THERMAL MODELING FOR DESIGN OPTIMIZATION OF A MICROFLUIDIC DEVICE FOR CONTINUOUS FLOW POLYMERASE CHAIN REACTION (PCR)

Dow

Proceedings of 2008 ASME Summer Heat Transfer Conference HT2008

August 10-14, 2008, Jacksonville, Florida USA

HT2008-56198

THERMAL MODELING FOR DESIGN OPTIMIZATION OF A MICROFLUIDIC DEVICE FOR CONTINUOUS FLOW POLYMERASE CHAIN REACTION (PCR)

Sumeet Kumar/ Massachusetts Institute of Technology, 77 Massachusetts Avenue,

Cambridge, MA – 02139, USAemail: [email protected]

Todd Thorsen/ Massachusetts Institute of Technology, 77 Massachusetts Avenue,

Cambridge, MA – 02139, USA

Sarit Kumar Das/ Massachusetts Institute of Technology, 77 Massachusetts Avenue,

Cambridge, MA – 02139, USA

ABSTRACTPolymerase Chain Reaction (PCR) is a molecular

biological method for the in vitro amplification of nucleic acid molecules which has wide applications in the area of genetics, medicine and biochemistry. The typical three step PCR cycle consists of heating the sample to 90-94 ºC to denature double-stranded DNA, cooling down to 50–54 ºC to anneal the specific primers to the single stranded DNA and finally increasing the temperature to 70–75 ºC for extension of the primers with thermostable DNA polymerase. The temperature sensitivity of the reaction requires precise temperature control and proper thermal isolation of these three zones. In this paper we present the design of a continuous flow PCR microfluidic device with the channels fabricated in (poly) dimethylsiloxane (PDMS) and thin film Platinum Resistance Temperature Detector (RTD) elements fabricated on glass substrate to define the three different temperature zones. The fluidic arrangement has a water jacket layer to minimize evaporation from the porous PDMS walls. A detailed thermo fluidic model of the device is presented to predict the performance and efficacy of the proposed design. Numerical simulations are carried out to find the temperature distribution and temperature gradients in the device and a parametric study is done by varying flow rate, heat flux and channel dimensions in order to optimize the design for achieving temperature isolation and sharp temperature gradients between different zones.

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INTRODUCTIONPolymerase chain reaction (PCR) is an enzymatic method

for the in vitro amplification of nucleic acid molecules, which has wide applications in the area of genetics, medicine and biochemistry [1, 2]. The major objective of PCR is to replicate a nucleic acid sequence, ultimately yielding of the order of 105

– 106 copies from a single template. The amplification process of PCR can be partitioned into three discrete temperature zones: (A) denaturation: double-strand DNA segment is separated in single strands at high temperature (90-94 °C); (B) annealing: the separated single-stranded DNA attaches to a complimentary primer (50-54 °C); (C) extension: DNA polymerase adds nucleotides to the 3’ end of the primer , replicating the target DNA sequence (70-75°C) [3, 4].Commercially available PCR equipment (e.g. MJ Research, Inc.) performs PCR simultaneously in 96 or more plastic tubes or wells containing sample DNA and PCR mixtures. However, conventional 96 well PCR devices usually have a thermal ramping rate of 1–2 °C/s, accounting for a significant contribution to the run time of a typical 30 cycle PCR reaction (1-2 hours). Moreover, while using conventional tube-based PCR methods, both sample preparation and post-PCR product detection need to be performed offline, thus resulting in the longer analysis process and a higher risk of cross contamination [1]. The use of micro electro-mechanical systems (MEMS) technology offers several advantages for PCR, including fasterthermal ramping times, reduced sample volumes, disposability, and functional integration of sample preparation and post-analysis [1, 3, 5, 6]. To date, most micro PCR devices can be

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classified into, static chamber PCR chips and continuous flow PCR chips. Chamber-type PCR chips consist of a micro or nanoliter volume of reservoir and integrated film heaters/sensors that cycle under the static sample. These chips have advantages such as rapid thermal heating/cooling, easy temperature control, and nanoliter sample volumes. In contrast, flow-type PCR chips typically consist of three independent, fixed temperature zones fabricated from thin, conductive films with the PCR sample continually flowing between them via a microchannel with a serpentine configuration. Sample volumes of continuous flow PCR chips are typically on the order of 1 –10 µl, and can be used for real-time PCR analysis, in which amplified product is analyzed as a function of cycle number. Additionally, thermal ramping times are even shorter for continuous flow PCR devices (vs. static microchambers), enabling faster PCR cycle times [5, 6, 7, 8]. The temperature sensitivity of continuous flow PCR devices requires precise temperature control and proper thermal isolation of the three zones. For PCR, it is desirable to minimizeramp times between the extension, denaturation and annealing temperatures to maximize yield and fidelity of the amplified products [1, 2, 4]. In this paper, we present a design for a continuous flow PCR microfluidic device with the channels fabricated in (poly) dimethylsiloxane (PDMS) and thin film platinum Resistance Temperature Detector (RTD) elements fabricated on glass substrate, which define the three discrete temperature zones. The microfluidic serpentine channel acting as a conduit for the PCR mixture is covered by an enclosed water jacket reservoir, separated from the sample channel by a thin (~30 µm) layer of PDMS, to minimize evaporation from the water-permeable PDMS walls. A detailed thermofluidic model of the device is presented to simulate the temperature profile of the fluid as it transits between the RTD elements within the device. Numerical simulations are carried out using the commercial software Fluent to find the temperature distribution and temperature gradients in the device as a function of flow rate, heat flux and channel dimensions to optimize the design for achieving temperature isolation and sharp temperature gradients between different zones.

NOMENCLATURE A = Cross sectional area of the rectangular channel

pfC = Specific heat capacity of the fluid

airh = Convective heat transfer co efficient of air

fk = Thermal conductivity of fluid

pk = Thermal conductivity of PDMS

gk = Thermal conductivity of glass

wk = Thermal conductivity of wood

L = Length of the channel

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wl = Thickness of the wooden bench top

Pe = Peclet number ( LkuC fopff /2 )

Q = Volume flow rate''q = Heat flux

Re = Reynolds number = AQuo T = Temperaturet = Timeu = Velocity

ou = Characteristic velocity scale = Q A*t = Non dimensional time = uot L*u = Non dimensional velocity = ouu*x = Non dimensional stream wise co-ordinate = Lx /*y = Non dimensional co ordinate perpendicular to the

stream wise direction = /y*z = Non dimensional co ordinate perpendicular to the

stream wise direction = /zP = Pressure head across the microfluidic channel2 = Laplacian

f = Thermal diffusivity of the fluid = pfff Ck /

p = Thermal diffusivity of PDMS

g = Thermal diffusivity of Glass

f = Density of the fluid

= Height of the fluidic channel

p = Thickness of the PDMS domain

g = Thickness of the glass domain''/ LqTk f = Non dimensional temperature

= Fluid viscosity

DESIGN OF MICROFLUIDIC PCR CHIPThe design of the microfluidic channels follow the basic

serpentine design proposed by Manz et al. with some modifications [8]. The reagents are designed to flow through the three different zones, namely denaturation, annealing and extension, as shown in Fig.1. To achieve good amplification, a serpentine channel is implemented to pass through the zones 30 times, comparable to the 25-30 cycles used in conventional PCR thermocyclers. The desired temperature zones are achieved by using three sets of thin film platinum RTD elements fabricated on glass substrate as shown in Fig.2. Each of these sets of heaters can be independently regulated to control the heat flux dissipated within each zone. The fluidic layer is then bonded to the top surface of the glass layer after aligning the fluid layer on top of the corresponding heater zones. Thus, a

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closed microfluidic device is formed in which the fluid is in direct contact with the thin film heaters.

Fig. 1: PCR microfluidic device channel layout.

Fig. 2: Patterned thin film Platinum heaters (black strips) on glass substrate (white background)

THERMAL MODELING OF THE DEVICEA thermal model of the proposed design is useful to predict

the performance of the device. The important variables are channel dimensions, heat flux imparted by the thin film heaters, and the volumetric flow rate. The objective function for design optimization is the temperature distribution within the device and, more importantly, the temperature distribution experienced by a fluid element as it flows through the microchannel.

Unlike momentum and species transport analysis, which is confined to the fluidic domain, thermal modeling in microfluidics presents some unique challenges as the presence of thermal diffusion necessarily extends the simulation domain from the region of interest (i.e. the fluidic domain) to encompass the materials bounding the microchannels (glass, PDMS). Contrasting with a macroscale system, where the fluidic domain is most often of comparable size to the solid

Zone A

Zone B

Zone C

1 cm

1 cm

Zone C, Extension (70-75 ˚C)

Zone B, Annealing (50-54 ˚C)

Zone A, Denaturation (90-95 ˚C)


regions, a microchannel system typically encompasses only a very small fraction of the substrate and thus heat transfer is typically governed by a large timescale thermal diffusion process through the solid region [9].

The model involves three-dimensional, unsteady conjugate heat transfers between the fluidic and solid PDMS/glass regions of the device when the three thin film heaters are active. Different length scales are involved due to the large difference in the size of the fluid domain (height ~ 75µm, width ~ 100µm) and the solid domain (height ~ 1mm). Within the fluidic domain the non-dimensional energy equation neglecting the viscous dissipation term can be written as

2*

2

2*

2

**

*.

zyxu

tPe

(1)

The requirement of large number of cycles for effective amplification by PCR dictates a long effective microchannel length for continuous-flow microfluidic PCR devices to allow sufficient residence time for samples flowing through the threerespective temperature zones (denaturation, annealing and extension). Our design consists of 30 identical passes through the three zones, with a total length of the microfluidic channel = 1.602 m. Modeling the channel as a cylinder with an effective hydraulic diameter of 85.7 µm and assuming the fluid viscosity to be equal to that of water, the pressure head required to drive the flow is P1.213x1010Q, where Q is the volumetric flow rate. Under standard operating conditions, we would like to operate the devices using flow rates on the order of 1 − 50 nl/s, providing short loading times for sub-µl scale samples while allowing sufficient sample residence times over the temperature zones for complete amplification. For Q ~ 1 − 50 nl/s, P 0.012 – 0.6 bar. At these flow rates, viscous forces are dominant, with Reynolds numbers (Re) between 0.01Re0.5. The Peclet number (Pe) for such flows, characterizing comparison of convective to diffusive forces, ranges between 0.5×10-5 Pe 2.5×10-4.

Inside the upper substrate (PDMS) and lower substrate (glass) zones, the energy equation takes on a simplified form, consisting of transient and diffusion terms only, which can be written in dimensional form as

1

i

T

t 2T (2)

where the generic thermal diffusivity () subscript, i, denotes either PDMS (i=p) or glass (i=g).

The glass substrate has patterned thin film heaters (Fig. 2), which act as constant heat flux sources when a current is passed through them. The thin film heaters are subsequently sealed with the microchannel-patterned PDMS, and the heaters are in direct contact with the fluid when the device is operated. This leads to a constant heat flux boundary condition at the lower boundary of the fluidic domain. Most of the heat within the fluid flowing through the microchannel is transferred via



thermal diffusion due to the low Peclet number of the flow. Since the heaters are fabricated on the glass and kg>kf>kp, the bulk of the heat generated by the heaters is transferred to the glass.

NUMERICAL SIMULATION AND RESULTSAs shown in Fig.3 the simulation domain consists of three

domains (fluid, glass and PDMS). The domain represents one pass through the PCR microfluidic device (with a pass defined as fluid flow through the denaturation, annealing, and extension zones respectively). The dimensions of the fluidic domain for a single pass are as follows; height = 75µm, width = 100µm, length of the serpentine channel = 5.34 cm. The glass and the PDMS domains are chosen in such a way that they encompass the fluidic domain and represent one pass of the microfluidic device. The thickness of the PDMS and glass domains are; δp = 0.5 mm, δg = 1 mm. The top face of the glass domain is partitioned in the model according to the different heater zones, facilitating simulation of different heat flux dissipated by respective zones.

Fig.3: Computational domain for simulation

Since the pattern of heaters and fluidic channel is geometrically periodic in the microfluidic device, it should be sufficient to simulate one pass to understand the temperature profile in the device. We first support this assumption by presenting the simulation of heat diffusion in the glass substrate with ten repeating pattern of heaters. The glass domain is meshed using Hybrid Hexcore scheme of size 0.25 mm. 3 dimensional unsteady solver with energy equations was used in order to obtain the temperature distribution in glass domain with time. Figure 4 shows the isotherms to be perpendicular to the flow direction under steady state conditions. Convective heat transfer boundary conditions were given on the side walls with hair = 15 W/m2K. An effective heat transfer coefficient for the lower surface of the glass was calculated to account for the fact that the microfluidic device will be operated on a wooden bench top of thickness lw ~ 1cm. Assuming 1-D heat transfer model for heat transfer from the glass to air through wooden base we can write;

wwaireff klhh //1/1 (3)

For kw = 0.1 W/mK, Eqn. 3 is used to calculate heff = 6 W/m2K.

PDMS (p)

Glass (g)

1mm

Fluid Domain (f)


In the actual device, PDMS layer on top of glass provides additional thermal resistance. For PDMS layer of thickness =0.5 mm and kp = 0.15 W/mK, Eqn. 3 is used to calculate heff forthe top surface of the glass (= 14 W/m2K). The heat flux values for the heater zones were chosen to be the same as the one used for single pass simulation (justified later); Zone A = 11200 W/ m2, Zone B = 1000 W/ m2, Zone C = 7000 W/ m2. Thermal properties of glass used are; kg = 1.3 W/mK, αg = 7.81×10-7

m2/s.From Fig.5 the temperature variations in the transverse

direction (neglecting end effects) are found to be small, ~ 1-2 K over 10 mm, equivalent to the width of 10 passes. As the transverse temperature gradients are much smaller than the temperature gradients in the direction of flow (between heater regions), variations in temperature profiles between different passes as a function of chip position were assumed to be negligible.



Flow directionTransverse direction

Fig.4: Unsteady simulation of heat diffusion in the glass domain at different times. Simulation predicts the system to reach steady state at t ~ 410 s.

40

50

60

70

80

90

100

0 0.002 0.004 0.006 0.008 0.01

Distance (m)

Tem

pera

ture

(C

)

Zone A

Zone C

Zone B

Fig.5: Variation of temperature in transverse direction for the 3 zones.

Simulations were carried out with a three-dimensional, segregated, steady/unsteady solver. Hexahedral meshing of Submap scheme was used to mesh the three domains. The three domains had mesh of different resolutions. The fluid domain had cubic mesh elements of volume = 25 µm × 25 µm × 25 µm; glass domain had cubic mesh elements of size = 25 µm × 25 µm × 100 µm; PDMS domain had cubic mesh elements of size = 25 µm × 25 µm × 100 µm. Thermal boundary conditions are as follows; 1) a convective heat transfer coefficient of hair = 15 W/m2K on the side walls of glass and the top PDMS surface exposed air, 2) zero heat flux boundary conditions on the side walls of PDMS and glass which form the cutting plane along which the simulation domain is separated from the actual device, 3) an effective heat transfer coefficient for the lower surface of the glass (described earlier) of heff = 6 W/m2K. Thermal properties of the fluid, PDMS and glass used are; kf = 0.6 W/mK, αf = 1.44×10-7 m2/s, kp = 0.15 W/mK, αp = 9.34×10-

8 m2/s, kg = 1.3 W/mK, αg = 7.81×10-7 m2/s. The fluid properties were taken to be that of water which were assumed to be constant during the PCR cycle. The concentration of reagents in the PCR mixture is of the order of millimolar (mM). There will be some change in the fluid properties as the reaction progresses but since we are considering dilute solutions of nucleotides, the variations can be neglected.

Steady state temperature profiles in the fluid, glass and PDMS domain are shown in Fig.6. Numerical experimentation was carried out by changing heat flux values of the different heaters in order to achieve the desired temperature distribution. The following values of heat fluxes gave the temperature


distribution consistent with our target zonal temperature requirement; Zone A = 11200 W/ m2, Zone B = 1000 W/ m2, Zone C = 7000 W/ m2. The inlet velocity for the simulation was uo = 0.5 mm/s. or Q = 3.75 nl/s. The inlet temperature (360 K) was defined to match the outlet temperature in order to simulate the periodicity in flow.



Fig.6: Steady state temperature distribution in fluid, PDMS and glass domain respectively.

From Fig.6, we can observe the extent of lateral diffusion in glass and PDMS and their contributions to the temperature distribution in the fluid domain. The dominance of conduction over convection is illustrated by the similarity of spatial temperature distribution between fluid and glass or PDMS domain.

Simulations were carried by varying the inlet velocity in the range 0.5 mm/s ≤ uo ≤ 5 mm/s or 3.75 nl/s ≤ Q ≤ 37.5 nl/s. The spatial temperature distribution in the fluid domain is shown in Fig.7. The results show that change in volume flow rate has a negligible effect on spatial temperature distribution over the defined flow rate range due to the dominance of conduction over convection.

50

55

60

65

70

75

80

85

90

95

0 0.01 0.02 0.03 0.04 0.05 0.06

Distance (m)

Tem

pera

ture

(C

)

u=0.0005 m/s

u=0.001 m/s

u=0.002 m/s

u=0.003 m/s

u = 0.005 m/s

Fig.7: Steady state spatial temperature distribution in the fluid domain along the flow direction.


Furthermore, as conduction is the dominant mode of heat transfer in the fluid regime, and thermal resistance across the height of the fluidic channel is small (δ/kf ~ 1.25×10-4 Km2/W), there is little variation in temperature as a function of height of the fluidic channel (<1K) (Fig.8).

50

55

60

65

70

75

80

85

90

95

0.00 20.00 40.00 60.00 80.00

Height (microns)

Tem

per

atu

re (

C)

Zone A

Zone B

Zone C

Fig.8: Temperature variation along the height of the microfluidic channel at three different locations which are representative of the respective zones

From an engineering perspective in the design of PCR devices, the most important parameter is the temperature variation which a fluid particle experiences as it passed through the fluidic channel. The material derivative of temperature can be written as

x

Tu

t

T

Dt

DT

(4)

The material derivative represents the rate of change of T moving with a fluid element. The first term represents the local rate of change of T at a particular point and the second term represents the change in T as a result of advection of fluid from one location to other. Since we are considering fully developed flow at low Reynolds number, the advective term has contribution only from the streamwise velocity u.

Figure 9 shows the variation in temperature profile of the fluid with time as it flows through the channel. The spatial variation of temperature with flow rate being negligible, the total derivative or the material derivative of temperature varies linearly with flow rate.

The ramp rate of a zone was calculated as the average rate of change of temperature moving from the zone to the next zone. The residence time was calculated as the average time for which the fluid remains in a particular zone. Their variations with mean velocity are plotted in Fig. 10. The ramp rate (being the average of material derivative) under steady state conditions depends on the mean flow rate and the spatial temperature distribution (Eqn. 4). The spatial temperature distribution is controlled by the thin film heaters geometry, their spatial



arrangement and the heat flux dissipated by them. The design presented here creates temperature distribution which helps in getting higher ramp rates at reasonable volume flow rates (Fig. 10). The residence time of the fluid in a particular zone varies inversely with flow rate (Fig.10). Hence a trade off exists between ramp rate and residence time. Addition of nucelotides during the extension phase of PCR is processive, as the Taqpolymerase enzyme replicating the DNA sequence adds bases to the 3’ end of the sequence at a rate of 10-60 bases s-1. Hence, longer replication sequences require longer extension times, achieved by reducing the linear flow rate across the zones.

50

55

60

65

70

75

80

85

90

95

0 20 40 60 80 100 120Time(s)

Tem

pera

ture

(C)

u=0.001 m/s

u=0.002 m/s

u=0.003 m/s

u=0.005 m/s

u=0.0005 m/s

Fig.9: Variation of temperature with time (as experienced by a fluid particle) for different flow rates

-12

-9

-6

-3

0

3

6

9

12

15

18

21

24

0 0.001 0.002 0.003 0.004 0.005 0.006

Average velocity (m/s)

Zone A ramp rate

Zone B ramp rate

Zone C ramp rate

Zone A residencetime

Zone B residencetime

Zone C residencetime

Fig.10: Variation of ramp rate between the zones (C/s) and residence time (s) with average velocity.


CONCLUSIONA detailed thermo-fluidic simulation has been developed to

model the temperature profile in a continuous flow microfluidic PCR device. A single pass of the microfluidic device has been simulated as a representative model for the entire microfluidic device consisting of 30 passes. The above model was justified by carrying out numerical simulation on a glass substrate having 10 sets of patterned heaters. The results show that the single pass model is valid for understanding the temperature distribution within the device when edge effects are neglected. The heat flux values dissipated by the heaters were chosen to be the same for the entire glass simulation and single pass simulation. The results show a good correlation in spatial temperature distribution for the glass regime in both simulations.

Simulations clearly showed the dominance of conduction over convection in the chosen range of flow and thermal variables. Hence the most important factor in determining temperature distribution is the spatial arrangement of heaters and the heat flux dissipated by them. The results show that our design meets the requirement of defined temperature zones for PCR.

The temperature variation experienced by a fluid particle moving through the channel depends on the volume flow rate and the spatial temperature distribution. The simulations suggest that higher ramp rates compared to the conventional thermocyclers can be achieved in the continuous flow microfluidic PCR device. An important trade off exists between the ramp rate and the residence time. Different PCR reactions have different residence time requirements and hence the operating conditions need to be tuned for optimum amplification.

We anticipate that numerical simulations for thermofluidic modeling of microfluidic devices for applications like PCR will serve as valuable tools in the physical microfluidic chip design process, reducing the time required to fabricate functional prototypes while maximizing reliability and robustness.

ACKNOWLEDGMENTSThis work was supported in part by a grant from the

Singapore/MIT alliance (SMA2-MST).

REFERENCES

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2. Zhang C. et al, PCR microfluidic devices for DNA amplification, Biotechnology Advances, Vol. 24, pp. 243-284, 2006.

3. Shin Y. S. et al, PDMS-based micro PCR chip with Parylene coating, Journal of Micromechanics and Microengineering, Vol. 13, pp. 768-774, 2003.



4. Tsai N. C. and Sue C. Y., SU-8 based continuous flow RT-PCR bio chips under high precision temperature control, Biosensors and Bioelectronics, Vol. 22, pp. 313-317, 2006.

5. Xiang Q. et al, Real Time PCR on disposable PDMS Chip with a miniaturized thermal cycler, Biomedical Microdevices, Vol. 7, Issue 4, pp. 273-279, 2005.

6. Noh J. et al, In situ thermal diagnostics of the micro-PCR system using liquid crystals, Sensors and Actuators A, Vol. 122, pp. 196-202, 2005.

7. Kim J. A. et al, Fabrication and characterization of o PDMS-glass hybrid continuous-flow PCR chip, Biochemical Engineering Journal, Vol. 29, pp. 91-97, 2006.

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THERMAL MODELING FOR DESIGN OPTIMIZATION OF A MICROFLUIDIC DEVICE FOR CONTINUOUS FLOW POLYMERASE CHAIN REACTION (PCR)