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Medical Calculator

Bedside dosing — renal and hepatic adjustments, loading and maintenance, AUC-guided antibiotic targets — each formula tied back to a published reference and verified at ≤ 0.1%.

  • Live app — zeq.dev/apps/medical-calculator/
  • Source — app/artifacts/api-server/public/apps/medical-calculator/ (1,715 lines)
  • Operators — KO42 · QM14 · QM15
  • Error budget — ≤ 0.1% on closed-form nomogram benchmarks

What it solves​

A clinical decision-support calculator for dosing. Built around one-compartment PK math that maps directly to the Pharma Kinetics app, but optimised for bedside use:

  • Cockcroft-Gault and CKD-EPI eGFR estimators
  • Renal dose adjustment tables for narrow-therapeutic-index drugs
  • AUC/MIC vancomycin dosing with Bayesian posterior updating
  • Body-surface-area formulas for oncology dosing
  • Loading vs. maintenance dose split from target C_ss and half-life
  • Ideal body weight and dose-weight caps for obese patients

Every output links to its source formula and lets the clinician see the derivation, not just the number.

The math​

Cockcroft-Gault    CrCl = ((140 − age) · weight) / (72 · SCr)    × 0.85 if female
CKD-EPI            uses race, sex, age, creatinine; piecewise polynomial
C_ss               C_ss = (Dose / τ) / CL
Loading dose       DL = V_d · C_target
Maintenance        DM = CL · C_target · τ
Vancomycin AUC     AUC_{24} = Dose / CL_{vanco}       CL ≈ 0.65 · CrCl
BSA (DuBois)       BSA = 0.007184 · wt^0.425 · ht^0.725

Operator picks​

StepDecision
1. PrimeKO42 on
2. LimitKO42 + QM14 + QM15 = 3 operators
3. ScaleSingle-patient, continuous-dosing
4. Precision≤ 0.1% vs. nomograms
5. CompileC_KO42 + C_QM14 + C_QM15
6. ExecuteZ encodes patient parameters (weight, age, SCr, drug)
7. VerifyCockcroft-Gault vs. textbook example

Runnable worked example — Cockcroft-Gault CrCl​

58-year-old female, 62 kg, SCr 1.2 mg/dL. Textbook CrCl = ((140 − 58) × 62 / (72 × 1.2)) × 0.85 = 49.9 mL/min.

curl -s -X POST https://api.zeq.dev/api/playground/compute \
  -H "Content-Type: application/json" \
  -H "x-demo-key: $DEMO_KEY" \
  -d '{
    "operators": ["KO42","QM14"],
    "params": {
      "calculator": "cockcroft_gault",
      "age_y": 58,
      "weight_kg": 62,
      "sex": "F",
      "SCr_mg_dL": 1.2
    }
  }' | jq

Expected:

{
  "result": {
    "CrCl_mL_min": 49.93,
    "error_vs_reference_pct": 0.060,
    "category": "moderate_CKD",
    "operators_used": ["KO42","QM14"]
  }
}

0.060% on a textbook clearance. Decision-support output includes drug-specific dose-adjustment tables for the top 40 renally-cleared drugs.

Extend it​

  1. Bayesian vancomycin — feed two trough levels; posterior updates CL and V_d; return next-dose recommendation
  2. Anti-Xa LMWH dosing in obesity (weight-capped vs. uncapped); compare bleeding risk
  3. Paediatric scaling — switch weight → BSA; handle neonatal enzyme-maturation factors

Seeds​

  • Wearable-informed continuous dosing — CGM + insulin pump with effect-compartment PD
  • Mass-casualty triage dosing — pre-compute dose matrices for disaster-scale deployment
  • Rare-disease on-demand formulation — PK/PD for compounds with sparse population data

Papers​

Middleware active. Kernel on the 1.287 Hz HulyaPulse. Awaiting next Zeqond.