Convexity Of Curve Research Articles

The influence of leaf anatomy on the internal light environment and photosynthetic electron transport rate: exploration with a new leaf ray tracing model.

Leaf photosynthesis is determined by biochemical properties and anatomical features. Here we developed a three-dimensional leaf model that can be used to evaluate the internal light environment of a leaf and its implications for whole-leaf electron transport rates (J). This model includes (i) the basic components of a leaf, such as the epidermis, palisade and spongy tissues, as well as the physical dimensions and arrangements of cell walls, vacuoles and chloroplasts; and (ii) an efficient forward ray-tracing algorithm, predicting the internal light environment for light of wavelengths between 400 and 2500nm. We studied the influence of leaf anatomy and ambient light on internal light conditions and J The results show that (i) different chloroplasts can experience drastically different light conditions, even when they are located at the same distance from the leaf surface; (ii) bundle sheath extensions, which are strips of parenchyma, collenchyma or sclerenchyma cells connecting the vascular bundles with the epidermis, can influence photosynthetic light-use efficiency of leaves; and (iii) chloroplast positioning can also influence the light-use efficiency of leaves. Mechanisms underlying leaf internal light heterogeneity and implications of the heterogeneity for photoprotection and for the convexity of the light response curves are discussed.

Idiopathic and normal lateral lumbar curves: muscle effects interpreted by 12th rib length asymmetry with pathomechanic implications for lumbar idiopathic scoliosis.

BackgroundThe historical view of scoliosis as a primary rotation deformity led to debate about the pathomechanic role of paravertebral muscles; particularly multifidus, thought by some to be scoliogenic, counteracting, uncertain, or unimportant. Here, we address lateral lumbar curves (LLC) and suggest a pathomechanic role for quadrates lumborum, (QL) in the light of a new finding, namely of 12th rib bilateral length asymmetry associated with idiopathic and small non-scoliosis LLC.MethodsGroup 1: The postero-anterior spinal radiographs of 14 children (girls 9, boys 5) aged 9–18, median age 13 years, with right lumbar idiopathic scoliosis (IS) and right LLC less that 10°, were studied. The mean Cobb angle was 12° (range 5–22°). Group 2: In 28 children (girls 17, boys 11) with straight spines, postero-anterior spinal radiographs were evaluated similarly to the children with the LLC, aged 8–17, median age 13 years. The ratio of the right/left 12th rib lengths and it’s reliability was calculated. The difference of the ratio between the two groups was tested; and the correlation between the ratio and the Cobb angle estimated. Statistical analysis was done using the SPSS package.ResultsThe ratio’s reliability study showed intra-observer +/−0,036 and the inter-observer error +/−0,042 respectively in terms of 95 % confidence limit of the error of measurements. The 12th rib was longer on the side of the curve convexity in 12 children with LLC and equal in two patients with lumbar scoliosis. The 12th rib ratios of the children with lumbar curve were statistically significantly greater than in those with straight spines. The correlation of the 12th rib ratio with Cobb angle was statistically significant. The 12th thoracic vertebrae show no axial rotation (or minimal) in the LLC and no rotation in the straight spine group.ConclusionsIt is not possible, at present, to determine whether the 12th convex rib lengthening is congenitally lengthened, induced mechanically, or both. Several small muscles are attached to the 12th ribs. We focus attention here on the largest of these muscles namely, QL. It has attachments to the pelvis, 12th ribs and transverse processes of lumbar vertebrae as origins and as insertions. Given increased muscle activity on the lumbar curve convexity and similar to the interpretations of earlier workers outlined above, we suggest two hypotheses, relatively increased activity of the right QL muscle causes the LLCs (first hypothesis); or counteracts the lumbar curvature as part of the body’s attempt to compensate for the curvature (second hypothesis). These hypotheses may be tested by electrical stimulation studies of QL muscles in subjects with lumbar IS by revealing respectively curve worsening or correction. We suggest that one mechanism leading to relatively increased length of the right 12 ribs is mechanotransduction in accordance with Wolff’s and Pauwels Laws.

Electrophysiological and histological changes of paraspinal muscles in adolescent idiopathic scoliosis.

The pathogenesis of adolescent idiopathic scoliosis (AIS) remains poorly understood. To date, potentially involved local changes in the deep paraspinal muscles still remain unknown. Needle electromyography (EMG) and muscle biopsy of paraspinal muscles at convexity and concavity of the AIS main thoracic curve were performed in 25 subjects. In this group, EMG was performed in 16 AIS subjects (12 females, 12-27years), muscle biopsy in 18 AIS subjects (15 females, 11-31years) compared to 10 non-scoliotic controls (6 females, 12-55years). Samples of muscle tissue were removed during corrective surgery and were examined histologically, enzyme histochemically and immunohistochemically. Both methods of EMG and muscle biopsy were performed in 9 subjects (7 women, 12-27years). Right curve convexity was found in 24 AIS subjects. Amplitudes of motor unit action potentials (MUPs) were significantly increased on the AIS curve convexity versus concavity. Turns, duration and phases of MUPs were without any significant changes. In all 18 subjects, the histological examination revealed muscle fiber redistribution with numerical predominance of type I on the curve convexity which strongly correlated with the progression of the Cobb angle. Our findings demonstrate significant changes of muscle fiber redistribution in the paraspinal muscles of AIS with increased proportion of type I on the convexity corresponding to a significantly higher amplitude of MUPs on the same side. A possible explanation of this alteration is a secondary adaptation due to chronic high load demand.

Morphometric Analysis of the Thoracic Intervertebral Foramen Osseous Anatomy in Adolescent Idiopathic Scoliosis Using Low-Dose Computed Tomography

PurposeThe dimensions of the thoracic intervertebral foramen in adolescent idiopathic scoliosis (AIS) have not previously been quantified. Better understanding of the dimensions of the foramen may be useful in surgical planning. This study describes a reproducible method for measurement of the thoracic foramen in AIS using computed tomography (CT). MethodsIn 23 preoperative female patients with Lenke 1 type AIS with right-side convexity major curves confined to the thoracic spine the foraminal height (FH), foraminal width (FW), pedicle to superior articular process distance (P-SAP), and cross-sectional foraminal area (FA) were measured using multiplanar reconstructed CT. Measurements were made at entrance, midpoint, and exit of the thoracic foramina from T1–T2 to T11–T12. Results were also correlated with dependent variables of major curve Cobb angle measured on X-ray and CT, age, weight, Lenke classification subtype, Risser grade, and number of spinal levels in the major curve. ResultsThe FH, FW, P-SAP, and FA dimensions and ratios are all significantly larger on the convexity of the major curve and maximal at or close to the apex. Mean thoracic foraminal dimensions change in a predictable manner relative to position on the major thoracic curve. There was no statistically significant correlation with the measured foraminal dimensions or ratios and the individual dependent variables. The average ratio of convexity to concavity dimensions at the apex foramina for entrance, midpoint, and exit, respectively, are FH (1.50, 1.38, 1.25), FW (1.28, 1.30, 0.98), FA (2.06, 1.84, 1.32), and P-SAP (1.61, 1.47, 1.30). ConclusionForaminal dimensions of the thoracic spine are significantly affected by AIS. Foraminal dimensions have a predictable convexity-to-concavity ratio relative to the proximity to the major curve apex. Surgeons should be aware of these anatomical differences during scoliosis correction surgery.

ID 113 – Neurophysiology and biopsy of paraspinal muscles in idiopathic scoliosis

Objective The pathogenesis of idiopathic scoliosis (IS) remains poorly understood. Local changes in deep paraspinal muscles and/or dysfunction of spinal inhibitory circuits are not fully elucidated. We compared the morphological and functional changes of paraspinal muscles on both sides of the scoliosis curve. Methods Before corrective surgery we performed EMG and muscle biopsy of paraspinal muscles at convexity and concavity of scoliotic curve in 10 subjects with IS (8 women, 11–29years). Cutaneous silent period (CSP) induced by noxious digit II stimulation in thenar muscles was recorded in IS patients and in healthy volunteers. Results Right curve convexity had 8 subjects. All of them presented changes in muscle fiber distribution with numerical predominance of type I on the curve convexity. Seven subjects have increased MUP amplitude on this side (range 10–62%). CSP did not significantly differ between concavity and convexity but shortening of CSP duration was observed in more pronounced scoliotic curve. Conclusion Our findings demonstrate a significant asymmetry in fiber type distribution corresponding with an altered function in paraspinal muscles with predominance on convexity of scoliotic curve. Spinal inhibitory reflex is preserved; however, it could be modulated in more progressive IS. Supported by Grants PRVOUK P34, IGA-NT 13693.

薄板溶接における座屈変形の発生特性に関する実験的研究

In this study, a systematic investigation on the effect of welding conditions on longitudinal bending and angular distortions generated in welded thin plate was experimentally performed with a focus on whether or not the weld buckling distortion occurs. Real-time measurements of temperature profiles and distortion behavior during welding of thin plate were also performed for a more detailed understanding of generation process of weld distortion in thin plate. As the results, longitudinal bending distortion monotonically increases, in which the degree is different depending on the plate thickness, with the weld heat input. Meanwhile, angular distortion does not show a linear increase with the weld heat input and can be arranged coordinately by a curve convex to the parameter of mechanical melting zone, which was proposed based on the theory of inherent strain by authors in previous study, when the weld buckling distortion does not occur. In this regard, however, angular distortion also approximately monotonically increases with either the weld heat input or the parameter of mechanical melting zone, when the weld buckling distortion occurs. This is because the angular distortion-generation process proceeds in the following two stages; angular distortion is primary generated due to inhomogeneous temperature distribution through thickness during welding and secondary in association with buckling behavior during cooling process after welding. This secondary stage results in buckling-induced large angular distortion in welded thin plate. It was thus clarified that it is important to understand the generation characteristics of weld buckling-induced inherent stress and strain especially in the secondary stage for accurate predicting and controlling the weld buckling distortion in thin plate.

The link between coherent burst oscillations, burst spectral evolution and accretion state in 4U 1728–34

Coherent oscillations and the evolution of the X-ray spectrum during thermonuclear X-ray bursts in accreting neutron-star X-ray binaries have been studied intensively but separately. We analysed all the X-ray bursts of the source 4U 1728-34 with the Rossi X-ray Timing Explorer. We found that the presence of burst oscillations can be used to predict the behaviour of the blackbody radius during the cooling phase of the bursts. If a burst shows oscillations, during the cooling phase the blackbody radius remains more or less constant for ~2 - ~8s, whereas in bursts that do not show oscillations the blackbody radius either remains constant for more than ~2 - ~8s or it shows a rapid (faster than ~2s) decrease and increase. Both the presence of burst oscillations and the time-dependent spectral behaviour of the bursts are affected by accretion rate. We also found that the rise time and convexity of the bursts' light curve are different in bursts with and without oscillations in 4U 1728--34. Bursts with oscillations have a short rise time (~0.5s) and show both positive and negative convexity, whereas bursts without oscillations have a long rise time (~1s) and mostly positive convexity. This is consistent with the idea that burst oscillations are associated with off-equator ignition.

Why do restaurants serve lunch cheaper than dinner?

The article explores a question why restaurants serve lunch meals cheaper than dinner meals. Departing from traditional demand curves derived from utility functions, the article uses a distribution function of reservation prices of patrons to represent a market demand curve. Given identical convex market demand curves in two distinct markets isolated by the time, restaurants exploit the convexity of the market demand curves by setting two prices whose average price is higher than the competitive market equilibrium price. This exploitation opportunity induces restaurants to adopt oligopolistic pricing behaviours.

The Effect of Metal Density on Coronal and Sagittal Curve Correction in Thoracic Adolescent Idiopathic Scoliosis

Introduction The literature is contradictory regarding the effect of metal density on correction of thoracic AIS. Given the rising cost of surgery for AIS, instrumentation should be used rationally. We aim to assess the impact of metal density on coronal and sagittal correction of AIS and assess if larger, less flexible curves necessitate high metal density. Material and Methods It is a retrospective multicenter case series. Inclusion criteria: Lenke 1–2 AIS, curve flexibility assessed by fulcrum-bending technique, single stage posterior only surgery, constructs using > 80% screws, variable metal density, and > 2-year follow-up. Outcome measures: Coronal main thoracic (MT) and lumbar curve correction, fulcrum-bending correction index (FBCI), thoracic kyphosis, lumbosacral lordosis, metal density (number of instrumented pedicles vs. total available), and fusion length. Surgical technique: Standard technique used in all centers employed extra hard titanium–aluminum–niobium alloy 6 mm diameter rods (DePuy Synthes, Raynham, Pennsylvania, United States) with reduction of the curvature via cantilever-segmental translation maneuvers. Implant location and density was according to curve stiffness and intraoperative bone density. The majority of the implants were on the thoracic curve convexity. Analysis: Bivariate analysis of outcome measures. Given the numerous correlations performed, a Bonferroni corrected p value was used, p < 0.005. Two groups of pairs matched by curve type and exact fusion levels but differing MT curve magnitude were compared using student t-test. Outcomes for the quartiles of preoperative MT flexibility were compared using an ANOVA. Results A total of 106 patients, 94 were female patients. A total of 78 patients had Lenke 1 and 28 had Lenke 2. Mean age was 14 years. Bivariate analysis: No significant correlations were present between metal density and coronal curve correction rates of the MT (r = 0.13, p = 0.19) or lumbar curves (r = ␂ 0.15, p = 0.12) or FBCI; MT (r = ␂ 0.1, p = 0.31), lumbar (r = 0.00, p = 0.97). Metal density had no effect on change in thoracic kyphosis (r = 0.22, p = 0.04) or lumbosacral lordosis (r = 0.27 p = 0.01). Longer fusion length was associated with greater loss of thoracic kyphosis (r = ␂ 0.31, p = 0.003) and less postoperative thoracic kyphosis (r = ␂ 0.31, p = 0.003) but did not affect lumbosacral lordosis. Curve magnitude: Two groups of 21 matched cases from preoperative MT curve magnitude (< 70 vs. ≥ 70 degrees) treated with comparable metal density (54 vs. 57%, p = 0.4) had equivalent MT and lumbar curve correction rates and FBCI. Sagittal profile changes did not differ significantly. Flexibility: No significant differences in MT, lumbar, and sagittal curve changes were present among the four MT flexibility quartiles (< 32, 33–43, 43–51, 52–87%) despite all groups receiving comparable metal density (58, 58, 60, 62%, p = 0.2). Conclusion Metal density does not affect coronal and sagittal plane correction in surgery for thoracic AIS. Longer fusion length adversely affects sagittal profile. Larger and less flexible curves do not necessarily require high metal density.

3. Cutaneous silent period in idiopatic scoliosis: A pilot study

Objective The pathogenesis of idiopathic scoliosis (IS) remains poorly understood. One of the hypothesis of the development of IS could be an abnormal sensorimotor integration. Cutaneous silent period (CSP) is a plurisegmental spinal inhibitory reflex, which occurs after painful stimulation of small diameter A-delta fibers. To date, CSPs have not been extensively studied in patients with idiopathic scoliosis. Materials and methods We recorded CSPs induced by noxious digit II stimulation in both thenar muscles while the subject maintains a moderately strong voluntary muscle contraction in 6 patients with idiopatic scoliosis before surgery (1 male; age 14–28 years) and in 9 healthy volunteers (4 males; age 20–34 years). The beginning, duration and end of the CSP have been measured in individual traces. Results CSP onset, duration and end latencies in IS did not significantly differ between concavity and convexity of the scoliotic curve. Moreover, there was not any significant difference in CSP onset, duration and end latencies in IS as compared to controls. Conclusion We conclude that plurisegmental spinal inhibitory reflex is well preserved in idiopatic scolioisis. These findings did not support the hypothesis of disturbances in sensorimotor integration at the spinal level. Supported by Research Projects of Charles University PRVOUK P34, Grant Project of Czech Ministry of Health NT12282, NT13693.

Does curve convexity affect the surgical outcomes of thoracic adolescent idiopathic scoliosis?

Major left thoracic (LT) curve is an atypical type in adolescent idiopathic scoliosis (AIS) and showed independent clinical characteristics and natural history compared to major right thoracic (RT)curve. However, it's unclear whether the convexity of major thoracic curve would affect the surgical outcomes and risk of complications. A retrospective follow-up study was conducted to investigate whether the convexity of major thoracic curve would affect the surgical outcomes of patients with main thoracic AIS. Twelve LT-AIS patients underwent corrective spinal instrumentation and fusion were retrieved, and twelve patients with main RT-AIS matched for gender, chronological age, curve type, magnitude and surgical strategy were selected as control. All patients underwent at least 2-year follow-up. The pre- and post-operative radiographic parameters, intraoperative data and functional outcome assessed by Scoliosis Research Society questionnaire 22 (SRS-22) were analyzed and compared between two groups. Patients with LT- and RT-AIS presented with similar magnitudes of thoracic curves, flexibility, fusion level and correction rate. Compared with RT-AIS, patients with LT-AIS showed longer operation time (average, 364 vs. 348min) and larger amount intraoperative estimated blood loss (2,060 vs. 1,720ml) although the differences were not statistically significant (p>0.05). With at least 2-year follow-up, patients in two groups showed comparable loss of correction, coronal and sagittal balance, and the sagittal profiles. With regard to functional outcome, the scores of five categories of SRS-22 questionnaire were similar between two groups. No neurological or vascular complication was observed in these patients. The radiographic and functional outcomes of LT-AIS patients underwent operation were comparable to those with RT-AIS. Longer operation time and more intraoperative blood loss may be expected in instrumentation and fusion for patients with LT-AIS, which might be because of the inconvenience on the surgical procedure.

Novel Experimental Scoliosis Model in Immature Rat Using Nickel-Titanium Coil Spring

Follow-up of animals after surgically initiated scoliosis. To develop quantitatively asymmetric loads on rat lumbar to create scoliosis. Current animal models for scoliosis use mostly rigid or flexible posterior asymmetric tethers. The curve progression can only be expected for the growth potential, leading to insufficient growth potential for validation of corrective techniques. Scoliosis was induced in 55 five-week-old female Sprague-Dawley rats using a nickel-titanium coil spring. The experimental rats were randomly divided into 2 groups: in group A (n = 15), the nickel-titanium coil spring was not removed until these rats reached physical maturity (age, 12 wk). Group B (n = 40) was further randomly subdivided into 5 subgroups (n = 8 for each subgroup): removal of the spring after 1 week (group B1), 2 weeks (group B2), 3 weeks (group B3), 4 weeks (group B4), and 5 weeks (group B5). All rats were followed for a 7-week period with serial radiographs to document change of the deformity. All experimental animals of group A developed progressive, structural scoliotic curves convex to the left in the lumbar segment. In group B, the deformity of the lumbar progressed after the spring load was applied and regressed after the spring was removed. The scoliosis in group B1-B3 (the spring removed before sexual maturity) regressed after spring removal until the rats reached sexual maturity (4 wk after spring implant surgery). The scoliosis in group B4-B5 (the spring removed after sexual maturity) regressed only during the first week after spring removal surgery. The average coronal Cobb angle was 7.8° ± 1.3° (range: 6.0° -10.2°) in group B1 at the final follow-up, and there was only 1 experimental rat that maintained a curve more than 108. The models of group B2-B5 maintained stable scoliotic curves (coronal Cobb angle of L2-L5 > 10°) convex to the left in the lumbar segment at the final follow-up. This study establishes a rat lumbar scoliosis model via asymmetric load. This method develops lumbar scoliosis in a short time and maintains the essential elements along the curve. It is suitable for the investigation of scoliosis.

A Spectral Graph Uncertainty Principle

The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed. Just as the classical result provides a tradeoff between signal localization in time and frequency, this result provides a fundamental tradeoff between a signal's localization on a graph and in its spectral domain. Using the eigenvectors of the graph Laplacian as a surrogate Fourier basis, quantitative definitions of graph and spectral "spreads" are given, and a complete characterization of the feasibility region of these two quantities is developed. In particular, the lower boundary of the region, referred to as the uncertainty curve, is shown to be achieved by eigenvectors associated with the smallest eigenvalues of an affine family of matrices. The convexity of the uncertainty curve allows it to be found to within $\varepsilon$ by a fast approximation algorithm requiring $O(\varepsilon^{-1/2})$ typically sparse eigenvalue evaluations. Closed-form expressions for the uncertainty curves for some special classes of graphs are derived, and an accurate analytical approximation for the expected uncertainty curve of Erd\H{o}s-R\'enyi random graphs is developed. These theoretical results are validated by numerical experiments, which also reveal an intriguing connection between diffusion processes on graphs and the uncertainty bounds.

Magnetic resonance imaging of scoliosis

•. Most cases of scoliosis are idiopathic. Typically, the patient is female and there is a painless thoracolumbar curve convex to the right. •. Atypical features include a curve convex to the left, rapid progression, pain and neurological symptoms. •. MRI has a key role in evaluating scoliosis when atypical features are present to determine whether there is an underlying cause, such as a tumour, or an associated neuro-axial anomaly. •. In many institutions, MRI is routinely performed pre-operatively in all cases of scoliosis surgery to exclude an underlying anomaly. The assessment of scoliosis involves excluding a structural cause of the abnormality, determining the degree of deformity and identifying any associated anomalies. In many institutions MRI is routinely performed pre-operatively in all cases of scoliosis surgery to exclude an underlying anomaly.

Is Curve Direction Correlated With the Dominant Side of Tonsillar Ectopia and Side of Syrinx Deviation in Patients With Single Thoracic Scoliosis Secondary to Chiari Malformation and Syringomyelia?

A retrospective imaging study. To conduct an assessment of the correlation of the coronal asymmetries between tonsillar ectopia, syrinx, and scoliosis. A few reports have shown that the convex side of scoliosis was on the same side as the dominant tonsillar ectopia or syrinx deviation in a majority of patients. However, this issue remains controversial. A retrospective study was conducted on young patients with a single thoracic scoliosis secondary to Chiari malformation type I and syringomyelia. The curve direction, side of the dominant tonsillar ectopia and side of the syrinx deviation were recorded and assessed quantitatively. The correlations between the asymmetrically displaced tonsils, eccentrically located syrinx, and curve convexity were investigated. A total of 39 patients were included. The concordance between the deviated side of the eccentrically located syrinx and dominant side of the asymmetrically displaced tonsils was 87.0%. In 88.5% of the patients with an asymmetrically displaced tonsil, the convex side of the scoliosis was concordant with the dominant side of the tonsillar ectopia, and in 86.2% of patients with an eccentrically located syrinx, the convex side of the scoliosis was on the same side as the deviated side of the syrinx. In addition, the dominant tonsillar ectopia, syrinx deviation, and curve direction were all on the same side in 82.6% patients with asymmetrically displaced tonsils and eccentrically located syrinx. Asymmetrically displaced tonsils and eccentrically located syrinxes were common imaging features in these patients. The thoracic spine tended to be convex to not only the dominant side of the asymmetrically displaced tonsil, but also the deviated side of the eccentrically located syrinx. The effect of syrinx deviation on curve convexity is similar to that of dominant tonsillar ectopia in the majority of patients.

Evaluation of Scoliosis Deviation with Clinical Measurements during Physical Therapy

Aim: Scoliosis is a 3D deformation, in a vast related medical literature, we can find quit a few scoliosis evaluation indices, which are based on back surface data and are generally measured along three planes. The purpose of this study was to assess the usefulness of surface clinical measurements for evaluation of condition by patients with scoliosis in shorter terms. Materials and Method: A total of 40 scoliosis patients, with an average age of 13 years, the average Risser sign 3 and an average angle of curvature of 23.67° according to Cobb were included in this study. In research were looking a correlation between convexity of curve by x-ray picture and asymmetry of measurement distances. Results: the data analyze is showing a correlation between decrease of clinical asymmetry and reduction of curve by treatment with significance p < 0.01. The trunk surface asymmetry is still difficult to objectify and it depended of new examination technique shall be done more. Conclusion: External measurements of some anatomical points can be use in physical therapy practice for evaluation of condition by patients with scoliosis with significant correlation of convexity of curve.

Regularity and Convexity of NURBS Curves

Determining regularity and convexity of NURBS curves is necessary in computer aided geometric design. In this paper, the problems above are converted to the questions related to polynomials. Then based on properties of algebraic equations and isolation theorem of roots, a simple and practical method for determining those geometric properties of NURBS curves is put forward. Compared with traditional method it will save us much computation

Local Convexity Shape-Preserving Data Visualization by Spline Function

The main purpose of this paper is the visualization of convex data that results in a smooth, pleasant, and interactive convexity-preserving curve. The rational cubic function with three free parameters is constructed to preserve the shape of convex data. The free parameters are arranged in a way that two of them are left free for user choice to refine the convex curve as desired, and the remaining one free parameter is constrained to preserve the convexity everywhere. Simple data-dependent constraints are derived on one free parameter, which guarantee to preserve the convexity of curve. Moreover, the scheme under discussion is, C1 flexible, simple, local, and economical as compared to existing schemes. The error bound for the rational cubic function is O(h3).

Safe Pedicle Screw Placement in Thoracic Scoliotic Curves Using t-EMG

A cross-sectional study of nonconsecutive cases (level III evidence). In a series of young patients with thoracic scoliosis who were treated with pedicle screw constructs, data obtained from triggered electromyography (t-EMG) screw stimulation and postoperative computed tomographic scans were matched to find different threshold limits for the safe placement of pedicle screws at the concavity (CC) and convexity (CV) of the scoliotic curves. The influence of the distance from the medial pedicle cortex to the spinal cord on t-EMG threshold intensity was also investigated at the apex segment. Whether the t-EMG stimulation threshold depends on pedicle bony integrity or on the distance to neural tissue remains elusive. Studying pedicle screws at the CC and CV at the apex segments of scoliotic curves is a good model to address this issue because the spinal cord is displaced to the CC in these patients. A total of 23 patients who underwent posterior fusions using 358 pedicle thoracic screws were reviewed. All patients presented main thoracic scoliosis, with a mean Cobb angle of 58.3 degrees (range, 46-87 degrees). Accuracy of the screw placement was tested at surgery by the t-EMG technique. During surgery, 8 screws placed at the CC showed t-EMG threshold values below 7 mA and were carefully removed. Another 25 screws disclosed stimulation thresholds within the range of 7 to 12 mA. After checking the screw positions by intraoperative fluoroscopy, 15 screws were removed because of clear signs of malpositioning. Every patient underwent a preoperative magnetic resonance imaging examination, in which the distances from the spinal cord to the pedicles of the concave and convex sides at 3 apex vertebrae were measured. Postoperative computed tomographic scans were used in all patients to detect screw malpositioning of the final 335 screws. According to postoperative computed tomographic scans, 44 screws (13.1%) showed different malpositions: 40 screws (11.9%) perforated the medial pedicle wall, but only 11 screws (3.2%) were completely inside the spinal canal. If we considered the 23 screws removed during surgery, the true rate of misplaced screws increased to 18.7%. In those screws that preserved the pedicle cortex (well-positioned screws), EMG thresholds from the CC showed statistically significantly lower values than those registered at the CV of the deformity (21.1 ± 8.2 vs 23.9 ± 7.7 mA, P < 0.01). In the concave side, t-EMG threshold values under 8 mA should be unacceptable because they correspond to screw malpositioning. Threshold values above 14 mA indicate an accurate intrapedicular position with certainty. At the convex side, threshold values below 11 mA always indicate screw malpositioning, and values above 19 mA imply accurate screw placement. At the 3 apex vertebrae, the average pedicle-spinal cord distance was 2.2 ± 0.7 mm at the concave side and 9.8 ± 4.3 mm at the convex side (P < 0.001). In well-positioned screws, a correlation between pedicle-dural sac distance and t-EMG threshold values was found at the concave side only (Pearson r = 0.467, P < 0.05). None of the patients with misplaced screws showed postoperative neurological impairment. Independent of the screw position, average t-EMG thresholds were always higher at the CV in the apex and above the apex regions, presuming that the distance from the pedicle to the spinal cord plays an important role in electrical transmission. The t-EMG technique has low sensitivity to predict screw malpositioning and cannot discriminate between medial cortex breakages and complete invasion of the spinal canal.

Brace technology thematic series: the progressive action short brace (PASB)

BackgroundThe Progressive Action Short Brace (PASB) is a custom-made thoraco-lumbar-sacral orthosis (TLSO), devised in 1976 by Dr. Lorenzo Aulisa (Institute of Orthopedics at the Catholic University of the Sacred Heart, Rome, Italy). The PASB was designed to overcome the limits imposed by the trunk anatomy. Indeed, the particular geometry of the brace is able to generate internal forces that modify the elastic reaction of the spine. The PASB is indicated for the conservative treatment of lumbar and thoraco-lumbar scoliosis. The aim of this article is to explain the biomechanic principles of the PASB and the rationale underlying its design. Recently published studies reporting the results of PASB-based treatment of adolescent scoliotic patients are also discussed.Description and principlesOn the coronal plane, the upper margin of the PASB, at the side of the curve concavity, prevents the homolateral bending of the scoliotic curve. The opposite upper margin ends just beneath the apical vertebra. The principle underlying such configuration is that the deflection of the inferior tract of a curved elastic structure, fixed at the bottom end, causes straightening of its upper tract. Therefore, whenever the patient bends towards the convexity of the scoliotic curve, the spine is deflected. On the sagittal plane, the inferior margins of the PASB reach the pelvitrochanteric region, in order to stabilize the brace on the pelvis. The transverse section of the brace above the pelvic grip consists of asymmetrical ellipses. This allows the spine to rotate towards the concave side only, leading to the continuous generation of derotating moments. On the sagittal plane, the brace is contoured so as to reduce the lumbar lordosis. The PASB, by allowing only those movements counteracting the progression of the curve, is able to produce corrective forces that are not dissipated. Therefore, the brace is based on the principle that a constrained spine dynamics can achieve the correction of a curve by inverting the abnormal load distribution during skeletal growth.ResultsSince its introduction in 1976, several studies have been published supporting the validity of the biomechanical principles to which the brace is inspired. In this article, we present the outcome of a case series comprising 110 patients with lumbar and thoraco-lumbar curves treated with PASB brace. Antero-posterior radiographs were used to estimate the curve magnitude (CM) and the torsion of the apical vertebra (TA) at 5 time points: beginning of treatment (t1), one year after the beginning of treatment (t2), intermediate time between t1 and t4 (t3), end of weaning (t4), 2-year minimum follow-up from t4 (t5). The average CM value was 29.3°Cobb at t1 and 13.0°Cobb at t5. TA was 15.8° Perdroille at t1 and 5.0° Perdriolle at t5. These results support the efficacy of the PASB in the management of scoliotic patients with lumbar and thoraco-lumbar curves.ConclusionThe results obtained in patients treated with the PASB confirm the validity of our original biomechanical approach. The efficacy of the PASB derives not only from its unique biomechanical features but also from the simplicity of its design, construction and management.