The pulmonary interstitium is the supporting tissue framework between and around the epithelial and vascular structures of the lung. Its thickness and composition affect mechanics and gas-transfer distance. It is distinct from the air-filled alveolar lumen.

A compressional wave is a longitudinal wave whose propagation produces changes of volume or density. In an isotropic elastic solid its displacement is parallel to the wavevector; substituting that polarization into the dynamic Navier-Cauchy equation gives the displayed speed. In a fluid without static shear stiffness the analogous speed is $\sqrt{K/\rho }$, with the appropriate compressional bulk modulus. Reflection at a rigid elastic boundary can convert part of its energy into a shear wave.

A hepatic sinusoid is a specialized microvascular channel through which blood passes between hepatocyte plates. Its exchange interface permits close interaction between circulating material and liver cells. It is distinct from a bile canaliculus despite their close spatial relationship.

The hepatic artery supplies arterial blood to the liver and associated territories through its branches. Hepatic tissue also receives portal venous blood. The dual input means flow volume and oxygen delivery cannot be inferred from the arterial route alone.

A Kupffer cell is a resident macrophage associated with hepatic sinusoids. It samples and processes material carried through the liver’s vascular spaces. Its immune role differs from the metabolic and secretory roles of adjacent hepatocytes.

A bile canaliculus is a small bile-collecting channel formed at adjacent hepatocyte surfaces. It begins the biliary flow pathway before the larger duct system. Its lumen is separate from the nearby sinusoidal blood space.

A bile duct conducts bile toward larger biliary passages and ultimately the intestine. Its epithelial lining participates in fluid modification as well as conduction. It is anatomically distinct from vessels carrying blood through the liver.

The portal vein carries blood from major splanchnic drainage territories to the liver. Its branches distribute this blood into hepatic microvascular pathways. A portal vein connects two vascular beds in sequence, rather than returning its entire flow directly to the heart.

Portal venous blood reaches a second capillary-type vascular bed through a portal route before returning to the main venous circulation. In hepatic physiology it carries intestinal and other splanchnic outflow toward the liver. Its composition reflects upstream absorption and metabolism.

Recovery of substances secreted into the intestine and their return to the liver through portal venous blood; bile salt recycling is a major example.

Liver failure is inadequate hepatic function severe enough to disrupt major physiological tasks. Impaired synthesis, metabolism and clearance can contribute differently. It is therefore broader than one abnormal biochemical concentration or an isolated structural change in the liver.

Paul Ehrenfest connected quantum expectation values with classical-looking equations of motion. For suitable quantum states evolving under the Hamiltonian $H=p^2/(2m)+V(x)$, the Ehrenfest theorem gives $d⟨x⟩/dt=⟨p⟩/m$ and $d⟨p⟩/dt=-⟨V^{\prime }(x)⟩$. Here $V$ is potential energy. The mean force need not equal the force evaluated at the mean position. If $V$ is a quadratic function, it does; for more general potential energy functions, a sufficiently narrow wave packet can justify an approximation. The theorem therefore states precisely which comparison between quantum mechanics and classical mechanics is exact and which step needs another assumption.^[ref]

A physicist associated with the Ehrenfest theorem and, with Tatyana Afanasyeva-Ehrenfest, the Ehrenfest model.

Leopoldo Nobili developed an astatic galvanometer for detecting small electric currents. A mechanically linked pair of nearly opposing magnetic dipoles reduces the torque from the approximately uniform geomagnetic field, while the coil geometry retains sensitivity to the current being measured. A many-turn coil increases the response and a scale makes the deflection observable. The preserved Nobili-pattern instrument used by Carlo Matteucci connects these design choices with measurements of weak physiological currents.^[ref]

A physicist associated with the astatic galvanometer.

Hans Christian Ørsted showed that an electric current can deflect a nearby compass needle. His 1820 announcement emphasized that the electric circuit had to be complete in these experiments and described repeating the observations with a more powerful battery. The compass needle supplied a mechanical readout connecting the electric current with magnetism. The wire's arrangement relative to the compass made this a direct experiment on the magnetic field associated with an electric current.^[ref]

A physicist associated with Ørsted's experiment.

Carlo Matteucci investigated electric currents associated with muscle using sensitive galvanometers. Museo Galileo preserves an instrument marked for his muscle-current work in 1840: an astatic galvanometer with suspended needles, many turns of fine wire and a readable scale. The apparatus connects a weak electrical signal with a mechanical deflection, illustrating why instrument sensitivity and suppression of the background geomagnetic field mattered for early physiological measurements.^[ref]

A physicist who, with Robert Bunsen, developed spectrum analysis as a method of chemical identification. Their 1860 apparatus put a salt sample in a hot, weakly luminous flame and passed its light through a slit, a collimating telescope and a prism. A second telescope revealed characteristic bright lines. Comparing these lines made it possible to recognize an element even when its light was mixed with that of other substances, connecting laboratory spectroscopy with the analysis of distant light sources.^[ref]

A physicist whose 2012 analysis of two charged conducting spheres gives a striking limit to the rule that like charges repel. Charges redistribute over each conducting surface, so sufficiently close spheres can attract even when their total charges have the same sign. The exceptional charge ratio is the one obtained by bringing the spheres into electrical contact. His exact analysis connects this attraction with the spheres’ capacitance coefficients.^[ref]

André-Marie Ampère investigated the mutual mechanical action of electric currents. Parallel currents in the same direction attract, while reversing one reverses the force; changing the circuit geometry provides further tests. James Clerk Maxwell's contemporary account distinguishes Ampère's experimental facts from the assumption used to model the interaction between individual current elements. The contribution therefore links an observable force between complete electrical circuits with a mathematical description of the interaction, rather than identifying the model's smallest parts directly with separately measured forces.^[ref]

Portrait source. Julien Léopold Boilly; Wellcome Collection, image V0000147, library reference ICV No 329. Creative Commons Attribution 4.0 International.

Wilhelm Eduard Weber developed a description of magnetization in which the microscopic magnets already exist and respond to an applied magnetic field. James Clerk Maxwell's treatise contrasts this with a model in which the field induces molecular magnetism. The distinction matters because changing the orientation of persistent magnetic dipoles can change the bulk magnetization without creating each magnetic moment from zero. A material can therefore have a small net magnetic response even when its microscopic magnetic contributions are individually nonzero.^[ref]

Portrait source. Gottlieb Biermann; scanned by Michael Schönitzer in November 2008 from Die großen Deutschen im Bilde (1936). Public-domain artwork; faithful photographic reproduction, PD-Art / Public Domain Mark.

A mathematician and physicist associated with statistical mechanics and the Ehrenfest model with Paul Ehrenfest.