BioMedical Engineering OnLine

, 11:27

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Bench and mathematical modeling of the effects of breathing a helium/oxygen mixture on expiratory time constants in the presence of heterogeneous airway obstructions

  • Andrew R MartinAffiliated withSenior Research Scientist, Medical Gases, American Air Liquide, Delaware Research and Technology Center (DRTC) Email author 
  • , Ira M KatzAffiliated withMedical Gases Group, Air Liquide Santé InternationalDepartment of Mechanical Engineering, Lafayette College
  • , Karine TerzibachiAffiliated withMedical Gases Group, Air Liquide Santé International
  • , Laure GouinaudAffiliated withMedical Gases Group, Air Liquide Santé International
  • , Georges CaillibotteAffiliated withMedical Gases Group, Air Liquide Santé International
  • , Joëlle TexereauAffiliated withMedical Gases Group, Air Liquide Santé International



Expiratory time constants are used to quantify emptying of the lung as a whole, and emptying of individual lung compartments. Breathing low-density helium/oxygen mixtures may modify regional time constants so as to redistribute ventilation, potentially reducing gas trapping and hyperinflation for patients with obstructive lung disease. In the present work, bench and mathematical models of the lung were used to study the influence of heterogeneous patterns of obstruction on compartmental and whole-lung time constants.


A two-compartment mechanical test lung was used with the resistance in one compartment held constant, and a series of increasing resistances placed in the opposite compartment. Measurements were made over a range of lung compliances during ventilation with air or with a 78/22% mixture of helium/oxygen. The resistance imposed by the breathing circuit was assessed for both gases. Experimental results were compared with predictions of a mathematical model applied to the test lung and breathing circuit. In addition, compartmental and whole-lung time constants were compared with those reported by the ventilator.


Time constants were greater for larger minute ventilation, and were reduced by substituting helium/oxygen in place of air. Notably, where time constants were long due to high lung compliance (i.e. low elasticity), helium/oxygen improved expiratory flow even for a low level of resistance representative of healthy, adult airways. In such circumstances, the resistance imposed by the external breathing circuit was significant. Mathematical predictions were in agreement with experimental results. Time constants reported by the ventilator were well-correlated with those determined for the whole-lung and for the low-resistance compartment, but poorly correlated with time constants determined for the high-resistance compartment.


It was concluded that breathing a low-density gas mixture, such as helium/oxygen, can improve expiratory flow from an obstructed lung compartment, but that such improvements will not necessarily affect time constants measured by the ventilator. Further research is required to determine if alternative measurements made at the ventilator level are predictive of regional changes in ventilation. It is anticipated that such efforts will be aided by continued development of mathematical models to include pertinent physiological and pathophysiological phenomena that are difficult to reproduce in mechanical test systems.


Helium Heliox Exhalation Time constant Hyperinflation Gas trapping Ventilation distribution Airway resistance Mechanical ventilation Lung