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Cardiac Output & Hemodynamics

The equations behind flow, pressure, and where fluid leaks

Cardiovascular·Physiology·6 min read·9 high-yield points·Reviewed by Veli Bakalov, MD @HemeOncBuddy
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Cardiac output and the Fick principle

Cardiac output. CO = stroke volume × heart rate, about 5 L/min at rest (roughly 70 mL × 70 beats/min). Cardiac index (CO ÷ body surface area) normalizes output to body size.

Exercise. CO can rise about fivefold. Heart rate and stroke volume both climb early; SV plateaus at moderate intensity, so later gains come from heart rate alone. At very fast rates (e.g., ventricular tachycardia) diastolic filling is cut short and CO falls.

Fick principle. Whole-body oxygen uptake equals blood flow times the oxygen removed from each liter: VO2 = CO × (CaO2 − CvO2), so CO = VO2 ÷ (CaO2 − CvO2). With a VO2 of 250 mL/min, arterial O2 content of 200 mL/L, and mixed venous content (sampled from the pulmonary artery) of 150 mL/L, CO = 250 ÷ 50 = 5 L/min.

Reading the a–v O2 difference. When output falls, tissues extract more O2 from each liter of blood, so the arteriovenous difference widens and mixed venous O2 drops. A narrow difference with high venous O2 suggests high output or failed extraction (e.g., septic shock, cyanide poisoning).

Stroke volume: preload, afterload, contractility

Stroke volume and ejection fraction. SV = EDV − ESV, about 70 mL. Ejection fraction = SV ÷ EDV, normally 55–70%, and indexes contractility. EF is reduced (about 40% or less) in systolic heart failure (HFrEF) and preserved (50% or more) in diastolic dysfunction (HFpEF); values in between are termed mildly reduced.

Three levers. More filling (preload) and more squeeze (contractility) raise SV; more resistance (afterload) lowers it, and heart failure or β-blockade lowers it by weakening contraction.

Preload and Frank-Starling. Preload approximates end-diastolic volume, which depends on venous return. Greater diastolic stretch brings sarcomeres toward optimal actin–myosin overlap, so the next beat is more forceful and SV rises (the Frank-Starling length–tension relationship). Volume loading and lying down raise preload; hemorrhage, standing, and venodilators lower it.

Nitroglycerin is mainly a venodilator: pooling blood in capacitance veins lowers preload, ventricular radius, wall stress, and myocardial oxygen demand — the core of its antianginal effect.

Afterload and Laplace. Afterload approximates the arterial pressure or SVR the ventricle ejects against. By Laplace, wall stress (often called wall tension) = (pressure × radius) ÷ (2 × wall thickness). Chronic pressure overload (hypertension, aortic stenosis) drives concentric hypertrophy (sarcomeres added in parallel), and the thicker wall normalizes stress; volume overload causes eccentric hypertrophy (sarcomeres added in series), and the larger radius raises stress. Hydralazine, an arteriolar dilator, lowers afterload.

Contractility. Inotropy is the force generated at a given preload; it shifts the Frank-Starling curve up or down. β1 stimulation increases Ca2+ entry through L-type channels and phosphorylates phospholamban, speeding sarcoplasmic reticulum Ca2+ reuptake and enlarging the releasable store. Digoxin blocks the Na+/K+-ATPase; the higher intracellular Na+ slows Ca2+ extrusion by the Na+/Ca2+ exchanger.

Determinants of stroke volume
DeterminantApproximated byIncreased byDecreased byEffect on SV
PreloadEDV, venous returnVolume loading, lying downHemorrhage, venodilators (nitroglycerin)↑ with ↑ preload
AfterloadArterial pressure, SVR, wall stressHypertension, aortic stenosis, vasoconstrictionArteriolar dilators (hydralazine), ACE inhibitors↓ with ↑ afterload
ContractilityEjection fractionCatecholamines (β1), ↑ intracellular Ca2+, ↓ extracellular Na+, digoxinβ-blockers, systolic heart failure, acidosis, hypoxia or hypercapnia, non-dihydropyridine Ca2+ channel blockers↑ with ↑ contractility
Myocardial O2 demand rises with contractility, afterload, heart rate, and ventricular diameter.

Resistance, flow, and arterial pressure

Flow and Poiseuille. Flow = pressure gradient ÷ resistance. By Poiseuille, resistance = 8 × viscosity × length ÷ (π × radius⁴), so radius dominates: halving it raises resistance 16-fold, and a small arteriolar constriction produces large changes in pressure and flow. Arterioles are the main resistance vessels, and the steepest pressure drop in the circulation occurs across them.

16×rise in resistance when radius halves (1/r⁴)
≥60 mmHgMAP needed to perfuse organs
55–70%normal ejection fraction

Viscosity and arrangement. Viscosity depends mostly on hematocrit (↑ in polycythemia and hyperproteinemic states such as multiple myeloma, ↓ in anemia). Resistances in series add; organs are perfused in parallel (1/R total = 1/R1 + 1/R2 + …), so total resistance is lower than that of any single bed.

Mean arterial pressure. MAP = CO × SVR. At rest it is estimated as DBP + 1/3 pulse pressure (= 2/3 DBP + 1/3 SBP) because diastole occupies about two-thirds of the cycle; 120/80 gives about 93 mmHg. Rearranged, SVR = (MAP − right atrial pressure) ÷ CO. Organ perfusion needs a MAP of at least 60 mmHg.

Pulse pressure. SBP − DBP rises with stroke volume and falls with arterial compliance.

Pulse pressure patterns
PatternMechanismClassic causes
WidenedLarge SV, stiff aorta, or rapid diastolic runoffAortic regurgitation (bounding water-hammer pulses, early diastolic decrescendo murmur), aortic stiffening (isolated systolic hypertension in the elderly), hyperthyroidism, PDA, anemia
NarrowedSmall or obstructed SVAortic stenosis, cardiogenic shock, cardiac tamponade, hemorrhage, advanced heart failure

Reflex control of blood pressure

Baroreceptors. Stretch receptors in the carotid sinus (at the carotid bifurcation; afferents in CN IX) and the aortic arch (afferents in CN X) project to the nucleus tractus solitarius in the medulla. The carotid sinus senses both rises and falls in pressure; aortic arch receptors respond mainly to rises.

Rising pressure. More stretch increases firing, raising vagal tone and lowering sympathetic tone, so heart rate, contractility, and SVR fall. Carotid sinus massage exploits this: the vagal surge slows the heart and AV nodal conduction and can terminate SVT.

  1. Hemorrhage lowers BPLess arterial stretch in the carotid sinus and aortic arch.
  2. Baroreceptor firing fallsLess afferent input to the medulla.
  3. Sympathetic outflow risesVagal tone withdraws.
  4. Tachycardia and vasoconstrictionFaster, stronger beats, arteriolar constriction (↑ SVR), and venoconstriction (↑ preload) restore pressure.

Cushing reflex: raised intracranial pressure → cerebral ischemia with rising PCO2 → sympathetic surge and hypertension → baroreceptor-mediated reflex bradycardia. Hypertension, bradycardia, and irregular breathing form the Cushing triad, a sign of impending herniation.

Microcirculation: Starling forces and edema

Starling equation. Net filtration = Kf × [(Pc − Pi) − (πc − πi)], where Kf is the filtration coefficient, P is hydrostatic and π oncotic pressure, c is capillary, and i is interstitium. Capillary hydrostatic pressure pushes fluid out; capillary oncotic pressure, generated mainly by albumin, pulls it in.

Along the capillary. Hydrostatic pressure falls from the arteriolar to the venular end, so filtration dominates at the arteriolar end and reabsorption at the venular end. Lymphatics return the small net excess; edema appears when filtration outpaces lymphatic return.

Four routes to edema
Deranged forceWhy fluid accumulatesExamples
↑ Capillary hydrostatic pressure (Pc)More outward pushHeart failure (left → pulmonary edema, right → peripheral edema), venous obstruction such as DVT
↓ Plasma oncotic pressure (πc)Less inward pull from albuminNephrotic syndrome (urinary albumin loss), cirrhosis (↓ albumin synthesis), kwashiorkor (protein malnutrition)
↑ Capillary permeability (Kf)Fluid and protein leakSepsis, burns, histamine release
↓ Lymphatic drainage (↑ πi)Filtered fluid and protein are not clearedFilariasis (Wuchereria bancrofti), post-mastectomy axillary node dissection or radiation
Chronic lymphedema is protein-rich and becomes firm and non-pitting as the skin fibroses.