Sphincter-gate disorders (GERD, achalasia, spasm, Oddi)

The esophageal and outlet motor disorders ride one Tier-2 primitive: a gate, the R19 switch held closed, opening only past tone plus spinodal. GERD is the gate failing closed, reflux burden rising as LES tone falls; achalasia is the same gate stuck closed into stasis: two opposite failures of one gate. Spasm is a coordination fault; Oddi the biliary-outlet gate.

The first Tier-2 primitive is a gate: the §2 R19 switch ds/dt = g·s − s³ + h held in its closed basin by a tonic bias, opening only when a coordinated drive clears the opening spinodal (resistance = tone + spinodal). One gate gives two opposite diseases — the gate analogue of the §11/§14 one-ICC-lesion mirror: GERD (failing closed → retrograde reflux burden rising monotonically as tone falls) and achalasia (failing open → antegrade stasis, with aperistalsis compounding). Esophageal spasm is a §4 coordination pathology where amplitude cannot rescue lost coordination; sphincter of Oddi is the same gate at the biliary outlet. Motor readings [V]; felt pain and absolute frequencies/clearance/outflow [O] with stated obstacles.

The esophageal and outlet motor disorders need one element the transport and homeostat modules do not contain: a gate — a tonically-closed valve that opens only on a coordinated relaxation signal. This is the first Tier-2 primitive, and it is not new dynamics: a gate is the §2 R19 switch ds/dt = g·s − s³ + h held in its closed basin by a tonic closing bias, which a relaxation or pressure drive flips open only once it clears the opening spinodal (bistable hysteresis). The gate resistance is tone + spinodal(g); nothing is fitted.

This single gate produces two diseases that are exact opposites — the gate analogue of the one-ICC-lesion mirror of §11/§14. GERD is the gate failing closed: as resting lower-esophageal-sphincter tone falls, more of a fixed spectrum of intra-gastric pressure transients clears the gate resistance, so retrograde reflux burden rises monotonically — continent at high tone (0 events), incompetent at low tone (18 of 21). The reflux source is the gate; the mucosal-injury consequence is the §15 reflux-erosion curve.

Treatment (model reading). GERD -- RAISE the gate tone / lower the intra-gastric opening drive: the model reduces reflux events by lifting the gate resistance (tone + spinodal) back above the pressure-transient spectrum (anti-reflux barrier / fundoplication; weight loss lowers the driving pressure). The mucosal-injury CONSEQUENCE is treated on the s15 reflux-erosion curve (acid suppression). Target direction [V]; absolute reflux frequency [O].

Achalasia is the same gate failing open: the coordinated swallow relaxation can no longer flip it, so the bolus is retained at the junction (stasis, then dilatation). Two routes reach the identical stuck gate — a failing relaxation drive (shown below) and a rising gate tone — both making the open drive fall below the gate resistance; aperistalsis (loss of the §4 wave) compounds the upstream clearance.

Treatment (model reading). achalasia -- FORCE the gate-open transition: pneumatic dilation / myotomy / botulinum to the gate all drop the gate resistance so the (preserved) relaxation drive can again clear it; the model predicts efficacy tracks how far the resistance is lowered below the available open drive. Aperistalsis (the s4 wave) is not restored by opening the gate -- the residual transit deficit is the falsifiable prediction. Direction [V]; efficacy [O].

Esophageal spasm / jackhammer / nutcracker is a §4 coordination pathology, not a gate fault: net directed transport collapses as the aboral phase coordination is lost, and — the jackhammer signature — raising contraction amplitude does not rescue transit. Vigorous but uncoordinated contraction fails to move the bolus, and more vigor only makes it worse.

Treatment (model reading). spasm / jackhammer -- RESTORE coordination and/or REDUCE the excessive amplitude (smooth-muscle relaxants, nitrates / calcium-channel blockers): the model shows lowering amplitude alone does not restore transit unless coordination returns, which is exactly why these disorders are refractory -- the falsifiable prediction. The felt chest-pain component is afferent-gain (B3 / `mind`), out of scope here. Direction [V]; efficacy [O].

Sphincter of Oddi dysfunction is the same gate primitive at the biliary / pancreatic outlet: a stuck-closed gate gives an outflow-obstruction proxy — outflow ceases when the gate cannot open — and the treatment mirror (sphincterotomy = force the gate open) is identical to achalasia.

Treatment (model reading). sphincter of Oddi dysfunction -- RELAX / ablate the gate (endoscopic sphincterotomy): the same force-the-gate-open mirror as achalasia, restoring biliary / pancreatic outflow. Direction [V]; absolute outflow and patient selection [O] (biliary layer is group C).

All four motor readings are forced by the substrate [V] — the gate (GERD continence, achalasia/Oddi stuck-closed stasis) and the §4 coordination (spasm). What stays open [O], each with its obstacle: the absolute reflux frequency, the absolute achalasia clearance and Oddi outflow (clinical manometry / pH-impedance / scintigraphy), and the felt chest-pain component of spasm, which is afferent gain (group B3, with the felt interpretation in mind behind the firewall; the non-opioid lever that raises that peripheral visceral afferent's firing threshold is mapped in §28).