arXiv subjects

Michael Manhart

Publications and source records attributed to Michael Manhart.

At least 19 recordsLinked to original sources

arXiv2026

Similarity of start-up flow in porous media for large pressure gradients

We investigate the start-up flows through ordered porous media (hexagonal close-packed, face-centred cubic and body-centred sphere packs) by means of direct numerical simulations. The flows are initiated from rest and driven by a constant pressure gradient, allowing us to examine the transient development across a wide range of Hagen numbers. Dimensional analysis identifies two relevant time scales: the viscous diffusion time $\tau_\mathrm{visc}$ and the inviscid time $\tau_\mathrm{inv}$. While the small-time behaviour follows the viscous asymptotics of Johnson et al. [J. Fluid. Mech. 176, 379 (1987)], the subsequent emergence of nonlinear effects is universally governed by the inviscid time $\tau_\mathrm{inv}$, rather than by any critical Reynolds number. At the pore scale, the transient evolution is characterised by the growth of thin vorticity layers on the sphere surfaces, their detachment into the pore space around $t \sim \tau_\mathrm{inv}$, and the formation of inertial cores. Despite geometric differences, these processes occur in a remarkably similar sequence across all three packings. Vorticity magnitude exhibits laminar boundary-layer scaling with Hagen number, while in the body-centred cubic sphere pack case a transition towards turbulent-type scaling is observed. These results establish $\tau_\mathrm{inv}$ as a unifying measure for the onset of nonlinearity in strongly accelerated porous media flows, with direct implications for the modelling of unsteady transport in natural and engineered systems.

physics.flu-dyn↗

arXiv2024

Model-Based Perfusion Reconstruction with Time Separation Technique in Cone-Beam CT Dynamic Liver Perfusion Imaging

The success of embolisation, a minimally invasive treatment of liver cancer, could be evaluated in the operational room with cone-beam CT by acquiring a dynamic perfusion scan. The reconstruction algorithm must address the issues of low temporal sampling and higher noise levels inherent in cone-beam CT systems, compared to conventional CT. Therefore, a model-based perfusion reconstruction based on the time separation technique (TST) was applied. TST uses basis functions to model time attenuation curves. These functions are either analytical or based on prior knowledge, extracted using singular value decomposition from CT perfusion data. To explore how well the prior knowledge can model perfusion dynamics and what the potential limitations are, the dynamic CBCT perfusion scan was simulated under different noise levels. The TST method was compared to static reconstruction. It was demonstrated that a set consisting of only four basis functions results in perfusion maps that preserve relevant information, denoises the data, and outperforms static reconstruction under higher noise levels. TST with prior knowledge would not only outperform static reconstruction, but also the TST with analytical basis functions. Furthermore, it has been shown that only eight CBCT rotations, unlike previously assumed ten, are sufficient to obtain the perfusion maps comparable to the reference CT perfusion maps. This contributes to saving dose and reconstruction time. The real dynamic CBCT perfusion scan, reconstructed under the same conditions as the simulated scan, shows potential for maintaining the accuracy of the perfusion maps. By visual inspection, the embolised region was matching to that in corresponding CT perfusion maps. Further analysis of a larger cohort of patient data is needed to draw final conclusions regarding the expected advantages of the time separation technique.

physics.med-ph↗

arXiv2024

Assessment of models for nonlinear oscillatory flow through a hexagonal sphere pack

We review models for unsteady porous media flow in the volume-averaging framework and we discuss the theoretical relations between the models and the definition of the model coefficients (and the uncertainty therein). The different models are compared against direct numerical simulations of oscillatory flow through a hexagonal sphere pack. The model constants are determined based on their definition in terms of the Stokes flow, the potential flow and steady nonlinear flow. Thus, the discrepancies between the model predictions and the simulation data can be attributed to shortcomings of the models' parametrisation. We found that an extension of the dynamic permeability model of Pride et al. [Physical Review B 47(9), 1993] with a Forchheimer-type nonlinearity performs very well for linear flow and for nonlinear flow at low and medium frequencies, but the Forchheimer term with a coefficient obtained from the steady-state overpredicts the nonlinear drag at high frequencies. The model reduces to the unsteady Forchheimer equation with an acceleration coefficient based on the static viscous tortuosity for low frequencies. The unsteady Forchheimer equation with an acceleration coefficient based on the high frequency limit of the dynamic tortuosity has large errors for linear flow at medium and high frequencies, but low errors for nonlinear flow at all frequencies. This is explained by an error cancellation between the inertial and the nonlinear drag.

physics.flu-dyn↗

arXiv2024

A gradient-based approach to fast and accurate head motion compensation in cone-beam CT

Cone-beam computed tomography (CBCT) systems, with their flexibility, present a promising avenue for direct point-of-care medical imaging, particularly in critical scenarios such as acute stroke assessment. However, the integration of CBCT into clinical workflows faces challenges, primarily linked to long scan duration resulting in patient motion during scanning and leading to image quality degradation in the reconstructed volumes. This paper introduces a novel approach to CBCT motion estimation using a gradient-based optimization algorithm, which leverages generalized derivatives of the backprojection operator for cone-beam CT geometries. Building on that, a fully differentiable target function is formulated which grades the quality of the current motion estimate in reconstruction space. We drastically accelerate motion estimation yielding a 19-fold speed-up compared to existing methods. Additionally, we investigate the architecture of networks used for quality metric regression and propose predicting voxel-wise quality maps, favoring autoencoder-like architectures over contracting ones. This modification improves gradient flow, leading to more accurate motion estimation. The presented method is evaluated through realistic experiments on head anatomy. It achieves a reduction in reprojection error from an initial average of 3mm to 0.61mm after motion compensation and consistently demonstrates superior performance compared to existing approaches. The analytic Jacobian for the backprojection operation, which is at the core of the proposed method, is made publicly available. In summary, this paper contributes to the advancement of CBCT integration into clinical workflows by proposing a robust motion estimation approach that enhances efficiency and accuracy, addressing critical challenges in time-sensitive scenarios.

eess.IV↗

arXiv2022

Gradient-Based Geometry Learning for Fan-Beam CT Reconstruction

Incorporating computed tomography (CT) reconstruction operators into differentiable pipelines has proven beneficial in many applications. Such approaches usually focus on the projection data and keep the acquisition geometry fixed. However, precise knowledge of the acquisition geometry is essential for high quality reconstruction results. In this paper, the differentiable formulation of fan-beam CT reconstruction is extended to the acquisition geometry. This allows to propagate gradient information from a loss function on the reconstructed image into the geometry parameters. As a proof-of-concept experiment, this idea is applied to rigid motion compensation. The cost function is parameterized by a trained neural network which regresses an image quality metric from the motion affected reconstruction alone. Using the proposed method, we are the first to optimize such an autofocus-inspired algorithm based on analytical gradients. The algorithm achieves a reduction in MSE by 35.5 % and an improvement in SSIM by 12.6 % over the motion affected reconstruction. Next to motion compensation, we see further use cases of our differentiable method for scanner calibration or hybrid techniques employing deep models.

eess.IV↗

arXiv2020

Appearance Learning for Image-based Motion Estimation in Tomography

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 0.013mm 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.

eess.IV↗

arXiv2020

Data Consistent CT Reconstruction from Insufficient Data with Learned Prior Images

Image reconstruction from insufficient data is common in computed tomography (CT), e.g., image reconstruction from truncated data, limited-angle data and sparse-view data. Deep learning has achieved impressive results in this field. However, the robustness of deep learning methods is still a concern for clinical applications due to the following two challenges: a) With limited access to sufficient training data, a learned deep learning model may not generalize well to unseen data; b) Deep learning models are sensitive to noise. Therefore, the quality of images processed by neural networks only may be inadequate. In this work, we investigate the robustness of deep learning in CT image reconstruction by showing false negative and false positive lesion cases. Since learning-based images with incorrect structures are likely not consistent with measured projection data, we propose a data consistent reconstruction (DCR) method to improve their image quality, which combines the advantages of compressed sensing and deep learning: First, a prior image is generated by deep learning. Afterwards, unmeasured projection data are inpainted by forward projection of the prior image. Finally, iterative reconstruction with reweighted total variation regularization is applied, integrating data consistency for measured data and learned prior information for missing data. The efficacy of the proposed method is demonstrated in cone-beam CT with truncated data, limited-angle data and sparse-view data, respectively. For example, for truncated data, DCR achieves a mean root-mean-square error of 24 HU and a mean structure similarity index of 0.999 inside the field-of-view for different patients in the noisy case, while the state-of-the-art U-Net method achieves 55 HU and 0.995 respectively for these two metrics.

eess.IV↗

arXiv2019

Deep autofocus with cone-beam CT consistency constraint

High quality reconstruction with interventional C-arm cone-beam computed tomography (CBCT) requires exact geometry information. If the geometry information is corrupted, e. g., by unexpected patient or system movement, the measured signal is misplaced in the backprojection operation. With prolonged acquisition times of interventional C-arm CBCT the likelihood of rigid patient motion increases. To adapt the backprojection operation accordingly, a motion estimation strategy is necessary. Recently, a novel learning-based approach was proposed, capable of compensating motions within the acquisition plane. We extend this method by a CBCT consistency constraint, which was proven to be efficient for motions perpendicular to the acquisition plane. By the synergistic combination of these two measures, in and out-plane motion is well detectable, achieving an average artifact suppression of 93 [percent]. This outperforms the entropy-based state-of-the-art autofocus measure which achieves on average an artifact suppression of 54 [percent].

cs.LG↗

arXiv2019

Image Quality Assessment for Rigid Motion Compensation

Diagnostic stroke imaging with C-arm cone-beam computed tomography (CBCT) enables reduction of time-to-therapy for endovascular procedures. However, the prolonged acquisition time compared to helical CT increases the likelihood of rigid patient motion. Rigid motion corrupts the geometry alignment assumed during reconstruction, resulting in image blurring or streaking artifacts. To reestablish the geometry, we estimate the motion trajectory by an autofocus method guided by a neural network, which was trained to regress the reprojection error, based on the image information of a reconstructed slice. The network was trained with CBCT scans from 19 patients and evaluated using an additional test patient. It adapts well to unseen motion amplitudes and achieves superior results in a motion estimation benchmark compared to the commonly used entropy-based method.

eess.IV↗

arXiv2019

Data Consistent Artifact Reduction for Limited Angle Tomography with Deep Learning Prior

Robustness of deep learning methods for limited angle tomography is challenged by two major factors: a) due to insufficient training data the network may not generalize well to unseen data; b) deep learning methods are sensitive to noise. Thus, generating reconstructed images directly from a neural network appears inadequate. We propose to constrain the reconstructed images to be consistent with the measured projection data, while the unmeasured information is complemented by learning based methods. For this purpose, a data consistent artifact reduction (DCAR) method is introduced: First, a prior image is generated from an initial limited angle reconstruction via deep learning as a substitute for missing information. Afterwards, a conventional iterative reconstruction algorithm is applied, integrating the data consistency in the measured angular range and the prior information in the missing angular range. This ensures data integrity in the measured area, while inaccuracies incorporated by the deep learning prior lie only in areas where no information is acquired. The proposed DCAR method achieves significant image quality improvement: for 120-degree cone-beam limited angle tomography more than 10% RMSE reduction in noise-free case and more than 24% RMSE reduction in noisy case compared with a state-of-the-art U-Net based method.

eess.IV↗

arXiv2018

Maximum Likelihood Estimation of Head Motion using Epipolar Consistency

Open gantry C-arm systems that are placed within the interventional room enable 3-D imaging and guidance for stroke therapy without patient transfer. This can profit in drastically reduced time-totherapy, however, due to the interventional setting, the data acquisition is comparatively slow. Thus, involuntary patient motion needs to be estimated and compensated to achieve high image quality. Patient motion results in a misalignment of the geometry and the acquired image data. Consistency measures can be used to restore the correct mapping to compensate the motion. They describe constraints on an idealized imaging process which makes them also sensitive to beam hardening, scatter, truncation or overexposure. We propose a probabilistic approach based on the Student's t-distribution to model image artifacts that affect the consistency measure without sourcing from motion.

physics.med-ph↗

arXiv2018

Fast Epipolar Consistency without the Need for Pseudo Matrix Inverses

Interventional C-arm systems allow flexible 2-D imaging of a 3-D scene while being capable of cone beam computed tomography. Due to the flexible structure of the C-arm, the rotation speed is limited, increasing the acquisition time compared to conventional computed tomography. Therefore, patient motion frequently occurs during data acquisition inducing inconsistencies in the projection raw data. A framework using Grangeat's theorem and epipolar consistency was successfully applied for compensating rigid motion. This algorithm was efficiently parallelized, however, before each iteration, the pseudoinverse of each projection matrix must be calculated. We present a geometric modification of the presented algorithm which can be used without a pseudo-inverse. As such, the complete algorithm can be implemented for low-level hardware without the need of a linear algebra package that supports the calculation of matrix inverse. Both algorithms are applied for head motion compensation and the runtime of both is compared.

physics.med-ph↗

arXiv2018

Numerical simulation of transport in porous media: some problems from micro to macro scale

This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of tracers is strongly influenced by pore scale velocity structure and large scale inhomogeneities in the permeability field. The velocity structure on the pore scale is investigated by direct numerical simulations of the 3D velocity field in a random sphere pack. The velocity probability density functions are strongly skewed, including some negative velocities. The large probability for very small velocities might be the reason for non-Fickian dispersion in the initial phase of contaminant transport. We present a method to determine large scale distributions of the permeability field from point-wise velocity measurements. The adjoint-based optimisation algorithm delivers fully satisfying agreement between input and estimated permeability fields. Finally numerical methods for convection dominated tracer transports are investigated from a theoretical point of view. It is shown that high order Finite Element Methods can reduce or even eliminate non-physical oscillations in the solution without introducing additional numerical diffusivity.

math.NA↗

arXiv2018

Double Your Views - Exploiting Symmetry in Transmission Imaging

For a plane symmetric object we can find two views - mirrored at the plane of symmetry - that will yield the exact same image of that object. In consequence, having one image of a plane symmetric object and a calibrated camera, we can automatically have a second, virtual image of that object if the 3-D location of the symmetry plane is known. In this work, we show for the first time that the above concept naturally extends to transmission imaging and present an algorithm to estimate the 3-D symmetry plane from a set of projection domain images based on Grangeat's theorem. We then exploit symmetry to generate a virtual trajectory by mirroring views at the plane of symmetry. If the plane is not perpendicular to the acquired trajectory plane, the virtual and real trajectory will be oblique. The resulting X-shaped trajectory will be data-complete, allowing for the compensation of in-plane motion using epipolar consistency. We evaluate the proposed method on a synthetic symmetric phantom and, in a proof-of-concept study, apply it to a real scan of an anthropomorphic human head phantom.

physics.med-ph↗

arXiv2018

Growth tradeoffs produce complex microbial communities on a single limiting resource

The relationship between the dynamics of a community and its constituent pairwise interactions is a fundamental problem in ecology. Higher-order ecological effects beyond pairwise interactions may be key to complex ecosystems, but mechanisms to produce these effects remain poorly understood. Here we show that higher-order effects can arise from variation in multiple microbial growth traits, such as lag times and growth rates, on a single limiting resource with no other interactions. These effects produce a range of ecological phenomena: an unlimited number of strains can exhibit multistability and neutral coexistence, potentially with a single keystone strain; strains that coexist in pairs do not coexist all together; and the champion of all pairwise competitions may not dominate in a mixed community. Since variation in multiple growth traits is ubiquitous in microbial populations due to pleiotropy and non-genetic variation, our results indicate these higher-order effects may also be widespread, especially in laboratory ecology and evolution experiments.

q-bio.PE↗

arXiv2018

Tradeoffs between microbial growth phases lead to frequency-dependent and non-transitive selection

Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple life-history traits to selection is a critical question for evolutionary biology as we seek to predict the evolutionary fates of mutations. Here we use a model of microbial growth to show there are two distinct components of selection corresponding to the growth and lag phases, while the yield modulates their relative importance. The model predicts rich population dynamics when there are tradeoffs between phases: multiple strains can coexist or exhibit bistability due to frequency-dependent selection, and strains can engage in rock-paper-scissors interactions due to non-transitive selection. We characterize the environmental conditions and patterns of traits necessary to realize these phenomena, which we show to be readily accessible to experiments. Our results provide a theoretical framework for analyzing high-throughput measurements of microbial growth traits, especially interpreting the pleiotropy and correlations between traits across mutants. This work also highlights the need for more comprehensive measurements of selection in simple microbial systems, where the concept of an ordinary fitness landscape breaks down.

q-bio.PE↗

arXiv2015

Path statistics, memory, and coarse-graining of continuous-time random walks on networks

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states, for example those employed in studies of molecular kinetics, and models with spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. We therefore use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach is valuable for calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN, a Python script that users can easily apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.

cond-mat.stat-mech↗

arXiv2015

Pore-scale lattice Boltzmann simulation of laminar and turbulent flow through a sphere pack

The lattice Boltzmann method can be used to simulate flow through porous media with full geometrical resolution. With such a direct numerical simulation, it becomes possible to study fundamental effects which are difficult to assess either by developing macroscopic mathematical models or experiments. We first evaluate the lattice Boltzmann method with various boundary handling of the solid-wall and various collision operators to assess their suitability for large scale direct numerical simulation of porous media flow. A periodic pressure drop boundary condition is used to mimic the pressure driven flow through the simple sphere pack in a periodic domain. The evaluation of the method is done in the Darcy regime and the results are compared to a semi-analytic solution. Taking into account computational cost and accuracy, we choose the most efficient combination of the solid boundary condition and collision operator. We apply this method to perform simulations for a wide range of Reynolds numbers from Stokes flow over seven orders of magnitude to turbulent flow. Contours and streamlines of the flow field are presented to show the flow behavior in different flow regimes. Moreover, unknown parameters of the Forchheimer, the Barree--Conway and friction factor models are evaluated numerically for the considered flow regimes.

cs.CE↗