type of P-DMFBs that has open and closed part. APHC enjoys more convenience than common P-DMFBs since it has no need to fabricate and maintain the micro gap between glass and paper chip, which requires highly delicate treatments. However, the pattern rails of electrodes in APHCs are denser than traditional P-DMFBs, which makes existed electrode routing algorithm fail in APHCs. To deal with the challenge in electrode routing of APHCs, this paper proposes a multi-commodity network flow-based routing algorithm, which simultaneously maximizes the routability and minimizes the total wire length of control lines. The multi-commodity flow model can utilize the pin-sharing between electrodes, which can improve routability and reduce the detour of routing lines. Moreover, the activation sequences of electrodes are considered, which guarantees that the bioassay will not be interfered with after pin-sharing. The proposed method achieves a 100% successful routing rate on real-life APHCs while other electrode routing method cannot solve the electrode routing of APHCs successfully.

摘要 i
Acknowledgement ii
Abstract iii
1 Introduction 1
2 Problem Formulation 6
3 Proposed Methodology 9
3.1 Minimum-Cost Maximum-Flow Formulation 9
3.2 Multi-Commodity Minimum-Cost Maximum-Flow Formulation 12
4 Experimental Results 18
5 Conclusion 20
References 21

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