Modeling Math made Easy or at least Easier

Exposure models involve mathematical calculations and that is often a problem for those of us prone to make math errors.  When I first started working with exposure models calculators were plentiful but personal computers were just getting started.    I would run through a series of equations on a calculator and then to check myself I would run it again.   Often I got a different answer!    Clearly I was making simple math errors and just as clearly it was very frustrating.    Enter the IBM Compatible PC and an early programming language, BASICA.   Now I could invest the time in a simple program that could automatically run a long series of calculations and render consistent results.   Once I invested the time to program and check the answer(s), I had it made.

Enter, Lotus 1-2-3 and later Microsoft Excel, now we could do the same thing in a spreadsheet program which was considerably easier.   It also provided some really nice graphing capabilities.    Now we really had it made!   Everyone pretty much knew how to operate a spreadsheet and we could much more easily spread the word about modeling in our classes.

Flash forward a number of years and enter some remarkably talented and dedicated colleagues like Daniel Drolet and Tom Armstrong.    Tom is a very capable modeler and Daniel is a technology artist who is truly gifted in his ability to program model into Visual Basic.    Together with some of our other colleagues they developed IH MOD which is a compilation of inhalation concentration models and modeling tools.    Just about every important model of this type is included in this super spreadsheet.  Input fields are clearly noted and graphics and output columns are built-in.     Most important, it is an evergreen tool which has undergone numerous revisions and will undergo many more in the years to come as it gets better and better.   It is available in multiple languages and it is offered free of charge.   In my opinion it is the single most important tool ever developed in the history of occupational exposure modeling.

There are currently 12 models (modules) in IH MOD.   I am not going to list them all here but will recount some of the most important or most used models, some of which should look familiar if you have been reading this blog:

• Well Mixed Box Model with Constant Emission Rate
• Well Mixed Box Model with Exponentially Decreasing Emission Rate
• Well Mixed Box Model with Backpressure
• Well Mixed  Box with Purging (decay) from ventilation
• The Two Zone Model: Near field Far field Constant Emission Rate
• The Two Zone Model: Near field Far field Decreasing Mass Emission Rate
• Estimating Contaminant Evaporation Emission Rate from small spills

The IH MOD super spreadsheet (along with other tools) is available online for download from a link at: http://www.aiha.org/get-involved/VolunteerGroups/Pages/Exposure-Assessment-Strategies-Committee.aspx

The documentation for all of the models presented in IH MOD is available in the publication:  Mathematical Models for Estimating Occupational Exposure to Chemicals, 2nd Edition
Edited by Charles B. Keil, Catherine E. Simmons, and T. Renee Anthony.   https://webportal.aiha.org/Purchase/ProductDetail.aspx?Product_code=abe7072a-4778-de11-96b0-0050568361fd. 

All of this is for the estimation of airborne concentration for inhalation modeling but there is also another super spreadsheet dedicated to dermal exposure.   Its name is IHSkinPerm which will be the subject of a future blog.

Also covered in future blogs will be the evaporation estimating module mentioned above and the rest of the modules in IHMOD.