Mathematical Relationships in Fluence Settings for Q‑Switched and Picosecond Lasers [Reference Values Only]

Laser parameter selection is not governed by a fixed formula, but rather involves a balanced consideration of multiple variables—wavelength, pulse duration, lesion color, clinical endpoints, and lesion depth. The following proportional relationships are derived from clinical practice and are intended for reference purposes only.

1. Laser Wavelength

Commonly used wavelengths include 1064nm, 755nm, 694nm, and 532nm.

The relative absorption coefficients of these wavelengths by melanin and other target chromophores are approximately 1 : 3 : 4 : 10. For superficial pigmented lesions (epidermal), the corresponding fluence settings follow an inverse proportion of roughly 1 : 0.33 : 0.25 : 0.1.

In other words: longer wavelengths exhibit weaker absorption and thus require higher fluence, while shorter wavelengths are more strongly absorbed and require lower fluence to achieve similar effects.

2. Pulse Duration

Typical Q‑switched lasers deliver pulse widths around 5ns, while picosecond lasers offer 900ps or even 450ps.

For longer wavelengths (e.g., 1064nm), fluence is roughly linearly proportional to pulse duration, with an approximate ratio of 1 : 0.6 : 0.2 (corresponding to 5ns : 900ps : 450ps).

That is: shorter pulse durations amplify mechanical disruption, thereby requiring lower fluence to achieve equivalent fragmentation.

3. Lesion Color

Lesion color depth reflects pigment density and accumulation. The denser the pigment, the darker the lesion and the stronger the absorption of laser energy.

Taking common pigmentary conditions as examples, color depth decreases in the order of: blue‑black > brown‑blue > yellowish‑brown.

To achieve comparable fragmentation, each step down in pigment intensity (i.e., lighter color) typically requires an increase in fluence of approximately 30% ~ 60%. Lighter lesions demand higher fluence to ensure sufficient energy deposition for effective disruption.

4. Clinical Endpoints

Clinical endpoints serve as real‑time indicators of treatment adequacy. Common manifestations include erythema, purpura, and frosting (whitening).

The more intense the desired endpoint, the higher the fluence required. A general proportional relationship among endpoints is approximately frosting : purpura : erythema ≈ 4 : 2 : 1.

That is: if erythema is achieved at a baseline fluence (1×), purpura may require approximately 2×, and frosting approximately 4×.

5. Lesion Depth

Pigmented lesions may be located at varying depths—epidermal, dermal‑epidermal junction, or dermal. During laser penetration, a portion of the energy is absorbed and scattered by overlying pigment and other dermal structures, resulting in attenuation before reaching deeper targets.

This factor involves the three‑dimensional architecture of the skin, spatial distribution of pigment, and competing absorption and scattering by other chromophores—making precise numerical calculation highly complex. Consequently, final parameter selection must be guided by clinical endpoint observation, individualized adjustment, and cumulative practical experience, rather than relying solely on theoretical ratios.

Important Note

All numerical relationships provided above are empirical reference approximations derived from clinical practice, not absolute formulas. Treatment parameters should always be tailored to the patient's skin type, lesion characteristics, treatment site, device performance, and individual response—striking an optimal balance between efficacy and safety within clinically acceptable limits.