A Simple Exposure Modeling Example as a way of Getting Started

One of the really nice things about doing a blog is the connection with colleagues.  As a prime example, I received the following note from Dr. Gurumurthy Ramachandran (Ram) about last week’s blog. 

“You hit the nail on the head when you said that all hygienists need to become explicit modelers, not subliminal ones.  Just the process of thinking about each input parameter to even a simple model will lead to a much better understanding of the workplace and the limitations in that understanding. I remember reading somewhere that these two elements correspond to knowledge and self-knowledge.”

Ram is a brilliant teacher and researcher at the University of Minnesota so I consider these words to be very heartening. Indeed they, along with the other comments I received last week, are enough to encourage me to hopefully provide more insight this week to newbies into the modeling process. 

  

The basic elements of all inhalation models are relatively simple.  In every case, you have a volume of air and a rate of contaminant input to that volume.  The model is simply using these elements to predict the concentration in the air that might be inhaled by a worker. 

The model I am going to discuss this week is one of the simplest but still very useful; namely, the well mixed box model at equilibrium.   Any room (or box of air) which is receiving a steady inflow of contaminant will reach a steady (or equilibrium) concentration of contaminant as the amount of contaminant that is put into the room is balanced with the amount that is leaving via ventilation removal.  All volumes or spaces in which we exist have some fresh air ventilation – even our well-insulated homes in winter exchange air with the outside via infiltration/ex-filtration through cracks and other openings.   This exchange typically occurs in the range of 30 to 60% per hour in the rooms of homes and is often well above 100-300% in industrial rooms.

At equilibrium the airborne concentration (C) in the box (room) is equal to the generation or emission rate (G) of contaminant into the box divided by the ventilation rate (Q).                 C = G/Q    G = wt/time.    Q = volume/time     C = wt/volume.   Pretty simple uh?

So how does one estimate G?   Let’s consider an example of a small (20m³) bedroom in which someone is painting with a water-based paint that has 0.5% ethylene glycol (EG) as a drying agent.  If they use 4,000 gram (4,000,000 mg) of paint, that is 20 grams (20,000 mg) of EG.   If it is assumed to take 8 hr to dry and that all of the EG comes out that is an average of 2,500 mg of EG being emitted into the room air per hour.   There are quite a few ways of estimating G and I can go over these in future blogs.

Estimating Q:  The 20m³ room with 60% ventilation/hr is (20 m3)(0.6/hr) = Q = 12 m³/hr.   There are a number of ways of getting a Q which could also be a topic of a future blog.

Using C = G/Q = 2,500/12 = 208 mg/m³ of EG at equilibrium.

That wasn't too bad was it?

This is a simple model – like all models it is a portrayal of reality but NOT reality.  The generation rate is most likely not constant but this exercise does give one some reasonable insight into the process and into the magnitude of the exposure potential.   If the EG comes out of the paint more quickly it could have a peak concentration higher than 200 mg/m³ but perhaps not very much higher.  The time-weight average concentration would always be lower than 200 mg/m³ if our assumption about all of the EG being vaporized in 8 hr is correct. 

If the EG takes much longer to come out it changes a lot of things.  Indeed, rework the above so that it takes 24 hours for all of the EG to come out and again assume that it comes out evenly.  Then the estimated equilibrium concentration for that 24 hour day would be about 70 mg/m³ and if one was only exposed during 8 hrs of that day their exposure could never be higher than about 25 mg/m³.  

There are a number of assumptions here in this simple model but I hope you can see how it might be helpful and how it might encourage you to go and manipulate the inputs to gain more insight or go to more sophisticated models.    IH MOD is a freeware Excel spreadsheet available on the AIHA web site that can do all of the math with ease and it provides a graphical output so that you can better see what is happening.   

I am again at a point where I need some feedback.   Do you good folks need or want information on:

• Specifically where to get IH MOD and exactly what does it do?
• Some of the math background that you may want to brush up on to help you with modeling (Note: It’s not a lot)
• The difference between equilibrium, point-in-time and time-weight average airborne concentrations
• Well mixed models versus models that consider air concentrations close to the source
• How to do source estimation (G)
• How to measure or estimate ventilation rates (Q)
• All or none of the above

Send your wishes/comments to me at mjayjock@gmail.com or in comments to this blog.  Absent any feedback I will go back to talking in generalities about risk assessment, risk management and modeling which many or most of you may find to be preferable.