Browsing by Author "Ricken, Tim"

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Open Access
About the applicability of the theory of porous media for the modelling of non‐isothermal material injection into porous structures
(2023) Völter, Jan-Sören L.; Ricken, Tim; Röhrle, Oliver
In this contribution we investigate the relevance of the theory of porous media for the non-isothermal modelling of material injection into porous structures. In particular, we provide a model describing the injection of cement during percutaneous vertebroplasty, which is derived by consistently following the theory of porous media. We demonstrate numerically that this model elicits unphysical behaviour under local thermal non-equilibrium conditions. No distinct unphysical behaviour is observed under local thermal equilibrium conditions. We conclude that heuristic modifications of the model equations are necessary and suspect the unphysical behaviour to be caused by contradictory modelling assumptions.
Open Access
Affine transformations accelerate the training of physics-informed neural networks of a one-dimensional consolidation problem
(2023) Mandl, Luis; Mielke, André; Seyedpour, Seyed Morteza; Ricken, Tim
Physics-informed neural networks (PINNs) leverage data and knowledge about a problem. They provide a nonnumerical pathway to solving partial differential equations by expressing the field solution as an artificial neural network. This approach has been applied successfully to various types of differential equations. A major area of research on PINNs is the application to coupled partial differential equations in particular, and a general breakthrough is still lacking. In coupled equations, the optimization operates in a critical conflict between boundary conditions and the underlying equations, which often requires either many iterations or complex schemes to avoid trivial solutions and to achieve convergence. We provide empirical evidence for the mitigation of bad initial conditioning in PINNs for solving one-dimensional consolidation problems of porous media through the introduction of affine transformations after the classical output layer of artificial neural network architectures, effectively accelerating the training process. These affine physics-informed neural networks (AfPINNs) then produce nontrivial and accurate field solutions even in parameter spaces with diverging orders of magnitude. On average, AfPINNs show the ability to improve the L2relative error by 64.84%after 25,000 epochs for a one-dimensional consolidation problem based on Biot’s theory, and an average improvement by 58.80%with a transfer approach to the theory of porous media.
Open Access
Analysing the bone cement flow in the injection apparatus during vertebroplasty
(2023) Trivedi, Zubin; Gehweiler, Dominic; Wychowaniec, Jacek K.; Ricken, Tim; Gueorguiev-Rüegg, Boyko; Wagner, Arndt; Röhrle, Oliver
Vertebroplasty, a medical procedure for treating vertebral fractures, requires medical practitioners to inject bone cement inside the vertebra using a cannula attached to a syringe. The required injection force must be small enough for the practitioner to apply it by hand while remaining stable for a controlled injection. Several factors could make the injection force unintuitive for the practitioners, one of them being the non‐Newtonian nature of the bone cement. The viscosity of the bone cement varies as it flows through the different parts of the injection apparatus and the porous cancellous interior of the vertebra. Therefore, it is important to study the flow of bone cement through these parts. This work is a preliminary study on the flow of bone cement through the injection apparatus. Firstly, we obtained the rheological parameters for the power law model of bone cement using experiments using standard clinical equipment. These parameters were then used to obtain the shear rate, viscosity, and velocity profiles of the bone cement flow through the cannula. Lastly, an analysis was carried out to understand the influence of various geometrical parameters of the injection apparatus, in which the radius of the cannula was found to be the most influential parameter.
Open Access
Application of magnetic resonance imaging in liver biomechanics : a systematic review
(2021) Seyedpour, Seyed M.; Nabati, Mehdi; Lambers, Lena; Nafisi, Sara; Tautenhahn, Hans-Michael; Sack, Ingolf; Reichenbach, Jürgen R.; Ricken, Tim
MRI-based biomechanical studies can provide a deep understanding of the mechanisms governing liver function, its mechanical performance but also liver diseases. In addition, comprehensive modeling of the liver can help improve liver disease treatment. Furthermore, such studies demonstrate the beginning of an engineering-level approach to how the liver disease affects material properties and liver function. Aimed at researchers in the field of MRI-based liver simulation, research articles pertinent to MRI-based liver modeling were identified, reviewed, and summarized systematically. Various MRI applications for liver biomechanics are highlighted, and the limitations of different viscoelastic models used in magnetic resonance elastography are addressed. The clinical application of the simulations and the diseases studied are also discussed. Based on the developed questionnaire, the papers' quality was assessed, and of the 46 reviewed papers, 32 papers were determined to be of high-quality. Due to the lack of the suitable material models for different liver diseases studied by magnetic resonance elastography, researchers may consider the effect of liver diseases on constitutive models. In the future, research groups may incorporate various aspects of machine learning (ML) into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification.
Open Access
Comparing durability and compressive strength predictions of hyperoptimized random forests and artificial neural networks on a small dataset of concrete containing nano SiO2 and RHA
(2024) Arasteh-Khoshbin, Omolbanin; Seyedpour, Seyed Morteza; Mandl, Luis; Lambers, Lena; Ricken, Tim
Open Access
A continuum mechanical porous media model for vertebroplasty : numerical simulations and experimental validation
(2023) Trivedi, Zubin; Gehweiler, Dominic; Wychowaniec, Jacek K.; Ricken, Tim; Gueorguiev, Boyko; Wagner, Arndt; Röhrle, Oliver
The outcome of vertebroplasty is hard to predict due to its dependence on complex factors like bone cement and marrow rheologies. Cement leakage could occur if the procedure is done incorrectly, potentially causing adverse complications. A reliable simulation could predict the patient-specific outcome preoperatively and avoid the risk of cement leakage. Therefore, the aim of this work was to introduce a computationally feasible and experimentally validated model for simulating vertebroplasty. The developed model is a multiphase continuum-mechanical macro-scale model based on the Theory of Porous Media. The related governing equations were discretized using a combined finite element-finite volume approach by the so-called Box discretization. Three different rheological upscaling methods were used to compare and determine the most suitable approach for this application. For validation, a benchmark experiment was set up and simulated using the model. The influence of bone marrow and parameters like permeability, porosity, etc., was investigated to study the effect of varying conditions on vertebroplasty. The presented model could realistically simulate the injection of bone cement in porous materials when used with the correct rheological upscaling models, of which the semi-analytical averaging of the viscosity gave the best results. The marrow viscosity is identified as the crucial reference to categorize bone cements as ‘high- ’or ‘low-’ viscosity in the context of vertebroplasty. It is confirmed that a cement with higher viscosity than the marrow ensures stable development of the injection and a proper cement interdigitation inside the vertebra.
Open Access
Editorial - computational modeling for liver surgery and interventions
(2022) Christ, Bruno; Dahmen, Uta; Radde, Nicole; Ricken, Tim
Open Access
The effect of Caspian Sea water on mechanical properties and durability of concrete containing rice husk ash, nano SiO2, and nano Al2O3
(2022) Arasteh-Khoshbin, Omolbanin; Seyedpour, Seyed Morteza; Ricken, Tim
Various studies have been recently conducted aiming at developing more sustainable cementitious systems so that concrete structures may not have a negative effect on the environment and are decomposed. It has been attempted to build sustainable binders by substituting silica fume, cement with fly ash, nano-silica, nano-alumina, and rice husk ash. In this paper, a series of experiments on concrete with different contents of rice husk ash (10%, 15%, and 20%), nano SiO2(1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%), and nano Al2O3(1%, 2%, 3%, 4%) are performed to analyze the durability and mechanical properties of samples under the curing condition of Caspian seawater. The workability, density, water penetration, chloride ion penetration, and compressive strength (at 7, 14, 28, and 90 day) of the samples were determined. The experimental results showed that workability decreased gradually with increasing additives content, while the compressive gradually increased. Among the additives, adding 8% of the nano SiO2had the most significant effect on the improvement of compressive strength. Adding 8% nano SiO2and 4% nano Al2O3 reduced the depth of water permeability by 53% and 30%, respectively. Furthermore, adding 8% nanoSiO2 reduced chloride ion penetration by 85%.
Open Access
Hepatectomy-induced alterations in hepatic perfusion and function : toward multi-scale computational modeling for a better prediction of post-hepatectomy liver function
(2021) Christ, Bruno; Collatz, Maximilian; Dahmen, Uta; Herrmann, Karl-Heinz; Höpfl, Sebastian; König, Matthias; Lambers, Lena; Marz, Manja; Meyer, Daria; Radde, Nicole; Reichenbach, Jürgen R.; Ricken, Tim; Tautenhahn, Hans-Michael
Liver resection causes marked perfusion alterations in the liver remnant both on the organ scale (vascular anatomy) and on the microscale (sinusoidal blood flow on tissue level). These changes in perfusion affect hepatic functions via direct alterations in blood supply and drainage, followed by indirect changes of biomechanical tissue properties and cellular function. Changes in blood flow impose compression, tension and shear forces on the liver tissue. These forces are perceived by mechanosensors on parenchymal and non-parenchymal cells of the liver and regulate cell-cell and cell-matrix interactions as well as cellular signaling and metabolism. These interactions are key players in tissue growth and remodeling, a prerequisite to restore tissue function after PHx. Their dysregulation is associated with metabolic impairment of the liver eventually leading to liver failure, a serious post-hepatectomy complication with high morbidity and mortality. Though certain links are known, the overall functional change after liver surgery is not understood due to complex feedback loops, non-linearities, spatial heterogeneities and different time-scales of events. Computational modeling is a unique approach to gain a better understanding of complex biomedical systems. This approach allows (i) integration of heterogeneous data and knowledge on multiple scales into a consistent view of how perfusion is related to hepatic function; (ii) testing and generating hypotheses based on predictive models, which must be validated experimentally and clinically. In the long term, computational modeling will (iii) support surgical planning by predicting surgery-induced perfusion perturbations and their functional (metabolic) consequences; and thereby (iv) allow minimizing surgical risks for the individual patient. Here, we review the alterations of hepatic perfusion, biomechanical properties and function associated with hepatectomy. Specifically, we provide an overview over the clinical problem, preoperative diagnostics, functional imaging approaches, experimental approaches in animal models, mechanoperception in the liver and impact on cellular metabolism, omics approaches with a focus on transcriptomics, data integration and uncertainty analysis, and computational modeling on multiple scales. Finally, we provide a perspective on how multi-scale computational models, which couple perfusion changes to hepatic function, could become part of clinical workflows to predict and optimize patient outcome after complex liver surgery.
Open Access
In silico modeling of coupled physical‐biogeochemical (P‐BGC) processes in Antarctic Sea ice
(2021) Thom, Andrea; Ricken, Tim
Antarctic sea ice formation in the Marginal Ice Zone (MIZ) and its mutual effects on ocean biology and chemistry is very sensitive to climate change. The formation of ’pancake’ ice floes and the coupled physical‐biogeochemical (P‐BGC) processes can be modeled by using the continuum mechanical multi‐phase description of the extended Theory of Porous Media (eTPM), and simulated with the Finite Element Method (FEM). The ice formation is described via a salinity‐temperature equilibrium of the enclosed ocean water. The growth of the thriving ice algae, enclosed and attached to the pancake ice floes, is modeled with a phenomenological approach given with an ordinary differential equation.
Open Access
A mesh‐in‐element method for the theory of porous media
(2024) Maike, S.; Schröder, Jörg; Bluhm, J.; Ricken, Tim
While direct homogenisation approaches such as the FE method are subject to the assumption of scale separation, the mesh‐in‐element (MIEL) approach is based on an approach with strong scale coupling, which is based on a discretization with finite elements. In this contribution we propose a two‐scale MIEL scheme in the framework of the theory of porous media (TPM). This work is a further development of the MIEL method which is based on the works of the authors A. Ibrahimbegovic, R.L. Taylor, D. Markovic, H.G. Matthies, R. Niekamp (in alphabetical order); where we find the physical and mathematical as well as the software coupling implementation aspects of the multi‐scale modeling of heterogeneous structures with inelastic constitutive behaviour, see for example, [Eng Comput, 2005;22(5‐6):664‐683.] and [Eng Comput , 2009;26(1/2):6‐28.]. Within the scope of this contribution, the necessary theoretical foundations of TPM are provided and the special features of the algorithmic implementation in the context of the MIEL method are worked out. Their fusion is investigated in representative numerical examples to evaluate the characteristics of this approach and to determine its range of application.
Open Access
Model order reduction for deformable porous materials in thin domains via asymptotic analysis
(2021) Armiti-Juber, Alaa; Ricken, Tim
We study fluid-saturated porous materials that undergo poro-elastic deformations in thin domains. The mechanics in such materials are described using a biphasic model based on the theory of porous media (TPM) and consisting of a system of differential equations for material’s displacement and fluid’s pressure. These equations are in general strongly coupled and nonlinear, such that exact solutions are hard to obtain and numerical solutions are computationally expensive. This paper reduces the complexity of the biphasic model in thin domains with a scale separation between domain’s width and length. Based on standard asymptotic analysis, we derive a reduced model that combines two sub-models. Firstly, a limit model consists of averaged equations that describe the fluid pore pressure and displacement in the longitudinal direction of the domain. Secondly, a corrector model re-captures the mechanics in the transverse direction. The validity of the reduced model is finally tested using a set of numerical examples. These demonstrate the computational efficiency of the reduced model, while maintaining reliable solutions in comparison with original biphasic TPM model in thin domain.
Open Access
Modeling freezing and BioGeoChemical processes in Antarctic sea ice
(2024) Pathak, Raghav; Seyedpour, Seyed Morteza; Kutschan, Bernd; Thom, Andrea; Thoms, Silke; Ricken, Tim
The Antarctic sea ice, which undergoes annual freezing and melting, plays a significant role in the global climate cycle. Since satellite observations in the Antarctic region began, 2023 saw a historically unprecedented decrease in the extent of sea ice. Further ocean warming and future environmental conditions in the Southern Ocean will influence the extent and amount of ice in the Marginal Ice Zones (MIZ), the BioGeoChemical (BGC) cycles, and their interconnected relationships. The so‐called pancake floes are a composition of a porous sea ice matrix with interstitial brine, nutrients, and biological communities inside the pores. The ice formation and salinity are both dependent on the ambient temperature. To realistically model these multiphasic and multicomponent coupled processes, the extended Theory of Porous Media (eTPM) is used to develop Partial Differential Equations (PDEs) based high‐fidelity models capable of simulating the different seasonal variations in the region. All critical variables like salinity, ice volume fraction, and temperature, among others, are considered and have their equations of state. The phase transition phenomenon is approached through a micro‐macro linking scheme. In this paper, a phase‐field solidification model [4] coupled with salinity is used to model the microscale freezing processes and up‐scaled to the macroscale eTPM model. The evolution equations for the phase field model are derived following Landau‐Ginzburg order parameter gradient dynamics and mass conservation of salt allowing to model the salt trapped inside the pores. A BGC flux model for sea ice is set up to simulate the algal species present in the sea ice matrix. Ordinary differential equations (ODE) are employed to represent the diverse environmental factors involved in the growth and loss of distinct BGC components. Processes like photosynthesis are dependent on temperature and salinity, which are derived through an ODE‐PDE coupling with the eTPM model. Academic simulations and results are presented as validation for the mathematical model. These high‐fidelity models eventually lead to their incorporation into large‐scale global climate models.
Open Access
On effects of freezing and thawing cycles of concrete containing nano-SiO2 : experimental study of material properties and crack simulation
(2023) Arasteh-Khoshbin, Omolbanin; Seyedpour, Seyed Morteza; Brodbeck, Maximilian; Lambers, Lena; Ricken, Tim
Construction during cold weather can lead to freezing accidents in concrete, causing significant hidden threats to the project’s performance and safety by affecting the mechanical properties and durability reduction. This study aims to deduce the compressive strength and durability of the concrete containing nano- SiO2under freezing-thawing cycles with the Caspian seawater curing condition. The specimens were subjected to freezing-thawing cycles according to ASTM C666. Furthermore, crack propagation in the concrete after freezing-thawing cycles is simulated. The results reveal that adding until nano- SiO2until 6% improved compressive strength before and after freezing-thaw cycles. The water permeability experiences a substantial reduction as the amount of nano- SiO2increases. Furthermore, the water permeability exhibits a positive correlation with the number of cycles, resulting in significantly higher values after 150 cycles compared to the initial sample. Moreover, adding 8% nano- SiO2reduced the depth of water permeability and chloride ion penetration after 150 cycles by 57% and 86%, respectively. The crack simulation results indicate that concrete containing 6% nano- SiO2shows an optimal resistance against crack formation. Concrete with 6% nano- SiO2requires 13.88% less force for crack initialization after 150 freezing and thawing cycles. Among different nano- SiO2percentages, 6% shows the best crack resistance and 8% the minimum water permeability and chloride ion penetration.
Open Access
Optimization of the groundwater remediation process using a coupled genetic algorithm-finite difference method
(2021) Seyedpour, Seyed Morteza; Valizadeh, Iman; Kirmizakis, Panagiotis; Doherty, Rory; Ricken, Tim
In situ chemical oxidation using permanganate as an oxidant is a remediation technique often used to treat contaminated groundwater. In this paper, groundwater flow with a full hydraulic conductivity tensor and remediation process through in situ chemical oxidation are simulated. The numerical approach was verified with a physical sandbox experiment and analytical solution for 2D advection-diffusion with a first-order decay rate constant. The numerical results were in good agreement with the results of physical sandbox model and the analytical solution. The developed model was applied to two different studies, using multi-objective genetic algorithm to optimise remediation design. In order to reach the optimised design, three objectives considering three constraints were defined. The time to reach the desired concentration and remediation cost regarding the number of required oxidant sources in the optimised design was less than any arbitrary design.
Open Access
Patient‐specific simulation of brain tumour growth and regression
(2023) Suditsch, Marlon; Ricken, Tim; Wagner, Arndt
The medical relevance of brain tumours is characterised by its locally invasive and destructive growth. With a high mortality rate combined with a short remaining life expectancy, brain tumours are identified as highly malignant. A continuum‐mechanical model for the description of the governing processes of growth and regression is derived in the framework of the Theory of Porous Media (TPM). The model is based on medical multi‐modal magnetic resonance imaging (MRI) scans, which represent the gold standard in diagnosis. The multi‐phase model is described mathematically via strongly coupled partial differential equations. This set of governing equations is transformed into their weak formulation and is solved with the software package FEniCS. A proof‐of‐concept simulation based on one patient geometry and tumour pathology shows the relevant processes of tumour growth and the results are discussed.
Open Access
Phase transition in porous materials : effects of material parameters and deformation regime on mass conservativity
(2024) Brodbeck, Maximilian; Suditsch, Marlon; Seyedpour, Seyed Morteza; Ricken, Tim
Phase transition in porous materials is relevant within different engineering applications, such as freezing in saturated soil or pancake sea ice. Mathematical descriptions of such processes can be derived based on Biot’s consolidation theory or the Theory of Porous Media. Depending on parameters such as density ratio, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the general, finite deformation case, suffers from instabilities and high computational costs. Simplifications, assuming small deformations, increases stability and computational efficiency. Within this work shortcomings of simplified theories based on Biot and linearisations of the Theory of Porous Media (TPM) are systematically studied. In order to determine the interaction of the different model parameters a non-dimensional model for poro-elasticity is presented. Based on a characteristic test-case including phase-transition and consolidation, the simplified models are compared to the fully non-linear TPM, focusing on mass errors as well as the time behaviour of the solution. Taking further into account the efficiency of discretisation based on different primal variables and finite-element-spaces, a guideline for selecting an appropriate combination of model, kinematic assumption and discretisation scheme is presented.
Open Access
Quantifying fat zonation in liver lobules : an integrated multiscale in silico model combining disturbed microperfusion and fat metabolism via a continuum biomechanical bi-scale, tri-phasic approach
(2024) Lambers, Lena; Waschinsky, Navina; Schleicher, Jana; König, Matthias; Tautenhahn, Hans-Michael; Albadry, Mohamed; Dahmen, Uta; Ricken, Tim
Metabolic zonation refers to the spatial separation of metabolic functions along the sinusoidal axes of the liver. This phenomenon forms the foundation for adjusting hepatic metabolism to physiological requirements in health and disease (e.g., metabolic dysfunction-associated steatotic liver disease/MASLD). Zonated metabolic functions are influenced by zonal morphological abnormalities in the liver, such as periportal fibrosis and pericentral steatosis. We aim to analyze the interplay between microperfusion, oxygen gradient, fat metabolism and resulting zonated fat accumulation in a liver lobule. Therefore we developed a continuum biomechanical, tri-phasic, bi-scale, and multicomponent in silico model, which allows to numerically simulate coupled perfusion-function-growth interactions two-dimensionally in liver lobules. The developed homogenized model has the following specifications: (i) thermodynamically consistent, (ii) tri-phase model (tissue, fat, blood), (iii) penta-substances (glycogen, glucose, lactate, FFA, and oxygen), and (iv) bi-scale approach (lobule, cell). Our presented in silico model accounts for the mutual coupling between spatial and time-dependent liver perfusion, metabolic pathways and fat accumulation. The model thus allows the prediction of fat development in the liver lobule, depending on perfusion, oxygen and plasma concentration of free fatty acids (FFA), oxidative processes, the synthesis and the secretion of triglycerides (TGs). The use of a bi-scale approach allows in addition to focus on scale bridging processes. Thus, we will investigate how changes at the cellular scale affect perfusion at the lobular scale and vice versa. This allows to predict the zonation of fat distribution (periportal or pericentral) depending on initial conditions, as well as external and internal boundary value conditions.
Open Access
Simulation of contaminant transport through the vadose zone : a continuum mechanical approach within the framework of the extended Theory of Porous Media (eTPM)
(2023) Seyedpour, Seyed Morteza; Thom, Andrea; Ricken, Tim
The simulation of contaminant transport through the vadose zone enjoys high significance for decision makers and contaminated site planners since the vadose zone can serve as a filter, but many contaminants can be transported from this region to aquifers. The intention of this paper is to utilize the extended Theory of Porous Media (eTPM) to develop a ternary model for the simulation of contaminant transport in the vadose zone whose application is subsequently shown via a numerical example. The simulation was conducted for 140 days, during which the contamination source was removed after 25 days. The results indicate that the contaminant reached the water table after 76 days. The concentration of the contaminant reaching the groundwater was 17% less than that of the contaminant source.
Open Access
Transient high-frequency spherical wave propagation in porous medium using fractional calculus technique
(2023) Soltani, Kamran; Seyedpour, Seyed Morteza; Ricken, Tim; Rezazadeh, Ghader
Transient high-frequency spherical wave propagation in the porous medium is studied using the Biot-JKD theory. The porous media is considered to be a composed of deformable solid skeleton and viscous incompressible fluid inside the pores. In order to treat the fractional proportionality of the dynamic tortuosity to the frequency (or equivalently, to time) due to the viscous interaction between solid and fluid phases, the fractional calculus theory along with the Laplace and Fourier transforms are used to solve the coupled governing partial differential equations of the scaler and vector potential functions obtained from the Helmholtz’s decomposition in the Laplace domain. Both the longitudinal and transverse waves, additionally the reflection and transmission kernels are determined in detail at the Laplace domain. For the Laplace-to-time inversion transform, Durbin’s numerical formula is used and the independence of the results from the involved tuning and accuracy parameters is checked. The effects of the porosity, dynamic tortuosity, characteristics length, etc. on the reflected pressure and stress are investigated. The general pattern of the results is similar to our previous knowledge of wave propagation. Further works and experiments may be conducted in future works for various applications.