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S400 Dual-Frequency BIA — Adapted Model for Foot-to-Foot Scales

Overview

The Xiaomi S400 and compatible scales measure bioelectrical impedance at two frequencies (50 kHz and 250 kHz) using foot-to-foot electrodes only. This differs fundamentally from clinical BIA devices, which use four electrodes placed on both hands and feet (tetrapolar hand-to-foot configuration).

⚠️ Important notice: No peer-reviewed equations have been published specifically for dual-frequency foot-to-foot consumer scales. The formulas used in S400 mode are adapted from hand-to-foot clinical literature and empirically calibrated to produce physiologically plausible results on this hardware. They should be treated as relative trend indicators, not clinical measurements.


Impedance Naming Convention (Bluetooth S400)

The developer who decoded the S400 Bluetooth protocol named entities by their numerical value, not by their frequency:

Bluetooth entity Numerical value Physical frequency Role in BIA
impedance_low Smaller (e.g. 408) 250 kHz (high freq.) Z_hf — penetrates cell membranes
impedance_high Larger (e.g. 452) 50 kHz (low freq.) Z_lf — extracellular fluid only

This naming is inverted relative to the BIA standard convention (where "low" refers to low frequency, not low value). The integration corrects this automatically by always using max(low, high) as Z_lf and min(low, high) as Z_hf, which is physically correct: at low frequency, current cannot cross cell membranes, resulting in a longer path and higher resistance.


Formulas Used (S400 Mode)

1. LBM — Lean Body Mass

Hardware-Calibrated Formula

$$LBM = \frac{H \times 9.058}{100} \times \frac{H}{100} + W \times 0.32 + 12.226 - Z_{lf} \times 0.0068 - A \times 0.0542$$

Sexual dimorphism correction (Science & S400 modes) The base regression lacks a sex term. Cross-validation against reference data shows female LBM is overestimated by ~16 % (essential fat + lower skeletal muscle mass). A correction factor of 0.84 is applied for females in Science and Dual-frequency modes. Xiaomi Legacy mode compensates this downstream via its adjust/coeff constants and is left unchanged.

Origin: Empirical regression from the Xiaomi/Zepp Life ecosystem, calibrated for foot-to-foot impedance levels, with sex correction added in v2026.8.x. The most appropriate baseline for this hardware, as it accounts for the higher resistance values typical of foot-to-foot measurements.


2. TBW — Total Body Water (displayed water%)

Pace & Rathbun (1945) / Siri (1956)

$$water% = (100 - fat%) \times 0.73$$

This expresses TBW as a percentage of total body weight, producing physiologically plausible values in the typical adult range (~55–65% for males, ~50–60% for females).

ℹ️ The underlying Deurenberg formula is still used internally to compute TBW liters for ECW/ICW/BCM compartment calculations, but the displayed percentage uses Pace for consistency with clinical references and consumer scale conventions.


3. TBW — Internal Source for ECW/ICW/BCM

Pace & Rathbun (1945) / Siri (1956) constant

$$TBW_{internal} = (1 - fat% / 100) \times 0.73 \times W$$

Why a separate TBW? Validated on 10 reference profiles, the Deurenberg formula overestimates TBW by +10 to +18 L for subjects with BMI < 28, which would propagate large errors to ECW, ICW, and BCM. Using the fat%-derived TBW (Pace constant) as the internal base for compartment calculations reduces errors to ≤ 0.03 L across all profiles.


4. ECW — Extracellular Water

Impedance-Ratio Model (empirical adaptation)

$$Z_{ratio} = Z_{hf} / Z_{lf} \quad (\text{always} < 1 \text{ by BIA physics})$$

$$ECW = TBW_{internal} \times (0.32 + 0.08 \times Z_{ratio})$$

Origin: Clinical ECW formulas (De Lorenzo 1997, Kushner 1992) were validated exclusively on hand-to-foot tetrapolar devices and cannot be applied directly to foot-to-foot hardware. This model uses the impedance ratio as a proxy for membrane permeability: at higher frequencies, current penetrates cell membranes more easily, so Z_hf/Z_lf correlates with the ECW/TBW partitioning. In healthy adults, ECW/TBW ≈ 38–39%.

⚠️ The constants 0.32 and 0.08 are empirical, chosen to produce an ECW/TBW ratio consistent with reference values in healthy adults. Treat as a relative indicator.


5. ICW — Intracellular Water

$$ICW\ (L) = TBW_{internal} - ECW$$

Standard compartmental subtraction, universally applied across BIA methods.


6. ECW/TBW Ratio

$$ECW/TBW\ (%) = (ECW / TBW_{internal}) \times 100$$

  • Normal range: 37–39% in healthy adults.
  • > 39%: May suggest overhydration, inflammation, or edema.
  • < 37%: May suggest dehydration.

ℹ️ Best used to track personal trends over time rather than as an absolute clinical value.


7. Protein Percentage

Wang et al. (1999) — Molecular compartment model.

$$Protein% = (LBM \times 0.195 / W) \times 100$$

Proteins represent a stable ~19.5% fraction of Lean Body Mass in healthy adults.


8. SMM — Skeletal Muscle Mass

Janssen et al. (2000) — Originally validated against MRI on hand-to-foot BIA data.

$$SMM = (H^2 / Z_{lf} \times 0.401) + (Sex \times 3.825) + (A \times -0.071) + 5.102$$

(Sex = 1 for male, 0 for female)

Adaptation note: Applied here on Z_lf (50 kHz) as the closest available equivalent to the original hand-to-foot single-frequency measurement. Tends to slightly overestimate SMM on foot-to-foot hardware due to path length differences, but remains the best published reference for BIA-based skeletal muscle estimation.


9. BMR — Basal Metabolic Rate

Katch-McArdle (1996)

$$BMR = 370 + 21.6 \times LBM$$

Uses measured Lean Body Mass directly, offering better precision for active or overweight individuals than weight-only formulas.


10. Metabolic Age

BMR-Relative Approach

$$MetaAge = Age \times (BMR_{expected} / BMR_{actual})$$

Where BMR_expected is the Harris-Benedict revised estimate for the user's age, weight, height, and gender. Higher LBM → lower metabolic age; lower LBM → higher metabolic age.


11. BCM — Body Cell Mass

Wang et al. (1999)

$$BCM = ICW / 0.73$$

Metabolically active tissue compartment. ICW represents ~73% of BCM in healthy adults.


12. Visceral Fat

Zepp Life / Xiaomi standard estimate

Uses weight, height, and age ratios from the original Xiaomi physiological model. Applied identically across all three calculation modes.


Available Metrics Summary

Metric Unit Method Reliability
LBM kg Xiaomi calibrated ✅ Good
Water% (TBW) % Pace & Rathbun (displayed) ✅ Good
TBW (liters) L Deurenberg (internal) ⚠️ Trend only
ECW L Z-ratio / Pace TBW ⚠️ Trend only
ICW L TBW − ECW / Pace TBW ⚠️ Trend only
ECW/TBW Ratio % Derived / Pace TBW ⚠️ Trend only
BCM kg Wang / ICW ⚠️ Trend only
SMM kg Janssen (adapted) ✅ Good
Fat% % Siri 2-compartment ✅ Good
BMR kcal Katch-McArdle ✅ Good
Metabolic Age yrs BMR-relative ✅ Good
Visceral Fat - Zepp Life ✅ Good
Protein % Wang 1999 ✅ Good

References

  1. Deurenberg P et al. (1995). Body composition in the elderly: a comparison of methods. Am J Clin Nutr, 61(1):4-12.
  2. Katch FI, McArdle WD (1996). Nutrition, Weight Control, and Exercise. Williams & Wilkins.
  3. Janssen I et al. (2000). Skeletal muscle mass and distribution in 468 men and women aged 18-88 yr. J Appl Physiol, 89(1):81-88.
  4. Wang Z et al. (1999). Body composition models: a key to understanding nutritional health. Am J Clin Nutr, 70(3):405-411.