The concept of "tortuosity" introduced by Reitzen et al. (2011) to measure nasal septal deviation is mathematically grounded in comparing the actual length of the nasal septum to its ideal, or straight, length. Mathematically, this approach provides a quantifiable measure that can objectively assess the degree of deviation from the norm, allowing for consistent comparisons across subjects or over time.

Mathematical Basis

Tortuosity is calculated as the ratio of the actual length of the septum to the ideal length of the septum (a straight line drawn from the superior to the inferior aspect of the septum). Mathematically, if we denote:

• Lactual as the actual length of the nasal septum,

• Lideal as the ideal (straight) length of the nasal septum,

then tortuosity (T) can be defined as:

Lactual

T = ————

Lideal

For a perfectly straight septum,

Lactual equals Lideal, and thus T=1. Any value of T>1 indicates a deviation from the straight path, with higher values representing greater degrees of tortuosity, and hence, deviation.

Strengths and Limitations

Quantifiable and Objective

This ratio provides a clear, numerical value for the degree of septal deviation, facilitating objective assessment and comparison.

Simple Concept

The concept is straightforward, making it potentially useful in clinical settings for evaluating septal deviations without needing overly complex equipment or calculations.

Lacks Dimensionality

While tortuosity offers a direct measure of deviation length, it doesn't account for the direction of deviation (left, right, S-shaped, C-shaped, etc.) or variations in septal thickness, which could be clinically relevant.

Sensitive to Measurement Accuracy

The accuracy of T heavily depends on precise measurements of Lactual and Lideal, which could be challenging, particularly in complex anatomical structures and with varying imaging techniques.

Assumption of Ideal Line

The concept assumes a straight line as the "ideal" septum, which may not account for natural variations in nasal anatomy across individuals or potential developmental differences.

In summary, the tortuosity measure introduced for assessing nasal septal deviation holds up mathematically as a straightforward, quantifiable method for evaluating the extent of deviation. However, it should ideally be complemented with other assessments to provide a comprehensive evaluation of septal deviation, including its direction, impact on nasal airflow, and potential clinical significance.