Aortic dissection is a severe cardiovascular disease caused by the occurrence of a tear in the aortic wall. As a result, the blood penetrates the wall and makes a new blood channel called the false lumen. The haemodynamic conditions in the false lumen may contribute to the formation of thrombi, which influence the patient's diagnosis and outcomes. In this study, the focus is on a haemodynamic-based model of thrombus formation. Since the model construction entails uncertainties in the model parameters, a variance-based sensitivity analysis is performed. Thrombus formation at a backward-facing step is considered as a benchmark for the numerical simulations and sensitivity analysis. This geometry is capable of representing the main contributions of the model in thrombus formation. The study aims at improving the understanding of the model's structure and at preparing model simplifications to enable efficient patient-specific simulations in the future. A polynomial chaos expansion is employed as a surrogate model, from which the quantitative sensitivity indices are derived. In this study, nine model parameters are selected, whose proper values are not well known. The model responses taken into account are the maximum volume fraction of thrombus, its time development, and the thrombus growth rate. The results show that the model lends itself to model reduction since some of the model parameters show little to no influence on the model's outputs. A threshold value related to the concentration of bounded platelets and the bounded platelets reaction rate are identified as the key input parameters dominating the thrombus model predictions in the current geometry. Furthermore, the introduced thrombus characteristic growth time is driven by both the aforementioned variables.
Aortic dissection is a cardiovascular disease with a disconcertingly high mortality. When it comes to diagnosis, medical imaging techniques such as Computed Tomography, Magnetic Resonance Tomography or Ultrasound certainly do the job, but also have their shortcomings. Impedance cardiography is a standard method to monitor a patients heart function and circulatory system by injecting electric currents and measuring voltage drops between electrode pairs attached to the human body. If such measurements distinguished healthy from dissected aortas, one could improve clinical procedures. Experiments are quite difficult, and thus we investigate the feasibility with finite element simulations beforehand. In these simulations, we find uncertain input parameters, e.g., the electrical conductivity of blood. Inference on the state of the aorta from impedance measurements defines an inverse problem in which forward uncertainty propagation through the simulation with vanilla Monte Carlo demands a prohibitively large computational effort. To overcome this limitation, we combine two simulations: one simulation with a high fidelity and another simulation with a low fidelity, and low and high computational costs accordingly. We use the inexpensive low-fidelity simulation to learn about the expensive high-fidelity simulation. It all boils down to a regression problem—and reduces total computational cost after all.
In 2000, Kennedy and O’Hagan proposed a model for uncertainty quantification that combines data of several levels of sophistication, fidelity, quality, or accuracy, e.g., a coarse and a fine mesh in finite-element simulations. They assumed each level to be describable by a Gaussian process, and used low-fidelity simulations to improve inference on costly high-fidelity simulations. Departing from there, we move away from the common non-Bayesian practice of optimization and marginalize the parameters instead. Thus, we avoid the awkward logical dilemma of having to choose parameters and of neglecting that choice’s uncertainty. We propagate the parameter uncertainties by averaging the predictions and the prediction uncertainties over all the possible parameters. This is done analytically for all but the nonlinear or inseparable kernel function parameters. What is left is a low-dimensional and feasible numerical integral depending on the choice of kernels, thus allowing for a fully Bayesian treatment. By quantifying the uncertainties of the parameters themselves too, we show that “learning” or optimising those parameters has little meaning when data is little and, thus, justify all our mathematical efforts. The recent hype about machine learning has long spilled over to computational engineering but fails to acknowledge that machine learning is a big data problem and that, in computational engineering, we usually face a little data problem. We devise the fully Bayesian uncertainty quantification method in a notation following the tradition of E.T. Jaynes and find that generalization to an arbitrary number of levels of fidelity and parallelisation becomes rather easy. We scrutinize the method with mock data and demonstrate its advantages in its natural application where high-fidelity data is little but low-fidelity data is not. We then apply the method to quantify the uncertainties in finite element simulations of impedance cardiography of aortic dissection. Aortic dissection is a cardiovascular disease that frequently requires immediate surgical treatment and, thus, a fast diagnosis before. While traditional medical imaging techniques such as computed tomography, magnetic resonance tomography, or echocardiography certainly do the job, Impedance cardiography too is a clinical standard tool and promises to allow earlier diagnoses as well as to detect patients that otherwise go under the radar for too long.
Purpose This paper aims to introduce a non-invasive and convenient method to detect a life-threatening disease called aortic dissection. A Bayesian inference based on enhanced multi-sensors impedance cardiography (ICG) method has been applied to classify signals from healthy and sick patients. Design/methodology/approach A 3D numerical model consisting of simplified organ geometries is used to simulate the electrical impedance changes in the ICG-relevant domain of the human torso. The Bayesian probability theory is used for detecting an aortic dissection, which provides information about the probabilities for both cases, a dissected and a healthy aorta. Thus, the reliability and the uncertainty of the disease identification are found by this method and may indicate further diagnostic clarification. Findings The Bayesian classification shows that the enhanced multi-sensors ICG is more reliable in detecting aortic dissection than conventional ICG. Bayesian probability theory allows a rigorous quantification of all uncertainties to draw reliable conclusions for the medical treatment of aortic dissection. Originality/value This paper presents a non-invasive and reliable method based on a numerical simulation that could be beneficial for the medical management of aortic dissection patients. With this method, clinicians would be able to monitor the patient’s status and make better decisions in the treatment procedure of each patient.
Aortic dissection is caused by a tear on the aortic wall that allows blood to flow through the wall layers. Usually, this tear involves the intimal and partly the medial layer of the aortic wall. As a result, a new false lumen develops besides the original aorta, denoted then as the true lumen. The local hemodynamic conditions such as flow disturbances, recirculations and low wall shear stress may cause thrombus formation and growth in the false lumen. Since the false lumen status is a significant predictor for late-dissection-related deaths, it is of great importance in the medical management of patients with aortic dissection. The hemodynamic changes in the aorta also alter the electrical conductivity of blood. Since the blood is much more conductive than other tissues in the body, such changes can be identified with non-invasive methods such as impedance cardiography. Therefore, in this study, the capability of impedance cardiography in monitoring thrombosis in the false lumen is studied by multiphysics simulations to assist clinicians in the medical management of patients under treatment.To tackle this problem, a 3D computational fluid dynamics simulation has been set up to model thrombosis in the false lumen and its impact on the blood flow-induced conductivity changes. The electrical conductivity changes of blood have been assigned as material properties of the blood-filled aorta in a 3D finite element electric simulation model to investigate the impact of conductivity changes on the measured impedance from the body's surface.The results show remarkable changes in the electrical conductivity distribution in the measurement region due to thrombosis in the false lumen, which significantly impacts the morphology of the impedance cardiogram. Thus, frequent † Vahid Badeli and Alireza Jafarinia contributed equally to this work
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