ABSTRACT Pectus excavatum (PEX) is the most common chest deformity in children, which is usually corrected by using the minimally invasive Nuss method. The orthopedic effect of the Nuss

operation is mainly evaluated by both the Haller index and the appearance of the chest wall configuration, which is dependent on the operator’s clinical experience to a great extent. To

improve the orthopedic effect, we proposed a novel method to individually design and optimize the shape of the Nuss bar and to advise its location as well as the incisions. By using the CT

imaging data, the three-dimensional model of the PEX thoracic structure is reconstructed, which is further employed in finite element analysis to determine the operation plan. By referring

determine the incision position of the Nuss bar. Experiments were carried out to verify the orthopedic effect of the customized Nuss bar, which showed that this method is more accurate and

individualized, compared to conventional methods. SIMILAR CONTENT BEING VIEWED BY OTHERS ENHANCING PECTUS EXCAVATUM DIAGNOSIS WITH AN AUTOMATED BATCH EVALUATION TOOL FOR CHEST COMPUTED

TOMOGRAPHY IMAGES Article Open access 08 October 2024 A LARGE SINGLE-CENTER PROPENSITY SCORE-MATCHED COHORT STUDY ON OUTCOMES AND COMPLICATIONS BASED ON THE NUMBER OF CORRECTIVE BARS USED IN

THE NUSS PROCEDURE Article Open access 16 November 2024 THE CHANGES OF DISTANCE BETWEEN NIPPLES FOLLOWING CORRECTION OF WOMEN PECTUS EXCAVATUM Article Open access 09 January 2023

INTRODUCTION Pectus excavatum (PEX) is the most common chest deformity in children, which is characterized by a depressed sternal region relative to the frontal rib cage1. The deformity

decreases the volume of the chest and affects the circulatory and respiratory systems, and it even has a negative impact on the patient’s mental health2. In 1998, a minimally invasive repair

of pectus excavatum was reported by Nuss _et al_.3. This procedure involves inserting a convex Nuss bar under the sternum through small bilateral thoracic incisions without incising the

anterior chest wall4. Because of small skin incisions, shorter preoperative, intraoperative and post-operative time, and minimal blood loss, this method is accepted by an increasing number

of patients with pectus excavatum5,6,7. Although the Nuss procedure is routinely performed, the outcome depends mostly on the correct placement of the bar8. From the mechanic view, the

sternum is a beam with displacement constraint from ribs, so when the beam is elevated with a distance at one point, ribs would constrain the elevation of the sternum by elastic deformation,

which could complicatedly influence the deformation of the thoracic structure. And thus, the interaction forces among sternum and ribs should be taken into consideration during determining

the placement position of the Nuss bar. Since the deformation of thoracic structure is very complicated, a Nuss procedure surgical planner would be an invaluable planning tool ensuring the

optimal aesthetic outcome9. This means that the location of the incisions and the shape of the Nuss bar are determined only by the physician with clinical experience. Sometimes the physician

needs to adjust the shape of the Nuss bar many times during operation, especially when the depression of the patients’ chest is complicated, which may lead to prolonged the operation time,

increased blood loss and the possibility of damage to the patient. To determine the shape of the Nuss bar before operation, some researchers have developed a non-invasive procedure to

reconstruct the thorax and construct the shape of the Nuss bar by referring to healthy subjects10,11,12,13,14; although these methods can obtain the desired shape of the Nuss bar, the chest

wall deformity and stress distribution after Nuss bar implantation was not investigated. Actually, Nuss bar has a high risk of failure due to poor stress distribution in pectus excavatum.

Quan Li drew the conclusion that stainless steel instruments introduce higher risk for rod failure and are less favorable for lumboiliac arthrodesis than titanium instruments15. Mingyi Wang

gave advice on restoring unilateral maxilla defects after simulating the defects in the maxillofacial model and reconstructing the model with different methods16, where the finite element

analysis to optimize prostheses surgery can be a good reference for the Nuss operation. Thus, both the shape of the Nuss bar and the stress distribution of the chest after implantation are

of equal importance. In this study, we proposed a novel method to individually design and optimize the shape of the Nuss bar and to advise its location of the incisions using CT imaging data

of the patient’s thorax. In the proposed method, a three-dimensional model of the human thorax is established first using the data obtained from a CT scan of a patient with a funnel chest.

Then, we construct the finite element model, in which different operative plans are simulated. The optimum plan is chosen according to the chest wall configuration and the stress

distribution. Then, we compare it with a normal person whose chest wall configuration is similar to the patient and adjust the shape of the Nuss bar. Finally, experiments using customized

Nuss bars were carried out to validate the method in this paper. METHODS 3D RECONSTRUCTION OF THORACIC STRUCTURE The shape design and analysis of the Nuss bar are based on the thoracic

structure of PEX patients, thus the first step to reconstruct the three-dimensional model of the thoracic structure is to use imaging data from a CT scan. The chest of the PEX patient is

scanned by a clinical CT scanner with a slice thickness of 0.625 mm, and the imaging data is saved as Digital Imagine and Communications in Medicine (DICOM) files. Then, the DICOM data is

imported into the MIMICS® software (Materialise, Belgium) which is good at reconstructing accurate 3D models from CT imaging data. This procedure has served to separate the thoracic

structure from the rest of the chest structures on each image, such as the shoulder blades. Based on the analysis of the pixel intensity curve of the CT image, threshold selection can remove

redundant data and create a new mask by region growing. Based on this mask, the three-dimensional model can be reconstructed by calculation. Figure 1(a) gives an example of a reconstructed

3D model of the thoracic structure. In addition to designing the bar shape, the thoracic structure is also used to determine the location of the incisions and to analyze the stress by finite

element method. By using imaging examination, it can be observed that ribs, cartilage and sternum vary significantly while spine has only slightly change after Nuss operation. In order to

reduce the amount of calculation, the spine is treated as a rigid object and simplified as a cylinder in finite element analysis. With the simplified thoracic structure, ribs are also

reconstructed in solid models to decrease the computational complexity in finite element analysis. Figure 1(b) shows the simplified thoracic structure model reconstructed in SolidWorks®

software. SHAPE DESIGN OF NUSS BAR BY REFERRING TO A SIMILAR HEALTHY CHEST The Haller index is usually used to assess the severity of chest wall deformities, which is convenient to measure

and calculate. The Haller index is based on computed tomography of the chest and is defined as the quotient between the maximum laterolateral distance and the minimum anteroposterior

distance from the anterior portion of the vertebral body to the posterior surface of the sternum, as shown in Fig. 2 17. From the formula for the Haller index H = A/B, it can be noted that

there are two indices that affect the index value, that is, the thoracic transverse diameter A and the anterior-posterior diameter B. Therefore, both of these two influence factors should be

taken into consideration during the shape design of Nuss bars. The severest depression of the patient’s chest wall is determined by the model reconstructed by the MIMICS® software. The pre-

and post-operative thoracic transverse diameter A and \(A^{\prime} \) of twelve patients with funnel chests, as well as the ratio of A and \(A^{\prime} ,\) are presented in Table 1. From

data in the table, it can be evidently noted that thoracic transverse diameter decreases after the Nuss procedure, and the shrinkage rate (A′/A) is approximately 95%. As the shrinkage will

affect the value of the Haller index, it must be taken into account in the Nuss bar design to avoid overcorrection. Therefore, when selecting a healthy person as a reference for Nuss bar

design, the referenced person is determined according to both the thoracic transverse diameter and the shrinkage rate. Similar to the thoracic transverse diameter, the minimum

anteroposterior distance from the anterior portion of the vertebral body to the posterior surface of the sternum is also changed after operation. As shown in Fig. 3, the minimum

anteroposterior distance before operation is B, which is measured in the CT images, and the desired orthopedic minimum anteroposterior distance is marked as \(B^{\prime} \), which could be

determined using finite element analysis (FEA). In the FEA procedure, the Nuss bar is placed at different intercostal space and the sternum is elevated by different distances, and then the

values of the orthopedic anteroposterior distance can be measured from the simulation results. From these values, the desired orthopedic minimum anteroposterior distance is evaluated by

calculation of the Haller index. Let \(\bigtriangleup =B^{\prime} -{\rm{B}}\) be the orthopedic distance of the PEX chest, which can be a design reference of the Nuss bar shape. The initial

shape of the Nuss bar is designed by referring to a healthy person who has similar thoracic transverse diameter, age and gender to the PEX patient. For example, before designing the bar

shape for a PEX patient, a referenced healthy person is selected from a CT imaging database. The cases in the CT imaging database, collecting CT scan data, are identified by age, gender, and

thoracic transverse diameter. As shown in Fig. 4, the similar healthy person was selected to be a reference for designing the bar shape. Using the same method of reconstructing the PEX

thoracic structure, the thoracic 3D model of the referenced healthy person is also reconstructed using the MIMICS software. The curvature is positive when the curve is convex, and vice

versa. Analyzing the curvature of the chest wall boundary of a healthy person, as shown in Fig. 5(a), it could be obviously noted that the chest wall boundary is almost convex with positive

curvature. Taking the chest wall boundary of PEX patients into consideration, its curvature shows positive and negative variations in the patient’s chest wall boundary, as shown in Fig. 

5(b). Thus, the Nuss bar shape should be designed as a convex curve to ensure the correction; Fig. 6 gives an example of a Nuss bar design, which has a convex curve. Considering that the

Nuss bar used in clinical practice is an integral length and with one fixed end18, the Nuss bar is rounded off to a standard size. EVALUATION OF ORTHOPEDIC OPERATION BY FINITE ELEMENT

ANALYSIS The initial shape and dimension of the Nuss bar is analyzed using finite element analysis to evaluate the orthopedic effect after implantation. With the 3D model built in

SolidWorks®, ANSYS® workbench is used to conduct the finite element analysis (FEA). All materials involved in the model are assumed to be isotropic, homogenous, linearly elastic and static.

The spine and ribs are assumed to be cancellous bone19 to simplify the model and reduce calculation time. Thus, there are two kinds of materials in this model, cancellous bone and costal

cartilage. The properties of materials used in this study, including Young’s modulus, Poisson’s ratio and density, obtained from the literature20,21,22,23, are listed in Table 2. To make the

finite element analysis possible, two boundary conditions are assumed in the analysis. First, considering that the rib, cartilage and sternum vary significantly while the spine does not

obviously change in the Nuss operation, the spine is assumed to be fixed during the thorax correction simulation. Second, the elevation of the sternum is assumed to be vertical during

operation. Based on these assumptions, the boundary condition of the spine is a fixed constraint and the loading direction of the sternum is vertical. To evaluate the efficacy of the

surgical simulation in finite element analysis, the Haller index is measured before and after correction in the 2nd, 3rd, 4th and 5th intercostal space, as shown in Fig. 7. Then, we simulate

different operative strategies, including placing the Nuss bar in the 2nd, 3rd, 4th and 5th intercostal space, respectively, and set different elevations in every intercostal space. The

results of deformation and equivalent stress of each operative plan are recorded which is used as criteria for determining the optimal plan. The study was done in accordance with the

regulations of the National Health and Family Planning Commission of the People’s Republic of China. Guangdong General Hospital medical ethics committee approved this study and All study

participants provided informed consent. RESULTS Because of its nature of being non-invasive and flexible to simulate different plans of operation for the same patient and to see the

therapeutic effects of the patients clearly, finite element analysis using ANSYS is employed to assess the correction effect of the Nuss bar chest implantation. First, the Nuss bar is

simulated to be placed at the 2nd intercostal space with the sternum elevated 15 mm, 20 mm and 25 mm, respectively, and the efficacy is compared, as shown in Fig. 8. The values of the Haller

index in four cross sections before and after operation are given in Tables 3~6. According to the conclusion drawn by Lin24, who analyzed 252 patients with funnel chest pre- and

post-operative Haller index, their mean value of post-operative Haller index of 2.68 was used as the criterion of corrective Haller index in this study. Therefore, the operative plans of

elevating 15 mm and 20 mm in the 2nd intercostal space cannot meet the demand. When the elevation distance is 25 mm, the post-operative Haller index barely meets the requirement.

Nevertheless, this plan causes hypercorrection of the upper end of the sternum, which can be obviously seen in the sectional view, as shown in Fig. 9. The overcorrection not only leads to

unreasonable appearance but also results in stress concentration in the sternum. All of the analysis shows that putting the Nuss bar in the 2nd intercostal space is not a suitable scheme for

the patient. When placing the Nuss bar in the 3rd intercostal space with the sternum elevated 15 mm, 20 mm 25 mm and 30 mm, respectively, as shown in Fig. 10, the Haller index in four cross

sections changes by different degrees after the operation, of which, values are given in Tables 7~10. The operative plans of elevating 15 mm and 20 mm at the 3rd intercostal space cannot

meet our demand while elevating 25 mm and 30 mm can. However, when the value of elevation is 30 mm, the sternum appears hypercorrected from the 2nd to 3rd intercostal space, as shown in Fig.

 11. Thus, if placing the Nuss bar at the 3rd intercostal space, an elevation distance of 25 mm would be suitable. DISCUSSION As discussed in the above sections, by using a three-dimensional

finite element method, different operative plans are simulated and analyzed, and the optimal operative plan is determined according to both the chest wall configuration and the stress

distribution. According to the CAD model of the Nuss bar, the prototype of the Nuss bar is manufactured, as shown in Fig. 16, to validate the Nuss bar design and its analysis. The Nuss bar

was placed at the 4th intercostal space of the patient’s pectus excavatum chest. As shown in Fig. 17, comparing with the pre-operative chest (Fig. 17(a)), the thoracic deformity is corrected

effectively, and the surgical result is also satisfactory to the patient. More than ten such PEX cases have been corrected using the method in this paper. From the practice of orthopedic

operation of the funnel chest patient, the feasibility and rationality of our method is verified. Determining the shape and position of the Nuss bar before operation can shorten operation

time, decrease blood loss and the possibility of damage to the patient, and ensure post-operative effects. In brief, this method is more accurate and individualized compared to conventional

surgery. The proposed approach in this study gave a new solution to design the Nuss bar and to determine the incision position in pectus excavatum surgery; the procedure of design and finite

element analysis is conducted by hand and is employed several different software, including Mimics®, Solidworks®, Ansys®, and etc. These different software are independent and require

different format, so that the transformation among these software platforms is inconvenient. So, it is time-consuming to deal with the design and analysis among these software platforms. The

second limitation of this proposed approach is the manufacturing cost of customized Nuss bar, which is pretty higher than that of traditional method in Nuss operation. And thus, the future

directions of this study will be focused on two aspects: (1) to develop an integrated software platform, which can be employed to reconstruct 3D model of skeleton from CT imaging data, to

design the 3D model of Nuss bar, and to conduct finite element analysis; (2) to develop a quick and low-cost manufacturing method for customized Nuss bar, such as the 3D printing technology.

With these two further researches, the design and manufacture of customized Nuss bar in pectus excavatum surgery can be greatly facilitated, and the proposed method in this study can be a

good reference for other areas of surgery. Similarly, placing the Nuss bar at the 4th intercostal space with the sternum elevated 15 mm, 20 mm 25 mm, 30 mm and 35 mm, respectively, as shown

in Fig. 12, the Haller index in four cross sections were recorded and listed in Tables 11~14. The elevation distance of 15 mm and 20 mm at the 4th intercostal space cannot meet the

requirement while an elevation distance of more than 25 mm can. However, when the elevation distance is over 30 mm, such as 35 mm, there appears to be hypercorrection in the sternum, as

shown in Fig. 13. Compared to the effect of elevating 25 mm to that of 30 mm, the latter obviously has a better effect. Therefore, if we place the Nuss bar at the 4th intercostal space, an

elevation distance of 30 mm would be suitable. Finally, placing the Nuss bar at the 5th intercostal space with elevating the sternum 20 mm, 25 mm and 30 mm, respectively, as shown in Fig. 

14, the Haller index in four cross sections are listed in Tables 15~17. All of these operative plans cannot meet the demand, and there appears to be hypercorrection in the sternum when

elevated 30 mm or more. Therefore, it is not a suitable operative plan for patient A to place the Nuss bar at the 5th intercostal space. Analysis indicates that placing the Nuss bar in the

2nd or 5th intercostal space is unable to meet the correction requirement. There are two suitable plans for patient A: placing the Nuss bar either at the 3rd intercostal space with 25 mm

elevation or at the 4th intercostal space with 30 mm elevation. In addition to the evaluation of the Haller Index, the maximum stress of the chest after operation should also be taken into

consideration. Comparing the maximum stress in the above-mentioned candidate operative plans, as shown in Fig. 15, the maximum stress of placing Nuss bar at the 4th intercostal space with 30

 mm elevation is lower than the other, therefore, the operation plan is determined. Based on the discussion above, the following conclusions can be drawn: * (1) By using the CT imaging data

and referring to a similar healthy person, the shape of the Nuss bar is designed for pectus excavatum patients. * (2) It is found that the thoracic transverse of the chest wall boundary is

almost convex, the Nuss bar shape is finely tuned to be convex to ensure the orthopedic effect. * (3) By using the CT imaging data of a PEX chest, the thoracic structure is reconstructed for

finite element analysis. Through the analysis of different operation plans of incision position and sternum elevation, the optimal operation plan is determined by evaluating the Haller

index and the stress distribution after the Nuss bar implantation. * (4) Experiments were conducted to validate the method in this paper. Determining the shape and position of the Nuss bar

before operation can shorten the operation time, decrease blood loss and the possibility of damage to the patient, and ensure post-operative effects. REFERENCES * Sabiston, S. _Surgery of

the Chest_. (Science Press, Beijing, 2001). * Male, M. H., Fonkalsrud, E. W. & Cooper, C. B. Ventilatory and cardiovascular response to exercise in patients with pectus excavatum.

_Chest_ 124, 870–882 (2003). Article  Google Scholar  * Nuss, D., Ekelly, R. & Pcroitoru, D. A 10-year review of a minimally invasive technique for the correction of pectus excavatum.

_Journal of Pediatric Surgery_ 33, 4 (1998). Article  Google Scholar  * Tahmassebi, R. _et al_. Intra-abdominal pectus bar migration–a rare clinical entity: case report. _Journal of

Cardiothoracic Surgery_ 3, 1–4 (2008). Article  Google Scholar  * Hebra, A. Minimally invasive pectus surgery. _Chest Surgery Clinics of North America_ 10, 329 (2000). CAS  PubMed  Google

Scholar  * Croitoru, D. P. _et al_. Experience and modification update for the minimally invasive Nuss technique for pectus excavatum repair in 303 patients. _Journal of Pediatric Surgery_

37, 437–445 (2002). Article  PubMed  Google Scholar  * Park, H. J. _et al_. The Nuss procedure for pectus excavatum: evolution of techniques and early results on 322 patients. _Annals of

Thoracic Surgery_ 77, 289–295 (2004). Article  PubMed  Google Scholar  * Francis, R. Editorial comment: The Nuss procedure. _European Journal of Cardio-Thoracic Surgery_ 40, 337 (2011).

Google Scholar  * Rechowicz, K. J. _et al_. Development of an Average Chest Shape for Objective Evaluation of the Aesthetic Outcome in the Nuss Procedure Planning Process. _IFMBE

Proceedings_ 32, 528–531 (2010). Article  Google Scholar  * Müller, R., Hildebrand, T. & Rüegsegger, P. Non-invasive bone biopsy: a new method to analyse and display the

three-dimensional structure of trabecular bone. _Physics in Medicine & Biology_ 39, 145–64 (1994). Article  ADS  Google Scholar  * Aubin, C. E. _et al_. Geometrical modeling of the spine

and the thorax for the biomechanical analysis of scoliotic deformities using the finite element method. _Annales De Chirurgie_ 49, 49–761 (1995). Google Scholar  * DENG, Y.C., Kong W. &

Ho H. Development of a finite element human thorax model for impact injury studies. No.1999-01-0715. _SAE Special Publications_ (1999). * Kimpara, H. _et al_. Development of a

Three-Dimensional Finite Element Chest Model for the 5th Percentile Female. _Stapp Car Crash Journal_ 49, 251–69 (2005). PubMed  Google Scholar  * Kimpara, H. _et al_. Effect of assumed

stiffness and mass density on the impact response of the human chest using a three-dimensional FE model of the human body. _Journal of Biomechanical Engineering_ 128, 772–776 (2006). Article

  PubMed  Google Scholar  * Li, Q. _et al_. Biomechanical evaluation of lumbosacral reconstruction after subtotal sacrectomy: A three-dimensional finite element analysis. _The Chinese-German

Journal of Clinical Oncology_ 8, 638–641 (2009). Article  Google Scholar  * Wang, M. _et al_. Biomechanical three-dimensional finite element analysis of prostheses retained with/without

zygoma implants in maxillectomy patients. _Journal of Biomechanics_ 46, 1155–1161 (2013). Article  PubMed  Google Scholar  * Haller, J. A., Kramer, S. S. & Lietman, S. A. Use of CT scans

in selection of patients for pectus excavatum surgery: a preliminary report. _Journal of Pediatric Surgery_ 22, 904–906 (1987). Article  PubMed  Google Scholar  * Miguel, L. T. _et al_. The

search for stability: bar displacement in three series of pectus excavatum patients treated with the Nuss technique. _Clinics_ 66, 1743–1746 (2011). Article  Google Scholar  * Zhang, C.C.

_Human skeleton digital model and simulation_. (Shanghai Second Military Medical University press, Shanghai, 2004). * Ma, X. _et al_. Finite element study on spatial distribution and

mechanical properties of cancellous bone from femoral head. _Journal of Medical Biomechanics_ 6, 465–470 (2010). Google Scholar  * Zhang, H. _et al_. The value of analysis of bone mineral

density in lumbar vertebrae and ratio of cortical to spongy bone. _Journal of China Clinical Medical Imaging_ 1, 35–37 (2003). Google Scholar  * Hu, H. Y. _et al_. Establish the three -

dimensional finite element model of the human thorax and stress analysis. _Chinese Journal of Critical Care Medicine_ 12, 1098–1100 (2007). Google Scholar  * Pang, J. _et al_.

Reproducibility and validity of measuring tibial subchondral bone density with dual-energy X0ray absorptiometry: A Preliminary Assessment. _Chinese Journal of Medical Imaging Technology_ 4,

655–658 (2013). Google Scholar  * Tao, Q. _et al_. Nuss procedure for the correction of pectus excavatum in children: report of 252 cases. _Fudan University Journal of Medical Sciences_ 40,

319–322 (2013). Google Scholar  Download references ACKNOWLEDGEMENTS This study was funded by the Guangdong Province Medical Scientific Research Foundation (A2015333 and B2010004) and

Guangdong Province Science and Technology Planning Project (No. 2014A020212406 and No. 20120318090). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * School of Mechanical and Automotive

Engineering, South China University of Technology, Guangzhou, 510640, China Longhan Xie & Siqi Cai * Department of Thoracic Surgery, Guangdong General Hospital & Guangdong Academy of

Medical Sciences, Guangzhou, 510080, China Liang Xie, Gang Chen & Haiyu Zhou * School of Medicine, South China University of Technology, Guangzhou, 510640, China Haiyu Zhou Authors *

Longhan Xie View author publications You can also search for this author inPubMed Google Scholar * Siqi Cai View author publications You can also search for this author inPubMed Google

Scholar * Liang Xie View author publications You can also search for this author inPubMed Google Scholar * Gang Chen View author publications You can also search for this author inPubMed 

Google Scholar * Haiyu Zhou View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS Longhan Xie and Siqi Cai developed the CAD and FEA methods, as

well as built the prototypes for clinical experiments. Liang Xie, Gang Chen and Haiyu Zhou conducted the clinical experiments and evaluation. All authors discussed the results and

implications and commented on the manuscript at all stages. CORRESPONDING AUTHORS Correspondence to Longhan Xie or Haiyu Zhou. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare

that they have no competing interests. ADDITIONAL INFORMATION PUBLISHER'S NOTE: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional

affiliations. RIGHTS AND PERMISSIONS OPEN ACCESS This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution

and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if

changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the

material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to

obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Reprints and permissions ABOUT THIS ARTICLE CITE THIS

ARTICLE Xie, L., Cai, S., Xie, L. _et al._ Development of a computer-aided design and finite-element analysis combined method for customized Nuss bar in pectus excavatum surgery. _Sci Rep_

7, 3543 (2017). https://doi.org/10.1038/s41598-017-03622-y Download citation * Received: 10 January 2017 * Accepted: 27 April 2017 * Published: 14 June 2017 * DOI:

https://doi.org/10.1038/s41598-017-03622-y SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not

currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative