We consider a solution to the problem of time in quantum gravity by deparameterisation of the ADM action in terms of York time, a parameter proportional to the extrinsic curvature of a spatial hypersurface. We study a minisuperspace model together with a homogeneous scalar field, for which we can solve the Hamiltonian constraint exactly and arrive at an explicit expression for the physical (non-vanishing) Hamiltonian. The scale factor and associated momentum cease to be dynamical variables, leaving the scalar field as the only physical degree of freedom. We investigate the resulting classical theory, showing how the dynamics of the scale factor can be recovered via an appropriate interpretation of the Hamiltonian as a volume. We then quantise the system in the Schrödinger picture. In the quantum theory we recover the dynamics of the scale factor by interpreting the spectrum and expectation value of the Hamiltonian as being associated with volume rather than energy. If trajectories in the sense of de Broglie-Bohm are introduced in the quantum theory, these are found to match those of the classical theory. We suggest that these trajectories may provide the basis for a perturbation theory in which both background and perturbations are quantised.
In tomographic imaging, anatomical structures are reconstructed by applying a pseudo-inverse forward model to acquired signals. Geometric information within this process is usually depending on the system setting only, i. e., the scanner position or readout direction. Patient motion therefore corrupts the geometry alignment in the reconstruction process resulting in motion artifacts. We propose an appearance learning approach recognizing the structures of rigid motion independently from the scanned object. To this end, we train a siamese triplet network to predict the reprojection error (RPE) for the complete acquisition as well as an approximate distribution of the RPE along the single views from the reconstructed volume in a multi-task learning approach. The RPE measures the motioninduced geometric deviations independent of the object based on virtual marker positions, which are available during training. We train our network using 27 patients and deploy a 21-4-2 split for training, validation and testing. In average, we achieve a residual mean RPE of 0.013 mm with an inter-patient standard deviation of 0.022 mm. This is twice the accuracy compared to previously published results. In a motion estimation benchmark the proposed approach achieves superior results in comparison with two state-of-the-art measures in nine out of twelve experiments. The clinical applicability of the proposed method is demonstrated on a motion-affected clinical dataset.
Purpose Radiation doses accumulated during very complicated image‐guided x‐ray procedures have the potential to cause stochastic, but also deterministic effects, such as skin rashes or even hair loss. To monitor and reduce radiation‐related risks to patients’ skin, x‐ray imaging devices are equipped with online air kerma monitoring components. Traditionally, such measurements have been used to estimate skin entrance dose by (a) estimating air kerma at the interventional reference point (IRP), (b) forward projecting the dose distribution, and (c) considering a backscatter factor among other correction factors. Unfortunately, the complicated interaction between incident x‐ray photons, secondary electrons, and skin tissue cannot be properly accounted for by assuming a linear relationship between forward projected air kerma and a backscatter factor. Gold standard skin dose models are therefore determined using Monte Carlo (MC) techniques. However, MC simulations are computationally complex in general and possible acceleration mainly depends on the employed hardware and variance reduction techniques. To obtain reliable and fast dose estimates, we propose to combine MC‐based simulations with learning‐based methods. Methods The basic idea of our method is to approximate the radiation physics to calculate a first‐order exposure estimate quickly. This initial estimate is then refined using prior knowledge derived from MC simulations. To this end, the primary photon propagation inside a voxelized patient model is estimated using a less accurate but fast photon ray casting (RC) simulation based on the Beer–Lambert law. The results of the RC simulation are then fed into a convolutional neural network (CNN), which maps the propagation of primary photons to the dose deposition inside the patient model. Additionally, the patient model itself including anatomy and material properties, such as mass density and mass energy‐absorption coefficients, are fed into the CNN as well. The CNN is trained using smoothed results of MC simulations as output and RC simulations of identical imaging settings and patient models as input. Results In total, 163 MC and associated RC simulations are carried out for the head, thorax, abdomen, and pelvis in three different voxel phantoms. We used 108 or 109 primarily emitted photons sampled from a 125 kV peak voltage spectrum, respectively. Edge‐preserving smoothing (EPS) is applied to reduce (a) general stochastic uncertainties and (b) stochastic uncertainty concerning MC simulations of less primary photons. The CNN is trained using seven imaging settings of the abdomen in a single phantom. Testing its performance on the remaining datasets, the CNN is capable of estimating skin dose with an error of below 10% for the majority of test cases. Conclusion The combination of deep neural networks and MC simulation of particle physics has the potential to decrease the computational complexity of accurate skin dose estimation. The proposed approach can provide dose distributions in under one second when runni...
Purpose With X-ray radiation protection and dose management constantly gaining interest in interventional radiology, novel procedures often undergo prospective dose studies using anthropomorphic phantoms to determine expected reference organ-equivalent dose values. Due to inherent uncertainties, such as impact of exact patient positioning, generalized geometry of the phantoms, limited dosimeter positioning options, and composition of tissue-equivalent materials, these dose values might not allow for patient-specific risk assessment. Therefore, first the aim of this study is to quantify the influence of these parameters on local X-ray dose to evaluate their relevance in the assessment of patientspecific organ doses. Second, this knowledge further enables validating a simulation approach, which allows employing physiological material models and patient-specific geometries.Methods Phantom dosimetry experiments using MOSFET dosimeters were conducted reproducing imaging scenarios in prostatic arterial embolization (PAE). Associated organequivalent dose of prostate, bladder, colon and skin was determined. Dose deviation induced by possible small displacements of the patient was reproduced by moving the X-ray source. Dose deviation induced by geometric and material differences was investigated by analyzing two different commonly used phantoms. We reconstructed the experiments using Monte Carlo (MC) simulations, a reference male geom-1 Pattern Recognition Lab, FAU Erlangen-Nürnberg, etry, and different material properties to validate simulations and experiments against each other. ResultsOverall, MC simulated organ dose values are in accordance with the measured ones for the majority of cases. Marginal displacements of X-ray source relative to the phantoms lead to deviations of 6 % to 135 % in organ dose values, while skin dose remains relatively constant. Regarding the impact of phantom material composition, underestimation of internal organ dose values by 12 % to 20 % is prevalent in all simulated phantoms. Skin dose, however, can be estimated with low deviation of 1 % to 8 % at least for two materials.Conclusions Prospective reference dose studies might not extend to precise patient-specific dose assessment. Therefore online organ dose assessment tools, based on advanced patient modeling and MC methods are desirable.
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