System-level modeling and simulation of biochemical assays in lab-on-a-chip devices

Abstract

We present a ''mixed-methodology'' based system-level modeling and simulation for biochemical assays in lab-on-a-chip (LoC) devices. The methodology uses a combination of numerical schemes and analytical approaches to simulate biological and physicochemical processes, specifically, an integral approach for fluid flow and electric field, method of lines (MOL) and two-compartment models for biochemical reactions, and Fourier series-based model for analyte mixing. The solution procedure begins with decomposing the LoC device into a system of inter-connected components (e.g., channels and junctions) and the models are solved in a network fashion. Models are developed to accurately capture the multi-physics (e.g., flow, mixing, and reaction) behavior of individual components. The assembly of the components is facilitated via exchange of fluid flux and Fourier series coefficients (or average concentration) of analytes between various components, which enables network solution of the models. The system models are validated against both experimental and numerical models on various biochemical assays (e.g. immunoassays and enzymatic reactions), showing significant computational speedup (100-10,000-fold depending on the assay) without appreciably compromising accuracy (<10% error relative to numerical analysis).

Scaling law for cross-stream diffusion in microchannels under combined electroosmotic and pressure driven flow

“…The following assumptions are made to simplify the development of the analytical model:

The flow in the main microchannel is steady and laminar featuring a low Reynolds number.

The EDL is very thin (typically ≤100 nm) relative to the transverse dimension of the channel.

The length of the channel is significantly larger than its width and height (i.e., L >> W and L >> H ). Note that in distinct contrast to prior models (Holden et al 2003; Lam et al 2005; Wang et al 2007; Wang et al 2006), no constraint of the relative magnitude of W and H is imposed in the present model. The flow entry effect after the merging junction is neglected as its length is negligible compared to the main channel length.

Convective mass transport in the axial direction dominates over the axial diffusion, and the latter is neglected in the model (refer to (Song et al 2012) for detailed discussion about validity of this assumption in microfluidics.

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“…Their effects on the position-dependent scaling law are extensively investigated. (2) The analysis is undertaken by virtue of accurate 3D analytical models applicable to microchannels with arbitrary transverse aspect ratios, which eliminates errors due to numerical diffusion and the approximation of the depth-wise average in prior analytical models (Holden et al 2003; Lam et al 2005; Wang et al 2007; Wang et al 2006) and provides direct physical insight into the underlying transport mechanism.…”

Design optimization of an enzymatic assay in an electrokinetically-driven microfluidic device

“…Based on electric current analogy (Chatterjee and Aluru 2005) reduced order models have been developed to evaluate fluid flow in the network of microchannels of a biochip and to quickly study diffusive mixing in electrokinetically driven passive mixers and steady state enzymatic analysis (Wang et al 2005(Wang et al , 2007. Chein et al (2006) proposed a reduced model to estimate temperature buildup associated with joule heating in an electrokinetically driven microfluidic system.…”

Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model

“…Therefore, several assumptions have been made in prior analytical models, including (1) the aspect ratio of the channel has to be large (i.e., flat, slit-like channels) and (2) the depth-wise diffusion is assumed to be negligible (i.e., depth-wise concentration distribution is assumed to be uniform). For instance, by replacing the non-uniform velocity profile with the average flow velocity and neglecting the terms associated with axial and depth-wise diffusion, an analytical model was obtained (Holden et al 2003; Wang et al 2006, 2007) to predict analyte concentration profile in the 2D domain (width-wise and axial). Wu et al (2004) improved this solution by incorporating axial diffusion.…”