SHOX gene is expressed in vertebral body growth plates in idiopathic and congenital scoliosis : implications for the etiology of scoliosis in Turner Syndrome

Reduced SHOX gene expression has been demonstrated to be associated with all skeletal abnormalities in Turner syndrome, other than scoliosis (and kyphosis). There is evidence to suggest that Turner syndrome scoliosis is clinically and radiologically similar to idiopathic scoliosis, although the phenotypes are dissimilar. This pilot gene expression study used relative quantitative real-time PCR (qRT-PCR) of the SHOX (short stature on X) gene to determine whether it is expressed in vertebral body growth plates in idiopathic and congenital scoliosis. After vertebral growth plate dissection, tissue was examined histologically and RNA was extracted and its integrity was assessed using a Bio-Spec Mini, NanoDrop ND-1000 spectrophotometer and standard denaturing gel electrophoresis. Following cDNA synthesis, gene-specific optimization in a Corbett RotorGene 6000 real-time cycler was followed by qRT-PCR of vertebral tissue. Histological examination of vertebral samples confirmed that only growth plate was analyzed for gene expression. Cycling and melt curves were resolved in triplicate for all samples. SHOX abundance was demonstrated in congenital and idiopathic scoliosis vertebral body growth plates. SHOX expression was 11-fold greater in idiopathic compared to congenital (n = 3) scoliosis (p = 0.027). This study confirmed that SHOX was expressed in vertebral body growth plates, which implies that its expression may also be associated with the scoliosis (and kyphosis) of Turner syndrome. SHOX expression is reduced in Turner syndrome (short stature). In this study, increased SHOX expression was demonstrated in idiopathic scoliosis (tall stature) and congenital scoliosis.

Groucho homologue Grg5 interacts with the transcription factor Runx2-Cbfa1 and modulates its activity during postnatal growth in mice

Runx2-Cbfal, a Runt transcription factor, plays important roles during skeletal development. It is required for differentiation and function of osteoblasts. In its absence, chondrocyte hypertrophy is severely impaired and there is no vascularization of cartilage templates during skeletal development. These tissue-specific functions of Runx2 are likely to be dependent on its interaction with other proteins. We have therefore searched for proteins that may modulate the activity of Runx2. The yeast two-hybrid system was used to identify a groucho homologue, Grg5, as a Runx2-interacting protein. Grg5 enhances Runx2 activity in a cell culture-based assay and by analyses of postnatal growth in mice we demonstrate that Grg5 and Runx2 interact genetically. We also show that Runx2 haploinsufficiency in the absence of Grg5 results in a more severe delay in ossification of cranial sutures and fontanels than occurs with Runx2 haploinsufficiency on a wild-type background. Finally, we find shortening of the proliferative and hypertrophic zones, and expansion of the resting zone in the growth plates of Runx2(+/-)Grg5(-/-) mice that are associated with reduced Ihh expression and Indian hedgehog (Ihh) signaling. We therefore conclude that Grg5 enhances Runx2 activity in vivo.

Growth defect in Grg5 null mice is associated with reduced Ihh signaling in growth plates

Gene-targeted disruption of Grg5, a mouse homologue of Drosophila groucho (gro), results in postnatal growth retardation in mice. The growth defect, most striking in approximately half of the Grg5 null mice, occurs during the first 4-5 weeks of age, but most mice recover retarded growth later. We used the nonlinear mixed-effects model to fit the growth data of wild-type, heterozygous, and Grg5 null mice. On the basis of preliminary evidence suggesting an interaction between Grg5 and the transcription factor Cbfa1/Runx2, critical for skeletal development, we further investigated the skeleton in the mice. A long bone growth plate defect was identified, which included shorter zones of proliferative and hypertrophic chondrocytes and decreased trabecular bone formation. This decreased trabecular bone formation is likely caused by a reduced recruitment of osteoblasts into the growth plate region of Grg5 null mice. Like the growth defect, the growth plate and trabecular bone abnormality improved as the mice grew older. The growth plate defect was associated with reduced Indian hedgehog expression and signaling. We suggest that Grg5, a transcriptional coregulator, modulates the activities of transcription factors, such as Cbfa1/Runx2 in vivo to affect Ihh expression and the function of long bone growth plates.

Pituitary gigantism treated successfully with the growth hormone receptor antagonist, pegvisomant

A Caucasian male aged 15 years presented with 2 years accelerated linear growth. He was 202 cm tall at presentation, with calculated mid-parental height of 173 cm. There were no features of hypopituitarism or acral growth. His visual fields and optic discs were normal...

The anatomical and biomechanical consequences of anterior vertebral stapling for the fusionless correction of scoliosis

Fusionless scoliosis surgery is an emerging treatment for idiopathic scoliosis as it offers theoretical advantages over current forms of treatment. Anterior vertebral stapling using a nitinol staple is one such treatment. Despite increasing interest in this technique, little is known about the effects on the spine following insertion, or the mechanism of action of the staple. The aims of this study were threefold; (1) to measure changes in the bending stiffness of a single motion segment following staple insertion, (2) to describe the forces that occur within the staple during spinal movement, and (3) to describe the anatomical changes that occur following staple insertion. Results suggest that staple insertion consistently decreased stiffness in all directions of motion. An explanation for the finding may be found in the outcomes of the strain gauge testing and micro-CT scan. The strain gauge testing showed that once inserted, the staple tips applied a baseline compressive force to the surrounding trabecular bone and vertebral end-plate. This finding would be consistent with the current belief that the clinical effect of the staples is via unilateral compression of the physis. Interestingly however, as each specimen progressed through the five cycles of each test, the baseline load on the staple tips gradually decreased, implying that the force at the staple tip-bone interface was decreasing. We believe that this was likely occurring as a result of structural damage to the trabecular bone and vertebral end-plate by the staple effectively causing ‘loosening’ of the staple. This hypothesis is further supported by the findings of the micro-CT scan. The pictures depict significant trabecular bone and physeal injury around the staple blades. These results suggest that the current hypothesis that stapling modulates growth through physeal compression may be incorrect, but rather the effect occurs through mechanical disruption of the vertebral growth plate.

The genetic basis of human height : the role of estrogen

Height is a complex physical trait that displays strong heritability. Adult height is related to length of the long bones, which is determined by growth at the epiphyseal growth plate. Longitudinal bone growth occurs via the process of endochondral ossification, where bone forms over the differentiating cartilage template at the growth plate. Estrogen plays a major role in regulating longitudinal bone growth and is responsible for inducing the pubertal growth spurt and fusion of the epiphyseal growth plate. However, the mechanism by which estrogen promotes epiphyseal fusion is poorly understood. It has been hypothesised that estrogen functions to regulate growth plate fusion by stimulating chondrocyte apoptosis, angiogenesis and bone cell invasion in the growth plate. Another theory has suggested that estrogen exposure exhausts the proliferative capacity of growth plate chondrocytes, which accelerates the process of chondrocyte senescence, leading to growth plate fusion. The overall objective of this study was to gain a greater understanding of the molecular mechanisms behind estrogen-mediated growth and height attainment by examining gene regulation in chondrocytes and the role of some of these genes in normal height inheritance. With the heritability of height so well established, the initial hypothesis was that genetic variation in candidate genes associated with longitudinal bone growth would be involved in normal adult height variation. The height-related genes FGFR3, CBFA1, ER and CBFA1 were screened for novel polymorphisms using denaturing HPLC and RFLP analysis. In total, 24 polymorphisms were identified. Two SNPs in ER (rs3757323 C>T and rs1801132 G>C) were strongly associated with adult male height and displayed an 8 cm and 9 cm height difference between homozygous genotypes, respectively. The TC haplotype of these SNPs was associated with a 6 cm decrease in height and remarkably, no homozygous carriers of the TC haplotype were identified in tall subjects. No significant associations with height were found for polymorphisms in the FGFR3, CBFA1 or VDR genes. In the epiphyseal growth plate, chondrocyte proliferation, matrix synthesis and chondrocyte hypertrophy are all major contributors to long bone growth. As estrogen plays such a significant role in both growth and final height attainment, another hypothesis of this study was that estrogen exerted its effects in the growth plate by influencing chondrocyte proliferation and mediating the expression of chondrocyte marker genes. The examination of genes regulated by estrogen in chondrocyte-like cells aimed to identify potential regulators of growth plate fusion, which may further elucidate mechanisms involved in the cessation of linear growth. While estrogen did not dramatically alter the proliferation of the SW1353 cell line, gene expression experiments identified several estrogen regulated genes. Sixteen chondrocyte marker genes were examined in response to estrogen concentrations ranging from 10-12 M to 10-8 M over varying time points. Of the genes analysed, IHH, FGFR3, collagen II and collagen X were not readily detectable and PTHrP, GHR, ER, BMP6, SOX9 and TGF1 mRNAs showed no significant response to estrogen treatments. However, the expression of MMP13, CBFA1, BCL-2 and BAX genes were significantly decreased. Interestingly, the majority of estrogen regulated genes in SW1353 cells are expressed in the hypertrophic zone of the growth plate. Estrogen is also known to regulate systemic GH secretion and local GH action. At the molecular level, estrogen functions to inhibit GH action by negatively regulating GH signalling. GH treated SW1353 cells displayed increases in MMP9 mRNA expression (4.4-fold) and MMP13 mRNA expression (64-fold) in SW1353 cells. Increases were also detected in their respective proteins. Treatment with AG490, an established JAK2 inhibitor, blocked the GH mediated stimulation of both MMP9 and MMP13 mRNA expression. The application of estrogen and GH to SW1353 cells attenuated GH-stimulated MMP13 levels, but did not affect MMP9 levels. Investigation of GH signalling revealed that SW1353 cells have high levels of activated JAK2 and exposure to GH, estrogen, AG490 and other signalling inhibitors did not affect JAK2 phosphorylation. Interestingly, AG490 treatment dramatically decreased ERK2 signalling, although GH did stimulate ERK2 phosphorylation above control levels. AG490 also decreased CBFA1 expression, a transcription factor known to activate MMP9 and MMP13. Finally, GH and estrogen treatment increased expression of SOCS3 mRNA, suggesting that SOCS3 may regulate JAK/STAT signalling in SW1353 cells. The modulation of GH-mediated MMP expression by estrogen in SW1353 cells represents a potentially novel mechanism by which estrogen may regulate longitudinal bone growth. However, further investigation is required in order to elucidate the precise mechanisms behind estrogen and GH regulation of MMP13 expression in SW1353 cells. This study has provided additional evidence that estrogen and the ER gene are major factors in the regulation of growth and the determination of adult height. Newly identified polymorphisms in the ER gene not only contribute to our understanding of the genetic basis of human height, but may also be useful in association studies examining other complex traits. This study also identified several estrogen regulated genes and indicated that estrogen modifies the expression of genes which are primarily expressed in the hypertrophic region of the epiphyseal growth plate. Furthermore, synergistic studies incorporating GH and estrogen have revealed the ability of estrogen to attenuate the effects of GH on MMP13 expression, revealing potential pathways by which estrogen may modulate growth plate fusion, longitudinal bone growth and even arthritis.

Anterior vertebral stapling for the fusionless correction of scoliosis

Fusionless scoliosis surgery is an emerging treatment for idiopathic scoliosis as it offers theoretical advantages over current forms of treatment. Currently the treatment options for idiopathic scoliosis are observation, bracing and fusion. While brace treatment is non-invasive, and preserves the growth, motion, and function of the spine, it does not correct deformity and is only modestly successful in preventing curve progression. In adolescents who fail brace treatment, surgical treatment with an instrumented spinal fusion usually results in better deformity correction but is associated with substantially greater risk. Furthermore in younger patients requiring surgical treatment, fusion procedures are known to adversely effect the future growth of the chest and spine. Fusionless treatments have been developed to allow effective surgical treatment of patients with idiopathic scoliosis who are too young for fusion procedures. Anterior vertebral stapling is one such fusionless treatment which aims to modulate the growth of vertebra to allow correction of scoliosis whilst maintaining normal spinal motion The Mater Misericordiae Hospital in Brisbane has begun to use anterior vertebral stapling to treat patients with idiopathic scoliosis who are too young for fusion procedures. Currently the only staple approved for clinical use is manufactured by Medtronic Sofamor Danek (Memphis, TN). This thesis explains the biomechanical and anatomical changes that occur following anterior vertebral staple insertion using in vitro experiments performed on an immature bovine model. Currently there is a paucity of published information about anterior vertebral stapling so it is hoped that this project will provide information that will aid in our understanding of the clinical effects of staple insertion. The aims of this experimental study were threefold. The first phase was designed to determine the changes in the bending stiffness of the spine following staple insertion. The second phase was designed to measure the forces experienced by the staple during spinal movements. The third and final phase of testing was designed to describe the structural changes that occur to a vertebra as a consequence of staple insertion. The first phase of testing utilised a displacement controlled testing robot to compare the change in stiffness of a single spinal motion segment following staple insertion for the three basic spinal motions of flexion-extension, lateral bending, and axial rotation. For the second phase of testing strain gauges were attached to staples and used to measure staple forces during spinal movement. In the third and final phase the staples were removed and a testing specimen underwent micro-computed tomography (CT) scanning to describe the anatomical changes that occur following staple insertion. The displacement controlled testing showed that there was a significant decrease in bending stiffness in flexion, extension, lateral bending away from the staple, and axial rotation away from the staple following staple insertion. The strain gauge measurements showed that the greatest staple forces occurred in flexion and the least in extension. In addition, a reduction in the baseline staple compressive force was seen with successive loading cycles. Micro-CT scanning demonstrated that significant damage to the vertebral body and endplate occurred as a consequence of staple insertion. The clinical implications of this study are significant. Based on the findings of this project it is likely that the clinical effect of the anterior vertebral staple evaluated in this project is a consequence of growth plate damage (also called hemiepiphysiodesis) causing a partial growth arrest of the vertebra rather than simply compression of the growth plate. The surgical creation of a unilateral growth arrest is a well established treatment used in the management of congenital scoliosis but has not previously been considered for use in idiopathic scoliosis.

A biomechanical investigation of vertebral staples for fusionless scoliosis correction

Background: Fusionless scoliosis surgery is an early-stage treatment for idiopathic scoliosis which claims potential advantages over current fusion-based surgical procedures. Anterior vertebral stapling using a shape memory alloy staple is one such approach. Despite increasing interest in this technique, little is known about the effects on the spine following insertion, or the mechanism of action of the staple. The purpose of this study was to investigate the biomechanical consequences of staple insertion in the anterior thoracic spine, using in vitro experiments on an immature bovine model. Methods: Individual calf spine thoracic motion segments were tested in flexion, extension, lateral bending and axial rotation. Changes in motion segment rotational stiffness following staple insertion were measured on a series of 14 specimens. Strain gauges were attached to three of the staples in the series to measure forces transmitted through the staple during loading. A micro-CT scan of a single specimen was performed after loading to qualitatively examine damage to the vertebral bone caused by the staple. Findings: Small but statistically significant decreases in bending stiffness occurred in flexion,extension, lateral bending away from the staple, and axial rotation away from the staple. Each strain-gauged staple showed a baseline compressive loading following insertion which was seen to gradually decrease during testing. Post-test micro-CT showed substantial bone and growth plate damage near the staple. Interpretation: Based on our findings it is possible that growth modulation following staple insertion is due to tissue damage rather than sustained mechanical compression of the motion segment.

Application of Mesenchymal Stem Cells for repair and regeneration of cartilage and bone

Australian efforts to provide orthopaedic surgeons with living, load-bearing scaffolds suitable for current joint (knee and hip) replacement surgery, non-union fracture repair, and miniscal and growth plate cartilage regeneration are being lead by teams at the Institute for Medical and Veterinary Science and Women's and Children's Hospital in Adelaide; the Peter MacCallum and St Vincent's Medical Research Institutes in Melbourne; and the Mater Medical Research Institute and new Institute for Health and Biomedical Innovation at QUT, Brisbane. In each case multidisciplinary teams are attempting to develop autologous living tissue constructs, utilising mesenchymal stem cells (MSC), with the intention of effecting seamless repair and regeneration of skeletal trauma and defects. In this article we will briefly review current knowledge of the phenotypic properties of MSC and discuss the potential therapeutic applications of these cells as exemplified by their use in cartilage repair and tissue engineering based approaches to the treatment of skeletal defects.

Effects of hyperbaric oxygen and inducible nitric oxide synthase inhibitor treatment on femoral head osteonecrosis in a rat model

Introduction: Apoptosis is the final destiny of many cells in the body, though this process has been observed in some pathological processes. One of these pathological processes is femoral head non-traumatic osteonecrosis. Among many pro/anti-apoptotic factors, nitric oxide has recently been an area of further interest. Osteocyte apoptosis and its relation to pro-apoptotic action invite further research, and the inducible form of nitric oxide synthase (iNOS)—which produces a high concentration of nitric oxide—has been flagged. The aim of this study was to investigate the effect of hyperbaric oxygen (HBO) and inducible NOS suppressor (Aminoguanidine) in prevention of femoral head osteonecrosis in an experimental model of osteonecrosis in spontaneous hypertensive rats (SHRs). Methods: After animal ethic approval 34 SHR rats were divided into four groups. Ten rats were allocated to the control group without any treatment, and eight rats were allocated to three treatment groups namely: HBO, Aminoguanidine (AMG), and the combination of HBO and AMG treatments (HBO+AMG). The HBO group received 250 kPa of oxygen via hyperbaric chamber for 30 days started at their 5th week of life; the AMG group received 1mg/ml of AMG in drinking water from the fifth week till the 17th week of life; and the last group received a combination of these treatments. Rats were sacrificed at the end of the 17th week of life and both femurs were analysed for evidence of osteonecrosis using Micro CT scan and H&E staining. Also, osteocyte apoptosis and the presence of two different forms of NOS (inducible (iNOS) and endothelial (eNOS)) were analysed by immunostaining and apoptosis staining (Hoechst and TUNEL). Results: Bone morphology of metaphyseal and epiphyseal area of all rats were investigated and analysed. Micro CT findings revealed significantly higher mean fractional trabecular bone volume (FBV) of metaphyseal area in untreated SHRs compared with all other treatments (HBO, P<0.05, HBO+AMG, P<0.005, and AMG P<0.001). Bone surface to volume ratio also significantly increased with HBO+AMG and AMG treatments when compared with the control group (18.7 Vs 20.8, P<0.05, and 18.7 Vs 21.1, P<0.05). Epiphyseal mean FBV did not change significantly among groups. In the metaphyseal area, trabecular thickness and numbers significantly decreased with AMG treatment, while trabecular separation significantly increased with both AMG and HBO+AMG treatment. Histological ratio of no ossification and osteonecrosis was 37.5%, 43.7%, 18.7% and 6.2% of control, HBO, HBO+AMG and AMG groups respectively with only significant difference observed between HBO and AMG treatment (P<0.01). High concentration of iNOS was observed in the region of osteonecrosis while there was no evidence of eNOS activity around that region. In comparison with the control group, the ratio of osteocyte apoptosis significantly reduced in AMG treatment (P<0.005). We also observed significantly fewer apoptotic osteocytes in AMG group comparing with HBO treatment (P<0.05). Conclusion: None of our treatments prevents osteonecrosis at the histological or micro CT scan level. High concentration of iNOS in the region of osteonecrosis and significant reduction of osteocyte apoptosis with AMG treatment were supportive of iNOS modulating osteocyte apoptosis in SHRs.

A mouse model for spondyloepiphyseal dysplasia congenita with secondary osteoarthritis due to a Col2a1 mutation

Progeny of mice treated with the mutagen N-ethyl-N-nitrosourea (ENU) revealed a mouse, designated Longpockets (Lpk), with short humeri, abnormal vertebrae, and disorganized growth plates, features consistent with spondyloepiphyseal dysplasia congenita (SEDC). The Lpk phenotype was inherited as an autosomal dominant trait. Lpk/+ mice were viable and fertile and Lpk/Lpk mice died perinatally. Lpk was mapped to chromosome 15 and mutational analysis of likely candidates from the interval revealed a Col2a1 missense Ser1386Pro mutation. Transient transfection of wild-type and Ser1386Pro mutant Col2a1 c-Myc constructs in COS-7 cells and CH8 chondrocytes demonstrated abnormal processing and endoplasmic reticulum retention of the mutant protein. Histology revealed growth plate disorganization in 14-day-old Lpk/+ mice and embryonic cartilage from Lpk/+ and Lpk/Lpk mice had reduced safranin-O and type-II collagen staining in the extracellular matrix. The wild-type and Lpk/+ embryos had vertical columns of proliferating chondrocytes, whereas those in Lpk/Lpk mice were perpendicular to the direction of bone growth. Electron microscopy of cartilage from 18.5 dpc wild-type, Lpk/+, and Lpk/Lpk embryos revealed fewer and less elaborate collagen fibrils in the mutants, with enlarged vacuoles in the endoplasmic reticulum that contained amorphous inclusions. Micro-computed tomography (CT) scans of 12-week-old Lpk/+ mice revealed them to have decreased bone mineral density, and total bone volume, with erosions and osteophytes at the joints. Thus, an ENU mouse model with a Ser1386Pro mutation of the Col2a1 C-propeptide domain that results in abnormal collagen processing and phenotypic features consistent with SEDC and secondary osteoarthritis has been established.

Identification of acoustic emission wave modes for accurate source location in plate-like structures

Acoustic emission (AE) technique is a popular tool used for structural health monitoring of civil, mechanical and aerospace structures. It is a non-destructive method based on rapid release of energy within a material by crack initiation or growth in the form of stress waves. Recording of these waves by means of sensors and subsequent analysis of the recorded signals convey information about the nature of the source. Ability to locate the source of stress waves is an important advantage of AE technique; but as AE waves travel in various modes and may undergo mode conversions, understanding of the modes (‘modal analysis’) is often necessary in order to determine source location accurately. This paper presents results of experiments aimed at finding locations of artificial AE sources on a thin plate and identifying wave modes in the recorded signal waveforms. Different source locating techniques will be investigated and importance of wave mode identification will be explored.

Simulation of inplane and out of plane AE source in thin plate

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in a wide spectrum of areas, ranging from nondestructive testing for the detection of materials defects to monitoring of microseismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary longitudinal waves), S waves (shear/transverse waves) and Rayleigh (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use acoustic emission technique for accurate identification of source, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals along with the characteristics of the source. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location and its characteristics in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

Scaling of natural convection of an inclined flat plate : ramp cooling condition

A scaling analysis is performed for the transient boundary layer established adjacent to an inclined flat plate following a ramp cooling boundary condition. The imposed wall temperature decreases linearly up to a specific value over a specific time. It is revealed that if the ramp time is sufficiently large then the boundary layer reaches quasi-steady mode before the growth of the temperature is finished. However, if the ramp time is shorter then the steady state of the boundary layer may be reached after the growth of the temperature is completed. In this case, the ultimate steady state is the same as if the start up had been instantaneous. Note that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh-Bénard instability if the Rayleigh number exceeds a certain critical value for this cooling case. The onset of instability may set in at different stages of the boundary layer development. A proper identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is presented in this study. Different flow regimes based on the stability of the boundary layer have also been discussed with numerical results.

Natural convection boundary-layer adjacent to an inclined flat plate subject to sudden and ramp heating

The natural convection thermal boundary layer adjacent to an inclined flat plate subject to sudden heating and a temperature boundary condition which follows a ramp function up until a specified time and then remains constant is investigated. The development of the flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. Different flow regimes based on the Rayleigh number are discussed with numerical results for both boundary conditions. For ramp heating, the boundary layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady state time, the layer reaches a quasi steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.