An Eigenfunction Approach to Parameter Estimation for 1D Diffusion Problems - Schäfer, Maximilian; Rabenstein, Rudolf; Ruderer, Alexander (European Control Conference (ECC), 2019)
The behavior of a distributed parameter system can be represented by an expansion into eigenfunctions. It allows to calculate the output signal in dependence on the parameters of the system. This contribution considers the inverse problem: Estimate the system parameters from noisy measurements of the output. To this end, an eigenfunction expansion serves to establish a state-space description of the distributed parameter system. The corresponding state-space matrices define an extended Kalman filter to perform estimation and tracking of parameter values. This approach is shown here for a diffusion problem in one spatial dimension. The value of the diffusion parameter is estimated from a simulated particle concentration under varying conditions. Problems of this kind arises for example in the emerging field of molecular communication
Keywords: Modeling; Distributed parameter systems; Biological systems

Channel Modeling for Drug Carrier Matrices - Schäfer, Maximilian; Salinas, Yolanda; Ruderer, Alexander; Enzenhofer, Franz; Brueggemann, Oliver; Schober, Robert; Haselmayr, Werner (2021 IEEE GLOBAL COMMUNICATIONS CONFERENCE (GLOBECOM), 2021)
CRIS-Team WoS Importer:2022-05-27

Channel Responses for the Molecule Release from Spherical Homogeneous Matrix Carriers - Schäfer, Maximilian; Salinas, Yolanda; Enzenhofer, Franz; Bruggemann, Oliver; Martinez-Manez, Ramon; Rabenstein, Rudolf; Schober, Robert; Haselmayr, Werner; Ruderer, Alexander (IEEE Transactions on Molecular, Biological and Multi-Scale Communications, 2022)
Molecular communications is a promising framework for the design of controlled-release drug delivery systems. Under this framework, drug carriers, diseased cells, and the channel in between are modeled as transmitters, absorbing receivers, and diffusive channel, respectively. However, existing works on drug delivery systems consider only simple drug carrier models, which limits their practical applicability. In this paper, we investigate diffusion-based spherical matrix-type drug carriers, which are employed in medical applications. In a matrix carrier, the drug molecules are dispersed in the matrix core and diffuse from the inner to the outer layers of the carrier once immersed in a dissolution medium. We derive the channel response of the matrix carrier transmitter for an absorbing receiver. The results are validated by particle-based simulations and compared with commonly used point and transparent spherical transmitters to highlight the necessity of considering practical models. Moreover, we show that a transparent spherical transmitter, with the drug molecules uniformly distributed over the entire volume, is a special case of the considered matrix system. For this case, we provide an analytical expression for the channel response. Furthermore, we derive a criterion for evaluating whether the release process or the channel dynamics are more important for the overall characteristics of the channel response of a drug delivery system. For the limiting regimes, where only the release process or only the channel determine the behavior of the end-to-end system, we propose closed-form approximations for the channel response. Finally, as a scenario of practical relevance, we investigate the channel responses for the release of common therapeutic drugs, e.g., doxorubicin, from a diblock copolymer micelle acting as drug carrier.
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Keywords: Analytical models; Biological system modeling; Biology; Diseases; Drugs; Polymers; Transmitters