OBJECTIVE: To describe the physiology of spinal growth in patients with adolescent idiopathic scoliosis (AIS).
METHODS: Narrative review of the literature with a focus on mechanisms of growth.
RESULTS: In his landmark publication On Growth and Form, D\'Arcy Thompson wrote that the anatomy of an organism reflects the forces it is subjected to. This means that mechanical forces underlie the shape of tissues, organs and organisms, whether healthy or diseased. AIS is called idiopathic because the underlying cause of the deformation is unknown, although many factors are  associated. Eventually, however, any deformity is due to mechanical forces. It has long been shown that the typical curvature and rotation of the scoliotic spine could result from vertebrae and intervertebral discs growing faster than the ligaments attached to them. This raises the question why in AIS the ligaments do not keep up with the speed of spinal growth. The spine of an AIS patient deviates from healthy spines in various ways. Growth is later but faster, resulting in higher vertebrae and intervertebral discs. Vertebral bone density is lower, which suggests  less spinal compression. This also preserves the notochordal cells and the swelling pressure in the nucleus pulposus. Less spinal compression is due to limited muscular activity, and low muscle mass indeed underlies the lower body mass index (BMI) in AIS patients. Thus, AIS spines grow faster because there is less spinal compression that counteracts the force of growth (Hueter-Volkmann Law). Ligaments consist of collagen fibres that grow by tension, fibrillar sliding and the remodelling of cross-links. Growth and remodelling are enhanced by dynamic loading and by hormones like estrogen. However, they are opposed by static loading.
CONCLUSIONS: Increased spinal elongation and reduced ligamental growth result in differential strain and a vicious circle of scoliotic deformation. Recognising the physical and biological cues that contribute to differential growth  allows earlier diagnosis of AIS and prevention in children at risk.

This paper is concerned with the growth-driven shape-programming problem, which involves determining a growth tensor that can produce a deformation on a hyperelastic body reaching a given target shape. We consider the two cases of globally compatible growth, where the growth tensor is a deformation gradient over the undeformed domain, and the incompatible one, which discards such hypothesis. We formulate the problem within the framework of optimal control theory in hyperelasticity. The Hausdorff distance is used to quantify dissimilarities between shapes; the complexity of the actuation is incorporated in the cost functional as well. Boundary conditions and external loads are allowed in the state law, thus extending previous works where the stress-free hypothesis turns out to be essential. A rigorous mathematical analysis is then carried out to prove the well-posedness of the problem. The numerical approximation is performed using gradient-based optimisation algorithms. Our main goal in this part is to show the possibility to apply inverse techniques for the numerical approximation of this problem, which allows us to address more generic situations than those covered by analytical approaches. Several numerical experiments for beam-like and shell-type geometries illustrate the performance of the proposed numerical scheme.

BACKGROUND: The aqeductus vestibuli (aqueduct) is believed to connect to the saccule in embryos and adults. However, in embryos, the saccule and utricle are known to communicate widely to provide a common endolymph space \"atrium\".
METHODS: Using sagittal histological sections from five embryos (crown-rump length or CRL, 14-21 mm), nine early fetuses (CRL 24-35 mm) and 12 midterm and near-term fetuses (CRL 82-272 mm), we revisited the development and growth of the human ear aqueduct.
RESULTS: The atrium took on a thick tube-like appearance as an antero-inferior continuation of the aqueduct, but soon divided into multiple gulfs. Most of the gulfs corresponded to the ampullae of semicircular ducts, while one gulf at the antero-medio-inferior corner corresponded to the future saccule. Notably, in eight of the 14 embryos and early fetuses, the aqueduct ended at the utricle near the primitive ampulla of the anterior (superior) or posterior semicircular duct. Conversely, an embryo of CRL 21 mm was the smallest specimen in which the aqueduct joined the gulf-like saccule. At midterm and near-term, the growing perilymph space separated the aqueduct from the utricle and appeared to push the aqueduct toward the saccule. A topographical change occurred between the embryonic superiorly located utricle and the inferiorly-located saccule to create the antero-posterior arrangement in adults.
CONCLUSIONS: Consequently, the vestibular end of the aqueduct was most likely to migrate anteriorly from the utricle to the saccule at 6-8 weeks possibly due to differential growth of the endothelium. Previous reconstructions of the embryonic aqueduct might be biased by the adult morphology.

Apical hook is a simple curved structure formed at the upper part of hypocotyls when dicot seeds germinate in darkness. The hook structure is transient but essential for seedlings\' survival during soil emergence due to its efficient protection of the delicate shoot apex from mechanical injury. As a superb model system for studying plant differential growth, apical hook has fascinated botanists as early as the Darwin age, and significant advances have been achieved at both the morphological and molecular levels to understand how apical hook development is regulated. Here, we will mainly summarize the research progress at these two levels. We will also briefly compare the growth dynamics between apical hook and hypocotyl gravitropic bending at early seed germination phase, with the aim to deduce a certain consensus on their connections. Finally, we will outline the remaining questions and future research perspectives for apical hook development.

The trachea is a long tube that enables air passage between the larynx and the bronchi. C-shaped cartilage rings on the ventral side stabilise the structure. On its esophagus-facing dorsal side, deformable smooth muscle facilitates the passage of food in the esophagus. While the symmetry break along the dorsal-ventral axis is well understood, the molecular mechanism that results in the periodic Sox9 expression pattern that translates into the cartilage rings has remained elusive. Here, we review the molecular regulatory interactions that have been elucidated, and discuss possible patterning mechanisms. Understanding the principles of self-organisation is important, both to define biomedical interventions and to enable tissue engineering.

This study aimed to determine (1) does vertebral body tethering (VBT) produce differential growth modulation in individual vertebrae in patients with idiopathic scoliosis, (2) does VBT change disc shape, and (3) does VBT affect total spine length?
Patients with idiopathic scoliosis treated with VBT of the main thoracic curve and minimum 2-year follow-up were included. Vertebrae and discs were categorized as uninstrumented proximal thoracic, instrumented main thoracic, or uninstrumented thoracolumbar-lumbar. The left- and right-sided heights of each vertebra and disc were measured on subsequent radiographs to assess for differential growth. T1-T12 thoracic and T1-S1 thoracolumbar growth velocities were compared with standardized reference data.
Fifty-one patients (764 vertebrae and 807 discs) were analyzed. The average major curve magnitude improved from 46° ± 11° to 17° ± 11° at 2-year follow-up. Differential growth was observed in MT vertebrae, in which the left/concave side grew 2.0 ± 2.2 mm compared with 1.5 ± 2.3 mm on the right/convex (tethered) side (p < 0.001). Differential height changes were observed for all discs, but were most pronounced in instrumented MT discs, in which the right/convex sides decreased by an average of 1.2 mm each, compared with no significant height change on the left/concave side. Total spinal growth velocities were not significantly different from standard reference data.
Vertebral body tethering limits convex spinal growth as designed while permitting concave growth. Curve correction results from differential vertebral growth and decreased convex disc height. Overall spinal growth continues at the expected rate.
Level IV case series.

The bending of epithelial tubes is a fundamental process in organ morphogenesis, driven by various multicellular behaviours. The cochlea in the mammalian inner ear is a representative example of spiral tissue architecture where the continuous bending of the duct is a fundamental component of its morphogenetic process. Although the cochlear duct morphogenesis has been studied by genetic approaches extensively, it is still unclear how the cochlear duct morphology is physically formed. Here, we report that nuclear behaviour changes are associated with the curvature of the pseudostratified epithelium during murine cochlear development. Two-photon live-cell imaging reveals that the nuclei shuttle between the luminal and basal edges of the cell is in phase with cell-cycle progression, known as interkinetic nuclear migration, in the flat region of the pseudostratified epithelium. However, the nuclei become stationary on the luminal side following mitosis in the curved region. Mathematical modelling together with perturbation experiments shows that this nuclear stalling facilitates luminal-basal differential growth within the epithelium, suggesting that the nuclear stalling would contribute to the bending of the pseudostratified epithelium during the cochlear duct development. The findings suggest a possible scenario of differential growth which sculpts the tissue shape, driven by collective nuclear dynamics.

Plants allocate biomass to above- and below-ground organs in response to environmental conditions. While the broad patterns are well-understood, the mechanisms by which plants allocate new growth remain unclear. Modeling approaches to biomass allocation broadly split into functional equilibrium type models and more mechanistically based transport resistance type models. We grew Poa annua plants in split root boxes under high and low light levels, high and low N supplies, with N supplied equally or unequally. Our data suggest that light level had the strongest effect on root mass, with N level being more important in controlling shoot mass. Allocation of growth within the root system was compatible with phloem partitioning models. The root mass fraction was affected by both light and N levels, although within light levels the changes were primarily due to changes in shoot growth, with root mass remaining relatively invariant. Under low light conditions, plants exhibited increased specific leaf area, presumably to compensate for low light levels. In a follow-up experiment, we showed that differential root growth could be suppressed by defoliation under low light conditions. Our data were more compatible with transport resistance type models.

The 3-hinge gyral folding is the conjunction of gyrus crest lines from three different orientations. Previous studies have not explored the possible mechanisms of formation of such 3-hinge gyri, which are preserved across species in primate brains. We develop a biomechanical model to mimic the formation of 3-hinge patterns on a real brain and determine how special types of 3-hinge patterns form in certain areas of the model. Our computational and experimental imaging results show that most tertiary convolutions and exact locations of 3-hinge patterns after growth and folding are unpredictable, but they help explain the consistency of locations and patterns of certain 3-hinge patterns. Growing fibers within the white matter is posited as a determining factor to affect the location and shape of these 3-hinge patterns. Even if the growing fibers do not exert strong enough forces to guide gyrification directly, they still may seed a heterogeneous growth profile that leads to the formation of 3-hinge patterns in specific locations. A minor difference in initial morphology between two growing model brains can lead to distinct numbers and locations of 3-hinge patterns after folding.

We present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots driven by differential growth. We discuss the evolution laws for endogenous oscillators, straightening mechanisms, and reorientations to directional cues, such as gravitropic reactions governed by the avalanche dynamics of statoliths. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of an instability triggered by exogenous factors. When also oscillations due to endogenous cues are present, their weight relative to those associated with the instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the exogenous oscillations becomes dominant.