Research

Mathematical modelling to centre low tidal volumes following acute lung injury: A study with biologically variable ventilation

M Ruth Graham^1* , Craig J Haberman¹ , John F Brewster² , Linda G Girling¹ , Bruce M McManus³ and W Alan C Mutch^1*

¹  Department of Anesthesia, University of Manitoba, Winnipeg, Manitoba, Canada

²  Institute of Industrial Mathematical Sciences, University of Manitoba, Winnipeg, Manitoba, Canada

³  Department of Pathology and Laboratory Medicine, James Hogg iCAPTURE Centre for Cardiovascular and Pulmonary Research, University of British Columbia, Vancouver, British Columbia, Canada

author email corresponding author email* Contributed equally

Respiratory Research 2005, 6:64doi:10.1186/1465-9921-6-64

Published:	28 June 2005

Abstract

Background

With biologically variable ventilation [BVV – using a computer-controller to add breath-to-breath variability to respiratory frequency (f) and tidal volume (V_T)] gas exchange and respiratory mechanics were compared using the ARDSNet low V_T algorithm (Control) versus an approach using mathematical modelling to individually optimise V_T at the point of maximal compliance change on the convex portion of the inspiratory pressure-volume (P-V) curve (Experimental).

Methods

Pigs (n = 22) received pentothal/midazolam anaesthesia, oleic acid lung injury, then inspiratory P-V curve fitting to the four-parameter logistic Venegas equation F(P) = a + b[1 + e^-(P-c)/d]^-1 where: a = volume at lower asymptote, b = the vital capacity or the total change in volume between the lower and upper asymptotes, c = pressure at the inflection point and d = index related to linear compliance. Both groups received BVV with gas exchange and respiratory mechanics measured hourly for 5 hrs. Postmortem bronchoalveolar fluid was analysed for interleukin-8 (IL-8).

Results

All P-V curves fit the Venegas equation (R² > 0.995). Control V_T averaged 7.4 ± 0.4 mL/kg as compared to Experimental 9.5 ± 1.6 mL/kg (range 6.6 – 10.8 mL/kg; p < 0.05). Variable V_Ts were within the convex portion of the P-V curve. In such circumstances, Jensen's inequality states "if F(P) is a convex function defined on an interval (r, s), and if P is a random variable taking values in (r, s), then the average or expected value (E) of F(P); E(F(P)) > F(E(P))." In both groups the inequality applied, since F(P) defines volume in the Venegas equation and (P) pressure and the range of V_Ts varied within the convex interval for individual P-V curves. Over 5 hrs, there were no significant differences between groups in minute ventilation, airway pressure, blood gases, haemodynamics, respiratory compliance or IL-8 concentrations.

Conclusion

No difference between groups is a consequence of BVV occurring on the convex interval for individualised Venegas P-V curves in all experiments irrespective of group. Jensen's inequality provides theoretical proof of why a variable ventilatory approach is advantageous under these circumstances. When using BVV, with V_T centred by Venegas P-V curve analysis at the point of maximal compliance change, some leeway in low V_T settings beyond ARDSNet protocols may be possible in acute lung injury. This study also shows that in this model, the standard ARDSNet algorithm assures ventilation occurs on the convex portion of the P-V curve.