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Morphology-based realization of a rapid scoliosis correction simulation system
Computers in Biology and Medicine 94 (2018) 85–98
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Computers in Biology and Medicine journal homepage: www.elsevier.com/locate/compbiomed
Morphology-based realization of a rapid scoliosis correction simulation system Kun Shao a, Hao Wang a, Bingnan Li a, Dasheng Tian b, Juehua Jing b, Jieqing Tan a, Xing Huo a, * a b
Hefei University of Technology, Hefei, PR China The Second Hospital of Anhui Medical University, Hefei, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Automatic scoliosis correction Cobb angles Spatial curve deform Simulated spine models CT images
Objective: Scoliosis is a complex spinal deformity in 3D space that commonly occurs in teenagers, especially teenage girls, and judging the actual deformed spine situation using only CT images is difficult. However, using 3D finite element models to help doctors analyse the deformed spine is also time-consuming and laborious. Therefore, software that can quickly and easily perform scoliosis correction analysis is needed. To achieve rapid preoperative simulation of scoliosis correction in 3D space and help doctors construct surgical programmes faster, a morphology-based system was developed for simulating scoliosis correction performance. Methods: The simulation system first takes advantage of the centre point of each vertebra on the entire spine model to fit a space curve. Then the system obtains information from the models and the space curve, and finally, uses the information to simulate scoliosis correction. The deformed spine model in the system can be corrected to a better state. Results: During the simulation process, doctors can easily and clearly see how the vertebral models move, and the deformed spine parameters are also updated and shown. Using this system, doctors can easily simulate scoliosis correction according to their experience and quickly construct a surgical programme. Conclusions: The experimental results show that this system is capable of simulating scoliosis correction according to a doctor's own experience to speed up the operation and provides a scientific basis for the development of surgical programmes.
1. Introduction Scoliosis is a common orthopaedic disease that occurs frequently in adolescents [1]. Minor scoliosis affects physical coordination and aesthetics, while serious scoliosis affects the growth and development of infants and young children, resulting in bodily deformation. Serious scoliosis even affects heart and lung functions, resulting in serious consequences [2]. For scoliosis corrections, mild scoliosis (Cobb angle less than 25 ) should be observed and corrected using external orthosis, while severe scoliosis (Cobb angle greater than 25 ) requires surgical treatment, which usually has high risks. To diminish the risks as much as possible, doctors need to observe and analyse the shape of the patient's spinal cord in advance, obtain essential parameters, such as the Cobb angle, correctly determine the type of spinal deformity, and finally, construct a reasonable operation programme. Because a standard set of rules has not yet been established in the field of surgical scoliosis correction, most doctors must construct an operation plan and produce
an orthopaedic bent bar on the basis of spinal parameters and their own experience [3]. However, during the actual operation, doctors typically must temporarily adjust the bent bar shape and the operation plan, undoubtedly wasting operation time and increasing the patient's surgical risk. Currently, with the development of medical imaging technology [4, 5], diagnosing and characterizing these spinal lesions mostly relies on medical imaging, and computed tomography (CT) is a first-line imaging procedure [6]. Doctors mostly observe and execute measurements on 2D CT images [7], which is time-consuming, and single slices of CT images limits the field of view. But scoliosis is actually a spinal deformity in 3D space [8], so 2D images cannot provide a visual impression of the spine, potentially affecting the doctor's accurate judgement of the situation. Although software capable of reconstructing 3D models of the spine that allows the spine to be visualized in an intuitive way is available [9], these models reconstructed from CT images are mostly of the entire spine, which can be used for only some basic observations and measurements and cannot be adjusted at will. Furthermore, some software
* Corresponding author. Hefei university of technology, 420#building Feicui road, Economic& Development Area, Hefei, Anhui, PR China. E-mail address: [email protected] (X. Huo). https://doi.org/10.1016/j.compbiomed.2018.01.004 Received 26 December 2017; Received in revised form 17 January 2018; Accepted 17 January 2018 0010-4825/© 2018 Elsevier Ltd. All rights reserved.
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correction surgery in 3D space. It allows doctors to observe the effects of surgery in advance and obtain the corresponding parameter changes (such as the Cobb angle) so that they can make operation plans according to simulation results from this system and construct the spinal orthopaedic bent bar in advance. Simulation results are proven to effectively assist doctors in performing corrective surgery.
Nomenclature OCA UCA OP PT ODA UDA PVA CVA
original center point array updated center point array original point point original distance array updated distance array previous vector array current vector array
2. Methods 2.1. Brief introduction to the system The human spine is composed of 26 vertebrae, inter-vertebral discs and ligaments that are connected to each other, and there is a narrow spinal canal in the middle that contains the spinal cord [10]. Therefore, this system regards the spine as a smooth curve in 3D space [11], since scoliosis is a disease of the spinal deformity in three-dimensional space which mainly affects the spinal curve on the coronal plane, the curve will be straightened as much as possible in the correction process to achieve a perfect correction effect on the coronal plane. In the process of scoliosis correction simulation, vertebral models extracted from the whole-spine model beforehand will be scanned into the system and ranked according to the Z axis value of each model's centre. Since the spine in 3D space can approximately be regarded as a curve, the correction should conform to the shape of the curve. After the models are scanned into the system, the centre of the spine model is used
operation processes are complicated and difficult, which is not suitable for making rapid, personalized analysis. Thus, herein, we developed a simulation system based on spatial curve construction that can rapidly simulate scoliosis correction using a sequence of vertebral models of a patient and assist doctors in effective surgical planning in advance. This system utilizes a sequence of single vertebral models segmented from the whole spine model which is reconstructed from a patient's CT images to simulate the morphological process of scoliosis correction. The model segmentation is implemented with the bounding box by our partners, and we will not make more explanation in this paper. This system aims to provide quick and intuitive simulations of scoliosis
Algorithm 1: Obtain Points From Models Input: Vertebral Models Output: Array OriginalCentre, Array UpdatedCentre & Point OriginalPoint Process: n= NumberOfVertebrae OriginalPoint= {0,0,0} for i = 1 to n: Get OriginalCentre[i] From ith Model; Set UpdatedCentre[i] To the Value of OriginalCentre[i]; If
OriginalPoint.Z < OriginalCentre[i].Z Then OriginalPoint= OriginalCentre[i];
end if end for Parameter Values Number Of Models: Number of vertebral models OriginalPoint: OriginalCentre[]: UpdatedCentre[]:
A point that stands for point OP An array that stands for the above array OCA An array that stands for the above array UCA
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to prevent the spinal cord from being injured by not altering the length of the spine. Therefore, in the simulation process, the length of the spine should be maintained as much as possible to obtain good simulation results. However, because the shape of the spine may not be perfect after the automatic scoliosis correction simulation, and unpredictable results may occur, our system is designed to allow for manually fine-tuning the function to fix defects according to the doctor's own experience. After the scoliosis correction simulation, the corrected vertebral models can be saved as model files, and doctors can use these models to perform subsequent operations, such as implanting screws and generating the orthopaedic bent bar. 2.2. Automatic correction method & theory The system is composed of three modules: the interface layer, the model control layer and the calculation layer. The calculation layer controls the process of simulation and has two functions: overall rapid automatic correction and local, manual fine-tuning. The model control layer is responsible for the vertebral model's translation and rotation
Fig. 1. The baseline γ in automatic correction.
to generate a spline curve in 3D space. In the automatic correction operation, morphological analysis is performed to calculate the new position of each vertebral model using spinal curve information after each automatic correction, and each vertebral model is then transformed to the correct position. By continuously implementing the process described above, the automatic correction process can be achieved. However, during scoliosis correction, not only does the shape of the spine need to be optimized but the spinal cord deformation should also be considered to protect the spinal cord from damage and prevent other serious consequences. Although the system relies on only doctors to determine the extent of simulation correction, the basic problem underlying spinal cord deformation in the simulation process still needs to be considered. To most effectively accomplish this, we adopted a method
Fig. 3. Tangent vector of a vertebra on the spinal curve.
Fig. 2. The mapping of two-dimensional curve to three-dimensional curve. 87
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Algorithm 2: Calculate Vector Input: kDTree Output: PreVec & NewVec Process: N= NumberOfModels; FOR i= 1 TO N FIND the nearest Point1 TO UpdatedCentre[i] ON kDTree; FIND another nearest Point2 TO Point1; Vec= Point1 - Point2; IF FirstTime THEN PreVec[i] := Vec; CurrentVec[i] := Vec; ELSE THEN PreVec[i] := CurrentVec[i]; CurrentVec[i] := Vec; END IF END FOR Parameter Values Number Of Models: Number of input vertebral models FirstTime:
This is the first time calculating vectors (true/false)
PreVec:
Previous model curve vectors (PVA)
CurrentVec:
Current model curve vectors (CVA)
2.2.1. Data preparation Before the automatic correction step is carried out, the data to be used for subsequent calculations should be prepared. Some variables will be used to store data generated during the calculations, and the variables used in this manuscript are defined as follows: The OCA is an array that stores original vertebral centre points. The UCA is an array that stores updated vertebral centre points. The OP is a point whose data type is double. The PT is an array that stores points on the spinal curve. The ODA is an array that stores the original distance between adjacent models. The UDA is an array that stores updated distances between adjacent models. The PVA is an array that stores previous vectors. The CVA is an array that stores current vectors. The Scale is a value that controls the distance of a model moving to baseline each time.
adjustment, and the interface layer underlies the model display and user interaction. The automatic correction function is the core function of the system, as it processes the spinal models step-by-step iteratively following three steps: – Obtaining the model's information and preparing the required data; – Using the prepared data to calculate the parameters required in an automatic correction step; – Transforming the spinal models to the corresponding location according to the above data. After repeated iterations of the above steps, the deformed spine model will eventually be corrected to a relatively normal state. More details are described below.
2.2.1.1. Determination of centre coordinates and the correction reference line. In the automatic correction process, the first step is to obtain
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The point OP is regarded as the benchmark, and a straight line will be identified as the baseline according to this value. Using point OP, the baseline γ is generated, which is parallel to the Z axis, and γ will be used as the reference line in the automatic simulation of scoliosis correction. This algorithm is as follows: After obtaining calculations using algorithm 1, the arrays OCA and UCA and the point OP are obtained and initialized, and all the points on the baseline γ are defined as follows: fðx; y; zÞjx ¼ OP½0; y ¼ OP½0; z 2 Rg
(1)
The schematic diagram is as follows (see Fig. 1): The role of array UCA is crucial in the automatic correction calculation, as it preserves the latest location of each vertebra after each automatic adjustment and is used as the basis for the next step. 2.2.1.2. Acquiring the distance between vertebral models. In this step, the calculation layer will traverse the centre point of each vertebra to calculate the distance D between adjacent models. D¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðx1 x2 Þ2 þ ðy1 y2 Þ2 þ ðz1 z2 Þ2
(2)
The distance D obtained by this calculation will be saved in the array ODA, and Di is regarded as the initial distance between adjacent vertebrae at the beginning. ODA is the basis for the subsequent adjustment of spinal length, which will not change during automatic correction. However, in the next steps, the distance between adjacent vertebral centre points will be stored in array UDA instead of ODA.
Fig. 4. The process of the move operation.
2.2.1.3. Generation of the spatial spinal curve and curve points. Using the vertebral centre point data saved in array UCA, the calculation layer can generate the spatial parameter spline curve f1 and obtain all the points fP1 ; P2 ; :::; Ps g on the curve. The number of points on this curve is finite and depends on the resolution when generating the curve. To generate a spatial curve, every vertebral centre point is first taken as the control point, projecting these control points onto the XOY, XOZ, YOZ planes to generate three 2D parametric spline curves [12]. The three 2D parametric spline curves are then mapped in space to form a 3D curve f1 . To satisfy the needs of computational convenience, this manuscript describes how the spatial points on curve f1 were directly obtained to meet all the needs of the subsequent calculation steps instead of using the mathematical formula. Because we merely use these points to calculate tangent vector and the tangent vectors can be represented by two adjacent two points on the curve. All the points fP1 ; P2 ; :::; Pn g on curve f1 are stored in array PT. The curve generation principle is shown in Fig. 2. 2.2.1.4. Calculating the tangent vector. In this step, all the spatial points in array PT are placed in a binary search tree called the kDTree, which is used to find the closest points and is much faster than linear look-up. First, two adjacent points, P1 and P2, are found on curve f1 , which are the closest to the vertebral model's centre point. Then, two points are used to obtain the vertebra's tangent vector on the spinal curve. However, a numerical limit does exist, as point P1 is above P2 to ensure that the directions of the generated vectors are uniform, which is beneficial to the subsequent calculation.
Fig. 5. The rotation angle α and rotation axis C.
coordinate point data from the original centres of each single vertebral model and sort these points according to the Zi value (components on the Z axis); the coordinate points will then be stored in OCA. Because of the computational requirements, the coordinates of the centre points in OCA will not change during the simulation process and are preserved as raw data. The array UCA will be initialized to save the new centre points if the vertebral model points are altered during the automatic correction process. Next, when reading vertebral models, the model control layer will obtain the centre coordinates ðXi ; Yi ; Zi Þ of each vertebral model. The calculation layer then sorts the points according to their Z axis value and selects the point whose Zi value is smallest, and the point is finally stored in OP.
! ! P1 ¼ ðx1 ; y1 ; z1 Þ; P2 ¼ ðx2 ; y2 ; z2 Þjz1 > z2 ! ! ! V ¼ P1 P2
(3)
The diagram is shown as follows (See Fig. 3): According to this method, the approximate tangent vectors fν1 ; ν2 ; :::; νs g of each vertebral model in the curve can be obtained sequentially. These tangent vectors will be first stored in arrays PVA and CVA. In the next steps, CVA is used to store the current tangent vector results, while PVA is used to store previous tangent vector results. The two arrays are important for the calculation of each model's rotation 89
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Fig. 6. Distance adjustment process of two adjacent vertebrae.
reduce the curvature of the spine curve, which is achieved by moving the vertebral model to the baseline. First, calculate the distance d between each vertebra and the baseline (the distance shown by the red line in the figure below), and then set the Scale value. At the beginning, every vertebral model will move a distance MoveDis to the baseline according to d, which is the distance between the vertebral model's centre point and the baseline γ.
angle and rotation axis before and after the correction. 2.2.2. Automatic correction The correction effect of scoliosis deformity in the system depends mainly on the smoothness of the curve after correction. Since scoliosis is mainly manifested on the coronal plane, most of the correction is done using the corresponding X-axis component. The specific steps are described as follows:
2.2.2.1. The move operation. The first step in automatic correction is to 90
MoveDis ¼ d*Scale d' ¼ d MoveDis
(4)
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Obviously, greater distances between the vertebral centre and the baseline equivalate to higher MoveDis values. By changing the size of Scale, the system can control the distance that each vertebra moves to the baseline each time. d' is the new distance between one vertebral model and the baseline, and the centre point of each vertebral model saved in array UCA is updated. The diagram is as follows in Fig. 4:
To obtain the rotation axis C, vector cross product is adopted, and the direction of the rotation angle can be determined by the following formula:
2.2.2.2. Calculating the vertebral rotation angle and rotation axis. As shown in Fig. 4, after each vertebra model moves a distance MoveDis to the baseline γ, the former curve f1 is rebuilt to the new curve f2 using the new centre points stored in array UCA of each vertebral model. Then, some steps above need to be re-executed to update the data for some variables, such as CVA, PVA and UDA. Next, the system uses vectors in CVA and PVA to compute the rotation angle α and rotation axis C of each vertebral model. The principle is shown in Fig. 5. The formula for calculating the angle of rotation between the vector ! v1 ¼ ðx1 ; y1 ; z1 Þ and vector ! v2 ¼ ðx2 ; y2 ; z2 Þ is as follows:
(6)
x x þy y þz z
i ! ! ! C ¼ v1 v2 ¼ det x1 x2
ðx1 þ y1 þ z1 Þ ðx2 þ y2 þ z2 Þ
k z1 ¼ ðy1 z2 z1 y2 ; z1 x2 x1 z2 ; x1 y2 y1 x2 Þ z2
After calculating the rotation angle and rotation axis of each vertebra before and after a correction, the calculation layer calls the model manipulation layer, which rotates the model around line C such that the initial results after automatic correction are available [13]. The Algorithm is as follows: 2.2.2.3. Spinal length adjustment. After finishing the above steps, the scoliosis correction effects have basically been achieved. However, because the length of the corrected spine was not considered in the beginning, some vertebral models will crowd together after straightening the spine, which is not consistent with the actual situation and needs to be corrected.
!
1 2 1 2 1 2 α ¼ arccos pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 2
j y1 y2
(5)
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Fig. 7. The flow chart of automatic correction.
2.3. Manual fine-tuning and real-time parameter updating
The spine is regarded as a smooth curve in this system. Because the spinal cord cannot be stretched or compressed too much to prevent serious consequences in the actual situation [14], the total length of the spine should be minimally altered before and after scoliosis correction. The following steps are taken to ensure that the length of the spine is not changed before or after simulation: First, the initial distances fD1 ; D2 ; :::; Ds g saved in array ODA, are compared with the new distances fD'1 ; D'2 ; :::; D's g saved in array UDA. If D0 i 6¼ Di , then the calculation layer attempts to translate the vertebral model into the proper position by changing its Z axis component while computing the new D0 i value until Di D0 i . The schematic diagram is as follows (See Fig. 6): Algorithm is as follows:
The manual fine-tuning function serves to adjust the irrational result in an automatic simulation. Some essential functions, such as translation and rotation, can be called by the calculation layer. Any vertebral model can be converted to the best position using a combination of these functions. To improve the adjustment efficiency, the system sets a vertebra selection function, which is divided into single-select and multi-select. Then, users can adjust the position of each vertebra by using the selection function at will. Although doctors can directly observe the vertebral models during the correction process and determine the degree of correction according to their own experience, their experiences are mostly based on various vertebrae measurement parameters. If no parameter support exists, doctors cannot accurately judge whether the degree of correction is reasonable. Therefore, the parameter display in the correction process is necessary, which requires the input measurement data to be updated automatically during the correction process. When processing automatic and manual corrections, the rotation and translation parameters of each vertebra are available, which makes automatically updating measurement parameters possible. By recording
2.2.3. Summary The steps in sections 2.2.1 and 2.2.2 are required to perform automatic correction. By repeating the above steps again and again, the morphology of the spine will become increasingly normal. The next step is to use the manual fine-tuning function to adjust the irrational model to the appropriate position in the automatic correction. The overall flowchart of automatic correction is shown below (See Fig. 7).
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Fig. 8. The automatic correction interface.
Fig. 9. The process of automatic correction.
then added to the Cobb angle to obtain the updated value of the Cobb angle.
the parameters of each vertebra at each adjustment using the parameters and input values to update the input values, automatically updating the spine parameters in 3D space can be achieved [15,16]. Here, implementation of the Cobb angle parameter update is given below, and other updated parameter implementations follow the same rules.
Using the above steps, updating the Cobb angle in real-time during the correction process is possible, and tedious operations after measurement are avoided. Using the parameter changes, doctors can simulate the scoliosis correction according to changes in the 3D model and parameters. The interface diagram is shown below (see Fig. 8).
(1) Before the simulation correction operation starts, every Cobb angle should be measured by the measurement module, and the numbers of the two vertebrae that generate this Cobb angle should be entered. (2) During the correction process, the amounts of changes in the position ΔD and the angle Δθ of each vertebra are recorded in the corresponding variables. (3) When the Cobb angle updating operation is performed, the system will obtain the serial numbers of the two vertebrae that generate the Cobb angle and the angle change amount Δθ. The Δθ value is
3. Experiments and results Medical imaging data from three patients were obtained prior to the experiments upon consent of the hospital and the patients. The system described herein was developed in the Cþþ language and operated by the Windows operation system. In this experiment, the spinal surface model of patient 3 was first
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the spine models were divided into single vertebral models. Then, the segmented models of each patient were entered into the system, and experienced doctors performed automatic and manual correction. We considered a number of factors and chose parameters to measure the effectiveness of the simulation [17–19]. The illustration and figures of the correction effects on spinal parameters and CT images are shown below (see Table 1). The following is a comparison of simulated and actual results before and after correction for the three patients, which were performed on both the sagittal and coronal planes. Because we obtained pictures of only the sagittal and coronal planes of the three patients, we had to compare the pictures with the models, but the difference between the simulated and actual results was obviously not large (see Fig. 11). The purpose of this experiment was to verify that the system can be applied to patients with varying degrees of scoliosis and to obtain satisfactory corrective predictive results. The system can approximately display the shape of the corrected spine and obtain simulated parameters after correction. Doctors used these simulated parameters and models to produce orthopaedic bent bars before surgery, and they reported that the simulated spine models were capable of guiding their orthopaedic surgery. Furthermore, they did not have to change the shape of the orthopaedic bent bar much during surgery. However, for some patients with hunchback symptoms, sagittal kyphosis and lumbar lordosis were not significantly improved by the automatic correction process and could be improved by only manual correction if a deformity occurred. Furthermore, excessive correction was easily possible because only the deformity in the coronal plane was considered at the time of automatic correction. We also compared the results of patient 1 before and after surgery with those of three doctors performing the simulated correction to see differences between the simulated and actual results (see Table 2). Few differences existed between the actual surgery results and the doctors' simulations. In addition, the results obtained by doctor 1 were more in line with the actual results. Thus, experienced doctors yield similar results to those of surgery, and the results obtained by experienced physicians are useful for instructive surgeries. Because the apical vertebra offset directly reflects severity of scoliosis, to evaluate the quality of simulating scoliosis correction, we used the top vertebral deviation (TVD) and showed images of the apical vertebra offsets in 3 patients [20]. Results showed that the apical vertebra offset was much better than that before surgery and before our simulation, and the results of simulation and surgery varied minimally. The comparison results are listed in the following figures (see Fig. 12): Finally, in order to further verify the effectiveness of this system, we compared the parameters simulated by our system with those from the manual measurement. 10 patients involved in this experiment, we
Fig. 10. The effect of manual correction.
generated, and single vertebral models were then extracted from the spinal model and put into the system. After automatic correction and manual correction simulation, the corrected spinal model was obtained. In the automatic correction process, the spinal model was corrected to the normal state bit by bit, and doctors determined the degree of correction according to the model and parameters on the panel. Fig. 9 shows the process of the automatic correction. After automatic correction, We get corrected spinal models just like the models in Fig. 9, and we can see that the shape of the spine is basically in good condition, but Fig. 10 shows that the positions of some vertebral models were not reasonable. Thus, doctors could use the manual finetuning function to correct the flaws to obtain the optimized models. According to Figs. 9 and 10, the spine model's thoracic section was obviously corrected, and the shape of the spinal curve was sufficient. During automatic correction, the deformed spine was corrected bit by bit, and the result basically conformed to the biological characteristics of the spine. Manual correction corrected vertebral models whose positions were unreasonable in the automatic correction, in order to make them more consistent with the actual shape of the spine. To evaluate the effects of simulated correction in patients, the 3D spine models of the three patients were rebuilt using their CT images, and Table 1 Illustration of the correction effects on spinal parameters. Cobb's Angle ( )
Patient1
Patient2
Patient3
before surgery after simulation after surgery simulation correction rate surgery correction rate before surgery after simulation after surgery simulation correction rate surgery correction rate before surgery after simulation after surgery simulation correction rate surgery correction rate
Kyphosis ( )
T1-T5
T6-T12
L1-L5
T1-T12
20.8 0.5 3.5 0.5 2.3 0.5 83.17% 88.94% 18.0 0.5 3.0 0.5 4.3 0.5 83.33% 76.11% 48.7 0.5 22.8 0.5 28.2 0.5 53.18% 42.10%
39.8 0.5 6.9 0.5 6.5 0.5 82.67% 83.67% 51.3 0.5 21.6 0.5 18.4 0.5 57.89% 64.13% 83.4 0.5 41.2 0.5 40.3 0.5 50.60% 51.68%
27.6 0.5 9.9 0.5 10.9 0.5 64.13% 60.51% 22.0 0.5 10.0 0.5 9.0 0.5 54.55% 59.09% 44.7 0.5 26.9 0.5 24.3 0.5 39.82% 45.64%
39.7 0.5 35.1 0.5 32.0 0.5 4.03% 19.40% 28.5 0.5 26.9 0.5 23.5 0.5 5.61% 17.54% 46.8 0.5 38.7 0.5 32.5 0.5 17.30% 30.56%
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Height (mm)
389.5 5 445.2 5 440.5 5 55.7 mm 51 mm 476.7 5 509.4 5 510.0 5 32.7 mm 33.3 mm 365.5 5 426.5 5 436.5 5 61.0 mm 71.0 mm
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Fig. 11. Comparison of the correction effect on the patients on different planes.
From the illustrations above, we find that the parameters gathered manually are often conservative and with larger fluctuation. We also find that the parameters re-estimated by our simulation system are more stable and closer to actual applied ones. The absolute differences between parameters obtained by three ways are illustrated in Table 3, where V1 represents the absolute difference between manual parameters and actual applied ones. V2 stands for the
selected the thoracic cobb angle T1-T5, T6-T12 and the lumbar cobb angle L1-L5 as the representative parameters. Doctors first manually measured the patient's CT diagram, and got the expected parameters of corrected spine according to their experience, which is shown as black columns in Figs. 13–15. Then parameters are revaluated by our system, which is shown as green columns in Figs. 13–15, and the yellow columns are actual applied parameters in surgery.
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Table 2 Comparison of simulation results reported by several doctors. Cobb's Angle ( )
Before surgery Doctor 1's simulation Doctor 2's simulation Doctor 3's simulation Mean values of simulation Correction rate of simulation After surgery Correction rate of surgery
Kyphosis ( )
Lordosis ( )
T1-T5
T6-T12
L1-L5
T1-T12
L1-L5
20.8 0.5 3.5 0.5 4.7 0.5 1.5 0.5 3.2 0.5 84.6% 2.3 0.5 88.9%
39.8 0.5 6.9 0.5 1.3 0.5 0.2 0.5 2.8 0.5 93.0% 6.5 0.5 83.7%
27.6 0.5 9.9 0.5 8.8 0.5 2.3 0.5 7.0 0.5 74.6% 7.9 0.5 71.4%
39.7 0.5 35.1 0.5 35.6 0.5 35.8 0.5 35.5 0.5 8.1% 32.0 0.5 19.4%
14.8 0.5 14.7 0.5 4.5 0.5 14.7 0.5 11.3 0.5 10.1% 7.2 0.5 51.4%
Height (mm) 389.5 5 445.2 5 440.2 5 452.7 5 446.0 5 56.5 mm 440.5 5 51 mm
Fig. 12. Comparison of the results of the top vertebral deviation of patients.
simulated orthopaedic bent bar can be used as a reference for the actual bent rod manufactured. The biggest advantage of the system is its ability to quickly simulate scoliosis correction according to the doctor's own experience to speed up the operation. However, this system also has several defects. First, the degree of scoliosis correction is determined only by the user according to their own judgement, and the programme provides few hints when less experienced doctors use this system. In consequence, doctors with less experience may not obtain good simulation results. Second, during the automatic correction process, only deformities of the coronal plane are considered. The deformity of the sagittal plane is not corrected automatically but can be adjusted manually, which is
absolute difference between system simulated parameters and actual applied ones. We see that the average value of V1 is greater than that of V2, it is obvious that the simulation results are more reliable. 4. Conclusions This system has been proven to assist doctors in simulating scoliosis surgery and can help doctors develop surgical procedures. This system can also shorten the surgery time required and reduce both the doctor's pressure and the patient's surgical risk. In addition, the corrected model produced by the system can be used for subsequent simulations of implanting screws and generating orthopaedic bent bars, and the
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Fig. 13. The comparison of parameters on cobb angle T1-T5.
Fig. 14. The comparison of parameters on cobb angle T6-T12.
Fig. 15. The comparison of parameters on cobb angle L1-L5.
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Table 3 The absolute difference between parameters obtained by three ways.
T1-T5 T6-T12 L1-L5
V1 V2 V1 V2 V1 V2
1
2
3
4
5
6
7
8
9
10
avg
3.95 1.32 4.37 0.68 0.67 0.24
4.12 0.64 1.96 0.41 0.89 0.02
3.67 1.20 4.71 0.76 1.87 0.14
3.99 0.83 0.85 0.22 0.39 0.29
2.16 0.87 2.68 0.45 1.22 0.34
4.37 1.81 3.54 0.18 4.51 0.36
1.92 0.66 1.53 0.29 2.48 0.60
4.68 0.23 4.50 0.76 4.40 1.51
2.17 0.91 0.42 0.59 0.25 1.12
0.85 0.14 2.86 0.06 0.37 0.15
3.188 0.861 2.742 0.44 1.705 0.477
slightly time-consuming and laborious. Further analyses of spine morphological characteristics should be performed to obtain an automatic, comprehensive simulation system utilized for doctors to simulate scoliosis correction more conveniently. In conclusion, this system can be used to aid scoliosis surgery, although it has several defects. Further research will gradually correct these defects to simulate the scoliosis auxiliary system more conveniently and quickly.
[3] M.J. Tormenti, M.B. Maserati, C.M. Bonfield, et al., Complications and radiographic correction in adult scoliosis following combined transpsoas extreme lateral interbody fusion and posterior pedicle screw instrumentation, Neurosurg. Focus 28 (3) (2010) 1–7. [4] B.N. Li, X. Shan, K. Xiang, et al., Evaluation of robust wave image processing methods for magnetic resonance elastography, Comput. Biol. Med. 54 (C) (2014) 100–108. [5] B.N. Li, C.K. Chui, S. Chang, et al., A new unified level set method for semiautomatic liver tumor segmentation on contrast-enhanced CT images, Expert Syst. Appl. 39 (10) (2012) 9661–9668. [6] E.S. Moon, H.S. Kim, J.O. Park, et al., Comparison of the predictive value of myelography, computed tomography and MRI on the treadmill test in lumbar spinal stenosis, Yonsei Med. J. 46 (6) (2005) 806–811. [7] B.N. Li, Q. Yu, R. Wang, et al., Block principal component analysis with nongreedy ℓ₁-norm maximization, IEEE Trans. Cybern. (2015), https://doi.org/10.1109/ TCYB.2015.2479645. [8] I.A.F. Stokes, Three-dimensional terminology of spinal deformity, Spine 19 (2) (1994) 236–248. [9] L. Humbert, J.A. De Guise, B. Aubert, et al., 3D reconstruction of the spine from biplanar X-rays using parametric models based on transversal and longitudinal inferences, Med. Eng. Phys. 31 (6) (2009) 681–687. [10] J.S. Pooni, D.D. Hukins, P.F. Harris, et al., Comparison of the structure of human intervertebral discs in the cervical, thoracic and lumbar regions of the spine, Surg. Radiol. Anat. 8 (3) (1986) 175–182. [11] S. Somoske€ oy, M. Tunyogi, Clinical validation of coronal and sagittal spinal curve measurements based on three-dimensional vertebra vector parameters, Spine J. 12 (10) (2012) 960–968. [12] B.A. Barsky, T.D. Derose, Geometric continuity of parametric curves: three equivalent characterizations, IEEE Comput. Graph. Appl. 9 (6) (1989) 60–69. [13] J.J. Jonas, Y. He, G. Langelaan, The rotation axes and angles involved in the formation of self-accommodating plates of Widmanst€atten ferrite, Acta Mater. 72 (2014) 13–21. [14] J.H. Yang, S.W. Suh, H.N. Modi, et al., Effects of vertebral column distraction on transcranial electrical stimulation-motor evoked potential and histology of the spinal cord in a porcine model, J. Bone Jt. Surg. Am. Vol. 95 (9) (2013) 835–842. [15] X. Huo, J.Q. Tan, J. Qian, et al., An integrative framework for 3D cobb angle measurement on CT images, Comput. Biol. Med. 82 (C) (2017) 111–118. [16] M. Gstoettner, K. Sekyra, N. Walochnik, et al., Inter- and intraobserver reliability assessment of the Cobb angle: manual versus digital measurement tools, Eur. Spine J. 16 (10) (2007) 1587–1592. [17] S.D. Glassman, S. Berven, K. Bridwell, et al., Correlation of radiographic parameters and clinical symptoms in adult scoliosis, Spine 30 (6) (2005) 682–688. [18] M.L. Nault, P. Allard, S. Hinse, et al., Relations between standing stability and body posture parameters in adolescent idiopathic scoliosis, Spine 27 (17) (2002) 1911–1917. [19] Y.M. Baghdadi, A.N. Larson, M.B. Dekutoski, et al., Sagittal balance and spinopelvic parameters after lateral lumbar interbody fusion for degenerative scoliosis: a casecontrol study, Spine 39 (3) (2014) 166–173. [20] J.H. Lim, J. Lee, S.E. Koh, et al., Reliability and reproducibility of interapical distance assessment of the lateral deviation of vertebrae in scoliosis, J. Phys. Ther. Sci. 27 (4) (2015) 1199–1202.
Conflicts of interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements This work was partially supported by the Key Science and Technology Program of Anhui Province (grant no. 1501041149), the International S&T Cooperation Program of China (2015DFA11450) and the National Natural Science Foundation of China (grant no. 61571176, 61271123 and 61502136). In memoriam: Tragically, one of our co-authors, Prof. Li, who greatly contributed to public health and biomedical imaging research efforts, lost his battle with a disease before this manuscript was published, and we wish to honour his memory. Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi. org/10.1016/j.compbiomed.2018.01.004. References [1] S. Negrini, J.C. De Mauroy, T.B. Grivas, P. Knott, T. Kotwicki, T. Maruyama, et al., Actual evidence in the medical approach to adolescents with idiopathic scoliosis, Eur. J. Phys. Rehabil. Med. 50 (1) (2014) 87–92. [2] Y. Harada, K. Furukawa, T. Asari, et al., Osteogenic lineage commitment of mesenchymal stem cells from patients with ossification of the posterior longitudinal ligament, Biochem. Biophys. Res. Commun. 443 (3) (2014) 1014–1020.
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Contents lists available at ScienceDirect
Computers in Biology and Medicine journal homepage: www.elsevier.com/locate/compbiomed
Morphology-based realization of a rapid scoliosis correction simulation system Kun Shao a, Hao Wang a, Bingnan Li a, Dasheng Tian b, Juehua Jing b, Jieqing Tan a, Xing Huo a, * a b
Hefei University of Technology, Hefei, PR China The Second Hospital of Anhui Medical University, Hefei, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Automatic scoliosis correction Cobb angles Spatial curve deform Simulated spine models CT images
Objective: Scoliosis is a complex spinal deformity in 3D space that commonly occurs in teenagers, especially teenage girls, and judging the actual deformed spine situation using only CT images is difficult. However, using 3D finite element models to help doctors analyse the deformed spine is also time-consuming and laborious. Therefore, software that can quickly and easily perform scoliosis correction analysis is needed. To achieve rapid preoperative simulation of scoliosis correction in 3D space and help doctors construct surgical programmes faster, a morphology-based system was developed for simulating scoliosis correction performance. Methods: The simulation system first takes advantage of the centre point of each vertebra on the entire spine model to fit a space curve. Then the system obtains information from the models and the space curve, and finally, uses the information to simulate scoliosis correction. The deformed spine model in the system can be corrected to a better state. Results: During the simulation process, doctors can easily and clearly see how the vertebral models move, and the deformed spine parameters are also updated and shown. Using this system, doctors can easily simulate scoliosis correction according to their experience and quickly construct a surgical programme. Conclusions: The experimental results show that this system is capable of simulating scoliosis correction according to a doctor's own experience to speed up the operation and provides a scientific basis for the development of surgical programmes.
1. Introduction Scoliosis is a common orthopaedic disease that occurs frequently in adolescents [1]. Minor scoliosis affects physical coordination and aesthetics, while serious scoliosis affects the growth and development of infants and young children, resulting in bodily deformation. Serious scoliosis even affects heart and lung functions, resulting in serious consequences [2]. For scoliosis corrections, mild scoliosis (Cobb angle less than 25 ) should be observed and corrected using external orthosis, while severe scoliosis (Cobb angle greater than 25 ) requires surgical treatment, which usually has high risks. To diminish the risks as much as possible, doctors need to observe and analyse the shape of the patient's spinal cord in advance, obtain essential parameters, such as the Cobb angle, correctly determine the type of spinal deformity, and finally, construct a reasonable operation programme. Because a standard set of rules has not yet been established in the field of surgical scoliosis correction, most doctors must construct an operation plan and produce
an orthopaedic bent bar on the basis of spinal parameters and their own experience [3]. However, during the actual operation, doctors typically must temporarily adjust the bent bar shape and the operation plan, undoubtedly wasting operation time and increasing the patient's surgical risk. Currently, with the development of medical imaging technology [4, 5], diagnosing and characterizing these spinal lesions mostly relies on medical imaging, and computed tomography (CT) is a first-line imaging procedure [6]. Doctors mostly observe and execute measurements on 2D CT images [7], which is time-consuming, and single slices of CT images limits the field of view. But scoliosis is actually a spinal deformity in 3D space [8], so 2D images cannot provide a visual impression of the spine, potentially affecting the doctor's accurate judgement of the situation. Although software capable of reconstructing 3D models of the spine that allows the spine to be visualized in an intuitive way is available [9], these models reconstructed from CT images are mostly of the entire spine, which can be used for only some basic observations and measurements and cannot be adjusted at will. Furthermore, some software
* Corresponding author. Hefei university of technology, 420#building Feicui road, Economic& Development Area, Hefei, Anhui, PR China. E-mail address: [email protected] (X. Huo). https://doi.org/10.1016/j.compbiomed.2018.01.004 Received 26 December 2017; Received in revised form 17 January 2018; Accepted 17 January 2018 0010-4825/© 2018 Elsevier Ltd. All rights reserved.
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correction surgery in 3D space. It allows doctors to observe the effects of surgery in advance and obtain the corresponding parameter changes (such as the Cobb angle) so that they can make operation plans according to simulation results from this system and construct the spinal orthopaedic bent bar in advance. Simulation results are proven to effectively assist doctors in performing corrective surgery.
Nomenclature OCA UCA OP PT ODA UDA PVA CVA
original center point array updated center point array original point point original distance array updated distance array previous vector array current vector array
2. Methods 2.1. Brief introduction to the system The human spine is composed of 26 vertebrae, inter-vertebral discs and ligaments that are connected to each other, and there is a narrow spinal canal in the middle that contains the spinal cord [10]. Therefore, this system regards the spine as a smooth curve in 3D space [11], since scoliosis is a disease of the spinal deformity in three-dimensional space which mainly affects the spinal curve on the coronal plane, the curve will be straightened as much as possible in the correction process to achieve a perfect correction effect on the coronal plane. In the process of scoliosis correction simulation, vertebral models extracted from the whole-spine model beforehand will be scanned into the system and ranked according to the Z axis value of each model's centre. Since the spine in 3D space can approximately be regarded as a curve, the correction should conform to the shape of the curve. After the models are scanned into the system, the centre of the spine model is used
operation processes are complicated and difficult, which is not suitable for making rapid, personalized analysis. Thus, herein, we developed a simulation system based on spatial curve construction that can rapidly simulate scoliosis correction using a sequence of vertebral models of a patient and assist doctors in effective surgical planning in advance. This system utilizes a sequence of single vertebral models segmented from the whole spine model which is reconstructed from a patient's CT images to simulate the morphological process of scoliosis correction. The model segmentation is implemented with the bounding box by our partners, and we will not make more explanation in this paper. This system aims to provide quick and intuitive simulations of scoliosis
Algorithm 1: Obtain Points From Models Input: Vertebral Models Output: Array OriginalCentre, Array UpdatedCentre & Point OriginalPoint Process: n= NumberOfVertebrae OriginalPoint= {0,0,0} for i = 1 to n: Get OriginalCentre[i] From ith Model; Set UpdatedCentre[i] To the Value of OriginalCentre[i]; If
OriginalPoint.Z < OriginalCentre[i].Z Then OriginalPoint= OriginalCentre[i];
end if end for Parameter Values Number Of Models: Number of vertebral models OriginalPoint: OriginalCentre[]: UpdatedCentre[]:
A point that stands for point OP An array that stands for the above array OCA An array that stands for the above array UCA
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to prevent the spinal cord from being injured by not altering the length of the spine. Therefore, in the simulation process, the length of the spine should be maintained as much as possible to obtain good simulation results. However, because the shape of the spine may not be perfect after the automatic scoliosis correction simulation, and unpredictable results may occur, our system is designed to allow for manually fine-tuning the function to fix defects according to the doctor's own experience. After the scoliosis correction simulation, the corrected vertebral models can be saved as model files, and doctors can use these models to perform subsequent operations, such as implanting screws and generating the orthopaedic bent bar. 2.2. Automatic correction method & theory The system is composed of three modules: the interface layer, the model control layer and the calculation layer. The calculation layer controls the process of simulation and has two functions: overall rapid automatic correction and local, manual fine-tuning. The model control layer is responsible for the vertebral model's translation and rotation
Fig. 1. The baseline γ in automatic correction.
to generate a spline curve in 3D space. In the automatic correction operation, morphological analysis is performed to calculate the new position of each vertebral model using spinal curve information after each automatic correction, and each vertebral model is then transformed to the correct position. By continuously implementing the process described above, the automatic correction process can be achieved. However, during scoliosis correction, not only does the shape of the spine need to be optimized but the spinal cord deformation should also be considered to protect the spinal cord from damage and prevent other serious consequences. Although the system relies on only doctors to determine the extent of simulation correction, the basic problem underlying spinal cord deformation in the simulation process still needs to be considered. To most effectively accomplish this, we adopted a method
Fig. 3. Tangent vector of a vertebra on the spinal curve.
Fig. 2. The mapping of two-dimensional curve to three-dimensional curve. 87
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Algorithm 2: Calculate Vector Input: kDTree Output: PreVec & NewVec Process: N= NumberOfModels; FOR i= 1 TO N FIND the nearest Point1 TO UpdatedCentre[i] ON kDTree; FIND another nearest Point2 TO Point1; Vec= Point1 - Point2; IF FirstTime THEN PreVec[i] := Vec; CurrentVec[i] := Vec; ELSE THEN PreVec[i] := CurrentVec[i]; CurrentVec[i] := Vec; END IF END FOR Parameter Values Number Of Models: Number of input vertebral models FirstTime:
This is the first time calculating vectors (true/false)
PreVec:
Previous model curve vectors (PVA)
CurrentVec:
Current model curve vectors (CVA)
2.2.1. Data preparation Before the automatic correction step is carried out, the data to be used for subsequent calculations should be prepared. Some variables will be used to store data generated during the calculations, and the variables used in this manuscript are defined as follows: The OCA is an array that stores original vertebral centre points. The UCA is an array that stores updated vertebral centre points. The OP is a point whose data type is double. The PT is an array that stores points on the spinal curve. The ODA is an array that stores the original distance between adjacent models. The UDA is an array that stores updated distances between adjacent models. The PVA is an array that stores previous vectors. The CVA is an array that stores current vectors. The Scale is a value that controls the distance of a model moving to baseline each time.
adjustment, and the interface layer underlies the model display and user interaction. The automatic correction function is the core function of the system, as it processes the spinal models step-by-step iteratively following three steps: – Obtaining the model's information and preparing the required data; – Using the prepared data to calculate the parameters required in an automatic correction step; – Transforming the spinal models to the corresponding location according to the above data. After repeated iterations of the above steps, the deformed spine model will eventually be corrected to a relatively normal state. More details are described below.
2.2.1.1. Determination of centre coordinates and the correction reference line. In the automatic correction process, the first step is to obtain
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The point OP is regarded as the benchmark, and a straight line will be identified as the baseline according to this value. Using point OP, the baseline γ is generated, which is parallel to the Z axis, and γ will be used as the reference line in the automatic simulation of scoliosis correction. This algorithm is as follows: After obtaining calculations using algorithm 1, the arrays OCA and UCA and the point OP are obtained and initialized, and all the points on the baseline γ are defined as follows: fðx; y; zÞjx ¼ OP½0; y ¼ OP½0; z 2 Rg
(1)
The schematic diagram is as follows (see Fig. 1): The role of array UCA is crucial in the automatic correction calculation, as it preserves the latest location of each vertebra after each automatic adjustment and is used as the basis for the next step. 2.2.1.2. Acquiring the distance between vertebral models. In this step, the calculation layer will traverse the centre point of each vertebra to calculate the distance D between adjacent models. D¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðx1 x2 Þ2 þ ðy1 y2 Þ2 þ ðz1 z2 Þ2
(2)
The distance D obtained by this calculation will be saved in the array ODA, and Di is regarded as the initial distance between adjacent vertebrae at the beginning. ODA is the basis for the subsequent adjustment of spinal length, which will not change during automatic correction. However, in the next steps, the distance between adjacent vertebral centre points will be stored in array UDA instead of ODA.
Fig. 4. The process of the move operation.
2.2.1.3. Generation of the spatial spinal curve and curve points. Using the vertebral centre point data saved in array UCA, the calculation layer can generate the spatial parameter spline curve f1 and obtain all the points fP1 ; P2 ; :::; Ps g on the curve. The number of points on this curve is finite and depends on the resolution when generating the curve. To generate a spatial curve, every vertebral centre point is first taken as the control point, projecting these control points onto the XOY, XOZ, YOZ planes to generate three 2D parametric spline curves [12]. The three 2D parametric spline curves are then mapped in space to form a 3D curve f1 . To satisfy the needs of computational convenience, this manuscript describes how the spatial points on curve f1 were directly obtained to meet all the needs of the subsequent calculation steps instead of using the mathematical formula. Because we merely use these points to calculate tangent vector and the tangent vectors can be represented by two adjacent two points on the curve. All the points fP1 ; P2 ; :::; Pn g on curve f1 are stored in array PT. The curve generation principle is shown in Fig. 2. 2.2.1.4. Calculating the tangent vector. In this step, all the spatial points in array PT are placed in a binary search tree called the kDTree, which is used to find the closest points and is much faster than linear look-up. First, two adjacent points, P1 and P2, are found on curve f1 , which are the closest to the vertebral model's centre point. Then, two points are used to obtain the vertebra's tangent vector on the spinal curve. However, a numerical limit does exist, as point P1 is above P2 to ensure that the directions of the generated vectors are uniform, which is beneficial to the subsequent calculation.
Fig. 5. The rotation angle α and rotation axis C.
coordinate point data from the original centres of each single vertebral model and sort these points according to the Zi value (components on the Z axis); the coordinate points will then be stored in OCA. Because of the computational requirements, the coordinates of the centre points in OCA will not change during the simulation process and are preserved as raw data. The array UCA will be initialized to save the new centre points if the vertebral model points are altered during the automatic correction process. Next, when reading vertebral models, the model control layer will obtain the centre coordinates ðXi ; Yi ; Zi Þ of each vertebral model. The calculation layer then sorts the points according to their Z axis value and selects the point whose Zi value is smallest, and the point is finally stored in OP.
! ! P1 ¼ ðx1 ; y1 ; z1 Þ; P2 ¼ ðx2 ; y2 ; z2 Þjz1 > z2 ! ! ! V ¼ P1 P2
(3)
The diagram is shown as follows (See Fig. 3): According to this method, the approximate tangent vectors fν1 ; ν2 ; :::; νs g of each vertebral model in the curve can be obtained sequentially. These tangent vectors will be first stored in arrays PVA and CVA. In the next steps, CVA is used to store the current tangent vector results, while PVA is used to store previous tangent vector results. The two arrays are important for the calculation of each model's rotation 89
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Fig. 6. Distance adjustment process of two adjacent vertebrae.
reduce the curvature of the spine curve, which is achieved by moving the vertebral model to the baseline. First, calculate the distance d between each vertebra and the baseline (the distance shown by the red line in the figure below), and then set the Scale value. At the beginning, every vertebral model will move a distance MoveDis to the baseline according to d, which is the distance between the vertebral model's centre point and the baseline γ.
angle and rotation axis before and after the correction. 2.2.2. Automatic correction The correction effect of scoliosis deformity in the system depends mainly on the smoothness of the curve after correction. Since scoliosis is mainly manifested on the coronal plane, most of the correction is done using the corresponding X-axis component. The specific steps are described as follows:
2.2.2.1. The move operation. The first step in automatic correction is to 90
MoveDis ¼ d*Scale d' ¼ d MoveDis
(4)
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Obviously, greater distances between the vertebral centre and the baseline equivalate to higher MoveDis values. By changing the size of Scale, the system can control the distance that each vertebra moves to the baseline each time. d' is the new distance between one vertebral model and the baseline, and the centre point of each vertebral model saved in array UCA is updated. The diagram is as follows in Fig. 4:
To obtain the rotation axis C, vector cross product is adopted, and the direction of the rotation angle can be determined by the following formula:
2.2.2.2. Calculating the vertebral rotation angle and rotation axis. As shown in Fig. 4, after each vertebra model moves a distance MoveDis to the baseline γ, the former curve f1 is rebuilt to the new curve f2 using the new centre points stored in array UCA of each vertebral model. Then, some steps above need to be re-executed to update the data for some variables, such as CVA, PVA and UDA. Next, the system uses vectors in CVA and PVA to compute the rotation angle α and rotation axis C of each vertebral model. The principle is shown in Fig. 5. The formula for calculating the angle of rotation between the vector ! v1 ¼ ðx1 ; y1 ; z1 Þ and vector ! v2 ¼ ðx2 ; y2 ; z2 Þ is as follows:
(6)
x x þy y þz z
i ! ! ! C ¼ v1 v2 ¼ det x1 x2
ðx1 þ y1 þ z1 Þ ðx2 þ y2 þ z2 Þ
k z1 ¼ ðy1 z2 z1 y2 ; z1 x2 x1 z2 ; x1 y2 y1 x2 Þ z2
After calculating the rotation angle and rotation axis of each vertebra before and after a correction, the calculation layer calls the model manipulation layer, which rotates the model around line C such that the initial results after automatic correction are available [13]. The Algorithm is as follows: 2.2.2.3. Spinal length adjustment. After finishing the above steps, the scoliosis correction effects have basically been achieved. However, because the length of the corrected spine was not considered in the beginning, some vertebral models will crowd together after straightening the spine, which is not consistent with the actual situation and needs to be corrected.
!
1 2 1 2 1 2 α ¼ arccos pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 2
j y1 y2
(5)
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Fig. 7. The flow chart of automatic correction.
2.3. Manual fine-tuning and real-time parameter updating
The spine is regarded as a smooth curve in this system. Because the spinal cord cannot be stretched or compressed too much to prevent serious consequences in the actual situation [14], the total length of the spine should be minimally altered before and after scoliosis correction. The following steps are taken to ensure that the length of the spine is not changed before or after simulation: First, the initial distances fD1 ; D2 ; :::; Ds g saved in array ODA, are compared with the new distances fD'1 ; D'2 ; :::; D's g saved in array UDA. If D0 i 6¼ Di , then the calculation layer attempts to translate the vertebral model into the proper position by changing its Z axis component while computing the new D0 i value until Di D0 i . The schematic diagram is as follows (See Fig. 6): Algorithm is as follows:
The manual fine-tuning function serves to adjust the irrational result in an automatic simulation. Some essential functions, such as translation and rotation, can be called by the calculation layer. Any vertebral model can be converted to the best position using a combination of these functions. To improve the adjustment efficiency, the system sets a vertebra selection function, which is divided into single-select and multi-select. Then, users can adjust the position of each vertebra by using the selection function at will. Although doctors can directly observe the vertebral models during the correction process and determine the degree of correction according to their own experience, their experiences are mostly based on various vertebrae measurement parameters. If no parameter support exists, doctors cannot accurately judge whether the degree of correction is reasonable. Therefore, the parameter display in the correction process is necessary, which requires the input measurement data to be updated automatically during the correction process. When processing automatic and manual corrections, the rotation and translation parameters of each vertebra are available, which makes automatically updating measurement parameters possible. By recording
2.2.3. Summary The steps in sections 2.2.1 and 2.2.2 are required to perform automatic correction. By repeating the above steps again and again, the morphology of the spine will become increasingly normal. The next step is to use the manual fine-tuning function to adjust the irrational model to the appropriate position in the automatic correction. The overall flowchart of automatic correction is shown below (See Fig. 7).
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Fig. 8. The automatic correction interface.
Fig. 9. The process of automatic correction.
then added to the Cobb angle to obtain the updated value of the Cobb angle.
the parameters of each vertebra at each adjustment using the parameters and input values to update the input values, automatically updating the spine parameters in 3D space can be achieved [15,16]. Here, implementation of the Cobb angle parameter update is given below, and other updated parameter implementations follow the same rules.
Using the above steps, updating the Cobb angle in real-time during the correction process is possible, and tedious operations after measurement are avoided. Using the parameter changes, doctors can simulate the scoliosis correction according to changes in the 3D model and parameters. The interface diagram is shown below (see Fig. 8).
(1) Before the simulation correction operation starts, every Cobb angle should be measured by the measurement module, and the numbers of the two vertebrae that generate this Cobb angle should be entered. (2) During the correction process, the amounts of changes in the position ΔD and the angle Δθ of each vertebra are recorded in the corresponding variables. (3) When the Cobb angle updating operation is performed, the system will obtain the serial numbers of the two vertebrae that generate the Cobb angle and the angle change amount Δθ. The Δθ value is
3. Experiments and results Medical imaging data from three patients were obtained prior to the experiments upon consent of the hospital and the patients. The system described herein was developed in the Cþþ language and operated by the Windows operation system. In this experiment, the spinal surface model of patient 3 was first
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the spine models were divided into single vertebral models. Then, the segmented models of each patient were entered into the system, and experienced doctors performed automatic and manual correction. We considered a number of factors and chose parameters to measure the effectiveness of the simulation [17–19]. The illustration and figures of the correction effects on spinal parameters and CT images are shown below (see Table 1). The following is a comparison of simulated and actual results before and after correction for the three patients, which were performed on both the sagittal and coronal planes. Because we obtained pictures of only the sagittal and coronal planes of the three patients, we had to compare the pictures with the models, but the difference between the simulated and actual results was obviously not large (see Fig. 11). The purpose of this experiment was to verify that the system can be applied to patients with varying degrees of scoliosis and to obtain satisfactory corrective predictive results. The system can approximately display the shape of the corrected spine and obtain simulated parameters after correction. Doctors used these simulated parameters and models to produce orthopaedic bent bars before surgery, and they reported that the simulated spine models were capable of guiding their orthopaedic surgery. Furthermore, they did not have to change the shape of the orthopaedic bent bar much during surgery. However, for some patients with hunchback symptoms, sagittal kyphosis and lumbar lordosis were not significantly improved by the automatic correction process and could be improved by only manual correction if a deformity occurred. Furthermore, excessive correction was easily possible because only the deformity in the coronal plane was considered at the time of automatic correction. We also compared the results of patient 1 before and after surgery with those of three doctors performing the simulated correction to see differences between the simulated and actual results (see Table 2). Few differences existed between the actual surgery results and the doctors' simulations. In addition, the results obtained by doctor 1 were more in line with the actual results. Thus, experienced doctors yield similar results to those of surgery, and the results obtained by experienced physicians are useful for instructive surgeries. Because the apical vertebra offset directly reflects severity of scoliosis, to evaluate the quality of simulating scoliosis correction, we used the top vertebral deviation (TVD) and showed images of the apical vertebra offsets in 3 patients [20]. Results showed that the apical vertebra offset was much better than that before surgery and before our simulation, and the results of simulation and surgery varied minimally. The comparison results are listed in the following figures (see Fig. 12): Finally, in order to further verify the effectiveness of this system, we compared the parameters simulated by our system with those from the manual measurement. 10 patients involved in this experiment, we
Fig. 10. The effect of manual correction.
generated, and single vertebral models were then extracted from the spinal model and put into the system. After automatic correction and manual correction simulation, the corrected spinal model was obtained. In the automatic correction process, the spinal model was corrected to the normal state bit by bit, and doctors determined the degree of correction according to the model and parameters on the panel. Fig. 9 shows the process of the automatic correction. After automatic correction, We get corrected spinal models just like the models in Fig. 9, and we can see that the shape of the spine is basically in good condition, but Fig. 10 shows that the positions of some vertebral models were not reasonable. Thus, doctors could use the manual finetuning function to correct the flaws to obtain the optimized models. According to Figs. 9 and 10, the spine model's thoracic section was obviously corrected, and the shape of the spinal curve was sufficient. During automatic correction, the deformed spine was corrected bit by bit, and the result basically conformed to the biological characteristics of the spine. Manual correction corrected vertebral models whose positions were unreasonable in the automatic correction, in order to make them more consistent with the actual shape of the spine. To evaluate the effects of simulated correction in patients, the 3D spine models of the three patients were rebuilt using their CT images, and Table 1 Illustration of the correction effects on spinal parameters. Cobb's Angle ( )
Patient1
Patient2
Patient3
before surgery after simulation after surgery simulation correction rate surgery correction rate before surgery after simulation after surgery simulation correction rate surgery correction rate before surgery after simulation after surgery simulation correction rate surgery correction rate
Kyphosis ( )
T1-T5
T6-T12
L1-L5
T1-T12
20.8 0.5 3.5 0.5 2.3 0.5 83.17% 88.94% 18.0 0.5 3.0 0.5 4.3 0.5 83.33% 76.11% 48.7 0.5 22.8 0.5 28.2 0.5 53.18% 42.10%
39.8 0.5 6.9 0.5 6.5 0.5 82.67% 83.67% 51.3 0.5 21.6 0.5 18.4 0.5 57.89% 64.13% 83.4 0.5 41.2 0.5 40.3 0.5 50.60% 51.68%
27.6 0.5 9.9 0.5 10.9 0.5 64.13% 60.51% 22.0 0.5 10.0 0.5 9.0 0.5 54.55% 59.09% 44.7 0.5 26.9 0.5 24.3 0.5 39.82% 45.64%
39.7 0.5 35.1 0.5 32.0 0.5 4.03% 19.40% 28.5 0.5 26.9 0.5 23.5 0.5 5.61% 17.54% 46.8 0.5 38.7 0.5 32.5 0.5 17.30% 30.56%
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Height (mm)
389.5 5 445.2 5 440.5 5 55.7 mm 51 mm 476.7 5 509.4 5 510.0 5 32.7 mm 33.3 mm 365.5 5 426.5 5 436.5 5 61.0 mm 71.0 mm
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Fig. 11. Comparison of the correction effect on the patients on different planes.
From the illustrations above, we find that the parameters gathered manually are often conservative and with larger fluctuation. We also find that the parameters re-estimated by our simulation system are more stable and closer to actual applied ones. The absolute differences between parameters obtained by three ways are illustrated in Table 3, where V1 represents the absolute difference between manual parameters and actual applied ones. V2 stands for the
selected the thoracic cobb angle T1-T5, T6-T12 and the lumbar cobb angle L1-L5 as the representative parameters. Doctors first manually measured the patient's CT diagram, and got the expected parameters of corrected spine according to their experience, which is shown as black columns in Figs. 13–15. Then parameters are revaluated by our system, which is shown as green columns in Figs. 13–15, and the yellow columns are actual applied parameters in surgery.
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Table 2 Comparison of simulation results reported by several doctors. Cobb's Angle ( )
Before surgery Doctor 1's simulation Doctor 2's simulation Doctor 3's simulation Mean values of simulation Correction rate of simulation After surgery Correction rate of surgery
Kyphosis ( )
Lordosis ( )
T1-T5
T6-T12
L1-L5
T1-T12
L1-L5
20.8 0.5 3.5 0.5 4.7 0.5 1.5 0.5 3.2 0.5 84.6% 2.3 0.5 88.9%
39.8 0.5 6.9 0.5 1.3 0.5 0.2 0.5 2.8 0.5 93.0% 6.5 0.5 83.7%
27.6 0.5 9.9 0.5 8.8 0.5 2.3 0.5 7.0 0.5 74.6% 7.9 0.5 71.4%
39.7 0.5 35.1 0.5 35.6 0.5 35.8 0.5 35.5 0.5 8.1% 32.0 0.5 19.4%
14.8 0.5 14.7 0.5 4.5 0.5 14.7 0.5 11.3 0.5 10.1% 7.2 0.5 51.4%
Height (mm) 389.5 5 445.2 5 440.2 5 452.7 5 446.0 5 56.5 mm 440.5 5 51 mm
Fig. 12. Comparison of the results of the top vertebral deviation of patients.
simulated orthopaedic bent bar can be used as a reference for the actual bent rod manufactured. The biggest advantage of the system is its ability to quickly simulate scoliosis correction according to the doctor's own experience to speed up the operation. However, this system also has several defects. First, the degree of scoliosis correction is determined only by the user according to their own judgement, and the programme provides few hints when less experienced doctors use this system. In consequence, doctors with less experience may not obtain good simulation results. Second, during the automatic correction process, only deformities of the coronal plane are considered. The deformity of the sagittal plane is not corrected automatically but can be adjusted manually, which is
absolute difference between system simulated parameters and actual applied ones. We see that the average value of V1 is greater than that of V2, it is obvious that the simulation results are more reliable. 4. Conclusions This system has been proven to assist doctors in simulating scoliosis surgery and can help doctors develop surgical procedures. This system can also shorten the surgery time required and reduce both the doctor's pressure and the patient's surgical risk. In addition, the corrected model produced by the system can be used for subsequent simulations of implanting screws and generating orthopaedic bent bars, and the
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Fig. 13. The comparison of parameters on cobb angle T1-T5.
Fig. 14. The comparison of parameters on cobb angle T6-T12.
Fig. 15. The comparison of parameters on cobb angle L1-L5.
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Table 3 The absolute difference between parameters obtained by three ways.
T1-T5 T6-T12 L1-L5
V1 V2 V1 V2 V1 V2
1
2
3
4
5
6
7
8
9
10
avg
3.95 1.32 4.37 0.68 0.67 0.24
4.12 0.64 1.96 0.41 0.89 0.02
3.67 1.20 4.71 0.76 1.87 0.14
3.99 0.83 0.85 0.22 0.39 0.29
2.16 0.87 2.68 0.45 1.22 0.34
4.37 1.81 3.54 0.18 4.51 0.36
1.92 0.66 1.53 0.29 2.48 0.60
4.68 0.23 4.50 0.76 4.40 1.51
2.17 0.91 0.42 0.59 0.25 1.12
0.85 0.14 2.86 0.06 0.37 0.15
3.188 0.861 2.742 0.44 1.705 0.477
slightly time-consuming and laborious. Further analyses of spine morphological characteristics should be performed to obtain an automatic, comprehensive simulation system utilized for doctors to simulate scoliosis correction more conveniently. In conclusion, this system can be used to aid scoliosis surgery, although it has several defects. Further research will gradually correct these defects to simulate the scoliosis auxiliary system more conveniently and quickly.
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Conflicts of interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements This work was partially supported by the Key Science and Technology Program of Anhui Province (grant no. 1501041149), the International S&T Cooperation Program of China (2015DFA11450) and the National Natural Science Foundation of China (grant no. 61571176, 61271123 and 61502136). In memoriam: Tragically, one of our co-authors, Prof. Li, who greatly contributed to public health and biomedical imaging research efforts, lost his battle with a disease before this manuscript was published, and we wish to honour his memory. Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi. org/10.1016/j.compbiomed.2018.01.004. References [1] S. Negrini, J.C. De Mauroy, T.B. Grivas, P. Knott, T. Kotwicki, T. Maruyama, et al., Actual evidence in the medical approach to adolescents with idiopathic scoliosis, Eur. J. Phys. Rehabil. Med. 50 (1) (2014) 87–92. [2] Y. Harada, K. Furukawa, T. Asari, et al., Osteogenic lineage commitment of mesenchymal stem cells from patients with ossification of the posterior longitudinal ligament, Biochem. Biophys. Res. Commun. 443 (3) (2014) 1014–1020.
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