The INVIVE project: Biomechanical simulation of the respiratory muscles
Individual virtual ventilator (INVIVE). Logo designed by Eliott Baltz, Guillaume Courtes and Nicolas Boudière.
Motivation
The motivation for the project is the serious medical condition, called ventilator induced diaphragmatic dysfunction (VIDD). The diaphragm is the main muscle involved in natural breathing. When the diaphragm contracts, the rib cage expands and the pressure gradient that is generated causes air to flow into the lungs. During mechanical ventilation, air is instead pushed into the lungs resulting in a passive displacement of the diaphragm. This unnatural forcing results in loss of function in the muscle tissue, which in turn complicates and prolongs the restoration of the respiratory independence. This dysfunction ensues even after relatively short periods of mechanical ventilation.
Goal
To develop a simulator that allows for an in-silico exploration of the respiratory function with and without mechanical ventilation in combination with intervention measures that can reduce or prevent the risk for VIDD in the patients.
That requires a thorough investigation of the physical model of the diaphraghm and the methods to solve the resulting partial differential equations. Coupling of the diaphragm with other human body parts has to be taken into account in order to assure well-posedness of the problem. Validation with respect to the real patient-data has to be performed on a continuous basis.
Resources
- Modeling: nonlinear, time-dependent equations of hyperelasticity.
- Numerics: The least-squares radial basis function partition of unity method (LS-RBF-PUM) and the least-squares RBF-generated finite difference method (RBF-FD-LS) for approximating the solutions to the partial differential equations.
- Geometry: realistic three dimensional representation of the diaphragm extracted from medical images.
A 3-D reconstruction of a diaphragm from a manual segmentation of a CT-scan.
The computed surface curvature for another diaphragm reconstruction.
The team
- Elisabeth Larsson, Scientific Computing, Dept. of Information Technology, Uppsala University.
- Nicola Cacciani, Department of Physiology and Pharmacology, Karolinska Institutet.
- Pierre-Frédéric Villard, University of Lorraine, Computer Science.
- Bostjan Mavric, Scientific Computing, Dept. of Information Technology, Uppsala University.
- Igor Tominec, Scientific Computing, Dept. of Information Technology, Uppsala University. Defended his PhD in May 2022.
- Ulrika Sundin, Scientific Computing, Dept. of Information Technology, Uppsala University.
- Andreas Michael, Scientific Computing, Dept. of Information Technology, Uppsala University.
The INVIVE team during the first meeting in Uppsala, August 2017. From left to right: Elisabeth Larsson, Nicola Cacciani, Igor Tominec, Pierre-Frédéric Villard.
PhD theses
- Oversampled radial basis function methods for solving partial differential equations. Ph.D. thesis, Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology nr 2142, Acta Universitatis Upsaliensis, Uppsala, 2022. (fulltext, preview image).
Publications
- A numerical investigation of some RBF-FD error estimates. In Dolomites Research Notes on Approximation, volume 15, number 5, pp 78-95, Padova University Press, 2022. (DOI).
- An unfitted radial basis function generated finite difference method applied to thoracic diaphragm simulations. In Journal of Computational Physics, volume 469, p 111496, Elsevier, 2022. (DOI, Fulltext, fulltext:print).
- An unfitted RBF-FD method in a least-squares setting for elliptic PDEs on complex geometries. In Journal of Computational Physics, volume 436, Elsevier, 2021. (DOI, Fulltext, fulltext:print).
- A Least Squares Radial Basis Function Finite Difference Method with Improved Stability Properties. In SIAM Journal on Scientific Computing, volume 43, number 2, pp A1441-A1471, Society for Industrial and Applied Mathematics, 2021. (DOI).
- A first meshless approach to simulation of the elastic behaviour of the diaphragm. In Spectral and High Order Methods for Partial Differential Equations: ICOSAHOM 2018, volume 134 of Lecture Notes in Computational Science and Engineering, pp 501-512, Springer, 2020. (DOI, fulltext:postprint).
- A least squares radial basis function partition of unity method for solving PDEs. In SIAM Journal on Scientific Computing, volume 39, pp A2538-A2563, 2017. (DOI).