Modeling of cellular morphologies in Neurodegeneration

Modeling of cellular morphologies in Neurodegeneration

 

Modeling of cellular morphologies in Neurodegeneration

neur.001Nowadays, one of the big challenges in medicine is to understand neurodegenerative diseases, as Parkinson and Alzheimer’s Diseases. While the cause of these diseases is still unknown, it has been observed that cells in the brain change their usual behaviour. Indeed the interplay between neurones and different glia cells is essential for a healthy homeostasis of the brain. Thus the progression of neurodegenerative diseases lead to dysfunction in cellular metabolism and in their communication, but also in their morphologies.

Mathematical models and simulations are widely used to perform physical phenomena. In this work, to describe intra- and inter-cellular dynamics of metabolic processes Reaction-Diffusion PDE systems will be consider and also the geometry of cells will be taken into account using different mesh discretisation methods.

Aim

The objective of this project is to develop a model for cell interactions by considering the different physiological conditions inferred from images to better understand brain dynamics and obtain new insights in the progression of neurodegenerative diseases.

 

References

  • Agathos K., Chatzi E., and Bordas S. (2018) Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization, Computer Methods in Applied Mechanics and Engineering
  • De Young G. W.,  Keizer J. (1992). A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration.
  • Duddu R., Bordas S., Chopp D. and Moran B. (2004) A Combined extended finite element and level set method for biofilm growth.
  • Hodgkin A. L., and A. F. Huxley. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117:500–544.
  • Pods J (2015). A Comparison of Computational Models for the Extracellular Potential of Neurons.
  • Salamanca L., Mechawar N., Murai K. K., Balling R.Bouvier D. S. and Skupin A. (2018) MIC-MAC: High-throughput analysis of three-dimensional microglia morphology in mammalian brains
  • Skupin A., Kettenmann H., Falcke M. (2010) Calcium Signals Driven by Single Channel Noise

Links

http://www.fnr.lu/funding-instruments/pride/

https://driven.uni.lu

https://2020driven.uni.lu/

https://wwwen.uni.lu/fstc/doctoral_school_in_science_and_engineering_dsse

 

Supported by the Luxembourg National Research Fund (PRIDE17/12252781/DRIVEN).

Breast modeling and simulation

Breast modeling and simulation

Breast modeling and simulation for a better cancer treatment

Context

About 1 in 8 U.S women will develop invasive breast cancer over the course of her lifetime (www.breast cancer.org) depending on her age, genetic, relatives, etc… About 80 % of breast cancers are Invasive Ductal Caricnomas (IDC), invasive means that the cancer has spread to the surrounding breast tissues. Ductal means that the cancer began in the milk ducts, which are the pipes that carry milk from the milk producing lobules to the nipple. Carcinoma refers to any cancer that begins in the skin or other tissues that cover internal organs.

index

Breast anatomy (Original author: Patrick J. Lynch)

 

There are several ways to get rid of these tumours but two procedures are mainly used. The total ablation of the breast if the tumour is too big (mastectomy) or the removal of the tumour and some surrounding tissues (lumpectomy). In this study, we will be more interested in the lumpectomy because less traumatic for the patient, this procedure requires more precision and the surgery can be improved thanks to simulation.

Problematic

The lumpectomy is divided into two principal operations. First, a MRI in prone position (face to the ground) in order to localize the tumour in the position where the breast is the most expended. Then, the day before the surgery, a radioactive marker or a hook is placed on the patient tumour in order to be able to remove it during the surgery. The next day, the surgery will be effectuated in supine position (the back of the patient is facing the ground easier for the surgeon) and thanks to the previous marker, the surgeon is able to remove the tumour.

Using these kind of markers is on one hand dangerous for the patient (radioactivity or infection risk) and on the other hand inaccurate during the surgery. Indeed, even if a marker is placed, detect radioactivity areas precisely or cut exactly the right amount of tumour around a hook is impossible for the moment. To overcome this problem surgeons usually cut more healthy tissues to be sure to completely remove the growth.

Aims

Breast simulations would allow the tracking of the tumour based on MRI images to fit patient specific data. Several difficulties and challenges sur round this kind of simulation: unknown material properties of the patient breast (depending on a large set of parameters), specific anatomy of each patient, unknown unloaded configuration of the breast, etc. . .

Methods

This thesis is part of the RAINBOW project financed by The Marie Sklodowska-Curie European Training Network and also the H2020-EU.1.3.1. – Fostering new skills by means of excellent initial training of researchers . The project involves 2 main actors : The University of Luxembourg (UL) and a french company Anatoscope.

Anatoscope is a young start-up specialized in patient specific modelling and also real-time multi-physics simulation by using the open source simulator SOFA. So a first work is to propose a model fitting patient specific data in collaboration with Anatoscope.

Then with the University of Luxembourg, Faculty of Science, Technology and Communication (FSTC), Doctoral Programme in Computer Science and Computer Engineering (DSSE) in Professor Bordas’ team specialized in mechanical simulations. We will use inverse methods to find mechanical properties of the breast based on tumor’s displacement. And set patient-specific simulation models that are rapidly set for a particular patient, easy-to-use by clinical experts and do not require assistance from a technical team.

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 764644.

References

[1] B. Eiben, V. Vavourakis, J. H. Hipwell, S. Kabus, C. Lorenz, T. Buelow, and D. J. Hawkes. Breast deformation modelling: comparison of methods to obtain a patient specific unloaded configuration. page 903615.
[2] T. Hopp, A. Stromboni, N. Duric, and N. V. Ruiter. Evaluation of breast tissue characterization by ultrasound computer tomography using a 2d/3d image registration with mammograms. In 2013 IEEE International Ultrasonics Symposium (IUS), pages 647–650. IEEE.
[3] A. L. Kellner, T. R. Nelson, L. I. Cervino, and J. M. Boone. Simulation of mechanical compression of breast tissue. 54(10):1885–1891.
[4] H. Khatam, G. P. Reece, M. C. Fingeret, M. K. Markey, and K. Ravi Chandar. In-vivo quantification of human breast deformation associated with the position change from supine to upright. 37(1):13–22.
[5] A. Mîra, A.-K. Carton, S. Muller, and Y. Payan. aUniv. grenoble alpes, CNRS, grenoble INP, VetAgro sup, TIMC-IMAG, 38000 grenoble, france. page 21.
[6] N. G. Ramião, P. S. Martins, R. Rynkevic, A. A. Fernandes, M. Barroso, and D. C. Santos. Biomechanical properties of breast tissue, a state-of-the-art review. 15(5):1307–1323.
[7] T.-C. Shih, J.-H. Chen, D. Liu, K. Nie, L. Sun, M. Lin, D. Chang, O. Nalcioglu, and M.-Y. Su. Computational simulation of breast compression based on segmented breast and fibroglandular tissues on magnetic resonance images. 55(14):4153–4168.
[8] G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars. Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation: FE compression for population of breast phantoms. 43(5):2207–2217.
[9] C. Wessel, J. A. Schnabel, and M. Brady. Realistic biomechanical model of a cancerous breast for the registration of prone to supine deformations. In 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pages 7249–7252. IEEE.

Real-time Error Control for Surgical Simulation

Real-time Error Control for Surgical Simulation

Real-time Error Control for Surgical Simulation

Real-time simulations are becoming increasingly common for various applications, from geometric design to medical simulation.

Two of the main factors concurrently involved in defining the accuracy of surgical simulations are: the modeling error and the discretization error. Most work in the area has been looking at the above sources of error as a compounded, lumped, overall error. Little or no work has been done to discriminate between modeling error (e.g. needle-tissue interaction, choice of constitutive models) and discretization error (use of approximation methods like FEM). However, it is impossible to validate the complete surgical simulation approach and, more importantly, to understand the sources of error, without evaluating both the discretization error and the modeling error.

Our objective is thus to devise a robust and fast approach to measure the discretization error via a posteriori error estimates, which are then used for local remeshing in surgical simulations. To ensure that the approach can be used in clinical practice, the method should be robust enough to deal, as realistically as possible, with the interaction of surgical tools with the organ, and fast enough for real-time simulations. The approach should also lead to an improved convergence so that an economical mesh is obtained at each time step. The final goal is to achieve optimal convergence and the most economical mesh, which will be studied in our future work.

The work was submitted to IEEE Transaction on Biomedical Engineering. This is the joint project between Legato team (Huu Phuoc Bui, Satyendra Tomar, Stéphane Bordas) and Stéphane Cotin (Mimesis Inria team, Strasbourg), and Hadrien Courtecuisse (ICube, Strasbourg).

Interested readers can refer to http://hdl.handle.net/10993/28624 or http://arxiv.org/abs/1610.02570 for more details.

This work is partially supported by University of Strasbourg Institute for Advanced Study, the European project RASimAs, and the  European Research Council Starting Independent Research Grant RealTCut (Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery).

 

liverliver_force_displacement

 

Useful links:

Computational Sciences at UL
http://wwwen.uni.lu/recherche/fstc/computational_sciences

Computational Engineering at UL
http://wwwen.uni.lu/recherche/fstc/research_unit_in_engineering_sciences_rues/research_areas/computational_engineering

Computational Sciences NEWS
http://wwwfr.uni.lu/fstc/actualites/computational_sciences_conclude_a_flourishing_year

Chargés de mission
http://wwwfr.uni.lu/universite/presentation/organigramme/organigramme_rectorat_administration_centrale/charge_de_mission

Uncertainty quantification for soft tissue biomechanics

Uncertainty quantification for soft tissue biomechanics

Uncertainty quantification for soft tissue biomechanics

GENERAL AIM OF THE WORK

– Assessing the effects of uncertainty in material parameters in soft tissue models.
– The sensitivity derivative Monte Carlo method provides one to two orders of magnitude better convergence than the standard Monte Carlo method.
– Complex models with only few lines of Python code (DOLFIN/FEniCS).

SUMMARY

– Stochastic FE analysis.
– Uncertainty quantification (material properties, loading, geometry, etc.).
– Random variables/fields.

image_RF

Two realisations (log-normal distribution)

– Global and local sensitivity analysis.
– Biomechanical modeling, simulation and analysis with random parameters.

fig_brain   ci

METHODS

– Monte Carlo and quasi Monte Carlo methods (Caflisch, 1998).
– Accelerating Monte Carlo estimation with sensitivity derivatives (Hauseux, Hale, and Bordas, 2016).
– Non-intrusive multi-level polynomial chaos expansion method.
– Multi Level Monte Carlo methods (Giles, 2015).

NUMERICAL IMPLEMENTATION

– DOLFIN/FEniCS:
– UFL (Unified Form Language) (Logg, Mardal, and Wells, 2012).
– Automatically deriving tangent linear models with FEniCS !
– Parallel computing (Ipyparallel and mpi4py).
– Python package for uncertainty quantification (Chaospy, SALib).

PUBLICATIONS

Accelerating Monte Carlo estimation with derivatives of high-level finite element models: Hauseux P., Hale J. and Bordas S.
Image to analysis pipeline: single and double balloons kyphoplasty: Baroli D., Hauseux P., Hale J. and Bordas S.
Bayesian statistical inference on the material parameters of a hyperelastic body: Hale J., Farrel P. and Bordas, S.

Computational Sciences at UL
http://wwwen.uni.lu/recherche/fstc/computational_sciences

Computational Engineering at UL
http://wwwen.uni.lu/recherche/fstc/research_unit_in_engineering_sciences_rues/research_areas/computational_engineering

Computational Sciences NEWS
http://wwwfr.uni.lu/fstc/actualites/computational_sciences_conclude_a_flourishing_year

Chargés de mission
http://wwwfr.uni.lu/universite/presentation/organigramme/organigramme_rectorat_administration_centrale/charge_de_mission

Real-time error controlled adaptive mesh refinement in surgical simulation: Application to needle insertion

http://hdl.handle.net/10993/28624

Real-time error controlled adaptive mesh refinement in surgical simulation: Application to needle insertion

 

submitted to the International Journal for Numerical Methods in Bioengineering. This is collaborative work with @tomar.sk here at Legato (on ERC RealTCut), @phuoc who starts with us in a few weeks and was funded by my Strasbourg Institute of Advanced Studies Fellowship and the team of Stéphane Cotin (Inria MEMESIS) and Hadrien Courtecuisse (former post-doc now at ICube in Strasbourg). Congratulations to everyone. This paper shows is the result of a long-lasting collaboration between Mathematics, Computer Science and Engineering and shows that error estimators can be useful also in real-time simulations through an example in liver surgery.

Congratulations!

Stéphane Bordas

Today’s Legato Themes: Wang Tiles and Computational Biomechanics

The planning for today’s group meeting:

1. At 0930, we will have a one hour discussion with Australia to put together the working plan for the visit of Grand Joldes and the PhD students he co-supervises with Karol Miller. They will visit us early June for 10 days.

2. At 1030, Jan Novák from Prague will present, along with his PhD students, jointly with Jan Zeman the most innovative and fascinating approach they have devised to generate arbitrary microstructures based on Wang Tilings.

— Stéphane Bordas

  

Mechanics of (sterile) needle insertion into Human skin

Mechanics of (sterile) needle insertion into Human skin

Several researchers have studied the force required to penetrate solid and some of constitutive models have been developed for the penetration of a soft solid but it seems non of them dealt with sterile needles insertion into human skin.

virtualwork

Understanding the total complexity of bio-mechanical/mechanical properties of the human skin and developing an advanced computational model (e.g. the Finite element skin models) that not differ (or not so much differ!) from experimental data would provide information which could be very useful for surgical training and practical use (special in this project, the goal is to inform the development of optimized device which can be used for effective and reproducible skin penetration in the clinical setting. This project will also provide and make it possible of generating a robust computational and physical model and an excellent technique for measuring skin deformation and in combination with advanced computational/mechanical methods it will also offer many possibilities for in vivo measurements).

For evaluation of simulation of needle insertion into human skin the development of the multilayer cutting will provide the required underlying basis.

Based in scientific and industrial progress,the multilayer cutting of soft solid is scattered over a considerable extent of interests and usefulness.As an application example is the remote robotic surgery or using created computer simulation program for surgical training.

The complex physics and mechanics of cutting process which requires advance knowledge of the fracture mechanics , deformation and friction additionally,can be modeled(3D Mixed-Mode Cracks Model) and imitated using different numerical computation methods such as the extended finite element method (XFEM)[a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM)] or cohesive elements method.In this study,the method used for simulation of cutting process is based on cohesive elements method.

Literature Review

In considering the complexity of non-linear mechanical behaviour of human skin and the Advanced Measurement Approaches, S Evans* and C A Holt School of Engineering, Cardiff University, UK (2008-2009)[mechanicalpropertiesofhumanskin][3], after a series of Experimental Measurements on human skin and related computational modelling which was the combination of digital image correlation and advanced Finite element modelling, found evidence to suggest,- due to reduction of the errors-,the applying stochastic optimization algorithms ,because output analysis of stochastic optimized algorithm will produce better result than Simplex algorithm and will enable the method to escape a local optimum and eventually to approach a global optimum.

In other studies by R.B. Grovesa, S.A. Coulmanb, J.C. Birchallb and S.L. Evans School of Engineering, Cardiff University, UK (2011)[Groves2012][Groves2012, hyperelasticmodelforskin][4,7], in order to optimised microneedle device designs, -which is completely depends on understanding of human skin biomechanics under small deformations-, after doing a series of optimized laboratory developed tests and using much more precise model(considering the skin as a multilayer composite)with applying multilayer finite element model( with the results of which show a remarkable degree of success) it could find out that because of not strictly accurate or precision between experimental and FEM measurements the problem with the precise approach! is still exist and it could be solved if some other materials property like viscoelasticity and anisotropy will be considered, which tends to reinforce the belief that optimum development of numerical-experimental procedure and modelling of very complex mechanical behavior of human skin, would require first the perfect understanding of dependency and independency of parts or elements of skin combined with mechanical description which can be used later for computational modeling.

Naturally all these studies were carried out in laboratory conditions with parallel load(Evans and Holt 2009) and perpendicular load( Grovesa, Coulmanb, Birchallb and Evans 2011) to the human skin surface.

Without being affected by complex nature of soft solid penetration, it is worth to say that the existing literature unfortunately provides not much insight the underlying mechanismus of penetration.Generally they indicate the deep penetration involves deformation and cracks and in most case without taking into account the existance of (sliding)friction.

There are two main studies which aim to help to develop this project.The first one is the study by Oliver A.Shergold and Norman A. Fleck (2004)[JonathanWainwright][9]with  development of the deep penetration of a soft solid by a flat-bottomed and by a sharp-tipped cylindrical punch with using one term Ogden strain energy function and considering the skin as an incompressible hyperelastic,isotropic solid and the second one is the study by Mohsen Mahvash and Vincent Hayward (2001)[vincenthayward][16] by developing the haptic rendering of cutting with a clarifying of the gemotry and mechanism of interaction of tools and sample.

References

[1] Enzo Berardesca. Bioengineering of the skin : methods and instrumentation. CRC series in dermatology. CRC Press, Boca Raton, 1995. lc95005294 edited by Enzo Berardesca … [et al.]ill ; 25 cm. Includes bibliographical references and index.

[2] Nuttapong Chentanez. Interactive simulation of surgical needle insertion and steering.

[3] Groves. Quantifying the mechanical properties of human skin to optimise future microneedle device design. Comput Methods Biomech Biomed Engin, 15(1):73–82, 2012. Groves, R B Coulman, S A Birchall, J C Evans, S L eng England 2011/07/14 06:00 Comput Methods Biomech Biomed Engin. 2012;15(1):73-82. doi: 10.1080/10255842.2011.596481. Epub 2011 Jul 12.

[4] Groves. An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. J Mech Behav Biomed Mater, 18:167–80, 2013. Groves, Rachel B Coulman, Sion A Birchall, James C Evans, Sam L eng Netherlands 2013/01/01 06:00 J Mech Behav Biomed Mater. 2013 Feb;18:167-80. doi: 10.1016/j.jmbbm.2012.10.021. Epub 2012 Nov 19.

[5] A. N. Guz, V. M. Nazarenko, and V. L. Bogdanov. Combined analysis of fracture under stresses acting along cracks. Archive of Applied Mechanics, 83(9):1273–1293, 2013.

[6] F.M. Hendriks. Mechanical behaviour of human skin in vivo.

[7] Holt and Evans. Measuring the mechanical properties of human skin in vivo using digital image correlation and finite element modelling. The Journal of Strain Analysis for Engineering Design, 44(5):337–345, 2009.

[8] Richard D. Wood Javier Bonet. Nonlinear continuum mechanics for finite element analysis.

[9] UK) 2367 2001 Feb 22 07:16:13 Jonathan Wainwright (T&T. Mechanisms of deep penetration of soft solids, with application to the injection and wounding of skin. 2004.

[10] Wen-mei Hwu Li-Wen Chang. A scalable, numerically stable, high-performance tridiagonal solver for gpus.

[11] Ronald Marks, P. A. Payne, and European Society for Dermatological Research. Bioengineering and the skin : based on the proceedings of the European Society for Dermatological Research symposium, held at the Welsh National School of Medicine, Cardiff, 19-21 July 1979. MTP, Lancaster, 1981. lc81014288 edited by R. Marks, P.A. Payne. ill ; 24 cm. Includes bibliographical references and index.

[12] Robert M. Nerem. Tissue engineering the science, the technology and the industry, 2007. : Robert Nerem. Animated audio-visual presentation with synchronized narration. Title from title frames. Contents: Historical perspective – Biomedical devices and diagnostics industry – Medical implant industry – Approved tissue products – Dermagraft – Tissue engineered skin substitutes – Cell source – Matrix – Immune tolerance – Off-the-shelf availability – Embryonic stem cells – Scaffolds – Bioreactor technology – Integration into the living system – Therapeutic products – Key industry trends – Advances envisioned. Mode of access: World Wide Web. System requirements: Operating System: PC Windows 2000+, Mac OSX+ 3.2. Browser Compatibility: IE6+, Firefox 2+, Opera 9+, Safari 2+ 3.3. Browser settings: enable JavaScript, enable popups from the Henry Stewart Talks site. 3.4. Required Browser Plugins & Viewers: Adobe (Macromedia) Flash Player 7+, Adobe Acrobat Reader 6.0+. Henry Stewart talks. * Cardiff University Internet Electronic Seminars.

[13] R. Radovitzky, A. Seagraves, M. Tupek, and L. Noels. A scalable 3d fracture and fragmentation algorithm based on a hybrid, discontinuous galerkin, cohesive element method. Computer Methods in Applied Mechanics and Engineering, 200(1-4):326–344, 2011.

[14] James R. Rice. Mathematical analysis in the mechanics of fracture.

[15] David Roylance. Introduction to fracture mechanics.

[16] vincent hayward. Haptic rendering of cutting: A fracture mechanics approach. 2001.

[17] M.T. Hayajneh V.P. Astakhov, M.O.M. Osman. Re-evaluation of the basic mechanics of orthogonal metal cutting: velocity diagram, virtual work equation and upper-bound theorem.

[18] H. U. I. Wang and Qing-Hua Qin. A fundamental solution-based finite element model for analyzing multi-layer skin burn injury. Journal of Mechanics in Medicine and Biology, 12(05):1250027, 2012.

[19] T. TYAN* YANG’ and WE1 H. Analysis of orthogonal metal cutting processes.

 

Hybrid lattice continuum approach to interactive cutting in soft tissues.

Hybrid lattice continuum approach to interactive cutting in soft tissues.

fractured_coupling

 

The outcome of cutting, tearing, needle insertion and similar operations which require topological changes, or contact detection, is significantly affected by the microstructure of the material (discontinuities, holes, interfaces) remaining some of the most difficult surgical gestures to simulate. We are interested in the development of a numerical tool capable of the interactive simulation of surgical cutting using a multi-domain lattice-continuum approach. Around the cutting region, a mesoscopic discrete lattice approach suitable for initiation of cuts and subsequent tears is used. The remaining regions can be modeled by a continuum approach or through model reduction approaches based on pre-computations. The algorithms are implemented within the SOFA framework which is  targets  real-time computations, with an emphasis on medical simulation and the work is being performed in collaboration with the group of Dr Hadrien Courtecuisse and Dr Stéphane Cotin in Strasbourg.

The final goal of this project is to simulate in real-time the cutting of heterogeneous of soft-tissues using two-scale model instead of using one macroscopic model as in Courtecuisse, H., Allard, J., Kerfriden, P., Bordas, S. P. a, Cotin, S., & Duriez, C. (2014). Real-time simulation of contact and cutting of heterogeneous soft-tissues. Medical Image Analysis, 18(2), 394–410. doi:10.1016/j.media.2013.11.001 [Download].

The work is partially funded by USIAS – University of Strasbourg Institute for Advanced Study. Details can be found here.

The work is being performed by Huu Phuoc Bui within Legato team led by Stéphane P.A. Bordas in direct collaboration with Stéphane Cotin, Hadrien Courtecuisse and Michel de Mathelin in MIMESIS and AVR teams in Strasbourg.

Coupling robotics and medical simulation for automatic procedures – CONECT

Coupling robotics and medical simulation for automatic procedures – CONECT

Coupling robotics and medical simulation for automatic procedures.– CONECT”.

The objective of this project is to develop a robotic system, controlled by simulation, for inserting medical needles in the context of interventional radiology for the treatment of cancer. Regarding this work, the aspect of our research can be split into two parts.The first concerns the improvment of the calculations of the simulation time in order to transmit this information quickly enough to the simulated robotic system. The second concerns the coupling of robotics for addressing  problems such as the simulation accuracy and  the error estimation.

This project is funded by Labex funding to Dr Hadrien Courtecuisse in collaboration with Michel de Mathelin and Stéphane P. A. Bordas

 

Statistical Parameter Identification

Statistical Parameter Identification

Core Team Members: Jack S. Hale, Team Legato, University of Luxembourg.
Collaborators: Patrick Farrell, Oxford University.

« Supported by the Fonds National de la Recherche, Luxembourg (#6693582) »

Logos_FNR_MC+CMYK

In this project we are developing computational methods to understand the uncertainty in the recovered material parameters from limited and noisy displacement observations of a hyperelastic material body. This has important applications in developing patient specific models for surgical simulation when direct observations of material properties cannot be made. The addition of statistical information allows the user understand limitations in experimental methodologies, equipment and poor model selection.

Using any suitable medical imaging method we calculate a displacement field of the body and then perform an adjoint based PDE-constrained optimisation problem to recover the material parameters.

Using Bayes’ theorem, we recover the statistical information about the posterior distribution (the probability that we have the material properties given the limited and noisy observations) by forming a low-rank decomposition of the Hessian matrix of the minimisation functional evaluated at the maximum aposteriori point.

Trailing Eigenvector of Hessian evaluated at the maximum aposteriori point.

Trailing Eigenvector of Hessian evaluated at the maximum aposteriori point. The truth value is a circular inclusion and limited and noisy observations are available only on the boundary of the domain. This eigenvector corresponds to the parameters that are least constrained by the given observation data, e.g. across the interface and inside the inclusion.