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Procedia Computer Science Volume 51, 2015, Pages 1118–1127 ICCS 2015 International Conference On Computational Science

A Multiscale and Patient-Specific Computational Framework of Atherosclerosis Formation and Progression: A Case Study in the Aorta and Peripheral Arteries Giulia Di Tomaso1, Cesar Pichardo-Almarza1, Obiekezie Agu2 and Vanessa Díaz-Zuccarini1

1

UCL Mechanical Engineering, Multiscale Cardiovascular Engineering Group (MUSE), Torrington Place, WC1E 7JE, London, UK 2 Lead Vascular Surgeon, Vascular Clinic, University College Hospital, Euston Road [email protected], [email protected]

Abstract Atherosclerosis is the main cause of mortality and morbidity in the western world. Atherosclerosis is a chronic disease defined by life-long processes, with multiple actors playing a role at different biological and time scales. Patient-specific in silico models and simulations can help to understand better the mechanisms of atherosclerosis formation, potentially improving patient management. A conceptual and computational multiscale framework for the modelling of atherosclerosis formation at its early stage was created from the integration of a fluid mechanics model and a biochemical model. The fluid mechanics model describes the interaction between arterial endothelium and blood flow using an artery-specific approach. The low density lipoprotein (LDL) oxidation and consequent immune reaction leading to chronic inflammatory process at the basis of plaque formation was described in the biochemical model. The integration of these modelling approaches led to the creation of a computational framework, an effective tool for the modelling of atherosclerosis plaque development. The model presented in this study was able to capture key features of atherogenesis such as the location of pro-atherogenic areas and to reproduce the formation of plaques detectable from in vivo observations. This framework is being currently tested at University College Hospital (UCH). Keywords: Atherosclerosis, Modelling, Multiscale, Patient-specific, Haemodynamics, CFD, Biochemical, LDL

1 Introduction Atherosclerosis is a degenerative condition in which an artery wall thickens as the result of a buildup of lipids (primarily cholesterol and fatty acids) and fibrosis. The aorta and peripheral arteries are

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Selection and peer-review under responsibility of the Scientiﬁc Programme Committee of ICCS 2015 c The Authors. Published by Elsevier B.V.

doi:10.1016/j.procs.2015.05.281

A Multiscale and Patient-Speciﬁc Computational Framework of Atherosclerosis

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among the prevalent sites for atherosclerosis formation in the human body [1]. Currently, clinical assessment of PAD (peripheral artery disease) is based on criteria such as walking distance and ankle brachial pressure index (ABPI) [2]. Further investigations that confirm the diagnosis on patients showing positive responses to those examinations include Doppler ultrasound imaging, or more invasive imaging techniques such as MRA and CT Angiography. Usually the patient has to undergo these semi-invasive procedures at regular time intervals to monitor the disease progression. A tool able to predict the prevalence and severity of the disease with only one initial invasive procedure required would improve the patients' quality of life, and provide a useful prognostic tool for clinicians. It is within this context that modelling and simulation will play an increasingly important role. Current work in the literature reports on the use of combined biochemical/CFD atherosclerosis models on idealised geometries [3, 4] and for patient-specific simulations [5, 6]. Here, we present the results of a modelling computational framework able to simulate plaque formation during very long time scales for individual patients [7]. This framework is expansible, flexible, fast and easily adaptable. The Vascular Unit at University College Hospital (UCH) supports this work and it is understood that this tool will be improved and refined in time, via our collaboration with UCH. This paper is organised as follows: Section 2 presents the biological process at the basis of atherosclerosis and the model workflow that is the cornerstone of this work. Sections 3 and 4 will present and discuss a patient-specific analysis using the multiscale framework. Finally, Section 5 will present the conclusions.

2 Atherosclerosis Remodelling Cycle: A Simulation Approach to Plaque Formation A key trigger of atherosclerosis formation is the entry of LDL into the subendothelial layer of the vessel [8, 9, 10]. Here LDL oxidises producing an anti-inflammatory reaction: monocytes first adhere to the endothelium, and then penetrate into the intima, where they transform into macrophages (see Figure 1). Macrophages uptake of oxidised LDL (oxLDL) leads to the formation of foam cells, which in turn may be removed by the immune system. This sets up a chronic inflammatory reaction by the secretion of pro-inflammatory cytokines that promote the recruitment of new monocytes and the production of new pro-inflammatory cytokines [11].

A.

B.

Monocyte

Arterial lumen Cytokines Endothelium LDL

oxidized LDL

Foam cell Macrophage

C.

Figure 1: Fatty streak formation. From LDL penetration and oxidation (A.) to foam cell formation (B.) and accumulation leading to intima swelling (C.).

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The atherosclerotic plaque, comprising fibrous cap and lipid deposit, changes the geometry of the vessel and interacts with the blood flow. This interaction may lead to a thrombus, or to the degradation and rupture of the plaque [12]. Whilst it is known that atherosclerosis is linked to environmental factors (e.g. diet) and other patient-specific factors (e.g. metabolism, genetics), plaque growth is also a flow-related problem. Atherosclerotic lesions preferentially localise near side branches or curved vessels [13]. Research has shown that low (or low and oscillating) shear stress is associated with plaque location [14]. Despite ample evidence, the precise mechanism underpinning this association is still not well understood. Evidence suggests that shear stress may act through endothelial gene expression or by a process of localised inflammation. Literature evidence supports a role for both mechanisms [15]. A workflow was developed to create a modelling and simulation tool that would consider the development of the initial state of atherosclerosis, from the penetration of LDL through the arterial wall to the formation of the atherosclerotic plaque. The atherosclerosis remodelling cycle, previously introduced in [7] defines the whole process of plaque formation, capturing key haemodynamic variables that affect the permeability of the endothelium and lumen remodelling as a consequence of atherosclerosis formation. Figure 2 illustrates this workflow, including its core components and the different model time scales [16]. The core elements can be a single or a series of equations and variables (for a mathematical description of the model please refer to [7]). The three arterial subdomains defining the arterial lumen, endothelium and arterial wall are represented by the three white boxes. Each subdomain has a different temporal definition, with the processes inside the arterial wall taking place in a time frame of seconds to weeks. Longer time scales define the endothelium and lumen model, spanning from months to years. The yellow coloured boxes are the patient-specific data used to model the arterial haemodynamics. The orange coloured boxes describe the LDL-related behaviour/processes within the three subdomains. The green coloured boxes define the monocytemacrophage behaviour in the artery. The grey colour boxes represent the starting process (haemodynamics) and the ending process (foam cell formation) modelled in the workflow. The arrows between boxes are an exchange of information from one box (output) to another box (input). The information exchanged is represented in the workflow by the symbol next to the arrow. The Navier-Stokes (NS) equations are used to model the dynamics of blood flow inside the arterial lumen. The endothelial transport properties are influenced by haemodynamic variables, here characterised by wall shear stress (WSS). WSS values are used to model the shear dependent properties of the endothelium represented by the shape index function (SI) [17]. Depending on the value of local WSS, the endothelium will have a proportion of cells that will behave as leaky. As the haemodynamics of the arteries can be very heterogeneous, the SI function was defined linking the endothelial SI with the ratio of local WSS (τ) to the normal WSS (τ0) assumed for the artery under study: ߬ ଴Ǥଷହଷ଻ (1) ܵ‫ ܫ‬ൌ െͲǤʹͶ͵ͷ ή ൬ ൰ ൅ ͲǤͶͲʹͷ ߬଴ with the ‘normal’ arterial WSS (τ0) calculated as [18]: ߬଴ ൌ

Ͷήߤήܳ ߨ ή ‫ݎ‬ଷ

(2)

where μ is the blood viscosity, r is the radius and Q the volumetric flow rate of the considered artery. The quantity of leaky cells Φ characterised by the SI function defines the permeability of the endothelium to LDL [7]. The portion of leaky cells together with the quantity of LDL available for transport, set as a fixed quantity in the lumen (lumen free modelling approach), defines the luminal conditions for the three pores transport model [19]. The constant and homogeneous concentration of

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LDL at the endothelium is a common assumption [20, 6]. In this model the LDL transport through the endothelium is described as a volumetric and solute flux [7]. Having passed through the endothelium LDL enters the arterial wall. Here its transport is characterised by a convection-diffusion-reaction equation, where the convection is driven by the transmural pressure gradient [7]. As LDL accumulates inside the arterial wall, its concentration in the arterial wall changes, altering the transport of LDL through the endothelium, as its solute flux is driven by a concentration gradient [7]. The reaction term accounts for the different LDL degradation processes leading to oxidation of native LDL particles [21]. Patient specific: Arterial geometry

Patient specific: Blood velocity

years

Arterial wall growth

ARTERIAL LUMEN

Haemodynamics : NS Equations Monocytes:

LDL: Lumen-free

Lumen-free

WSS

ENDOTHELIUM Shear dependent endothelium : SI function Ф

months

LDL Monocytes

Three pores transport model LDL flux: Js, Jv

ARTERIAL WALL weeks days

Foam cells Accumulation LDL

LDL : Convection-Diffusion-Reaction

hours min s

Monocytes/Macrophages Reaction

Diffusion-Reaction

Reaction LDL oxidation : Vitamin E-Free

oxLDL

radicals interaction

Temporal Scale

Figure 2: Workflow of the atherosclerosis remodelling cycle. The temporal scale definition can be seen [16]. Please note that the overall model is mechanistic, all the processes in the models are physics/chemistry based.

The presence of oxLDL leads to the recruitment of monocytes from the arterial lumen, initiating the inflammatory process. Monocytes are free to travel through the endothelium and their recruitment is dependent on the quantity of oxLDL. Inside the arterial wall, monocytes turn into macrophages and their transport follows a diffusive-reactive behavior. The reaction term represents the concentration of macrophages that interact with the oxLDL. The interaction between macrophages and the quantity of oxLDL leads to the formation of fatty laden macrophages called foam cells. Unable to leave the arterial wall, foam cells stratify, eventually leading to wall thickening. When the arterial wall growth reaches a threshold value equal to 1% of the arterial radius, the arterial geometry is remodelled,

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leading to the end of the atherosclerosis remodelling cycle. Alteration of lumen geometry caused by arterial wall growth has an impact on the haemodynamics. This influences the overall cycle, creating a feedback loop. After the lumen geometry has been altered, another atherosclerosis remodelling cycle can be initiated to simulate plaque progression further in time.

3 Modelling Atherosclerosis Formation: A Patient-Specific Case The implementation of the computational framework on the case of a patient with multiple plaques will be presented below, based on the model described in Section 2 [7]. Analysis was performed on a portion of the abdominal aorta and the left common iliac artery (CIA) (Figure 3). Descending abdominal aorta

Right CIA

Left CIA

Right EIA

A.

Left EIA

IIA

1

Plaque Patent Lumen

2 3

1

2 3

2 3

B.

Figure 3: a. Diagram of the human circulatory system, with the MSCT segmented 3D arterial geometry considered. Results will be shown in a portion of the abdominal aorta and the left common iliac artery (dashed region). b. MSCT segmented 3D geometries showing in vivo detected plaques (in light blue). Detected plaques within the region of interest are numbered.

Informed consent and approval from the ethical committee were obtained by the managing clinician. Multi-Slice Computed Tomography (MSCT) angiograms were performed with a SOMATOM Sensation Siemens 64 CT-system (Siemens Medical Solutions, Forchheim, Germany). An initial non-contrast enhanced scan was used for plaque scoring and calcification. Scan parameters: slice thickness 5 mm for non-contrast, 1 mm for the contrast; KVP 120, zero gantry/detector tilt, exposure time 500 ms, x-ray tube current of 305 mA for the non-contrast and 325 mA for the contrast,

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rotation direction CW, patient position FFS, convolution Kernel B30f for the non-contrast and B31f for the contrast. ScanIP (Simpleware Ltd, UK) was used for image processing and segmentation. An approximation of the patient’s healthy anatomical state was obtained through segmentation of the vessel lumen, including the detected calcified plaques. Plaque scoring was carried out on non-contrast MSCT slices; the 3D geometry of the lumen with plaques in contrasting colour is shown in Figure 3b. A Delaunay unstructured mesh of the patient’s patent lumen was created in Ansys ICEM CFD (Ansys, Inc., Canonsburg, PA). Prismatic layers were used at the wall boundary. A grid independence study showed that a mesh with 6.9 M elements was suitable to accurately describe the fluid dynamics [6]. At the inlet of the descending aorta a steady, time-averaged mean velocity (U0=24.574 cm/s) with parabolic profile was imposed. Blood flow values were extracted from Doppler echocardiography data taken at the time of the MSCT angiogram. Stress-free condition was imposed at the outlets [7]. In this analysis, artery walls were treated as rigid and blood was considered as a Netwonian fluid [6]. The haemodynamics were modelled with Ansys CfX v.14 (Ansys, Inc., Canonsburg, PA). The transport and biochemical models (within the arterial wall and endothelium) were implemented in Matlab (The MathWorks, Natick, MA). The model is modular and parallelisable, which makes the addition of particular processes simple and efficient, including sub-cellular or molecular mechanisms, such as for example the role of phosphorylation on the lipid-activated nuclear receptor LXR alpha function in macrophages [22], which is the object of current research.

4 Simulation Results and Discussion The Shape Index (SI) function contour plot characterising endothelial cell reaction [7] to local haemodynamics is shown in Figure 4. SI values close to 1 indicate higher presence of leaky cells, highlighting atherosclerosis-prone areas. Plaques detected in the MSCT (Figure 3b) correspond to areas of low WSS, showing an increased SI and endothelial permeability (Figure 4). Regions of slow flow can be identified from velocity contour plots (Figure 5) taken at the location of the atherosclerosis formations (Figure 7) prior to plaque development. Lumen remodelling as a consequence of plaque growth is visualised in Figure 6, where a transversal slice of the lumen has been zoomed in. The contour plot shows the mesh displacement that occurred to accommodate for plaque growth. The diseased lumen has been superimposed to the patent lumen here coloured in black. As this is an early atherosclerosis formation, there is only a slight lumen remodelling. Simulation results (Figure 7) show five plaques in the left CIA, two (a and e) of which closely correspond to plaques observed from MSCT plaque scoring (plaques 1 and 2, Figure 3b). Plaque development occurred in a simulation time of 16 years and 11 months. Time development of atherosclerosis has to be here intended as an effort to simulate the time dynamics as well as the spatial characterisation of atherosclerosis development. Considering remodelling of the arterial wall is a key factor in the atherosclerosis remodelling cycle as the whole process of atherosclerosis formation would change due to the plaque development in time (see Figure 2). Further tuning and validation of the model will be needed to refine the time modelling of plaque growth. The results of the model are encouraging when compared to in vivo observations. All areas showing plaques in vivo (Figure 3) were detected as atherosclerosis-prone, showing an endothelium with higher density of leaky cells (Figure 4). Two of the three plaques detected in vivo were replicated by the model. There was an over-prediction, with plaques developed and atherosclerosis-prone areas detected by the model not having a correspondence with the in vivo observations, suggesting the need to consider other factors when linking the local haemodynamics with the endothelial cell behaviour.

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Figure 4: Endothelial cells SI contour plot. The areas of higher SI indicate increased endothelial permeability.

1 1

4

2 3 4 5

2

5 3

Figure 5: Velocity contour plots at the areas of modelled plaque formation before disease development. Contour plots showed in the geometry are linked with numbers to their enlarged cross section.

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Total Mesh Displacement [m]

Patent Lumen

Figure 6: Total mesh displacement contour plot of plaque a in the left CIA (visualised on a transversal slice). The patent lumen before plaque formation is shown in black. Lumen narrowing due to mesh displacement and plaque formation can be visualised.

d c a

b

Total Mesh Displacement [m]

e

a

b

Figure 7: Total mesh displacement contour plot. Displacement of the mesh representing the arterial lumen indicate plaque formation. Simulated atherosclerosis formations corresponding to plaques observed in vivo from MSCT plaque scoring are plaque a and plaque e.

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Although the flow in this paper is steady-state, the effect of time-average WSS and oscillatory shear index have been identified as important variables to consider [23] in the presence of pulsatile flow. The implementation of transient haemodynamic conditions is currently under investigation to take into account potential WSS minima location changes when considering pulsatile velocity [20]. Anatomical data was obtained from images collected routinely as part of clinical care; increasing the model accuracy without the need of high quality anatomical data is amongst the goals of this model.

5 Conclusions This work presents a computational, expansible, pluralistic, multiscale framework for the study of atherosclerosis that provides the groundwork for a longer-term vision. This vision is that there is now the distinct prospect of harnessing modelling technology that would lead to a better management of the disease. The starting point for this must be an understanding of plaque formation using a combined engineering-mathematical biology approach. The model presented here shows good agreement with in vivo results and further developments will include refinement of cellular and sub-cellular mechanisms in order to capture key individual biomarkers of plaque formation. The framework is able to simulate plaque growth for individual patients and is able to handle long time scales.

References [1]

[2]

[3]

[4]

[5]

[6]

[7]

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M. J. Pentecost, M. H. Criqui, G. Dorros, J. Goldstone, K. W. Johnston, E. C. Martin, E. J. Ring and J. B. Spies, "Guidelines for Peripheral Percutaneous Transluminal Angioplasty of the Abdominal Aorta and Lower Extremity Vessels," Journal of Vascular and Interventional Radiology, vol. 14, no. 9, 2003. M. M. McDermott, S. Mehta, K. Liu, J. M. Guralnik, G. J. Martin, M. H. Criqui and P. Greenland, "Leg symptoms, the ankle-brachial index, and walking ability in patients with peripheral arterial disease," Journal of general internal medicine, vol. 14, 1999. G. Di Tomaso, V. Díaz-Zuccarini and C. Pichardo-Almarza, "A multiscale model of atherosclerotic plaque formation at its early stage.," Biomedical Engineering, IEEE Transactions on, vol. 58, no. 12, pp. 3460-3463, 2011. M. Cilla, E. Pena and M. Martinez, "Mathematical modelling of atheroma plaque formation and development in coronary arteries," Journal of The Royal Society Interface, vol. 11, 2013. N. Filipovic, Z. Teng, M. Radovic, I. Saveljic, D. Fotiadis and O. Parodi, "Computer simulation of three-dimensional plaque formation and progression in the carotid artery," Medical & Biological Engineering & Computing, vol. 51, p. 607–616, 2013. U. Olgac, D. Poulikakos, S. C. Saur, H. Alkadhi and V. Kurtcuoglu, "Patient-specific three-dimensional simulation of LDL accumulation in a human left coronary artery in its healthy and atherosclerotic states.," American Journal of Physiology-Heart and Circulatory Physiology, vol. 296, pp. H1969-H1982, 2009. V. Díaz-Zuccarini, G. Di Tomaso, O. Agu and C. Pichardo-Almarza, "Towards personalised management of atherosclerosis via computational models in vascular clinics: technology based on patient-specific simulation approach," Healthcare Technology Letters, vol. 1, pp. 13-18, 2014.


[8] [9] [10] [11] [12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

Di Tomaso et al.

J. Fan and T. Watanabe, "Inflammatory Reactions in the Pathogenesis of Atherosclerosis.," vol. 10, p. 63–71, 2003. F. Epstein and R. Ross, "Atherosclerosis — An Inflammatory Disease.," vol. 340, 1999. B. Osterud and E. Bjorklid, "Role of Monocytes in Atherogenesis.," vol. 83, 2003. P. Libby, "Inflammation in atherosclerosis," Nature, vol. 420, p. 868–874, 2002. Z.-Y. Li, S. Howarth, R. Trivedi, J. U-King-Im, M. Graves, A. Brown, L. Wang and J. Gillard, "Stress analysis of carotid plaque rupture based on in vivo high resolution MRI," Journal of Biomechanics, vol. 39, p. 2611–2622, 2006. M. Friedman, O. Deters, F. Mark, C. Bargeron and G. Hutchins, "Arterial geometry affects hemodynamics. A potential risk factor for atherosoclerosis," Atherosclerosis, vol. 46, 1983. V. Peiffer, J. S. Spencer and P. D. Weinberg, "Does low and oscillatory wall shear stress correlate spatially with early atherosclerosis? A systematic review.," Cardiovascular research, 2013. C. Cheng, R. de Crom, R. van Haperen, F. Helderman, B. Gourabi, L. van Damme, S. Kirschbaum, C. Slager, A. van der Steen and R. Krams, "The Role of Shear Stress in Atherosclerosis: Action Through Gene Expression and Inflammation?," Cell Biochemistry and Biophysics, vol. 41, p. 279–294, 2004. A. G. Hoekstra, J. L. Falcone, A. Caiazzo and B. Chopard, "Multi-scale modeling with cellular automata: The complex automata approach.," in Cellular Automata, Springer Berlin Heidelberg, 2008, pp. 192-199. M. Levesque, D. Liepsch, S. Moravec and R. Nerem, "Correlation of endothelial cell shape and wall shear stress in a stenosed dog aorta.," Arteriosclerosis, Thrombosis, and Vascular Biology, vol. 6, pp. 220-229, 1986. H. W. Hoogstraten, J. G. Kootstra, B. Hillen, J. K. B. Krijger and P. J. W. Wensing, "Numerical simulation of blood flow in an artery with two successive bends.," Journal of biomechanics, vol. 29, pp. 1075-1083, 1996. F. E. Curry, "Mechanics and thermodynamics of transcapillary exchange," in Handbook of Physiology, The Cardiovascular System, Microcirculation, Am Physiol Soc, 1984, pp. 309-374. N. Sun, N. B. Wood, A. D. Hughes, S. A. Thom and X. Y. Xu, "Influence of Pulsatile Flow on LDL Transport in the Arterial Wall," Annals of biomedical engineering, vol. 35, no. 10, pp. 1782-1790, 2007. C. A. Cobbold, J. A. Sherratt and S. R. J. Maxwell, "Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach.," Bulletin of mathematical biology, vol. 64, pp. 65-95, 2002. B. Pourcet and I. Pineda-Torra, "Transcriptional regulation of macrophage arginase 1 expression and its role in atherosclerosis.," Trends in cardiovascular medicine, vol. 23, pp. 143-152, 2013. J. R. Buchanan, C. Kleinstreuer, S. Hyun and G. A. Truskey, "Hemodynamics simulation and identification of susceptible sites of atherosclerotic lesion formation in a model abdominal aorta.," Journal of biomechanics, vol. 36, no. 8, pp. 1185-1196, 2003.

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