## 4 Dpd  
Dissipative particle dynamics method (also called DPD) is a Lagrangian, and coarse-grained mesoscale particle-based hydrodynamic method, in which the domain is represented by a distribution of discrete particles with separated physical properties and each particle consists of a collection of atoms and molecules, that was initially introduced to deal with complex Newtonian fluids and soft matters and is ideal for cell biophysics problems, such as blood flow behavior and blood flow particle interactions [89; 90; 91; 92]. Having a particle-based nature along with being able to reach higher time scales than methods such as MD, make it a relatively valuable and computationally efficient method for microfluidics in terms of accuracy in capturing the details and capability to reach higher time scales [90]. As discussed before, continuum methods have been proved to be applicable for many of the small-scale simulations, however, for some complex problems, there is a need for more microscopic details out of their grasps. There are many cases, where given a large number of particles such as proteins and cells in the computational domain, high computer resources are demanding. In this situation, applications of continuum-based models, where subtle microscopic delicacies and their interactions with the mainstream are ignored, might pose further precision issues. Mesoscale methodscan, thus, be useful for such problems. DPD is clustered under these methods and has proved itself an appropriate method for a variety of problems with significant hydrodynamics details and/or thermal fluctuations. DPM can be easily implemented to the code by just changing the equation used to model the conservative forces among the particles [90]. This method, as discussed, is capable of reaching higher time scales than some other particle-based method such as MD. However, the accuracy of the method depends highly on the time step chosen for simulation, and thus, this can be a tricky part specific to the problem in hand [90]. Original DPD method was, however, too simplistic, for instance in modeling the friction forces, and thus, not appropriate to capture the real physics in detail in many complex problems consisting of different types of particles. To maintain the accuracy of DPD method, one needs to input real values for some physical parameters, such as viscosity, which is case dependent, i.e., one would need to extract real data from experiments conducted on a comparable problem with the same details before using the method to numerically investigate the same problem [90; 91]. Lack of freedom of using different equations of states during the simulation makes the DPD method susceptible to having unrealistic thermodynamic behavior for complex systems, including complex simulations of blood flow and sustaining temperature gradients. In particular, for higher gradients in temperatures, because of lack of energy conservation in the method, unreliable results might be anticipated [90]. Furthermore, this method has yet deficiencies to face to model unbounded particle interactions [90]. There have been many improvements proposed in the literature since the arrival of the original method to make it capable of dealing with more complex fluids and systems and adopting with newly developed models to capture more accurate details in fluid flow simulations. The most important modified versions of this method are many-body DPD (MDPD), energy-conserving DPD (EDPD), fluid particle method (FPM) and finally, smoothed dissipative particle dynamics method (SDPD) and each tackled some of DPD drawbacks. For instance, MDPD introduced an independent equation for temperature distribution and a more general equation of state to ensure having more realistic temperature distribution, EDPD added an extra internal energy value for every particle for non-isothermal cases, and FPM tackled the problem of having too simplistic friction forces in the original method.