# ISD3

The ISD3 software program is an implementation of a particokinetic model (called ISD3) for predicting the combined effects of particle sedimentation, diffusion, and dissolution on cellular dosimetry for in vitro systems

ISD3 is an extension to ISDD to describe the influence of dissolution on the cellular dosimetry of soluble nanoparticles such as silver. ISD3 stands for In vitro Sedimentation, Diffusion, Dissolution, and Dosimetry. Compared to ISDD, the ISD3 model is based on the population balance equation (PBE) that allows for simultaneous tracking of changes in both the number and size of particles in the liquid media, by solving for the number density of particles as a function of size and spatial location. From the number density, all other quantities, such as mass, concentration, size distribution and surface areas are derived.

For the ISD3 model, the initial size distribution data can be fitted to a continuous function and then numerically discretized on to the simulation grid points when being represented by the number density. Therefore, any initial size distribution data can be represented in terms of the number density. As a result, time-dependent solutions can be obtained for all size ranges in a single run of the ISD3 simulation for a given system; which is irrespective of whether the dissolution effects are present or not. Whereas in ISDD, independent calculations have to be performed for each size class, and the results from the independent runs have to be consolidated to determine the total amount of cell-associated particles at any instant of time. Thus, ISD3 can also be used to model polydispersity. If dissolution effects are not important for the system of interest, then it is recommended to use the ISDD model. If it is easier to just represent the whole initial size distribution data and run the simulation once, then the ISD3 would be a suitable approach. However, compared to ISDD, the ISD3 MATLAB simulations take longer to run, and the simulation time increases with the particle size range in the system and the number of mesh grid points used for the particle size dimension.

The current implementation uses dissolution and cellular ion uptake models parameterized with data for silver nanoparticles and ions in fetal bovine serum (FBS). The parameters of silver particles and ions may not be transferrable to particles of other material types; and therefore, the kinetic models will need to be re-fitted using the experimental data that is unique to each material. The ISD3 code is modular; therefore, the current empirical equations for dissolution and ion uptake kinetics can be replaced with those appropriate for particles other than silver.