Modeling costal cartilage using local material properties with consideration for gross heterogeneities

Contemporary computer models of the thorax designed to predict injury in automobile collisions model the costal cartilage as a homogeneous material using properties derived from local material characterization tests. No studies have validated the accuracy of these models in predicting the structural mechanics of costal cartilage. Two heterogeneities - the perichondrium and calcified regions - may affect the behavior of costal cartilage in a manner not accounted for by current models. This study sought to investigate the predictive ability of subject-specific models of whole costal cartilage segments, with the calcified regions modeled distinctly and with the perichondrium removed (from the physical specimens as well as from the simulations). Finite element models were developed in the case of five cadaveric costal cartilage segments. The properties of the cartilage were derived from indentation testing of each specimen, where the characteristic average instantaneous elastic moduli ranged from 8.7 to 12.6 MPa. Matched simulations and experiments were then performed, subjecting each specimen to cantilever-like loading with a dynamic posterior displacement of the sternal boundary (all other boundary degrees-of-freedom fixed). The models predicted the resulting peak anterior-posterior forces generated on the costal boundary with a minimum error of 1% and a maximum error of 36%. These results provide support to the previous implicit assumption that insight can be gained into the structural behavior of costal cartilage by observing the local material properties (when calcified regions are included and the perichondrium is removed). Future work includes the addition of the perichondrium, so as to model the whole costal cartilage composite structure.     

The effect of calcification on the structural mechanics of the costal cartilage

The costal cartilage often undergoes progressive calcification with age. This study sought to investigate the effects of calcification on the structural mechanics of whole costal cartilage segments. Models were developed for five costal cartilage specimens, including representations of the cartilage, the perichondrium, calcification, and segments of the rib and sternum. The material properties of the cartilage were determined through indentation testing; the properties of the perichondrium were determined through optimisation against structural experiments. The calcified regions were then expanded or shrunk to develop five different sensitivity analysis models for each. Increasing the relative volume of calcification from 0% to 24% of the cartilage volume increased the stiffness of the costal cartilage segments by a factor of 2.3–3.8. These results suggest that calcification may have a substantial effect on the stiffness of the costal cartilage which should be considered when modelling the chest, especially if age is a factor.     

Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure.

Failure of articular cartilage has been investigated experimentally and theoretically, but there is only partial agreement between observed failure and predicted regions of peak stresses. Since trauma and repetitive stress are implicated in the etiopathogenesis of osteoarthritis, it is important to develop cartilage models which correctly predict sites of high stresses. Cartilage is anisotropic and inhomogeneous, though it has been difficult to incorporate these complexities into engineering analyses. The objectives of this study are to demonstrate that a transversely isotropic, biphasic model of cartilage can provide agreement between predicted regions of high stresses and observed regions of cartilage failure and that with transverse isotropy cartilage stresses are more sensitive to convexity and concavity of the surfaces than with isotropy. These objectives are achieved by solving problems of diarthrodial joint contact by the finite-element method. Results demonstrate that transversely isotropic models predict peak stresses at the cartilage surface and the cartilage-bone interface, in agreement with sites of fissures following impact loading; isotropic models predict peak stresses only at the cartilage-bone interface. Also, when convex cartilage layers contacted concave layers in this study, the highest tensile stresses occur in the convex layer for transversely isotropic models; no such differences are found with isotropic models. The significance of this study is that it establishes a threshold of modeling complexity for articular cartilage that provides good agreement with experimental observations under impact loading and that surface curvatures significantly affect stress and strain within cartilage when using a biphasic transversely isotropic model.     

A monoclonal antibody distinguishes growth cartilage from other types of cartilage: a new probe for osteogenic cartilage

Summary Monoclonal antibodies (mAbs) were raised by injection of a homogenate of cultured growth cartilage (GC) cells from young rabbit ribs. These mAbs were examined by immunohistochemical staining for their reactivity to paraffin sections of rabbit tissues. The results showed that an mAb reacted preferentially with late hypertrophic and calcified costal GC zones. The mAb also reacted with hypertrophic GC adjacent to bone that existed in sternum and femur, but not to other cartilages, including resting cartilage, articular cartilage, auricular cartilage, nasal cartilage, tracheal cartilage and meniscus cartilage, or with other tissues, including tendon, skin, muscles, lung, liver, heart, thymus, spleen, eye and gut. It reacted with a wider area of the GC zone when the sections were decalcified, although its reactivity with the extended area was much less intensive than that with late hypertrophic and calcified GC zones. On treatment of the sections with bacterial collagenase, neither the reactive area nor its intensity were changed, while when treated with trypsin the reactivity was lost.These results suggest the existence of a certain molecule which distinguishes GC (osteogenic cartilage) from other (non-osteogenic) cartilage. This mAb is a useful probe for distinguishing osteogenic cartilage from non-osteogenic cartilage, and for studying differentiation steps of cartilage cells in endochondral bone formation. The mAb can also be used as a probe for clinical and stored specimens because it reacts with decalcified and paraffin-embedded human specimens.     

Costal cartilages--a clue for determination of sex

Mineralization and ossification in the human costal cartilages were studied radiologically. The aim of our study was to evaluate differences between males and females with respect to patterns of costal cartilage calcification and also with respect to ageing. Material for this study consists of 1044 chest and abdominal radiograms of the Czech population from the Department of Radiology (537 males and 507 females). Further radiograms of 18 chest plates were obtained at routine necropsy of cadavers. The radiograms were examined for pattern of ossification of the costal cartilage. The first rib cartilages were not considered because there are no sex differences. The lower ribs exhibit sexual dimorphism. Mineralization and ossification changes appear at the end of puberty and their occurrence increases with age. The sexual difference in pattern of human costal cartilages is statistically significant and thus highly predictive of sex determination.     

A model for studies of mechanical interactions between the human spine and rib cage

A three-dimensional mathematical model useful for studies of the mechanics of the human skeletal thorax is described. To construct this model, rib cage elements are incorporated into a previously reported model of the thoracolumbar spine. The vertebrae and bony portions of the ribs and sternum are idealized as rigid bodies. The behavior of the discs, ligaments and costal cartilages are modelled by deformable elements. Appropriate geometric and stiffness property data are assigned to the elements of the model. In constructing the model, it was found that the mechanical response of the costo-vertebral joint is strongly influenced by articulation geometry. Although rigid bodies were used to model calcified portions of the ribs, the model predicted rib cage deformations in close agreement with those measured experimentally. These studies indicate that the rigid body motion of calcified portions of the rib makes a major contribution to the deformation of the rib cage in response to certain types of loadings. Quantitative results are also reported on the roles the rib cage plays in bending responses of the spine, the lateral stability of the spine, and the production and correction of several scoliotic deformities.     

A cadaveric analysis of the ideal costal cartilage graft for Asian rhinoplasty

Augmentation rhinoplasty of the Asian nose may be effectively accomplished with alloplastic materials. However, certain circumstances mandate the use of autologous grafts (e.g., dorsal augmentation that exceeds 8 mm and patient intolerance of alloplastic implants). Septal and auricular cartilages are inadequate for dorsal augmentation of the Asian nose. The use of costal cartilage for autologous augmentation in select Asian patients has proven to be a reliable method in more than 500 operative cases during a 10-year period. This study was designed to evaluate the ideal costal cartilage graft for augmentation rhinoplasty. Forty-two preserved cadavers were studied for the relationship of the individual rib cartilages to the surrounding tissue and for the length and caliber of each costal cartilage. The seventh rib was found to be the ideal rib graft by virtue of its safe location and overall size for grafting. The seventh rib is situated over the abdominal cavity, so the risk of pneumothorax is insignificant. The internal thoracic artery and vein descend in close apposition behind the first to sixth ribs but begin a course medial to the ribs inferior to this point, and therefore vascular injury during seventh-rib harvesting is unknown. The seventh rib also provides the greatest overall available length (90.7 mm, right; 89.6 mm, left) and thickness (17.6 mm, right; 17.5 mm, left). Despite the more conspicuous location of the incision required to harvest the seventh rib, the limited 3-cm incision that is used has healed favorably in almost all cases. The other major drawback for seventh-rib harvesting is the dissection required through the overlying rectus abdominis muscle, but little technical difficulty or postoperative morbidity is added with muscle dissection. The seventh rib is advocated as the ideal choice for augmentation rhinoplasty and potentially other recipient sites.     

Action of neck accessory muscles on rib cage in dogs

To investigate the action of the neck accessory muscles on the rib cage, we stimulated the sternocleidomastoid and the scalenus muscles separately in supine anesthetized dogs. Hooks screwed into the sternum and ribs were used to measure their axial displacements and the changes in anteroposterior (AP) and transverse (T) diameters of the rib cage. We found that the sternocleidomastoid and scalenus muscles, when they contract alone, cause a large axial displacement of the sternum and the ribs in a cephalad direction and expand the rib cage along both its AP and T diameters. Opening the abdomen increased the cephalad displacement of the ribs and the expansion of the lower rib cage, particularly along its T diameter, but reduced the increase in lung volume. These experiments indicate 1) that the action of the sternocleidomastoid and scalenus muscles on the rib cage is essentially the consequence of a rotation of the ribs' neck axes, resulting from the cephalad displacement of the ribs, and 2) that the fall in abdominal pressure, almost certainly by acting through the zone of apposition of the diaphragm to the rib cage, has a deflationary action on the lower rib cage, more markedly so on its lateral than its anterior wall. The experiments also suggest that the fall in abdominal pressure prevents the diaphragm from moving cephalad and aids the neck accessory muscles in inflating the lungs.     

Hox patterning of the vertebrate rib cage

Unlike the rest of the axial skeleton, which develops solely from somitic mesoderm, patterning of the rib cage is complicated by its derivation from two distinct tissues. The thoracic skeleton is derived from both somitic mesoderm, which forms the vertebral bodies and ribs, and from lateral plate mesoderm, which forms the sternum. By generating mouse mutants in Hox5, Hox6 and Hox9 paralogous group genes, along with a dissection of the Hox10 and Hox11 group mutants, several important conclusions regarding the nature of the ;Hox code' in rib cage and axial skeleton development are revealed. First, axial patterning is consistently coded by the unique and redundant functions of Hox paralogous groups throughout the axial skeleton. Loss of paralogous function leads to anterior homeotic transformations of colinear regions throughout the somite-derived axial skeleton. In the thoracic region, Hox genes pattern the lateral plate-derived sternum in a non-colinear manner, independent from the patterning of the somite-derived vertebrae and vertebral ribs. Finally, between adjacent sets of paralogous mutants, the regions of vertebral phenotypes overlap considerably; however, each paralogous group imparts unique morphologies within these regions. In all cases examined, the next-most posterior Hox paralogous group does not prevent the function of the more-anterior Hox group in axial patterning. Thus, the ;Hox code' in somitic mesoderm is the result of the distinct, graded effects of two or more Hox paralogous groups functioning in any anteroposterior location.     

Skeletal defects in paternal uniparental disomy for chromosome 14 are re-capitulated in the mouse model (paternal uniparental disomy 12)

Human paternal uniparental disomy for chromosome 14 (upd(14)pat) presents with skeletal abnormalities, joint contractures, dysmorphic facial features and developmental delay/mental retardation. Distal human chromosome 14 (HSA14) is homologous to distal mouse chromosome 12 (MMU12) and both regions have been shown to contain imprinted genes. In humans, consistent radiographic findings include a narrow, bell-shaped thorax with caudal bowing of the anterior ribs, cranial bowing of the posterior ribs and flaring of the iliac wings without shortening or dysplasia of the long bones. Mice with upd(12)pat have thin ribs with delayed ossification of the sternum, skull and feet. In both mice and humans, the axial skeleton is predominantly affected. We hypothesize that there is an imprinted gene or genes on HSA14/MMU12 that specifically affects rib/thorax development and the maturation of ossification centers in the sternum, feet and skull with little effect on long bone development.     

Computational model of rib movement and its application in studying the effects of age-related thoracic cage calcification on respiratory system

A 3D finite element model of rib cage movement is developed and used to study the role of age-related costal cartilage and sternocostal joint calcification, as well as respiratory muscle weakness on the ‘bucket-handle’ movement of human rib. The volume displacement of the rib cage is related to changes in its circumference using an empirical equation presented by Agostoni et al. (1965, J Appl Physiol, 20:1179–1186). A systematic study is carried out to quantify the role of costal cartilage, sternocostal joint calcification and muscle weakness on the volume displacement of the rib cage. The results provide insight into some of the mechanisms underlying age-related changes in the respiratory system.     

Sclerotomal origin of the ribs

The somites of vertebrate embryos give rise to sclerotomes and dermomyotomes. The sclerotomes form the axial skeleton, whereas the dermomyotomes give rise to all trunk muscles and the dermis of the back. The ribs were thought to be ventral processes of the axial skeleton and therefore to be derived from the sclerotomes; however, recently a dermomyotomal origin of the distal rib (the costal shaft) was suggested, with only the proximal parts (head and neck of the rib) being of sclerotomal origin. We have re-investigated the development of the ribs in quail-chick chimeras and carried out three experimental series. (1) Single dermomyotomes and (2) single sclerotomes were grafted homotopically, and (3) the ectoderm overlying the unsegmented paraxial mesoderm was removed in the prospective thoracic region. We found that the cells of the dermomyotome gave rise to epaxial and hypaxial trunk muscles, dermis of the back and endothelial cells, but not to ribs. Cells of the sclerotome formed the axial skeleton and all parts of the ribs. Ablation of the ectoderm, which affects dermomyotome development, results in severe malformations of the ribs, probably due to disturbed interactions between dermomyotome and sclerotome. Our results strongly confirm the traditional view of the sclerotomal origin of the ribs.     

Mechanism of the lung-deflating action of the canine diaphragm at extreme lung inflation

When lung volume in animals is passively increased beyond total lung capacity (TLC; transrespiratory pressure = +30 cmH(2)O), stimulation of the phrenic nerves causes a rise, rather than a fall, in pleural pressure. It has been suggested that this was the result of inward displacement of the lower ribs, but the mechanism is uncertain. In the present study, radiopaque markers were attached to muscle bundles in the midcostal region of the diaphragm and to the tenth rib pair in five dogs, and computed tomography was used to measure the displacement, length, and configuration of the muscle and the displacement of the lower ribs during relaxation at seven different lung volumes up to +60 cmH(2)O transrespiratory pressure and during phrenic nerve stimulation at the same lung volumes. The data showed that 1) during phrenic nerve stimulation at 60 cmH(2)O, airway opening pressure increased by 1.5 ± 0.7 cmH(2)O; 2) the dome of the diaphragm and the lower ribs were essentially stationary during such stimulation, but the muscle fibers still shortened significantly; 3) with passive inflation beyond TLC, an area with a cranial concavity appeared at the periphery of the costal portion of the diaphragm, forming a groove along the ventral third of the rib cage; and 4) this area decreased markedly in size or disappeared during phrenic stimulation. It is concluded that the lung-deflating action of the isolated diaphragm beyond TLC is primarily related to the invaginations in the muscle caused by the acute margins of the lower lung lobes. These findings also suggest that the inspiratory inward displacement of the lower ribs commonly observed in patients with emphysema (Hoover's sign) requires not only a marked hyperinflation but also a large fall in pleural pressure.     

Thoracic skeletal defects and cardiac malformations: A common epigenetic link?

Congenital heart defects (CHDs) are the most common birth defects in humans. In addition, cardiac malformations represent the most frequently identified anomaly in teratogenicity experiments with laboratory animals. To explore the mechanisms of these drug-induced defects, we developed a model in which pregnant rats are treated with dimethadione, resulting in a high incidence of heart malformations. Interestingly, these heart defects were accompanied by thoracic skeletal malformations (cleft sternum, fused ribs, extra or missing ribs, and/or wavy ribs), which are characteristic of anterior-posterior (A/P) homeotic transformations and/or disruptions at one or more stages in somite development. A review of other teratogenicity studies suggests that the co-occurrence of these two disparate malformations is not unique to dimethadione, rather it may be a more general phenomenon caused by various structurally unrelated agents. The coexistence of cardiac and thoracic skeletal malformations has also presented clinically, suggesting a mechanistic link between cardiogenesis and skeletal development. Evidence from genetically modified mice reveals that several genes are common to heart development and to formation of the axial skeleton. Some of these genes are important in regulating chromatin architecture, while others are tightly controlled by chromatin-modifying proteins. This review focuses on the role of these epigenetic factors in development of the heart and axial skeleton, and examines the hypothesis that posttranslational modifications of core histones may be altered by some developmental toxicants.     

Structuro-functional organization of the fibrillar component and ground substance of human rib cartilage

A complex morphological investigation (histology, histochemistry, scanning and transmissive electron microscopy, electron histochemistry) has been performed to study the intercellular substance of the costal hyalinous cartilage. It has been demonstrated that the fibrillar framework of the costal cartilage consists of branching collagenous fibrillae, chaotically scattering. The fibrillae are surrounded with the ground substance; one of its components is the reticular ruthenium-positive structure.     

Nasal reconstruction with autologous rib cartilage: a 43-year follow-up.

Autogenous costal cartilage has long been a popular material for nasal augmentation. The history of autogenous cartilage transplantation is reviewed. Two patients are presented who underwent nasal augmentation with autologous costal cartilage with a 43-year follow-up on each patient.     

Evaluation of a subject-specific finite-element model of the equine metacarpophalangeal joint under physiological load

The equine metacarpophalangeal (MCP) joint is frequently injured, especially by racehorses in training. Most injuries result from repetitive loading of the subchondral bone and articular cartilage rather than from acute events. The likelihood of injury is multi-factorial but the magnitude of mechanical loading and the number of loading cycles are believed to play an important role. Therefore, an important step in understanding injury is to determine the distribution of load across the articular surface during normal locomotion. A subject-specific finite-element model of the MCP joint was developed (including deformable cartilage, elastic ligaments, muscle forces and rigid representations of bone), evaluated against measurements obtained from cadaver experiments, and then loaded using data from gait experiments. The sensitivity of the model to force inputs, cartilage stiffness, and cartilage geometry was studied. The FE model predicted MCP joint torque and sesamoid bone flexion angles within 5% of experimental measurements. Muscle–tendon forces, joint loads and cartilage stresses all increased as locomotion speed increased from walking to trotting and finally cantering. Perturbations to muscle–tendon forces resulted in small changes in articular cartilage stresses, whereas variations in joint torque, cartilage geometry and stiffness produced much larger effects. Non-subject-specific cartilage geometry changed the magnitude and distribution of pressure and the von Mises stress markedly. The mean and peak cartilage stresses generally increased with an increase in cartilage stiffness. Areas of peak stress correlated qualitatively with sites of common injury, suggesting that further modelling work may elucidate the types of loading that precede joint injury and may assist in the development of techniques for injury mitigation.     

A finite element formulation and program to study transient swelling and load-carriage in healthy and degenerate articular cartilage

The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u-pi-c program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.     

A Finite Element Formulation and Program to Study Transient Swelling and Load-carriage in Healthy and Degenerate Articular Cartilage

The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u–π–c fortran program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.