FA-64086 / Medication dosing calculations / Open access
Pharmacokinetic loading and maintenance doses: maintenance bioavailability · case 01
Oral maintenance doses are smaller than the intravenous equivalent.
ROOT CAUSE
The maintenance dose multiplies by F instead of dividing by it.
THE FAILURE
The maintenance dose multiplies by F instead of dividing by it.
Unsuccessful approach: Dropping F entirely treats an oral dose as if fully absorbed.
Case contract
Input {target, current, vd_l_kg, weight_kg, f, cl_ml_min, tau_h, unit_mg}. Toy one-compartment rule: loading = max(0, (target-current)*Vd*weight/F); maintenance = target*CL*tau/F with CL in L/h = cl_ml_min*60/1000. Both are rounded half-up to a multiple of unit_mg. Return {loading_mg, maintenance_mg}.
Why this case matters
Loading and maintenance calculations chain unit conversions and bioavailability; each factor is an independent defect site.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
tgt, cur = Fraction(str(x['target'])), Fraction(str(x['current']))
f = Fraction(str(x['f']))
u = x['unit_mg']
vd = Fraction(str(x['vd_l_kg']))
wt = Fraction(str(x['weight_kg']))
cl = Fraction(x['cl_ml_min']) * 60 / 1000
def rnd(v):
return float(math.floor(v / u + Fraction(1, 2)) * u)
load = max(Fraction(0), (tgt - cur) * vd * wt / f)
maint = tgt * cl * x['tau_h'] * f
return {'loading_mg': rnd(load), 'maintenance_mg': rnd(maint)}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 71,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 750.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 6,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 700.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 13,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.5',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 240.0, 'maintenance_mg': 290.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 65,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 175.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 10,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 14.0})],
[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 72,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 750.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 7,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 650.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 14,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.8',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 150.0, 'maintenance_mg': 180.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 25,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 75.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 20,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 29.0})],
[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 73,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 750.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 8,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 600.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 15,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.25',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 480.0, 'maintenance_mg': 575.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 45,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 125.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 30,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 43.0})],
[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 74,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 800.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 9,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 550.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 16,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.4',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 300.0, 'maintenance_mg': 360.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 85,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 225.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 40,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 58.0})],
[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 75,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 800.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 10,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 500.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 17,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.6',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 200.0, 'maintenance_mg': 240.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 105,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 275.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 72.0})]]
for label, args, expected in fixtures[N-1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| drug-naive loading | {'loading_mg': 750.0, 'maintenance_mg': 1100.0} | {'loading_mg': 750.0, 'maintenance_mg': 1100.0} | Passed |
| partial existing level credited | {'loading_mg': 700.0, 'maintenance_mg': 625.0} | {'loading_mg': 700.0, 'maintenance_mg': 950.0} | Failed |
| level above target gives no load | {'loading_mg': 0.0, 'maintenance_mg': 650.0} | {'loading_mg': 0.0, 'maintenance_mg': 650.0} | Passed |
| oral bioavailability maintenance | {'loading_mg': 240.0, 'maintenance_mg': 70.0} | {'loading_mg': 240.0, 'maintenance_mg': 290.0} | Failed |
| half unit rounds up | {'loading_mg': 175.0, 'maintenance_mg': 50.0} | {'loading_mg': 175.0, 'maintenance_mg': 50.0} | Passed |
| slow clearance long interval | {'loading_mg': 10.0, 'maintenance_mg': 14.0} | {'loading_mg': 10.0, 'maintenance_mg': 14.0} | Passed |
SHA-256 / c21e29b2b078bf4080ff396ae7334fbd8190c8218725cc2493b77c67664d4723
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
tgt, cur = Fraction(str(x['target'])), Fraction(str(x['current']))
f = Fraction(str(x['f']))
u = x['unit_mg']
vd = Fraction(str(x['vd_l_kg']))
wt = Fraction(str(x['weight_kg']))
cl = Fraction(x['cl_ml_min']) * 60 / 1000
def rnd(v):
return float(math.floor(v / u + Fraction(1, 2)) * u)
load = max(Fraction(0), (tgt - cur) * vd * wt / f)
maint = tgt * cl * x['tau_h']
return {'loading_mg': rnd(load), 'maintenance_mg': rnd(maint)}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 71,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 750.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 6,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 700.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 13,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.5',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 240.0, 'maintenance_mg': 290.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 65,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 175.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 10,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 14.0})],
[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 72,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 750.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 7,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 650.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 14,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.8',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 150.0, 'maintenance_mg': 180.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 25,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 75.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 20,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 29.0})],
[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 73,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 750.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 8,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 600.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 15,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.25',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 480.0, 'maintenance_mg': 575.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 45,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 125.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 30,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 43.0})],
[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 74,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 800.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 9,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 550.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 16,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.4',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 300.0, 'maintenance_mg': 360.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 85,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 225.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 40,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 58.0})],
[('drug-naive loading',
{'target': 15,
'current': 0,
'vd_l_kg': '0.7',
'weight_kg': 75,
'f': 1,
'cl_ml_min': 100,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 800.0, 'maintenance_mg': 1100.0}),
('partial existing level credited',
{'target': 20,
'current': 10,
'vd_l_kg': '0.5',
'weight_kg': 80,
'f': '0.8',
'cl_ml_min': 80,
'tau_h': 8,
'unit_mg': 25},
{'loading_mg': 500.0, 'maintenance_mg': 950.0}),
('level above target gives no load',
{'target': 10,
'current': 17,
'vd_l_kg': '0.6',
'weight_kg': 70,
'f': 1,
'cl_ml_min': 90,
'tau_h': 12,
'unit_mg': 50},
{'loading_mg': 0.0, 'maintenance_mg': 650.0}),
('oral bioavailability maintenance',
{'target': 2,
'current': 0,
'vd_l_kg': '1.0',
'weight_kg': 60,
'f': '0.6',
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 5},
{'loading_mg': 200.0, 'maintenance_mg': 240.0}),
('half unit rounds up',
{'target': 5,
'current': 0,
'vd_l_kg': '0.5',
'weight_kg': 105,
'f': 1,
'cl_ml_min': 25,
'tau_h': 6,
'unit_mg': 25},
{'loading_mg': 275.0, 'maintenance_mg': 50.0}),
('slow clearance long interval',
{'target': 1,
'current': 0,
'vd_l_kg': '0.2',
'weight_kg': 50,
'f': 1,
'cl_ml_min': 50,
'tau_h': 24,
'unit_mg': 1},
{'loading_mg': 10.0, 'maintenance_mg': 72.0})]]
for label, args, expected in fixtures[N-1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| drug-naive loading | {'loading_mg': 750.0, 'maintenance_mg': 1100.0} | {'loading_mg': 750.0, 'maintenance_mg': 1100.0} | Passed |
| partial existing level credited | {'loading_mg': 700.0, 'maintenance_mg': 775.0} | {'loading_mg': 700.0, 'maintenance_mg': 950.0} | Failed |
| level above target gives no load | {'loading_mg': 0.0, 'maintenance_mg': 650.0} | {'loading_mg': 0.0, 'maintenance_mg': 650.0} | Passed |
| oral bioavailability maintenance | {'loading_mg': 240.0, 'maintenance_mg': 145.0} | {'loading_mg': 240.0, 'maintenance_mg': 290.0} | Failed |
| half unit rounds up | {'loading_mg': 175.0, 'maintenance_mg': 50.0} | {'loading_mg': 175.0, 'maintenance_mg': 50.0} | Passed |
| slow clearance long interval | {'loading_mg': 10.0, 'maintenance_mg': 14.0} | {'loading_mg': 10.0, 'maintenance_mg': 14.0} | Passed |
SHA-256 / c13036aa7a688e81111840804687b63d990ef891cecff787b3720f8af91271c2
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This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.
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A deterministic toy software model with explicitly stipulated thresholds and formulas; it is not clinical guidance, not a validated medical calculator, and makes no claim of conformance to any published protocol. Numbered variants vary patient and order inputs. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:47:21.158131+00:00.
Case digest / 9705666a30306d2cc5a887ce5a586e701e9b74c7d2d6c4e1041d97cad31e1d25