Cell nanoparticle dynamics within blood
To go the PBPK route:

I would recommend using the organism parameters and structure from the whole body platform model by Shah and Betts.


Shah, D.K. &amp; Betts, A.M. J Pharmacokinet Pharmacodyn (2012) 39: 67. doi:10.1007/s10928-011-9232-2


They have assigned a plasma space volume, plasma flow, blood cell space volume and blood cell flow for each organ and the total body.  The base model structure for circulation is complete if you use the equations for the blood cell space in this paper as the foundation (Eq 2 and Eq 5). 

Once the model structure is complete, step 2 is to model all processes that can affect the cell in each compartment.  If the cell is adhering to a nanoparticle, a compartment equation could then be:

d[cell]/dt = (flow in - flow out)/volume + Kon x [nano] x [cell] - Koff x [cell-nano complex]

To model the interaction of the cell with the nanoparticle you will need to model both within the same structure.  A review of PBPK modelling for nanoparticles can be found here:


Physiologically Based Pharmacokinetic Modeling of Nanoparticles
Mingguang Li, Khuloud T. Al-Jamal, Kostas Kostarelos, and Joshua Reineke
ACS Nano 2010 4 (11), 6303-6317 doi: 10.1021/nn1018818


A pharmacokinetic (top-down, classical) model for nanoparticles in the circulatory system may also give insight to how to model the processes that affect nanoparticles in vivo.  This model accounts for fluid dynamics, pore size and specific nanoparticle properties.


Kirtane, A. R., Siegel, R. A. and Panyam, J. (2015), A Pharmacokinetic Model for Quantifying the Effect of Vascular Permeability on the Choice of Drug Carrier: A Framework for Personalized Nanomedicine. J. Pharm. Sci., 104: 1174–1186. doi:10.1002/jps.24302