13.2 Derivation of Reference Values: RfD, RfC, ADI, TDI & Permissible Daily Exposure (PDE)

The reference value is the PoD after the factors

Handbook III.C.3 F asks you to name the number that exposure will be compared with: reference dose (RfD), reference concentration (RfC), acceptable daily intake (ADI), tolerable daily intake (TDI), permissible daily exposure (PDE), screening thresholds of toxicological concern (TTC), and under REACH a derived no-effect level (DNEL) or derived minimal-effect level (DMEL). Independent OpenExamPrep teaching derives those constructs, works the RfD arithmetic the examination expects, and flags health-based occupational exposure limits (OELs) as the same family with a worker receptor—detail belongs in Chapter 15. This section is not an ABT, EPA, FDA, JECFA, ICH, EFSA, or ECHA product and does not claim official approval, review, or partnership with those bodies.

Chapter 12 gave you a PoD. Section 13.1 gave you UFs. This section divides.

RfD and RfC

EPA IRIS definition of an RfD: an estimate (with uncertainty spanning perhaps an order of magnitude) of a daily oral exposure to the human population (including sensitive subgroups) that is likely to be without an appreciable risk of deleterious effects during a lifetime.

RfD = PoD / (UF × MF)

Units: mg/kg-day (sometimes written mg/kg/day). Compare with oral average daily dose (ADD) from Chapter 11, not with a lifetime cancer LADD unless you are in the wrong playbook.

RfC is the inhalation analog: same definition, units mg/m³ (sometimes converted to ppm for a gas). Compare with an exposure concentration, not with a mg/kg “inhalation intake” from old RAGS Part A. After HEC dosimetry, the formula is still

RfC = PoD_HEC / (UF × MF)

Worked RfD (required arithmetic). Critical-effect BMDL10 = 2.5 mg/kg-day. Uncertainty factors UFA = 10, UFH = 10, UFS = 3; UFL = UFD = MF = 1.

Composite UF = 10 × 10 × 3 = 300

RfD = 2.5 / 300 = 0.008333… mg/kg-day, which reports as 0.0083 mg/kg-day (or 8.3 × 10^−3 mg/kg-day).

Checks:

• 300 × 0.008333… = 2.50 exactly (2.5 ÷ 300 = 1/120).
• 300 × 0.0083 = 2.49, within ordinary rounding of 2.50.
• For a 70 kg adult, implied milligrams per day = 0.0083 × 70 = 0.581 mg/day. For 60 kg: 0.0083 × 60 = 0.498 mg/day. Those daily milligrams are a communication aid. The RfD remains 0.0083 mg/kg-day.

Failure modes:

• 2.5 / 30 = 0.083 — dropped one 10.
• 2.5 / 1,000 = 0.0025 — used three full tens (10 × 10 × 10) instead of 10 × 10 × 3.
• 2.5 × 300 = 750 — multiplied. An RfD cannot be larger than the BMDL10 unless a data-derived factor is < 1; a default stack is not.
• 2.5 / 23 = 0.109 — added 10 + 10 + 3.
• Using 2.5 / 300 as an RfC in mg/m³ without dosimetry.

If this BMDL had already been converted to an HED of 2.5 mg/kg-day, UFA should have been the residual 3, not 10. The problem as written uses 10 × 10 × 3, which is the administered-dose-style stack (full interspecies 10, full human 10, partial duration 3). Read the item stem: did they already make an HED?

RfC teaching twin. HEC BMDL = 2.5 mg/m³, same UF 300: RfC = 2.5 / 300 = 0.0083 mg/m³. Same arithmetic, different unit and route. Do not compare that RfC with an oral ADD.

ADI, TDI, and PDE

These are cousins, not synonyms.

ADI versus TDI. Acceptable is the word for a substance society chose to add (a colorant, a sweetener, a pesticide used according to label). Tolerable is the word for a substance nobody wants in food but that is hard to drive to zero (lead, cadmium, some process-formed contaminants). Numerically both are often NOAEL/100 when a chronic animal NOAEL is the PoD and only inter- and intra-species 10s are applied. Calling a food-additive ADI a contaminant TDI is a vocabulary error the examination will score. Provisional TDI/TWI means the committee is waiting on data.

FDA uses ADI language in food-additive and some veterinary-residue settings. It is not an EPA RfD. Same 100-fold habit, different statute.

ICH Q3C PDE (F1–F5)

Permissible daily exposure for a residual solvent:

PDE (mg/day) = (NOEL × weight adjustment) / (F1 × F2 × F3 × F4 × F5)

Weight adjustment = 50 kg (ICH’s deliberately low adult mass; 60 or 70 kg would give a larger PDE). Pediatric products need a lower mass.

Worked PDE. Rat oral NOEL = 50 mg/kg/day, 90-day study, no severe toxicity, NOEL established.

F1 = 5, F2 = 10, F3 = 5 (3-month rodent), F4 = 1, F5 = 1

Denominator = 5 × 10 × 5 × 1 × 1 = 250

Numerator = 50 × 50 = 2,500

PDE = 2,500 / 250 = 10 mg/day

Option 1 concentration (assumes 10 g/day drug product): ppm = 1,000 × PDE / dose = 1,000 × 10 / 10 = 1,000 ppm.

If the same NOEL came from mice, F1 = 12, denominator = 12 × 10 × 5 = 600, PDE = 2,500 / 600 = 4.17 mg/day. Species factor matters.

Q3C Class 1 solvents (benzene, carbon tetrachloride, others) are avoid / tight toxicology-specific limits, not this generic PDE recipe. Class 3 solvents with low toxic potential are often controlled at 5,000 ppm or 50 mg/day without a full F1–F5 rebuild. Know which class you are in before grinding F3.

F1 5 for rat is a surface-area species factor. It is cousin to FDA 0.16 (because 1/5 = 0.20, near 0.16) and not EPA UFA. Do not multiply F1 = 5 and UFA = 10 and BW^0.75 on one solvent.

TTC and Cramer classes

When structure is known but chemical-specific toxicity is thin, threshold of toxicological concern is a screening intake. It is not an RfD for a data-rich pesticide.

Cramer et al. (1978) decision tree → Class I (simple structures, efficient metabolism, low oral toxicity), Class II (intermediate), Class III (reactive structures, no basis for presumption of safety). Munro et al. (1996) took 5th-percentile NOAELs in each class and divided by 100 to produce the classic oral TTC values. Kroes et al. added a decision tree for genotoxicity alerts and a cohort of concern. EFSA 2019 restated the numbers in µg/kg as well as µg/person, using 60 kg.

Checks on the Cramer µg/kg figures: 30 × 60 = 1,800; 9 × 60 = 540; 1.5 × 60 = 90. Those multiplications are how the per-person and per-kg columns stay together.

Do not mix 0.15 with 1.5. The ten-fold difference is risk-level and context, not a rounding error. Food/public TTC for DNA-reactive chemicals is commonly 0.15 µg/day (about 10^−6 lifetime cancer risk in the Kroes calibration). ICH M7 sets 1.5 µg/day as the lifetime TTC for most mutagenic impurities in drugs (about 10^−5). Less-than-lifetime ICH M7 staged intakes are higher (for example 20 µg/day for 1–12 months and 120 µg/day for less than 1 month in widely cited M7 tables—learn that staging exists; confirm the current M7 table when you practice). Cohort of concern (aflatoxin-like, N-nitroso, alkyl-azoxy, and related high-potency groups named in the TTC tree) is excluded from TTC; those structures need compound-specific data.

If exposure is below TTC, the screening conclusion is low probability of appreciable risk, not “proven nontoxic.” If exposure is above TTC, you leave TTC and do a chemical-specific assessment (or generate data). TTC is not used when a regulation requires a full dossier (many food additives, pesticide active ingredients). Chapter 12 already used a compound-specific ICH M7 margin of 10,000 from a BMDL10; TTC 1.5 µg/day is the default when that BMDL does not exist, not a ceiling that overrides data.

REACH DNEL and DMEL

DNEL = (modified) dose descriptor / product of assessment factors. ECHA R.8 defaults (fallbacks, not a starting brag):

• Interspecies: allometric (rat oral 4) × remaining 2.5
• Intraspecies: 5 for workers, 10 for general population (workers treated as a healthier, adult, narrower group)
• Duration: 3 subacute to subchronic, 2 subchronic to chronic, 6 subacute to chronic
• LOAEL to NAEL: often 3 (sometimes 10)
• Quality of database: typically 1, raised when the package is weak

DNEL is threshold language (irritation, liver hypertrophy with a practical threshold, reproductive NOAEL). Several DNELs may exist (worker inhalation long-term, worker dermal, general-population oral). The leading (lowest) DNEL for that exposure pattern is the one that drives risk characterization.

Worked worker DNEL (threshold). Same BMDL 2.5 mg/kg-day, rat oral, subchronic to chronic, NOAEL/BMDL so no LOAEL factor. Assessment factors: 4 × 2.5 × 5 × 2 = 100. DNEL = 2.5 / 100 = 0.025 mg/kg-day, then converted to the worker route (inhalation or dermal) with absorption and ventilation as needed. The general-population twin replaces worker 5 with 10, doubling the divisor to 200 and halving the DNEL to 0.0125 mg/kg-day.

DMEL is for non-threshold endpoints, typically genotoxic carcinogens where a true no-effect level is not assumed. It is a derived minimal-effect level—not a no-effect level. ECHA R.8 discusses indicative lifetime extra-risk figures of about 10^−5 for workers and 10^−6 for the general population as policy-flavored illustrations, not EU-wide legal “acceptable risk” statutes. The alternative R.8 path is a large assessment-factor on a cancer PoD. Writing “DMEL = DNEL with a bigger UF” misses the risk-specific nature of DMEL.

Health-based OELs (preview of Chapter 15)

An OEL (TLV, REL, some PELs, IOELV) is a workplace air number for a healthy-adult worker, usually an 8-hour time-weighted average, sometimes with a STEL or ceiling. Derivation looks like RfC/DNEL math (PoD, dosimetry, assessment factors) but the receptor, duration, and risk-management body differ. OSHA PELs are often outdated legally adopted values, not current health-based science. Do not take an RfC in mg/m³, multiply by 8/24, and call it a TLV. Chapter 15 is where PEL/TLV/REL procedures live.

Putting the worked RfD next to the other machines

Same BMDL10 = 2.5 mg/kg-day:

• EPA RfD with UF 300: 0.0083 mg/kg-day (this section’s required example).
• JECFA-style ADI if a committee treated 2.5 as a chronic NOAEL and applied only 100: 0.025 mg/kg-day. Different policy stack.
• ICH PDE first converts 2.5 mg/kg-day × 50 kg = 125 mg/day, then divides by F1–F5, not by EPA’s 300. If the F-product were 250 (rat 90-day, F4 = F5 = 1), PDE = 0.50 mg/day, which at 50 kg is 0.010 mg/kg-day—again, a different number.
• TTC would ignore 2.5 if you had that BMDL; you already have chemical-specific data.
• ICH M7 TTC 1.5 µg/day applies to a mutagenic impurity without a compound-specific PoD, not to this 2.5 mg/kg-day liver BMDL.

Scenario

A solvent has a rat 90-day BMDL10 of 2.5 mg/kg-day for hepatocellular hypertrophy. The IRIS-style RfD is 0.0083 mg/kg-day after 300. The same laboratory number is used in a drug-substance residual-solvent file: Q3C F1 = 5, F2 = 10, F3 = 5, F4 = 1, F5 = 1, PoD treated as a NOEL of 2.5 mg/kg/day, PDE = (2.5 × 50) / 250 = 125 / 250 = 0.50 mg/day. A REACH registrant builds a worker DNEL with allometric 4 × 2.5, worker 5, duration 2: AF = 100, DNEL = 2.5/100 = 0.025 mg/kg-day (then converted to inhalation). A food-contaminant panel publishes a TDI of 0.025 mg/kg-day (NOAEL-style 100). Four numbers from one BMDL. The DABT skill is naming which machine you are in, not averaging them.

A mutagenic impurity with no bioassay uses ICH M7 TTC 1.5 µg/day, not Cramer Class III 90 µg/day, and not the food genotox TTC 0.15 µg/day unless you are actually in that food-screening context.

Traps

• Reporting RfD = 2.5/300 as 0.083 or 0.0025, or as 750.
• Calling a contaminant limit an ADI, or a food-additive ADI a PDE.
• Using 70 kg in a Q3C PDE when ICH specifies 50 kg.
• Applying Cramer III 90 µg/day to an aflatoxin-like structure or to an ICH M7 mutagenic impurity.
• Equating ICH M7 1.5 µg/day with Kroes 0.15 µg/day.
• Treating DMEL as a threshold DNEL.
• Converting an RfC into an OEL with a homemade 8/24 factor and calling it a TLV.