IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 1 Error-Oblivious Sample Preparation with Digital Microfluidic Lab-on-Chip Sudip Poddar, Robert Wille, Senior Member, IEEE, Hafizur Rahaman, Senior Member, IEEE, and Bhargab B. Bhattacharya, Fellow, IEEE Abstract—Microfluidic chips are now being increasingly used for fast and cost-effective implementation of biochemical proto- cols. Sample preparation involves dilution and mixing of fluids in certain ratios, which are needed for most of the protocols. On a digital microfluidic biochip (DMFB), these tasks are usually auto- mated as a sequence of droplet mix-split steps. In the most widely used (1:1) mix-split operation for DMFBs, two equal-volume droplets are mixed followed by a split operation, which, ideally, should produce two daughter-droplets of equal volume (balanced splitting). However, because of uncertain variabilities in fluidic operations, the outcome of droplet-split operations often becomes erroneous, i.e., they may cause unbalanced splitting. As a result, the concentration factor (CF) of each constituent fluid in the mixture may become erroneous during sample preparation. All traditional approaches aimed to recover from such errors deploy on-chip sensors to detect possible volumetric imbalance, and adopt either checkpointing-based rollback or roll-forward tech- niques. Most of them suffer from significant overhead in terms of assay-completion time, reactant-cost, and uncertainties in termination due to randomly occurring split-errors. In this paper, we propose a new approach to accurate dilution preparation on a DMFB that is oblivious to volumetric split-errors. It does not need any sensor and can handle multiple split-errors, deterministically. The proposed method is customized for each target-CF based on the criticality of split-errors in each mix-split step. Simulation experiments on various test-cases demonstrate the effectiveness of the proposed method. I. I NTRODUCTION D igital Microfluidic Biochips (DMFBs), as one possible plattform for Labs-on-chip (LoC), received significant attention of the VLSI CAD community over the last few years due to their versatile applications in biochemical domains such as point-of-care (PoC) testing, drug discovery, or high through- put DNA sequencing, to name a few [1], [2]. A DMFB is a Manuscript received October 18, 2017; revised March 02, 2018 and May 10; accepted June 29, 2018. This paper was recommended by Associate Editor Tsung-Yi Ho. S. Poddar, and B. B. Bhattacharya are with the Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India 700108. E- mail: {sudippoddar2006, bhargab.bhatta}@gmail.com. The work of S. Poddar is supported, in part, by the CSIR Research Associateship, India. The work of B. B. Bhattacharya was supported by INAE Chair Professorship and by the DST SERB Research Grant No. EMR/2016/005977. H. Rahaman is with the School of VLSI Technology, Indian Institute of Engineering Science and Technology, Shibpur, India 711103. E-mail: hafizur@vlsi.iiests.ac.in. R. Wille is with the Institute for Integrated Circuits, Johannes Kepler University Linz, Austria. E-mail: robert.wille@jku.at. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier xx.xxxx/TCAD.2018.xxxxxxx Copyright c  2018 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending an email to pubs-permissions@ieee.org. coin-sized device capable of performing several biochemical protocols by manipulating discrete fluid-droplets on the top of an electrostatically-controlled 2D-array of tiny electrodes. These chips are likely to replace expensive and bulky equip- ment currently used in hospitals, pathological and research laboratories as they offer more convenience in terms of high throughput, portability, automation, low reagent-consumption, fast reaction-time as well as low energy-consumption. Based on the principle of electrowetting-on-dielectric (EWOD) [3], discrete-sized droplets (with volume in the nano or pico-liter range) can be induced to perform various on-chip fluidic operations such as dispensing, transportation, mixing, splitting, incubation, or sensing by applying a time-varying voltage signal to the electrodes (actuation sequence). By ap- propriate synthesis of a given protocol, the actuation sequence needed for its execution can efficiently be generated [4]–[7]. One of the most important components of a bio-protocol is sample preparation, which includes, among others, the task of preparing fluid-dilutions and reagent-mixtures in certain ratios. The DMFB-technology offers a very convenient platform for automating sample preparation [8]–[12], where a desired target concentration factor (CF) of a sample or a mixing-ratio of reagents is produced by performing a sequence of droplet- mixing and splitting operations. Note that the CF of a fluid- sample indicates the volumetric ratio of the corresponding raw (pure) sample in a mixture of fluids, i.e., 0 ≤ CF ≤ 1. Also, the underlying mix-split sequence is usually abstracted using a directed graph called mix-split graph or task-graph [8], [9]. More precisely, in the discrete mixing model, a droplet with integral volume v 1 units with CF = c 1 is allowed to mix with another droplet with integral volume v 2 units with CF = c 2 . When the mixing is completed, the resulting droplet is split into two equal-size daughter-droplets (i.e., balanced splitting), each with volume (v1+v2) 2 , and the resulting CF becomes (c1×v1)+(c2×v2) v1+v2 . For the most widely used (1:1) mixing model, v 1 = v 2 = 1, and the corresponding unit volume is denoted as 1X. The objective of sample preparation is to achieve the desired CF for each of the constituents in a fluid mixture and to minimize the number of mix-split operations, reactant-cost, or waste production [8]–[14]. In the (1:1) mixing model, every mix-split operation is performed between two unit volume 1X droplets yielding a 2X droplet. Note that the resulting CF obtained through a sequence of (1:1) mix-split steps will be accurate only when the assumption of balanced splitting holds, that is, a droplet of volume 2X is always split into two daughter-droplets of