Inverse Heat Conduction Problem
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Cited by 2 publications
References 16 publications
Where did the tumor start? An inverse solver with sparse localization for tumor growth models
We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of Magnetic Resonance Imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver. Related work.Although there has been a lot of work on forward problems for tumor growth, there has been less work on inverse problems. The latter has different aspects. The first is the underlying biophysical model. The second is the inverse problem setup, observation operators and the existence of scans at multiple points, the noise models, inversion parameters and constraints. And the third one is the solution algorithm.Regarding the underlying model, like us, most researchers focus on parameter calibration of a handful of model parameters using single-species reaction-diffusion equations [7,22,24,28,33,39,51,58,59]. While more complex models describing processes like mass effect, angiogenesis and chemotaxis [23,26,48,54,60] exist, they have not been considered for calibration due to theoretical and computational challenges. However, several groups, including ours, are working to address these challenges.Regarding the inverse problem setup, in most studies t...
Where did the tumor start? An inverse solver with sparse localization for tumor growth models
We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of Magnetic Resonance Imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver. Related work.Although there has been a lot of work on forward problems for tumor growth, there has been less work on inverse problems. The latter has different aspects. The first is the underlying biophysical model. The second is the inverse problem setup, observation operators and the existence of scans at multiple points, the noise models, inversion parameters and constraints. And the third one is the solution algorithm.Regarding the underlying model, like us, most researchers focus on parameter calibration of a handful of model parameters using single-species reaction-diffusion equations [7,22,24,28,33,39,51,58,59]. While more complex models describing processes like mass effect, angiogenesis and chemotaxis [23,26,48,54,60] exist, they have not been considered for calibration due to theoretical and computational challenges. However, several groups, including ours, are working to address these challenges.Regarding the inverse problem setup, in most studies t...
Use of Inverse Method for Bonding Quality Assessment Between Bitumen and Aggregates Under Asphalt Mixes Manufacturing Conditions
To cite this version:Sâannibè Ciryle Some, Vincent Gaudefroy, Didier Delaunay. Use of inverse method for bonding quality assessment between bitumen and aggregates under asphalt mixes manufacturing conditions. Proceedings of the 11th Biennal Conference on Engineering Systems Design and Analysis, TRK 8, Jul 2012, France. 9p, 2012 ABSTRACTIn roads building, classical asphalt mix manufacturing commonly requires the heating (at 160°C) and the complete drying of aggregates. The induced energy cost has opened the way to develop alternatives processes and materials with low energy/carbon materials such as Warm Mix Asphalt (WMA). In warm mixes processes, aggregates manufacturing temperatures are different and lower than the Hot Mix ones. However, manufacturing temperature reduction can locally lead to poor bonding between bitumen and aggregate during the mixing step, due to the bitumen viscosity increasing, although bonding quality measurement remained a challenge. The aim of our study was to presents two thermal inverse methods for bonding quality assessment. These methods are based on Thermal Contact Resistance (TCR) assessment between bitumen and aggregate, during asphalt mix manufacturing. The experimental test principle consisted of heating both bitumen and cylindrical aggregate to their manufacturing temperatures (over 100°C) and to put them into contact thanks to a special experimental device. According to initial samples temperatures, heat transfer occurs from the bitumen to the aggregate. Two variants of the sequential Beck's method were used to solve the inverse heat conduction problem. The first one consisted of determining the TCR from heat flux and temperatures and the second one consisted of identifying directly the TCR. The TCR values were interpreted as bonding quality criteria.Results showed low sensitivity to temperature measurement noise in the second variant of the inverse method. Moreover our study showed that bonding quality depends on bitumen and aggregate temperatures. The higher the component's temperatures, the lower the TCR values and better is the bonding quality. INTRODUCTIONIn roads building, classical asphalt mix manufacturing commonly requires the heating (at 160°C) and the complete drying of aggregates. This operation induces high energy consumption. In the last decade roads companies have developed new processes based on fuel consumption reduction. In these processes coarses aggregates temperatures can be reduced significantly [1][2][3]. The component's temperatures reduction induces bitumen viscosity increases. However, the effect of this high viscosity on the bonding property between bitumen and aggregates are not well known. In the manufacturing step, hot liquid bitumen comes into contact with hot or warm aggregates. This leads to bonding between the bitumen and aggregates. The influence of bitumen and aggregates temperatures on the bonding quality has not been studied yet at manufacturing conditions. However, some studies
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