Modeling Anisotropic Electrical Conductivity of Blood: Translating Microscale Effects of Red Blood Cell Motion into a Macroscale Property of Blood.

Cardiovascular diseases are a leading global cause of mortality. The current standard diagnostic methods, such as imaging and invasive procedures, are relatively expensive and partly connected with risks to the patient. Bioimpedance measurements hold the promise to offer rapid, safe, and low-cost alternative diagnostic methods. In the realm of cardiovascular diseases, bioimpedance methods rely on the changing electrical conductivity of blood, which depends on the local hemodynamics. However, the exact dependence of blood conductivity on the hemodynamic parameters is not yet fully understood, and the existing models for this dependence are limited to rather academic flow fields in straight pipes or channels. In this work, we suggest two closely connected anisotropic electrical conductivity models for blood in general three-dimensional flows, which consider the orientation and alignment of red blood cells (RBCs) in shear flows. In shear flows, RBCs adopt preferred orientations through a rotation of their membrane known as tank-treading motion. The two models are built on two different assumptions as to which hemodynamic characteristic determines the preferred orientation. The models are evaluated in two example simulations of blood flow. In a straight rigid vessel, the models coincide and are in accordance with experimental observations. In a simplified aorta geometry, the models yield different results. These differences are analyzed quantitatively, but a validation of the models with experiments is yet outstanding.

Monitoring of false lumen thrombosis in type B aortic dissection by impedance cardiography - A multiphysics simulation study.

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 monitoring of impedance cardiography signals may allow tracking the thrombus formation and growth in the false lumen.

Bayesian Uncertainty Quantification with Multi-Fidelity Data and Gaussian Processes for Impedance Cardiography of Aortic Dissection.

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.