Electronic Supporting Material
Moving the solid phase: a platform technology for cartridge based sandwich immunoassays
Biomedical Microdevices
Raiah Gottheila*, Nadja Baura, Holger Beckerb, Gorden Linka, Dimitri Maiera, Nicole Schneiderhan- Marraa, and Martin Stelzlea*
aNMI Natural and Medical Sciences Institute, Markwiesenstr.55, 72770 Reutlingen, Germany.
Email: [email protected]; [email protected]
bmicrofluidic ChipShop GmbH, Stockholmerstr.20, 07747 Jena, Germany. Calculation of capillary burst pressures for valves and phaseguides
Valving is a method used to control the motion of liquid in a microfluidic system. Valving can be done by various means and one of the simplest ways is by means of geometric structures. This can be achieved by changing the channel geometry such as reducing its width using a restriction and then adding an expansion or opening abruptly. This will thus force the approaching liquid meniscus to change its shape ultimately requiring a larger pressure to overcome the geometry. The meniscus is thus pinned to the channel before the valve opening and will not move forward. Phaseguides are also based on the same meniscus pinning effects. They can be used to guide the meniscus front during filling of a microfluidic chamber. Phaseguides are patterned segments of material perpendicular to the direction of liquid flow. They protrude into the channel or chamber and thus act as obstacles, walls or barriers to the approaching liquid. The liquid upon reaching the strip of material stops and aligns itself to the wall. Upon application of a pressure larger, that withstood by the phaseguides the liquid flows further. The literature thus allows for theoretical calculation of burst pressures that can be withstood by geometrical construction for controlling flow in the micrometer scale.
Supplementary Fig. 1 Passive fluid control: a) Side view of a liquid meniscus reaching a passive geometry. b) The three-dimensional meniscus is pinned due to a structure in its path, with various contact angles.
Using these principles one is free to create geometries which serve functions as described in the above given paragraph. For design purposes one can assume a liquid flows in a restriction followed by an expansion where the top and bottom is made up of the same material, having a rectangular geometry with height h and width w and having a contact angle θ with a liquid as in Supplementary Fig.1 a). The fluid reaches the opening with angles β1, β2 top and bottom and angles α1, α2 with the walls (Supplementary Fig.1 b)). The fluid thus has to undergo a change of curvature at the point where the opening is present. The contact angle at the opening angle seen by the liquid will change from being just θ to (θ+β) and (θ+α). The pressure required for the meniscus to move forward would be:
1 1 cos 1 cos( 2 ) cos( 1 ) cos( 2 ) P R1 R2 h w Therefore assuming the parameters as given in Supplementary Table 1 and inserting them into given equation the different value would theoretically be able to withstand the following pressures.
Supplementary Table 1 Design parameters used to calculate the effective hydrodynamic resistance offered by the capillary stop valves to the advancing fluid.
Valves
Parameter Sample chamber valve Butterfly value
Height (h) 200 µm 200 µm Width (w) 900 µm 200 µm Contact angle (θ) 90° 90° Draft angle (α) 5° 5° Total angle top (β) 85° 85° Surface tension liquid (γ) 71.8 mN/m 71.8 mN/m Pressure (P) 370 Pa 420 Pa Data acquisition and analysis using ImageJ
Images (offset and aggregate) captured by the camera (exposure time 400 ms) were processed using the public domain software, ImageJ Version 1.44p (Wayne Rasband, National Institute of Mental Health). The exposure time was chosen so as to enable the exploitation of the entire dynamic range of the camera, for all protein concentrations measured. The images needed for the final quantification was an offset image IO(x,y), and an image of the aggregate I(x,y). The offset thus captured the detection chamber, filled with buffer, correctly positioned to the focal length, without influences from the beads or magnet. The captured images comprises of pixels with gray values x,y [0, K-1] where say K=212 for a 12-bit image.
I(x,y) = IF(x,y) + IO(x,y)
IO(x,y) = I(x,y) - IF(x,y)
Where IF(x,y) is the fluorescence purely from the aggregate without offset which we aim to quantify finally. Using the default function in ImageJ, thresholding was performed for the image I(x,y) as:
Mask(I) = K-1 for I(x,y) ≥ ith
0 for I(x,y) < ith
Where ith is the set gray value at which the image is thresholded, 0=black and K-1=white. Thus a white and black mask is created, separating the background which is black from the object in white.
To remove any influences caused by camera noise or diffusion of fluorophore from the previous chamber the two images I(x,y) and IO(x,y) were subtracted as follows:
Icorrect(x,y) = I(x,y) - IO(x,y)
= I(x,y) – (I(x,y) - IF(x,y))
= IF(x,y)
The previously created Mask(x,y) was then subtracted from the corrected image Icorrect(x,y), giving a final image which retained the fluorescence intensities of only the aggregate without the offset and the background being set to black or zero, as given:
Ifinal = Icorrect(x,y) - Mask(x,y)
Finally Ifinal was measured using the ImageJ functions provided Integrated Density and Area. This returned the sum of all gray values of only the selected aggregate corresponding to the fluorescence as the background is set to zero, as well as the area of the aggregate. The signal density was thus given by:
Signal Density = Ifinal / Area of aggregate
This made the signals independent of the area given by the number of beads present thus avoiding variations due to possible loss of beads. The same method was used analysing both the blank and the various concentrations of positive samples. Five parameter curve fit and control measurements
A five parameter-logistic model with weight 1/Y was used to fit the curves using Masterplex 2010, Version 2.0.0.68 (Hitachi Software Engineering Co., 2010)
D f x A B E X 1 C
Where A is lower asymptote (estimated response at zero concentration) and D is the upper asymptote (the estimated response at infinite concentration), B is the slope at the inflection point, C is the mid-range concentration, and parameter E is a compensation factor due to the asymmetric behaviour of the curve and adjusts it.
Calculated parameters:
IL-8
Fig. 5
A 4.58189
B -0.45355
C 5910.01386
D 40558.24153
E 2.80526
Limit of Detection 2,51 pg/mL
Limit of Quantitation 8,82 pg/mL
Dynamic range 2.4 - 2500 pg/mL
Limit of detection and limit of quantification are determined from the Y intercept between the calibration curve and the blank mean + 3 SD and blank mean + 10 SD respectively.