Free browser tool brings rigorous radiation dose equivalence to every radiotherapy clinic

Two radiotherapy schedules that deliver the same total physical dose can be profoundly different treatments. Twenty fractions of 3 Gy and thirty fractions of 2 Gy both add up to 60 Gy, yet the biological effect on tumor and healthy tissue differs sharply between them. Comparing such schedules requires converting physical dose into biologically effective dose and then into an equivalent dose in a reference fractionation, conventionally 2 Gy per fraction, a quantity known as EQD2. A newly released open-source package called LQL-Equiv-web, described in the journal SoftwareX by Cyril Voyant and Daniel Julian, makes that conversion available to anyone with a web browser, no installation, license, or operating system required.

The motivation is not academic. In a structured workshop where radiation oncologists, medical physicists, and technologists applied the same radiobiological models to the same standardized cases, mean agreement between practitioners reached only 25.8 percent on a Jaccard index, dropping to 10 percent for head-and-neck cases. Proposed dose-per-fraction adjustments for identical clinical situations ranged from 1.8 to 2.5 Gy, and nearly half of the surveyed centers reported they could not compute biologically equivalent schedules with the tools available to them. Multi-center studies of reirradiation have reached the same conclusion from another direction: variation in how centers scale radiobiological dose introduces clinically relevant differences in cumulative dose estimates.

Part of that dispersion reflects disagreement about vocabulary rather than radiobiology. Identical parameters yield substantially different reported EQD2 values depending on whether proliferation losses are applied to the evaluated schedule only or symmetrically to both the evaluated and the reference schedule. Three modeling elements are routinely omitted. First, the classic linear-quadratic model is widely held to overestimate cell kill at the large fraction sizes used in stereotactic treatments, so the linear-quadratic-linear form of Astrahan replaces the quadratic term with a straight line above a transition dose. Second, overall treatment time matters, because accelerated proliferation of surviving tumor cells after a kick-off time consumes dose every day, meaning an interruption is never neutral. Third, when two fractions are given in a single day, the incomplete-repair correction of Thames applies, since the second fraction arrives before sublethal damage has fully repaired.

The new release is a reimplementation of a validated 2014 MATLAB application, rebuilt as a dependency-free Python library and a browser application. The original was a Windows executable requiring a several-hundred-megabyte MATLAB runtime, with an interface in French and 3,567 lines of source in which the entire calculation sat inside a single callback. It could not be inspected, cited by version, or run by a colleague during a meeting. Version 3.0 separates the model, the calendar conversion, and a library of radiobiological tissue parameters into an auditable core that depends only on the Python standard library. The delivery layer embeds the sources into a single HTML page of about 112 kilobytes that runs the model locally in each visitor’s browser using WebAssembly, with no computation on a server, no analytics, and no forms.

The mathematics is deliberately complete. Each tissue carries seven parameters, including the alpha/beta ratio, a transition dose above which the response becomes linear, a repair half-time, and a kick-off time and doubling time for proliferation. The software computes biologically effective dose with the linear tail, subtracts proliferation losses once overall time exceeds the kick-off time, applies the incomplete-repair correction for twice-daily fractions, and then solves for the number of reference fractions carrying the same biological effect. Crucially, the reference schedule carries its own overall time and therefore its own proliferation loss, a point the authors identify as accounting for most disagreement between implementations. Treatment calendars run five days a week, weekends included, because cells do not rest on Saturdays, and successive courses are matched against one continuous reference schedule rather than restarting the clock each time.

Verification proceeded in two distinct steps. The first asked whether the calculation was transcribed correctly from MATLAB to Python: replaying 4,438 treatment schedules through the original 2014 program and the new library produced 69,131 compared values, of which 99.991 percent agreed at the reference’s own six-digit precision, with a largest single deviation of 0.04 Gy and every one of 34,403 paired equivalent doses clearing a pre-set tolerance of 0.05 Gy. The second step checked the equations against closed forms independently of the old code. The authors are careful to state that neither check constitutes clinical validation; both establish fidelity and correctness of the arithmetic.

One change between releases genuinely moves results. The 2014 code charged elapsed treatment time twice, once inside the equivalence equation at a flat rate and once afterward using the real calendar, which inflated organ doses for protracted schedules. Version 3.0 charges time once, on the calendar throughout. The magnitude is striking: for 60 Gy delivered at 12 Gy per fraction, the old treatment overstated lung equivalent dose by 74 percent, against 28 percent for the correct single charge. At the reference fraction size of 2 Gy the effect vanishes, and below it the sign reverses, with protracted schedules losing dose rather than gaining it. Four smaller defects of the old release, including a division by zero that reported complication probability as 100 percent for five tissues, were also fixed and documented rather than silently corrected.

External coherence checks place the tool against landmark trials. Against 78 Gy in 39 fractions, the software puts the ultra-hypofractionated arm of the HYPO-RT-PC prostate trial at 77.94 Gy, and it orders the two hypofractionated arms of CHHiP as the trial did. It disagrees with PROFIT, placing 60 Gy in 20 fractions 5.5 Gy below the conventional arm that demonstrated non-inferiority, but that gap closes when the alpha/beta ratio is set to 1.5 Gy, near the pooled clinical estimate of 1.4 Gy, evidence that the tabulated default of 3.1 Gy is not universal. On the normal-tissue side, the tabulated Lyman parameters fail outright for the spinal cord, returning a 5.1 percent complication probability where QUANTEC puts the risk near 0.2 percent, a discrepancy the authors report plainly.

The limitations are stated with unusual candor. This is a model comparison tool, not a treatment planning system: it knows nothing of dose distributions, volume effects, or plan constraints, and the authors explicitly warn that its outputs must not be used to choose or modify a prescription, compute compensation for a real interruption, sum dose in a reirradiation decision, or predict outcomes for an individual patient. The tumor control probability, newly exposed in this release, has not itself been validated against clinical outcome, and parameter uncertainties frequently exceed the differences the software displays, which is why it offers an alpha/beta sensitivity band and declines to name a best schedule when uncertainty bars overlap. Its purpose is comparing schedules under a stated model, seeing how the comparison moves when assumptions move, and teaching why.

The impact may ultimately lie in access and traceability. In a field where nearly half of surveyed centers report no usable tool, removing the installation barrier is the difference between a model being applied and being skipped. Every parameter’s provenance is recorded, the historical 2014 behavior remains reachable so that older published results can be reproduced, and the validation dataset ships with the code. A version-pinned, openly inspectable implementation that every participant in a multi-center study can run in a browser removes one term from the variance between centers, separating disagreement over arithmetic from the genuine scientific disagreement over parameters. A correction pushed to the repository goes live in browsers within a minute, and every version stays citable by its own DOI, an ambition the authors state explicitly: to give every department something independent against which to check a commercial planning system’s answer.

Subject of Research: Open-source software for biologically equivalent dose calculation in radiotherapy fractionation

Article Title: LQL-Equiv-web: a Python library and browser application for linear-quadratic-linear dose equivalence in radiotherapy

Article References: LQL-Equiv-web: a Python library and browser application for linear-quadratic-linear dose equivalence in radiotherapy. (n.d.). https://doi.org/10.1016/j.softx.2026.103085

Image Credits: AI Generated

DOI: 10.1016/j.softx.2026.103085

Keywords: radiotherapy, dose equivalence, EQD2, linear-quadratic model, hypofractionation, radiobiology, open-source software, WebAssembly, Python, treatment interruptions, reirradiation, tumor control probability