A few thoughts on pressure-mapping inhalers ... and Flohms

Currently there's no agreed standard method or practice to determine the airflow resistance of an inhaler, leaving scientists and engineers to their own devices (sorry!)

However, this is an important parameter to measure as accurately as possible. It's essential to determine Qout (the flowrate through the inhaler device corresponding to a "nominal" 4 kPa pressure drop across it) in a repeatable and reproducible manner.  If this measurement isn't performed correctly, in vitro data may be i) inaccurate and / or ii) more variable than desired; devices that are actually within specification may wrongly be failed, and in the worst case a potentially life-saving medical product may never reach the patient.

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So what is a sensible method to use?

To accurately measure the airflow resistance of an inhaler it's necessary to achieve a number of steady-state flows through it, whilst recording the pressure drops across it that correspond to those flowrates.  Ideally, the range of pressure drops should be representative of the likely pressure drops achieved in actual use - e.g. between 0.2 kPa and approximately 10 kPa.

The closest methodology (in terms of experimental setup) provided by the United States Pharmacopeia (USP) is given for the determination of Delivered Dose Uniformity.  However, particularly with high resistance inhalers, this method is not ideal, as replacing a high resistance inhaler with a low resistance flowmeter will change the flowrate through the system.  It is far more practical and indeed more accurate to keep the flowmeter in the fluid circuit throughout the duration of the measurements, with a HEPA filter placed upstream to ensure any particulates emitted from the inhaler cannot enter the sensitive flowmeter, where they could deposit on the thermal film sensor and affect measurement accuracy.  A simple schematic of the suggested experimental configuration is shown below:

Providing the following testing requirements are satisfied, then the measurement of the airflow resistance will be sufficiently accurate:

• Critical (choked) flow must be achieved across the needle valve to achieve steady flow through the inhaler:
  The pressure ratio of P2:P3 must equal or exceed the Critical Pressure Ratio, which is 1.89 for air
• The differential pressure across only the inhaler device must be measured
  (it's surprising how often filter paper resistance is included in the measurement)
• The volumetric flowrate at standard temperature and pressure must be measured - the Copley and TSI flowmeters should be set to display this value
• Ideally, there should be 10 diameters (in length) of straight pipe upstream of the flowmeter (to allow the flow to fully develop prior to entering the instrument)
• The static pressure on the downstream side of the inhaler device (P1) should be measured - i.e. there should be no remaining dynamic head component
  (In a DUSA - dose unit sampling apparatus - the velocity has reduced considerably at the location of the pressure tapping, so the dynamic head component is negligible.  However any equivalent plenum chamber is also suitable)
• And of course the fluid circuit must be free of leaks - i.e. all the air that flows through the flowmeter must flow through the subject inhaler device.

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Recommended Test Procedure

1. Configure the fluid circuit as recommended above
2. Download this Excel template that I created to automatically perform the analysis:  
   
   
   
   <Excel Pressure Mapping Template>
   
   
3. Enter test details into the yellow input cells on the spreadsheet
4. Adjust the needle valve until P1 reads between 0.3 kPa and 0.5 kPa
   (the first target range of the nine measurements)
5. Check that P2:P3 is greater or equal to 1.89
   (i.e. you have critical flow across the needle valve)
6. Record the actual pressure (in kPa) and the corresponding volumetric flowrate (in litres per minute) in the yellow input cells on the sheet
7. Repeat steps 4 to 6 for the remaining eight measurements
   (With some very low resistance devices it may not be possible to achieve critical flow across the needle valve all the way up to 10 kPa - if this is the case, ignore the recommended target pressure ranges and perform nine measurements, with even spacing, up to the maximum pressure that is achievable)

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A few notes on the template

• It calculates the line of best fit between the square root of the pressure drop (in Pa) and the flowrate (in LPM), forced through zero - i.e. a linear regression
• The gradient of this line is the airflow resistance of the inhaler, and the
  R-squared coefficient is an indicator of the goodness of fit
  (1.0000 being perfect)
• A second indicator of the quality of the data is the |Error| column, which reports the magnitude of deviation for each datum from the calculated Resistance value, as a percentage
• The bottom left of the sheet reports various calculated outputs...
  > Airflow resistance, R
  > Q4kPa - the real Qout (!)
  > Q2kPa and Q6kPa (other common test points)
  > Flow durations (in seconds) corresponding to a displaced volume
      (default is set to 4.0 L, but this is changeable)
• There are also a couple of additional input fields...
  > ΔP - enter any pressure drop and the corresponding flowrate will be
      calculated, together with the required flow duration
  > Q - enter any flowrate, and the corresponding pressure drop will be
      calculated, together with the required flow duration

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So what's all this about Flohms?

I've worked in the field of respiratory devices for perhaps a little too long, and the units of airflow resistance have always totally annoyed me.  They're so cumbersome!

I've talked a few times about renaming the units of resistance, √Pa min L ˉ1, to "Flohms" ("Flow"-"ohms") - or even more simply FΩ.  This is pure laziness, as I haven't the time to keep writing it out in full.

I hope you understand...