Alexander A. Danilov

A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes

Abstract We have developed a new monotone cell-centered finite volume method for the discretization of diffusion equations on conformal polyhedral meshes. The proposed method is based on a nonlinear two-point flux approximation. For problems with smooth diffusion tensors and Dirichlet boundary conditions the method is interpolation-free. An adaptive interpolation is applied on faces where diffusion tensor jumps or Neumann boundary conditions are imposed. The interpolation is based on physical relationships such as continuity of the diffusion flux. The second-order convergence rate is verified with numerical experiments.

Unstructured tetrahedral mesh generation technology

We present a robust unstructured tetrahedral mesh generation technology. This technology is a combination of boundary discretization methods, an advancing front technique and a Delaunay-based mesh generation technique. For boundary mesh generation we propose four different approaches using analytical boundary parameterization, interface with CAD systems, surface mesh refinement, and constructive solid geometry. These methods allow us to build a flexible grid generation technology with a user friendly interface.

Modelling of bioimpedance measurements: unstructured mesh application to real human anatomy

Abstract A technology for high-resolution efficient numerical modelling of bioimpedance measurements is considered that includes 3D image segmentation, adaptive unstructured tetrahedral mesh generation, finite-element discretization, and analysis of simulation data. The first-order convergence of the proposed numerical methods on a series of unmatched meshes and roughly second-order convergence on a series of nested meshes are shown. The current, potential, and sensitivity field distributions are computed for conventional schemes of bioimpedance measurements using segmented geometrical torso model of the Visible Human Project (VHP) man. Use of the adaptive tetrahedral meshes reduces significantly the number of mesh elements and, hence, the associated computational cost compared to rectangular meshes while keeping the model accuracy.

Virtual blunt injury of human thorax: age-dependent response of vascular system

Abstract This work is the numerical study of the age-dependent responses of the vascular system under low-mass high-speed impact scenario. The grid-characteristic method on the adaptive mesh model of the human thorax is the numerical tool of the study. Due to the lack of valid vascular injury criteria, the numerical model only provides information on injury risk. The numerical simulation demonstrates that an older age changes significantly the vascular response and increases the risk of aorta injury. We focused on the aorta because its rupture is the general consequence of vehicle accidents (great mass impacts at relatively low velocity). Our numerical results are in good agreement with previous studies of great-mass low-speed blunt thorax impact.

Transcranial ultrasound of cerebral vessels in silico: proof of concept

Abstract Correct diagnostics of vascular pathologies underlies treatment success for patients with cerebrovascular diseases. Transcranial ultrasound is the well-known method for diagnostic of cerebrovascular diseases. Despite high sensitivity and specificity of the method, transcranial ultrasound has some limitations related to the B-mode image quality and accurate insonation of vessels of interest. Overcoming these limitations enables to enhance the quality of the diagnostic procedure. The present work addresses the numerical simulation of ultrasound propagation in a human head by a grid-characteristic method. We used a human tissue-mimicking phantom to verify our numerical model in terms of the accuracy of distance estimation. We obtained pressure distributions within a 3D segmented model of a human head. Our pilot study has some limitations, nevertheless the simulation results demonstrate that mathematical modelling of the transcranial ultrasound can be an effective tool to enhance the ultrasound examination.

Patient-specific anatomical models in human physiology

Abstract Patient-specific simulations of human physiological processes remain the challenge for many years. Detailed 3D reconstruction of body anatomical parts on the basis of medical images is an important stage of individualized simulations in physiology. In this paper we present and develop the methods and algorithms for construction of patient-specific discrete geometric models. These models are represented by anatomically correct computational meshes. Practical use of these methods is demonstrated for two important medical applications: numerical evaluation of fractional flow reserve in coronary arteries and electrocardiography simulation

Personalized model adaptation for bioimpedance measurements optimization

Abstract In this work we propose several techniques for personalized model adaptation, including anthropometrical scaling, control point mapping and geometrical modification of the body extremities positions.We compare our previous results of segmental bioimpedance analysis using the Visible Human Project (VHP) man model to the modified model with a corrected position of the arms.

Sensitivity field distributions for segmental bioelectrical impedance analysis based on real human anatomy

In this work, an adaptive unstructured tetrahedral mesh generation technology is applied for simulation of segmental bioimpedance measurements using high-resolution whole-body model of the Visible Human Project man. Sensitivity field distributions for a conventional tetrapolar, as well as eight- and ten-electrode measurement configurations are obtained. Based on the ten-electrode configuration, we suggest an algorithm for monitoring changes in the upper lung area.

Mesh generation and computational modeling techniques for bioimpedance measurements: an example using the VHP data

A workflow for high-resolution efficient numerical modeling of bioimpedance measurements is suggested that includes 3D image segmentation, adaptive mesh generation, finite-element discretization, as well as the analysis of simulation results. Using the adaptive unstructured tetrahedral meshes enables us to decrease significantly the number of mesh elements while keeping model accuracy. The numerical results illustrate electric current, potential, and sensitivity field distributions for a conventional scheme of bioimpedance measurements using segmented geometric model of human torso based on Visible Human Project data. The full VHP man body computational mesh is constructed that contains 574 thousand vertices and 3.3 million tetrahedra. http://dodo.inm.ras.ru/research/bioimpedance Vassilevski Yu., Danilov A., Nikolaev D., Rudnev S., Salamatova V., Smirnov A. Finite element analisys for problems of bioimpedance diagnostics. Comp.Math. Math.Physics 52(4), 733-745, 2012. Danilov A., Nikolaev D., Rudnev S., Salamatova V., Vassilevski Yu. Modelling of bioimpedance measurements: unstructured mesh application to real human anatomy. Russ. J. Numer. Anal. Math. Modelling, 27(5), 431-440, 2012.

Image Segmentation for Cardiovascular Biomedical Applications at Different Scales

In this study, we present several image segmentation techniques for various image scales and modalities. We consider cellular-, organ-, and whole organism-levels of biological structures in cardiovascular applications. Several automatic segmentation techniques are presented and discussed in this work. The overall pipeline for reconstruction of biological structures consists of the following steps: image pre-processing, feature detection, initial mask generation, mask processing, and segmentation post-processing. Several examples of image segmentation are presented, including patient-specific abdominal tissues segmentation, vascular network identification and myocyte lipid droplet micro-structure reconstruction.