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.

Anisotropic minimum dissipation subgrid-scale model in hybrid aeroacoustic simulations of human phonation.

This article deals with large-eddy simulations of three-dimensional incompressible laryngeal flow followed by acoustic simulations of human phonation of five cardinal English vowels, /ɑ, æ, i, o, u/. The flow and aeroacoustic simulations were performed in OpenFOAM and in-house code openCFS, respectively. Given the large variety of scales in the flow and acoustics, the simulation is separated into two steps: (1) computing the flow in the larynx using the finite volume method on a fine moving grid with 2.2 million elements, followed by (2) computing the sound sources separately and wave propagation to the radiation zone around the mouth using the finite element method on a coarse static grid with 33 000 elements. The numerical results showed that the anisotropic minimum dissipation model, which is not well known since it is not available in common CFD software, predicted stronger sound pressure levels at higher harmonics, and especially at first two formants, than the wall-adapting local eddy-viscosity model. The model on turbulent flow in the larynx was employed and a positive impact on the quality of simulated vowels was found.

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.

Error detection and filtering of incompressible flow simulations for aeroacoustic predictions of human voice.

The presented filtering technique is proposed to detect errors and correct outliers inside the acoustic sources, respectively, the first time derivative of the incompressible pressure obtained from large eddy simulations with prescribed vocal fold motion using overlay mesh methods. Regarding the perturbed convective wave equation, the time derivative of the incompressible pressure is the primary sound source in the human phonation process. However, the incompressible pressure can be erroneous and have outliers when fulfilling the divergence-free constraint of the velocity field. This error is primarily occurring for non-conserving prescribed vocal fold motions. Therefore, the method based on a continuous stationary random process was designed to detect rare events in the time derivative of the pressure. The detected events are then localized and treated by a defined window function to increase their probability. As a consequence, the data quality of the non-linearly filtered data is enhanced significantly. Furthermore, the proposed method can also be used to assess convergence of the aeroacoustic source terms, and detect regions and time intervals, which show a non-converging behavior by an impulse-like structure.

3D-FV-FE Aeroacoustic Larynx Model for Investigation of Functional Based Voice Disorders.

For the clinical analysis of underlying mechanisms of voice disorders, we developed a numerical aeroacoustic larynx model, called simVoice, that mimics commonly observed functional laryngeal disorders as glottal insufficiency and vibrational left-right asymmetries. The model is a combination of the Finite Volume (FV) CFD solver Star-CCM+ and the Finite Element (FE) aeroacoustic solver CFS++. simVoice models turbulence using Large Eddy Simulations (LES) and the acoustic wave propagation with the perturbed convective wave equation (PCWE). Its geometry corresponds to a simplified larynx and a vocal tract model representing the vowel /a/. The oscillations of the vocal folds are externally driven. In total, 10 configurations with different degrees of functional-based disorders were simulated and analyzed. The energy transfer between the glottal airflow and the vocal folds decreases with an increasing glottal insufficiency and potentially reflects the higher effort during speech for patients being concerned. This loss of energy transfer may also have an essential influence on the quality of the sound signal as expressed by decreasing sound pressure level (SPL), Cepstral Peak Prominence (CPP), and Vocal Efficiency (VE). Asymmetry in the vocal fold oscillations also reduces the quality of the sound signal. However, simVoice confirmed previous clinical and experimental observations that a high level of glottal insufficiency worsens the acoustic signal quality more than oscillatory left-right asymmetry. Both symptoms in combination will further reduce the quality of the sound signal. In summary, simVoice allows for detailed analysis of the origins of disordered voice production and hence fosters the further understanding of laryngeal physiology, including occurring dependencies. A current walltime of 10 h/cycle is, with a prospective increase in computing power, auspicious for a future clinical use of simVoice.

Helmholtz's decomposition for compressible flows and its application to computational aeroacoustics.

The Helmholtz decomposition, a fundamental theorem in vector analysis, separates a given vector field into an irrotational (longitudinal, compressible) and a solenoidal (transverse, vortical) part. The main challenge of this decomposition is the restricted and finite flow domain without vanishing flow velocity at the boundaries. To achieve a unique and L 2 -orthogonal decomposition, we enforce the correct boundary conditions and provide its physical interpretation. Based on this formulation for bounded domains, the flow velocity is decomposed. Combining the results with Goldstein's aeroacoustic theory, we model the non-radiating base flow by the transverse part. Thereby, this approach allows a precise physical definition of the acoustic source terms for computational aeroacoustics via the non-radiating base flow. In a final simulation example, Helmholtz's decomposition of compressible flow data using the finite element method is applied to an overflowed rectangular cavity at Mach 0.8. The results show a reasonable agreement with the source data and illustrate the distinct parts of the Helmholtz decomposition.

Aeroacoustic source term computation based on radial basis functions.

In low Mach number aeroacoustics, the known disparity of length scales makes it possible to apply well-suited simulation models using different meshes for flow and acoustics. The workflow of these hybrid methodologies include performing an unsteady flow simulation, computing the acoustic sources, and simulating the acoustic field. Therefore, hybrid methods seek for robust and flexible procedures, providing a conservative mesh to mesh interpolation of the sources while ensuring high computational efficiency. We propose a highly specialized radial basis function interpolation for the challenges during hybrid simulations. First, the computationally efficient local radial basis function interpolation in conjunction with a connectivity-based neighbor search technique is presented. Second, we discuss the computation of spatial derivatives based on radial basis functions. These derivatives are computed in a local-global approach, using a Gaussian kernel on local point stencils. Third, radial basis function interpolation and derivatives are used to compute complex aeroacoustic source terms. These ingredients are necessary to provide flexible source term calculations that robustly connect flow and acoustics. Finally, the capabilities of the presented approach are shown in a numerical experiment with a co-rotating vortex pair.

Hybrid aeroacoustic approach for the efficient numerical simulation of human phonation.

A hybrid aeroacoustic approach was developed for the efficient numerical computation of human phonation. In the first step, an incompressible flow simulation on a three-dimensional (3 D) computational grid, which is capable of resolving all relevant turbulent scales, is performed using STARCCM+ and finite volume method. In the second step, the acoustic source terms on the flow grid are computed and a conservative interpolation to the acoustic grid is performed. Finally, the perturbed convective wave equation is solved to obtain the acoustic field in 3 D with the finite element solver CFS++. Thereby, the conservative transformation of the acoustic sources from the flow grid to the acoustic grid is a key step to allow coarse acoustic grids without reducing accuracy. For this transformation, two different interpolation strategies are compared and grid convergence is assessed. Overall, 16 simulation setups are compared. The initial (267 000 degrees of freedom) and the optimized (21 265 degrees of freedom) simulation setup were validated by measurements of a synthetic larynx model. To conclude, the total computational time of the acoustic simulation is reduced by 95% compared to the initial simulation setup without a significant reduction of accuracy, being 7%, in the frequency range of interest.

Aerodynamic impact of the ventricular folds in computational larynx models.

Ventricular folds (VeFs) act as passive, non-moving structures during normal phonation. According to the literature, VeFs potentially aid the flow-driven oscillations of the vocal folds (VFs) that produce the primary sound of human phonation. In this study, large eddy simulations were performed to analyze this influence in a numerical model with imposed VF motion as measured experimentally from a synthetic silicone vocal fold model. Model configurations with and without VeFs were considered. Furthermore, configurations with rectangular and elliptical glottis shapes were simulated to investigate the effects of three-dimensional glottal jet evolutions. Results showed that VeFs increased flow rate and transglottal pressure difference by a decrease in the pressure level in the ventricles immediately downstream of the VFs. This led to an increase in the glottal flow resistance, increased energy transfer rate between the flow and VFs, and a simultaneous decrease in the laryngeal flow resistance, which shows a higher amount of kinetic energy in the glottal flow. This enhancement was more pronounced in the rectangular glottis and varied with the subglottal pressure and VeF gap size.

Computational Models of Laryngeal Aerodynamics: Potentials and Numerical Costs.

Human phonation is based on the interaction between tracheal airflow and laryngeal dynamics. This fluid-structure interaction is based on the energy exchange between airflow and vocal folds. Major challenges in analyzing the phonatory process in-vivo are the small dimensions and the poor accessibility of the region of interest. For improved analysis of the phonatory process, numerical simulations of the airflow and the vocal fold dynamics have been suggested. Even though most of the models reproduced the phonatory process fairly well, development of comprehensive larynx models is still a subject of research. In the context of clinical application, physiological accuracy and computational model efficiency are of great interest. In this study, a simple numerical larynx model is introduced that incorporates the laryngeal fluid flow. It is based on a synthetic experimental model with silicone vocal folds. The degree of realism was successively increased in separate computational models and each model was simulated for 10 oscillation cycles. Results show that relevant features of the laryngeal flow field, such as glottal jet deflection, develop even when applying rather simple static models with oscillating flow rates. Including further phonatory components such as vocal fold motion, mucosal wave propagation, and ventricular folds, the simulations show phonatory key features like intraglottal flow separation and increased flow rate in presence of ventricular folds. The simulation time on 100 CPU cores ranged between 25 and 290 hours, currently restricting clinical application of these models. Nevertheless, results show high potential of numerical simulations for better understanding of phonatory process.

A modified and stable version of a perfectly matched layer technique for the 3-d second order wave equation in time domain with an application to aeroacoustics.

We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems.

Analysis of vocal fold function from acoustic data simultaneously recorded with high-speed endoscopy.

SUMMARY: Acoustic and endoscopic voice assessments are routinely performed to determine the vocal fold vibratory function as part of the voice assessment protocol in clinics. More often than not these data are separately recorded, resulting in information being obtained from two different phonation segments and an increase of time for the voice evaluation process. This study explores the use of acoustic data, simultaneously recorded during high-speed endoscopy (HSE), for the evaluation of vocal fold function. PATIENTS AND METHODS: HSE and acoustic data were recorded from the subjects simultaneously during sustained phonation. The data included voices of 73 healthy subjects, 148 paresis, 210 functional dysphonias, and 119 benign lesions of vocal folds. For this study, only acoustic data were analyzed using Dr. Speech software (Tiger electronics Inc., MA). Twelve parameters were computed; 82% of the acoustic voice recordings could be analyzed. Statistical analysis was performed with SPSS 17.0. RESULTS: Acoustic data was easily recorded simultaneously allowing analyses of the same phonation segment to determine vocal fold function and therefore eliminating the need for another voice recording. The acoustic voice parameters differed between genders in the healthy voice group. Most of the parameters showed significant differences between healthy and pathological groups. CONCLUSION: Simultaneously recorded endoscopic and acoustic data is valuable. Differentiation between healthy and pathological groups was possible using acoustic data only. We suggest that the synchronously recorded acoustic signal is of sufficient quality for objective analysis yielding reduced examination time.

Three-dimensional biomechanical properties of human vocal folds: parameter optimization of a numerical model to match in vitro dynamics.

The human voice signal originates from the vibrations of the two vocal folds within the larynx. The interactions of several intrinsic laryngeal muscles adduct and shape the vocal folds to facilitate vibration in response to airflow. Three-dimensional vocal fold dynamics are extracted from in vitro hemilarynx experiments and fitted by a numerical three-dimensional-multi-mass-model (3DM) using an optimization procedure. In this work, the 3DM dynamics are optimized over 24 experimental data sets to estimate biomechanical vocal fold properties during phonation. Accuracy of the optimization is verified by low normalized error (0.13 ± 0.02), high correlation (83% ± 2%), and reproducible subglottal pressure values. The optimized, 3DM parameters yielded biomechanical variations in tissue properties along the vocal fold surface, including variations in both the local mass and stiffness of vocal folds. That is, both mass and stiffness increased along the superior-to-inferior direction. These variations were statistically analyzed under different experimental conditions (e.g., an increase in tension as a function of vocal fold elongation and an increase in stiffness and a decrease in mass as a function of glottal airflow). The study showed that physiologically relevant vocal fold tissue properties, which cannot be directly measured during in vivo human phonation, can be captured using this 3D-modeling technique.

Flow-structure-acoustic interaction in a human voice model.

For the investigation of the physical processes of human phonation, inhomogeneous synthetic vocal folds were developed to represent the full fluid-structure-acoustic coupling. They consisted of polyurethane rubber with a stiffness in the range of human vocal folds and were mounted in a channel, shaped like the vocal tract in the supraglottal region. This test facility permitted extensive observations of flow-induced vocal fold vibrations, the periodic flow field, and the acoustic signals in the far field of the channel. Detailed measurements were performed applying particle-image velocimetry, a laser-scanning vibrometer, a microphone, unsteady pressure sensors, and a hot-wire probe, with the aim of identifying the physical mechanisms in human phonation. The results support the existence of the Coanda effect during phonation, with the flow attaching to one vocal fold and separating from the other. This behavior is not linked to one vocal fold and changes stochastically from cycle to cycle. The oscillating flow field generates a tonal sound. The broadband noise is presumed to be caused by the interaction of the asymmetric flow with the downstream-facing surfaces of the vocal folds, analogous to trailing-edge noise.

FEM-Based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials.

We propose an enhanced iterative scheme for the precise reconstruction of piezoelectric material parameters from electric impedance and mechanical displacement measurements. It is based on finite-element simulations of the full three-dimensional piezoelectric equations, combined with an inexact Newton or nonlinear Landweber iterative inversion scheme. We apply our method to two piezoelectric materials and test its performance. For the first material, the manufacturer provides a full data set; for the second one, no material data set is available. For both cases, our inverse scheme, using electric impedance measurements as input data, performs well.