health.bsa

pub fn body_surface_area(weight_kg: f64, height_cm: f64) -> BodySurfaceArea

/// Both formulas, so a caller uses the one its protocol names and never mixes them.
#[derive(Debug, Clone, Copy, PartialEq)]
pub struct BodySurfaceArea {
    /// m², √(height cm × weight kg ÷ 3600), rounded half away from zero to 2 places
    pub mosteller: f64,
    /// m², 71.84 × W^0.425 × H^0.725 cm² ÷ 10000, rounded half away from zero to 2 places
    pub du_bois: f64,
}

fune!(health.bsa@^1);  // then call body_surface_area(…)

use super::funejson::Value;  ← the fune runtime: the JSON value the test vectors use; fune build keeps it only where a signature takes one
use super::math_pow::pow;  ← from math.pow ^1.0.0 · built alongside by fune
use super::math_round_float::round_float;  ← from math.round-float ^1.0.0 · built alongside by fune

fn check_range(name: &str, value: f64, low: f64, high: f64, unit: &str) {
    if !value.is_finite() || value < low || value > high {
        panic!("{} must be a number from {} to {} {}, received {}", name, low, high, unit, value);
    }
}

/// Body surface area by both published formulas. They differ by up to a few
/// per cent, and a dose protocol names one, so both are returned rather than a
/// silent default. Powers go through math.pow, never `powf` or `sqrt`, so the
/// three languages agree to the bit before rounding.
///
/// # Panics
/// Panics when the weight or height is outside its range.
pub fn body_surface_area(weight_kg: f64, height_cm: f64) -> BodySurfaceArea {
    check_range("weightKg", weight_kg, 1.0, 650.0, "kg");
    // Height in metres (1.75) is the commonest unit slip.
    check_range("heightCm", height_cm, 30.0, 272.0, "cm");
    // Mosteller (1987): BSA (m²) = ([height (cm) × weight (kg)] / 3600)^½.
    let mosteller = pow((height_cm * weight_kg) / 3600.0, 0.5);
    // DuBois & DuBois (1916): A = W^0.425 × H^0.725 × 71.84, A in cm².
    let du_bois = (pow(weight_kg, 0.425) * pow(height_cm, 0.725) * 71.84) / 10000.0;
    BodySurfaceArea { mosteller: round_float(mosteller, 2), du_bois: round_float(du_bois, 2) }
}

pub fn body_surface_area_to_value(result: &BodySurfaceArea) -> Value {
    Value::obj(vec![("mosteller", Value::Float(result.mosteller)), ("duBois", Value::Float(result.du_bois))])
}

fn number_arg(value: &Value, name: &str, low: f64, high: f64, unit: &str) -> f64 {
    match value {
        Value::Int(_) | Value::Float(_) => value.as_f64(),
        _ => panic!("{} must be a number from {} to {} {}, received {:?}", name, low, high, unit, value),
    }
}

pub fn fune_vector(args: &[Value]) -> Value {
    body_surface_area_to_value(&body_surface_area(
        number_arg(&args[0], "weightKg", 1.0, 650.0, "kg"),
        number_arg(&args[1], "heightCm", 30.0, 272.0, "cm"),
    ))
}

Install

fune build

With that line in your source, in a Rust project (language rust in fune.project), fune build resolves it and its 2 dependencies, pins them in fune.lock, downloads only the Rust package of each, and builds the code above into your project’s .fune/build, one readable file per capability with a header linking back here. A crate’s build.rs runs it before every compile. Or pin a range in fune.project and build in one step:

fune add health.bsa

The manifest, vectors and README with only the Rust implementation. Install it without the registry with fune add ./health.bsa-1.0.0-rust.fune, or fetch it from a terminal with fune pull health.bsa@1.0.0:rust.

The whole function, every language, is one file too: health.bsa-1.0.0.fune, 12,035 bytes, sha256 81cf3f02076ab9cb46048c8c90ba49ad1655d6fda3d2ee260a6db0b00e886756. It installs into a project of any language.

// fune: before health.bsa

// fune: after health.bsa

// fune: replace math.pow in health.bsa
// fune: replace math.round-float in health.bsa

// fune: step health.bsa after <n|label>

More from the author

- **Mosteller**: BSA (m²) = √( height (cm) × weight (kg) ÷ 3600 ) - **DuBois & DuBois**: A = W^0.425 × H^0.725 × 71.84, with A in cm², W in kg and H in cm; divided by 10 000 for m² (the familiar 0.007184 × W^0.425 × H^0.725)

## Why both

The two disagree by up to a few per cent, more in obesity (150 kg at 165 cm is 2.62 m² by Mosteller and 2.45 m² by DuBois). Chemotherapy verification standards accept either but insist on consistency: a protocol, a prescriber and a pharmacist checking the prescription must all use the same formula. So both are returned, named, and nothing picks one silently.

## Edge cases

- Weight 1 to 650 kg, height 30 to 272 cm; anything else is refused, never clamped. Height in metres (1.75) is the usual slip. These ranges are guard rails for a clinician to confirm, not part of either formula. - DuBois & DuBois derived their formula from nine subjects, one a child; paediatric protocols often specify Mosteller (or another formula) instead. - Two decimal places is the precision BSA is prescribed at. Some units round further (to 0.1 m²) for dose banding; that is the caller's step. - Powers use `math.pow` (and the square root is `math.pow(x, 0.5)`), not the platform library, so the three languages agree to the bit (`floats exact`).

## Sources

- Du Bois D, Du Bois EF. *Clinical calorimetry, tenth paper: A formula to estimate the approximate surface area if height and weight be known.* Arch Intern Med 1916;17(6):863-871. The equation, the constant 71.84 and the worked example (150 cm, 60 kg, 1.55 m²) were read from the scanned original: https://archive.org/details/sim_jama-internal-medicine_1916-06-15_17_6 - Mosteller RD. *Simplified calculation of body-surface area.* N Engl J Med 1987;317(17):1098. doi:10.1056/NEJM198710223171717. The letter itself is behind a paywall and was not retrieved; the equation and constant 3600 were confirmed from the NHS Thames Valley Cancer Network, *Verification standards SOP* (2015), which states "BSA (m²) = ([Height(cm) x Weight(kg)]/3600)½" citing the letter, and that "the DuBois or Mosteller formulae are accepted as the standard BSA nomogram for adults": https://thamesvalleycanceralliance.nhs.uk/wp-content/uploads/2022/03/TVCN-Verification-SOP-November-2015.pdf

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