The Response of Pediatric Ribs to Quasi-static Loading: Mechanical Properties and Microstructure

Relation between mechanical and densimetric properties to fractal dimension in human rib cortical bone

BACKGROUND

Numerous prior studies hypothesized a power-law relationship (E∝ρ^α) between cortical bone Young's modulus (E) and density (ρ) with an exponent 2.3≤α≤3.0, that has not been previously justified in the literature on a theoretical level. Moreover, despite the fact microstructure have been extensively studied, the material correlate of Fractal Dimension (FD) as a descriptor of bone microstructure was not clear in previous studies.

METHODS

This study examined the effect of mineral content and density on the mechanical properties of a large number of human rib cortical bone samples. The mechanical properties were calculated using Digital Image Correlation and uniaxial tensile tests. CT scans were used to calculate the Fractal Dimension (FD) of each specimen. For each specimen, the mineral (f_min), organic (f_org) and water (f_wat) weight fractions were determined. In addition, density was measured after a drying-and-ashing process. Then, Regression Analysis was employed to investigate the relationship between anthropometric variables, weight fractions, density and FD, as well as its impact on the mechanical properties.

FINDINGS

Young's modulus exhibited a power-law relationship with an exponent of α>2.3 when using the conventional density (wet density), but α=2 when using dry density (desecated specimens). In addition, FD increases with decreasing cortical bone density. A significant relationship has been found between FD and density, whereby FD is correlated with the embedding of low density regions in cortical bone.

INTERPRETATION

This study provides a new insight in the exponent value of the power-law relation between Young's Modulus and density, and relates bone behavior with the fragile fracture theory in ceramic materials. Moreover, the results suggest that Fractal Dimension is related to presence of low-density regions.

Scoliosis assessment tools to reduce follow-up X-rays

Purpose

Clinical examinations of scoliosis often includes X-rays. Regular clinical monitoring is recommended in particular at young age, because of the high risk of progression during periods of rapid growth. Supplementary methods free of ionizing radiation thus could help to reduce the potential risk of ionizing radiation related health problems.

Methods

Twelve 3D scan images from female and male patients with different types and severities of spinal deformations were analysed using body scanner image analysis tools. The scan images were captured with a 3D body scanner, which used an infrared sensor and a video camera. To calculate and compare with the patient's specific spinal deformations, simulations based on finite elements methods were performed on biomechanical models of ribcage and spinal column.

Results

The methods and parameters presented here are in good agreement with corresponding X-rays, used for comparison. High correlation coefficients of ‖ρ _s ‖ ≥ 0.87 between Cobb angle and lateral deviation, as well as between Cobb angle and rotation of the vertebrae, indicate that the parameters could provide supplementary informations in the assessment of spinal deformations. So-called apex angles, in addition introduced to relate the results of the present method with Cobb angles, show strong correlations of ‖ρ _s ‖ ≥ 0.68 and thus could be used for comparison in later follow-up examinations.

Conclusion

The user-friendly 3D body scanner image analysis tools enable orthopaedic specialists to simulate, visualize and inspect patient's specific spinal deformations. The method is intended to provide supplementary information in complement to the Cobb angle for the assessment of spinal deformations in clinical daily routine and might have the potential to reduce X-rays in follow-up examinations.

The Translational Potential of this article

The study presents a new method, based on 3D body scanner images and biomechanical modelling, that has the potential to reduce X-rays when monitoring scoliosis especially in young patients.

The Influence of Mattress Stiffness on Spinal Curvature and Intervertebral Disc Stress-An Experimental and Computational Study

Sleeping support systems can influence spinal curvature, and the misalignment of the spinal curvature can lead to musculoskeletal problems. Previous sleep studies on craniocervical support focused on pillow variants, but the mattress supporting the pillow has rarely been considered. This study used a cervical pillow and three mattresses of different stiffnesses, namely soft, medium, and hard, with an indentation load deflection of 20, 42, and 120 lbs, respectively. A novel electronic curvature measurement device was adopted to measure the spinal curvature, whereby the intervertebral disc loading was computed using the finite element method. Compared with the medium mattress, the head distance increased by 30.5 ± 15.9 mm, the cervical lordosis distance increased by 26.7 ± 14.9 mm, and intervertebral disc peak loading increased by 49% in the soft mattress environment. Considering that the pillow support may increase when using a soft mattress, a softer or thinner pillow is recommended. The head distance and cervical lordosis distance in the hard mattress environment were close to the medium mattress, but the lumbar lordosis distance reduced by 10.6 ± 6.8 mm. However, no significant increase in intervertebral disc loading was observed, but contact pressure increased significantly, which could cause discomfort and health problems.

Assessment of adolescent idiopathic scoliosis from body scanner image by finite element simulations

Adolescent idiopathic scoliosis, is a three-dimensional spinal deformity characterized by lateral curvature and axial rotation around the vertical body axis of the spine, the cause of which is yet unknown. The fast progression entails regular clinical monitoring, including X-rays. Here we present an approach to evaluate scoliosis from the three-dimensional image of a patient’s torso, captured by an ionizing radiation free body scanner, in combination with a model of the ribcage and spine. A skeletal structure of the ribcage and vertebral column was modelled with computer aided designed software and was used as an initial structure for macroscopic finite element method simulations. The basic vertebral column model was created for an adult female in an upright position. The model was then used to simulate the patient specific scoliotic spine configurations. The simulations showed that a lateral translation of a vertebral body results in an effective axial rotation and could reproduce the spinal curvatures. The combined method of three-dimensional body scan and finite element model simulations thus provide quantitative anatomical information about the position, rotation and inclination of the thoracic and lumbar vertebrae within a three-dimensional torso. Furthermore, the simulations showed unequal distributions of stress and strain profiles across the intervertebral discs, due to their distortions, which might help to further understand the pathogenesis of scoliosis.

Anisotropic and strain rate-dependent mechanical properties and constitutive modeling of the cancellous bone from piglet cervical vertebrae

BACKGROUND AND OBJECTIVE

Characterizing the mechanical properties of the cancellous bone from the cervical vertebrae of child or child surrogate is important for the development of spine finite element models and the investigation of injury mechanism, however, there is currently no public data available as far as we know.

METHODS

Compression tests were conducted on the specimens from the cervical vertebrae of 8-week-old piglets (child surrogates) in axial and radial directions at the strain rates of 0.01, 0.1, 1 and 10/s. The influences of directionality and strain rate on the mechanical properties of the vertebral cancellous bone were statistically investigated. The typical transversely isotropic model, which was added a strain rate item and a plasticity item, was implemented into LS-DYNA finite element code. Based on the material subroutine code, simulation was conducted on the vertebral tissue under compression in axial and radial directions at different strain rates.

RESULTS

The mechanical properties of the cancellous bone of cervical vertebrae were obtained and most of the stress-strain curves showed major linear elastic stage and short plastic stage before fracture. Significant anisotropic behavior was observed for the vertebral tissue in axial and radial directions. The elastic modulus, ultimate stress,yield stress, and ultimate strain of the speimens in axial direction was obtained, with on average, 2.5 ± 0.6 times, 2.1 ± 0.15 times, and 2.1 ± 0.1 times higher and 0.86 ± 0.076 times lower respecitvely, than those in radial direction. In addition, with the strain rate varying from 0.01/s to 10/s, the mechanical parameters, like elastic modulus, yield and ultimte stresses exhibited significant strain rate effect, however, no significant difference was found for the ultimate strain.

CONCLUSIONS

The cervical vertebrae showed significant anisotropic and strain rate-dependent behaviors. The self-developed subroutine codes based on the strain rate-dependent transversely isotropic elastic and plastic constitutive model can simulate the behaviors well.

Ontogenetic changes to bone microstructure in an archaeologically derived sample of human ribs

There is considerable variation in the gross morphology and tissue properties among the bones of human infants, children, adolescents, and adults. Using 18 known-age individuals (n_female  = 8, n_male  = 9, n_unknown  = 1; birth to 21 years old), from a well-documented cemetery collection, Spitalfields Christ Church, London, UK, this study explores growth-related changes in cortical and trabecular bone microstructure. Micro-CT scans of mid-shaft middle thoracic ribs are used for quantitative analysis. Results are then compared to previously quantified conventional histomorphometry of the same sample. Total area (Tt.Ar), cortical area (Ct.Ar), cortical thickness (Ct.Th), and the major (Maj.Dm) and minor (Min.Dm) diameters of the rib demonstrate positive correlations with age. Pore density (Po.Dn) increases, but age-related changes to cortical porosity (Ct.Po) appear to be non-linear. Trabecular thickness (Tb.th) and trabecular separation (Tb.Sp) increase with age, whereas trabecular bone pattern factor (Tb.Pf), structural model index (SMI), and connectivity density (Conn.D) decrease with age. Sex-based differences were not identified for any of the variables included in this study. Some samples display clear evidence of diagenetic alteration without corresponding changes in radiopacity, which compromises the reliability of bone mineral density (BMD) data in the study of past populations. Cortical porosity data are not correlated with two-dimensional measures of osteon population density (OPD). This suggests that unfilled resorption spaces contribute more significantly to cortical porosity than do the Haversian canals of secondary osteons. Continued research using complementary imaging techniques and a wide array of histological variables will increase our understanding of age- and sex-specific ontogenetic patterns within and among human populations.

Regional maps of rib cortical bone thickness and cross-sectional geometry

Here we present detailed regional bone thickness and cross-sectional measurements from full adult ribs using high resolution CT scans processed with a cortical bone mapping technique. Sixth ribs from 33 subjects ranging from 24 to 99 years of age were used to produce average cortical bone thickness maps and to provide average ± 1SD corridors for expected cross-section properties (cross-sectional areas and inertial moments) as a function of rib length. Results obtained from CT data were validated at specific rib locations using direct measurements from cut sections. Individual thickness measurements from CT had an accuracy (mean error) and precision (SD error) of -0.013 ± 0.167 mm (R² coefficient of determination of 0.84). CT-based measurement errors for rib cross-sectional geometry were -0.1 ± 13.1% (cortical bone cross-sectional area) and 4.7 ± 1.8% (total cross-sectional area). Rib cortical bone thickness maps show the expected regional variation across a typical rib's surface. The local mid-rib maxima in cortical thickness along the pleural rib aspect ranged from range 0.9 to 2.6 mm across the study population with an average map maximum of 1.4 mm. Along the cutaneous aspect, rib cortical bone thickness ranged from 0.7 to 1.9 mm with an average map thickness of 0.9 mm. Average cross-sectional properties show a steady reduction in total cortical bone area from 10% along the rib's length through to the sternal end, whereas overall cross-sectional area remains relatively constant along the majority of the rib's length before rising steeply towards the sternal end. On average, male ribs contained more cortical bone within a given cross-section than was seen for female ribs. Importantly, however, this difference was driven by male ribs having larger overall cross-sectional areas, rather than by sex differences in the bone thickness observed at specific local cortex sites. The cortical bone thickness results here can be used directly to improve the accuracy of current human body and rib models. Furthermore, the measurement corridors obtained from adult subjects across a wide age range can be used to validate future measurements from more widely available image sources such as clinical CT where gold standard reference measures (e.g. such as direct measurements obtained from cut sections) are otherwise unobtainable.

Comparing rib cortical thickness measurements from computed tomography (CT) and Micro-CT

BACKGROUND

The objective of this study was to compare cortical thickness of rib specimens scanned with clinical computed tomography (clinical-CT) at 0.5 and 1.0 mm slice thickness versus micro-CT at 0.05 mm slice thickness. Cortical thickness variation and accuracy was explored by anatomical region (anterior vs. lateral) and cross-sectional quadrants (superior, interior, inferior, and exterior).

METHODS

A validated cortical thickness algorithm was applied to clinical-CT and micro-CT scans of 17 rib specimens from six male post mortem human subjects aged 42-81 years. Each rib specimen was segmented and the thickness measurements were partitioned into cross-sectional quadrants in the anterior and lateral regions of the rib. Within each rib quadrant, the following were calculated: average thickness ± standard deviation, mean thickness difference between clinical-CT and micro-CT, and a thickness ratio between clinical-CT and micro-CT. Correlations from linear regression and paired-t tests were determined for paired clinical-CT and micro-CT results.

RESULTS

On average, the 0.5 mm clinical-CT underestimated the micro-CT thickness by 0.005 mm, while the 1.0 mm clinical-CT overestimated the micro-CT thickness by 0.149 mm. Thickness derived from 0.5 mm clinical-CT showed greater significant linear correlations (p < 0.05) with micro-CT thickness compared to 1.0 mm clinical-CT.

CONCLUSIONS

The small mean differences and thickness ratios near 1 show validation for the cortical thickness algorithm when applied to rib clinical-CT scans. Using clinical-CT scans as way to accurately measure rib cortical thickness offers a non-invasive way to analyze millions of CT scans collected each year from males and females of all ages.

Sources of Variability in Structural Bending Response of Pediatric and Adult Human Ribs in Dynamic Frontal Impacts

Despite safety advances, thoracic injuries in motor vehicle crashes remain a significant source of morbidity and mortality, and rib fractures are the most prevalent of thoracic injuries. The objective of this study was to explore sources of variation in rib structural properties in order to identify sources of differential risk of rib fracture between vehicle occupants. A hierarchical model was employed to quantify the effects of demographic differences and rib geometry on structural properties including stiffness, force, displacement, and energy at failure and yield. Three-hundred forty-seven mid-level ribs from 182 individual anatomical donors were dynamically (~2 m/s) tested to failure in a simplified bending scenario mimicking a frontal thoracic impact. Individuals ranged in age from 4 - 108 years (mean 53 ± 23 years) and included 59 females and 123 males of diverse body sizes. Age, sex, body size, aBMD, whole rib geometry and cross-sectional geometry were explored as predictors of rib structural properties. Measures of cross-sectional rib size (Tt.Ar), bone quantity (Ct.Ar), and bone distribution (Z) generally explained more variation than any other predictors, and were further improved when normalized by rib length (e.g., robustness and WBSI). Cortical thickness (Ct.Th) was not found to be a useful predictor. Rib level predictors performed better than individual level predictors. These findings moderately explain differential risk for rib fracture and with additional exploration of the rib's role in thoracic response, may be able contribute to ATD and HBM development and alterations in addition to improvements to thoracic injury criteria and scaling methods.

Mechanical properties of infant bone

Although an understanding of bone material properties is crucial for interpreting and predicting fracture patterns due to injury or defining the effects of disease on bone strength, information about infant bone properties is scant in the literature. In this study we present the mechanical testing results from 47 tibia and 52 rib specimens taken from 53 infant decedents in order to further our understanding of infant bone strength. Bone specimens were imaged using microCT and tested in three-point bending until failure. Extrinsic and intrinsic properties demonstrated an increase in strength and stiffness over the first year of life, while ductility measures remained largely unchanged. Donor race had no effect on the material properties, but tibia bone specimens showed significant sex differences, with the elastic modulus from females being larger than males. When compared to properties from adolescent and adult donors, infant bone is less strong, less stiff, and more ductile.

In Vivo Assessment of Elasticity of Child Rib Cortical Bone Using Quantitative Computed Tomography

Elasticity of the child rib cortical bone is poorly known due to the difficulties in obtaining specimens to perform conventional tests. It was shown on the femoral cortical bone that elasticity is strongly correlated with density for both children and adults through a unique relationship. Thus, it is assumed that the relationships between the elasticity and density of adult rib cortical bones could be expanded to include that of children. This study estimated in vivo the elasticity of the child rib cortical bone using quantitative computed tomography (QCT). Twenty-eight children (from 1 to 18 y.o.) were considered. Calibrated QCT images were prescribed for various thoracic pathologies. The Hounsfield units were converted to bone mineral density (BMD). A relationship between the BMD and the elasticity of the rib cortical bone was applied to estimate the elasticity of children's ribs in vivo. The estimated elasticity increases with growth (7.1 ± 2.5 GPa at 1 y.o. up to 11.6 ± 1.9 GPa at 18 y.o.). This data is in agreement with the few previous values obtained using direct measurements. This methodology paves the way for in vivo assessment of the elasticity of the child cortical bone based on calibrated QCT images.

Rib biomechanical properties exhibit diagnostic potential for accurate ageing in forensic investigations

Age estimation remains one of the most challenging tasks in forensic practice when establishing a biological profile of unknown skeletonised remains. Morphological methods based on developmental markers of bones can provide accurate age estimates at a young age, but become highly unreliable for ages over 35 when all developmental markers disappear. This study explores the changes in the biomechanical properties of bone tissue and matrix, which continue to change with age even after skeletal maturity, and their potential value for age estimation. As a proof of concept we investigated the relationship of 28 variables at the macroscopic and microscopic level in rib autopsy samples from 24 individuals. Stepwise regression analysis produced a number of equations one of which with seven variables showed an R2 = 0.949; a mean residual error of 2.13 yrs ±0.4 (SD) and a maximum residual error value of 2.88 yrs. For forensic purposes, by using only bench top machines in tests which can be carried out within 36 hrs, a set of just 3 variables produced an equation with an R2 = 0.902 a mean residual error of 3.38 yrs ±2.6 (SD) and a maximum observed residual error 9.26yrs. This method outstrips all existing age-at-death methods based on ribs, thus providing a novel lab based accurate tool in the forensic investigation of human remains. The present application is optimised for fresh (uncompromised by taphonomic conditions) remains, but the potential of the principle and method is vast once the trends of the biomechanical variables are established for other environmental conditions and circumstances.

The Effect of Rib Shape on Stiffness

This study investigates the isolated effect of rib shape on the mechanical characteristics of ribs subjected to multiple forms of loading. It aims to measure the variation in stiffness due to shape that is seen throughout the population and, in particular, provide a tool for researchers to better understand the influence of shape on resulting stiffness. A previously published six-parameter shape model of the central axis of human ribs was used. It has been shown to accurately model the overall rib path using intrinsic geometric properties such as size, aspect ratio, and skewness, through shapes based on logarithmic spirals with high curvature continuity. In this study the model was fitted to 19,500 ribs from 989 adult female and male CT scans having demographic distributions matching the US adult population. Mechanical loading was simulated through a simplified finite element model aimed at isolating rib shape from other factors influencing mechanical response. Four loading scenarios were used representing idealized free and constrained loading conditions in axial (body-anterior) and lateral directions. Characteristic rib stiffness and maximum stress location were tracked as simulation output measures. Regression models of rib stiffness found that all shape model parameters added information when predicting stiffness under each loading condition, with their linear combination able to account for 95% of the population stiffness variation due to shape in midlevel ribs for free axial loading, and 92%-98% in other conditions. Full regression models including interactive terms explained up to 99% of population variability. Results allow researchers to better evaluate the differences in stiffness results that are obtained from physical testing by providing a framework with which to explain variation due to rib shape.

A novel ex vivo model of compressive immature rib fractures at pathophysiological rates of loading

INTRODUCTION

Compressive rib fractures are considered to be indicative of non-accidental injury (NAI) in infants, which is a significant and growing issue worldwide. The diagnosis of NAI is often disputed in a legal setting, and as a consequence there is a need to model such injuries ex vivo in order to characterise the forces required to produce non-accidental rib fractures. However, current models are limited by type of sample, loading method and rate of loading. Here, we aimed to: i) develop a loading system for inducing compressive fractures in whole immature ribs that is more representative of the physiological conditions and mechanism of injury employed in NAI and ii) assess the influence of loading rate and rib geometry on the mechanical performance of the tissue.

METHODS

Porcine ribs (5-6 weeks of age) from 12 animals (n=8 ribs/animal) were subjected to axial compressive load directed through the anterior-posterior rib axis at loading rates of 1, 30, 60 or 90 mm/s. Key mechanical parameters (including peak load, load and percentage deformation to failure and effective stiffness) were quantified from the load-displacement curves. Measurements of the rib length, thickness at midpoint, distance between anterior and posterior extremities, rib curvature and fracture location were determined from radiographs.

RESULTS

This loading method typically produced incomplete fractures around the midpoint of the ribs, with 87% failing in this manner; higher loads and less deformation were required for ribs to completely fracture through both cortices. Loading rate, within the range of 1-90 mm/s, did not significantly affect any key mechanical parameters of the ribs. Load-displacement curves displaying characteristic and quantifiable features were produced for 90% of the ribs tested, and multiple regression analyses indicate that, in addition to the geometrical variables, there are other factors such as the micro- and nano-structure that influence the measured mechanical data.

CONCLUSIONS

A reproducible method of inducing fractures in a consistent location in immature porcine ribs has been successfully developed. Fracture appearance may be indicative of the amount of load and deformation that produced the fracture, which is an important finding for NAI, where knowledge of the aetiology of fractures is vital. Characteristic rib behaviour independent of loading rate and, to an extent, rib geometry has been demonstrated, allowing further investigation into how the complex micro- and nano-structure of immature ribs influences the mechanical performance under compressive load. This research will ultimately enable improved characterisation of the loading pattern involved in non-accidental rib fractures.