Lars Walczak

Computation of a finite element-conformal tetrahedral mesh approximation for simulated soft tissue deformation using a deformable surface model.

In this article, we present a new method for the generation of surface meshes of biological soft tissue. The method is based on the deformable surface model technique and is extended to histological data sets. It relies on an iterative adjustment towards polygonal segments describing the histological structures of the soft tissue. The generated surface meshes allow for the construction of volumetric meshes through a standard constrained Delaunay approach and, thus, for the application in finite element methods. The geometric properties of volumetric meshes have an immediate influence on the numerical conditioning and, therewith, on the stability of the finite element method and the convergence of iterative solvers. In this article, the influence of the surface meshes on the quality of the volumetric meshes is analysed in terms of the spectral condition number of the stiffness matrices, which are assembled within Newton’s method. The non-linear material behavior of biological soft tissue is modeled by the Mooney–Rivlin material law. The subject is motivated by the requirements of virtual surgery.

Simulation of Intra-Aneurysmal Blood Flow by Different Numerical Methods

The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs) and lattice Boltzmann methods (LBMs). The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD) and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms.

High-resolution MRI velocimetry compared with numerical simulations

Alterations of the blood flow are associated with various cardiovascular diseases. Precise knowledge of the velocity distribution is therefore important for understanding these diseases and predicting the effect of different medical intervention schemes. The goal of this work is to estimate the precision with which the velocity field can be measured and predicted by studying two simple model geometries with NMR micro imaging and computational fluid dynamics. For these initial experiments, we use water as an ideal test medium. The phantoms consist of tubes simulating a straight blood vessel and a step between two tubes of different diameters, which can be seen as a minimal model of the situation behind a stenosis. For both models, we compare the experimental data with the numerical prediction, using the experimental boundary conditions. For the simpler model, we also compare the data to the analytical solution. As an additional validation, we determine the divergence of the velocity field and verify that it vanishes within the experimental uncertainties. We discuss the resulting precision of the simulation and the outlook for extending this approach to the analysis of specific cases of arteriovascular problems.

A novel approach for connecting temporal-ontologies with blood flow simulations.

In this paper an approach for developing a temporal domain ontology for biomedical simulations is introduced. The ideas are presented in the context of simulations of blood flow in aneurysms using the Lattice Boltzmann Method. The advantages in using ontologies are manyfold: On the one hand, ontologies having been proven to be able to provide medical special knowledge e.g., key parameters for simulations. On the other hand, based on a set of rules and the usage of a reasoner, a system for checking the plausibility as well as tracking the outcome of medical simulations can be constructed. Likewise, results of simulations including data derived from them can be stored and communicated in a way that can be understood by computers. Later on, this set of results can be analyzed. At the same time, the ontologies provide a way to exchange knowledge between researchers. Lastly, this approach can be seen as a black-box abstraction of the internals of the simulation for the biomedical researcher as well. This approach is able to provide the complete parameter sets for simulations, part of the corresponding results and part of their analysis as well as e.g., geometry and boundary conditions. These inputs can be transferred to different simulation methods for comparison. Variations on the provided parameters can be automatically used to drive these simulations. Using a rule base, unphysical inputs or outputs of the simulation can be detected and communicated to the physician in a suitable and familiar way. An example for an instantiation of the blood flow simulation ontology and exemplary rules for plausibility checking are given.

New details on the clefted uvular muscle: analyzing its role at histological scale by model-based deformation analyses.

Objective As an initial step to a complex reconstruction model for virtual surgery, the present study was carried out to provide data on the prenatal cleft lip and palate uvular muscle in eight specimens. Method Serial sections of viscerocrania of 18 aborted embryos and fetuses were studied microscopically and segmented manually. Registration, three-dimensional reconstruction, and finite element analyses were conducted. Results Incompletely clefted uvulae showed anterior fusion and dorsal fission of the bilateral uvular muscle bodies. A complete cleft lip and palate specimen evidenced single bilateral uvular muscle bodies lying medially and orally below the cleft shelf, its central longitudinal fibers running beneath the oral-median mucosa. In incompletely clefted uvulae, 10% to 50% of circular peripheral fibers crossed the midline within the central third of the anterioposterior muscle, behind the levator loop. Of the fibers, 30% to 60% crossed to the ipsilateral palatopharyngeus muscle. Fibers inserted into the uvular basal membrane in a 60% nasal and 40% oral distribution at the middle third of the macroscopically clefted uvula. The macroscopic uvula itself consisted of loose connective tissue and salivary glands. Deformation analysis did disclose local stress, suggesting the uvular muscle contributes to velopharyngeal closure in normal anatomy and extends the cleft edges in cleft palate. Conclusion Cleft lip and palate reconstruction should reasonably use the uvular muscle to augment the velar midline bulk. Uvular muscle deformation calculation was successful, permitting functional insight on the basis of microanatomical specimens, so far a bigger complete velar model can be ventured.

Finite element simulation of skeletal muscular structures obtained from images of histological serial sections

In this study, we present a method for the three-dimensional reconstruction of objects obtained from histological serial sections (exemplified by those of a pennate striated skeletal muscle) and its application to the finite element method. A hyperelastic material model is used for modeling biological soft tissue. The reconstruction process relies on the direct construction of a volumetric mesh using an octree approach which leads to a stable finite element method. Stability can be expressed in the spectral matrix condition number. To visualize stress patterns within the underlying anatomy the simulation results are projected onto images of the histological scenario.

Histology and Function: Analyzing the Uvular Muscle

Objective Virtual surgery and virtual patients necessitate quantitative data on the area of interest. The study was conducted to exactly describe the embryonic and fetal uvular muscle (MU), relevant for clinical as well as virtual surgery and virtual patient generation. Method Serially sectioned viscerocrania of 10 aborted embryos and fetuses underwent three-dimensional reconstruction to obtain detailed anatomic data and perform finite element analyses. Results The MU was paired in 80% of cases, while 20% allowed no clear-cut distinction. The MU merged with the levator muscle beneath the palatal aponeurosis without a hard palate insertion. Superior longitudinal central fibers ran below the nasal mucosa, and few circular peripheral fibers crossed in the central third to the contralateral side. This was seen in 30% of the paired muscles and in all cases when no differentiation was possible; about 40% to 80% MU fibers crossed to the ipsi lateral and contralateral palatopharyngeus muscle behind the levator loop. MU fibers inserted 60% nasal and 40% oral to the basal membrane at the middle third of the macroscopic uvula, made of loose connective tissue and salivary glands. The results of the finite element simulation of the uvula showed no distinct patterns or distributions of local stress. Conclusions Detailed anatomical study supported the concept of mediocranial MU repositioning during corrective surgery, although the impact is minor to the levator muscles action. Future mathematical models describing effects of such a maneuver should integrate surrounding structures.

Evaluating the impact of shape on finite element simulations in a medical context

Competing concepts exist regarding surgery for instance of the cleft lip and palate to date. In order to support the surgeon to predict the possible outcome of a variety of the approaches a promising procedure are morphology-based finite element simulations at histological scale. It however can be a challenge to generate volume meshes that are applicable to the mathematical modeling of three-dimensional spatial modifications. In this study we discuss the variation of the segmentations by different anatomy experts with respect to shape, analyze the associated reconstructions by the finite element method and compare them among one another. The gist of the study is that an exact segmentation is fundamental precedent for a simulation and minor deviations in shape may arise deviations in a finite element simulation.

Measurement with microscopic MRI and simulation of flow in different aneurysm models

PURPOSE The impact and the development of aneurysms depend to a significant degree on the exchange of liquid between the regular vessel and the pathological extension. A better understanding of this process will lead to improved prediction capabilities. The aim of the current study was to investigate fluid-exchange in aneurysm models of different complexities by combining microscopic magnetic resonance measurements with numerical simulations. In order to evaluate the accuracy and applicability of these methods, the fluid-exchange process between the unaltered vessel lumen and the aneurysm phantoms was analyzed quantitatively using high spatial resolution. METHODS Magnetic resonance flow imaging was used to visualize fluid-exchange in two different models produced with a 3D printer. One model of an aneurysm was based on histological findings. The flow distribution in the different models was measured on a microscopic scale using time of flight magnetic resonance imaging. The whole experiment was simulated using fast graphics processing unit-based numerical simulations. The obtained simulation results were compared qualitatively and quantitatively with the magnetic resonance imaging measurements, taking into account flow and spin-lattice relaxation. RESULTS The results of both presented methods compared well for the used aneurysm models and the chosen flow distributions. The results from the fluid-exchange analysis showed comparable characteristics concerning measurement and simulation. Similar symmetry behavior was observed. Based on these results, the amount of fluid-exchange was calculated. Depending on the geometry of the models, 7% to 45% of the liquid was exchanged per second. CONCLUSIONS The result of the numerical simulations coincides well with the experimentally determined velocity field. The rate of fluid-exchange between vessel and aneurysm was well-predicted. Hence, the results obtained by simulation could be validated by the experiment. The observed deviations can be caused by the noise in the measurement and by the limited resolution of the simulation. The resulting differences are small enough to allow reliable predictions of the flow distribution in vessels with stents and for pulsed blood flow.

Netzgenerierung und Finite-Elemente-Simulation muskulärer Strukturen unter Beachtung korrespondierender histologischer Schnittpräparate

In dieser Arbeit wird ein Verfahren zur Netzgenerierung und Finite-Elemente-Simulation muskularer Strukturen vorgestellt. Eine Herausforderung liegt dabei in der Fusion der Simulationsergebnisse mit den Daten histologischer Schnittpraparate. Basierend auf segmentierten histologischen Daten wird eine Rekonstruktion der relevanten muskularen Strukturen mittels eines BCC-Tetraedernetzes initiiert. Dieses wird getriggert uber einen Level-Set-Ansatz. Die Deformation des Muskels wird dann mittels eines hyperelastischen Materialgesetzes modelliert und mithilfe der Finite-Elemente-Methode simuliert. Anschliesend erfolgt eine Projektion der Ergebnisse der Simulation auf die histologischen Schnittpraparate. Als Anwendungsfall wurden Daten abortiver Feten mit einer Spaltbildung im Bereich der Lippen-, Kiefer- und Gaumenregion herangezogen.