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The coronary circulation supplies and drains the heart's own tissue. Coronary arteries branch from the aorta to supply the myocardium; cardiac veins return blood toward the right atrium.^[ref] Blood moving through a ventricular cavity is not the same flow as blood perfusing the surrounding muscle.

Much coronary venous return passes through the coronary sinus, while anterior cardiac veins provide a direct route to the right atrium.^[ref] Consequently a coronary-sinus sample represents its drainage territory rather than automatically every part of the heart. Anatomical pathways must match the region whose blood flow and oxygen uptake are being estimated.

An original tissue-balance example uses regional flow $Q=80\mathrm{mL}\mathrm{mi}{\mathrm{n}}^{-1}$, arterial oxygen content $C_a=0.20\mathrm{mL}{\mathrm{O}}_2\mathrm{m}{\mathrm{L}}^{-1}$ and matching venous oxygen content $C_v=0.08$ in the same units. Then regional coronary oxygen uptake isThe arterial delivery rate is $Q{C}_a=16$ in those units. Delivery and uptake differ because oxygen remains in the returning blood. The values are stipulated, not normal-reference limits.

A primary 2007 experiment measured coronary volumetric flow using continuous saline thermodilution, an infusion catheter and a pressure/temperature guidewire, with comparisons in dogs and patients.^[ref] This provides a concrete way to investigate the flow term; it does not by itself measure the oxygen-content difference.

The arterial map also varies among hearts. A radiopaque-injection study classified 178 of 200 examined hearts as right dominant by the origin of the posterior interventricular artery.^[ref] Dominance names an anatomical branching criterion, not a claim that one artery supplies the entire heart.

A heart valve permits predominantly one-way blood flow through the heart. Leaflet motion follows changing pressure differences and structural constraints. The four main human valves occupy different chamber or outflow boundaries, so valve dysfunction has location-specific consequences.^[ref]

The left atrium is the heart chamber receiving blood through the pulmonary veins and delivering it through the mitral valve to the left ventricle. It is the receiving chamber on the oxygenated return side of the pulmonary circulation.^[ref]

Its role changes during the cardiac cycle. The chamber can accumulate incoming blood while its outlet is closed, pass blood onward during ventricular filling, and contribute to late filling through atrial contraction. The storage role is called atrial reservoir function.^[ref]

A volume balance makes this more precise:Here the sum includes the incoming pulmonary vein blood flow rates, and the outlet term is signed net flow through the mitral valve. In a constructed interval with total inflow $5$ L/min and zero outlet flow for $0.10$ s, the stored volume increases byThe example describes transient storage, not an indefinitely sustained steady state. Over a repeating cycle with no net accumulation, average inflow must equal average outflow.

The entering streams can also differ in oxygen content. Their mixed content is weighted by their blood flow rates, not by the number of vessels. Thus the same anatomical chamber supports two distinct balance questions: how its volume changes with time, and how transported oxygen combines. Its volume alone determines neither the stroke volume of the left ventricle nor the oxygen content entering the left ventricle.

Mixed venous oxygen content is the oxygen content of blood after the returning venous streams have mixed, representing whole-body venous return to the right side of the heart. It is the venous quantity required with arterial oxygen content in the whole-body Fick principle. A single regional vein need not have this content: different tissues remove different amounts of oxygen and return different blood flow rates.

The mixing rule follows from conservation of mass. If streams have blood flow rates $Q_i$ and venous oxygen content values $C_i$, with no oxygen exchange during mixing,For two constructed streams, $100$ mL/min at $0.05$ mL of oxygen per mL of blood and $50$ mL/min at $0.20$ mL/mL carry $5$ and $10$ mL/min of oxygen. Their mixture has content $15/150=0.10$ mL/mL, not the unweighted mean $0.125$ mL/mL. The correct weights are volume blood flow rates.

The right atrium receives several returns before blood passes through the right ventricle and pulmonary trunk.^[ref] A downstream sample can represent their mixture only to the extent that the streams have actually mixed and the sampling interval represents the desired state. Replacing that sample with one taken from a particular upstream vein introduces a representativeness assumption. Likewise, averaging oxygen saturation values is not generally an oxygen-content balance when hemoglobin concentrations differ. The whole-body balance is about amounts of transported oxygen, not averages of instrument displays.

The pulmonary trunk is the common artery leaving the right ventricle through the pulmonary valve before dividing into the vessels supplying the two lungs. It is the initial shared segment of the pulmonary artery route in the pulmonary circulation. The name artery describes flow away from the heart; the blood in the pulmonary trunk has not yet acquired oxygen in the lungs.^[ref]

At a junction with negligible storage, conservation of mass givesA constructed total blood flow of $5$ L/min could therefore divide into $3$ and $2$ L/min. Measuring the total does not establish equal flow to the two lungs. In a simple steady model with a common upstream and downstream pressure, branch blood flow rates depend on their respective vascular resistance values; the shared inlet does not force the resistances to be equal.

The pulmonary trunk also supplies an important distinction between two measurements. Right ventricular ejection fraction describes change in a chamber volume, whereas forward blood flow in the pulmonary trunk describes transport through a vessel. They agree through stroke volume and heart rate only under the relevant balance assumptions, including negligible backward flow. An anatomical connection is therefore the starting point for a flow model, rather than a substitute for its assumptions.

The pulmonary valve is the heart valve between the right ventricle and pulmonary trunk. During forward ventricular ejection it allows blood to enter the pulmonary circulation; closure limits return from the pulmonary trunk into the relaxing right ventricle.^[ref]

Its pocket-like cusps respond to the changing pressure difference. Unlike the tricuspid valve, the pulmonary valve has no attached chordae tendineae or papillary muscles.^[ref] Thus the same direction-control task is achieved by different supporting structures at the chamber inlet and outlet.

A deliberately idealized valve model sets forward blood flow to zero when the downstream pressure exceeds the upstream pressure, and permits positive flow when ventricular pressure exceeds trunk pressure. This model captures direction but omits the inertia and deformation of real cusps. It is useful for checking the sign of a flow term, not for predicting an exact opening time.

For example, if a constructed cycle sends 80 mL forward and 10 mL backward across the pulmonary valve, net transport is 70 mL. Counting only the positive part of blood flow overestimates net delivery. This is why stroke volume inferred from changing chamber volume and net forward flow in the pulmonary trunk require compatible assumptions about valve function.

A pulmonary vein returns blood from a lung to the left atrium. The pulmonary veins complete the return side of the pulmonary circulation, after blood has received oxygen in the lungs. They are veins because they carry blood toward the heart, even though their oxygen content is higher than that of the blood arriving through the pulmonary artery.^[ref]

Following a parcel of blood makes the sequence clear: right ventricle, pulmonary trunk, vessels of the lungs, pulmonary vein, left atrium, then left ventricle. The pulmonary vein connects the lung circuit to the receiving chamber of the left heart; it does not drain directly into the right atrium.

A simple oxygen balance illustrates why both content and flow matter. Suppose two returning streams have blood flow rates $Q_1,Q_2$ and oxygen contents $C_1,C_2$. If they mix without further oxygen exchange, the left atrium's inflow content isFor constructed values $Q_1=3$ L/min, $Q_2=2$ L/min, $C_1=0.20$ and $C_2=0.15$ mL/mL, this gives $0.18$ mL/mL. An unweighted average would give $0.175$ mL/mL. A specimen's vessel connections establish where the streams meet; conservation of mass establishes how their transported oxygen combines.

The systemic circulation carries blood from the left ventricle through body tissues and back to the right atrium. Its main arterial outflow is the aorta, and major venous return channels include the superior vena cava and inferior vena cava.^[ref] The separate pulmonary circulation then passes through the lungs before blood returns to the left heart.

The two circuits operate in series, while many systemic tissue beds receive arterial supply in parallel. In an original fixed-resistance model, beds sharing pressure difference $\Delta p$ haveFor a stipulated $\Delta p=90$ mmHg and two resistances 30 and $60\mathrm{mmHg}\min {\mathrm{L}}^{-1}$, flows are 3 and 1.5 litres per minute, totaling 4.5. The equivalent resistance is 20 in those resistance units. Adding flows is appropriate here; adding parallel resistances is not.

Real vascular resistance changes with vessel geometry and physiology. Some routes also contain successive exchange beds, as in a portal system. The parallel-bed calculation is therefore a deliberately reduced model, not a complete vessel map.

Conservation of mass constrains sustained output from the right and left heart. If their flows differ, a vascular compartment must gain or lose blood. For the pulmonary pool,A hypothetical imbalance of $0.2\mathrm{L}\mathrm{mi}{\mathrm{n}}^{-1}$ adds 0.2 litres in one minute if maintained. Long-term matching of flows is a consequence of finite storage, rather than a rule that both instantaneous waveforms must be identical.

For a whole-body oxygen balance, systemic cardiac output must be paired with compatible arterial and mixed venous oxygen content. A regional venous sample answers a regional question; it does not become whole-body return simply because it was taken from a large vein.

The tricuspid valve is the right atrioventricular heart valve, between the right atrium and right ventricle. It permits filling from the right atrium and limits backward blood flow during ventricular contraction.^[ref]

The leaflets are supported by chordae tendineae attached to papillary muscles. Rising ventricular pressure brings the leaflets together; tension in the supporting apparatus helps prevent their displacement into the right atrium. The papillary muscles do not need to pull the leaflets open to initiate filling.^[ref]

A useful mechanical analogy is a pressure-loaded flap restrained by tethers. The pressure difference supplies a load, while the tethers limit how far the flap can move. The analogy distinguishes the role of the chordae tendineae from the action of a motorized door.

The valve also determines how to interpret right ventricular ejection fraction. Suppose a constructed ventricular contraction reduces cavity volume by 80 mL, but 20 mL of that loss returns through the tricuspid valve into the right atrium. Only 60 mL remains for forward transport through the pulmonary valve, if other transfers are negligible. The measured cavity-volume change is still 80 mL. An ejection fraction calculated from chamber volumes therefore does not by itself measure the useful forward stroke volume of the pulmonary circulation.