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The influence of hemodynamics on graft patency prediction model based on support vector machine
Journal Pre-proofs The influence of hemodynamics on graft patency prediction model based on support vector machine Boyan Mao, Yue Feng, Wenxin Wang, Bao Li, Zhou Zhao, Xiaoyan Zhang, Chunbo Jin, Dandan Wu, Youjun Liu PII: DOI: Reference:
S0021-9290(19)30673-6 https://doi.org/10.1016/j.jbiomech.2019.109426 BM 109426
To appear in:
Journal of Biomechanics
Accepted Date:
13 October 2019
Please cite this article as: B. Mao, Y. Feng, W. Wang, B. Li, Z. Zhao, X. Zhang, C. Jin, D. Wu, Y. Liu, The influence of hemodynamics on graft patency prediction model based on support vector machine, Journal of Biomechanics (2019), doi: https://doi.org/10.1016/j.jbiomech.2019.109426
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© 2019 Published by Elsevier Ltd.
The influence of hemodynamics on graft patency prediction model based on support vector machine
Boyan Mao1&, Yue Feng1&, Wenxin Wang1, Bao Li1, Zhou Zhao2, Xiaoyan Zhang1, Chunbo Jin1, Dandan Wu1, Youjun Liu1*
1 College
of Life Science and Bio-Engineering, Beijing University of Technology, No. 100 Pingleyuan, Chaoyang District, Beijing 100124, China 2Cardiac
Surgery Department, PeKing University People’s Hospital. 11th.South Ave. Xizhimen, Beijing, China
Original Article For Submission To Journal of Biomechanics Date: March 29, 2019
1
Number of words: 3273 (Introduction through Discussion, exclusive of references) Number of figures: 4 (4 color) Number of tables: 3
*Corresponding author: Youjun Liu College of Life Science and Bio-Engineering Beijing University of Technology No. 100 Pingleyuan, Chaoyang District, Beijing 100124 China [email protected]
& These authors contribute equally to this paper Abstract: In the existing patency prediction model of coronary artery bypass grafting (CABG), the characteristics are based on graft flow, but no researchers selected hemodynamic factors as the characteristics. The purpose of this paper is to study whether the introduction of hemodynamic 2
factors will affect the performance of the prediction model. Transit time flow-meter (TTFM) waveforms and 1-year postoperative patency results were obtained from 50 internal mammary arterial grafts (LIMA) and 82 saphenous venous grafts (SVG) in 60 patients. Taking TTFM waveforms as the boundary conditions, the CABG ideal models were constructed to obtain hemodynamic factors in grafts. Based on clinical characteristics and combination of clinical and hemodynamic characteristics, patency prediction models based on support vector machine (SVM) were constructed respectively. For LIMA, after the introduction of hemodynamic factors, the accuracy, sensitivity and specificity of the prediction model increased from 70.35%, 50% and 74.17% to 78.02%, 70% and 78.89%, respectively. For SVG, the accuracy, sensitivity and specificity of the prediction model increased from 63.24%, 40% and 76.91% to 74.41%, 60.1% and 82.73%, respectively. The performance of the prediction model can be improved by introducing hemodynamic factors into the characteristics of the model. The accuracy, sensitivity and specificity of the prediction results are higher with the addition of hemodynamic characteristics.
Keywords: Hemodynamics, coronary artery bypass grafting, graft patency, support vector machine, transit time flow-meter,
Introduction 3
Coronary artery bypass grafting (CABG) is a commonly used surgical procedure for coronary heart disease (CHD) (Beck et al., 1935). The main problem is the risk of postoperative graft failure. According to statistics, the failure rate of venous grafts in the early postoperative period is 15-30%, and it will reach 50% after 10 years (Mehta et al., 1997). And for arterial grafts, the 10 - year patency and 15 - year patency are 95% and 88% respectively (Tatoulis et al., 2004). After the graft fails, the patient will have myocardial ischemia again, which will be seriously life-threatening. Therefore, for each patient, how to predict the graft patency is of great significance, which can help patients avoid possible adverse cardiovascular events in the future, and also help surgeons make the next treatment plan. Transit time flow-meter (TTFM) is a flow measurement technique based on the principle of ultrasound and is currently widely used to measure the flow of grafts during bypass surgery (Amin et al., 2018; Kentaro et al., 2015; Niclauss et al., 2018). After surgeons complete all the graft anastomosis, they will use the TTFM probe to clamp the graft and measure the flow waveform before closing the chest cavity. With TTFM results, surgeons can assess whether the graft anastomosis is successful or not. Low average flow rate, high pulsatility index (PI) and low diastolic velocity time fraction (DF) are considered as risk factors reflecting the obstructed anastomosis (Tokuda et al., 2008; Tokuda et al., 2007; Kim et al., 2005; Papadopoulou et al., 2006). At present, many scholars have studied the method of using TTFM results to predict graft patency. Lehnert et al. used logistic regression analysis to study the risk of graft failure within one year after surgery based on intraoperative TTFM measurements and postoperative coronary angiography (Lehnert et al., 2015). Tsai et al. assessed radial arterial graft patency by intraoperative 4
TTFM measurement and postoperative CTA (Tsai et al., 2014). Using TTFM data, Handa et al. proposed that the maximum diastolic blood flow acceleration is an effective characteristics for predicting the graft patency (Handa et al., 2015). Takami et al. proposed that after the Fast Fourier transform (FFT) of TTFM waveform, the ratio of fundamental wave to harmonic wave can be used as an effective characteristics to predict the graft patency (Takami et al., 2001; Takami et al., 2001). In summary, the existing studies only use the data obtained from TTFM as the characteristics to construct the prediction model, but hemodynamic factors are not considered. According to the research, hemodynamics is the key factor affecting graft patency. Graft failure is mainly caused by intimal hyperplasia and atherosclerosis (Whittemore et al., 1981; Butany et al., 1998; Agnieszka et al., 2017; De et al., 2018), and poor hemodynamic factors are considered to be the most important factors in their occurrence and development (Bassiouny et al., 1992; Hofer et al., 1996; Shahrokh et al., 2018). Studies have shown that in the end-to-side anastomosis, intimal hyperplasia mainly occurs in the toe and heel of the anastomosis where disturbance flow is severe (Sottiurai et al., 1989; Ojha et al., 1994; Min et al., 2018). Therefore, it is of great significance to study the influence of hemodynamics on the graft patency and explore its value in the patency prediction model. The difficulty in predicting the graft patency lies in the small number of samples and the large number of influencing factors. Support vector machine (SVM) is an effective machine learning method, which has many unique advantages in solving high-dimensional, nonlinear and small sample pattern recognition, and is widely used in classification and regression problems. In the field of cardiovascular diseases, most researchers use the image data obtained from coronary angiography, 5
CTA and IVUS as well as the collected ECG data as characteristics, and use SVM to carry out diagnosis and postoperative effect prediction (Ismail et al., 2010; Araki et al., 2015; Azam et al., 2017; Ismail et al., 2010; Matheny et al., 2007; Jawaid et al., 2017). Among them, Dursun et al. used a variety of machine learning methods to predict the surgical results of CABG, and the results showed that SVM worked best (Delen et al., 2012). However, hemodynamic factors were not included in the selection of characteristics. The purpose of this paper is to study whether the prediction performance can be improved after hemodynamic factors are included in the characteristics of the patency prediction model based on SVM.
Methods Collection of patient data This study collected data from 60 patients who received bypass surgery in Peking University people's hospital and returned to the hospital for review about 1 year after the surgery. Among them, there were 50 internal mammary arterial grafts (LIMA) and 82 saphenous venous grafts (SVG). The LIMA was anastomosed to the anterior descending branch in all cases. The detailed information is shown in Table 1. All the selected patients used TTFM to measure the blood flow waveform of each graft at the completion of bypass surgery, and used CTA to check the patency of each coronary artery and graft
6
about 1 year after the surgery. According to the patency of grafts, LIMA and SVG were divided into patent and failure groups respectively.
Clinical data extraction and digital processing of TTFM waveform The TTFM waveform measured clinically is shown on the left side of Fig.2. The measured location of TTFM waves is in the middle of the graft. The indexes in blue dotted frame are commonly used in clinical evaluation of graft patency, including average flow, pulsatility index (PI), diastolic velocity time fraction (DF). Average flow is defined as: total flow/time, PI is defined as: (maximum flow - minimum flow)/average flow, and DF is defined as diastolic flow/total flow. When the flow waveform was stable, three consecutive cycles were selected, as shown in the red dotted frame. Set the time interval as 0.005s and conduct digital processing on the waveform to obtain the flow value corresponding to each time, as shown on the right side of Fig.1.
Construction of calculation model In order to obtain the hemodynamic results of each graft, this study constructed an ideal model of CABG, as shown in Fig.2. The ideal model represents the anastomosis of a graft to the target coronary artery at an angle of 45 degrees. The yellow area in the figure is the area where hemodynamic factors were extracted, including graft and anastomotic site. Since the stenosis rates were greater than 90% in all collected 7
cases, it was assumed in this study that the anterior end of the anastomotic site was completely occluded. The diameter of the target coronary artery was set as 3mm, and the diameter of the graft was determined by the size of the selected TTFM probe, as shown on the left side of Fig.1. The blue dotted frame on the bottom left part is the size of the probe. The surgeon selected probes of different sizes according to the diameter of the graft. L1 represents the length of the graft, SVG was set as 120mm, and LIMA was set as 180mm. L2 and L3 represent the target coronary artery. L2 is the length of the proximal of the anastomosis, which is 10mm. L3 is the distal of the anastomosis, and the length was extended to 90mm in order to fully develop the blood flow. L4 represents the length of the anastomotic site, which is defined as the site where blood flow is not sufficiently developed. The value is given by formula (1): L4=0.06•d•Re (Krishnan et al., 2012)
(1)
Among them, d is the diameter of the tube, Re is the Reynolds number. Re=
𝜌𝑣𝑑 𝜇
(2)
Among them, ρ is the density of blood which was set as 1050kg/𝑚3. 𝑣 is the average velocity of blood flow in the coronary artery which was measured from the end of the coronary artery after calculation. μ is dynamic viscosity which was set as 0.0035Pa•s. After completing the calculation of the model, the average velocity at the outlet position was measured, and then calculated the length of the underdeveloped region according to the formulas (1) and (2). The inlet boundary condition of the graft was set as the digital TTFM waveform, and the
8
outlet boundary condition of the coronary artery was set as 0 mmHg. The ANSYS ICEM CFD software was used to mesh the above models, and the hexahedral meshing method was used to mesh. The meshes passed the grid sensitivity analysis. Using ANSYS CFX for finite element simulation, it was assumed that the vascular wall is impermeable and non-slip rigid wall. The material property of blood is adiabatic and incompressible viscous Newtonian fluid, and its flow is unsteady laminar flow.
Support vector machine method SVM is a commonly used machine learning method based on the VC dimension theory of statistical learning theory and the principle of structural risk minimization, it was first proposed by Vapnik et al (Vapnik et al., 1995). The key of SVM is kernel function, which will lead to different SVM algorithm. The kernel function maps a vector that is indivisible in a low-dimensional space to a high-dimensional space, making the vector divisible. The kernel functions of SVM mainly include polynomial kernel functions, linear kernel functions, Sigmoid kernel functions and radial basis kernel functions (RBF), and their mathematical principle was introduced in the article of Ismail Babaoglu et al (Ismail et al., 2010). This study adopted the libsvm toolbox based on Matlab (Chih-Chung et al., 2001), using the most commonly used RBF kernel function. For RBF SVM, in order to obtain the most accurate classification results, it is necessary to find the appropriate penalty coefficient (C) and kernel function radius (g). 9
There are many methods to find the optimal (C, g), and this paper adopted the simplest and most accurate method -- grid search. Grid search is a traversal algorithm, that is, within a certain range, each value of C and g is detected one by one according to a certain step size. Finally, the value (C, g) with the highest classification accuracy is selected. 2 ―𝑚 < 𝐶 < 2𝑚
(3)
2 ―𝑛 < 𝑔 < 2𝑛
(4)
In this paper, m and n were set as 5, and the search step size of m and n was 0.2. For each search step of (C, g), the average accuracy of the model was calculated by cross validation method. Cross validation is a method for finding optimal parameters and evaluating the performance of prediction models. In this paper, k-fold cross validation method was adopted, that is, all samples were divided into k sub-samples, a single sub-sample was retained as the test data, and other k-1 sub-samples were used for training. The process was repeated k times, each sub-sample was verified once, and the accuracy of these k times’ results was averaged. The results of cross validation can be expressed as: 1
𝑘
𝐶𝑉(𝐾) = 𝑘∑𝑖 = 1𝐴𝐶𝐶𝑖
(5)
ACC is the accuracy rate of each time, and its value is: number of correctly classified samples/total number of samples. And the k value was set as 5 in this study. By comparing all the values of 𝐶𝑉(𝐾) , the corresponding (C, g) is the optimal parameter when the value is the largest, and the SVM also achieves the optimal performance. 10
In SVM training, when the number of a group of samples is small, the parameter wi (weight) can set a large penalty coefficient for it, so as to improve the classification accuracy of this group of samples. In this study, the number of samples in LIMA failure group was significantly less than that in the patent group, so the wi of the failure group was set as 5. The wi of LIMA patent group and two groups of SVG were set as default values (the default value was 1). In order to avoid the influence of dimension of each characteristic, the data were normalized. The study used the 0-1 method to process the data, and all the data were within the interval of [0, 1]. The formula is: 𝑥 ― 𝑚𝑖𝑛
𝑥 ∗ = 𝑚𝑎𝑥 ― 𝑚𝑖𝑛
(6)
𝑥 is the original data, 𝑥 ∗ is the normalized data.
Statistical method Data in this study were expressed in the form of average value ± standard deviation. For the data of patent group and failure group, one-way ANOVA was used to compare whether there were significant differences between the average values of the two groups. All statistical results were obtained by SPSS software.
Hemodynamic factors Wall shear stress (WSS), oscillatory shear index (OSI) and relative residence time (RRT) 11
were selected as hemodynamic factors (Meirson et al., 2015; Meirson et al., 2015). WSS is an important factor affecting vascular lesions, such as plaque rupture and atherosclerosis. Some researchers have suggested that low WSS can reduce the graft patency (Malek et al., 1999). The formula is shown below: 𝑑𝑢
(7)
WSS = ―μ 𝑑𝑟
μ is blood viscosity, u is flow axial velocity, r is vessel radial distance. OSI is also a commonly used hemodynamic factor, which represents the oscillation degree of blood flow in vessels. It is related to string phenomenon of the graft (Zhao et al., 2015). It is defined as:
[
OSI = 0.5 1 ―
|∫𝑇0𝑊𝑆𝑆𝑑𝑡| 𝑇
]
∫0|𝑊𝑆𝑆|𝑑𝑡
(8)
RRT is used to describe how long the particles stay on the endothelial cells. It is generally believed that the high RRT area has a longer time of blood aggregation and is prone to endometrial hyperplasia (Himburg et al., 2004). The calculation formula is as follows: 1
RRT = （1 ― 2•OSI）•TAWSS
(9)
TAWSS is the time average WSS. After the model was calculated, the hemodynamic results of the graft and the anastomotic site (yellow area) were extracted, as shown in Fig.3. Fig.3 shows the contours of WSS, OSI and RRT, taking a certain bridging vessel as an example. TAWSS is the average value of WSS over the whole 12
calculated period of time (three cardiac cycles). OSI and RRT are the values of the last moment. All characteristics are now prepared. Clinical characteristics include average flow rate, PI and DF. Hemodynamic characteristics include TAWSS, OSI and RRT.
Result Statistical results In the samples selected in this study, it was found that there were 43 patent LIMA grafts and 7 failure LIMA grafts in the total 50 LIMA grafts. And there were 50 patent SVG grafts and 32 failure SVG grafts in the total 82 SVG grafts. Their average flow rate, PI, DF, TAWSS, OSI and RRT were obtained, and they were shown on Table 2. For LIMA, it can be seen from the Table 2 that flow rate and TAWSS in the patent group are significantly higher than those in the failure group, while PI and RRT in the failure group are significantly higher than those in the patent group. DF and OSI show little difference between the two groups. For SVG, flow rate and TAWSS of the patent group are significantly higher than those of the failure group, while OSI and RRT of the failure group are significantly higher than those of the patent group. There is little difference between PI and DF between the two groups. For clear contrast, all the factors were normalized so that their values were in the interval of [0, 1]. For PI, OSI and RRT, we used 1 minus their values. Making radar maps of LIMA and SVG for these 6 characteristics, as shown in Fig.4. At this time, the 6 dimensions of the radar map all 13
represent favorable characteristics of graft patency. In other words, the size of the area enclosed by the radar map represents the ability of the graft to maintain patency, and the larger the area, the more likely it is to maintain patency. Through the comparison of the radar graph, it can intuitively feel the difference between the patent and the failure groups of LIMA and SVG. While the patent group in LIMA has a significantly greater advantage over the failure group, the differences between the two groups in SVG are smaller than in LIMA.
SVM prediction results In order to study the influence of hemodynamic factors on prediction models, two prediction models were constructed. One was the SVM prediction model based only on clinical factors, and the selected characteristics were flow rate, PI and DF. The other was the SVM prediction model that combined clinical factors with hemodynamic factors. The selected characteristics were flow rate, PI, DF, TAWSS, OSI and RRT. All the data has been normalized to eliminate dimension effects. The performance of SVM prediction is deeply influenced by the selected parameters (C, g) and the selected training set and test set. In order to eliminate the influence of parameters and sample selection, and to better compare the performance of the two prediction models, the optimal parameters of the two prediction models were obtained by grid search and cross-validation methods respectively.
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In this study, cross validation was also used to test the performance of two prediction models. All samples were divided into 5 parts and recorded as A, B, C, D, E respectively. The sample number, and the proportion of patent and failure grafts were maintained almost equivalent in each part. 4 parts were used as the training set and 1 part as the test set. Repeat 5 times until every part is tested. The results of each prediction were recorded in the Table 3, in which failure graft was recorded as positive, and patent graft was recorded as negative. The average accuracy, average sensitivity and specificity were obtained under the optimal parameters. The results are shown in Table 4. It can be seen from the table, for LIMA, the accuracy of the prediction model based only on TTFM clinical factors is 70.35%, and the sensitivity and specificity are 50% and 74.17%. The accuracy of the prediction model based on the combination of clinical factors and hemodynamics is 78.02%, and the sensitivity and specificity are 70% and 78.89%. For SVG, the accuracy of the prediction model based only on TTFM clinical factors is 63.24%, and the sensitivity and specificity are 40% and 76.91%. The accuracy of the prediction model based on the combination of clinical factors and hemodynamics is 74.41%, and the sensitivity and specificity are 60.1% and 82.73%. From the above results, it can be seen that the introduction of hemodynamic factors as characteristics can improve the performance of the prediction model. The accuracy, sensitivity and specificity of the prediction model are improved, especially for the sensitivity.
Discussion 15
Analysis of statistical results In this study, three clinical characteristics including flow rate, PI and DF, as well as three hemodynamic characteristics including TAWSS, OSI and RRT, were statistically analyzed. It is generally believed that low flow rate, high PI and low DF are not conducive to graft patency, while low WSS, high OSI and RRT are not conducive to graft patency either. According to the clinical data we collected, LIMA is superior to SVG in both clinical and hemodynamic characteristics, which partly explains why LIMA is significantly more patent than SVG. This study also compared the patent group and the failure group. For LIMA, the flow rate, PI, TAWSS and RRT are different between the two groups. The p values of DF and OSI reach above 0.7, indicating that there is no difference between the two groups. For SVG, the flow rate, TAWSS, OSI and RRT have significant difference between the two groups, but PI and DF have no difference. In summary, it is known that flow rate, TAWSS and RRT all have significant difference both in LIMA and SVG, while the manifestations of PI and OSI in the two types of grafts are not consistent. However, whether in LIMA or SVG, DF shows no difference in patent and failure groups. In particular, hemodynamic characteristics TAWSS and RRT have significant differences in both two kinds of grafts, which will be conducive to classification.
Analysis of prediction results When the prediction models are consistent, the degree of difference between the two groups'
16
characteristics determines the accuracy of classification. The more information that is significantly different between the two groups, the higher the accuracy of the classification. Hemodynamic characteristics have been proved to affect the graft patency, so there should be a significant difference in hemodynamic characteristics between the patent group and the failure group (this has been demonstrated by our statistical results). This makes it possible to introduce hemodynamic characteristics to improve classification accuracy, which is also the basis of this study. The experimental results confirms the conjecture. From our study, it can be seen that the performance of the prediction model can be improved after hemodynamic characteristics are introduced. Especially for sensitivity, both of LIMA and SVG improve 20%. This greatly enhances the ability of the predictive model to correctly identify the postoperative failure graft.
Meanwhile,
it is noticed that the accuracy of LIMA is higher than SVG whether in the model based on clinical characteristics or the model based on the combination of clinical and hemodynamic characteristics. This can be explained in Fig.4. In the comparison between patent grafts and failure grafts, the differences of various data in LIMA are higher than that in SVG. And this makes the LIMA classification more accurate.
Prediction model In this study, the CABG ideal model was used to calculate the hemodynamic characteristics. This is not just for simplicity, but also for practical considerations. The ideal model used for all patients does lose some accuracy, but the construction of computational model should consider the 17
practical application scenarios of the model. The prediction model designed in this paper is used in the following scenarios: after surgeons complete the anastomosis of all grafts, and before stitching the chest cavity, the prediction model is used to judge the graft patency after 1 year, and then to determine whether modification of the graft is needed. At this time, the model construction only relies on preoperative image data and intraoperative TTFM data. Based on the obtained data, the model is personalized in terms of graft diameter and boundary conditions, while uniform mean values are adopted in other aspects, such as stenosis, anastomotic angle and target coronary artery diameter. The stenosis rate was assumed to be 100% because preoperative coronary angiographic data showed that the stenosis rate was greater than 90% in all patients undergoing bypass surgery (Patients with a stenosis rate of less than 90% were generally treated with PCI). In our previous studies, it was found that the hemodynamic environment of the graft and the anastomotic site showed little difference in the stenosis rate of 90% and 100% (Li et al., 2016). Therefore, the 100% stenosis rate assumption is reasonable. For anastomotic angle, our surgeons have comprehensively considered the hemodynamic environment and the difficulty of operation, and most anastomotic angles adopted are around 45 degrees, especially for single-point bypass. Therefore, the anastomotic angle was uniformly set to 45 degrees in this study. For the target coronary artery diameter, there are indeed personalized differences, but the prediction model can not accurately obtain the target coronary artery diameter in practice. Intraoperative TTFM data can not provide information about the target coronary artery diameter, and for severe stenosis which is applicable to CABG, preoperative images also could not accurately determine the coronary artery diameter at the distal end of the stenosis. 18
Therefore, when constructing the model, the target coronary diameter was set to a statistical mean value. Moreover, it should be noted that although the prediction accuracy has been improved after the introduction of hemodynamic factors, the prediction model still has room for further improvement. To further improve the prediction accuracy, the inclusion range of characteristics should be expanded. In this study, only the three most representative clinical factors and hemodynamic factors are selected. But for clinical factor, there are many literatures that suggest many other factors, such as backward flow ratio, the ratio of systolic peak flow and diastolic peak flow, maximum diastolic slope, etc. All these factors have been proved to be helpful in improving the prediction accuracy. Hemodynamics also has some other factors, such as vorticity and shear stress gradient. Then, methods that can reduce the dimension of data set, such as principal component analysis, are used to reduce the dimension of characteristics. Finally, surgeons can adjust the sensitivity and specificity of the prediction model (which can be achieved by adjusting the parameter wi) to obtain the model of the most suitable for clinical needs.
Conclusion The introduction of hemodynamic factors can indeed improve the accuracy, sensitivity and specificity of the graft patency prediction model, especially for the improvement of sensitivity. In the future, hemodynamic factors should also be included in the selection of characteristics when building the graft patency prediction model. 19
Acknowledgement This research is supported by National Natural Science Foundation of China (11832003, 11772016, 11472022). Competing interests The authors declare that there is no conflict of interests of this article. Additional Requirements This study was approved by the medical ethics committee of Peking University people's hospital, and the patient signed the informed consent. References Agnieszka M, Zuzanna P, et al. (2017). Caveolin 2: a facultative marker of unfavourable prognosis in long-term patency rate of internal thoracic artery grafts used in coronary artery bypass grafting. Preliminary report. Interactive CardioVascular and Thoracic Surgery. 24(5): 714-720 Amin S , Werner R S , Madsen P L , et al. (2018).Intraoperative Bypass Graft Flow Measurement with Transit Time Flowmetry: A Clinical Assessment. The Annals of Thoracic Surgery. 106(2):532-538. Araki T , Ikeda N , Shukla D , et al. (2015). A New Method for IVUS-based Coronary Artery Disease Risk Stratification: A Link between Coronary & Carotid Ultrasound Plaque Burdens. Computer methods and programs in biomedicine, 124: 161-179. Azam DD, Siamak EZK, Babak MA. (2017). Automated diagnosis of coronary artery disease (CAD) patients using optimized SVM. Computer Methods and Programs in Biomedicine, 138:117-126 Bassiouny, H. S., White, S., Glagov, S., Choi, E., Giddens, D. P., & Zarins, C. K. (1992). Anastomotic intimal hyperplasia: mechanical injury or flow induced. Journal of Vascular Surgery, 15(4), 708. 20
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an end-to-side anastomosis. J Vasc Surg 19:1067-1073 Papadopoulou, M., Spengos, K., Papapostolou, A., Tsivgoulis, G., & Karandreas, N. (2006). Predictive value of intraoperative transit-time flow measurement for short-term graft patency in coronary surgery. Journal of Thoracic & Cardiovascular Surgery. 132(3): 468. Shahrokh S , Mohammad T S , Ali S M , et al. (2018). Stress phase angle regulates differentiation of human adipose-derived stem cells toward endothelial phenotype. Progress in Biomaterials, 7(2): 121-131 Sottiurai VS, Yao JST, Batson RC, Sue SL, Jones R, Nakamura YA. (1989). Distal anastomotic intimal hyperplasia: histopathologic character and biogenesis. Ann Vasc Surg 3:26-33 Takami, Y., & Ina, H. (2001). A simple method to determine anastomotic quality of coronary artery bypass grafting in the operating room. Cardiovascular Surgery, 9(5), 499. Takami, Y., & Ina, H. (2001). Relation of intraoperative flow measurement with postoperative quantitative angiographic assessment of coronary artery bypass grafting. Annals of Thoracic Surgery, 72(4), 1270-4. Tatoulis J, Buxton BF, Fuller JA. (2004). Patencies of 2127 arterial to coronary conduits over 15 years. Ann Thorac Surg. 77: 93-101 Tokuda, Y., Song, M. H., Ueda, Y., Usui, A., & Akita, T. (2008). Predicting early coronary artery bypass graft failure by intraoperative transit time flow measurement. Annals of Thoracic Surgery. 84(6): 1928-1933. Tokuda, Y., Song, M. H., Usui, A., & Ueda, Y. (2007). Predicting midterm coronary artery bypass graft failure by intraoperative transit time flow measurement. Annals of Thoracic Surgery. 86(2): 532-536. Tsai, F. C., Yeh, T. F., & Jing, L. P. (2014). Use of graft flow measurement and computerized tomography angiography to evaluate patency of endoscopically harvested radial artery as sequential graft in coronary artery bypass surgery. Journal of Cardiovascular Surgery, 55(3), 415-422. Vapnik, V. (1995). The nature of statistical learning theory. New York: Springer. Whittemore, A. D., Clowes, A. W., Couch, N. P., & Mannick, J. A. (1981). Secondary femoropopliteal reconstruction. Annals of Surgery, 193(1), 35-42. Zhao, X.; Liu, Y.; Li, L.; Wang, W.; Xie, J.; Zhao, Z. (2015): Hemodynamics of the string phenomenon in the internal thoracic artery grafted to the left anterior descending artery with 23
moderate stenosis. Journal of Biomechanics, 49(7): 983-991.
24
Table 1. Basic information of patients Total patients
60
LIMA number
50
SVG number
82
Gender
41(male):19(female)
Height
165.55±7.07 (cm)
Weight
71.42±11.61 (kg) 25
Review interval
11.08±5.79 (months)
26
Table 2. LIMA and SVG statistical results
LIMA
patent(N=43)
failure(N=7)
30.51±15.76
12.29±6.52
PI
2.61±0.91
DF(%) WSS(Pa)
Flow(ml/min)
OSI
RRT(Pa-1)
SVG p
p
patent(N=52)
failure(N=30)
0.004*
34.79±15.60
23.87±16.03 0.003*
3.46±1.05
0.03*
3.13±2.36
73.35±9.51
72.14±5.93
0.748
63.60±11.49
2.01±0.91
0.80±0.34
0.001*
0.68±0.27
value
0.0030±0.0007 0.0031±0.0011 0.701
1.862±1.136
4.268±1.564 0.001*
3.63±2.02
value
0.328
64.20±13.12 0.828 0.48±0.28
0.003*
0.0040±0.0015 0.0055±0.0022 0.001*
4.449±2.423
6.772±3.831 0.001* 27
28
Table 3
Prediction results based on two SVM models
clinic
LIMA
SVG
clinic & hemodynamics
TP
FN
TN
FP
TP
FN
TN
FP
A
1
0
6
2
1
0
6
2
B
1
0
5
3
1
0
6
2
C
0
1
8
1
0
1
8
1
D
1
1
6
3
2
0
7
2
E
0
2
7
2
1
1
7
2
A
2
4
8
2
4
2
8
2
B
2
4
8
2
4
2
9
1
C
1
5
7
3
3
3
8
2
D
4
2
9
2
4
2
9
2
E
3
3
8
3
3
3
9
2
* TP means true positive, FN means false negative, TN means true negative, FP means false positive. 29
30
Table 4. Classification results of two SVM prediction models
graft
accuracy
sensitivity
specificity
LIMA
70.35%
50%
74.17%
SVG
63.24%
40%
76.91%
LIMA
78.02%
70%
78.89%
SVG
74.41%
60.1%
82.73%
clinic
clinic & hemodynamics
31
Figure Legends Fig.1. Clinical data extraction and digital processing of TTFM waveform Fig.2. The ideal model of CABG Fig.3. Contours of WSS, OSI and RRT Fig.4. Radar graphs of grafts, the left is for LIMA, the right is for SVG
32
33
34
35
36
S0021-9290(19)30673-6 https://doi.org/10.1016/j.jbiomech.2019.109426 BM 109426
To appear in:
Journal of Biomechanics
Accepted Date:
13 October 2019
Please cite this article as: B. Mao, Y. Feng, W. Wang, B. Li, Z. Zhao, X. Zhang, C. Jin, D. Wu, Y. Liu, The influence of hemodynamics on graft patency prediction model based on support vector machine, Journal of Biomechanics (2019), doi: https://doi.org/10.1016/j.jbiomech.2019.109426
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© 2019 Published by Elsevier Ltd.
The influence of hemodynamics on graft patency prediction model based on support vector machine
Boyan Mao1&, Yue Feng1&, Wenxin Wang1, Bao Li1, Zhou Zhao2, Xiaoyan Zhang1, Chunbo Jin1, Dandan Wu1, Youjun Liu1*
1 College
of Life Science and Bio-Engineering, Beijing University of Technology, No. 100 Pingleyuan, Chaoyang District, Beijing 100124, China 2Cardiac
Surgery Department, PeKing University People’s Hospital. 11th.South Ave. Xizhimen, Beijing, China
Original Article For Submission To Journal of Biomechanics Date: March 29, 2019
1
Number of words: 3273 (Introduction through Discussion, exclusive of references) Number of figures: 4 (4 color) Number of tables: 3
*Corresponding author: Youjun Liu College of Life Science and Bio-Engineering Beijing University of Technology No. 100 Pingleyuan, Chaoyang District, Beijing 100124 China [email protected]
& These authors contribute equally to this paper Abstract: In the existing patency prediction model of coronary artery bypass grafting (CABG), the characteristics are based on graft flow, but no researchers selected hemodynamic factors as the characteristics. The purpose of this paper is to study whether the introduction of hemodynamic 2
factors will affect the performance of the prediction model. Transit time flow-meter (TTFM) waveforms and 1-year postoperative patency results were obtained from 50 internal mammary arterial grafts (LIMA) and 82 saphenous venous grafts (SVG) in 60 patients. Taking TTFM waveforms as the boundary conditions, the CABG ideal models were constructed to obtain hemodynamic factors in grafts. Based on clinical characteristics and combination of clinical and hemodynamic characteristics, patency prediction models based on support vector machine (SVM) were constructed respectively. For LIMA, after the introduction of hemodynamic factors, the accuracy, sensitivity and specificity of the prediction model increased from 70.35%, 50% and 74.17% to 78.02%, 70% and 78.89%, respectively. For SVG, the accuracy, sensitivity and specificity of the prediction model increased from 63.24%, 40% and 76.91% to 74.41%, 60.1% and 82.73%, respectively. The performance of the prediction model can be improved by introducing hemodynamic factors into the characteristics of the model. The accuracy, sensitivity and specificity of the prediction results are higher with the addition of hemodynamic characteristics.
Keywords: Hemodynamics, coronary artery bypass grafting, graft patency, support vector machine, transit time flow-meter,
Introduction 3
Coronary artery bypass grafting (CABG) is a commonly used surgical procedure for coronary heart disease (CHD) (Beck et al., 1935). The main problem is the risk of postoperative graft failure. According to statistics, the failure rate of venous grafts in the early postoperative period is 15-30%, and it will reach 50% after 10 years (Mehta et al., 1997). And for arterial grafts, the 10 - year patency and 15 - year patency are 95% and 88% respectively (Tatoulis et al., 2004). After the graft fails, the patient will have myocardial ischemia again, which will be seriously life-threatening. Therefore, for each patient, how to predict the graft patency is of great significance, which can help patients avoid possible adverse cardiovascular events in the future, and also help surgeons make the next treatment plan. Transit time flow-meter (TTFM) is a flow measurement technique based on the principle of ultrasound and is currently widely used to measure the flow of grafts during bypass surgery (Amin et al., 2018; Kentaro et al., 2015; Niclauss et al., 2018). After surgeons complete all the graft anastomosis, they will use the TTFM probe to clamp the graft and measure the flow waveform before closing the chest cavity. With TTFM results, surgeons can assess whether the graft anastomosis is successful or not. Low average flow rate, high pulsatility index (PI) and low diastolic velocity time fraction (DF) are considered as risk factors reflecting the obstructed anastomosis (Tokuda et al., 2008; Tokuda et al., 2007; Kim et al., 2005; Papadopoulou et al., 2006). At present, many scholars have studied the method of using TTFM results to predict graft patency. Lehnert et al. used logistic regression analysis to study the risk of graft failure within one year after surgery based on intraoperative TTFM measurements and postoperative coronary angiography (Lehnert et al., 2015). Tsai et al. assessed radial arterial graft patency by intraoperative 4
TTFM measurement and postoperative CTA (Tsai et al., 2014). Using TTFM data, Handa et al. proposed that the maximum diastolic blood flow acceleration is an effective characteristics for predicting the graft patency (Handa et al., 2015). Takami et al. proposed that after the Fast Fourier transform (FFT) of TTFM waveform, the ratio of fundamental wave to harmonic wave can be used as an effective characteristics to predict the graft patency (Takami et al., 2001; Takami et al., 2001). In summary, the existing studies only use the data obtained from TTFM as the characteristics to construct the prediction model, but hemodynamic factors are not considered. According to the research, hemodynamics is the key factor affecting graft patency. Graft failure is mainly caused by intimal hyperplasia and atherosclerosis (Whittemore et al., 1981; Butany et al., 1998; Agnieszka et al., 2017; De et al., 2018), and poor hemodynamic factors are considered to be the most important factors in their occurrence and development (Bassiouny et al., 1992; Hofer et al., 1996; Shahrokh et al., 2018). Studies have shown that in the end-to-side anastomosis, intimal hyperplasia mainly occurs in the toe and heel of the anastomosis where disturbance flow is severe (Sottiurai et al., 1989; Ojha et al., 1994; Min et al., 2018). Therefore, it is of great significance to study the influence of hemodynamics on the graft patency and explore its value in the patency prediction model. The difficulty in predicting the graft patency lies in the small number of samples and the large number of influencing factors. Support vector machine (SVM) is an effective machine learning method, which has many unique advantages in solving high-dimensional, nonlinear and small sample pattern recognition, and is widely used in classification and regression problems. In the field of cardiovascular diseases, most researchers use the image data obtained from coronary angiography, 5
CTA and IVUS as well as the collected ECG data as characteristics, and use SVM to carry out diagnosis and postoperative effect prediction (Ismail et al., 2010; Araki et al., 2015; Azam et al., 2017; Ismail et al., 2010; Matheny et al., 2007; Jawaid et al., 2017). Among them, Dursun et al. used a variety of machine learning methods to predict the surgical results of CABG, and the results showed that SVM worked best (Delen et al., 2012). However, hemodynamic factors were not included in the selection of characteristics. The purpose of this paper is to study whether the prediction performance can be improved after hemodynamic factors are included in the characteristics of the patency prediction model based on SVM.
Methods Collection of patient data This study collected data from 60 patients who received bypass surgery in Peking University people's hospital and returned to the hospital for review about 1 year after the surgery. Among them, there were 50 internal mammary arterial grafts (LIMA) and 82 saphenous venous grafts (SVG). The LIMA was anastomosed to the anterior descending branch in all cases. The detailed information is shown in Table 1. All the selected patients used TTFM to measure the blood flow waveform of each graft at the completion of bypass surgery, and used CTA to check the patency of each coronary artery and graft
6
about 1 year after the surgery. According to the patency of grafts, LIMA and SVG were divided into patent and failure groups respectively.
Clinical data extraction and digital processing of TTFM waveform The TTFM waveform measured clinically is shown on the left side of Fig.2. The measured location of TTFM waves is in the middle of the graft. The indexes in blue dotted frame are commonly used in clinical evaluation of graft patency, including average flow, pulsatility index (PI), diastolic velocity time fraction (DF). Average flow is defined as: total flow/time, PI is defined as: (maximum flow - minimum flow)/average flow, and DF is defined as diastolic flow/total flow. When the flow waveform was stable, three consecutive cycles were selected, as shown in the red dotted frame. Set the time interval as 0.005s and conduct digital processing on the waveform to obtain the flow value corresponding to each time, as shown on the right side of Fig.1.
Construction of calculation model In order to obtain the hemodynamic results of each graft, this study constructed an ideal model of CABG, as shown in Fig.2. The ideal model represents the anastomosis of a graft to the target coronary artery at an angle of 45 degrees. The yellow area in the figure is the area where hemodynamic factors were extracted, including graft and anastomotic site. Since the stenosis rates were greater than 90% in all collected 7
cases, it was assumed in this study that the anterior end of the anastomotic site was completely occluded. The diameter of the target coronary artery was set as 3mm, and the diameter of the graft was determined by the size of the selected TTFM probe, as shown on the left side of Fig.1. The blue dotted frame on the bottom left part is the size of the probe. The surgeon selected probes of different sizes according to the diameter of the graft. L1 represents the length of the graft, SVG was set as 120mm, and LIMA was set as 180mm. L2 and L3 represent the target coronary artery. L2 is the length of the proximal of the anastomosis, which is 10mm. L3 is the distal of the anastomosis, and the length was extended to 90mm in order to fully develop the blood flow. L4 represents the length of the anastomotic site, which is defined as the site where blood flow is not sufficiently developed. The value is given by formula (1): L4=0.06•d•Re (Krishnan et al., 2012)
(1)
Among them, d is the diameter of the tube, Re is the Reynolds number. Re=
𝜌𝑣𝑑 𝜇
(2)
Among them, ρ is the density of blood which was set as 1050kg/𝑚3. 𝑣 is the average velocity of blood flow in the coronary artery which was measured from the end of the coronary artery after calculation. μ is dynamic viscosity which was set as 0.0035Pa•s. After completing the calculation of the model, the average velocity at the outlet position was measured, and then calculated the length of the underdeveloped region according to the formulas (1) and (2). The inlet boundary condition of the graft was set as the digital TTFM waveform, and the
8
outlet boundary condition of the coronary artery was set as 0 mmHg. The ANSYS ICEM CFD software was used to mesh the above models, and the hexahedral meshing method was used to mesh. The meshes passed the grid sensitivity analysis. Using ANSYS CFX for finite element simulation, it was assumed that the vascular wall is impermeable and non-slip rigid wall. The material property of blood is adiabatic and incompressible viscous Newtonian fluid, and its flow is unsteady laminar flow.
Support vector machine method SVM is a commonly used machine learning method based on the VC dimension theory of statistical learning theory and the principle of structural risk minimization, it was first proposed by Vapnik et al (Vapnik et al., 1995). The key of SVM is kernel function, which will lead to different SVM algorithm. The kernel function maps a vector that is indivisible in a low-dimensional space to a high-dimensional space, making the vector divisible. The kernel functions of SVM mainly include polynomial kernel functions, linear kernel functions, Sigmoid kernel functions and radial basis kernel functions (RBF), and their mathematical principle was introduced in the article of Ismail Babaoglu et al (Ismail et al., 2010). This study adopted the libsvm toolbox based on Matlab (Chih-Chung et al., 2001), using the most commonly used RBF kernel function. For RBF SVM, in order to obtain the most accurate classification results, it is necessary to find the appropriate penalty coefficient (C) and kernel function radius (g). 9
There are many methods to find the optimal (C, g), and this paper adopted the simplest and most accurate method -- grid search. Grid search is a traversal algorithm, that is, within a certain range, each value of C and g is detected one by one according to a certain step size. Finally, the value (C, g) with the highest classification accuracy is selected. 2 ―𝑚 < 𝐶 < 2𝑚
(3)
2 ―𝑛 < 𝑔 < 2𝑛
(4)
In this paper, m and n were set as 5, and the search step size of m and n was 0.2. For each search step of (C, g), the average accuracy of the model was calculated by cross validation method. Cross validation is a method for finding optimal parameters and evaluating the performance of prediction models. In this paper, k-fold cross validation method was adopted, that is, all samples were divided into k sub-samples, a single sub-sample was retained as the test data, and other k-1 sub-samples were used for training. The process was repeated k times, each sub-sample was verified once, and the accuracy of these k times’ results was averaged. The results of cross validation can be expressed as: 1
𝑘
𝐶𝑉(𝐾) = 𝑘∑𝑖 = 1𝐴𝐶𝐶𝑖
(5)
ACC is the accuracy rate of each time, and its value is: number of correctly classified samples/total number of samples. And the k value was set as 5 in this study. By comparing all the values of 𝐶𝑉(𝐾) , the corresponding (C, g) is the optimal parameter when the value is the largest, and the SVM also achieves the optimal performance. 10
In SVM training, when the number of a group of samples is small, the parameter wi (weight) can set a large penalty coefficient for it, so as to improve the classification accuracy of this group of samples. In this study, the number of samples in LIMA failure group was significantly less than that in the patent group, so the wi of the failure group was set as 5. The wi of LIMA patent group and two groups of SVG were set as default values (the default value was 1). In order to avoid the influence of dimension of each characteristic, the data were normalized. The study used the 0-1 method to process the data, and all the data were within the interval of [0, 1]. The formula is: 𝑥 ― 𝑚𝑖𝑛
𝑥 ∗ = 𝑚𝑎𝑥 ― 𝑚𝑖𝑛
(6)
𝑥 is the original data, 𝑥 ∗ is the normalized data.
Statistical method Data in this study were expressed in the form of average value ± standard deviation. For the data of patent group and failure group, one-way ANOVA was used to compare whether there were significant differences between the average values of the two groups. All statistical results were obtained by SPSS software.
Hemodynamic factors Wall shear stress (WSS), oscillatory shear index (OSI) and relative residence time (RRT) 11
were selected as hemodynamic factors (Meirson et al., 2015; Meirson et al., 2015). WSS is an important factor affecting vascular lesions, such as plaque rupture and atherosclerosis. Some researchers have suggested that low WSS can reduce the graft patency (Malek et al., 1999). The formula is shown below: 𝑑𝑢
(7)
WSS = ―μ 𝑑𝑟
μ is blood viscosity, u is flow axial velocity, r is vessel radial distance. OSI is also a commonly used hemodynamic factor, which represents the oscillation degree of blood flow in vessels. It is related to string phenomenon of the graft (Zhao et al., 2015). It is defined as:
[
OSI = 0.5 1 ―
|∫𝑇0𝑊𝑆𝑆𝑑𝑡| 𝑇
]
∫0|𝑊𝑆𝑆|𝑑𝑡
(8)
RRT is used to describe how long the particles stay on the endothelial cells. It is generally believed that the high RRT area has a longer time of blood aggregation and is prone to endometrial hyperplasia (Himburg et al., 2004). The calculation formula is as follows: 1
RRT = （1 ― 2•OSI）•TAWSS
(9)
TAWSS is the time average WSS. After the model was calculated, the hemodynamic results of the graft and the anastomotic site (yellow area) were extracted, as shown in Fig.3. Fig.3 shows the contours of WSS, OSI and RRT, taking a certain bridging vessel as an example. TAWSS is the average value of WSS over the whole 12
calculated period of time (three cardiac cycles). OSI and RRT are the values of the last moment. All characteristics are now prepared. Clinical characteristics include average flow rate, PI and DF. Hemodynamic characteristics include TAWSS, OSI and RRT.
Result Statistical results In the samples selected in this study, it was found that there were 43 patent LIMA grafts and 7 failure LIMA grafts in the total 50 LIMA grafts. And there were 50 patent SVG grafts and 32 failure SVG grafts in the total 82 SVG grafts. Their average flow rate, PI, DF, TAWSS, OSI and RRT were obtained, and they were shown on Table 2. For LIMA, it can be seen from the Table 2 that flow rate and TAWSS in the patent group are significantly higher than those in the failure group, while PI and RRT in the failure group are significantly higher than those in the patent group. DF and OSI show little difference between the two groups. For SVG, flow rate and TAWSS of the patent group are significantly higher than those of the failure group, while OSI and RRT of the failure group are significantly higher than those of the patent group. There is little difference between PI and DF between the two groups. For clear contrast, all the factors were normalized so that their values were in the interval of [0, 1]. For PI, OSI and RRT, we used 1 minus their values. Making radar maps of LIMA and SVG for these 6 characteristics, as shown in Fig.4. At this time, the 6 dimensions of the radar map all 13
represent favorable characteristics of graft patency. In other words, the size of the area enclosed by the radar map represents the ability of the graft to maintain patency, and the larger the area, the more likely it is to maintain patency. Through the comparison of the radar graph, it can intuitively feel the difference between the patent and the failure groups of LIMA and SVG. While the patent group in LIMA has a significantly greater advantage over the failure group, the differences between the two groups in SVG are smaller than in LIMA.
SVM prediction results In order to study the influence of hemodynamic factors on prediction models, two prediction models were constructed. One was the SVM prediction model based only on clinical factors, and the selected characteristics were flow rate, PI and DF. The other was the SVM prediction model that combined clinical factors with hemodynamic factors. The selected characteristics were flow rate, PI, DF, TAWSS, OSI and RRT. All the data has been normalized to eliminate dimension effects. The performance of SVM prediction is deeply influenced by the selected parameters (C, g) and the selected training set and test set. In order to eliminate the influence of parameters and sample selection, and to better compare the performance of the two prediction models, the optimal parameters of the two prediction models were obtained by grid search and cross-validation methods respectively.
14
In this study, cross validation was also used to test the performance of two prediction models. All samples were divided into 5 parts and recorded as A, B, C, D, E respectively. The sample number, and the proportion of patent and failure grafts were maintained almost equivalent in each part. 4 parts were used as the training set and 1 part as the test set. Repeat 5 times until every part is tested. The results of each prediction were recorded in the Table 3, in which failure graft was recorded as positive, and patent graft was recorded as negative. The average accuracy, average sensitivity and specificity were obtained under the optimal parameters. The results are shown in Table 4. It can be seen from the table, for LIMA, the accuracy of the prediction model based only on TTFM clinical factors is 70.35%, and the sensitivity and specificity are 50% and 74.17%. The accuracy of the prediction model based on the combination of clinical factors and hemodynamics is 78.02%, and the sensitivity and specificity are 70% and 78.89%. For SVG, the accuracy of the prediction model based only on TTFM clinical factors is 63.24%, and the sensitivity and specificity are 40% and 76.91%. The accuracy of the prediction model based on the combination of clinical factors and hemodynamics is 74.41%, and the sensitivity and specificity are 60.1% and 82.73%. From the above results, it can be seen that the introduction of hemodynamic factors as characteristics can improve the performance of the prediction model. The accuracy, sensitivity and specificity of the prediction model are improved, especially for the sensitivity.
Discussion 15
Analysis of statistical results In this study, three clinical characteristics including flow rate, PI and DF, as well as three hemodynamic characteristics including TAWSS, OSI and RRT, were statistically analyzed. It is generally believed that low flow rate, high PI and low DF are not conducive to graft patency, while low WSS, high OSI and RRT are not conducive to graft patency either. According to the clinical data we collected, LIMA is superior to SVG in both clinical and hemodynamic characteristics, which partly explains why LIMA is significantly more patent than SVG. This study also compared the patent group and the failure group. For LIMA, the flow rate, PI, TAWSS and RRT are different between the two groups. The p values of DF and OSI reach above 0.7, indicating that there is no difference between the two groups. For SVG, the flow rate, TAWSS, OSI and RRT have significant difference between the two groups, but PI and DF have no difference. In summary, it is known that flow rate, TAWSS and RRT all have significant difference both in LIMA and SVG, while the manifestations of PI and OSI in the two types of grafts are not consistent. However, whether in LIMA or SVG, DF shows no difference in patent and failure groups. In particular, hemodynamic characteristics TAWSS and RRT have significant differences in both two kinds of grafts, which will be conducive to classification.
Analysis of prediction results When the prediction models are consistent, the degree of difference between the two groups'
16
characteristics determines the accuracy of classification. The more information that is significantly different between the two groups, the higher the accuracy of the classification. Hemodynamic characteristics have been proved to affect the graft patency, so there should be a significant difference in hemodynamic characteristics between the patent group and the failure group (this has been demonstrated by our statistical results). This makes it possible to introduce hemodynamic characteristics to improve classification accuracy, which is also the basis of this study. The experimental results confirms the conjecture. From our study, it can be seen that the performance of the prediction model can be improved after hemodynamic characteristics are introduced. Especially for sensitivity, both of LIMA and SVG improve 20%. This greatly enhances the ability of the predictive model to correctly identify the postoperative failure graft.
Meanwhile,
it is noticed that the accuracy of LIMA is higher than SVG whether in the model based on clinical characteristics or the model based on the combination of clinical and hemodynamic characteristics. This can be explained in Fig.4. In the comparison between patent grafts and failure grafts, the differences of various data in LIMA are higher than that in SVG. And this makes the LIMA classification more accurate.
Prediction model In this study, the CABG ideal model was used to calculate the hemodynamic characteristics. This is not just for simplicity, but also for practical considerations. The ideal model used for all patients does lose some accuracy, but the construction of computational model should consider the 17
practical application scenarios of the model. The prediction model designed in this paper is used in the following scenarios: after surgeons complete the anastomosis of all grafts, and before stitching the chest cavity, the prediction model is used to judge the graft patency after 1 year, and then to determine whether modification of the graft is needed. At this time, the model construction only relies on preoperative image data and intraoperative TTFM data. Based on the obtained data, the model is personalized in terms of graft diameter and boundary conditions, while uniform mean values are adopted in other aspects, such as stenosis, anastomotic angle and target coronary artery diameter. The stenosis rate was assumed to be 100% because preoperative coronary angiographic data showed that the stenosis rate was greater than 90% in all patients undergoing bypass surgery (Patients with a stenosis rate of less than 90% were generally treated with PCI). In our previous studies, it was found that the hemodynamic environment of the graft and the anastomotic site showed little difference in the stenosis rate of 90% and 100% (Li et al., 2016). Therefore, the 100% stenosis rate assumption is reasonable. For anastomotic angle, our surgeons have comprehensively considered the hemodynamic environment and the difficulty of operation, and most anastomotic angles adopted are around 45 degrees, especially for single-point bypass. Therefore, the anastomotic angle was uniformly set to 45 degrees in this study. For the target coronary artery diameter, there are indeed personalized differences, but the prediction model can not accurately obtain the target coronary artery diameter in practice. Intraoperative TTFM data can not provide information about the target coronary artery diameter, and for severe stenosis which is applicable to CABG, preoperative images also could not accurately determine the coronary artery diameter at the distal end of the stenosis. 18
Therefore, when constructing the model, the target coronary diameter was set to a statistical mean value. Moreover, it should be noted that although the prediction accuracy has been improved after the introduction of hemodynamic factors, the prediction model still has room for further improvement. To further improve the prediction accuracy, the inclusion range of characteristics should be expanded. In this study, only the three most representative clinical factors and hemodynamic factors are selected. But for clinical factor, there are many literatures that suggest many other factors, such as backward flow ratio, the ratio of systolic peak flow and diastolic peak flow, maximum diastolic slope, etc. All these factors have been proved to be helpful in improving the prediction accuracy. Hemodynamics also has some other factors, such as vorticity and shear stress gradient. Then, methods that can reduce the dimension of data set, such as principal component analysis, are used to reduce the dimension of characteristics. Finally, surgeons can adjust the sensitivity and specificity of the prediction model (which can be achieved by adjusting the parameter wi) to obtain the model of the most suitable for clinical needs.
Conclusion The introduction of hemodynamic factors can indeed improve the accuracy, sensitivity and specificity of the graft patency prediction model, especially for the improvement of sensitivity. In the future, hemodynamic factors should also be included in the selection of characteristics when building the graft patency prediction model. 19
Acknowledgement This research is supported by National Natural Science Foundation of China (11832003, 11772016, 11472022). Competing interests The authors declare that there is no conflict of interests of this article. Additional Requirements This study was approved by the medical ethics committee of Peking University people's hospital, and the patient signed the informed consent. References Agnieszka M, Zuzanna P, et al. (2017). Caveolin 2: a facultative marker of unfavourable prognosis in long-term patency rate of internal thoracic artery grafts used in coronary artery bypass grafting. Preliminary report. Interactive CardioVascular and Thoracic Surgery. 24(5): 714-720 Amin S , Werner R S , Madsen P L , et al. (2018).Intraoperative Bypass Graft Flow Measurement with Transit Time Flowmetry: A Clinical Assessment. The Annals of Thoracic Surgery. 106(2):532-538. Araki T , Ikeda N , Shukla D , et al. (2015). A New Method for IVUS-based Coronary Artery Disease Risk Stratification: A Link between Coronary & Carotid Ultrasound Plaque Burdens. Computer methods and programs in biomedicine, 124: 161-179. Azam DD, Siamak EZK, Babak MA. (2017). Automated diagnosis of coronary artery disease (CAD) patients using optimized SVM. Computer Methods and Programs in Biomedicine, 138:117-126 Bassiouny, H. S., White, S., Glagov, S., Choi, E., Giddens, D. P., & Zarins, C. K. (1992). Anastomotic intimal hyperplasia: mechanical injury or flow induced. Journal of Vascular Surgery, 15(4), 708. 20
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24
Table 1. Basic information of patients Total patients
60
LIMA number
50
SVG number
82
Gender
41(male):19(female)
Height
165.55±7.07 (cm)
Weight
71.42±11.61 (kg) 25
Review interval
11.08±5.79 (months)
26
Table 2. LIMA and SVG statistical results
LIMA
patent(N=43)
failure(N=7)
30.51±15.76
12.29±6.52
PI
2.61±0.91
DF(%) WSS(Pa)
Flow(ml/min)
OSI
RRT(Pa-1)
SVG p
p
patent(N=52)
failure(N=30)
0.004*
34.79±15.60
23.87±16.03 0.003*
3.46±1.05
0.03*
3.13±2.36
73.35±9.51
72.14±5.93
0.748
63.60±11.49
2.01±0.91
0.80±0.34
0.001*
0.68±0.27
value
0.0030±0.0007 0.0031±0.0011 0.701
1.862±1.136
4.268±1.564 0.001*
3.63±2.02
value
0.328
64.20±13.12 0.828 0.48±0.28
0.003*
0.0040±0.0015 0.0055±0.0022 0.001*
4.449±2.423
6.772±3.831 0.001* 27
28
Table 3
Prediction results based on two SVM models
clinic
LIMA
SVG
clinic & hemodynamics
TP
FN
TN
FP
TP
FN
TN
FP
A
1
0
6
2
1
0
6
2
B
1
0
5
3
1
0
6
2
C
0
1
8
1
0
1
8
1
D
1
1
6
3
2
0
7
2
E
0
2
7
2
1
1
7
2
A
2
4
8
2
4
2
8
2
B
2
4
8
2
4
2
9
1
C
1
5
7
3
3
3
8
2
D
4
2
9
2
4
2
9
2
E
3
3
8
3
3
3
9
2
* TP means true positive, FN means false negative, TN means true negative, FP means false positive. 29
30
Table 4. Classification results of two SVM prediction models
graft
accuracy
sensitivity
specificity
LIMA
70.35%
50%
74.17%
SVG
63.24%
40%
76.91%
LIMA
78.02%
70%
78.89%
SVG
74.41%
60.1%
82.73%
clinic
clinic & hemodynamics
31
Figure Legends Fig.1. Clinical data extraction and digital processing of TTFM waveform Fig.2. The ideal model of CABG Fig.3. Contours of WSS, OSI and RRT Fig.4. Radar graphs of grafts, the left is for LIMA, the right is for SVG
32
33
34
35
36