## 4 Practical Implementation: Identification and Separation of Leukemic Cells from Healthy Ones
### The DMP Model  
Figure 6 shows the (two-dimensional) domain used in the simulations. The lattice spring model (LSM), which models the mechanical properties of solid material by means of linear bonds and angular springs, is used for both the cilia and the cell. In this study, all bonds are rigid (i.e., inextensible) with fixed distance \(\Delta r\) = 2 \(\upmu\)m, while the force \(F\) generated by an angular spring that connects three consecutive particles is given by the gradient of the potential  
\[U_{a}=\frac{1}{2}k(\theta-\theta_{0})^{2}, \tag{1}\]  
where \(k\) is the stiffness of the spring, \(\theta_{0}\) the equilibrium angle at rest, and \(\theta\) the angle after deformation. In a real microfluidic application, liquid would flow into the device and convey the cells by means of drag forces. To simplify the model, liquid is not directly considered in this work, and the effect of drag is accounted for by [PERSON] law  
\[F_{v}=3\pi\mu dv, \tag{2}\]  
where \(\mu\) is the dynamic viscosity, \(d\) the radius of the cell and \(v\) the flow velocity relative to the object. This force is distributed among all the computational particles that compose the cell. A body force is applied to the cell (\(a\) = 4 \(\times\) 10\({}^{-3}\) m\(\cdot\)s\({}^{-2}\)) to move it along the channel with velocities typical of microfluidic channels (\(\sim\)1 mm s\({}^{-1}\) without cilia). Non-penetration among computational particles is achieved by a soft repulsive potential of the type  
\[E=A\Big{(}1+\cos\frac{\pi r}{r_{c}}\Big{)}\quad(r<r_{c}), \tag{3}\]  
Figure 6: The concept of the proposed microfluidic separator.  
where \(r\) is the distance between the two particles, \(r_{c}\) is a cut-off distance and \(A\) is an energy constant. In the simulation, the same repulsion force and cut-off (\(A=4\times 10^{-5}\) J, \(r_{c}=2\) um) are used for all particles.  
Different types of computational particles are used to represent the system. A schematic representation is shown in Figure 7. Type-1 (red) particles represent the wall and are stationary during the simulation.  
Type-2 (blue) particles represent the cilia and are connected by rigid bonds and angular springs with \(k=2.5\times 10^{-14}\) J and \(\theta_{0}=180^{\circ}\). Type-3 (white) particles represent the cell membrane and are connected with rigid bonds and angular springs with \(k\) variables (depending on the cell population) and \(\theta_{0}=172^{\circ}\); the cytoplasm is neglected and all its mechanical properties are attributed to the membrane. Type-4 (yellow) particles represent the root of the cilium. They are connected with rigid bonds and angular springs similar to type-2 particles. These are the particles where the stress caused by the bending of the cilia is measured. Type-4 particles are, therefore, anchored to their initial position by means of a self-tethered linear bond  
\[F_{s}=k_{s}r, \tag{4}\]  
where \(k_{s}=0.01\) N m\({}^{-1}\) is the stiffness of the bond, and \(r\) is the distance between the actual position of the particle and its initial position. The force \(F_{s}\) generated by this bond is recorded during the simulation and is used to train the ANN. There is also a type-5 particle, which is used for the gates in Figure 6, but is not represented in Figure 7. Type-5 particles are interconnected with rigid bonds and angles. They are also connected with the closest wall particles with an angular spring. This spring can be switched on and off to allow for the opening of the gate according to the output of the ANN. Overall, in the model there are 776 particles of type-1, 154 particles of type-2, 44 particles of type-3, 47 particles of type-4 and 48 particles of type-5.