Toxicology Body Burden

Mode A vs Mode B (Why the volumes look so different)

If you felt a moment of whiplash going from Mode A (a few liters) to Mode B (tens of liters), you are not misunderstanding anything - those two modes intentionally represent very different "reference volumes."

Mode A: Blood Volume Model (Intravascular)

Mode A approximates the intravascular space using circulating blood volume. In the reference table, blood volume is stored as mL/kg (a standard way these values appear in animal sampling guidance). The calculator converts this into liters with: Vblood(L) = (BW(kg) × BV(mL/kg)) / 1000.
Example (human default): 70 kg × 70 mL/kg = 4900 mL = 4.9 L. Values in the 50-90 mL/kg range (species dependent) are commonly used in toxicology/IACUC blood-volume tables.^[BV5][BV2]

Use Mode A when you want a conservative "blood-space amount" estimate (e.g., substances largely confined to vascular space), or when you explicitly do not want to assume broad distribution beyond blood. Practical caveat: plasma concentration is not always identical to whole-blood concentration, and protein binding / tissue binding can matter.^[VD2]

Human blood volume is also variable by sex, size, and method. Many practical guidance documents use a broad "rule-of-thumb" range on the order of ~55-70 mL/kg, while some sources quote about ~70 mL/kg for adult males and ~65 mL/kg for adult females.^[BV3][BV1] This tool uses 70 mL/kg as an engineering default for adults; change species/weight (or use Mode C) if you need a more specific scenario.

Mode B: Total Body Water Model (Water-space proxy)

Mode B approximates total body water (TBW) as a fraction of body mass (e.g., 0.60 for 60%). The calculator uses the engineering approximation 1 kg water ≈ 1 L, so: VTBW(L) ≈ BW(kg) × TBW(L/kg).
Example (human default): 70 kg × 0.60 = 42 L. Multi-species TBW values are tabulated in physiology references (e.g., Davies & Morris 1993 tables as mirrored in BioNumbers).^[TBW1]

Mode B does not claim that "60% of the entire body is pharmacologically active." It is simply a rough physical proxy for distribution into aqueous compartments (intracellular + extracellular water). Many substances distribute far beyond blood volume; others do not. This is why pharmacokinetics uses an apparent volume of distribution: Vd = Amount / Cplasma.^{[VD1][VD2][VD3]}

In other words:

• Mode A ≈ "blood-space amount" (small V)
• Mode B ≈ "water-space proxy" (larger V)
• Mode C ≈ "apparent V_d/kg from literature" (often best when available)

References for Mode A / Mode B

1. [BV1] BioNumbers (Harvard Medical School). Circulating Blood Volumes of Healthy Adult Animals. PDF
2. [BV2] Brown University (Policy & Procedures). Table 1. Circulating Blood Volumes and Withdrawal Volume Examples for Common Species. PDF
3. [BV3] Virginia Tech Office of Research / IACUC. Guidelines for Regulating the Volume of Experimental Blood Sample Withdrawals in Animals. PDF
4. [BV4] Reynolds M. Plasma and Blood Volume in the Cow Using the T-1824 Hematocrit Method. American Journal of Physiology. 1953;173(3):421-427. doi:10.1152/ajplegacy.1953.173.3.421
5. [BV5] Diehl K-H, Hull R, Morton D, Pfister R, Rabemampianina Y, Smith D, Vidal J-M, van de Vorstenbosch C. A good practice guide to the administration of substances and removal of blood, including routes and volumes. Journal of Applied Toxicology. 2001;21(1):15-23. doi:10.1002/jat.727 • PDF
6. [BV6] Drexel University College of Medicine (ULAR). A Compendium of Drugs Used for Laboratory Animal Anesthesia, Analgesia, Tranquilization and Restraint (archived April 2011 capture). Archived PDF
7. [BV7] Wolfensohn S, Lloyd M. Handbook of Laboratory Animal Management and Welfare. 3rd ed. Blackwell Publishing; 2003. Google Books
8. [BV8] Lee MH, et al. Improved Estimation of Total Blood Volume Can Provide a Better Unit of Normalization for Pharmacokinetic Studies. 2019 (open-access). PMC
9. [TBW1] Davies B, Morris T. Physiological parameters in laboratory animals and humans. Pharmaceutical Research. 1993;10(7):1093-1095. doi:10.1023/A:1018943613122 • PubMed
10. [TBW2] Merck Manual Professional Edition. Drug Distribution to Tissues (includes discussion of distribution into body water and factors affecting distribution). Web
11. [VD1] Deranged Physiology. Volume of distribution. Web
12. [VD2] Merck Manual Professional Edition. Drug Distribution to Tissues. Web
13. [VD3] StatPearls (NCBI Bookshelf). Volume of Distribution (NBK545280). NCBI

---

Technical Documentation

This tool estimates an apparent amount in the body ("body burden") from a measured concentration and an estimated apparent volume of distribution (V_d). It is a pharmacokinetic back-of-the-envelope calculator intended for engineering-style dimensional checks and scenario exploration - not a substitute for clinical judgment or medical decision-making.

0. What the Tool Computes

At a high level, the pipeline is:

• Normalize the input concentration to mg/L (with MW required for molar units).
• Optional: apply a first-order elimination back-calculation to estimate an earlier concentration (C₀) from a later measured concentration (C_t).
• Estimate V_d (L) using one of three modes (Blood, TBW, or Custom).
• Compute apparent amount (mg) as A ≈ C × V_d.

1. Volume of Distribution (V_d) - What It Is (and What It Is Not)

The apparent volume of distribution is a proportionality constant relating the amount of substance in the body to a plasma (or blood) concentration. A widely used definition is:

Critically, V_d is an apparent (theoretical) volume: it does not have to match any real anatomical fluid volume, and it can exceed total body volume when plasma concentrations are low relative to the amount stored in tissues (e.g., strong tissue binding). In other words, V_d summarizes "how much the measured plasma concentration under-represents the total amount" rather than literally describing where the compound is.

2. Apparent Body Burden (Amount) from Concentration

Rearranging the definition above gives the tool's core "body burden" estimate:

This is best interpreted as the apparent amount implied by the model. If your measured concentration is not a true plasma/blood concentration (e.g., urine, saliva, tissue biopsy), or if the compound is not in a well-mixed phase, the interpretation changes. Multi-compartment kinetics (distribution phase vs terminal elimination) can also make the "right" V_d phase-dependent.

3. Optional Kinetic Back-Calculation (First-Order Elimination)

If you enable kinetics, the tool assumes first-order elimination in a one-compartment model during the period of interest. The concentration-time relationship is:

The elimination rate constant k is derived from the half-life:

Important modeling constraints:

• No absorption model: This is not an oral/dermal inhalation absorption model (no k_a, no lag time).
• Post-distribution assumption: Back-calculations are most defensible when the sample is in the terminal elimination phase.
• Constant half-life: Assumes half-life is stable across the interval and not concentration-dependent.
• Numerical stability: Extremely large k·t will make e^(-k·t) approach zero; this tool flags those cases.

4. V_d Estimation Modes

The tool offers three V_d modes. Modes A and B attempt to anchor V_d to a physical fluid space; Mode C allows explicit apparent V_d scaling for tissue-binding / lipophilicity.

Mode A - Blood / Vascular Space (Species blood volume)

Uses an estimated blood volume (mL/kg) for the selected species and converts to liters:

Then optionally subtracts a user-entered fluid loss (L) as a crude "effective circulating volume": V_eff = max(0, V_blood - loss).

Mode B - Total Body Water (TBW fraction)

Uses a TBW fraction and treats 1 kg body mass as approximately 1 L water for this approximation:

As with Mode A, fluid loss (L) is subtracted only as a coarse adjustment: V_eff = max(0, V_TBW - loss).

Mode C - Custom Apparent V_d (L/kg)

Uses a user-entered coefficient:

Fluid loss is intentionally ignored here: if you are using an apparent V_d/kg from the literature, it already implicitly encodes typical distribution behavior for the context that produced it.

5. Unit Normalization (Everything Becomes mg/L)

To keep the math dimensionally consistent, the tool converts your input concentration into mg/L before doing anything else.

5.1 Molar units (MW required)

If you enter molar units, the tool requires molecular weight (MW in g/mol) and uses:

• mol/L: mg/L = C × MW × 1000
• mmol/L: mg/L = C × MW
• µmol/L: mg/L = (C × MW) / 1000
• nmol/L: mg/L = (C × MW) / 10⁶
• pmol/L: mg/L = (C × MW) / 10⁹

5.2 Mass units (direct scaling)

• g/L: mg/L = C × 1000
• g/dL: mg/L = C × 10000
• mg/dL: mg/L = C × 10
• µg/mL: mg/L = C
• ng/mL: mg/L = C / 1000
• µg/L: mg/L = C / 1000
• ng/L: mg/L = C / 10⁶
• pg/mL: mg/L = C / 10⁶

6. Interpretation Guidance (Why V_d Can Be Huge)

High V_d values commonly arise when plasma concentrations are low relative to tissue stores (e.g., extensive tissue binding or high lipophilicity). Conversely, strong plasma protein binding or confinement to vascular space tends to yield smaller V_d. V_d also provides only limited information about where a substance goes; different distribution patterns can yield similar V_d.

7. Validation, Guardrails, and Failure Modes

• Molecular weight must be > 0 when molar units are selected.
• Weight must be > 0; concentration and fluid loss must be non-negative.
• Kinetics: time must be ≥ 0 and half-life must be > 0; numerical underflow is flagged.
• Custom V_d/kg must be > 0.
• Unknown units are treated as an error (rather than silently producing 0).

8. References (Primary Concepts)

The conceptual framing here follows standard pharmacokinetics definitions of apparent volume of distribution and general distribution/binding considerations:

1. StatPearls / NCBI Bookshelf - Volume of Distribution (definition, V_d = amount / plasma concentration, single vs multi-compartment notes).
2. Merck Manual Professional - Drug Distribution to Tissues (V_d is theoretical, not anatomical, tissue vs plasma binding).
3. Deranged Physiology - Volume of distribution (V_d is not a "real volume"; relates plasma concentration to total amount).

Tip: If you want traceable reports, copy the calculation ledger into your notes. The ledger is designed to be audit-friendly and makes each step explicit.