The Hydraulic Impedance

Otto Frank, Ernest Starling, and Myocardial Compliance in London

Inside the physiology laboratory at University College London in the spring of 1914, Ernest Starling observed an isolated canine heart. The organ sat mounted within a scaffold of glass cannulae, brass pressure reservoirs, and mercury manometers. Together with Solomon Markwalder and Gleb von Anrep, Starling had engineered the heart-lung preparation. They severed the heart completely from the central nervous system and circulated warm, oxygenated venous blood through external rubber resistance tubes. Stripped of brain commands, vagal nerve brakes, and adrenal hormones, the isolated pump displayed a striking mechanical property. Whenever Starling raised the venous supply reservoir to pour a larger volume of blood into the right atrium, the heart did not engorge into passive failure. Within a single beat, the ventricular walls contracted with proportionally greater force. They ejected the entire extra volume against arterial resistance.

Two decades earlier at the Physiological Institute in Munich, German physicist and physician Otto Frank had recorded the same phenomenon in the isolated frog ventricle. By clamping the aortic outflow valve and filling the chamber to precise steps of volume, Frank plotted families of isovolumetric pressure curves. Combined, their measurements established the primary autoregulatory mechanism of the vertebrate circulation—the Frank-Starling law of the heart. The right and left ventricles sit in series within a closed hydraulic loop. Even a one-milliliter mismatch in stroke volume between the two pumps would flood the lungs within minutes. Intrinsic length-dependent activation guarantees that whatever volume enters a chamber during filling is automatically expelled during the next contraction.

This mechanical feedback resides inside the geometry of the cardiac sarcomere. In skeletal muscle, active force peaks at a resting sarcomere length near 2.2 micrometers and drops off if the muscle is stretched further. Cardiac muscle operates exclusively on the steep ascending limb of its length-tension curve, between 1.8 and 2.2 micrometers. When elevated venous return expands end-diastolic volume, the ventricular muscle fibers stretch axially. Because each muscle cell maintains a constant internal fluid volume, axial stretching forces the cylindrical cell to narrow radially. This radial compression narrows the lateral lattice spacing between thick myosin filaments and thin actin filaments:

As this interfilament distance shrinks by fractions of a nanometer, myosin motor heads are brought closer to their binding targets on the actin strand. Simultaneously, passive tension in the giant elastic protein titin uncoils and pulls myosin cross-bridges outward from the thick filament backbone. At the same time, the regulatory protein troponin C increases its binding affinity for intracellular calcium ions. More cross-bridges engage per unit of calcium released, converting passive preload stretch directly into active systolic force.

The mechanical wall stress ($\sigma_{\text{wall}}$) borne by the myocardium while generating intraventricular pressure ($P$) obeys the law of Laplace. For a thick-walled sphere of internal radius $r$ and wall thickness $h$, wall stress follows:

When a failing heart dilates chronically, chamber radius $r$ grows while wall thickness $h$ thins. Wall stress spikes for every millimeter of mercury of arterial pressure, trapping the muscle in a high-oxygen-consumption penalty. In a healthy heart exposed to sustained high pressure, the myocardium counters Laplace's penalty through concentric hypertrophy, thickening $h$ to normalize wall stress.

Downstream of the aortic valve, intermittent ventricular ejection is smoothed into continuous capillary flow by the Windkessel effect. First formulated by Stephen Hales in 1733 and quantified by Otto Frank in 1899, arterial compliance ($C = dV / dP$) in the elastic elastin lamellae of the ascending aorta absorbs roughly half of each stroke volume during systole. That elastic expansion stores kinetic energy as wall tension and recoils during diastole to keep blood moving smoothly through peripheral tissue beds.