A study of intracortical porosity's area fractions and aspect ratios using computer vision and pulse-coupled neural networks.

Employing computer vision (CV) and optimized pulse-coupled neural networks (PCNN), this work automatically quantifies the geometrical attributes of intracortical bone porosity (namely lacunae and canaliculi (L-C), Haversian canals, and resorption cavities). Fifty pathological slides of cortical bone (× 20 magnification) were prepared from middiaphysis of bovine forelegs collected fresh from butcher. Biopsies were subdivided into sectors encircling arcs (θ of 10°) and radial distances (R) originating from the bone's geometric center toward posterior regions and spanning 3.3 mm. Microscopically, each pore is classified according to whether it belonged to primary or secondary osteon. Globally, each pore is assigned as being located in anterior or posterior regions. For each pore, area and major/minor axes lengths were determined as raw measures from which derived geometric measures, namely, area fraction (AF) and aspect ratio (AR), were derived. Said measures were plotted versus R (for different angles). Plots of AF and AR trends were found to vary linearly along the radial distance. Area fractions (%) significantly decreased linearly with R (p < 0.01) in the anterior region. In the posterior region, area fraction values are flat versus R. These findings are indicative of maturing osteons at the outer cortex with predominately near circular-shaped pores. Graphical abstract (Left) Grids of slides (magnified at 20X) of intra-cortical bone showing Lacunar-canalicular porosity (LCP). Areas marked with the dotted square represent a group of 25 images. The dashed line is a hand-drawn line that demarcates the anterior and posterior regions and the solid line is the best-fit arc radii (R =16.4 mm) of the dashed demarcation line. (Right) Images rotated in the polar coordinate system with their respective angles and radii shown.

Intracortical stiffness of mid-diaphysis femur bovine bone: lacunar-canalicular based homogenization numerical solutions and microhardness measurements.

Microscale lacunar-canalicular (L-C) porosity is a major contributor to intracortical bone stiffness variability. In this work, such variability is investigated experimentally using micro hardness indentation tests and numerically using a homogenization scheme. Cross sectional rings of cortical bones are cut from the middle tubular part of bovine femur long bone at mid-diaphysis. A series of light microscopy images are taken along a line emanating from the cross-section center starting from the ring's interior (endosteum) ring surface toward the ring's exterior (periosteum) ring surface. For each image in the line, computer vision analysis of porosity is conducted employing an image segmentation methodology based on pulse coupled neural networks (PCNN) recently developed by the authors. Determined are size and shape of each of the lacunar-canalicular (L-C) cortical micro constituents: lacunae, canaliculi, and Haversian canals. Consequently, it was possible to segment and quantify the geometrical attributes of all individual segmented pores leading to accurate determination of derived geometrical measures such as L-C cortical pores' total porosity (pore volume fraction), (elliptical) aspect ratio, orientation, location, and number of pores in secondary and primary osteons. Porosity was found to be unevenly (but linearly) distributed along the interior and exterior regions of the intracortical bone. The segmented L-C porosity data is passed to a numerical microscale-based homogenization scheme, also recently developed by the authors, that analyses a composite made up of lamella matrix punctuated by multi-inclusions and returns corresponding values for longitudinal and transverse Young's modulus (matrix stiffness) for these micro-sized spatial locations. Hence, intracortical stiffness variability is numerically quantified using a combination of computer vision program and numerical homogenization code. These numerically found stiffness values of the homogenization solution are corroborated experimentally using microhardness indentation measurements taken at the same points that the digital images were taken along a radial distance emanating from the interior (endosteum) surface toward the bone's exterior (periosteum) surface. Good agreement was found between numerically calculated and indentation measured stiffness of Intracortical lamellae. Both indentation measurements and numerical solutions of matrix stiffness showed increasing linear trend of compressive longitudinal modulus (E11) values vs. radial position for both interior and exterior regions. In the interior (exterior) region of cortical bone, stiffness modulus values were found to range from 18.5 to 23.4 GPa (23 to 26.0 GPa) with the aggregate stiffness of the cortical lamella in the exterior region being 12% stiffer than that in the interior region. In order to further validate these findings, experimental and FEM simulation of a mid-diaphysis bone ring under compression is employed. The FEM numerical deflections employed nine concentric regions across the thickness with graded stiffness values based on the digital segmentation and homogenization scheme. Bone ring deflections are found to agree well with measured deformations of the compression bone ring.

Geometric-attributes-based segmentation of cortical bone slides using optimized neural networks.

In cortical bone, solid (lamellar and interstitial) matrix occupies space left over by porous microfeatures such as Haversian canals, lacunae, and canaliculi-containing clusters. In this work, pulse-coupled neural networks (PCNN) were used to automatically distinguish the microfeatures present in histology slides of cortical bone. The networks' parameters were optimized using particle swarm optimization (PSO). When forming the fitness functions for the PSO, we considered the microfeatures' geometric attributes-namely, their size (based on measures of elliptical perimeter or area), shape (based on measures of compactness or the ratio of minor axis length to major axis length), and a two-way combination of these two geometric attributes. This hybrid PCNN-PSO method was further enhanced for pulse evaluation by combination with yet another method, adaptive threshold (AT), where the PCNN algorithm is repeated until the best threshold is found corresponding to the maximum variance between two segmented regions. Together, this framework of using PCNN-PSO-AT constitutes, we believe, a novel framework in biomedical imaging. Using this framework and extracting microfeatures from only one training image, we successfully extracted microfeatures from other test images. The high fidelity of all resultant segments was established using quantitative metrics such as precision, specificity, and Dice indices.

Segmentation of histology slides of cortical bone using pulse coupled neural networks optimized by particle-swarm optimization.

The aim of this study is to automatically discern the micro-features in histology slides of cortical bone using pulse coupled neural networks (PCNN). To the best knowledge of the authors, utilizing PCNN in such an application has not been reported in the literature and, as such, constitutes a novel application. The network parameters are optimized using particle swarm optimization (PSO) where the PSO fitness function was introduced as the entropy and energy of the bone micro-constituents extracted from a training image. Another novel contribution is combining the above with the method of adaptive threshold (T) where the PCNN algorithm is repeated until the best threshold T is found corresponding to the maximum variance between two segmented regions. To illustrate the quality of resulting segmentation according to this methodology, a comparison of the entropy/energy obtained of each pulse is reported. Suitable quality metrics (precision rate, sensitivity, specificity, accuracy, and dice) were used to benchmark the resulting segments against those found by a more traditional method namely K-means. The quality of the segments revealed by this methodology was found to be of much superior quality. Another testament to the quality of this methodology was that the images resulting from testing pulses were found to be of similarly good quality to those of the training images.