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Der Artikel gibt einen Einblick in das reiche Feld der Zusammenarbeit zwischen Mathematik und Medizin. Beispielhaft werden drei Erfolgsmodelle dargestellt: Medizinische Bildgebung, mathematische Modellierung und Biosignalverarbeitung im Bereich der Dynamik des Herzens sowie mathematische Modellierung und Simulation in der Krebstherapie Hyperthermie und der Mund-Kiefer-Gesichts-Chirurgie. In allen Fällen existiert ein Gleichklang der Interessen von Medizin und Mathematik: Beide Disziplinen wollen die Resultate schnell und zuverlässig. Für die Klinik heißt das, dass notwendige Rechnungen in möglichst kurzer Zeit, und zwar auf dem PC, ablaufen müssen und dass die Resultate so genau und belastbar sein müssen, dass medizinische Entscheidungen darauf aufbauen können. Für die Mathematik folgt daraus, dass höchste Anforderungen an die Effizienz der verwendeten Algorithmen und die darauf aufbauende Software in Numerik und Visualisierung zu stellen sind. Jedes Kapitel endet mit einer Darstellung der Perspektive des jeweiligen Gebietes. Abschließend werden mögliche Handlungsoptionen für Politik und Wirtschaft diskutiert.
It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and
density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.
This study’s objective was the generation of a standardized geometry of the healthy nasal cavity.
An average geometry of the healthy nasal cavity was generated using a statistical shape model based on 25 symptom-free subjects. Airflow within the average geometry and these geometries was calculated using fluid simulations. Integral measures of the nasal resistance, wall shear stresses (WSS) and velocities were calculated as well as cross-sectional areas (CSA). Furthermore, individual WSS and static pressure distributions were mapped onto the average geometry.
The average geometry featured an overall more regular shape that resulted in less resistance, reduced wall shear stresses and velocities compared to the median of the 25 geometries. Spatial distributions of WSS and pressure of average geometry agreed well compared to the average distributions of all individual geometries. The minimal CSA of the average geometry was larger than the median of all individual geometries (83.4 vs. 74.7 mm²).
The airflow observed within the average geometry of the healthy nasal cavity did not equal the average airflow of the individual geometries. While differences observed for integral measures were notable, the calculated values for the average geometry lay within the distributions of the individual parameters. Spatially resolved parameters differed less prominently.
Background: Currently, there is no fully sufficient way to differentiate between symptomatic and normal nasal breathing. Using the nose’s total resistance is disputed as a valid means to objectify nasal airflow, and the need for a more comprehensive diagnostic method is increasing. This work’s aim was to test a novel approach considering intranasal wall shear stress as well as static pressure maps obtained by computational fluid dynamics (CFD).
Methods: X-ray computed tomography (CT) scan data of six symptom-free subjects and seven symptomatic patients were used. Patient-specific geometries of the nasal cavity were segmented from these data sets. Inspiratory and expiratory steady airflow simulations were performed using CFD. Calculated static pressures and wall shear stresses (WSS) were mapped onto a common template of the nasal septum, allowing for comparison of these parameters between the two patient groups.
Results: Significant differences in wall shear stress distributions during the inspiratory phase could be identified between the two groups, whereas no differences were found for the expiratory phase. It is assumed that one essential feature of normal nasal breathing probably consists in distinctively different intranasal flow fields for inspiration and expiration. This is in accordance with previous investigations.
Conclusion: The proposed method seems to be a promising tool for developing a new kind of patient-specific assessment of nasal breathing. However, more studies and a greater case number of data with an expanded focus, would be ideal.