Three-part differential of unlabeled leukocytes with a compact lens-free imaging flow cytometer Supplementary Information

A compelling clinical need exists for inexpensive, portable haematology analyzers that can be utilized at the point-of-care in emergency settings or in resource-limited settings. Development of a label-free, microfluidic blood analysis platform is the first step towards such a miniaturized, cost-effective system. Here we assemble a compact lens-free in-line holographic microscope and employ it to image blood cells flowing in a microfluidic chip, using a high-speed camera and stroboscopic illumination. Numerical reconstruction of the captured holograms allows classification of unlabeled leukocytes into three main subtypes: lymphocytes, monocytes and granulocytes. A scale-space recognition analysis to evaluate cellular size and internal complexity is also developed and used to build a 3-part leukocyte differential. The lens-free image-based classification is compared to the 3-part white blood cell differential generated by using a conventional analyzer on the same blood sample and is found to be in good agreement with it.

Figure S1a depicts a raw hologram taken with the high speed camera of a cell flowing under the pinhole.Figure S1b is captured under the same conditions, but as it does not contain a cell, it consequently serves as background.Note that a faint vertical line runs through the both images.This corresponds to the laminar flow generated by the central hydrodynamic focusing channel which delivers the blood cells, and is triggered by a small difference between the refractive index of sample-containing medium and the focusing medium.All cells follow this line, as is depicted in Figure S1a.Prior to reconstruction, the background is subtracted and the image is normalized.The normalization is done by dividing the background-subtracted image by the value of the background at the maximum of the hologram.The normalized image is subsequently cropped around the central maxima of the fringe pattern to form a 1024 by 1024 pixel image, as shown in Figure S1c.The hologram is then diffracted back to the channel plane by using the spectral algorithm approach: with H, the captured hologram, d, the reconstruction depth and m and n the spatial frequencies.The reconstruction depth for this geometry is a combination of the distance from the camera to the pinhole, Zcc, and the distance from Supplementary Information the camera to the sample, Zco,: The amplitude and phase of the reconstruction are shown in Figures S1d and S1e.The cell is clearly detectable in both images although the concomitant presence of the virtual image diminishes their clarity.This extra fringe pattern can be observed in the background of the amplitude image (Figure S1d) and in the background of Figure S1e as a phase well.There are multiple methods describing virtual image removal, but they often require multiple reconstruction steps moving back and forth between the hologram, image and virtual image plane, which tends to slow down the reconstruction algorithm.It should be noted that the virtual image is not a major concern when a single small object is being imaged, since in the absence of neighbouring objects no high frequency fringes will overlap with the object.This is almost always the case in our system, since there are no cells present in the focusing medium in the left and right channels, and since the cell concentration is low enough so that there is typically only one cell passing at a time.
To roughly remove the virtual image, a 2D fourth order polynomial is fitted based on points outside the cell of the 2D cross-section as indicated in Figures S1d and S1e.This is done for the amplitude as well as the phase.Figures S1f and S1g depict the amplitude and phase on the blue cross-section.The dashed green lines represent the points used for the fit, and they lie outside the cell border indicated by the vertical dashed black line and arrows.The red curve is the fitted on a fourth order polynomial.The difference between the reconstruction and the fit for the amplitude and phase is shown in Figures S1h and S1g, respectively.Since the fit only applies to the region within the green boundaries, only this section shown in these images.
Starting from Figure S1h, the axes are labeled in micrometers.In order to correctly measure distances in the reconstruction, the system needs to be calibrated.Several images of the central microfluidic focusing channel are acquired at different pinhole heights.Based on the known width of this channel, the size of the pixel pitch in the reconstruction is linked to the reconstruction dept.A linear fit through these points is used to find the reconstruction pixel pitch once the reconstruction depth of the cell is known.Finally, a scale space analysis is applied to locate the cell edge and estimate its internal complexity.In a scale-space analysis the analyzed image is typically smoothed by a Gaussian prior to applying a recognition operator.The standard deviation of the Gaussian is a measure of the smoothing and determines the size of the detected features in the image.It is therefore also called the scale parameter.The operator applied to find edges is the second local derivative.The zero-crossing of this derivative is considered an edge.Since we are only interested in the zero-crossings, this condition can be simplified to an expression which only contains partial derivatives in the xy-system: 2 with L x and L xx , the first and second partial derivative in the x-direction, with L y L yy , the first and second partial derivative in the y-direction, and with L xy , the partial derivative in x-and y-direction.In order to find the cell edge this method is applied on the phase image.The detected edges can be visualized in green and red in Figure S1k.The scale parameter applied here is 5µm, since the target structure, a cell, is large.The average intensity over each edge is subsequently calculated.The edge with a average diameter between 5 and 11 µm with the lowest value is labeled the cell edge.The diameter of a circle fitted through this edge is the cell diameter.For the internal complexity, the ridges inside the cell edge need to be detected.A ridge is defined as a zero-crossing in a first-order local derivative.This condition can be formulated as follows: with L q and L qq , the first and second local derivative in the local q-direction, with L pp second local derivative in the p-direction and with the pq-system the local coordinate system as defined in ref 2. The ridges detected in the intensity images are depicted in green and blue in Figure S1j.The internal complexity is only evaluated inside the cell edge (green).Once identified, the internal complexity is evaluated by the contrast of the internal edges which is gauged by the average of the Laplacian on the edge.

Computation time
The presented analysis was performed with a series of MATLAB scripts, dividing the total analysis in 3 separate parts: checking an image for presence of a cell in its center, reconstructing the hologram, and a scale space analysis to measure cell size and internal complexity.This MATLAB implementation contains some redundancy, saving and plotting many of the intermediate results causing the analysis on a set of 12000 images to take over an hour.A short study of this algorithm was performed in order to evaluate the required analysis time to process one 12000 image set on an Intel(R) Core(TM) i7 920 at 2.67GHz (=quad core with HyperThreading).A concise version of the algorithm based on open source code from [3] and [4] was used for this exercise.In the table below the execution times as well as analysis frames per second (fps) are shown for each part.For the first part, checking the images for, presence of cells, the values are given with and without taking the image load kernel into account.This is done since in a more integrated solution the images might immediately go to analysis hardware and avoid a file system.After the cell check, we assume that about 14% of the images contained a cell, which agrees with what was observed in the experiments.We subsequently ran the reconstruction and scale space analysis on this 14%.When summing up all the execution times, the 12000 images can be analysed in approximately 10 min or 5.9 min without accounting for the image load kernel.Most of this analysis time is taken up by the cell check, since it has to go through all the images, and the reconstructions, since it uses ffts on 1024x1024 images.The scale space analysis requires much less time because it is executed on a much smaller image, the 200x200 center of the reconstruction, where the cell is located.

FIGURE S 1 :
FIGURE S 1: Hologram analysis: (a) hologram of in-flow cell, (b) background, (c) cropped normalized hologram with background subtraction, (d) amplitude of the reconstructed hologram, (e) phase of the reconstruction, (f) crosssection of the amplitude(blue) and the estimated fit of the virtual image(red) based on the green curves, (g) cross section of the phase and the estimated fit of the virtual image, (h) amplitude image with virtual image subtraction, (i) phase with virtual image subtraction, (j) amplitude image with detected ridges and the cell edge in red, (k) phase image with detected edges.