Optimal design of deterministic lateral displacement device for cell sorting

We solve a design optimization problem for deterministic lateral displacement (DLD) device to efficiently sort same-size red blood cells by their deformability. Such optimal designs enable rapid medical diagnoses of several diseases such as malaria since infected cells are stiffer than their healthy counterparts. DLD device consists of pillar arrays in which pillar rows are tilted and hence are not orthogonal to the columns. This arrangement separates cells laterally depending on their deformability. 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 cells with different deformability we seek optimal DLD designs. We fix all the parameters except the pillar cross section which we parameterize with uniform 5th order B-splines. We propose an objective function to capture efficient cell sorting. The objective function is evaluated by simulating the cell flows through a DLD using our 2D model based on a boundary integral method. We solve the optimization problem using a stochastic, derivative-free algorithm. We present several scenarios where the optimal designs can sort cells with slightly different deformability. These designs have cross sections that have features similar to a triangle.