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Research Papers

Transport of Dynamic Biochemical Signals in Steady Flow in a Shallow Y-Shaped Microfluidic Channel: Effect of Transverse Diffusion and Longitudinal Dispersion

[+] Author and Article Information
Yong-Jiang Li

Department of Biomedical Engineering,
Faculty of Electronic Information
and Electrical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: liner0805@126.com

Yizeng Li

Department of Mechanical Engineering,
University of Michigan-Ann Arbor,
Ann Arbor, MI 48109
e-mail: yizengli@umich.edu

Tun Cao

e-mail: caotun1806@dlut.edu.cn

Kai-Rong Qin

e-mail: krqin@dlut.edu.cn
Department of Biomedical Engineering,
Faculty of Electronic Information
and Electrical Engineering,
Dalian University of Technology,
Dalian 116024, China

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received February 4, 2013; final manuscript received October 2, 2013; accepted manuscript posted October 19, 2013; published online November 12, 2013. Assoc. Editor: Jeffrey Ruberti.

J Biomech Eng 135(12), 121011 (Nov 12, 2013) (9 pages) Paper No: BIO-13-1063; doi: 10.1115/1.4025774 History: Received February 04, 2013; Revised October 02, 2013; Accepted October 19, 2013

Dynamic biochemical signal control is important in in vitro cell studies. This work analyzes the transportation of dynamic biochemical signals in steady and mixing flow in a shallow, Y-shaped microfluidic channel. The characteristics of transportation of different signals are investigated, and the combined effect of transverse diffusion and longitudinal dispersion is studied. A method is presented to control the widths of two steady flows in the mixing channel from two inlets. The transfer function and the cutoff frequency of the mixing channel as a transmission system are presented by analytically solving the governing equations for the time-dependent Taylor–Aris dispersion and molecular diffusion. The amplitude and phase spectra show that the mixing Y-shaped microfluidic channel acts as a low-pass filter due to the longitudinal dispersion. With transverse molecular diffusion, the magnitudes of the output dynamic signal are reduced compared to those without transverse molecular diffusion. The inverse problem of signal transportation for signal control is also solved and analyzed.

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Figures

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Fig. 1

(a) Schematics of a shallow, Y-shaped microfluidic channel with cells cultured on the bottom of the mixing channel. (b) The geometry and the coordinate system of a shallow, Y-shaped microfluidic channel (not to scale).

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Fig. 2

Predicted temporal outputs signals in the Y-channel under sine ((a) and (c)) and triangle ((b) and (d)) input signals (thin solid lines) released from the inlet A. The output signals are taken at z = L and x = 3 W/4. The baseline of the dynamic input signals is 1 mmol/m3, with amplitude 0.5 mmol/m3. Thick solid lines: predication from the analytic solution; thick dashed lines: prediction from the 3D numerical solution. (a) and (b) Dynamic signal frequency: 0.25 Hz. (c) and (d) Dynamic signal frequency: 1 Hz.

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Fig. 3

Concentration profiles of biochemical signal distribution in the mixing channel. Both input signals and volume flow rates are constant. The scaling bars indicating the signal concentration have units of mmol/m3. (a) and (b) ε = 0.3; (c) and (d) ε = 0.7; (a) and (c) Q = 0.8 × 10−10 m3/s and τw = 1.33 Pa; (b) and (d) Q = 2 × 10−10 m3/s and τw = 3.33 Pa.

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Fig. 4

Spectra of the transfer function of the mixing Y-channel taken at z = L. Solid lines: ε = 0; dashed lines: ε = 0.5. (a) Spectral amplitude. The four dashed lines from top to bottom represent the transfer function taken at x = 3 W/4, 5 W/8, W/2, and 3 W/8, respectively, with transverse dispersion. The dotted vertical line marks the bandwidth that is defined by the drop of the maximum amplitude by 70.7% from a channel without transverse dispersion. The corresponding cutoff frequency is designated by an arrow. (b) Spectral phase. All lines are overlapping and cannot be differentiated.

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Fig. 5

Approximated cutoff frequencies in the mixing Y-channel. Cutoff frequencies as functions of shear stress under different channel heights (a), fluid viscosities (c), and diffusivities (e). Cutoff frequencies as functions of longitudinal coordinate z under different channel heights (b), fluid viscosities (d), and diffusivities (f). While the variables of the functions are varied, the other parameters are fixed at the default values as shown in Table 1.

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Fig. 6

Maximum amplitudes corresponding to the zero frequency of the transfer function in the mixing Y-channel with ε = 0.5. The x locations are taken at 3 W/4 for all. Maximum amplitudes at z = L as functions of shear stress under different channel heights (a), fluid viscosities (c), and diffusivities (e). Maximum amplitudes as functions of longitudinal coordinate z under different channel heights (b), fluid viscosities (d), and diffusivities (f). While the variables of the functions are varied, the other parameters are fixed at the default values as shown in Table 1.

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Fig. 7

Predicted input signals from the inlet A in the mixing Y-channel under desired sine (a) and triangle (b) signals (thin solid lines) at z = L and x = 3 W/4. The baseline of the desired dynamic output signals is 1 mmol/m3, with amplitude 0.5 mmol/m3. Both sine (a) and triangle (b) signals have period 4 s (corresponding to 0.25 Hz). Thick solid lines: predicted input for ε = 0; thick dashed lines: predicted input for ε = 0.5. (a) No frequency truncation is needed. (b) Frequencies higher than 0.75 Hz are truncated.

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