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 refer the reader to @cite_17 for the review of related work on deformability-based cell sorting and the details of our numerical scheme for cell flow simulations. Here, we review the literature on DLD designs.
@cite_17
2809308122 1992413315 2133774049 2106248527
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. We study the scaling limits of three different aggregation models on ℤd: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, all three models are found to have the same scaling limit, which we describe as the solution to a certain PDE free boundary problem in ℝd. In particular, internal DLA has a deterministic scaling limit. We find that the scaling limits are quadrature domains, which have arisen independently in many fields such as potential theory and fluid dynamics. Our results apply both to the case of multiple point sources and to the Diaconis-Fulton smash sum of domains. This review introduces a novel deformable image registration paradigm that exploits Markov random field formulation and powerful discrete optimization algorithms. We express deformable registration as a minimal cost graph problem, where nodes correspond to the deformation grid, a node's connectivity corresponds to regularization constraints, and labels correspond to 3D deformations. To cope with both iconic and geometric (landmark-based) registration, we introduce two graphical models, one for each subproblem. The two graphs share interconnected variables, leading to a modular, powerful, and flexible formulation that can account for arbitrary image-matching criteria, various local deformation models, and regularization constraints. To cope with the corresponding optimization problem, we adopt two optimization strategies: a computationally efficient one and a tight relaxation alternative. Promising results demonstrate the potential of this approach. Discrete methods are an important new trend in medical im... In this paper, we show how to train a deformable part model (DPM) fast-typically in less than 20 minutes, or four times faster than the current fastest method-while maintaining high average precision on the PASCAL VOC datasets. At the core of our approach is "latent LDA," a novel generalization of linear discriminant analysis for learning latent variable models. Unlike latent SVM, latent LDA uses efficient closed-form updates and does not require an expensive search for hard negative examples. Our approach also acts as a springboard for a detailed experimental study of DPM training. We isolate and quantify the impact of key training factors for the first time (e.g., How important are discriminative SVM filters? How important is joint parameter estimation? How many negative images are needed for training?). Our findings yield useful insights for researchers working with Markov random fields and part-based models, and have practical implications for speeding up tasks such as model selection.