Shape and Enhancement Analysis as a Useful Tool for the Presentation of Blood Hemodynamic Properties in the Area of Aortic Dissection

The aim of this study was to create a mathematical approach for blood hemodynamic description with the use of brightness analysis. Medical data was collected from three male patients aged from 45 to 65 years with acute type IIIb aortic dissection that started proximal to the left subclavian artery and involved the renal arteries. For the recognition of wall dissection areas Digital Imaging and Communications in Medicine (DICOM) data were applied. The distance from descending aorta to the diaphragm was analyzed. Each time Feret (DF) and Hydraulic (DHy) diameter were calculated. Moreover, an average brightness (BAV) was analyzed. Finally, to describe blood hemodynamic in the area of aortic wall dissection, mathematical function combining difference in brightness value and diameter for each computed tomography (CT) scan was calculated. The results indicated that DF described common duct more accurately compare to DHy. While, DHy described more accurately true and false ducts. Each time when connection of true and false duct appeared, true duct had lower brightness compare to common duct and false duct. Moreover, false duct characterized with higher brightness compare to common duct. In summary, the proposed algorithm mimics changes in brightness value for patients with acute type IIIb aortic dissection.


Introduction
Aortic dissection with tear formation in the inner lining of the aorta, is one of the worst cardiovascular emergencies, associated with considerable morbidity and mortality [1][2][3]. The type of aortic dissection is characterized with the use of Stanford classification [4]. Depending on the location of the aortic dissection, one distinguishes type A at ascending aorta which typically requires surgical interventions, and type B at descending aorta due to often recurrence, progressive dilatation of lumen and aortic rupture [5,6]. Hemodynamic parameters are believed to play a crucial role in the formation and the progression of the aortic dissection [7]. The blood flow pattern within the dissected aorta is dominated by locally highly disturbed and possibly turbulent flow with strong recirculation [8].
Various mathematical models have been recently developed to understand cardiovascular system [6,9,10]. Among those are bioreactors describing mechanical properties of veins and artificial vessels [7,11,12]. Moreover, application of computational methods, including the computational fluid dynamic (CFD) technique in the topic of blood flow in vessels is widely described in the literature [13,14]. Navier-Stokes equations are applied for the description of three-dimensional blood hemodynamic [15]. Depending on the analyzed case, blood is considered as a Newtonian [16] or non-Newtonian fluid [17]. Moreover, the influence of blood hemodynamic on a vessel's wall with the use of wall shear stress may be investigated with CFD technique [18]. Blood flow simulation provides important information, crucial for assessment of blood distribution for patients affected by vascular diseases, e.g., stenosis or aortic dissection [19,20]. Numerical methods as well as experimental devices require importing imaging [21,22]. Medical imaging techniques, e.g., computational tomography (CT) or magnetic resonance imaging (MRI), enable detail visualization of morphology of cardiovascular system dysfunction, e.g., aortic dissection [23]. Region growing or level set algorithms are applied for the vascular segmentation [24]. Furthermore, extraction of centerline for the vessel reconstruction is used [15]. However, none of the imaging techniques allow the prediction blood hemodynamic after surgical intervention [25][26][27]. The image processing of medical data allows the provision of realistic in vivo conditions for patient specific analysis, e.g., reliable anatomical 3D geometries of human cardiovascular system [28]. Thus, aortic dissection may be improved by a specific therapy and/or application of advanced prognostic tools, such as computer simulations [29]. Using this approach, it is possible to measure hemodynamic parameters within three-dimensional (3D) models that provide important information on hemodynamic changes within the true and false lumen. Moreover, changes in contrast enhancement with the use of contemporary computer tomography allow estimation of vessels' narrowness [30,31]. In our study we have a reliable enhanced reference point, i.e., both channels filled after heart systole. Therefore, the differences occurring in them result only from different outflow conditions from the canals and not from conditions related to heart efficiency. The assessment of the width of the channels currently adopted is not perfect and there is a margin of patients in whom, despite good communication of the channels, dissection progresses and there are symptoms of organ ischemia. Therefore, the aim of this study was to create a tool for visualization of blood hemodynamic properties in the area of aortic dissection with the use of quantitative analysis of MRI data.
The paper is organized as follows: In Section II medical data, mathematical model, and its verification was described. Section III presents the results directed in the mathematical description of brightness value, aortic diameter and relation of both parameters. In Section IV a discussion was proposed while, Section V concludes the paper.

Experimental Section
Medical data was collected from three male patients aged from 45 to 65 years after CT angiography (CTA) (GE Light-Speed 64 VCT; GE Healthcare, Fairfield, CT, USA) who underwent treatment in the Barlicki Hospital No. 2 in Lodz (Poland) in 2016. During CTA patients obtained a contrast (Visipaque) at a constant value of 1.5 mL per 1 kg of body weight. All participants gave written informed consent to the study. The study protocol was approved by the local ethics committee at the Medical University of Lodz (approval no.: RNN/126/07/KE). Inclusion criteria comprise acute type IIIb aortic dissection that started proximal to the left subclavian artery and involved the renal arteries in each of the analyzed cases [32,33] (Table 1).

End of dissection
Right iliac artery (zone number 9 according to Fillinger et al. 2010) Right iliac artery (zone number 9 according to Fillinger et al. 2010) Right iliac artery (zone number 9 according to Fillinger et al. 2010) For the recognition of wall dissection areas Digital Imaging and Communications in Medicine (DICOM) data (512 × 512 × 270 voxels, in-plane resolution of 0.78 × 0.78 mm, slice thickness 0.8 mm) from the aforementioned patients with acute complicated type B dissection was applied as previously described [7,35]. Segmentation process included the following steps: (1) CT angiography data was manually adjusted for brightness to achieve the highest contrast between analyzed aorta and surrounding tissue; (2) the region growing technique to extract aorta from the background was applied; and (3) gaps were eliminated manually using the ImageJ software and its tool for morphological holes filling. The implemented segmentation region-growing technique provided quite accurate results, since the aorta gray levels differed significantly from the image background. When compared to manual segmentation performed by the radiologist (the reference method), the estimated aorta parameter values (area, diameter) did not differ more than 5%. To reconstruct 3D model of aorta after segmentation process, a rendering process was performed. Moreover, a quantitative analysis of CT angiography data was performed [36]. Therefore, two parameters were calculated: (1) Brightness intensity to noise (BI) as a quotient of aorta brightness intensity and noise value, and (2) contrast to noise ratio (CNR) as a quotient of subtraction of aorta brightness intensity and background brightness to noise value ( Table 2). The highest brightness intensity was calculated in Pixels by placing Region of Interest in the center of the area represented by analyzed aorta (reaching 80 mm 2 ). This operation was performed for all slices for particular patient for common duct, false duct and true duct separately. The mean of these values was used for further calculations. While, image noise was calculated as standard deviation measured as well in pixels and calculated for 100 mm 2 drawn in two different regions outside the patient body (left, and right sides).
Furthermore, to describe spatial configuration of analyzed aortas geometric parameters were used [6,37]. On each CT scan Feret (D F ) [38] (Equation (1)) and Hydraulic (D Hy ) [39] (Equation (2)) diameters were calculated. The D F was calculated as an average value of horizontal and vertical diameter of analyzed object, while the D Hy was calculated as a division of cross-section area of the flow in channel to the wetted perimeter of the aortic cross-section.
where: D F -Feret diameter, (mm), D v -the highest distance between two points on the perimeter of analyzed aorta, calculated in vertical direction, (mm), D h -the highest distance between two points on the perimeter of analyzed aorta, calculated in horizontal direction, (mm).
With the use of Osirix software (Pixmeo SARL, Bernex, Switzerland) an average brightness value (B AV ) (Equation (3)) of the area representing blood inside aorta was calculated. The distance from descending aorta to the diaphragm was analyzed.
where: B AV -average brightness value, [Pixel], B i -brightness value for i Pixel, [pixel], APixeli-number of Pixels in the analyzed area, [-]. Finally, to describe blood hemodynamic in the area of aortic wall dissection, mathematical function combining difference in brightness values (Equation (4)) and diameter (Equation (5)) for each CT scan was calculated. Dif where: Dif B AV -difference in brightness value, [-], B AV Duct_i -average brightness value for analyzed duct, [Pixel].
where: Dif D HY/F -difference in diameter, [-], D HY/F Duct_i -average diameter for analyzed duct, (mm). Statistical analysis was performed using Statistica 12.0 software (StatSoft, Tulsa, OK, USA). Data were presented as mean ± standard deviation (SD). Moreover, the Bland-Altman method was utilized to analyze the agreement between Feret diameter and Hydraulic diameter. Spearman's correlation rho analysis was used in addition. Comparisons between analyzed groups were made using the U Mann-Whitney test after verifying normality and variance. Data were considered as significantly different when p < 0.05, unless otherwise noted.

Diameter Analysis
In the first step, to indicate the proper parameter to describe spatial configuration of analyzed domains, D F and D Hy for all three patients were analyzed. For patient number 1 (P1) (Figure 1a (Figure 1c), respectively. Moreover, average value of diameter for true duct was equal to 20.476 ± 5.18 mm and 15.71 ± 3.29 mm for D F and D Hy , respectively. Furthermore, average value of diameter for the false duct was equal to 41.57 ± 4.23 mm and 35.47 ± 2.46 mm for D F and D Hy , respectively.
Additionally, according to Bland-Altman analysis for the common duct for P1 the difference between Feret and Hydraulic diameter was equal to 3.35 mm for the range equal to 13.49 mm (Figure 2a), for the true duct it was 1.22 mm for the range 11.30 mm (Figure 2b), while for the false duct it was 1.55 mm for the range 14.02 mm (Figure 2c). In addition, for the common duct 19 points stand out the optimal range, for the true duct 20 points stand out the optimal range, while for the false duct 11 points stand out the optimal range.    The average cross-section for the common duct was equal to 1655.32 ± 258.03 mm and 1509.84 ± 244.77 mm for D F and D Hy , respectively. The average cross-section for the true duct was equal to 346.50 ± 131.90 mm and 268.46 ± 83.92 mm for D F and D Hy , respectively. While, average cross-section for the false duct was equal to 1358.24 ± 281.79 mm and 1139.17 ± 168.42 mm for D F and D Hy , respectively.
For P2 (Figure 1d) average value of diameter for the common duct was equal to 31.91 ± 2.64 mm and 30.90 ± 2.78 mm for D F (Figure 1e) and D Hy (Figure 1f), respectively. The average value of diameter for the true duct was equal to 20.74 ± 1.31 mm and 11.85 ± 1.90 mm for D F and D Hy , respectively. While average value of diameter for the false duct was equal to 27.14 ± 1.50 mm and 22.43 ± 1.44 mm for D F and D Hy , respectively.
Additionally, according to Bland-Altman analysis for the common duct for patient number 2 (P2) the difference between D F and D Hy was equal to 0.56 mm for the range equal to 3.94 mm (Figure 3a), for the true duct it was 3.95 mm for the range 17.60 mm (Figure 3b), while for the false duct it was 2.10 mm for the range 10.13 mm (Figure 3c). Moreover, for the common duct 11 points stand out the optimal range, for the true duct 0 points stand out the optimal range, while for the false duct 6 points stand out the optimal range.
The average cross-section for the common duct was equal to 805. 31  For P3 (Figure 1g) average value of diameter for the common duct was equal to 32.51 ± 2.96 mm and 31.92 ± 2.63 mm for D F and D Hy , respectively. The average value of diameter for the true duct was equal to 17.93 ± 3.53 mm and 9.95 ± 2.84 mm for D F (Figure 1h) and D Hy (Figure 1i), respectively. Furthermore, average value of diameter for the false duct was equal to 30.70 ± 2.61 mm and 25.50 ± 2.68 mm for D F and D Hy , respectively.
Additionally, according to Bland-Altman analysis for the common duct for patient number 3 (P3) the difference between D F and D Hy was equal to 0.16 mm for the range equal to 2.99 mm (Figure 4a), for the true duct it was 5.88 mm for the range 17.89 mm (Figure 4b), while for the false duct it was 3.83 mm for the range 12.07 mm (Figure 4c). What is more, for the common duct 12 points stand out the optimal range, for the true duct 0 points stand out the optimal range, while for the false duct 9 points stand out the optimal range.
The average cross-section for common duct was eq The distance from descending aorta to the diaphragm was analyzed equal to 836.69 ± 147.53 mm and 816.83 ± 120.46 mm for D F and D Hy , respectively. Moreover, average cross-section for the true duct was equal to 262.27 ± 92.29 mm and 139.82 ± 53.46 mm for D F and D Hy , respectively. While, average cross-section for the false duct was equal to 745.58 ± 125.29 mm and 625.40 ± 106.64 mm for Feret and Hydraulic diameter, respectively.

Brightness Value Analysis
Next, brightness value for each cross-section for all three patients was analyzed. It was observed that with decrease of diameter, brightness value increased for the common duct for both D F and D Hy ( Figure 5). For P1 decrease of diameter was from 49.27 to 47.37 (calculated for D F ) and from 43.62 to 43.08 (calculated for D Hy ) indicating an increase of brightness value from 161.51 to 164.81 for the common duct (for cross-section 3 and 4) ( Figure 6). Similar trend was observed for the true and false ducts. Decrease of diameter for P1 for the false duct was from 26.65 to 20.80 (calculated for D F ) and from 19.         Additionally, average difference between the common and false duct for all three patients was equal to 13.50 ± 8.31. Meanwhile, average difference between the true and false duct was equal to 60.33 ± 34.89. Furthermore, average difference between the common and true duct was equal to 51.30 ± 23.37 (Table 2).   Additionally, average difference between the common and false duct for all three patients was equal to 13.50 ± 8.31. Meanwhile, average difference between the true and false duct was equal to 60.33 ± 34.89. Furthermore, average difference between the common and true duct was equal to 51.30 ± 23.37 (Table 2).  Additionally, average difference between the common and false duct for all three patients was equal to 13.50 ± 8.31. Meanwhile, average difference between the true and false duct was equal to 60.33 ± 34.89. Furthermore, average difference between the common and true duct was equal to 51.30 ± 23.37 (Table 3).
It was also observed that each time when dissection appeared, brightness value in the true lumen was smaller compare to the common duct. While, brightness value calculated for the false lumen each time was higher compare to the common duct. For P1 when the common duct was divided into true and false (for cross-section 96 and 97) brightness value was changed from 178.15 (common duct) (Figure 8a) into 147.98 (true lumen) and 187.83 (false lumen) (Figure 8b). While, for the case when connection of the true and false duct appeared, brightness value between true and false lumen was observed. For P1 when true and false duct created common duct (for cross-section 115 and 116) brightness value was changed from 124.97 (true duct) and 176.57 (false duct) (Figure 9a) into 154.89 (common duct) (Figure 9b). It was also observed that each time when dissection appeared, brightness value in the true lumen was smaller compare to the common duct. While, brightness value calculated for the false lumen each time was higher compare to the common duct. For P1 when the common duct was divided into true and false (for cross-section 96 and 97) brightness value was changed from 178.15 (common duct) (Figure 8a) into 147.98 (true lumen) and 187.83 (false lumen) (Figure 8b). While, for the case when connection of the true and false duct appeared, brightness value between true and false lumen was observed. For P1 when true and false duct created common duct (for cross-section 115 and 116) brightness value was changed from 124.97 (true duct) and 176.57 (false duct) (Figure 9a) into 154.89 (common duct) (Figure 9b).   It was also observed that each time when dissection appeared, brightness value in the true lumen was smaller compare to the common duct. While, brightness value calculated for the false lumen each time was higher compare to the common duct. For P1 when the common duct was divided into true and false (for cross-section 96 and 97) brightness value was changed from 178.15 (common duct) (Figure 8a) into 147.98 (true lumen) and 187.83 (false lumen) (Figure 8b). While, for the case when connection of the true and false duct appeared, brightness value between true and false lumen was observed. For P1 when true and false duct created common duct (for cross-section 115 and 116) brightness value was changed from 124.97 (true duct) and 176.57 (false duct) (Figure 9a) into 154.89 (common duct) (Figure 9b).

Difference in Brightness Value and Diameter
Finally, difference in brightness value (Table 4) and diameter (Tables 5 and 6) was analyzed. It was observed that an increase of difference in diameter indicated a decrease of difference in brightness value. For P1 increase of difference in diameter from 0.13 to 0.33 (calculated for D F ) and from 0.40 to 0.54 (calculated for D Hy ) indicated a decrease of difference in brightness value from 0.18 to 0.11 (for cross-section 11 and 12) ( Figure 10). Table 4. Average difference in brightness value included standard deviation (±SD).

Patient Difference in Diameter
Pat I 0.46 ± 0.12 Pat II 0.56 ± 0.14 Pat III 0.45 ± 0.16 Table 6. Average difference in diameter for hydraulic diameter included standard deviation (±SD).

Discussion
The paper presents a new computational approach to standardize the image processing technique for the virtual prediction of blood hemodynamic in the area of aortic acute type B dissection. The novelty of this paper is associated with combination of brightness and diameter analysis to detect changes in blood hemodynamics in true and false channel simultaneously. We investigated how different configuration of aortic duct affects brightness intensity which reflects blood hemodynamic in this area. In our study analysis of Feret and hydraulic diameters, enabled to estimate the effect of changes in flow conditions in the region of false and true lumen connection.

Discussion
The paper presents a new computational approach to standardize the image processing technique for the virtual prediction of blood hemodynamic in the area of aortic acute type B dissection. The novelty of this paper is associated with combination of brightness and diameter analysis to detect changes in blood hemodynamics in true and false channel simultaneously. We investigated how different configuration of aortic duct affects brightness intensity which reflects blood hemodynamic in this area. In our study analysis of Feret and hydraulic diameters, enabled to estimate the effect of changes in flow conditions in the region of false and true lumen connection. Moreover, contrast enhancement analysis allowed deduction of blood hemodynamic including tearing position which may support the present model of radiological diagnosis limited to diameter analysis [30,31]. Additionally, there are situations when the pressure in both channels is equal, and then there will be no drug force and a patient may suffer from ischemia. Therefore, contrast enhancement in blood hemodynamic analysis provides information about the potential risk of such flow stagnation and for instance show places with potential risk of ischemia and/or thrombosis. It may even indicate the places of tears appearance in the intima, which is crucial and is not detected during diameter analysis. Of note, the amount of applied contrast is a constant parameter in the aorta and its concentration is a function of blood hemodynamic. Thus, both phenomena are correlated.
Analysis of spatial configuration of aortas confirmed that appearance of wall dissection had an impact on blood hemodynamic. Higher brightness was observed in the area of dissociation. It was in line with Rudenick et al. who noticed that tears existence and its size had impact on blood flow and velocity [40]. Also, Ahmed et al. indicated that a small tear decreases false lumen flow and velocity [41].
A similar approach was applied by Cheng et al. who successfully verified computational model with phase contrast magnetic resonance imaging (PC MRI) [42]. Changes in velocity profiles were based on the changes in spatial configuration of the geometry of aorta and aortic branches.
Moreover, it was noticed that higher brightness value appeared in the false ducts compare to the true ducts. It was in line with Dillon-Murphy et al. who found that during dissection around 80% of stroke volume enters the false lumen, which may further increase the dilation of the aorta [43]. Furthermore, it was recently described that changes in flow conditions influence mechanical properties of vessels [44][45][46]. Also Cheng et al. reported that high values of Wall Shear Stress around the entry tear inside the true lumen, could increase the likelihood of tear expansion [8]. Additionally, Doyle et al. observed that peak wall stress values are influenced by vessel centreline asymmetry and maximum diameter [47].

Limitations to the Study
Although our study demonstrates the novel methodology for the description of blood hemodynamic it has some limitations. Firstly, we analyzed only acute type IIIb aortic dissection (the distance from descending aorta to the diaphragm), therefore the obtained data may not be applicable for other types of aortic dissections without initial verification. Moreover, the small sample size could influence the obtained results. However, the patients were carefully selected to uniform the group, hence we believe the obtained results may be applicable to similar cases. Secondly, simulations accuracy depends on the resolution of CTA data. The higher the resolution the better is the three-dimensional reconstruction and the final results of brightness values reconstruction. The next step would be to extend this study and analyze wider group of patients. Moreover, in present study we analyze only patients before endovascular aortic repair. We are aware that metal structures from prosthesis may affect the brightness analysis and we would like to include this parameter in our further work.

Conclusions
In summary, the performed analysis of reconstructed aortic dissection from MR images enabled visualization of dissection cross-section and brightness distribution.
Our study indicates that brightness parameter is directly connected with the dissection appearance. Each time when connection of the true duct and false duct appeared, the true duct had lower brightness compare to the common and false duct. Moreover, false duct was characterized with higher brightness compare to the common duct. Therefore, the described method may become a useful non-invasive quantitative tool for the characterization of blood hemodynamic in the area of dissection.