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The mitral valve separates the left atrium from the left ventricle. In a reservoir model with the atrium incorporated into the venous filling compartment, ideal one-way flow is $Q_v=[p_v-p_{LV}{]}_{+}/R_v$, where $[x{]}_{+}=\max (x,0)$ and $R_v$ is open-valve hydraulic resistance. The positive-part rule prevents reverse flow in this idealization.

Let $p_a,p_v,p_{LV}$ be pressures in the arterial reservoir, venous reservoir and left ventricle. Constant vascular compliances $C_a,C_v$ relate volume changes to pressure changes. The ventricular elastance relation iswhere $V_0$ is the unstressed ventricular volume and $E_{LV}(t)>0$ is the time-dependent inverse compliance. Define the positive part $[x{]}_{+}=\max (x,0)$. The systemic, aortic-valve and mitral-valve flows areEach $R$ is a positive hydraulic resistance. The aortic valve permits outflow only when ventricular pressure exceeds arterial pressure, and the mitral valve permits filling only when venous pressure exceeds ventricular pressure.

Mass conservation, with blood treated as incompressible, givesSubstitution and multiplication of the first two equations by $R_c$ give exactlyAdding the three original balances gives zero total volume change. This is a three-compartment ventricular circulation model.

During isovolumetric contraction, ventricular pressure lies between the venous and arterial pressures, $p_v<p_{LV}<p_a$. Both valves are closed, so $Q_v=Q_a=0$ and ventricular volume remains at its end-filling value $V^{+}$. ConsequentlyHere $V^{+}$ is end-diastolic ventricular volume and $V_0$ is the zero-pressure/unstressed volume.

The arterial and venous reservoirs still exchange systemic blood:If contraction is short compared with both $R_c{C}_a$ and $R_c{C}_v$, the fractional changes are small andwhere the superscript values refer to the beginning of contraction. Thus pressure can rise rapidly in the left ventricle through increasing elastance while the other pressures are approximately fixed. This stage ends when $p_{LV}$ reaches $p_a$ and the aortic valve opens.

Modern hypertrophy means enlargement of individual biological cells; hyperplasia means an increase in their number. Both can enlarge an organ, and both can occur together. The historical question requires care because nineteenth-century authors sometimes included “numerical hypertrophy” within the broader discussion of growth. Rudolf Virchow's 1860 English edition explicitly distinguishes enlargement of existing elements from multiplication of elements, using simple and numerical hypertrophy for these different processes.^[ref]

At the minute structural level, true hypertrophy entails increased cellular substance and, in a contractile biological cell, more contractile apparatus. Enlarged cell nuclei can accompany it, but a large cell nucleus alone does not prove a proportional increase in functional tissue. Increased cell number belongs to hyperplasia. Apparent organ enlargement from oedema, fatty infiltration, amyloid or a tumour must be distinguished from a coordinated increase of the organ's working tissue.^[ref]

The clearest early-to-late examples compare adaptation with the possible effects of continued overload:

These illustrations compare different outcomes rather than proposing a universal stage in which every enlarged organ degenerates.^[ref][ref]

A second set illustrates growth in organs whose biological cells can also divide. The pregnant uterus combines marked enlargement of smooth muscle biological cells with an increase in their number; after delivery it undergoes involution. An enlarged remaining kidney after loss of its partner exemplifies compensatory growth. In a modern rat experiment comparing neonatal, weanling and adult animals after removal of one kidney, the younger groups showed greater compensatory growth; that experimental comparison does not make an age-independent prediction for every human kidney.^[ref] Thus organ size alone cannot distinguish the cellular processes: compare cell dimensions, numbers and tissue composition by histology.^[ref]

An arterial reservoir, venous reservoir and a left ventricle exchange flows $Q_a,Q_v,Q_c$. Their volume balances are $C_a{\dot{p}}_a=Q_a-Q_c$, $C_v{\dot{p}}_v=Q_c-Q_v$, and $d(p_{LV}/E_{LV})/dt=Q_v-Q_a$. Ideal one-way valves give $Q_a=[p_{LV}-p_a{]}_{+}/R_a$, $Q_v=[p_v-p_{LV}{]}_{+}/R_v$; systemic resistance gives $Q_c=(p_a-p_v)/R_c$. Summing the three equations verifies total mass conservation for incompressible blood.