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

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The goal of this paper is to investigate the validity of a hybrid embedded/homogenized in-silico approach for modeling perfusion through solid tumors. The rationale behind this novel idea is that only the larger blood vessels have to be explicitly resolved while the smaller scales of the vasculature are homogenized. As opposed to typical discrete or fully resolved 1D–3D models, the required data can be obtained with in-vivo imaging techniques since the morphology of the smaller vessels is not necessary. By contrast, the larger vessels, whose topology and structure is attainable noninvasively, are resolved and embedded as one-dimensional inclusions into the three-dimensional tissue domain which is modeled as a porous medium. A sound mortar-type formulation is employed to couple the two representations of the vasculature. We validate the hybrid model and optimize its parameters by comparing its results to a corresponding fully resolved model based on several well-defined metrics. These tests are performed on a complex data set of three different tumor types with heterogeneous vascular architectures. The correspondence of the hybrid model in terms of mean representative elementary volume blood and interstitial fluid pressures is excellent with relative errors of less than 4%. Larger, but less important and explicable errors are present in terms of blood flow in the smaller, homogenized vessels. We finally discuss and demonstrate how the hybrid model can be further improved to apply it for studies on tumor perfusion and the efficacy of drug delivery.

Original languageEnglish (US)
Article numbere3508
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Issue number8
StatePublished - Aug 2021


  • 1D-3D coupling
  • homogenization
  • hybrid models
  • microcirculation
  • tissue perfusion

ASJC Scopus subject areas

  • Software
  • Biomedical Engineering
  • Modeling and Simulation
  • Molecular Biology
  • Computational Theory and Mathematics
  • Applied Mathematics


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