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Author: search.filters.author.Haasdonk, BernardSubject: search.filters.subject.570

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    ItemOpen Access
    A novel model extended from the Bouguer-Lambert-Beer law can describe the non-linear absorbance of potassium dichromate solutions and microalgae suspensions
    (2023) Yeh, Yen-Cheng; Haasdonk, Bernard; Schmid-Staiger, Ulrike; Stier, Matthias; Tovar, Günter E. M.
    The Bouguer-Lambert-Beer law is widely used as the fundamental equation for quantification in absorption spectroscopy. However, deviations from the Bouguer-Lambert-Beer law have also been observed, such as chemical deviation and light scattering effect. While it has been proven and shown that the Bouguer-Lambert-Beer law is valid only under very restricted limitations, there are only a few alternatives of analytical models to this law. Based on the observation in the experiments, we propose a novel model to solve the problem of chemical deviation and light scattering effect. To test the proposed model, a systematic verification was conducted using potassium dichromate solutions and two types of microalgae suspensions with varying concentrations and path lengths. Our proposed model demonstrated excellent performance, with a correlation coefficient (R2) exceeding 0.995 for all tested materials, significantly surpassing the Bouguer-Lambert-Beer law, which had an R2 as low as 0.94. Our results confirm that the absorbance of pure pigment solutions follows the Bouguer-Lambert-Beer law, while the microalgae suspensions do not due to the light scattering effect. We also show that this scattering effect leads to huge deviations for the commonly used linear scaling of the spectra, and we provide a better solution based on the proposed model. This work provides a powerful tool for chemical analysis and especially for the quantification of microorganisms, such as the concentration of biomass or intracellular biomolecules. Not only the high accuracy but also the simplicity of the model makes it a practical alternative to the existing Bouguer-Lambert-Beer law.
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    A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs
    (2024) Hammer, Maria; Wenzel, Tizian; Santin, Gabriele; Meszaros-Beller, Laura; Little, Judith Paige; Haasdonk, Bernard; Schmitt, Syn
    The aim of this study was to design physics-preserving and precise surrogate models of the nonlinear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, we used greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque-potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the same time, they were capable of predicting disc forces in a physiological range of motion and for the coupling of all six degrees of freedom of an intervertebral joint. The performance of all surrogate models for a subject-specific L4|5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional), and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth-order polynomial model. Both clearly outperformed the second-order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations. Hence, the proposed model architectures have the potential to improve the accuracy and, therewith, validity of load predictions in neuro-musculoskeletal spine models.