Intracycle power distribution in a heterogeneous multi-compartmental mathematical model: possible links to strain and VILI

Abstract

Background: Repeated expenditure of energy and its generation of damaging strain are required to injure the lung by ventilation (VILI). Mathematical modeling of passively inflated, single-compartment lungs with uniform parameters for resistance and compliance indicates that standard clinical modes (flow patterns) differ impressively with respect to the timing and intensity of energy delivery-the intracycle power (ICP) that determines parenchymal stress and strain. Although measures of elastic ICP may accurately characterize instantaneous rates of global energy delivery, how the ICP component delivered to a compartment affects the VILI-linked variable of strain is determined by compartmental mechanics, compartmental size and mode of gas delivery. We extended our one-compartment model of ICP to a multi-compartment setting that varied those characteristics.

Main findings: The primary findings of this model/simulation indicate that: (1) the strain and strain rate experienced within a modeled compartment are nonlinear functions of delivered energy and power, respectively; (2) for a given combination of flow profile and tidal volume, resting compartmental volumes influence their resulting maximal strains in response to breath delivery; (3) flow profile is a key determinant of the maximal strain as well as maximal strain rate experienced within a multi-compartment lung. By implication, different clinician-selected flow profiles not only influence the timing of power delivery, but also spatially distribute the attendant strains of expansion among compartments with diverse mechanical properties. Importantly, the contours and magnitudes of the compartmental ICP, strain, and strain rate curves are not congruent; strain and strain rate do not necessarily follow the compartmental ICP, and the hierarchy of amplitudes among compartments for these variables may not coincide.

Conclusions: Different flow patterns impact how strain and strain rate develop as compartmental volume crests to its final value. Notably, as inflation proceeds, strain rate may rise or fall even as total strain, a monotonic function of volume, steadily (and predictably) rises. Which flow pattern serves best to minimize the maximal strain rate and VILI risk experienced within any sector, therefore, may strongly depend on the nature and heterogeneity of the mechanical properties of the injured lung.

Keywords: Flow pattern; Mathematical model; Mechanical power; Mechanical ventilation; Multicompartment; Strain; Stress; VILI; Ventilation mode; Ventilator-induced lung injury.

Fig. 1

Schematic diagram of the 5-compartment model. Proximal shared resistances (R) are designated numerically; terminal, compartment-relevant resistances (R) and compliances (C) are designated alphabetically

Fig. 2

Compartmental volumes for a single complete tidal cycle of the same volume and inspiratory times during constant inspiratory flow (CF, A) and constant inspiratory pressure (CP, B). Note the variations among compartments in end-inspiratory volumes, accompanied by variations in deflation curvature

Fig. 3

Comparison of inspiratory compartmental intracycle elastic power (ICP_elastic) for all labeled modes of ventilation: constant inspiratory flow (CF), decelerating inspiratory flow (DF), constant inspiratory pressure (CP), sinusoidal inspiratory flow (SF)

Fig. 4

Compartmental strain (A) and strain rate (B) for all controlled flow and constant pressure ventilation modes. Note the marked differences among compartments, depending on flow profile

Fig. 5

Maximum compartmental strains as a function of PEEP for the four modes of ventilation. PEEP causes maximal strains to rise monotonically but to different degrees in all compartments

Fig. 6

A Effect of resting volume (V_rest) on maximal compartmental strains (S_max) for CF (A) and CP (B). Calculated strains rise in all compartments as inverse functions of V_rest. Variation of resting compartmental volumes at maximal strain during constant flow (C). Note that each compartment has a unique resting volume at which strain is maximized