Piston: bicarbonate below, ketoanions (the anion gap) aboveHopper: the liver; syringe: insulin; springs: glucagon, cortisol, adrenalineLeft column: blood glucose, spilling to the beaker (urine) above 180 mg/dLBellows: the lungs, blowing off CO₂Red marks: DKA thresholds, glucose 200 mg/dL, HCO₃⁻ 18, pH 7.30Insulin, the syringe, holds the yoke up and both liver valves shut; the springs above are the counter-regulatory hormones pushing them open. Take insulin away and the liver pours out glucose and, once lipolysis is unchecked, ketoacids (β-hydroxybutyrate and acetoacetate). Above the kidneys' threshold of about 180 mg/dL glucose spills into the urine and drags water with it: the osmotic diuresis that leaves up to ~7 L owed. Every ketoacid H⁺ uses up one HCO₃⁻, which leaves as CO₂ through the lungs, and the ketoanion it leaves behind is new anion gap, so the piston falls as the gap grows. The bellows breathe deeper and faster (Kussmaul breathing) toward Winter's PaCO₂ = 1.5 × HCO₃⁻ + 8, which holds pH up until bicarbonate is nearly gone. DKA is glucose ≥ 200 mg/dL or known diabetes, β-OHB ≥ 3.0 mmol/L, and pH < 7.30 and/or HCO₃⁻ < 18 mmol/L; with no insulin this model reaches glucose 550, β-OHB 14, HCO₃⁻ 5, PaCO₂ 16, pH 7.15, gap 31. Click to treat: fluids repay the water and insulin at 0.1 U/kg/h shuts the valves. Glucose reaches 200 mg/dL by about 5 h, so dextrose is added, but bicarbonate takes 5 h to pass 18 and β-OHB 15 h to fall below 0.6 mmol/L, so insulin runs until the ketones clear, not the glucose. Not drawn: potassium. Serum K⁺ often reads normal or high at first despite a total-body deficit, and insulin drives it into cells, so it must be ≥ 3.5 mmol/L before insulin starts and is replaced throughout. Readout: glucose mg/dL · β-OHB mmol/L · HCO₃⁻ mmol/L · pH · anion gap. Teaching model; breaths in real time, treatment hours compressed.