Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2201.05392

A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue

Marvin Fritz·Tobias Köppl·J. Tinsley Oden·Andreas Wagner·Barbara Wohlmuth·Chengyue Wu
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic PDEs is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D-0D-3D coupled models for simulating blood flow and transport processes: The first 1D-0D-3D model covers the whole path from the aorta to the breast, while the second model is a sub-model obtained by restriction to breast vasculature and tissue making possible a significant reduction in computational cost. Several numerical experiments are conducted that demonstrate realistic flow simulations compared to existing data on blood flow in human breast and vascular system.

Explore related subjects

q-bio.TOcs.NAmath.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Marvin Fritz, Tobias Köppl, J. Tinsley Oden, Andreas Wagner, Barbara Wohlmuth, Chengyue Wu. 2022-01-14. A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue. https://doi.org/10.1002/cnm.3612

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Adaptive therapy under parametric, structural, and measurement uncertainty

Adaptive therapy has emerged as a promising treatment strategy that exploits within-tumour competition to delay disease progression. Implementation, however, typically relies on indirect measurements of tumour burden and must account for potentially substantial patient heterogeneity. In this work, we capture patient-to-patient variability, parameter uncertainty, and imperfect biomarker measurements with a mathematical and statistical model that we calibrate to clinical prostate cancer data using a Bayesian inference framework. We use the resulting virtual cohort to demonstrate that, within the simple but now well-established Lotka-Volterra-based model, adaptive therapy robustly improves time-to-progression for the subset of patients that are predicted to eventually progress by the model. To account for other risk factors associated with larger tumour volumes, we introduce a new metric based on the risk of metastasis that demonstrates how adaptive therapy may be disadvantageous when sustained tumour burden is also considered. Given the ubiquity of uncertainty in oncology, we then describe several future modelling directions that also capture uncertainty in the temporal evolution of the underlying tumour or biomarker dynamics. Finally, we demonstrate how model misspecification and non-identifiability can lead to unreliable predictions, especially if uncertainty is inadequately captured.

q-bio.TO↗
arXiv2026

Head Impact Characterization and Cellular Response of a Live-neuron cell-integrated Biomechanical Full-body Surrogate Model

In this study, we develop a novel integrated framework that links the impact response with cellular dynamics using a live-neuron cell-integrated biomechanical full-body surrogate model. The impact event is simulated by allowing the surrogate model to fall from controlled seated release angles of 30-degree, 60-degree, and 90-degree. Three vertically stacked cell-culture Petri dishes, each containing live SH-SY5Y neuroblastoma cells, were placed inside the head of a commercially available surrogate model. The dynamic response of the impact event was evaluated using acceleration measurements from six accelerometers, comprising three sensors mounted on the head surface and three embedded in series with the cell stacks, along with kinematic measurements of the fall and deformation of the head model. In parallel, an OpenSim-based modified musculoskeletal model was used to simulate the fall experiment. We found that variation in contact stiffness produced the largest change in the predicted head acceleration in the simulation. When the cellular response and the measured accelerations are compared, oxidative stress and cell viability showed trends consistent with the regional acceleration and angle of fall. At the 90-degree fall, where median peak linear accelerations ranged from 170-258g, and the maximum headform deformation was approximately 9.4 mm, oxidative stress increased to approximately twice that of the control sample. We also quantified the cellular drift of SH-SY5Y cells, which is focal in nature for the 90-degree impact condition. The corresponding fall scenarios were also simulated in OpenSim and a preliminary calibration relationship was developed to compare the kinematic responses of the physical surrogate and musculoskeletal model. Finally, the framework provides a basis for relating experimental surrogate measurements to human head-neck response during impact.

q-bio.TO↗
arXiv2026

History Matters: Damage-Mediated Amplification of Brain Deformation and Injury Risk under Repeated Head Impacts

Computational head models are typically applied to isolated impacts, leaving repeated head loading largely unexplored. An Ogden-Roxburgh Mullins damage formulation was implemented in a high-fidelity finite element head model to represent loading-history-dependent softening during cyclic brain-tissue deformation. Repeated-loading histories derived from mixed martial arts head-impact data were applied and compared with damage-free hyperelastic (HE) and linear visco-hyperelastic (LVHE) model variants. Under five identical single-axis cycles, Mullins-type softening progressively increased strain and strain rate metrics relative to the HE model. Mullins-based injury probabilities progressively exceeded strain-based HE predictions and diverged from unchanged kinematics-based predictions, indicating that neglecting prior softening may underestimate injury risk. In a randomized twenty-cycle multiaxial sequence, cycles of similar kinematic intensity produced different deformation and injury-risk estimates depending on prior softening. HE and LVHE models predicted higher injury probabilities initially, whereas the Mullins-based model produced the largest later-cycle estimates and highest probability of at least one injury over the sequence. Regional amplification depended on loading direction and prior softening, with no direction-independent trend among brain substructures. Gyral elements exhibited higher cumulative maximum principal strain than sulcal elements, which showed greater amplification relative to initial responses. These findings demonstrate that short-term damage-mediated softening can substantially amplify tissue deformation and injury-risk estimates beyond damage-free head models under the same loading histories. Further experimental characterization of cyclic brain-tissue softening is needed to improve models of repeated head loading and traumatic brain injury.

q-bio.TO↗