> For the complete documentation index, see [llms.txt](https://docs.algenta.ai/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.algenta.ai/medical-and-health-sciences/nutrition-and-veterinary-science-kernels.md). # Nutrition and veterinary science kernels Human energy-balance and body-composition formulas (BMI, Mifflin-St Jeor BMR, TDEE, macros) alongside weight-based veterinary dosing, fluid therapy, and per-species reference constants for dogs, cats, Two modules for weight-driven clinical arithmetic in two different patients. `nutrition` is human energy balance and body composition — the formulas behind a BMI reading, a daily calorie target, a macro split, and a cardio zone. `veterinary` is the small-animal-practice equivalent: a per-kg drug dose, a fluid-therapy rate, a caloric requirement, and a set of per-species reference constants (gestation length, normal heart-rate range, packed-cell volume, blood volume, anesthetic MAC) keyed by an integer species code. Both modules take and return plain `Float64`/`Int`/`List[Float64]` values — no structs, no status-code vocabulary — so every function is a single formula that either returns the right number or a visibly wrong one; neither module validates its inputs beyond what the arithmetic itself happens to guard against, which matters more here than in most of this corpus because a caller building a real dosing or diet tool on top of these numbers has no status code to check. ```python from algenta import MojoRuntime runtime = MojoRuntime(mode="local") runtime.execute("nutrition", "bmi", [70.0, 1.75])["result"] # 22.857142857142858 -- BMI = weight_kg / height_m^2 runtime.execute("nutrition", "bmr_mifflin", [70.0, 175.0, 30, True])["result"] # 1648.75 -- Mifflin-St Jeor, male: 10*70 + 6.25*175 - 5*30 + 5 runtime.execute("veterinary", "dose_mg", [25.0, 10.0])["result"] # 250.0 -- a 25 kg dog at 10 mg/kg ``` ## The modules | Module | What it does | | ------------ | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | `nutrition` | Human energy-balance and body-composition formulas: BMI and its WHO-style category, Mifflin-St Jeor BMR, activity-scaled TDEE, a caloric-deficit target, an Atwater-factor macro split, Devine ideal body weight, Deurenberg body-fat percentage, a water-intake rule of thumb, and heart-rate-based cardio metrics (max HR, target zone, VO2max estimate). | | `veterinary` | Weight-based small-animal dosing and fluid therapy (drug dose, fluid rate, dehydration deficit, canine maintenance fluids, canine resting energy requirement) plus per-species reference constants — gestation length, normal heart-rate range, packed-cell-volume midpoint, blood-volume estimate, and anesthetic MAC — addressed by an integer species code that only one of the seven species-coded functions actually implements for all four species the module documents. | ## `nutrition`: energy balance and body composition | Function | What it does | | ---------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | `bmi(weight_kg, height_m)` | `weight_kg / height_m^2`. | | `bmi_category(bmi_val)` | WHO-style classification: `0` underweight (`< 18.5`), `1` normal (`< 25.0`), `2` overweight (`< 30.0`), `3` obese (`>= 30.0`). | | `bmr_mifflin(weight_kg, height_cm, age, is_male)` | Mifflin-St Jeor: `10*W + 6.25*H - 5*A + 5` for men, `10*W + 6.25*H - 5*A - 161` for women. | | `tdee(bmr_val, activity_level)` | `bmr_val * activity_level`. The docstring names the intended range as `1.2`-`1.9` (sedentary to very active); the function does not clamp or validate it. | | `caloric_deficit(tdee_val, target_loss_kg_per_week)` | `target_loss_kg_per_week * 7700 / 7` — the standard \~7700-kcal-per-kg-of-fat rule of thumb, spread over 7 days. `tdee_val` is accepted but never referenced in the arithmetic. | | `macro_split(calories, protein_pct, fat_pct)` | `[protein_g, fat_g, carb_g]` from Atwater factors (protein and carb at 4 kcal/g, fat at 9 kcal/g). `carb_pct = 1 - protein_pct - fat_pct` is not clamped, so percentages that sum past `1.0` silently produce a negative carb figure rather than an error. | | `ideal_body_weight(height_cm, is_male)` | Devine formula: `50 + 2.3*(inches - 60)` for men, `45.5 + 2.3*(inches - 60)` for women, where `inches = height_cm / 2.54`. The Devine formula is defined for adult heights at or above 60 inches (152.4 cm); below that the function still returns a number, just one the original formula was never validated for. | | `body_fat_estimate(bmi_val, age, is_male)` | Deurenberg (1991): `1.20*BMI + 0.23*age - 10.8*sex - 5.4`, `sex = 1` for male, `0` for female. | | `water_intake(weight_kg)` | `weight_kg * 0.033` liters/day — the common 33 mL/kg/day rule of thumb. | | `heart_rate_max(age)` | `220 - age` (the Fox formula). | | `target_heart_rate(hr_max, intensity_low, intensity_high)` | `[hr_max*intensity_low, hr_max*intensity_high]` — a percentage-of-max-HR zone, not the heart-rate-reserve (Karvonen) method, so it takes no resting heart rate. | | `vo2max_estimate(hr_rest, hr_max)` | `15.3 * (hr_max / hr_rest)` (the Uth-Sørensen-Overgaard-Pedersen estimate). `hr_rest = 0` divides by zero rather than being guarded. | **The formulas are the textbook ones, not simplifications of them.** Checking each against its published source: Mifflin-St Jeor's `+5`/`-161` sex offset, Devine's `50`/`45.5` base weights and `2.3` per-inch slope, and Deurenberg's `1.20`/`0.23`/`10.8`/`5.4` coefficients all match the original equations exactly — nothing here is a rounded-off or partial reimplementation. `tests/mojo/test_wave60.mojo` ("Wave 60 — Optics, Electrical Engineering, Nutrition Science", the 250-library-milestone wave) pins several of these against hand-worked values rather than just range-checking them: `bmr_mifflin(70.0, 175.0, 30, True)` must equal `1648.75` exactly (`10*70 + 6.25*175 - 5*30 + 5`), `tdee(1800.0, 1.55)` must equal `2790.0`, and `macro_split(2000.0, 0.3, 0.3)` must split into `protein_g = 150.0`, `fat_g = 66.667`, `carb_g = 200.0` — a split whose three components, fed back through the Atwater factors (`150*4 + 66.667*9 + 200*4`), sum back to `2000.0` kcal to within the test's own `0.1` tolerance. **`macro_split`'s missing clamp is reachable with ordinary-looking inputs.** A caller asking for a 40%-protein, 40%-fat plan — each individually plausible — gets `carb_pct = 1 - 0.4 - 0.4 = 0.2`, fine. But 60%-protein, 50%-fat (a caller stacking two "high" targets without checking they still sum under 1.0) gives `carb_pct = -0.1`, and `macro_split` returns that as a genuine negative `carb_g` rather than refusing — nothing in the function's `def` name or return type signals that the third slot can go negative. ## `veterinary`: weight-based dosing and species reference constants | Function | What it does | | ------------------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | `dose_mg(weight_kg, dose_per_kg)` | `weight_kg * dose_per_kg` — a linear per-kg drug dose. | | `fluid_rate_ml_hr(total_ml, hours)` | `total_ml / hours`. | | `fluid_deficit(weight_kg, dehydration_pct)` | `weight_kg * dehydration_pct / 100 * 1000` mL — the standard fluid-deficit estimate; `dehydration_pct` is taken as a whole number (`8` for 8% dehydrated), not a fraction. | | `maintenance_fluid_dog(weight_kg)` | `60 * weight_kg` mL/day. The module's own docstring calls this "simplified" — it is a flat per-kg rate rather than the allometric-scaling maintenance formulas (e.g. `~132 * weight^0.75`) veterinary practice uses across a wider weight range. | | `caloric_requirement_dog(weight_kg)` | `70 * weight_kg^0.75` kcal/day — the standard interspecies Resting Energy Requirement (RER) allometric formula. Despite the `_dog` suffix, the `70*BW^0.75` equation itself is not dog-specific in veterinary nutrition (the same formula is the standard RER for cats and other mammals too); `_dog` names this module's one entry point for it, not a species restriction in the math. `weight_kg^0.75` is computed as `sqrt(sqrt(weight_kg^3))` via 20 fixed iterations of a private Newton's-method square root (`_sqrt_approx`), not a general power or logarithm routine. | | `body_condition_score_ideal(species_code)` | Always returns `5.0` on the 1-9 BCS scale, regardless of `species_code` — the docstring's "Dog(0)=5.0, Cat(1)=5.0" describes the two species the rest of the module supports, but this particular function does not branch on its input at all. | | `anesthesia_mac(species_code, agent_code)` | Typical minimum alveolar concentration: Dog/isoflurane `1.3`, Dog/sevoflurane `2.4`, Cat/isoflurane `1.6`, Cat/sevoflurane `3.1`. The branch is `species_code == 0` (Dog) vs. everything else (Cat) — Horse (`2`) and Cow (`3`), both named in the module's own species-code comment, silently receive Cat's MAC values. | | `gestation_period_days(species_code)` | Dog `63`, Cat `65`, Horse `340`, Cow `283` days; any other code returns `0.0`. | | `heart_rate_normal_range_low(species_code)` / `heart_rate_normal_range_high(species_code)` | Dog `60`-`140`, Cat `120`-`220`, Horse `28`-`44` bpm; Cow and any other code return `0.0` for both bounds. | | `packed_cell_volume_normal(species_code)` | Dog `46.0`, Cat `37.5`; Horse, Cow, and any other code return `0.0`. | | `blood_volume_estimate(weight_kg, species_code)` | Dog `90` mL/kg, Cat `60` mL/kg; Horse, Cow, and any other code return `0.0` regardless of `weight_kg`. | **Seven of the twelve functions take a `species_code`; only one of those seven covers all four species the module's header comment lists.** The file opens with `# Species codes: 0=Dog, 1=Cat, 2=Horse, 3=Cow`, and `gestation_period_days` is the only species-coded function that actually branches on all four — every other one recognizes at most three (`heart_rate_normal_range_low`/`_high`, which cover Dog/Cat/Horse and fall through to `0.0` for Cow) or just two (`packed_cell_volume_normal` and `blood_volume_estimate`, Dog/Cat only; Horse and Cow both return `0.0`). `body_condition_score_ideal` ignores `species_code` entirely. **`anesthesia_mac` is the one case where the fallback is a wrong number, not an obviously-empty one.** Every other species-coded function's fallback for an unlisted species is `0.0` — a value a caller checking "did I get a real reading back" can catch. `anesthesia_mac` has no such tell: its `if species_code == 0` branch means any non-zero code, including Horse (`2`) and Cow (`3`), falls through to the Cat branch and returns a real-looking MAC value (`1.6` for isoflurane, `3.1` for sevoflurane) that belongs to a different species. `anesthesia_mac(2, 0)` — Horse, isoflurane — returns `1.6`, Cat's value, with nothing in the return distinguishing it from a genuine Horse reading. A worked chain from `tests/mojo/test_wave86.mojo` ("Wave 86 — Paper Science, Radar, Veterinary"), which pins exact values rather than just checking they're finite: ```python runtime.execute("veterinary", "fluid_deficit", [10.0, 8.0])["result"] # 800.0 -- a 10 kg patient, 8% dehydrated: 10 * 8 / 100 * 1000 runtime.execute("veterinary", "caloric_requirement_dog", [10.0])["result"] # 393.6389276332444 -- RER = 70 * 10^0.75 runtime.execute("veterinary", "blood_volume_estimate", [25.0, 0])["result"] # 2250.0 -- a 25 kg dog at 90 mL/kg ``` `caloric_requirement_dog(10.0)`'s expected value is independently reproducible outside the test file too: `70 * 10**0.75 == 393.6389276332444` and `70 * 5**0.75 == 234.0591067417477` in plain Python, matching the test's `393.64`/`234.06` comments to four significant figures — the module's sqrt-of-sqrt-of-cube approximation of a fractional power reproduces the closed-form result to full double precision for both weights checked. ## Verification `mojo/tests/libs/test_nutrition.mojo` and `mojo/tests/libs/test_veterinary.mojo` are auto-generated coverage smoke tests: each calls every function once with fixed placeholder arguments (`0.5`, small integers) and checks only that a `Float64` result is finite, or that a list has non-negative length — they pin no specific numeric output and would not catch a sign error or a swapped coefficient. The real numeric assertions live in the wave-suite files instead: `tests/mojo/test_wave60.mojo` pins `bmi`, `bmr_mifflin`, `tdee`, `caloric_deficit`, `macro_split`, `water_intake`, `heart_rate_max`, `target_heart_rate`, and `vo2max_estimate` against exact hand-computed values (plus range checks on `ideal_body_weight` and `body_fat_estimate`), and `tests/mojo/test_wave86.mojo` pins all twelve `veterinary` functions, including every species/agent combination `anesthesia_mac`, `gestation_period_days`, `heart_rate_normal_range_low`, `heart_rate_normal_range_high`, and `packed_cell_volume_normal` actually implement. The worked examples in this page are drawn from those pinned assertions, and the `caloric_requirement_dog` values were independently re-derived in plain Python (`70 * w**0.75`) to confirm the module's iterative square-root approximation of the fractional power is not losing precision anywhere the test tolerance would hide. **Next:** see the full function list in the [Runtime library catalog](/engine-runtime/runtime-library-catalog.md), or browse the [Engine catalog](/engine-runtime/catalog.md) for how `nutrition` and `veterinary` are exposed alongside every other engine. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation by asking a question. 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