pressure volume loops

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python3 -c " import pdfplumber path = '/tmp/workspace/attachments/658a1d12-0333-4529-9948-d864a1582940/cardiac physiology kaplan.pdf' with pdfplumber.open(path) as pdf: print(f'Total pages: {len(pdf.pages)}') for i, page in enumerate(pdf.pages[:3]): print(f'--- PAGE {i+1} ---') print(page.extract_text()[:2000]) "

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python3 -c " import pdfplumber path = '/tmp/workspace/attachments/658a1d12-0333-4529-9948-d864a1582940/cardiac physiology kaplan.pdf' with pdfplumber.open(path) as pdf: # Search for PV loop pages for i, page in enumerate(pdf.pages): text = page.extract_text() or '' if 'pressure-volume' in text.lower() or 'pressure volume' in text.lower() or 'P-V' in text or 'end-systolic' in text.lower(): print(f'=== PAGE {i+1} ===') print(text[:3000]) print() "

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Pressure-Volume (P-V) Loops

A pressure-volume (P-V) loop is a 2D "phase space" plot of left ventricular (LV) pressure (y-axis, mmHg) against LV volume (x-axis, mL) over one complete cardiac cycle. The loop is traversed counterclockwise and provides a powerful graphical framework for analyzing systolic function, diastolic function, preload, afterload, and contractility - all in one diagram.

The Basic Loop - Four Phases

Left ventricular PV loop with labeled phases (Costanzo Physiology)
Fig. 4.23 - Left ventricular pressure-volume loop (Costanzo Physiology 7th Ed.)

PV loop with valve events labeled (Boron & Boulpaep Medical Physiology)
Figure 22-9 - PV loop of the left ventricle showing valve events (Boron & Boulpaep)

Phase 1: Ventricular Filling (Diastole) - bottom limb, left to right

  • Mitral valve opens; LV fills passively from the LA
  • Volume rises from ~50 mL (end-systolic volume, ESV) to ~120-140 mL (end-diastolic volume, EDV)
  • Pressure rises only slightly (from ~5 to ~10 mmHg) because the ventricle is highly compliant during diastole
  • This low-pressure, high-volume filling segment defines the end-diastolic pressure-volume relationship (EDPVR)

Phase 2: Isovolumetric Contraction - right vertical limb, upward

  • Mitral valve closes (end of diastole); all valves are now closed
  • LV pressure rises sharply from ~10 to ~80 mmHg with no change in volume
  • Contraction continues until LV pressure exceeds aortic diastolic pressure, when the aortic valve opens

Phase 3: Ventricular Ejection - top limb, right to left

  • Aortic valve opens; blood is ejected into the aorta
  • Volume falls from EDV (~120 mL) to ESV (~50-70 mL) - the difference is stroke volume (SV)
  • Pressure rises to its peak (~130 mmHg at point E) then falls as ejection decelerates
  • The loop touches the end-systolic pressure-volume relationship (ESPVR) at the top-left corner - this is point 3 in the Costanzo diagram

Phase 4: Isovolumetric Relaxation - left vertical limb, downward

  • Aortic valve closes; all valves are closed again
  • Pressure falls precipitously from ~100 mmHg to ~7 mmHg with no change in volume
  • When LV pressure falls below LA pressure, the mitral valve opens and the cycle repeats

Key Boundaries: ESPVR and EDPVR

The LV loop is constrained to operate between two bounding curves:
CurveFull NameWhat it represents
ESPVREnd-Systolic Pressure-Volume RelationshipUpper-left boundary; slope = E_es (end-systolic elastance) = index of contractility
EDPVREnd-Diastolic Pressure-Volume RelationshipLower boundary; exponential curve reflecting LV compliance (stiffness during diastole)
  • The ESPVR is approximately linear; its slope (E_es) is the most load-independent index of myocardial contractility available in vivo
  • The EDPVR is exponential; increased stiffness (lower compliance) shifts it upward and to the left
  • The triangular area between ESPVR and EDPVR to the left of the loop represents potential energy remaining in the ventricle wall at end-systole

Stroke Work and Energetics

  • The area enclosed by the P-V loop = stroke work (SW) - the external mechanical work done by the LV per beat (in mmHg·mL, convertible to joules)
  • Total mechanical energy = SW (kinetic, the loop area) + potential energy (triangular area to the left) = pressure-volume area (PVA)
  • Myocardial oxygen consumption (MVO₂) is linearly proportional to PVA: MVO₂ = α·PVA + β (Suga's model)
  • The SW/PVA ratio is an index of mechanical efficiency

Effects of Loading and Contractility Changes

Increased Preload

  • Loop shifts right - larger EDV, larger SV
  • Peak pressure is maintained; the loop is wider
  • ESPVR and afterload (aortic pressure) are unchanged

Increased Afterload

  • Loop shifts upward - higher systolic pressure, but reduced SV (less ejection)
  • EDV may increase slightly (Frank-Starling compensation)
  • Loop becomes taller and narrower

Increased Contractility (positive inotrope)

  • ESPVR rotates upward/left (steeper slope = higher E_es)
  • SV increases at any given preload; the loop is taller and wider
  • ESV decreases (more complete emptying)

Decreased Contractility (HFrEF)

  • ESPVR rotates downward/right (shallower slope)
  • LV dilates (compensatory increase in preload/EDV)
  • SV may be preserved initially but at a much higher filling pressure
  • The loop shifts right along a normal EDPVR

Decreased Compliance (HFpEF)

  • EDPVR shifts upward - higher pressure for any given volume
  • Loop height increases (more pressure required to achieve same EDV)
  • EF may be preserved but filling pressures are elevated

LV-Arterial Coupling

Effective arterial elastance (E_a) is the slope of the aortic end-systolic pressure to stroke-volume relationship:
E_a = end-systolic pressure / SV
  • Optimal coupling (maximum efficiency): E_es / E_a ≈ 1
  • In HFrEF: E_es/E_a < 1 (depressed contractility + vasoconstriction)
  • In HFpEF: E_es/E_a > 1 (systolic stiffening predominates)
  • EF is mathematically related to this ratio: EF/(1-EF) = E_es/E_a, so an EF of 50% implies ideal coupling

Indices of Contractility Derived from P-V Analysis

IndexMethodAdvantageLimitation
E_es (ESPVR slope)Slope of ESPVR across varying loadsLoad-independent, gold standardRequires multiple beats at different preloads (e.g., IVC occlusion)
SW-EDV relation (preload recruitable SW, M_sw)Slope of SW vs. EDVHighly linear, afterload-independent, size-independentIntegrates systolic + diastolic events
dP/dt_maxPeak rate of LV pressure riseSensitive to acute changesPreload-dependent, requires invasive measurement
EF, FAC, FSEjection-phase indicesNoninvasive (TEE, echo)Load-dependent, afterload sensitive

Clinical Applications (from Kaplan Cardiac Physiology)

The Kaplan chapter (Pagel et al.) emphasizes several key clinical uses:
  • Cardiac anesthesia monitoring: Conductance catheters or real-time TEE allow P-V framework application intraoperatively
  • HFrEF vs HFpEF distinction: A depressed ESPVR slope (reduced E_es) signals HFrEF; an upward-shifted EDPVR signals HFpEF. Both can coexist
  • Myocardial ischemia: Regional ischemia causes the P-V loop to tilt and collapse - aneurysmal systolic lengthening appears as a rightward expansion of the loop in the ischemic zone
  • Pericardial disease: Tamponade shifts the EDPVR upward (parallel shift), restricting filling
  • Volatile anesthetics: Cause dose-dependent depression of E_es and reduction of SW/PVA, worsening LV-arterial coupling at higher MAC concentrations
  • Vasodilators in HFrEF: Reduce E_a, restore E_es/E_a toward unity, increase SV; effective because the ESPVR slope is shallow
  • Vasodilators in HFpEF: Cause marked hypotension with minimal SV gain because the steep ESPVR means the ventricle is resistant to volume unloading

Diastolic Function Assessment with P-V Loops

The LV P-V framework dissects diastole into three measurable periods (Kaplan key point 13):
  1. Isovolumic relaxation - quantified by the time constant τ (tau); increased τ = delayed relaxation (ischemia, hypertrophy)
  2. Early filling - assessed by the rate of EDPVR traversal; impaired relaxation or reduced compliance slows this
  3. Atrial systole - the "A" loop in LA P-V analysis; contributes 15-25% of LV stroke volume under normal conditions

Sources: Costanzo Physiology 7th Ed., p. 156-157 | Boron & Boulpaep Medical Physiology, p. 761 | Pagel et al. in Kaplan's Cardiac Anesthesia, Chapter 5 (Cardiac Physiology), pp. 128-148
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