Gastric dysrhythmia and gastroparesis
Gastric dysrhythmia and gastroparesis are perturbations of one slow-wave pacemaker. Moving the FitzHugh–Nagumo rate constant carries the recorded rhythm across the cited electrogastrography band: bradygastria below 2.5, normal near 3, tachygastria above 3.7 cpm. A faster distal ectopic focus that couples entrains the antrum upward, and reducing pacemaker density grades gastric emptying toward zero [V].
Gastric dysrhythmia and gastroparesis perturb one slow-wave pacemaker. The FitzHugh–Nagumo recovery constant carries the recorded rate across the cited EGG band (brady < 2.5, normal ~3, tachy > 3.7 cpm); a faster coupled ectopic focus entrains tachygastria; and ICC pacemaker density grades emptying from full to zero. Mechanisms [V], the normal band [L], absolute emptying rate [O].
Gastric dysrhythmia and gastroparesis are not new machinery; they are perturbations of the single gastric slow-wave pacemaker of §2. The pacemaker is the shared FitzHugh–Nagumo oscillator, and its recorded rate is set by the recovery constant τ_s through the one gastric-anchored clock K_TIME.
Sweeping τ_s carries the recorded rhythm monotonically across the cited electrogastrography band: a short constant gives tachygastria (> 3.7 cpm), the §2 anchor gives the normal ~3 cpm, and a long constant gives bradygastria (< 2.5 cpm). No rate is fitted — the band is traversed by one substrate parameter.
| recovery constant τ_s | recorded rate (cpm) | rhythm |
|---|---|---|
| 240 | 4.80 | tachygastria |
| 300 | 3.90 | tachygastria |
| 380 | 3.00 | normal |
| 520 | 2.10 | bradygastria |
| 760 | 1.50 | bradygastria |
Tachygastria has a second, mechanistic route: a distal ectopic focus. A normal-rate distal focus leaves the antral recording in band (3.12 cpm), but a faster focus that couples entrains the antrum upward to 6.36 cpm — tachygastria appears only when the focus is both faster and coupled, exactly the clinical picture.
Gastroparesis is the amplitude counterpart. Interstitial-cell (ICC) pacemaker density scales the antral contraction; as density falls, gastric emptying in a fixed window slows monotonically, holding through moderate loss (a functional reserve) and then collapsing — 24.3% of normal at severe depletion, and zero with no pacemakers at all.
| pacemaker density (fraction) | emptying rate (% of normal) |
|---|---|
| 1.0 | 100.0% |
| 0.8 | 100.0% |
| 0.6 | 99.9% |
| 0.4 | 98.7% |
| 0.3 | 93.9% |
| 0.2 | 73.2% |
| 0.1 | 24.3% |
| 0.0 | 0.0% |
Treatment (model reading). The therapeutic target is the rhythm parameter and the contraction amplitude. For tachy/bradygastria the goal is to restore the ~3 cpm rhythm; the ectopic-entrainment result above is exactly the mechanism of gastric electrical pacing — an external pacemaker that out-paces and couples to the antrum entrains the recording back to target. For gastroparesis the target is the effective contraction (ICC density): prokinetics raise it, but the model predicts efficacy tracks residual ICC density, so with severe depletion the rhythm-restoring route is refractory and stimulation/surgical options follow. The treatment-target direction is forced [V]; absolute efficacy is open [O].
The dysrhythmia bands, the ectopic entrainment, and the density-graded emptying are all forced by the substrate [V]; the cited normal band (2.5–3.7 cpm) is a physiological anchor [L]; the absolute emptying rate is open [O], needing clinical (scintigraphy) calibration, exactly as absolute organ size is open.