We solve a design optimization problem for deterministic lateral displacement (DLD) device to sort same-size biological cells by their deformability, in particular to sort red blood cells (RBCs) by their viscosity contrast between the fluid in the interior and the exterior of the cells. A DLD device optimized for efficient cell sorting enables rapid medical diagnoses of several diseases such as malaria since infected cells are stiffer than their healthy counterparts. The device consists of pillar arrays in which pillar rows are tilted and hence are not orthogonal to the columns. This arrangement leads cells to have different final vertical displacements depending on their deformability, therefore, it vertically separates the cells. Pillar cross section, tilt angle of the pillar rows and center-to-center distances between pillars define a unique device. For a given pair of viscosity contrast values of the cells we seek optimal DLD designs by fixing the tilt angle and the center-to-center distances. So the only design parameter is the pillar cross section which we parameterize with uniform 5th order B-splines. We propose an objective function to try to capture efficient cell sorting. The objective function is evaluated by simulating the cell flows through a device using our 2D model based on a boundary integral method ( Journal of Computational Physics, 357:43-77, 2018). We solve the optimization problem using the covariance matrix adaptation evolution strategy (CMA-ES), which is a stochastic, derivative-free algorithm. We present several scenarios where solving the optimization problem finds designs that can separate cells with similar viscosity contrast values. To the best of our knowledge, this is the first study which poses designing a DLD device as a constrained optimization problem and shows that solving this problem systematically discovers optimal designs.
We study deformability-based sorting of same-size RBCs via DLD using an in-house integral equation solver. Our goal is to quantitatively characterize the physical mechanisms that enable the cell separation. To this end, we systematically investigate the effects of the interior fluid viscosity and membrane elasticity of a cell on its behavior. In particular, we consider deep devices in which a cell can show rich dynamics such as taking a particular angular orientation depending on its mechanical property. We have found out that cells moving with a sufficiently high positive inclination angle with respect to the flow direction displace laterally while those with smaller angles travel with the flow streamlines. Thereby, deformability-based cell sorting is possible. The underlying mechanism here is cell migration due to the cell's positive inclination and the shear gradient. The higher the inclination is, the farther the cell can travel laterally. We also assess the efficiency of the technique for dense suspensions. It turns out that most of the cells in dense suspensions does not displace in the lateral direction no matter what their deformability is. As a result, separating cells using a DLD device becomes harder.