Compliance

Dynamic compliance is the apparent compliance that is measured in the presence of gas flow, i.e. during breathing.

$$C = \frac{\Delta V}{\Delta P}$$

$$C_{dyn} = \frac{TV}{PIP - PEEP}$$

This is affected by all the determinants of static compliance, but also by airway resistance and respiratory rate ('frequency dependence'). The latter is because

1. Increasing respiratory rate increases the pressure required to overcome a fixed resistance, and increases gas velocity, which favours turbulent flow and increases resistance
2. The respiratory units with lower compliance fill first due to shorter time constants. As inspiratory time shortens, the proportion of volume going to these units increases.

Static compliance is compliance measured in the absence of gas flow.

The compliance of the respiratory system is composed of the compliance of the chest wall and the compliance of the lung.

In this case, elastances add, not compliances. This is because the change in volume is constant across all the components, and the pressures are additive (consider stuffing one balloon inside another balloon and then inflating both balloons together. The total elastance is naturally the sum of the two balloon's elastances, since both are recoiling against the same volume).

Therefore

$$\text{Elastance}_{Total} = \text{Elastance}_{Lung} + \text{Elastance}_{wall}$$

$$\frac{1}{C_{Total}} = \frac{1}{C_{Lung}} + \frac{1}{C_{wall}}$$

\(C_{Lung}\) and \(C_{wall}\) are both about 200ml/cmH20, so \(C_{total}=200\mathrm{ml\ cmH2O^{-1}}\)

Specific compliance is compliance over FRC. Usual value is \(0.05 \mathrm{cmH2O^{-1}}\). 1cmH20 should drive five percent of FRC. For an adult with a 2L FRC, 1cmH2O should drive a \(\Delta V\) of 100mL (so a pressure support of 5cmH2O should drive a 500mL tidal volume).

Factors increasing \(C_{Lung}\)

1. Volume close to FRC
2. Upright position
3. Age
4. Emphysema

Factors decreasing \(C_{Lung}\)

1. Decreased effective volume: lobectomy, atelectasis, pneumonia
2. Interstitial changes: interstitial fibrosis, pulmonary oedema, increased pulmonary blood volume
3. Extremes of volume (derecruitment, overdistension)
4. Loss of surfactant (ARDS)

Factors increasing \(C_{Wall}\)

1. Open chest (\(C_{Wall} \to \infty\)) and it's cousins (flail segments, rib fractures)
2. Ehler-Danlos
3. Cachexia

Factors decreasing \(C_{Wall}\)

1. Bones: kyphoscoliosis, pectum exscavatum
2. Muscles: tentany, seizure
3. Skin: circumferential burns
4. Adipose: obesity
5. External compression: supine or lateral positoin, abdominal compartment syndrome

For any given pressure, the lung volume is higher during expiration than during inspiration. This is due to:

1. Surface tension forces which need to be overcome to inflate alveoli (\(\mu \propto \frac{Pr}{T} \to P \propto \frac{1}{r}\). Surfactant behaves differently during inspiration and expiration (with surfactant concerntrated at the air-fluid interface during expiration)
2. Re-recruitment of collapsed alveoli during inspiration
3. Stress relaxation of elastic polymers (loss of energy at end-inspiration)