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.

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, genus varus/valgus, tibia vara/ valga, as well as neuromuscular diseases and 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 the 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, physicochemical stimuli, mechanical degradation of matrix or cellular components and possible alterations of local blood supply.Address for notification, correspondence and reprints: Isabelle Villemure, P.Eng., Ph.D., Department of Mechanical Engineering, Ecole Polytechnique of Montreal, P.O. Box 6079, Station "Centre-Ville", Montréal, Québec, H3C 3A7, CANADA, Phone: 1 (514) 340-4711 ext. 4900, Fax: 1 (514) 340-4176, E-mail: isabelle.villemure@polymtl.ca. Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertai...

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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.

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IntroductionAdolescent idiopathic scoliosis (AIS) is a complex threedimensional (3D) anomaly of the spine involving lateral deviations in the frontal plane, modifications of the sagittal profile, spinal torsion and transverse plane deformations [16,21,23]. There is still no generally accepted scientific theory for its etiology [7,16,21,23]. The pathogenesis of AIS is not clearly defined regarding either how Abstract It is generally recognized that progressive adolescent idiopathic scoliosis (AIS) evolves within a selfsustaining biomechanical process involving asymmetrical growth modulation of vertebrae due to altered spinal load distribution. A biomechanical finite element model of normal thoracic and lumbar spine integrating vertebral growth was used to simulate the progression of spinal deformities over 24 months. Five pathogenesis hypotheses of AIS were represented, using an initial geometrical eccentricity (gravity line imbalance of 3 mm or 2°rotation) at the thoracic apex to trigger the self-sustaining deformation process. For each simulation, regional (thoracic Cobb angle, kyphosis) and local scoliotic descriptors (axial rotation and wedging of the thoracic apical vertebra) were evaluated at each growth cycle. The simulated AIS pathogeneses resulted in the development of different scoliotic deformities. Imbalance of 3 mm in the frontal plane, combined or not with the sagittal plane, resulted in the closest representation of typical scoliotic deformities, with the thoracic Cobb angle progressing up to 39°(26°when a sagittal offset was added). The apical vertebral rotation increased by 7°t owards the convexity of the curve, while the apical wedging increased to 8.5°(7.3°with the sagittal eccentricity) and this deformity evolved towards the vertebral frontal plane. A sole eccentricity in the sagittal plane generated a non-significant frontal plane deformity. Simulations involving an initial rotational shift (2°) in the transverse plane globally produced relatively small and nontypical scoliotic deformations. Overall, the thoracic segment predominantly was sensitive to imbalances in the frontal plane, although unidirectional geometrical eccentricities in different planes produced three-dimensional deformities at the regional and vertebral levels, and their deformities did not cumulate when combined. These results support the hypothesis of a prime lesion involving the precarious balance in the frontal plane, which could concomitantly be associated with a hypokyphotic component. They also suggest that coupling mechanisms are involved in the deformation process.

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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.