I am trying to mathematically model the dynamics of a particular cell in circulation and its binding to another nanoparticle that is intravenously injected. The concentration of this cell is very low (about 5 cells per mL of blood). I want to see how many nanoparticles are needed to bind to as many of these rare cells as possible.
So first, I am trying to model the cell dynamics in the blood flow. I am not sure how to start. I wanted to model the cell movement through the entire cardiovascular system, but I would have to simplify it. I am thinking of modeling the blood flow through some of the major organ systems, and estimating the absorption through the capillaries. I am thinking something like the physiologically-based pharmacokinetic model (PBPK). However, there would be some parameters that I wouldn't know about that I would need for the model (at least that is what I think, I am new to pharmacokinetics) Also for the actual fluid dynamics, I'm not sure how to model this, because the blood isn't just a fluid, and has many other cells, so I don't know if there are some other effects.
So, my question is, in what direction should I go to model the dynamics of this cell in circulation? I want to model the circulation in the entire cardiovascular system, because I need to also model the other nanoparticle dynamics, and how likely it is to find and bind to some of the receptors on the cell. Is there an example of a similar model that has been done?