Bias and precision of algorithms in estimating the cross-sectional area of rat tail tendons

The cross-section area (CSA) of rat tail tendons (RTTs), a common experimental model in biomechanics and mechanobiology, is often approximated using circle or ellipse models. This assumption may nevertheless be faulty given the sensitivity of the mechanical properties on CSA estimation. To investigate this issue, we designed a new optic micrometer to be used under a stereomicroscope. Images of specimen projections were captured at angular increments and specimen edges were localized within a local reference frame using an image analysis algorithm based on contrast. The cross-sectional areas estimated using four algorithms (single measurement circle, multiple measurement circle, two degrees of freedom ellipse, three degrees of freedom ellipse) were compared to those obtained using the best algorithm currently described in the literature: the profile reconstruction algorithm. We showed that the four tested algorithms exhibit moderate but uniform bias (mean systematic error between 7 and 11%) with very non-uniform precision, varying from excellent to very poor (adjusted root mean square deviation between 0 and 19%). The maximum CSA error was found to be as high as 99%. We therefore recommend avoiding the algorithms approximating the RTT CSA using circle or ellipse models in studies where accurate estimation of the CSA is required.