MNM
Foundation 5

The pressure-volume curve

Marmarou's exponential, why "ICP 18" tomorrow can mean trouble even though "ICP 18" today doesn't.

BLast reviewed 2026-05-177-min read

1. Bedside vignette: post-craniectomy infant, tense fontanelle

A 9-month-old infant has had a decompressive craniectomy 48 h ago after severe abusive head trauma. The skin flap is intact, the fontanelle is full but not bulging, ICP via parenchymal monitor reads 16 mmHg with RAP 0.75. The team wonders whether the infant has "run out of skull" already. You ask for a 3 mL/kg HTS bolus and watch.

Over the next 5 minutes the ICP drifts from 16 to 9 mmHg, the fontanelle softens, and RAP falls to 0.4. That large response to a small osmotic intervention is the bedside signature of a low-compliance operating point: the infant was on the steep segment of the Marmarou curve, even with the craniectomy. The craniectomy raised PVI; it did not eliminate elastance. The infant is still vulnerable to small re-accumulations of volume (rebound oedema, blood, CSF) and needs ICP and waveform-morphology surveillance, not reassurance from the open vault.

2. The equation

ICPtarget=ICPbaseline⋅exp⁡ ⁣(ΔVPVI)\mathrm{ICP_{target}} = \mathrm{ICP_{baseline}} \cdot \exp\!\left(\frac{\Delta V}{\mathrm{PVI}}\right)

PVI (pressure-volume index) is the volume change required to raise ICP by a factor of 10, typically ~20 mL in adults. Pediatric PVI scales roughly with intracranial volume but data are sparse.

Local elastance

The slope of the curve at the operating point:

E=dPdV=ICPbaselinePVI⋅exp⁡ ⁣(ΔVPVI)E = \frac{dP}{dV} = \frac{\mathrm{ICP_{baseline}}}{\mathrm{PVI}} \cdot \exp\!\left(\frac{\Delta V}{\mathrm{PVI}}\right)

At ICP 10, elastance is small: adding 1 mL barely moves the needle. At ICP 30, the same +1 mL drives ICP up several mmHg. The slope grows with the value; the value grows with the slope. That is why the curve is dangerous.

Clinical pearl

Two patients with ICP 18. One has just lost a lot of CSF buffer (steep curve, danger). The other is sitting on a flat curve (compensated). The number alone does not tell you which. and the waveform morphology (P2 dominance) tell you which.

Fig. 1
MARMAROU PRESSURE-VOLUME CURVEFour compliance phases · ICP = ICP₀·exp(ΔV/PVI) until microvascular collapseIntracranial VolumeIntracranial PressureCompensationHigh complianceCompensatory reservegradually depletedDecreasing complianceIncreased risk ofcerebral ischemia andherniationMinimal complianceCollapse of cerebralmicrovasculatureFOUR PHASES1 · CompensationCSF + venous buffer intact;large ΔV, small ICP rise.RAP < 0.32 · Decreasing complianceCompensatory reservegradually depleted.RAP 0.4 – 0.83 · Minimal complianceSmall ΔV → large ICP rise;ischemia / herniation risk.RAP rising → near 14 · Microvascular collapseCPP exhausted; vesselscollapse; pulse fails.RAP collapses to 0Pediatric PVI scales by ageMNM-Edu original schematic · Marmarou et al. 1975 · adult PVI ≈ 20 mL · sigmoid with terminal microvascular-collapse plateau
The Marmarou pressure-volume curve. The compensated phase (left) has a low slope: large volume changes produce small pressure changes. As the buffer compartments (CSF, then venous blood) exhaust, the curve bends upward at the knee. On the decompensated phase (right) the slope is steep: small volume changes produce large pressure changes. RAP and waveform morphology (P2 dominance) localise the operating point at the bedside.
MNM-Edu, original schematic. Marmarou 1975; Avezaat 1979.
MarmarouPVCurve
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Interactive tool (view online).

Time constant

After a volume change, ICP approaches its new equilibrium with τ ≈ 33 s. Do not read the bolus effect of mannitol or hypertonic saline at 30 seconds; wait at least 5 minutes for the full effect to settle.

3. Why it matters at the bedside

The exponential is not a curiosity, it changes the decisions you make.

  • A single ICP number is not enough. ICP 18 in a child with RAP 0.2 is a different patient from ICP 18 with RAP 0.85. Plan the next intervention for the slope, not the point.
  • Small interventions matter more on the steep slope. A 5 mL/kg HTS bolus drops ICP much more in a low-compliance brain than in a high-compliance one, because you are moving down the steep segment.
  • EVD drainage is more effective when compliance is low, for the same reason.
  • Small accumulations matter more on the steep slope. A 5 mL re-accumulation of CSF or blood is harmless in a compensated brain, dangerous in a near-decompensated one.
  • Tomorrow is not today. The same +1 mL can be tolerable now and disastrous in 8 hours if compliance has been steadily falling. RAP is the trend that warns you.

What you do at the bedside

A pragmatic protocol when RAP is climbing:

  1. Recheck the basics: head of bed 30°, no constricting neck lines, sedation adequate, PaCO₂ 35–40, normothermia, no occult seizure.
  2. Trend RAP, not just ICP. A creeping RAP from 0.4 to 0.7 over 4 hours is the early warning.
  3. Test osmolar response: a single 3 mL/kg HTS bolus that drops ICP from 22 to 12 confirms a steep operating point and earns you time.
  4. Plan the next escalation early: when RAP is high, the buffer for the next insult is small. Have CSF drainage capability ready; discuss decompression before it becomes emergent.
  5. Watch the waveform: P2 ≥ P1 (the "ICP triad" pattern) is the morphology signature of low compliance, often visible before RAP shifts.
In children

Smaller buffer, faster decompensation. Pediatric PVI scales roughly with intracranial volume, so a toddler's buffer is on the order of 8–12 mL versus the adult ~20 mL. The clinical implication is that pediatric ICP can decompensate over a shorter timeline for a given pathological volume. In infants with open fontanelles the surface can soften and bulge, but this is a slow buffer (days to weeks), not an acute rescue. Treat pediatric RAP creep as a stronger signal than the same trajectory in an adult.

4. Pattern library

  • Compensated: ICP 8–14, RAP 0.2–0.4, P1 > P2. Flat segment.
  • Borderline: ICP 14–20, RAP 0.4–0.6, P1 ≈ P2. Knee of curve.
  • Decompensated (steep): ICP 20–35, RAP 0.6–0.9, P2 ≥ P1. Steep segment; small additions costly.
  • Pre-terminal (paradoxical RAP collapse): ICP > 35, RAP < 0.2 (falling from previously high), pulse amplitude no longer follows mean. The brain can no longer transmit the pulse.
  • Plateau wave: ICP rises trapezoidally from 20 to 50–80 over 60 s, holds 5–20 min, falls. Marker of low compliance plus active vasomotor plus marginal CPP.

5. Pitfalls

  • Reading absolute ICP without RAP when both are available.
  • Acting on a single ICP point instead of a 30-minute trend.
  • Misreading paradoxical RAP collapse as recovery: at very high ICP, AMP can fall because the brain cannot transmit the pulse.
  • Forgetting τ: do not judge a bolus effect at 30 seconds; wait 3–5 minutes.
  • Treating craniectomy as elimination of elastance: it raises PVI but does not flatten the curve.

6. Combine with…

7. Why exponential?

The skull-dura-vasculature system has elastic and viscoelastic compartments. In small ΔV regimes, CSF translocation absorbs added volume without raising pressure. As CSF compartment is depleted and venous blood is compressed, the remaining tissue's elastic modulus dominates, and tissue elastance scales exponentially with strain.

8. RAP, the operational compliance index

RAP is the moving Pearson correlation between ICP pulse amplitude (AMP) and mean ICP, computed over a 4-minute window. Interpretations:

  • RAP < 0.3: flat segment of PV curve; reserve intact.
  • 0.3–0.6: borderline.
  • 0.6–0.9: steep segment; low compensatory reserve.
  • Sudden drop toward zero at high ICP: paradoxical pattern; the brain can no longer transmit pulse. This is decompensation.
RAPDemo
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Interactive tool (view online).

9. What changes the PVI

  • Hydrocephalus lowers PVI (smaller buffer).
  • Brain atrophy (post-traumatic, alcohol-related) raises PVI (more buffer).
  • Pediatric PVI scales with brain volume, roughly linearly.
  • Decompressive craniectomy dramatically raises PVI by adding a compliant compartment.

10. Plateau waves

Lundberg A waves are stochastic: they appear when low compliance plus active vasomotor plus marginal CPP align. Trapezoidal envelope: 60-second rise, 5–20-minute plateau, 60-second fall. If you see them, look for the underlying state, not the wave itself.

11. Therapeutic implications

  • A single 5 mL/kg bolus of HTS drops ICP more in a low-compliance brain than a high-compliance one, because you are moving down the steep slope.
  • EVD drainage is more effective in low-compliance brains for the same reason.
  • Conversely, a small volume gain (CSF re-accumulation, oedema, hyperaemia) is dangerous in proportion to where you are on the curve.

12. Evidence summary

TopicSourceGrade
Marmarou exponentialA
Avezaat pulse-amplitude relationshipB
RAP introductionB
RAP modern use B
Paradoxical RAP at very high ICPC
Plateau waves B
HTS vs mannitol in TBIB
Pediatric TBI guidelineexpert
Pediatric MMM reviewreview

13. Self-check

Retrieval check
A child has ICP 22 and PVI ~18 mL. By approximately how much will ICP rise after a 2 mL CSF re-accumulation?
What does a sudden drop in RAP from 0.85 to 0.05 at ICP 38 most likely indicate?
A post-craniectomy infant with ICP 16 and RAP 0.75 receives 3 mL/kg HTS. ICP falls to 9 over 5 minutes and RAP to 0.4. What does this large response tell you?

References

  1. Marmarou A, Shulman K, Rosende RM. A nonlinear analysis of the cerebrospinal fluid system and intracranial pressure dynamics. Journal of Neurosurgery 1978;48(3):332–344. doi:10.3171/jns.1978.48.3.0332 link
  2. Czosnyka M, Guazzo E, Whitehouse M, et al.. Significance of intracranial pressure waveform analysis after head injury. Acta Neurochirurgica 1996;138(5):531–541. doi:10.1007/BF01411173 link
  3. Kim DJ, Carrera E, Czosnyka M, Keong N, Smielewski P, Pickard JD. Index of cerebrospinal compensatory reserve in hydrocephalus. Neurosurgery 2009;64(3):494–501.
  4. Cottenceau V, Masson F, Mahamid E, et al.. Comparison of effects of equiosmolar doses of mannitol and hypertonic saline on cerebral blood flow and metabolism in traumatic brain injury. Journal of Neurotrauma 2011;28(10):2003–2012. doi:10.1089/neu.2011.1929 link
  5. Kochanek PM, Tasker RC, Carney N, et al.. Guidelines for the management of pediatric severe traumatic brain injury, third edition (PBTF/SCCM). Pediatric Critical Care Medicine 2019;20(3S):S1-S82.
  6. Tasker RC. Cerebrovascular reactivity in pediatric severe traumatic brain injury: a review. Pediatric Critical Care Medicine 2023.
  7. Lundberg N. Continuous recording and control of ventricular fluid pressure in neurosurgical practice. Acta Psychiatrica et Neurologica Scandinavica 1960;36(Suppl 149):1–193.
  8. Czosnyka M, Smielewski P, Piechnik S, et al.. Hemodynamic characterization of intracranial pressure plateau waves in head-injury patients. Journal of Neurosurgery 1999;91(1):11–19. doi:10.3171/jns.1999.91.1.0011 link
  9. Howells T, Johnson U, McKelvey T, Enblad P. An optimal frequency range for the analysis of pressure reactivity. Journal of Clinical Monitoring and Computing 2017;31(1):85–93.
  10. Kazimierska A, Kasprowicz M, Czosnyka M, et al.. Compliance of the cerebrospinal space: comparison of three methods. Acta Neurochirurgica 2021;163(7):1979–1989. doi:10.1007/s00701-021-04834-y link
  11. Avezaat CJJ, van Eijndhoven JHM, Wyper DJ. Cerebrospinal fluid pulse pressure and intracranial volume-pressure relationships. Journal of Neurology, Neurosurgery, and Psychiatry 1979;42(8):687–700. doi:10.1136/jnnp.42.8.687 link

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