ΔP

ΔP (Delta P) is a mathematical term symbolizing a change (Δ) in pressure (P).

This article is about the mathematical term used in fluid dynamics. For the concept of delta-P in diving safety, see Diving hazards.

Uses

• Young–Laplace equation

Darcy–Weisbach equation

Given that the head loss h_f expresses the pressure loss Δp as the height of a column of fluid,

${\displaystyle \Delta p=\rho \cdot g\cdot h_{f}}$

where ρ is the density of the fluid. The Darcy–Weisbach equation can also be written in terms of pressure loss:

${\displaystyle \Delta p=f\cdot {\frac {L}{D}}\cdot {\frac {\rho V^{2}}{2}}}$

Lung compliance

In general, compliance is defined by the change in volume (ΔV) versus the associated change in pressure (ΔP), or ΔV/ΔP:

${\displaystyle Compliance={\frac {\Delta V}{\Delta P}}}$

During mechanical ventilation, compliance is influenced by three main physiologic factors:

1. Lung compliance
2. Chest wall compliance
3. Airway resistance

Lung compliance is influenced by a variety of primary abnormalities of lung parenchyma, both chronic and acute. Airway resistance is typically increased by bronchospasm and airway secretions. Chest wall compliance can be decreased by fixed abnormalities (e.g. kyphoscoliosis, morbid obesity) or more variable problems driven by patient agitation while intubated.^[1]

Calculating compliance on minute volume (V_E: ΔV is always defined by tidal volume (V_T), but ΔP is different for the measurement of dynamic vs. static compliance.

Dynamic compliance (C_dyn)

${\displaystyle C_{dyn}={\frac {V_{T}}{\mathrm {PIP-PEEP} }}}$

where PIP = peak inspiratory pressure (the maximum pressure during inspiration), and PEEP = positive end expiratory pressure. Alterations in airway resistance, lung compliance and chest wall compliance influence C_dyn.

Static compliance (C_stat)

${\displaystyle C_{stat}={\frac {V_{T}}{P_{plat}-PEEP}}}$

where P_plat = plateau pressure. P_plat is measured at the end of inhalation and prior to exhalation using an inspiratory hold maneuver. During this maneuver, airflow is transiently (~0.5 sec) discontinued, which eliminates the effects of airway resistance. P_plat is never > PIP and is typically < 3-5 cmH₂O lower than PIP when airway resistance is normal.

See also

• Pressure measurement
• Pressure drop
• Head loss

References

1. Dellamonica J, Lerolle N, Sargentini C, Beduneau G, Di Marco F, Mercat A, et al. (2011). "PEEP-induced changes in lung volume in acute respiratory distress syndrome. Two methods to estimate alveolar recruitment". Intensive Care Med. 37 (10): 1595–604. doi:10.1007/s00134-011-2333-y. PMID 21866369. S2CID 36231036.

External links

• Delta P, Diving Pressure Hazard