Development of a Patient-Specific Multi-Scale Model to Understand Atherosclerosis and Calcification Locations: Comparison with In vivo Data in an Aortic Dissection

Patient-Specific Numerical Simulations of Coronary Artery Hemodynamics and Biomechanics: A Pathway to Clinical Use

PURPOSE

Numerical models that simulate the behaviors of the coronary arteries have been greatly improved by the addition of fluid-structure interaction (FSI) methods. Although computationally demanding, FSI models account for the movement of the arterial wall and more adequately describe the biomechanical conditions at and within the arterial wall. This offers greater physiological relevance over Computational Fluid Dynamics (CFD) models, which assume the walls do not move or deform. Numerical simulations of patient-specific cases have been greatly bolstered by the use of imaging modalities such as Computed Tomography Angiography (CTA), Magnetic Resonance Imaging (MRI), Optical Coherence Tomography (OCT), and Intravascular Ultrasound (IVUS) to reconstruct accurate 2D and 3D representations of artery geometries. The goal of this study was to conduct a comprehensive review on CFD and FSI models on coronary arteries, and evaluate their translational potential.

METHODS

This paper reviewed recent work on patient-specific numerical simulations of coronary arteries that describe the biomechanical conditions associated with atherosclerosis using CFD and FSI models. Imaging modality for geometry collection and clinical applications were also discussed.

RESULTS

Numerical models using CFD and FSI approaches are commonly used to study biomechanics within the vasculature. At high temporal and spatial resolution (compared to most cardiac imaging modalities), these numerical models can generate large amount of biomechanics data.

CONCLUSIONS

Physiologically relevant FSI models can more accurately describe atherosclerosis pathogenesis, and help to translate biomechanical assessment to clinical evaluation.

Effect of Beta Blockers on the Hemodynamics and Thrombotic Risk of Coronary Artery Aneurysms in Kawasaki Disease

This study aims to simulate beta blockers' (BB) effects on coronary artery aneurysms' (CAA) hemodynamics and thrombotic risk in Kawasaki disease (KD). BB are recommended in cases of large aneurysms due to their anti-ischemic effect. Coronary blood flow (CBF) was simulated in KD patient-specific CAA models using computational fluid dynamics. Hemodynamic indices that correlate with thrombotic risk were calculated following two possible responses to BB: (1) preserved coronary flow (third BB generation) and (2) reduction in coronary flow (first and second BB generations) at reduced heart rate. Following CBF reduction scenario, mean TAWSS and HOLMES significantly decreased compared to normal conditions, leading to a potential increase in thrombotic risk. Preserved CBF at lower heart rates, mimicking the response to vasodilating BBs, does not significantly affect local CAA hemodynamics compared with baseline, while achieving the desired anti-ischemic effects. Different BB generations lead to different hemodynamic responses in CAA.

In-silico investigations of haemodynamic parameters for a blunt thoracic aortic injury case

Accounting for 1.5% of thoracic trauma, blunt thoracic aortic injury (BTAI) is a rare disease with a high mortality rate that nowadays is treated mostly via thoracic endovascular aortic repair (TEVAR). Personalised computational models based on fluid-solid interaction (FSI) principals not only support clinical researchers in studying virtual therapy response, but also are capable of predicting eventual outcomes. The present work studies the variation of key haemodynamic parameters in a clinical case of BTAI after successful TEVAR, using a two-way FSI model. The three-dimensional (3D) patient-specific geometries of the patient were coupled with three-element Windkessel model for both prior and post intervention cases, forcing a correct prediction of blood flow over each section. Results showed significant improvement in velocity and pressure distribution after stenting. High oscillatory, low magnitude shear (HOLMES) regions require careful examination in future follow-ups, since thrombus formation was confirmed in some previously clinically reported cases of BTAI treated with TEVAR. The strength of swirling flows along aorta was also damped after stent deployment. Highlighting the importance of haemodynamic parameters in case-specific therapies. In future studies, compromising motion of aortic wall due to excessive cost of FSI simulations can be considered and should be based on the objectives of studies to achieve a more clinical-friendly patient-specific CFD model.

In silico model of atherosclerosis with individual patient calibration to enable precision medicine for cardiovascular disease

OBJECTIVE

Guidance for preventing myocardial infarction and ischemic stroke by tailoring treatment for individual patients with atherosclerosis is an unmet need. Such development may be possible with computational modeling. Given the multifactorial biology of atherosclerosis, modeling must be based on complete biological networks that capture protein-protein interactions estimated to drive disease progression. Here, we aimed to develop a clinically relevant scale model of atherosclerosis, calibrate it with individual patient data, and use it to simulate optimized pharmacotherapy for individual patients.

APPROACH AND RESULTS

The study used a uniquely constituted plaque proteomic dataset to create a comprehensive systems biology disease model for simulating individualized responses to pharmacotherapy. Plaque tissue was collected from 18 patients with 6735 proteins at two locations per patient. 113 pathways were identified and included in the systems biology model of endothelial cells, vascular smooth muscle cells, macrophages, lymphocytes, and the integrated intima, altogether spanning 4411 proteins, demonstrating a range of 39-96% plaque instability. After calibrating the systems biology models for individual patients, we simulated intensive lipid-lowering, anti-inflammatory, and anti-diabetic drugs. We also simulated a combination therapy. Drug response was evaluated as the degree of change in plaque stability, where an improvement was defined as a reduction of plaque instability. In patients with initially unstable lesions, simulated responses varied from high (20%, on combination therapy) to marginal improvement, whereas patients with initially stable plaques showed generally less improvement.

CONCLUSION

In this pilot study, proteomics-based system biology modeling was shown to simulate drug response based on atherosclerotic plaque instability with a power of 90%, providing a potential strategy for improved personalized management of patients with cardiovascular disease.

A stable and quantitative method for dimensionality reduction of aortic centerline

Aortic dissection (AD) is a fatal aortic disease with high mortality. Assessing the morphology of the aorta is critical for diagnostic and surgical decisions. Aortic centerline projection methods have been used to evaluate the morphology of the aorta. However, there is a big difference between the current model of primary plane projection (PPP) and the actual shape of individuals, which is not conducive to morphological statistical analysis. Finding a method to compress the three-dimensional information of the aorta into two dimensions is helpful to clinical decision-making. In this paper, the evaluation parameters, including contour length (CL), enclosure area, and the sum of absolute residuals (SAR), were introduced to objectively evaluate the optimal projection plane rather than artificial subjective judgment. Our results showed that the optimal projection plane could be objectively characterized by the three evaluation parameters. As the morphological criterion, SAR is optimal among the three parameters. Compared to the optimal projection plane selected by traditional PPP, our method has better AD discrimination in the analysis of aortic tortuosity, and is conducive to the clinical operation of AD. Thus, it has application prospects for the preprocessing techniques for the geometric morphology analysis of AD.

Using a reduced-order model to investigate the effect of the heart rate on the aortic dissection

The computational cost of a three-dimensional (3D) fluid-structure interaction (FSI) simulation of a dissected aorta has prevented researchers from investigating the effect of a wide range of the heart rate on the hemodynamic quantities in the disease. We have presented a systematic procedure to develop a zero-dimensional (0D) model for a dissected aorta. A series of numerical experiments were used to calculate the values for the resistance, inertance, and compliance of each lumen with irregular geometries. Having validated the results from the 0D model against those from the 3D model for one heart rate, we used the 0D model to investigate the effect of the heart rate of 50-150 bpm on the flow rates and the pressures in an idealized geometry of an aortic dissection. The 0D model showed acceptable accuracy when compared with the 3D FSI simulation. For instance, at peak systole, 7.18% relative error in the flow rate in the true lumen was observed for 0D and 3D simulations. The flow rate in the true lumen showed a stronger dependency on the heart rate, that is, 300% for the true lumen and 1.5% for the false lumen. The pressure difference between the lumina increased non-monotonically as the heart beats faster. Because of its efficiency, the reported procedure can be used for uncertainty and sensitivity analysis of the hemodynamic quantities in a diseased aorta with complex geometries such as that of the aortic dissection.

Numerical modeling of residual type B aortic dissection: longitudinal analysis of favorable and unfavorable evolution

Residual type B aortic dissection was numerically investigated to highlight the contribution of biomechanical parameters to the pathology's evolution. Patient-specific geometries from cases involving both favorable and unfavorable evolution were modeled to assess their hemodynamic features. This original approach was supported by a longitudinal study confirming the association between morphological changes, hemodynamic features, adverse clinical outcomes, and CT-angioscan observations on the same patient. Comparing one patient with unfavorable evolution with one with favorable one, we identify potential biomechanical indicators predictive of unfavorable evolution: (i) a patent false lumen with a flow rate above 50% of inlet flow rate; (ii) high wall shear stress above 18 Pa at entry tears, and above 10 Pa at some regions of the false lumen wall; (iii) low time-averaged wall shear stress in distal false lumen below 0.5 Pa; (iv) vortical structure dynamics. Although these comparisons could only be conducted on 2 patients and need to be confirmed by a larger number of cases, our findings point to these hemodynamic markers as possible candidates for early evaluation of the pathology's evolution towards an unfavorable scenario. Graphical Abstract Correlation between hemodynamics index and thrombus initiation for unfavorable case. ET₂ and ET₃ are entry tear numbers 2 and 3 respectively. WSS is wall shear stress. TAWSS is time average shear stress.

The effect of beta-blockers on hemodynamic parameters in patient-specific blood flow simulations of type-B aortic dissection: a virtual study

Aortic dissection (AD) is one of the fatal and complex conditions. Since there is a lack of a specific treatment guideline for type-B AD, a better understanding of patient-specific hemodynamics and therapy outcomes can potentially control the progression of the disease and aid in the clinical decision-making process. In this work, a patient-specific geometry of type-B AD is reconstructed from computed tomography images, and a numerical simulation using personalised computational fluid dynamics (CFD) with three-element Windkessel model boundary condition at each outlet is implemented. According to the physiological response of beta-blockers to the reduction of left ventricular contractions, three case studies with different heart rates are created. Several hemodynamic features, including time-averaged wall shear stress (TAWSS), highly oscillatory, low magnitude shear (HOLMES), and flow pattern are investigated and compared between each case. Results show that decreasing TAWSS, which is caused by the reduction of the velocity gradient, prevents vessel wall at entry tear from rupture. Additionally, with the increase in HOLMES value at distal false lumen, calcification and plaque formation in the moderate and regular-heart rate cases are successfully controlled. This work demonstrates how CFD methods with non-invasive hemodynamic metrics can be developed to predict the hemodynamic changes before medication or other invasive operations. These consequences can be a powerful framework for clinicians and surgical communities to improve their diagnostic and pre-procedural planning.

The effect of coarctation degrees on wall shear stress indices

Coarctation of the aorta (CoA) is a congenital tightening of the proximal descending aorta. Flow quantification can be immensely valuable for an early and accurate diagnosis. However, there is a lack of appropriate diagnostic approaches for a variety of cardiovascular diseases, such as CoA. An accurate understanding of the disease depends on measurements of the global haemodynamics (criteria for heart function) and also the local haemodynamics (detailed data on the dynamics of blood flow). Playing a significant role in clinical processes, wall shear stress (WSS) cannot be measured clinically; thus, computation tools are needed to give an insight into this crucial haemodynamic parameter. In the present study, in order to enable the progress of non-invasive approaches that quantify global and local haemodynamics for different CoA severities, innovative computational blueprint simulations that include fluid-solid interaction models are developed. Since there is no clear approach for managing the CoA regarding its severity, this study proposes the use of WSS indices and pressure gradient to better establish a framework for treatment procedures in CoA patients with different severities. This provides a platform for improving CoA therapy on a patient-specific level, in which physicians can perform treatment methods based on WSS indices on top of using a mere experience. Results show how severe CoA affects the aorta in comparison to the milder cases, which can give the medical community valuable information before and after any intervention.

The effect of the entry and re-entry size in the aortic dissection: a two-way fluid-structure interaction simulation

Aortic dissection (AD) is one of the most catastrophic cardiovascular diseases. AD occurs when a layer inside the aorta is disrupted and gives rise to the formation of a true lumen and a false lumen. These lumens can be connected through tears in the intimal flap which are known as entries. Despite being known for about two centuries, the effects of many factors on the morbidity and mortality of this disease are still unknown. As the blood interaction with the aorta is crucial in the severity and the progression of the aortic dissection, a biomechanical approach is chosen to investigate the influence of different morphologies on the severity of this disease. Using the finite element method (FEM) and the fluid-structure interaction (FSI) approach, we have evaluated the blood flow characteristics along the diseased aorta, in conjunction with the deformation of the aortic wall. In this study, an idealized geometry of a dissected descending aorta (type B) with two entries has been studied. The values for the diameter of the entry tear were chosen to be 5 mm and 10 mm. Therefore, a total of four conditions were investigated. According to our results, the retrograde flow through the proximal tear is dependent on the size of the distal re-entry and vice versa. Our results revealed that when both entry and re-entry tears are 10 mm in diameter, the flow passes through the true and false lumens with smaller resistance, resulting in a smaller flutter of the intimal flap, and therefore more stable intimal flap. Major oscillation frequencies of 2.5 Hz and 7.4 Hz were observed for the oscillation of the intimal flap, and amplitudes of the waves with higher frequencies were negligible.

Multiscale, patient-specific computational fluid dynamics models predict formation of neointimal hyperplasia in saphenous vein grafts

Stenosis due to neointimal hyperplasia (NIH) is among the major causes of peripheral graft failure. Its link to abnormal hemodynamics in the graft is complex, and isolated use of hemodynamic markers is insufficient to fully capture its progression. Here, a computational model of NIH growth is presented, establishing a link between computational fluid dynamics simulations of flow in the lumen and a biochemical model representing NIH growth mechanisms inside the vessel wall. For all three patients analyzed, NIH at proximal and distal anastomoses was simulated by the model, with values of stenosis comparable to the computed tomography scans.

An in silico study of the influence of vessel wall deformation on neointimal hyperplasia progression in peripheral bypass grafts

Neointimal hyperplasia (NIH) is a major obstacle to graft patency in the peripheral arteries. A complex interaction of biomechanical factors contribute to NIH development and progression, and although haemodynamic markers such as wall shear stress have been linked to the disease, these have so far been insufficient to fully capture its behaviour. Using a computational model linking computational fluid dynamics (CFD) simulations of blood flow with a biochemical model representing NIH growth mechanisms, we analyse the effect of compliance mismatch, due to the presence of surgical stitches and/or to the change in distensibility between artery and vein graft, on the haemodynamics in the lumen and, subsequently, on NIH progression. The model enabled to simulate NIH at proximal and distal anastomoses of three patient-specific end-to-side saphenous vein grafts under two compliance-mismatch configurations, and a rigid wall case for comparison, obtaining values of stenosis similar to those observed in the computed tomography (CT) scans. The maximum difference in time-averaged wall shear stress between the rigid and compliant models was 3.4 Pa, and differences in estimation of NIH progression were only observed in one patient. The impact of compliance on the haemodynamic-driven development of NIH was small in the patient-specific cases considered.

A multiscale modelling approach to understand atherosclerosis formation: A patient-specific case study in the aortic bifurcation

Atherogenesis, the formation of plaques in the wall of blood vessels, starts as a result of lipid accumulation (low-density lipoprotein cholesterol) in the vessel wall. Such accumulation is related to the site of endothelial mechanotransduction, the endothelial response to mechanical stimuli and haemodynamics, which determines biochemical processes regulating the vessel wall permeability. This interaction between biomechanical and biochemical phenomena is complex, spanning different biological scales and is patient-specific, requiring tools able to capture such mathematical and biological complexity in a unified framework. Mathematical models offer an elegant and efficient way of doing this, by taking into account multifactorial and multiscale processes and mechanisms, in order to capture the fundamentals of plaque formation in individual patients. In this study, a mathematical model to understand plaque and calcification locations is presented: this model provides a strong interpretability and physical meaning through a multiscale, complex index or metric (the penetration site of low-density lipoprotein cholesterol, expressed as volumetric flux). Computed tomography scans of the aortic bifurcation and iliac arteries are analysed and compared with the results of the multifactorial model. The results indicate that the model shows potential to predict the majority of the plaque locations, also not predicting regions where plaques are absent. The promising results from this case study provide a proof of concept that can be applied to a larger patient population.

Understanding the Effect of Statins and Patient Adherence in Atherosclerosis via a Quantitative Systems Pharmacology Model Using a Novel, Hybrid, and Multi-Scale Approach

Background and Objective: Statins are one of the most prescribed drugs to treat atherosclerosis. They inhibit the hepatic HMG-CoA reductase, causing a reduction of circulating cholesterol and LDL levels. Statins have had undeniable success; however, the benefits of statin therapy crystallize only if patients adhere to the prescribed treatment, which is far away from reality since adherence decreases with time with around half of patients discontinue statin therapy within the first year. The objective of this work is to; firstly, demonstrate a formal in-silico methodology based on a hybrid, multiscale mathematical model used to study the effect of statin treatment on atherosclerosis under different patient scenarios, including cases where the influence of medication adherence is examined and secondly, to propose a flexible simulation framework that allows extensions or simplifications, allowing the possibility to design other complex simulation strategies, both interesting features for software development. Methods: Different mathematical modeling paradigms are used to present the relevant dynamic behavior observed in biological/physiological data and clinical trials. A combination of continuous and discrete event models are coupled to simulate the pharmacokinetics (PK) of statins, their pharmacodynamic (PD) effect on lipoproteins levels (e.g., LDL) and relevant inflammatory pathways whilst simultaneously studying the dynamic effect of flow-related variables on atherosclerosis progression. Results: Different scenarios were tested showing the impact of: (1) patient variability: a virtual population shows differences in plaque growth for different individuals could be as high as 100%; (2) statin effect on atherosclerosis: it is shown how a patient with a 1-year statin treatment will reduce his plaque growth by 2-3% in a 2-year period; (3) medical adherence: we show that a patient missing 10% of the total number of doses could increase the plaque growth by ~1% (after 2 years) compared to the same "regular" patient under a 1-year treatment with statins. Conclusions: The results in this paper describe the effect of pharmacological intervention combined with biological/physiological or behavioral factors in atherosclerosis progression and treatment in specific patients. It also provides an exemplar of basic research that can be practically developed into an application software.

Patient-Specific, Multi-Scale Modeling of Neointimal Hyperplasia in Vein Grafts

Neointimal hyperplasia is amongst the major causes of failure of bypass grafts. The disease progression varies from patient to patient due to a range of different factors. In this paper, a mathematical model will be used to understand neointimal hyperplasia in individual patients, combining information from biological experiments and patient-specific data to analyze some aspects of the disease, particularly with regard to mechanical stimuli due to shear stresses on the vessel wall. By combining a biochemical model of cell growth and a patient-specific computational fluid dynamics analysis of blood flow in the lumen, remodeling of the blood vessel is studied by means of a novel computational framework. The framework was used to analyze two vein graft bypasses from one patient: a femoro-popliteal and a femoro-distal bypass. The remodeling of the vessel wall and analysis of the flow for each case was then compared to clinical data and discussed as a potential tool for a better understanding of the disease. Simulation results from this first computational approach showed an overall agreement on the locations of hyperplasia in these patients and demonstrated the potential of using new integrative modeling tools to understand disease progression.

Multi-component model of intramural hematoma

A novel multi-component model is introduced for studying interaction between blood flow and deforming aortic wall with intramural hematoma (IMH). The aortic wall is simulated by a composite structure submodel representing material properties of the three main wall layers. The IMH is described by a poroelasticity submodel which takes into account both the pressure inside hematoma and its deformation. The submodel of the hematoma is fully coupled with the aortic submodel as well as with the submodel of the pulsatile blood flow. Model simulations are used to investigate the relation between the peak wall stress, hematoma thickness and permeability in patients of different age. The results indicate that an increase in hematoma thickness leads to larger wall stress, which is in agreement with clinical data. Further simulations demonstrate that a hematoma with smaller permeability results in larger wall stress, suggesting that blood coagulation in hematoma might increase its mechanical stability. This is in agreement with previous experimental observations of coagulation having a beneficial effect on the condition of a patient with the IMH.