Prediction of coronary plaque location on arteries having myocardial bridge, using finite element models

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 7 ( 2 0 1 4 ) 137–144

journal homepage: www.intl.elsevierhealth.com/journals/cmpb

Prediction of coronary plaque location on arteries having myocardial bridge, using finite element models – Aleksandri´c c , Dalibor Nikoli´c a,b , Milosˇ Radovi´c a,b , Sr dan c a,b,∗ ˇ c , Nenad Filipovi´c Miloje Tomasevi´ a b c

Faculty of Engineering, University of Kragujevac, Sestre Janjic 6, 34000 Kragujevac, Serbia Bioengineering Research and Development Center – BioIRC, Prvoslava Stojanovi´ca 6, 34000 Kragujevac, Serbia Clinic of Cardiology Clinical Center of Serbia, Visegradska 26, 11000 Belgrade, Serbia

a r t i c l e

i n f o

a b s t r a c t

Article history:

This study was performed to evaluate the influences of the myocardial bridges on the plaque

Received 31 December 2013

initializations and progression in the coronary arteries. The wall structure is changed due

Received in revised form

to the plaque presence, which could be the reason for multiple heart malfunctions. Using

25 June 2014

simplified parametric finite element model (FE model) of the coronary artery having myocar-

Accepted 29 July 2014

dial bridge and analyzing different mechanical parameters from blood circulation through

Keywords:

prediction of “the best” position for plaque progression. We chose six patients from the

the artery (wall shear stress, oscillatory shear index, residence time), we investigated the Myocardial bridges

angiography records and used data from DICOM images to generate FE models with our

Finite element method

software tools for FE preprocessing, solving and post-processing. We found a good corre-

WSS

lation between real positions of the plaque and the ones that we predicted to develop at

OSI

the proximal part of the myocardial bridges with wall shear stress, oscillatory shear index

Residence time

and residence time. This computer model could be additional predictive tool for everyday clinical examination of the patient with myocardial bridge. © 2014 Elsevier Ireland Ltd. All rights reserved.

1.

Introduction

Coronary arteries and their major branches, which supply oxygenated and nutrient filled blood to the heart muscle (myocardium), lie on the surface of the heart, in the subepicardial space, between visceral pericardium (epicardium) and myocardium. Sometimes, a shorter or longer segment of the epicardial coronary artery or its branch is covered by a band of heart muscle that lies on top of it. This band of muscle

is called “bridge” and the intramural segment of coronary artery is called “tunneled artery”. Myocardial bridging (MB) is a congenital coronary anomaly defined as a segment of a major epicardial coronary artery that runs intramurally through the myocardium beneath the muscle bridge [1,2]. MB was initially described at autopsy by Reyman [3,4] and again by Black [3,5]. The first post-mortem examination of this anomaly was performed by Geiringer [3,6] while it was first recognized angiographically by Portsman and Iwig [1,3,7]. The typical angiographic finding in MB is systolic compression of

∗ Corresponding author at: Faculty of Engineering, University of Kragujevac, Sestre Janjica 6, 34000 Kragujevac, Serbia. Tel.: +381 34 334 379; fax: +381 34 333 192. ´ E-mail address: fi[email protected] (N. Filipovic). http://dx.doi.org/10.1016/j.cmpb.2014.07.012 0169-2607/© 2014 Elsevier Ireland Ltd. All rights reserved.

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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 7 ( 2 0 1 4 ) 137–144

the bridged segment of the coronary artery that disappears during diastole (“milking effect”) [1,7–10]. MB is the most often localized in the medial segment of the left anterior descending artery (LAD) [1–3,8,10]. The incidence of MB in adults is much higher in histopathology studies (5–86%) than in angiographic ones (0.5–16%) [1,2,9,10]. Angiographically, this anomaly occurs almost exclusively in the medial segment of LAD because the myocardial fibers that cover LAD are the direct extension of the powerful ventricular myocardium that can cause significant and visible systolic narrowing of the arterial lumen [2,9,11]. At autopsy, MB includes not only muscular fibers that overlie LAD, but also the fibers formed by a weak atrial myocardium that covered the left circumflex artery and the right coronary artery (“myocardial loops”) [2,9,11]. MB has been considered a benign anatomic variation, but there are several reports indicating that it could cause myocardial ischemia, arrhythmias, acute coronary syndromes and even sudden cardiac death [1–3,9,10,12,13]. MB causes coronary artery disease by two distinctive mechanisms [12]. One is systolic compression of the intramural segment of LAD, resulting in delayed arterial relaxation during diastole, reduced blood flow reserve and decreased myocardial perfusion [12]. The other is the development of atherosclerosis causing stenosis of the LAD proximal to the MB [12]. It has been widely recognized in autopsy, angiographic and multi-detector computer tomography studies that the intramural and distal segments of LAD remain free from atherosclerotic disease, while the LAD segment just proximal to the MB is vulnerable to atherosclerosis [1,2,6,10,12–18]. Although the mechanism of this discrepancy is largely unknown, there is some evidence that altered hemodynamic force of blood flow caused by systolic compression of the bridged segment of LAD leads to an altered distribution of the atherosclerotic lesions [3,12,14]. The compression of the LAD by overlying myocardial bridge causes retrograde blood flow at the segment proximal to MB at systole, which leads to increased blood flow velocity at early diastole and delayed diastolic relaxation at the bridged segment [1,2,12,13,16,19]. Thus, at the proximal segment of LAD, bidirectional flow occurs, generating an atherogenic low and oscillatory shear stress which may contribute to atherosclerotic plaque formation, whereas within and distal to the MB, the shear stress remains unidirectional and normal or even high which has a protective role in endothelial function [1,2,12,13]. Low and oscillatory shear stress, with a low time-averaged values (<1.5 N/m2 ), leads to the alterations in the expression of vasoactive agents, such as endothelial nitric oxide synthase (eNOS), endothelin-1 (ET-1), angiotensin-converting enzyme (ACE) and growth-promoting and prothrombotic phenotype, ultimately acquiring a predisposition to atherosclerosis [1,13,20,21]. On the other hand, the normal shear stress, with a positive time-average ranging between 1.5 N/m2 and 7.0 N/m2 , increases the production of nitric oxide (NO) in endothelial cells and down regulates the expression of proatherogenic molecules, related to an atheroprotective effect [1,13,20,21]. In addition, scanning electron microscopy reveals changes in the shape of the endothelial cells in LAD intima from flat and polygonal in the segment proximal to the MB to helical, spindle-shaped under the MB [2,12,14]. Similar hemodynamic condition to myocardial bridge is investigated in our previous publication Filipovic [22] where

Fig. 1 – Myocardial bridge – 3D presentation of MB obtained from CT scanner.

we compared numerical and experimental results from Cheng [23]. Mouse carotid vessel is partially obstructed with a cast which modifies the blood flow, and particularly the WSS patterns [23]. The growth of atheromatous plaques is correlated with the reduction of WSS (right before and after the cast). The composition of the plaques turn out to depend upon the WSS pattern: plaques associated with low WSS contain more oxidized LDL (low density lipoprotein), whereas plaques located in zone of recirculating flow (after the cast) contain less oxidized LDL [23]. In our previous publication [22] we investigated numerically the plaque initiation and formation with oxidized LDL, macrophages and foam cells concentrations. We found that for steady state condition low wall shear stress (WSS) appears after the cast which gives more LDL deposition in the recirculation zone. It three-dimensional model we found macrophages distributions in both zones of low WSS and recirculation WSS where more oxidized LDL distribution is found in the zone of low WSS which corresponds to plaque composition of Cheng measurement [23] which corresponds myocardial proximal and distal position of the bridge. Also our model of plaque initiation and progression was tested on real patient data for several patients [24,25]. A typical MB three-dimensional reconstruction from CT scanner is presented in Fig. 1. DICOM slice for MB from CT scanner is shown in Fig. 2. Given this alteration in hemodynamics and its potential impact on endothelial function, this study was designed to test the hypothesis that LAD segment proximal to the MB is prone to atherosclerotic disease. In what follows we firstly described clinical protocols for six patients, geometry of the model, mathematical procedures for solving the problem numerically. Afterwards, some results were given and methods for making correlation are

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 7 ( 2 0 1 4 ) 137–144

Fig. 2 – Myocardial bridge – 2D presentation of MB obtained from CT scanner.

examined statistically. At the end some concluding remarks are described.

2. Dataset section and geometrical modeling From October 2010 to June 2012, we analyzed six patients with previous stent implantation on LAD segment proximal to the MB dues to the clinical symptoms and/or objective signs of myocardial ischemia, without coronary artery disease (CHD) at present state. Pre-defined exclusion criteria were patients younger than 18 years old, present CAD, congenital and acquired valvular heart disease, left ventricular ejection fraction (LVEF) <40%, left ventricular hypertrophy, cardiomyopathias, uncontrolled systemic hypertension, atrial fibrillation, previous aorto-coronary bypass operation (CABG). All invasive studies were part of study protocols which were approved by the Institutional Review Board and Informed consent for the cardiac catheterization, physiologic assessment and transthoracic Doppler echocardiography were obtained from every patient. All antianginal drugs including nitrates, calcium channel blockers and beta-blockers, and also coffee, tea smoking, sugary drinks, chocolate and fruits, were discontinued 24–36 h before the examinations. Cardiac catheterization was performed by the Judkins technique with 6-French catheters using standard femoral percutaneous approach. The postero-anterior projection with cranial angulation or the right anterior oblique projection with cranial angulation was chosen for the assessment of the MB in the medial segment of LAD. Coronary angiograms were performed at the baseline and 1 min after 200 ␮g of intracoronary nitroglycerin. After calibration, a 0.014-in. micromanometer-tipped guide wire (PressureWire, Radi Medical Systems, Uppsala, Sweden) connected to its interface and through the guiding catheter was located approximately 3 cm distal to the MB under fluoroscopy, in order to avoid its entrapment and direct compression by the MB. Maximal hyperemia was obtained with intravenous infusion of adenosine at a dose of 140 ␮g/kg/min. Coronary angiography was then repeated.

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Heart rate and arterial blood pressure were measured at every stage of examination. Average (mean) aortic pressure (Pa), distal intracoronary pressure (Pd) and fractional flow reserve (FFR) were calculated during maximal hyperemia. FFR was defined as the ratio between pressures measured distal to and proximal to the MB during maximal hyperemia (Pd/Pa). Coronary angiography was, furthermore, reviewed offline for quantitative coronary angiography (QCA)-based analysis of minimal lumen diameter (MLD), reference diameter (RD), percent diameter stenosis (%DS), percent area stenosis (%AS) and length of the MB. Measurements were obtained proximal, within, and distal to the MB site in end systole, early diastole (isovolumetric relaxation), mid and late diastole. Vessel diameters (mm) were determined using the guiding catheter as a reference. The %DS and %AS at the most severe site were automatically calculated from the computer estimation of the original dimension of the artery along the MB, defined as an interpolation between proximal and distal RD. The data obtained by QCA method measured in real six patients is presented in Table 1. The measurements were performed in four periods of a heart cycle (end systole, early diastole, mid diastole and end diastole). We choose these six patients in order to validate our computer program. Dynamics movement of the straight part of artery for MB can be approximate with simplified geometrical model of straight tube with deformable wall. Maximal (peak) diastolic coronary flow velocity (CFV) at the baseline and during maximal hyperemia obtained with intravenous infusion of adenosine at dose 140 ␮g/kg/min was measured by transthoracic Doppler echocardiography using ultrasound system (Vivid 7, GE) with a frequency of 4–7 MHz matrix array transducer. Coronary flow reserve (CFR) was calculated as the ratio between peak diastolic CFV and baseline diastolic CFV; final values of flow velocity represented an average of three cardiac cycles.

2.1.

Geometrical modeling

Angiography is a diagnostic method used much more frequently than CT, therefore there is a lack of CT images of the patients having MB. This is the reason why we decided to develop software for generating simulation model based on data from QCA method and CFV. Also QCA measurements provide geometrical data for different time periods of a heart cycle. We generated finite elements model for every individual patient and used our FE in-house solver and analyzed the FE results. For these purposes we developed user friendly software application. The process is shown in Fig. 3. The application was developed in such a manner that the user has a complete freedom in generating FE models, input of geometrical parameters, divisions of mesh and functions of input velocity waveform (Fig. 4). Additionally, the software automatically generates four geometrically different meshes for each of the measured periods of a heart cycle (Fig. 5). Based on these four meshes software interpolate shape of model mesh throughout the cardiac cycle. This mesh movement is very important for accurate computation of blood flow through MB.

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Table 1 – Patient data derived from an artery having MB using QCA software. Diameters [mm] Proximal LAD (LD)

MB

Distal LAD (LD)

End systole

Early diastole

Mid diastole

End diastole

End systole

Early diastole

Mid diastole

End diastole

End systole

Early diastole

Mid diastole

End diastole

3.12 3.16 3.4 3.01 2.59 3.4

3.29 3.25 3.42 3.08 2.72 3.47

3.29 3.36 3.5 3.1 2.72 3.6

3.45 3.5 3.5 3.16 2.78 3.64

1.83 1.58 1.66 1.15 1.76 1.53

1.91 1.65 1.8 1 1.75 1.53

2.07 2.02 1.83 1.59 1.85 1.77

2.16 2.01 1.89 1.48 1.96 2.03

2.7 2.04 2.05 1.83 2.15 2.2

2.75 2.3 2.09 1.9 2.25 2.46

2.75 2.42 2.12 1.94 2.26 2.5

2.78 2.48 2.15 1.96 2.26 2.53

0.27 0.28 0.46 0.31 0.24 0.24

Fig. 3 – Method block diagram.

Description of mathematical method

After mesh generation and setup boundary conditions, the software application automatically starts the solver [21], collects the results and performs post-processing of the results.

2.2.

A finite element model of the bridge was employed. Flow in the coronary artery is a complex, time-dependent,

Fig. 4 – Application dialog menu for geometry set.

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Patient 01 Patient 02 Patient 03 Patient 04 Patient 05 Patient 06

CFV

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In addition to the velocity field, the wall shear stress computation was performed. The mean shear stress  mean within a time interval T is calculated as [27]

  1

mean = 

T

T

0

 

ts dt

(3)

where ts is the surface traction vector. Another scalar quantity is a time-averaged magnitude of the surface traction vector, calculated as

mag

1 = T



T

|ts | dt

(4)

0

Also, a very important scalar in the quantification of unsteady blood flow is the oscillatory shear index (OSI) defined as [27]

OSI =

1 2

 1−

mean mag



REST = ((1 − 2 · OSI) · mag ) Fig. 5 – Generated FE 2D axi-symmetric model meshes during four periods of a heart cycle.

three-dimensional flow. The time-dependent and full threedimensional Navier–Stokes equations have to be solved. A finite element mesh with 6123 2D 4 node axi-symmetric finite elements was generated using an automatic mesh generator as it is presented in Fig. 5. The mesh independence was reached at 5640–20,568 finite elements. The three-dimensional flow of a viscous incompressible fluid considered here is governed by the Navier–Stokes equations and continuity equation that can be written as

 

∂vi ∂v + vj i ∂t ∂xj

∂vi =0 ∂xi



∂p =− + ∂xi



∂2 vj ∂2 vi + ∂xj ∂xj ∂xj ∂xi

 (1)

−1

(6)

In order to make mesh moving algorithm we implemented ALE (arbitrary Lagrangian–Eulerian) formulation for fluid dynamics [28]. The governing equations, which include the Navier–Stokes equations of balance of linear momentum and the continuity equation, can be written in the ALE formulation as [28]. B v∗i + (vj − vm j )vi,j  = −p,i + vi,jj + fi

(7)

vi,i = 0

(8)

are the velocity components of a generic fluid where vi and vm i particle and of the point on the moving mesh occupied by the fluid particle, respectively;  is fluid density, p is fluid pressure,  is dynamic viscosity, and fiB are the body force components. The symbol “*” denotes the mesh-referential time derivative, i.e. the time derivative at a considered point on the mesh:



(2)

where vi is the blood velocity in direction xi ,  is the fluid density, p is pressure,  is the dynamic viscosity; and summation is assumed on the repeated (dummy) indices, i, j = 1, 2, 3. The first equation represents balance of linear momentum, while the Eq. (2) expresses incompressibility condition. Each waveform of and pulsatile flow was discretized into 500 uniformly spaced time steps. In the analysis, it was considered that the convergence was reached when the maximum absolute change in the nondimensional velocity between the respective times in two adjacent cycles was less than 10−3 . The code was validated using the analytical solution for shear stress and the velocities through curve tube [26]. The pressure is eliminated at the element level through the static condensation. A standard Petrov–Galerkin upwind stabilization technique was used for Re number [26].

(5)

∗

() =

∂( )  ∂t 

(9) i =const

and the symbol “,i” denotes partial derivative, i.e. ( ),i =

∂( ) ∂xi

(10)

We use xi and  i as Cartesian coordinates of a generic particle in space and of the corresponding point on the mesh, respectively. The repeated index means summation, from 1 to 3, i.e. j = 1, 2, 3 in Eq. (7), and i = 1, 2, 3 in Eq. (8). In deriving Eq. (7) we used the following expression for the material derivative (corresponding to a fixed material point) D(vi )/Dt:



∂(vj ) ∂(vi )  D(vi ) + (vj − vm = j ) ∂x Dt ∂t  i 

(11)

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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 7 ( 2 0 1 4 ) 137–144

Fig. 7 – FE results diagrams: Shear Stress, Oscillatory shear index, Residence time vs. length.

4.

Fig. 6 – FE result, velocity field presented at the velocity peak.

The derivatives on the right-hand side correspond to a generic point on the mesh, with the mesh-referential derivative and the convective term.

3.

Post-processing FE results

In this study we investigated the effect of mechanical parameters for prediction of plaque growing position using finite element method. The model provided velocity field (Fig. 6) and the diagrams of: Shear Stress, Oscillatory shear index, and Residence time vs. length (Fig. 7). Since the problem is axi-symmetric, we can present the results in a form of a graphic very simply. In Fig. 7, the vertical axe presents mechanical quantities along the model. Shear stress is changed during time steps, therefore the values presented in Fig. 7 are the peak velocity values.

Analyzing results – statistic

In all the cases two positions on the artery for plaque development were examined. For all patients at the position A there is a plaque and at the position B there is no plaque. The aim of our study was to find correlation between these two positions on the artery where they have similar (mechanical) results but NOT the same. The reason for this assumption is: all systemic biological factors in the whole artery are the same, so the trigger for developing plague should be mechanical factor which takes into account anatomy and blood flow. All results from FE calculation were processed by using statistical method F test. For this research we made calculation for six different patients with developed plaque. Two positions A and B on the artery (changing diameter of the arteries) were examined as it is presented in Fig. 7. From patient medical records for all tested patients plaque started to grow at the position A (Fig. 7). WSS, OSI and residence time at two positions A and B are presented in Table 2. By using data from Table 2, we calculated F-values for WSS, OSI and residence time (see Table 3). The critical F-value for this problem is Fcrit (1,10) = 4.96 at significance level ˛ = 0.05. Since calculated F-values (see Table 3) exceed Fcrit , we can conclude that there is a strong evidence that values in YES/NO groups differ (for all three cases: WSS, OSI and residence time). Fig. 8 illustrates how residence time obviously separates spots with and without plaque development.

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 7 ( 2 0 1 4 ) 137–144

Table 2 – WSS, OSI and residence time at two positions A and B. Plaque development

Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6

WSS

OSI

REST

A

B

A

B

A

B

0.9950 0.925 0.7525 0.915 0.9775 0.8575

1.4725 1.1325 0.8375 1.7 1.1175 1.6675

0.15 0.1 0.16 0.105 0.087 0.14

0.1 0.023 0.06 0.001 0.001 0.14

5.812 9.7 8.59 8.73 8.05 8.56

1.843 2.053 2.71 1.82 1.77 1.81

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two models is including dynamics of myocardial bridge model where geometry of artery is changed in time during heart cycle. We are aware that the present results are based on the small number of patients. In future research we will try to verify this correlation on much larger number of patients. Statistic methods which we used provided presented results, but for more comprehensive analysis of the results our goal will be to use data mining “smart methods” (like neural networks, etc.). It will also include analysis of our plaque progression mathematical model which will be compared on larger number of the patients.

Table 3 – F-values for WSS, OSI and residence time.

F-value

WSS

OSI

8.21

7.01

Residence time

Acknowledgments

127.21

This study was funded by a grant from FP7-ICT-2007 project (grant agreement 224297, ARTreat) and grants from Serbian Ministry of Science III41007 and ON174028.

references

Fig. 8 – Residence time values for six patients (proximal and distal).

5.

Discussion and conclusions

We examined six patients with MB and correlation between real positions of plaque location inside the MB (proximal and distal) with WSS, OSI and residence time. For this purpose we developed specific algorithms and software for automatic FE generation mesh, running FE solvers with ALE formulation and automatic mesh moving algorithm and post-processing of the results. CT images give static geometry of artery but QCA measurements provide geometrical data for different time periods of a heart cycle so we can monitor the movement of the artery wall during a heart cycle. Disadvantage of this method is that we do not have a realistic geometry of the patient arteries, but rely on simplify geometric model. It is reasonable because bridge is mostly happening in the straight part and mid-portion of LAD. This method demonstrated very good correlation between the real positions where the plaque started to grow, measured from DICOM images on six patients with coronary bridges with WSS, OSI and residence time in the proximal part of MB for all six patients. Based on these results, we can conclude that the plaque growing position and its development are caused by mechanical forces. MB environment is very similar with our previously published numerical model [22] which we compared with plaque composition of Cheng measurement [23]. We found macrophages distributions in both zones of low WSS and recirculation WSS where more oxidized LDL distribution is found in the zone of low WSS which corresponds to myocardial proximal and distal position of the bridge. Difference between these

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