Fractal geometry in wrist biomechanics: A preliminary study with implications for arthroplasty and surgery

Traditional biomechanical theories of wrist motion-such as row, column, and link joint models-offer limited explanations for the complex, multidirectional kinematics observed clinically. Emerging perspectives suggest fractal geometry, represented by the Golden Ratio (φ = 1.618), might underlie wrist biomechanics, providing a more comprehensive and clinically relevant framework.

This preliminary radiographic study aims to investigate whether wrist anthropometric ratios align significantly with fractal geometry principles, specifically evaluating their consistency with the Golden Ratio. Additionally, the study explores potential implications for wrist arthroplasty design and surgical practice.

A cross-sectional radiographic analysis was conducted on 210 healthy adult wrist radiographs. Anthropometric measurements included ratios between ulnar styloid, radial styloid, and the capitate bone, defined as A/B and (A + B)/C, and were statistically compared to the Golden Ratio. Statistical analyses incorporated tolerance intervals calculated under both normal and log-normal distribution assumptions, with a significance level set at P < 0.05.

Mean anthropometric ratios closely matched the Golden Ratio, with an A/B mean of 1.615 (95% CI: 1.503-1.735) and an (A + B)/C mean of 1.620 (95% CI: 1.503-1.735). Tolerance intervals indicated that 95% of the study population fell within the fractal range (1.503-1.735), irrespective of age, gender, or laterality. High interobserver reliability (ICC = 0.91) further validated the consistency of these measurements.

The findings support the hypothesis that wrist biomechanics may be fundamentally organized by fractal geometry. These preliminary results challenge existing biomechanical paradigms and highlight potential applications in designing more biomechanically accurate wrist prostheses and enhancing surgical precision. Future research should assess clinical outcomes related to fractal-based prosthetic designs and explore fractal deviations as early indicators of wrist pathology.