Monday, September 9, 2013

The Most Versatile and Well-Tested Inhalation Model

The standard box model is simple and relatively easy to understand but it has some problems.   To understand the standard box model all you have to do is consider a box of air and keep track of what goes into it and what comes out.   Typically the “box” is a room and what goes into it’s air volume is the airborne contaminant; that is, the emission or generation rate.   The other stuff that goes into it (and out of it) is air from outside the box; that is, the ventilation rate.

Like I said it is pretty simple, just keep track of what goes in and what comes out and you can estimate the amount that is in the box.     C = (amount in – amount out)/box volume.   Indeed, we have equations that will estimate C for any point-in-time or as time-weighted averages.    What could be easier? However, the careful reader will notice that the airborne concentration (C) in this equation is an AVERAGE within the box.   Averages are good except when there is a lot of variation.   Indeed, if you are boiling hot on one side of your body while freezing on the other it could render an average of 75F but that average does not mean much to your comfort level!

We have all seen high breathing zone concentrations near point or concentrated emission sources within a room that are not representative of the average concentration within the entire room.   Consider a solvent spill in a large garage.   Folks cleaning it up can get a lot of exposure while those in the far corner of the room may be exposed to essentially nothing in the time it takes to clean it.   

The model works great when the source is relatively large within the room or there are a lot of sources spread more or less evenly throughout the box.   Also if there is very good mixing of the source(s) within the box as might occur with fans, then the average concentration determined by the model is reasonably accurate and useful.   As such we now called it the Well Mixed Box Model (WMB) and it is available in IH MOD.

This basic problem of the WMB model inability to handle near field sources plagued modelers for many years and then Mark Nicas and other workers developed what has come to be known as the 2 zone (or Near Field(NF)/Far Field (FF) model.    In this model there is a far field (FF) or outer zone which is typically the room volume and a near field (NF) or inner zone which contains the source and the breathing zone of the exposed person.   The exact origin of this model goes back a while.  As best as we can determine, the original concept for the 2 zone model NF/FF model was first put forth by W.C.L. Hemeon in the 1950s.  In a paper on general ventilation and the limitations of the WMB model, Hemeon outlined the basic concepts of the 2 zone model.  In 1996, both Mark Nicas and Ed Furtaw published papers in separate journals further developing the concept.  It was Mark Nicas who derived the dynamic concentration equations for the model.   Also he has continuously demonstrated and promoted its utility in industrial hygiene during the last 17 years.   

So what do you need to run the model?  In addition to the typical emission rate, you need a measure of the random air speed within a room along with the room’s volume and the general ventilation rate within the room.   The equations are relatively complicated but easily handled using the IH MOD freeware spreadsheet (as described in the previous blog).  

A critical parameter for the 2 zone model is the size of the near field (NF). In general, it should be large enough to include both the breathing zone of the exposed person and the emitting source. In the case of hair spray (or similar cosmetic spray applications) it has been estimated to be less than 1 m3 in volume.  In recent work designed to estimate exposure from an evaporating spill in a laboratory or plant, it has been set at a volume of 25 m3 – the volume of a 2 m diameter, 2 m high hemisphere centered over the spill.

This model allows one to estimate the exposure to people close to the source (NF) but also allows for an estimated exposure for persons and in the same room but not close to the source (FF).

So how good is the model at predicting breathing zone concentrations near sources?   As it turns out, it is quite good and its performance is well documented in a recent paper which lays out the capabilities of the model relative to a legal standard as set out by the “Daubert” decision.   Ref: Jayjock MA,  TW Armstrong and M Taylor:  The Daubert Standard as Applied to Exposure Assessment Modeling Using the Two-Zone (NF/FF) Model Estimation of Indoor Air Breathing Zone Concentration as an Example,  Journal of Occupational and Environmental Hygiene, 8: D114–D122, ISSN: 1545-9624 print / 1545-9632 online, November 2011.

One of the supported conclusions of this work was that the NF/FF model predictions were usually within the range of 0.5- to 2-fold of the measured concentration.  I will send you a copy of this paper if you write to me at

For all of these reasons I consider this model to be the most versatile and well vetted tool of its type available.

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