Supervised discriminant analysis for droplet micro-magnetofluidics

We apply the technique of supervised discriminant analysis (SDA) for in-flow detection in droplet-based magnetofluidics. Based on the SDA, we successfully discriminate bivariant droplets of different volumes containing different encapsulated magnetic content produced by a GMR-based lab-on-chip platform. We demonstrate that the accuracy of discrimination is superior when the correlation of variables for data training is included to the case when the spatial distribution of variables is considered. Droplets produced with differences in ferrofluid concentration of 2.5 mg/ml and volume of 200 pl have been identified with high accuracy (98 %), indicating the significance of SDA for e.g. the discrimination in magnetic immuno-agglutination assays. Furthermore, the results open the way for the development of a unique magnetofluidic platform for future applications in multiplexed droplet-based barcoding assays and screening. Electronic supplementary material The online version of this article (doi:10.1007/s10404-015-1579-z) contains supplementary material, which is available to authorized users.


Fig. S1
Full range GMR curve of the spin valve sensor patterned into a size of 6 (width) x 100 (length) µm² (inset) which is integrated to the microfluidic channel. The pinning direction is along the short axis of the stripe.

Description of the algorithm of supervised discriminant analysis (SDA)
The principle of supervised discriminant analysis is to allocate unknown detection events into known classified groups. Prior training data (reference groups) should be used to maximize the differences between each reference group to which single detection events will be allocated. Two approaches have been used to compare the quality of analysis.

Approach A:
For the training of the data, the reference droplet group k is fitting to a 2D gauss function. A gauss function characterizing this group can be expressed as: here A is the amplitude; x, y is the parameters for the analysis, i.e. signal amplitude and peak width, respectively; x 0 , y 0 is the center of gauss function; and is the x and y spreads of the function.
The posterior probability q X k of a droplet detection event X belonging to a reference group k is calculated by:

Approach B:
The within-group covariance matrix of each group characterizes the group and is used to evaluate the Mahalanobis distance between each detection event within the group. the posterior probability of an unknown detection event from the measured sample can be evaluated based on the Mahalanobis distance of the detection event from each reference group and the covariance matrix of each reference group.
The within-group covariance matrix ∑ of a droplet group k is defined as [1]: with ∑ (i, j = 1, 2) the covariance of the ith-variable x i and jth-variables x j , and E(x i , x j ) the expectation of the product of variables x i and x j , x i and x j being the mean values of the variable x i and x j in the droplet group, respectively.
For our present analysis, the variables x i and x j are the signal amplitude and the peak width of the detection events of droplets measured by a GMR sensor.
The Mahalanobis distance D is used to measure the distance of a detection event of a droplet X=(x i , x j ) from the distribution of the detection events in a droplet group k. It is given by [2]: Here X is the mean value of the distribution of the droplet events in the droplet group k, ∑ is the inverse of the covariance matrix of the group k.
The posterior probability q Xk of a detection event X belonging to a reference droplet group k can be obtained based on the covariance matrix ∑ and the Mahalanobis distance D by the following expression: [3] log q Xk =- Here π k is the prior probability of observing the droplet event in the droplet group k, c 0 is used to normalize the posterior probability of all detection events. As indicated, a larger distance of a detection event from the reference group and a broader spread of the detection events in the reference droplet group lead to a lower probability of observing the detection event in the corresponding reference group.
To perform the discrimination, the posterior probability of each droplet is computed for every reference group and those posterior probabilities are compared with each other to allocate the droplet to the reference group which provides the largest posterior probability. 4. After the background minimization, the differential voltage signal from the Wheatstone bridge is fed into the differential input of the lock-in, which is modulated with an internal reference signal of lock-in (SRS-830)

Description of real time in-flow measurements of droplets
analog output ac source differential input the lock-in. With the modulation of the lock-in, the signal to noise ratio can be enhanced.
5. An external permanent magnet (AlNiCo 500, A1560, IBSMagnet) is placed below the sensor to bias the sensor and magnetize the ferrofluids. To correctly bias the sensor to the most sensitive region, the ferrofluid droplets are produced in the fluidic channel and passed across the sensor. The signal output from the droplets is monitored together with the careful adjustments of the position of the magnet until the maximum signal amplitude is achieved.
6. The analog output from the lock-in is sampled by a data acquisition box (NI USB 6009) and a computer program is made to control the settings of the real time measurements.

Protocol of the fabrication of GMR sensors
We describe two major steps to fabricate GMR sensors: (A) Substrate preparation (B) Magnetron sputtering deposition.

A. Substrate preparation
1. Choose thermally oxidized silicon wafers with 600 nm oxide (CrysTec GmbH) as the substrates.
The oxide layer should be sufficiently thick to prevent any current shunting through the bottom substrate during electrical measurements.
2. Clean the wafers with acetone in an ultrasonic bath and afterwards with isopropanol to remove any contaminants on the surface to ensure the quality of subsequent photolithography process. Rinse the wafers with DI water and bake at 120 °C for 5 min to dehydrate to be ready for lithography.
3. Place the wafer on to a spin coater and apply the photoresist (AZ 5124E). Set the spin coating speed at 4500 rpm and spin the resist for 30s.

Soft bake:
Transfer the photoresist-coated wafer to a hot plate at 90 °C for 4 min. 5. Exposure: Transfer the wafer to a mask aligner (MJB4, Karl Suss). Use a desired photomask with a designed sensor geometry (i.e. stripe). Expose the wafer for 2 s to initiate the photoactive compound.
6. Post bake: After exposure, place the wafer on a hot plate at 120 °C for 2 min. This step activates a cross-linking agent. Together with the exposed photoactive compound, the exposed area is insoluble in the developer. 2. Until the base pressure is suitable for deposition, fill the chamber with Ar (as the sputter gas). The sputter pressure is about 9.4 x 10 -4 mbar and a flow rate of 10 sccm which can be controlled by a flow and pressure controller. Presputter each target for 5 min to remove any contaminants on the target. When depositing each layer, the wafer is transferred under a specific target and a pressureactuated shutter is used to control precisely the deposition time and the final layer thickness. The whole deposition process is of full automation which is remotely controlled via a computer program.
3. After the deposition, take out the sample from the chamber for lift-off.

Lift-off process
1. Immerse the wafer with deposited GMR sensors in the acetone (depending on the residual resist on the wafer, the whole lift-off time varies from 1 to several hours; optionally ultrasonic bath can be used to assist the lift-off) to dissolve the photoresist to reveal the GMR sensors with a desired shape.
2. Rinse the wafer with isopropanol and dry it by compressed air.
Afterwards, a second lithography step is used to pattern electrical contacts for the GMR stack. This process is the same as described in Step A, except that to pattern the contacts, a different photomask with a designed geometry of electrical contacts is used. The pattern of contacts should be precisely aligned with the previous deposited GMR stack before exposure with the mask aligner. When a second lithography step is finished, the sample is again brought to the magnetron sputtering machine to deposite the contacts. In this case, Ta (5 nm) /Cu (200 nm) /Ta (5 nm) is used as the material.