Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement. (English) Zbl 1487.35371
Summary: The problem of parameter identification appears in many physical applications. A parameter of particular interest in cancer treatment is permeability, which modulates the fluidic streamlines in the tumor microenvironment. Most of the existing permeability identification techniques are invasive and not feasible to identify the permeability with minimal interference with the porous structure in their working conditions. In this paper, a theoretical framework utilizing partial differential equation (PDE)-constrained optimization strategies is established to identify a spatially distributed permeability of a porous structure from its modulated external velocity field measured around the structure. In particular, the flow around and through the porous media are governed by the steady-state Navier-Stokes-Darcy model. The performance of our approach is validated via numerical and experimental tests for the permeability of a 3D printed porous surrogate in a micro-fluidic chip based on the sampled optical velocity measurement. Both numerical and experimental results show a high precision of the permeability estimation.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 76S05 | Flows in porous media; filtration; seepage |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 92C37 | Cell biology |
| 92C50 | Medical applications (general) |
| 49M41 | PDE constrained optimization (numerical aspects) |
| 93B30 | System identification |
| 35R30 | Inverse problems for PDEs |
Keywords:
parameter identification; permeability; steady-state Navier-Stokes-Darcy model; PDE-constrained optimization; cancer treatmentReferences:
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