Validation and parameter optimization of a hybrid embedded/homogenized solid tumor perfusion model

Kremheller, Johannes; Brandstaeter, Sebastian; Schrefler, Bernhard A.; Wall, Wolfgang A.

doi:10.1002/cnm.3508

Cited by 5 publications

(8 citation statements)

References 54 publications

(219 reference statements)

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“…In order to avoid a discrete resolution of the capillary network, homogenized Darcy-type models have been investigated in the literature. 9,19,22,24,[45][46][47] Following this approach and modeling the lymphatic and venous systems by means of source terms (see Assumption (A5)), one obtains for the capillary bed (3D porous medium, flow problem)…”

Section: The 3d Modelmentioning

confidence: 99%

“…Here, n SEV is the number of capillaries passing a facet of a cubed REV, see Figure 3, having the area A REV . In References [22,24], the edge length of a cubed REV is about 1.0 mm. Thus, A REV ≈ 1.0 mm 2 .…”

Section: The 3d Modelmentioning

confidence: 99%

“…By including sink terms in the Darcy equation for the capillary continuum, the influence of the venous system draining the breast tissue is accounted for. For tissue permeability, values from Wu et al 12 are considered, whereas for capillary bed homogenization, existing results from literature [21][22][23][24][25] are adopted.…”

Section: Introductionmentioning

confidence: 99%

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

Fritz

Köppl

Oden

et al. 2022

Numer Methods Biomed Eng

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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. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (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 model results in a fully coupled 1D-0D-3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.

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Section: The 3d Modelmentioning

confidence: 99%

Section: The 3d Modelmentioning

confidence: 99%

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

Fritz

Köppl

Oden

et al. 2022

Numer Methods Biomed Eng

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show abstract

“…In order to avoid a discrete resolution of the capillary network, homogenized Darcy-type models have been investigated in literature. 14,25,28,35,39,52,59 Following this approach and modeling the lymphatic and venous systems by means of source terms (see Assumption (A5)), one obtains for the capillary bed (3D porous medium, flow problem)…”

Section: 2mentioning

confidence: 99%

“…By including sink terms in the Darcy equation for the capillary continuum, the influence of the venous system draining the breast tissue is accounted for. For tissue permeability, values from Wu et al 61 are considered, whereas for capillary bed homogenization, existing techniques from the literature 27,35,36,47,59 are adopted.…”

Section: Introductionmentioning

confidence: 99%

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

Fritz,

Köppl,

Oden

et al. 2022

Preprint

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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.

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An in silico model of the capturing of magnetic nanoparticles in tumour spheroids in the presence of flow

Wirthl,

Janko,

Lyer

et al. 2023

Biomed Microdevices

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One of the main challenges in improving the efficacy of conventional chemotherapeutic drugs is that they do not reach the cancer cells at sufficiently high doses while at the same time affecting healthy tissue and causing significant side effects and suffering in cancer patients. To overcome this deficiency, magnetic nanoparticles as transporter systems have emerged as a promising approach to achieve more specific tumour targeting. Drug-loaded magnetic nanoparticles can be directed to the target tissue by applying an external magnetic field. However, the magnetic forces exerted on the nanoparticles fall off rapidly with distance, making the tumour targeting challenging, even more so in the presence of flowing blood or interstitial fluid. We therefore present a computational model of the capturing of magnetic nanoparticles in a test setup: our model includes the flow around the tumour, the magnetic forces that guide the nanoparticles, and the transport within the tumour. We show how a model for the transport of magnetic nanoparticles in an external magnetic field can be integrated with a multiphase tumour model based on the theory of porous media. Our approach based on the underlying physical mechanisms can provide crucial insights into mechanisms that cannot be studied conclusively in experimental research alone. Such a computational model enables an efficient and systematic exploration of the nanoparticle design space, first in a controlled test setup and then in more complex in vivo scenarios. As an effective tool for minimising costly trial-and-error design methods, it expedites translation into clinical practice to improve therapeutic outcomes and limit adverse effects for cancer patients. Graphic Abstract

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Validation and parameter optimization of a hybrid embedded/homogenized solid tumor perfusion model

Cited by 5 publications

References 54 publications

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

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

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

An in silico model of the capturing of magnetic nanoparticles in tumour spheroids in the presence of flow

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