INTERACTIVE COMPANIONVOLUME 2, ISSUE 1FALL 2025

The Concentration Bench

A live model accompanying “The Dosing Schedule Decides Whether Resistance Wins”

Study: Computational study
Review: Peer-edited by the club review board
Article: 12 sectionsabout 35 min
Files: LaTeX source24 kB
Analysis code57 kB
Raw output73 kB

Nothing here is a new simulation. The pharmacokinetic and pharmacodynamic formulas below are the exact closed forms the analysis script evaluates before it ever draws a random number, so every curve and every peak-concentration or time-above-MIC readout matches a number the club could in principle print by hand. The probability of cure itself is not recomputed here — that number comes only from running thousands of stochastic replicates, which a page cannot do live — so those readouts are the club's own measured values from the 50,000-course grid and the matched-exposure ladder, looked up rather than resimulated.

Model 1. The concentration engine

One compartment, instantaneous input, first-order elimination at $k_{\text{elim}} = \ln 2 / 3 = 0.231049$ /h. At steady state the peak the day before the last dose is $C_{\max} = D / (1 - e^{-k_{\text{elim}}\tau})$ . The net-growth panel is the article's Figure 1, drawn from the same pharmacodynamic function, with a marker that slides to wherever your current peak concentration lands.

Dose per administration, mg/L32.0Dosing interval τ, hours8Dose 32 mg/L every 8 hours is the schedule the article leans on hardest: it clears every one of 2000 replicates in the main grid and its peak, 37.98 mg/L, is the number §11 uses to explain why widening the resistance step to 32× breaks high-dose treatment.Course length, days7

Doses given: -Peak C_max: - mg/LTotal AUC: - mg/L·hfT>MIC_S: -fT>MIC_R: -Peak clears MIC_R: -

Model 2. The matched-exposure ladder

Fix the dosing interval at 8 hours and the total drug delivered at $D \times n = 288$ mg/L, and only the shape of the course can change. Move the slider and the dose recomputes live as $D = 288/n$ ; the AUC recomputes live too, as $n D / k_{\text{elim}}$ , and always lands on the same number no matter which day you pick, because that is what “matched exposure” means. The cure and resistance probabilities are the club's seven measured values from the real ladder, not something this page can resimulate.

Course lengthDefault is the fourteen-day arm, the one the poster in the waiting room would call the safe choice. Switch to two days and watch P(resistance) collapse from 0.9110 to 0.0000 on the identical 1246.5 mg/L·h of drug.

Dose, computed live: - mg/LAUC, computed live: - mg/L·hP(cure): -P(resistance): -Gap to 2-day arm, in pooled SE: -

What stays fixed: τ = 8 h, dose × doses = 288 mg/L, k_elim = 0.231049 /h
What the article measured at this row: -

What the two models say together

Model 1 is the part of the study that is pure arithmetic: given a dose and an interval, the concentration curve and everything derived from it are fixed by the formulas, no randomness involved. Model 2 is the part that is not arithmetic at all: two schedules can deliver an identical, live-verifiable 1246.5 mg/L·h of drug and still land on 0.0000 and 0.9110 probability of resistance, a gap only a few thousand simulated courses could have found. That split is the article's whole argument in miniature: the drug curve is deterministic, and what a population does underneath it is not.