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Abstract
In the healthcare system, a goal is to provide effective diagnosis and treatment to patients. However, gaining a comprehensive understanding of the underlying mechanisms within the human body is often necessary to achieve this objective. Often, we cannot not directly observe these mechanisms, since it is not feasible and/or practical to gain access directly. Instead, we can describe the mechanisms using mathematical models that are characterized by a set of parameters. The mathematical models relate the parameters of interest to available noninvasive measurements, and we can use the parameters to, e.g., predict the response to treatment or assess the severity of diseases. In this thesis we explore the two applications:
• Computed tomography: A noninvasive imaging technique.
• Hemodialysis: A treatment for patients with kidney failure.
The aim of this thesis is to obtain a better understanding of the underlying mechanisms for the two applications such that we for instance might enable tailor patientspecific treatments in hemodialysis and improve the quality of low dose experiments in computed tomography. We employ Bayesian modeling and uncertainty quantification to formulate mathematical models for computed tomography and hemodialysis that allow us to estimate the parameters of interest along with their statistical properties such as mean, covariance and credible intervals.
In computed tomography, radiation is emitted from a source which is partially absorbed as it travels through the object of interest, e.g., the human body. Based on the absorption, images of the interior can be reconstructed. To obtain these images, it is necessary to know the intensity of the source which is typically estimated by flatfield measurements, i.e., measurements without an object in the scanner. However, for low dose and/or timelimited experiments, discrepancies between the true and estimated source can introduce systematic model errors which appear as concentric rings in the image, also known as ring artifacts. We employ modeling techniques for mitigating ring artifacts caused by model errors, and the key finding is that, by using explicit modeling of the source, it is possible to eliminate ring artifacts from the images.
We have also considered ring reduction for spectral computed tomography. In spectral computed tomography, the attenuation is measured at multiple energies, which enables the reconstruction of images at individual energy levels, which is referred to as a spectral reconstruction. The spectral reconstruction suffers from ring artifacts, and we propose an extended flatfield model for mitigating ring artifacts which exploits high correlation across energy channels in the spectral flatfields.
Patients with kidney failure often suffer from hyperphosphatemia which is associated with increased vascular calcification and mortality. Thus, it is of great importance to regulate the phosphate level of the kidneyfailure patients. Hemodialysis is a method for removing phosphate from the blood of the patient. The patient is connected to a dialyzer where blood and dialysate fluid are separated by a semipermeable membrane allowing phosphate to move from the blood of the patient to the dialysate fluid. We consider the phosphate removal during hemodialysis in a Bayesian framework. We compare two types of hemodialysis treatments, i.e., singlepass and multiplepass, and find that the uncertainty of the parameters estimated based on the singlepass model is greater than those estimated based on the multiplepass model. Moreover, a key finding is that the uncertainty of the parameter estimates is greatly reduced by measuring the patients for consecutive treatments whereas measurements in the relapse phase has limited effect on the precision of the parameter estimates.
This thesis contributes to an enhanced understanding of artifacts in computed tomography and phosphate removal during hemodialysis using Bayesian modeling and uncertainty quantification.
• Computed tomography: A noninvasive imaging technique.
• Hemodialysis: A treatment for patients with kidney failure.
The aim of this thesis is to obtain a better understanding of the underlying mechanisms for the two applications such that we for instance might enable tailor patientspecific treatments in hemodialysis and improve the quality of low dose experiments in computed tomography. We employ Bayesian modeling and uncertainty quantification to formulate mathematical models for computed tomography and hemodialysis that allow us to estimate the parameters of interest along with their statistical properties such as mean, covariance and credible intervals.
In computed tomography, radiation is emitted from a source which is partially absorbed as it travels through the object of interest, e.g., the human body. Based on the absorption, images of the interior can be reconstructed. To obtain these images, it is necessary to know the intensity of the source which is typically estimated by flatfield measurements, i.e., measurements without an object in the scanner. However, for low dose and/or timelimited experiments, discrepancies between the true and estimated source can introduce systematic model errors which appear as concentric rings in the image, also known as ring artifacts. We employ modeling techniques for mitigating ring artifacts caused by model errors, and the key finding is that, by using explicit modeling of the source, it is possible to eliminate ring artifacts from the images.
We have also considered ring reduction for spectral computed tomography. In spectral computed tomography, the attenuation is measured at multiple energies, which enables the reconstruction of images at individual energy levels, which is referred to as a spectral reconstruction. The spectral reconstruction suffers from ring artifacts, and we propose an extended flatfield model for mitigating ring artifacts which exploits high correlation across energy channels in the spectral flatfields.
Patients with kidney failure often suffer from hyperphosphatemia which is associated with increased vascular calcification and mortality. Thus, it is of great importance to regulate the phosphate level of the kidneyfailure patients. Hemodialysis is a method for removing phosphate from the blood of the patient. The patient is connected to a dialyzer where blood and dialysate fluid are separated by a semipermeable membrane allowing phosphate to move from the blood of the patient to the dialysate fluid. We consider the phosphate removal during hemodialysis in a Bayesian framework. We compare two types of hemodialysis treatments, i.e., singlepass and multiplepass, and find that the uncertainty of the parameters estimated based on the singlepass model is greater than those estimated based on the multiplepass model. Moreover, a key finding is that the uncertainty of the parameter estimates is greatly reduced by measuring the patients for consecutive treatments whereas measurements in the relapse phase has limited effect on the precision of the parameter estimates.
This thesis contributes to an enhanced understanding of artifacts in computed tomography and phosphate removal during hemodialysis using Bayesian modeling and uncertainty quantification.
Original language  English 

Publisher  Technical University of Denmark 

Number of pages  172 
Publication status  Published  2023 
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 1 Finished

Prior Modeling for Computational UQ for Inverse Problems
Bangsgaard, K. O., Andersen, M. S., Hansen, P. C., Jørgensen, J. S., Batenburg, K. J. & Gazzola, S.
01/09/2019 → 30/10/2023
Project: PhD