Patient-specific finite element model of the spine and spinal cord to assess the neurological impact of scoliosis correction: preliminary application on two cases with and without intraoperative neurological complications

Scoliosis is a 3D deformation of the spine and rib cage. For severe cases, surgery with spine instrumentation is required to restore a balanced spine curvature. This surgical procedure may represent a neurological risk for the patient, especially during corrective maneuvers. This study aimed to computationally simulate the surgical instrumentation maneuvers on a patient-specific biomechanical model of the spine and spinal cord to assess and predict potential damage to the spinal cord and spinal nerves. A detailed finite element model (FEM) of the spine and spinal cord of a healthy subject was used as reference geometry. The FEM was personalized to the geometry of the patient using a 3D biplanar radiographic reconstruction technique and 3D dual kriging. Step by step surgical instrumentation maneuvers were simulated in order to assess the neurological risk associated to each maneuver. The surgical simulation methodology implemented was divided into two parts. First, a global multi-body simulation was used to extract the 3D displacement of six vertebral landmarks, which were then introduced as boundary conditions into the personalized FEM in order to reproduce the surgical procedure. The results of the FEM simulation for two cases were compared to published values on spinal cord neurological functional threshold. The efficiency of the reported method was checked considering one patient with neurological complications detected during surgery and one control patient. This comparison study showed that the patient-specific hybrid model reproduced successfully the biomechanics of neurological injury during scoliosis correction maneuvers.     

A simple method for in vivo measurement of implant rod three-dimensional geometry during scoliosis surgery

Scoliosis is defined as a spinal pathology characterized as a three-dimensional deformity of the spine combined with vertebral rotation. Treatment for severe scoliosis is achieved when the scoliotic spine is surgically corrected and fixed using implanted rods and screws. Several studies performed biomechanical modeling and corrective forces measurements of scoliosis correction. These studies were able to predict the clinical outcome and measured the corrective forces acting on screws, however, they were not able to measure the intraoperative three-dimensional geometry of the spinal rod. In effect, the results of biomechanical modeling might not be so realistic and the corrective forces during the surgical correction procedure were intra-operatively difficult to measure. Projective geometry has been shown to be successful in the reconstruction of a three-dimensional structure using a series of images obtained from different views. In this study, we propose a new method to measure the three-dimensional geometry of an implant rod using two cameras. The reconstruction method requires only a few parameters, the included angle θ between the two cameras, the actual length of the rod in mm, and the location of points for curve fitting. The implant rod utilized in spine surgery was used to evaluate the accuracy of the current method. The three-dimensional geometry of the rod was measured from the image obtained by a scanner and compared to the proposed method using two cameras. The mean error in the reconstruction measurements ranged from 0.32 to 0.45 mm. The method presented here demonstrated the possibility of intra-operatively measuring the three-dimensional geometry of spinal rod. The proposed method could be used in surgical procedures to better understand the biomechanics of scoliosis correction through real-time measurement of three-dimensional implant rod geometry in vivo.     

Finite element simulation of spinal deformities correction by in situ contouring technique

Biomechanical models have been proposed in order to simulate the surgical correction of spinal deformities. With these models, different surgical correction techniques have been examined: distraction and rod rotation. The purpose of this study was to simulate another surgical correction technique: the in situ contouring technique. In this way, a comprehensive three-dimensional Finite Element (FE) model with patient-specific geometry and patient-specific mechanical properties was used. The simulation of the surgery took into account elasto-plastic behavior of the rod and multiple moments loading and unloading representing the surgical maneuvers. The simulations of two clinical cases of hyperkyphosis and scoliosis were coherent with the surgeon's experience. Moreover, the results of simulation were compared to post-operative 3D measurements. The mean differences were under 5 degrees for vertebral rotations and 5 mm for spinal lines. These simulations open the way for future predictive tools for surgical planning.     

Finite element simulation of spinal deformities correction by in situ contouring technique

Biomechanical models have been proposed in order to simulate the surgical correction of spinal deformities. With these models, different surgical correction techniques have been examined: distraction and rod rotation. The purpose of this study was to simulate another surgical correction technique: the in situ contouring technique. In this way, a comprehensive three-dimensional Finite Element (FE) model with patient-specific geometry and patient-specific mechanical properties was used. The simulation of the surgery took into account elasto–plastic behavior of the rod and multiple moments loading and unloading representing the surgical maneuvers. The simulations of two clinical cases of hyperkyphosis and scoliosis were coherent with the surgeon's experience. Moreover, the results of simulation were compared to post-operative 3D measurements. The mean differences were under 5° for vertebral rotations and 5 mm for spinal lines. These simulations open the way for future predictive tools for surgical planning.     

Biomechanical basis of optimal scoliosis surgical correction

For an optimal approach to surgical correction of scoliosis, it was deemed desirable to biomechanically simulate the set of corrective forces applied by alternative internal fixation systems, so as to determine and apply the internal fixation system producing the best correction under safe levels of forces applied by the fixation systems to the spinal structures. To this end, we have developed, and presented here, (1) a spinal finite-element model relating the applied corrective forces to the corrected spinal configurations, (2) a method for determining the stiffness of the patient's spine prior to surgery, (3) computerized finite-element analysis simulation of alternative internal correction-fixation systems, so as to determine the most efficacious system, (4) instrumentations for surgically implementing the recommendations of the surgical simulation analysis and (5) comparisons of the model-simulated and surgically-obtained corrected spinal configurations. These procedures together constitute the biomechanical foundations of scoliosis surgical correction.     

Optimization of skeletal configuration: studies of scoliosis correction biomechanics

A scheme for optimizing configurations in models of skeletal structures is presented. Use of the scheme is illustrated through determination of biomechanically optimal correction of a right-thoracic scoliosis by passive brace and active muscle forces. The locations and magnitudes of the passive brace forces, and the trunk muscle groups and their corresponding contraction intensity magnitudes that would optimally correct the geometric deformities of the spine were determined. The results suggest that, from a biomechanical viewpoint, both brace and muscle forces are capable of substantial correction of a model thoracic scoliosis. However, comparison of model results with long-term clinical results suggests that even under optimal conditions it is unlikely that scoliosis can be fully corrected by passive brace forces or active muscle contractions.     

Use of Neural Networks to Correlate Spine and Rib Deformity in Scoliosis

Artificial neural networks (ANN's) recognize patterns relating input and output data in a manner analogous to the function of biological neurons. Here, we show that ANN's can predict rib deformity in scoliosis more accurately than regression analysis. ANN's and linear regression models were developed to predict rib rotation from several combinations of input spinal indices including Cobb angle, vertebral rotation, apex location and orientation of the plane of maximal curvature. ANN's averaged 60% correct predictions compared to 34% for regression analysis. This study provides evidence for the utility of artificial neural networks in scoliosis research. These data lend credence to the use of ANN's in future work on the prediction of scoliotic spinal deformity from torso surface data, which would permit assessment of scoliosis severity with minimal use of harmful X-rays.     

Preliminary studies of neurosensory and cardiopulmonary health compromise in captive- bred Rhesus macaques (Macaca mulatta) suffering scoliosis

Background It has been widely documented that quadrupedal animals rarely display natural spontaneous scoliotic rachis deviations of the spinal column. The objective was to determine spinal deformities developed by geriatric monkeys of the Macaca mulatta species, by radiographical and tomographical studies of the vertebral column correlating morphological changes with altered physiological parameters and electrical neurosensorial conductivity of somatosensory‐evoked potentials (SEPs). Materials and methods A cohort of six geriatric monkeys was used: three non‐scoliotic subjects and three monkeys with naturally acquired true scoliosis. Results Radiographic and tomographic studies depicted a thoracic curvature displaying a left‐sided thoracic vertebral rotation. The evaluation of physiological parameters demonstrated significant differences in the respiratory rate, as it was observed for the diastolic blood pressures, which showed a decrease in the monkeys with scoliosis compared with healthy monkeys. Regarding the SEPs studies, the non‐parametric test for independent samples Mann–Whitney U test displayed a significant difference observed at the left and right thoracic derivative in P1; while regarding the study of upper limbs, a significant difference was seen at the Erb’s point derivative, left afferency in P1, showing in all the derivatives an increase in latency in monkeys with scoliosis versus monkeys in the control group. Conclusions This study has demonstrated that quadrupedal animals can develop true scoliosis showing an analogous way to that occurring in humans.     

Use of Neural Networks to Correlate Spine and Rib Deformity in Scoliosis

Abstract

Artificial neural networks (ANN's) recognize patterns relating input and output data in a manner analogous to the function of biological neurons. Here, we show that ANN's can predict rib deformity in scoliosis more accurately than regression analysis. ANN's and linear regression models were developed to predict rib rotation from several combinations of input spinal indices including Cobb angle, vertebral rotation, apex location and orientation of the plane of maximal curvature. ANN's averaged 60% correct predictions compared to 34% for regression analysis. This study provides evidence for the utility of artificial neural networks in scoliosis research. These data lend credence to the use of ANN's in future work on the prediction of scoliotic spinal deformity from torso surface data, which would permit assessment of scoliosis severity with minimal use of harmful X-rays.     

Biomechanical alterations in intact osteoporotic spine due to synthetic augmentation: finite element investigation

A three-dimensional nonlinear finite element model (FEM) was developed for a parametric study that examined the effect of synthetic augmentation on nonfractured vertebrae. The objective was to isolate those parameters primarily responsible for the effectiveness of the procedure; bone cement volume and bone density were expected to be highly important. Injection of bone cement was simulated in the FEM of a vertebral body that included a cellular model for the trabecular core. The addition of 10% and 20% cement by volume resulted in an increase in failure load, and the larger volume resulted in an increase in stiffness for the vertebral body. Placement of cement within the vertebral body was not as critical a parameter as cement amount. Simulated models of very poor bone quality saw the best therapeutic benefits.     

先天性脊柱侧弯采用后路半椎体切除短节段融合疗效分析

目的:探讨先天性脊柱侧弯采用后路半椎体切除短节段融合治疗的临床疗效。方法:选取2011年1月~2014年1月经我院治疗的120份先天性脊柱侧弯患者,采用后路半椎体切除短节段融合治疗法进行治疗,比较手术前后、最后一次随访的脊柱全长正侧位X线片,测量并记录治疗前后及随访期间脊柱侧弯程度及后凸的Cobb's角。结果:通过治疗患者脊柱侧弯得到明显改善,半椎体节段侧弯Cobb's角术前平均44.2°,术后平均15.1°,平均矫正率为65.8%,末次随访平均14.3°,矫正率64.2%;全主弯Cobb's角术后平均矫正率60.7%,末次随访平均矫正率65.6%;半椎体节段后凸Cobb's角术前平均15.3°,术后为正常范围值;术后和末次随访的头侧、尾侧代偿弯改善明显,5项指标手术前后对比差异有统计学意义(P0.05)。结论:先天性脊柱侧弯采用后路半椎体切除短节段融合治疗可以达到显著矫正先天性脊柱侧弯的效果。     

CT and radiographic analysis of sagittal profile changes following thoracoscopic anterior scoliosis surgery

ABSTRACT: BACKGROUND: Previous studies report an increase in thoracic kyphosis after anterior approaches and a flattening of sagittal contours following posterior approaches. Difficulties with measuring sagittal parameters on radiographs are avoided with reformatted sagittal CT reconstructions due to the superior endplate clarity afforded by this imaging modality. METHODS: A prospective study of 30 Lenke 1 adolescent idiopathic scoliosis (AIS) patients receiving selective thoracoscopic anterior spinal fusion (TASF) was performed. Participants had ethically approved low dose CT scans at minimum 24 months after surgery in addition to their standard care following surgery. The change in sagittal contours on supine CT was compared to standing radiographic measurements of the same patients and with previous studies. Inter-observer variability was assessed as well as whether hypokyphotic and normokyphotic patient groups responded differently to the thoracoscopic anterior approach. RESULTS: Mean T5-12 kyphosis Cobb angle increased by 11.8 degrees and lumbar lordosis increased by 5.9 degrees on standing radiographs two years after surgery. By comparison, CT measurements of kyphosis and lordosis increased by 12.3 degrees and 7.0 degrees respectively. 95% confidence intervals for inter-observer variability of sagittal contour measurements on supine CT ranged between 5-8 degrees. TASF had a slightly greater corrective effect on patients who were hypokyphotic before surgery compared with those who were normokyphotic. CONCLUSIONS: Restoration of sagittal profile is an important goal of scoliosis surgery, but reliable measurement with radiographs suffers from poor endplate clarity. TASF significantly improves thoracic kyphosis and lumbar lordosis while preserving proximal and distal junctional alignment in thoracic AIS patients. Supine CT allows greater endplate clarity for sagittal Cobb measurements and linear relationships were found between supine CT and standing radiographic measurements. In this study, improvements in sagittal kyphosis and lordosis following surgery were in agreement with prior anterior surgery studies, and add to the current evidence suggesting that anterior correction is more capable than posterior approaches of addressing the sagittal component of both the instrumented and adjacent non instrumented segments following surgical correction of progressive Lenke 1 idiopathic scoliosis.     

The three dimensional analysis of the Sforzesco brace correction

Background

The 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.

Methods

Group 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.

Results

The 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.

Conclusions

It 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.

     

A retrospective analysis of health-related quality of life in adolescent idiopathic scoliosis children treated by anterior instrumentation and fusion

Background

Idiopathic scoliosis is the most common type of spinal deformity. Scoliosis is defined as a lateral curvature of the spine greater than 10° accompanied by rotation of the vertebrae. The treatment available for adolescent idiopathic scoliosis is observation, orthosis, and surgery. The surgical options include open anterior release and instrumentation, posterior instrumentation, and thoracoscopic approaches. The Scoliosis Research Society Questionnaire (SRS-30) is a specific instrument to measure health-related quality of life in patients with scoliosis, who had or had not undergone surgery. The purpose was to assess the post-operative functional outcome using SRS-30 in children who underwent anterior release, instrumentation, and fusion using autogenous rib graft for adolescent idiopathic scoliosis (AIS).

Methods

In a retrospective cohort study, 25 patients between the ages of 11 and 17 years, who underwent anterior release, instrumentation, and fusion using autogenous rib graft for adolescent idiopathic scoliosis (AIS) between 2008 and 2014, were included in the study.

Results

The total average score was 4.26 with a SD of 0.014 and had maximum average score 4.5 (for pain) and minimum average score 3.8 (for self-image).

Conclusion

Anterior release, instrumentation, and fusion using autogenous rib graft is having good functional outcome in all domains.

     

Three-Dimensional Vertebral Wedging in Mild and Moderate Adolescent Idiopathic Scoliosis

Background

Vertebral wedging is associated with spinal deformity progression in adolescent idiopathic scoliosis. Reporting frontal and sagittal wedging separately could be misleading since these are projected values of a single three-dimensional deformation of the vertebral body. The objectives of this study were to determine if three-dimensional vertebral body wedging is present in mild scoliosis and if there are a preferential vertebral level, position and plane of deformation with increasing scoliotic severity.

Methodology

Twenty-seven adolescent idiopathic scoliotic girls with mild to moderate Cobb angles (10° to 50°) participated in this study. All subjects had at least one set of bi-planar radiographs taken with the EOS® X-ray imaging system prior to any treatment. Subjects were divided into two groups, separating the mild (under 20°) from the moderate (20° and over) spinal scoliotic deformities. Wedging was calculated in three different geometric planes with respect to the smallest edge of the vertebral body.

Results

Factorial analyses of variance revealed a main effect for the scoliosis severity but no main effect of vertebral Levels (apex and each of the three vertebrae above and below it) (F = 1.78, p = 0.101). Main effects of vertebral Positions (apex and above or below it) (F = 4.20, p = 0.015) and wedging Planes (F = 34.36, p<0.001) were also noted. Post-hoc analysis demonstrated a greater wedging in the inferior group of vertebrae (3.6°) than the superior group (2.9°, p = 0.019) and a significantly greater wedging (p≤0.03) along the sagittal plane (4.3°).

Conclusions

Vertebral wedging was present in mild scoliosis and increased as the scoliosis progressed. The greater wedging of the inferior group of vertebrae could be important in estimating the most distal vertebral segment to be restrained by bracing or to be fused in surgery. Largest vertebral body wedging values obtained in the sagittal plane support the claim that scoliosis could be initiated through a hypokyphosis.     

Biomechanical modeling of posterior instrumentation of the scoliotic spine

Scoliosis is a three-dimensional deformation of the spine that can be treated by vertebral fusion using surgical instrumentation. However, the optimal configuration of instrumentation remains controversial. Simulating the surgical maneuvers with personalized biomechanical models may provide an analytical tool to determine instrumentation configuration during the pre-operative planning. Finite element models used in surgical simulations display convergence difficulties as a result of discontinuities and stiffness differences between elements. A kinetic model using flexible mechanisms has been developed to address this problem, and this study presents its use in the simulation of Cotrel-Dubousset Horizon surgical maneuvers. The model of the spine is composed of rigid bodies corresponding to the thoracic and lumbar vertebrae, and flexible elements representing the intervertebral structures. The model was personalized to the geometry of three scoliotic patients (with a thoracic Cobb angle of 45 degrees, 49 degrees and 39 degrees ). Binary joints and kinematic constraints were used to represent the rod-implant-vertebra joints. The correction procedure was simulated using three steps: (1) Translation of hooks and screws on the first rod; (2) 90 degrees rod rotation; (3) Hooks and screws look-up on the rod. After the simulation, slight differences of 0-6 degrees were found for the thoracic spine scoliosis and the kyphosis, and of 1-8 degrees for the axial rotation of the apical vertebra and for the orientation of the plane of maximum deformity, compared to the real post-operative shape of the patient. Reaction loads at the vertebra-implant link were mostly below 1000 N, while reaction loads at the boundary conditions (representing the overall action of the surgeon) were in the range 7-470 N and maximum torque applied to the rod was 1.8 Nm. This kinetic modeling approach using flexible mechanisms provided a realistic representation of the surgical maneuvers. It may offer a tool to predict spinal geometry correction and assist in the pre-operative planning of surgical instrumentation of the scoliotic spine.     

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

Background

The 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.

Methods

Group 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.

Results

The 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.

Conclusions

It 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.

     

The construction of the scoliosis 3D finite element model and the biomechanical analysis of PVCR orthopaedy

ObjectiveThe objective is to investigate the biomechanical conditions of the Posterior Vertebral Column Resection (PVCR) of the constructed scoliosis 3D finite element model.MethodsA patient with scoliosis was selected; before the PVCR orthopaedy, the patient was submitted to the radiography of normal and lateral full-length vertebral column scans and the total magnetic resonance imaging (MRI) scans; then, the idiopathic scoliosis model was constructed by the 3D finite element method, and the 3D finite element software utilized in the process of model construction included Mimics software, Geomagic Studio 12 software, and Unigraphic 8.0 (UG 8.0) software; in addition, PVCR orthopaedy was utilized to correct the scoliosis of the patient, and the biomechanical parameters, such as orthodontic force, vertebral body displacement, orthopedic rod stress, stress on the pin-bone interface of the vertebral body surface, and the stress on the intervertebral disc, were studied.ResultsThe 3D effective finite element model of scoliosis was successfully constructed by the Mimics software, the Geomagic Studio 12 software, and the UG 8.0 software, and the effectiveness was tested. PVCR orthopaedy could effectively solve the problem of scoliosis. The magnitude of the orthodontic force that a patient needed depended on the physical conditions and the personal orthodontic requirements of the patient. The maximum vertebral body displacement on the X-axis was the vertebral body L1, the maximum displacement on the Y-axis was the vertebral body T3, the maximum displacement on the Z-axis was the vertebral body T1, and the rang of orthopedic rod stress was 0.0050214e⁷ MPa to 0.045217e⁷ MPa, in which the maximum stress of 2 vertebral bodies in, above, and below the osteotomy area reached 0.045217e⁷ MPa, the stress on the pin-bone interface of the T10 vertebral body surface reached 11.83 MPa, and the stress of T8/T9 intervertebral disc reached 13.84 MPa.ConclusionThe 3D finite element model based on 3D finite element software was highly efficient, and its numerical simulation was accurate, which was important for the subsequent biomechanical analysis of PVCR orthopaedy. In addition, the vertebral stress of PVCR orthopaedy was different in each body part, which was mainly affected by the applied orthodontic force and the sites of the orthodontic area.     

Geometry parameterization and multidisciplinary constrained optimization of coronary stents

Coronary stents are tubular type scaffolds that are deployed, using an inflatable balloon on a catheter, most commonly to recover the lumen size of narrowed (diseased) arterial segments. A common differentiating factor between the numerous stents used in clinical practice today is their geometric design. An ideal stent should have high radial strength to provide good arterial support post-expansion, have high flexibility for easy manoeuvrability during deployment, cause minimal injury to the artery when being expanded and, for drug eluting stents, should provide adequate drug in the arterial tissue. Often, with any stent design, these objectives are in competition such that improvement in one objective is a result of trade-off in others. This study proposes a technique to parameterize stent geometry, by varying the shape of circumferential rings and the links, and assess performance by modelling the processes of balloon expansion and drug diffusion. Finite element analysis is used to expand each stent (through balloon inflation) into contact with a representative diseased coronary artery model, followed by a drug release simulation. Also, a separate model is constructed to measure stent flexibility. Since the computational simulation time for each design is very high (approximately 24?h), a Gaussian process modelling approach is used to analyse the design space corresponding to the proposed parameterization. Four objectives to assess recoil, stress distribution, drug distribution and flexibility are set up to perform optimization studies. In particular, single objective constrained optimization problems are set up to improve the design relative to the baseline geometry—i.e. to improve one objective without compromising the others. Improvements of 8, 6 and 15% are obtained individually for stress, drug and flexibility metrics, respectively. The relative influence of the design features on each objective is quantified in terms of main effects, thereby suggesting the design features which could be altered to improve stent performance. In particular, it is shown that large values of strut width combined with smaller axial lengths of circumferential rings are optimal in terms of minimizing average stresses and maximizing drug delivery. Furthermore, it is shown that a larger amplitude of the links with minimum curved regions is desirable for improved flexibility, average stresses and drug delivery.