EF3 – Model-based Imaging




Mathematical Framework for MR Poroelastography

Project Heads

Alfonso Caiazzo, Karsten Tabelow, Ingolf Sack

Project Members

Felipe Galarce

Project Duration

01.01.2021 − 31.12.2021

Located at



Medical imaging of tissues based on MRI enables the non-invasive quantitative characterization of important biomarkers, and it is therefore a pillar of clinical diagnostic of tissue diseases. Biological tissues are by nature poroelastic and the understanding of biphasic aspects such as porosity and interstitial pressure might provide the identification of abnormal pressure increase in the cardiovascular system or cerebro-spinal fluid. To this purpose, the mechanical behavior of the tissue is modeled as a biphasic material. Due to the large number of unknowns, the quantification of poroelastic parameters requires additional knowledge about the tissue microstructure, typically beyond clinically available image resolution.

Magnetic resonance elastography (MRE) is an imaging technique sensitive to the stiffness properties of tissues. In MRE, the propagation of shear waves in the audible frequency range (10 – 1000 Hz) through the tissue – recorded as a three-dimensional image of the inner displacement field – is combined with suitable mathematical and computational tissue models in order to obtain elastograms, i.e., a 3D maps of tissue elastic parameters. The displacement data – with a typical resolution of the order of millimeters – currently allow the reconstruction of tissue models only at the effective scale, i.e., with mechanical parameters varying only at a coarse spatial resolution level. Therefore, in the context of poroelastic tissues, MRE shall be supported by advanced computational and mathematical models in order to bridge the gap between the scale of available data (tissue displacement) and the scale of the microstructural parameters.

Inversion recovery (IR) denotes a spin echo MR sequence with a 180-degree inverting pulse. The following relaxation of the MRI signal is governed by the T1 relaxation time which depends on the tissue properties. This observation motivated recent experiments performed at the Charité Berlin (MRE Group of Prof. Sack) aimed at obtaining T1 and porosity maps in the tissue via IR, using different times for the inversion pulse and describing the MR signal via a bi-exponential model.

We propose a novel mathematical framework combining these two types of medical imaging modalities, IRMRI and MRE, with the goal of developing efficient and high-resolution protocol for estimating poroelastic parameters of tissues.

In particular, the main objectives of the research will be

  • to increase the robustness of the porosity map estimation via IR,
  • to design an optimal acquisition sequence for the inversion recovery experiment,
  • to develop efficient numerical methods for addressing the multiscale inverse problems of recovering poroelastic parameters from MRE data, and
  • to validate the algorithms in realistic clinical settings.


Related Publications

L. LilajT. FischerJ. GuoJ. BraunI. SackS. Hirsch. Separation of fluid and solid shear wave fields and quantification of coupling density by magnetic resonance poroelastography. Mag. Reson. Med. 2021 Mar;85(3):1655-1668

L. Lilaj, H. Herthum, T. Meyer, M. Shahryari, G. Bertalan, A. Caiazzo, J. Braun, T. Fischer, S. Hirsch, and I. Sack. Inversion recovery MR elastography of the human brain for improved stiffness quantification near fluid-solid boundaries. Mag. Reson. Med. 2021, 86(5):2552-2561

Related Pictures

Estimation of the T1 time of the tissue from inversion recovery (IR) data

Porosity estimation of a tofu phantom