Novel linear intercept method for characterizing micropores and grains in calcium phosphate bone substitutes

• The NLI algorithm is developed to measure the CaP micropore and grain thicknesses.
• Micropores and grains in CaP are snakelike and very challenging in measurements.
• Significant errors are inherent in standard and commonly-used algorithms.
• In the NLI, linear intercept algorithm is integrated with the distance transform.
• The NLI also enables measuring the orientation angles to examine isotropy level.

The micropore and grain thicknesses of calcium phosphate (CaP) bone substitutes are believed to have strong influence on in vivo biological responses. The thickness measurement is challenging due to complex morphologies of the elongated CaP micropores and grains. This study aimed to develop and verify a novel linear intercept (NLI) algorithm based on SEM images to calculate thicknesses accurately for elongated geometrical features. The standard linear intercept (SLI) algorithm overestimates the thickness of micropores and grains wherever the defined lines are not perpendicular to such geometrical features. The NLI was developed by integrating the standard algorithm with a distance transform map to exclude the overestimation errors. Besides the accurate thickness calculation, the NLI measures the orientation angle of architectural features as an indication for isotropy level. The NLI-based thicknesses of five groups of β-TCP scaffolds were compared and verified with those of a refined centerline (RC) algorithm. The RC algorithm was accurate yet human assisted and very time intensive. Compared with RC algorithm, the NLI-based results were 2 ± 13 and 4 ± 9% (Mean ± SD) lower for average micropore and grain thicknesses, respectively. The NLI results were also compared with two standard and commonly used algorithms. The SLI and maximal-fitted-circle (MFC) algorithms resulted in 72 ± 25 and 91 ± 47% overestimation errors, respectively.