Cell-morphodynamic phenotype classification with application to cancer metastasis using cell magnetorotation and machine-learning

We define cell morphodynamics as the cell’s time dependent morphology. It could be called the cell’s shape shifting ability. To measure it we use a biomarker free, dynamic histology method, which is based on multiplexed Cell Magneto-Rotation and Machine Learning. We note that standard studies looking at cells immobilized on microscope slides cannot reveal their shape shifting, no more than pinned butterfly collections can reveal their flight patterns. Using cell magnetorotation, with the aid of cell embedded magnetic nanoparticles, our method allows each cell to move freely in 3 dimensions, with a rapid following of cell deformations in all 3-dimensions, so as to identify and classify a cell by its dynamic morphology. Using object recognition and machine learning algorithms, we continuously measure the real-time shape dynamics of each cell, where from we successfully resolve the inherent broad heterogeneity of the morphological phenotypes found in a given cancer cell population. In three illustrative experiments we have achieved clustering, differentiation, and identification of cells from (A) two distinct cell lines, (B) cells having gone through the epithelial-to-mesenchymal transition, and (C) cells differing only by their motility. This microfluidic method may enable a fast screening and identification of invasive cells, e.g., metastatic cancer cells, even in the absence of biomarkers, thus providing a rapid diagnostics and assessment protocol for effective personalized cancer therapy.

(pg/cell). Error (±) represents the standard deviation of the 4 samples values in the set. The control sample (no Fe NP added) did not have a detectable Fe instrument signal under either dilution condition, indicating that the Fe detected in the ICP-MS was purely from the Fe MNP. Experimental Set-up and Image Acquisition S2 Fig below shows a cartoon schematic of the experimental set-up. Prior to loading, the microfluidic device is hot glued to a Petri dish. Once the cells have been loaded, the dish is placed on a motorized microscope stage. The Petri dish is then filled with water, which acts as a warm bath to keep the cells in the microfluidic device at 37 • C. A thermometer reads the temperature of the microfluidic device's inlet port in real time. Both the Petri dish cap and the motorized stage are equipped with strip heaters, which allow us to actively monitor and maintain temperature. The microfluidic device, Petri dish, and thermometer cable are all covered by a transparent box that ensures that the humidity of the sample is maintained.
Sitting on this box are four solenoids with iron cores. The current running through each solenoid comes from two function generators (Agilent 33220A) outputting sinusoidal currents with a frequency of 15Hz. The phase of these two wave currents is offset by 90 • . Both currents pass through an amplifier (Europower EP4000) before going directly to the solenoids themselves. This set-up provides, at the position of the microfluidic device, an oscillating magnetic field with an amplitude of 1mT.
Acquisition of cell images is a fully automated process. Once the microfluidic device is appropriately positioned on stage, we look for a position in the microfluidic device where a high percentage of the microwells contain single cells in the field of view. From 10 to 16 similar areas are then found, and the x, y, and z coordinates of these positions recorded so that the motorized stage can cycle between them automatically. When no images are being taken, a shutter blocks incident light from the microfluidic device to reduce phototoxicity. When images are being taken, the shutter opens for 700ms, allowing us to capture an image of the cells. At each position, an image is taken once every minute for an hour, though we note that our refined decision functions required data from only a single time point.

Viability Test
Cells were stained with Propidium Iodide at times 0 and 60 mins, so as to assess cell viability and cell survival rate during the experiment. In the control test, cells were kept in an incubator after loading in the single-cell trapping device.

Image Processing
After images are gathered, individual cells are cropped to allow CellProfiler to quantify information about each given cell. Here, an exemplary images of MDA-MB-231 cells are provided in the first and third rows, while the morphological delineation found by CellProfiler is given in the second and fourth rows. Scale bar represents 20µm. The one cell depicted here is representative of the cells tested. Initially, this cell is rounded, but as time passes it begins to explore it shapes space and reveals itself to be of a motile phenotype. Using our approach, cells that would be difficult to impossible to classify by eye are easily sorted by the computer.

Feature Generation -Geometric Features
After the cell object in each image has been delineated, we use CellProfiler to measure a variety of parameters in each cell image, which can be broadly broken down into three categories: geometric features, radial features, and texture related features. The geometric features are the easiest to interpret, and include things such as cell area, form factor, orientation, Euler number, extent, eccentricity, axes lengths, and compactness. A complete list with appropriate definitions is found below in S1 Table. Measurements refer or pertain to the cell object. S1 Table. Geometric features measured by CellProfiler. Measurements refer or pertain to the cell object.

Feature Generation -Radial Features
The radial features, better known as Zernike moments, are calculated by superimposing a unit disk onto the object of interest, with the unit disk sharing the object's center. All of the coordinates inside the object are converted to polar coordinates, with any coordinate outside of the unit disk (r=1) discarded. The largest disc fitting inside the object is used to calculate the Zernike moments, which are defined below with m and n being two integers and I(x,y) being the intensity of the pixel at the (x,y) coordinate. For the cases where n subtracted from m is even, we have: and If n subtracted from m is odd, the polynomial Rmn becomes 0. In this work, only the first 10 Zernike moments were measured. A table listing the selected values for 'm' and 'n' is found below. Table. A list of values taken by the parameters 'm' and 'n' during the calculation of Zernike moments.

S2
To measure radial distributions, the region of interest is split into n concentric circular bins (8 bins were used in this analysis), the center of each bin being the center of the object. FractAtD is the fraction of total stain of the object within a given bin. MeanFrac is the mean fractional intensity at a given radius, and finally, RadialCV is the coefficient of variation of intensity within a ring.

Feature Generation -Texture Features
The final set of features we measured pertain to texture, and are commonly known as Haralick features. To understand how these features are calculated, we must first introduce the gray-level co-occurrence matrix, G. This matrix is a square matrix of dimension N, where N is the number of values in a grayscale image. Each element G(I,j) is defined as the probability that a pixel of value I is adjacent to a pixel of value j. Pixels in diagonal directions are also considered to be adjacent pixels. G =      p(1, 1) p ( 1, 2) · · · p ( 1, N ) p ( 2, 1) p ( 2, 2) · · · p ( 2, N ) . . . . . . . . . . . .
Once the coefficients of the co-occurrence matrix are known, a number of additional features may be calculated.
Angular Second Moment: i j p(i, j) 2