Isabelle Villemure

Growth Plate Mechanics and Mechanobiology. A Survey of Present Understanding

The longitudinal growth of long bones occurs in growth plates where chondrocytes synthesize cartilage that is subsequently ossified. Altered growth and subsequent deformity resulting from abnormal mechanical loading is often referred to as mechanical modulation of bone growth. This phenomenon has key implications in the progression of infant and juvenile musculoskeletal deformities, such as adolescent idiopathic scoliosis, hyperkyphosis, genu varus/valgus and tibia vara/valga, as well as neuromuscular diseases. Clinical management of these deformities is often directed at modifying the mechanical environment of affected bones. However, there is limited quantitative and physiological understanding of how bone growth is regulated in response to mechanical loading. This review of published work addresses the state of knowledge concerning key questions about mechanisms underlying biomechanical modulation of bone growth. The longitudinal growth of bones is apparently controlled by modifying the numbers of growth plate chondrocytes in the proliferative zone, their rate of proliferation, the amount of chondrocytic hypertrophy and the controlled synthesis and degradation of matrix throughout the growth plate. These variables may be modulated to produce a change in growth rate in the presence of sustained or cyclic mechanical load. Tissue and cellular deformations involved in the transduction of mechanical stimuli depend on the growth plate tissue material properties that are highly anisotropic, time-dependent, and that differ in different zones of the growth plate and with developmental stages. There is little information about the effects of time-varying changes in volume, water content, osmolarity of matrix, etc. on differentiation, maturation and metabolic activity of chondrocytes. Also, the effects of shear forces and torsion on the growth plate are incompletely characterized. Future work on growth plate mechanobiology should distinguish between changes in the regulation of bone growth resulting from different processes, such as direct stimulation of the cell nuclei, physico-chemical stimuli, mechanical degradation of matrix or cellular components and possible alterations of local blood supply.

Finite Element Model of Polar Growth in Pollen Tubes

The generation of different shapes in plant cells depends on the spatial regulation of the cell wall mechanical properties. A finite element modeling approach was used to simulate the unidirectional growth process in pollen tubes. Predictions made by the model suggest a crucial role for the chemical configuration of pectin in determining cell shape. Cellular protuberance formation in walled cells requires the local deformation of the wall and its polar expansion. In many cells, protuberance elongation proceeds by tip growth, a growth mechanism shared by pollen tubes, root hairs, and fungal hyphae. We established a biomechanical model of tip growth in walled cells using the finite element technique. We aimed to identify the requirements for spatial distribution of mechanical properties in the cell wall that would allow the generation of cellular shapes that agree with experimental observations. We based our structural model on the parameterized description of a tip-growing cell that allows the manipulation of cell size, shape, cell wall thickness, and local mechanical properties. The mechanical load was applied in the form of hydrostatic pressure. We used two validation methods to compare different simulations based on cellular shape and the displacement of surface markers. We compared the resulting optimal distribution of cell mechanical properties with the spatial distribution of biochemical cell wall components in pollen tubes and found remarkable agreement between the gradient in mechanical properties and the distribution of deesterified pectin. Use of the finite element method for the modeling of nonuniform growth events in walled cells opens future perspectives for its application to complex cellular morphogenesis in plants.

Progression of vertebral and spinal three-dimensional deformities in adolescent idiopathic scoliosis : A longitudinal study

Study Design. The evolution of scoliotic descriptors was analyzed from three-dimensionally reconstructed spines and assessed statistically in a group of adolescents with progressive idiopathic scoliosis. Objectives. To conduct an intrasubject longitudinal study quantifying evolution of two- and three-dimensional geometrical descriptors characterizing the scoliotic spine and vertebral deformities. Summary of Background Data. The data available on geometric descriptors usually are based on cross-sectional studies comparing scoliotic configurations of different individuals. The literature reports very few longitudinal studies that evaluated different phases of scoliotic progression in the same patients. Methods. The evolution of regional and local descriptors between two scoliotic visits was analyzed in 28 adolescents with scoliosis. Several statistical analyses were performed to determine how spinal curvatures and vertebral deformities change during scoliosis progression. Results. At the thoracic level, vertebral wedging increases with curve severity in a relatively consistent pattern for most patients with scoliosis. Axial rotation mainly increases toward curve convexity with scoliosis severity, worsening the progression of vertebral body deformities. No consistent evolution is associated with the angular orientation of the maximum wedging. Thoracic kyphosis varies considerably among subjects. Both increasing and decreasing kyphosis are observed in nonnegligible proportions. A decrease in kyphosis is associated with a shift in the plane of maximum deformity toward the frontal plane, which worsens the three-dimensional shape of the spine. Conclusions. The results of this study challenge the existence of a typical scoliotic evolution pattern and suggest that scoliotic evolution is quite variable and patient specific.

Simulation of progressive deformities in adolescent idiopathic scoliosis using a biomechanical model integrating vertebral growth modulation

While the etiology and pathogenesis of adolescent idiopathic scoliosis are still not well understood, it is generally recognized that it progresses within a biomechanical process involving asymmetrical loading of the spine and vertebral growth modulation. This study intends to develop a finite element model incorporating vertebral growth and growth modulation in order to represent the progression of scoliotic deformities. The biomechanical model was based on experimental and clinical observations, and was formulated with variables integrating a biomechanical stimulus of growth modulation along directions perpendicular (x) and parallel (y, z) to the growth plates, a sensitivity factor beta to that stimulus and time. It was integrated into a finite element model of the thoracic and lumbar spine, which was personalized to the geometry of a female subject without spinal deformity. An imbalance of 2 mm in the right direction at the 8th thoracic vertebra was imposed and two simulations were performed: one with only growth modulation perpendicular to growth plates (Sim1), and the other one with additional components in the transverse plane (Sim2). Semi-quantitative characterization of the scoliotic deformities at each growth cycle was made using regional scoliotic descriptors (thoracic Cobb angle and kyphosis) and local scoliotic descriptors (wedging angle and axial rotation of the thoracic apical vertebra). In all simulations, spinal profiles corresponded to clinically observable configurations. The Cobb angle increased non-linearly from 0.3 degree to 34 degrees (Sim1) and 20 degrees (Sim2) from the first to last growth cycle, adequately reproducing the amplifying thoracic scoliotic curve. The sagittal thoracic profile (kyphosis) remained quite constant. Similarly to clinical and experimental observations, vertebral wedging angle of the thoracic apex progressed from 2.6 degrees to 10.7 degrees (Sim1) and 7.8 degrees (Sim2) with curve progression. Concomitantly, vertebral rotation of the thoracic apex increased of 10 degrees (Sim1) and 6 degrees (Sim2) clockwise, adequately reproducing the evolution of axial rotation reported in several studies. Similar trends but of lesser magnitude (Sim2) suggests that growth modulation parallel to growth plates tend to counteract the growth modulation effects in longitudinal direction. Overall, the developed model adequately represents the self-sustaining progression of vertebral and spinal scoliotic deformities. This study demonstrates the feasibility of the modeling approach, and compared to other biomechanical studies of scoliosis it achieves a more complete representation of the scoliotic spine.

Mechanical properties of the porcine growth plate and its three zones from unconfined compression tests

The aim of the study was to determine intrinsic mechanical properties of the complete growth plate and its reserve, proliferative and hypertrophic zones. Growth plate disk samples from newborn swines ulnae were tested using stress relaxation tests under unconfined compression. The Transversely Isotropic Biphasic Model (TIBPE) derived by [Cohen, B., Lai, W. M., Mow, V. C., 1998. A transversely isotropic biphasic model for unconfined compression of growth plate and chondroepiphysis. Journal of Biomechanical Engineering, 120, pp. 491-496] was used to extract intrinsic mechanical properties using a four-parameter optimization procedure. Significant differences were found for the transverse permeability k(1), the Poissons ratio in the transverse plane nu(21), the out-of-plane Poissons ratio nu(31) and the out-of-plane Youngs modulus E(3) between the reserve zone and the proliferative zone as well as between the reserve zone and the hypertrophic zone. The same trends were obtained for the Youngs modulus in the transverse plane E(1), but significant differences were also found between the reserve zone and the complete growth plate. The proliferative and hypertrophic zones are half as stiff as the reserve zone along the compression axis and about three times less stiff than the reserve zone in the transverse plane. These two zones are also three times as permeable as the reserve zone in the radial direction. The mechanical behavior of the newborn porcine distal ulna growth plate is non-uniform along its thickness. The reserve zone, with its greater zonal component at that development stage, has noteworthy effects on the complete growth plate intrinsic mechanical properties. This study provides, for the very first time, an investigation of the intrinsic mechanical properties of the reserve, proliferative and hypertrophic zones of the growth plate.

Effects of in vivo static compressive loading on aggrecan and type II and X collagens in the rat growth plate extracellular matrix.

Mechanical loads are essential to normal bone growth, but excessive loads can lead to progressive deformities. In addition, growth plate extracellular matrix remodelling is essential to regulate the normal longitudinal bone growth process and to ensure physiological bone mineralization. In order to investigate the effects of static compression on growth plate extracellular matrix using an in vivo animal model, a loading device was used to precisely apply a compressive stress of 0.2 MPa for two weeks on the seventh caudal vertebra (Cd7) of rats during the pubertal growth spurt. Control, sham and loaded groups were studied. Growth modulation was quantified based on calcein labelling, and three matrix components (type II and X collagens, and aggrecan) were assessed using immunohistochemistry/safranin-O staining. As well, extracellular matrix components and enzymes (MMP-3 and -13, ADAMTS-4 and -5) were studied by qRT-PCR. Loading reduced Cd7 growth by 29% (p<0.05) and 15% (p=0.07) when compared to controls and shams respectively. No significant change could be observed in the mRNA expression of collagens and the proteolytic enzyme MMP-13. However, MMP-3 was significantly increased in the loaded group as compared to the control group (p<0.05). No change was observed in aggrecan and ADAMTS-4 and -5 expression. Low immunostaining for type II and X collagens was observed in 83% of the loaded rats as compared to the control rats. This in vivo study shows that, during pubertal growth spurt, two-week static compression reduced caudal vertebrae growth rates; this mechanical growth modulation occurred with decreased type II and X collagen proteins in the growth plate.

Tissue and cellular morphological changes in growth plate explants under compression

The mechanisms by which mechanical loading may alter bone development within growth plates are still poorly understood. However, several growth plate cell or tissue morphological parameters are associated with both normal and mechanically modulated bone growth rates. The aim of this study was to quantify in situ the three-dimensional morphology of growth plate explants under compression at both cell and tissue levels. Growth plates were dissected from ulnae of immature swine and tested under 15% compressive strain. Confocal microscopy was used to image fluorescently labeled chondrocytes in the three growth plate zones before and after compression. Quantitative morphological analyses at both cell (volume, surface area, sphericity, minor/major radii) and tissue (cell/matrix volume ratio) levels were performed. Greater chondrocyte bulk strains (volume decrease normalized to the initial cell volume) were found in the proliferative (35.4%) and hypertrophic (41.7%) zones, with lower chondrocyte bulk strains (24.7%) in the reserve zone. Following compression, the cell/matrix volume ratio decreased in the reserve and hypertrophic zones by 24.3% and 22.6%, respectively, whereas it increased by 35.9% in the proliferative zone. The 15% strain applied on growth plate explants revealed zone-dependent deformational states at both tissue and cell levels. Variations in the mechanical response of the chondrocytes from different zones could be related to significant inhomogeneities in growth plate zonal mechanical properties. The ability to obtain in situ cell morphometry and monitor the changes under compression will contribute to a better understanding of mechanisms through which abnormal growth can be triggered.

The role of spinal concave–convex biases in the progression of idiopathic scoliosis

Inadequate understanding of risk factors involved in the progression of idiopathic scoliosis restrains initial treatment to observation until the deformity shows signs of significant aggravation. The purpose of this analysis is to explore whether the concave–convex biases associated with scoliosis (local degeneration of the intervertebral discs, nucleus migration, and local increase in trabecular bone-mineral density of vertebral bodies) may be identified as progressive risk factors. Finite element models of a 26° right thoracic scoliotic spine were constructed based on experimental and clinical observations that included growth dynamics governed by mechanical stimulus. Stress distribution over the vertebral growth plates, progression of Cobb angles, and vertebral wedging were explored in models with and without the biases of concave–convex properties. The inclusion of the bias of concave–convex properties within the model both augmented the asymmetrical loading of the vertebral growth plates by up to 37% and further amplified the progression of Cobb angles and vertebral wedging by as much as 5.9° and 0.8°, respectively. Concave–convex biases are factors that influence the progression of scoliotic curves. Quantifying these parameters in a patient with scoliosis may further provide a better clinical assessment of the risk of progression.

Static Compressive Loading Reduces the mRNA Expression of Type II and X Collagen in Rat Growth-Plate Chondrocytes During Postnatal Growth

The mechanisms by which chondrocytes modulate longitudinal bone growth are not well understood. This in vitro study investigated the effects of loading on the mRNA expression pattern of key molecular components of the growth-plate related to the extracellular matrix (type II and type X collagen) and the PTH-PTHrP feedback loop. Short-term static compressive loading was applied to rat proximal tibial growth-plate explants. Four age groups at specific developmental stages were investigated. The spatial variation in the mRNA expression was compared among loaded explants, their contralateral sham controls, and uncultured growth plates from normal animals. Basic cell metabolism (18S rRNA) was unaffected by load. Results indicated a narrower spatial distribution of mRNA expression of type II collagen throughout the growth plate; similarly, a narrowed distribution of expression of type X collagen was noted in the lower hypertrophic zone of the growth-plate. This suggests that mechanical compression influences chondrocytes of the hypertrophic zone to alter their expression of specific genes encoding proteins of the extracellular matrix, while PTH-PTHrP receptor mRNA, a regulatory protein, remained unaffected by loading. The effects of compression were similar at the different stages of growth, suggesting that additional factors may be involved in the clinical progression of skeletal deformities observed during growth spurts. Although this study was done in vitro and limited to static loading, it furthers our understanding of growth-plate mechanobiology as a first step toward providing a scientific rationale for treating progressive musculoskeletal deformities.

Finite element modeling of the growth plate in a detailed spine model

Very few computer models of the spine integrate vertebral growth plates to investigate their mechanical behavior and potential impacts on bone growth. An approach was developed to generate a finite element (FE) model of the lumbar spine and their connective tissues including the growth plate, which allowed a personalization of the geometry based on patients’ bi-planar radiographs. The geometrical validation was performed by deforming meshed vertebrae to reference vertebral specimens and comparing geometrical indices. No significant difference was found between the measured parameters, with errors under 1% in 83% of the geometrical parameters. Mechanical validation was done by simulating loading cases on a functional unit representing experimental testing on cadaveric spines. The flexibility of the functional unit remained between expected ranges of motion, but was more linear than experimental data. The mechanical behavior of the growth plate was evaluated under various loading cases: greater stresses were located in the proliferative zone for the different spinal loading cases tested. This modeling approach is a useful tool to study the effect of mechanical stresses on bone growth.