MEMS-based fabrication and microfluidic analysis of three-dimensional perfusion systems

Abstract

This paper describes fabrication and fluidic characterization of 3D microperfusion systems that could extend the viability of high-density 3D cultures in vitro. High-aspect ratio towers serve as 3D scaffolds to support the cultures and contain injection sites for interstitial delivery of nutrients, drugs, and other reagents. Hollow and solid-top tower arrays with laser ablated side-ports were fabricated using SU-8. Appropriate sizing of fluidic ports improves the control of agent delivery. Microfluidic perfusion can be used to continuously deliver equal amount of nutrients through all ports, or more media can be delivered at some ports than the others, thus allowing spatial control of steady concentration gradients throughout the culture thickness. The induced 3D flow around towers was validated using micro particle image velocimetry. Based on experimental data, the flow rates from the characteristic ports were found to follow the analytical predictions.

Appendix

$$\frac{{p_0 }}{\gamma } + \alpha \frac{{v_0^2 }}{{2g}} = \frac{{p_1 }}{\gamma } + h_1 + \left\{ {f_{v_0 } ,_{d_0 } \frac{{h_1 }}{{d_0 }}\frac{{v_0^2 }}{{2g}} + f_{v_1 } ,_{d_1 } \frac{t}{{d_1 }}\frac{{v_1^2 }}{{2g}}} \right\} + \alpha \left\{ {K_a \frac{{v_1^2 }}{{2g}} + K_1 \frac{{v_1^2 }}{{2g}}} \right\}$$

(1)

$$\frac{{p_0 }}{\gamma } + \alpha \frac{{v_0 ^2 }}{{2g}} = \frac{{p_2 }}{\gamma } + \left( {h_1 + h_2 } \right) + \left\{ {f_{v_0 ,d_0 } \frac{{h_1 }}{{d_0 }}\frac{{v_0^2 }}{{2g}} + f_{v_b ,d_0 } \frac{{h_2 }}{{d_0 }}\frac{{v_b^2 }}{{2g}} + f_{v_2 ,d_2 } \frac{t}{{d_2 }}\frac{{v_2^2 }}{{2g}}} \right\} + \alpha \left\{ {K_b \frac{{v_b^2 }}{{2g}} + K_c \frac{{v_2^2 }}{{2g}} + K_2 \frac{{v_2^2 }}{{2g}}} \right\}$$

(2)

$$\frac{{p_0 }}{\gamma } + \alpha \frac{{v_0^2 }}{{2g}} = \frac{{p_3 }}{\gamma } + \left( {h_1 + h_2 + h_3 } \right) + \left\{ {f_{v_0 ,d_0 } \frac{{h_1 }}{{d_0 }}\frac{{v_0^2 }}{{2g}} + f_{v_b ,d_0 } \frac{{h_2 }}{{d_0 }}\frac{{v_b^2 }}{{2g}} + f_{v_m ,d_0 } \frac{{h_3 }}{{d_0 }}\frac{{v_m^2 }}{{2g}} + f_{v_3 ,d_3 } \frac{t}{{d_3 }}\frac{{v_3^2 }}{{2g}}} \right\} + \alpha \left\{ {K_b \frac{{v_b^2 }}{{2g}} + K_m \frac{{v_m^2 }}{{2g}} + K_e \frac{{v_3^2 }}{{2g}} + K_3 \frac{{v_3^2 }}{{2g}}} \right\}$$

(3)

$$\begin{aligned} & \frac{{p_0 }}{\gamma } + \alpha \frac{{v_0^2 }}{{2g}} = \frac{{p_4 }}{\gamma } + \left( {h_1 + h_2 + h_3 + h_4 } \right) + \left\{ {f_{v_0 ,d_0 } \frac{{h_1 }}{{d_0 }}\frac{{v_0^2 }}{{2g}} + f_{v_b ,d_0 } \frac{{h_2 }}{{d_0 }}\frac{{v_b^2 }}{{2g}} + f_{v_m ,d_0 } \frac{{h_3 }}{{d_0 }}\frac{{v_m^2 }}{{2g}} + f_{v_4 ,d_0 } \frac{{h_4 }}{{d_0 }}\frac{{v_4^2 }}{{2g}}} \right\} \\ & \mathop {}\limits_{}^{} \mathop {\mathop {}\nolimits_{} \mathop {}\nolimits_{}^{} }\limits_{}^{} \mathop {}\nolimits_{} + \alpha \left\{ {K_b \frac{{v_b^2 }}{{2g}} + K_m \frac{{v_m^2 }}{{2g}} + K_s \frac{{v_4^2 }}{{2g}} + K_4 \frac{{v_4^2 }}{{2g}}} \right\} \\ \end{aligned} $$

(4)

$$K_1 = K_2 = K_3 = K_4 = 1$$

(5)

$$p_0 = p_1 + \gamma h_1 = p_2 + \gamma \left( {h_1 + h_2 } \right) = p_3 + \gamma \left( {h_1 + h_2 + h_3 } \right) = p_4 + \gamma \left( {h_1 + h_2 + h_3 + h_4 } \right)$$

(6)

$$f_{v_1 ,d_1 } \frac{t}{{d_{_1 } }}\frac{{v_1^2 }}{{2g}} = f_{v_b ,d_0 } \frac{{h_2 }}{{d_0 }}\frac{{v_b^2 }}{{2g}} + f_{v_2 ,d_2 } \frac{t}{{d_2 }}\frac{{v_2^2 }}{{2g}}$$

(7)

$$f_{v_2 ,d_2 } \frac{t}{{d_2 }}\frac{{v_2^2 }}{{2g}} = f_{v_m ,d_0 } \frac{{h_2 }}{{d_0 }}\frac{{v_m^2 }}{{2g}} + f_{v_3 ,d_3 } \frac{t}{{d_3 }}\frac{{v_3^2 }}{{2g}}$$

(8)

$$f_{v_3 ,d_3 } \frac{t}{{d_3 }}\frac{{v_3^2 }}{{2g}} = f_{v_4 ,d_4 } \frac{{h_4 }}{{d_0 }}\frac{{v_4^2 }}{{2g}}$$

(9)

$$\left[ v \right] = \frac{4}{\pi }\frac{{\left[ Q \right]}}{{\left[ d \right]^2 }} f_{\left[ v \right],\left[ d \right]} = \frac{{64}}{{\left[ {{\text{Re}}} \right]}} = \frac{{64\mu }}{{\rho \left[ v \right]\left[ d \right]}}$$

(10)

$$d_1 = d_0 \left( {\frac{t}{{5h_2 + 3h_3 + h_4 }}} \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$4$}}} d_2 = d_0 \left( {\frac{t}{{3h_3 + h_4 }}} \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$4$}}} d_3 = d_0 \left( {\frac{t}{{h_4 }}} \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$4$}}} $$

(11)

$${{d_j } \mathord{\left/ {\vphantom {{d_j } {d_0 }}} \right. \kern-\nulldelimiterspace} {d_0 }} = \left\{ {{t \mathord{\left/ {\vphantom {t {\sum\limits_{i = j}^N {\left[ {2\left( {N - i} \right) + 1} \right]h_{i + 1} } }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{i = j}^N {\left[ {2\left( {N - i} \right) + 1} \right]h_{i + 1} } }}} \right\}^{0.25} , j = 1,..,N$$

(12)

$$d_{j - 1} = \left[ {{1 \mathord{\left/ {\vphantom {1 {d_N^4 + \sum\limits_{i = j}^N {2\left( {N - i + 1} \right){{h_i } \mathord{\left/ {\vphantom {{h_i } {\left( {td_0^4 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {td_0^4 } \right)}}} }}} \right. \kern-\nulldelimiterspace} {d_N^4 + \sum\limits_{i = j}^N {2\left( {N - i + 1} \right){{h_i } \mathord{\left/ {\vphantom {{h_i } {\left( {td_0^4 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {td_0^4 } \right)}}} }}} \right]^{ - 0.25} , j = 2,..,N \lim _{d_0 \to \infty } d_{j - 1} = d_N $$

(13)