## What is Modeling and Simulation?

I am currently attending a short conference on modeling and simulation in pediatric clinical pharmacology, and I noticed that many people in the conference don’t have a good grasp on what “Modeling and Simulation” means. I think most of them think that it is an extremely complicated mathematical concoction that is intended to keep everyone confused and in awe of the speaker that is presenting. They couldn’t be further from the truth. But, first, let’s talk about saving money.

Imagine you are given \$1,000 from a relative. You would like to use that money to “make some money”, so you put it into an investment that is guaranteed to make 8% growth annually. If you left that money there for 20 years, how much money would you have?

To solve this problem, you need to know what the future value of the principle given the 8% annual growth, compounded monthly for 20 years. There is an equation for that: $FV=PV*(1+i)^t$ Equation 1 $PV=\char36 1,000\;\;\;i=\frac {0.08}{12} = 0.00667\;\;\;t=20*12=240$ $FV=\char36 1,000*(1+0.00667)^{240} = \char36 4,930.72$ Equation 2

So after 20 years, you have almost 5 times as much money as you were given. The method we just worked through to determine how much we would have in the future can be thought of as modeling and simulation. Equation 1 is the model, and Equation 2 is the simulation.

I think I just heard you say, “What! It can’t be that simple! No way!”Well, it is true, the estimation of future savings is nothing more than a simulation of a known financial model for compounding interest.

Now we can convert this into the pharmaceutical world. A model is a set of mathematical equations that describe observations. In some cases the observations are plasma concentrations, in other cases it is intraocular pressure, or enzyme inhibition. The “parameters” of the model are derived from the observations. (In Equation 1, the parameters are PV, i and t.)

A simulation is when you use a model to predict something. Instead of estimating parameters from observed data, you take the model, and a set of parameters to simulate some data. As we did in Equation 2, we set PV, i and t to specific values for the desired situation, then we calculated FV. Or, in other words, we simulated FV given a set of parameters.

So, when you hear about modeling and simulation, just think about your bank savings account and remember that you and your bank do modeling and simulation every month.

The use of modeling and simulation (M&S) in drug development has evolved from being a research nicety to a regulatory necessity. Today, modeling and simulation is leveraged to some extent, across most development programs to understand and optimize key decisions related to safety, efficacy, dosing, special populations, and others.

Read our white paper to learn about the many benefits of M&S across a drug development program. 