This is significant because these two parameters are directly related to longer stride length and larger foot clearance during swing phase. Both variables work toward correcting common issues with hemiparetic gait, such as a shorter stride and toe drag during swing phase of the paretic leg. The results of this work could aid in the design of future model-based stroke rehabilitation methods that would perturb the subject in a systematic way and allow targeted interventions with specific functional outcomes on gait. Additionally, this work-along with future studies-could assist in improving controllers for robust bipedal robots as well as our understanding of how the brain controls balance during perturbed walking.Magnetomotive Ultrasound (MMUS) is an emerging imaging modality in which magnetic nanoparticles (MNPs) are used as contrast agents. MNPs are driven by a time-varying magnetic force, and the resulting movement of the surrounding tissue is detected with a signal processing algorithm. However, there is currently no analytical model to quantitatively predict this magnetically-induced displacement. Toward the goal of predicting motion due to forces on a distribution of MNPs, in this work a model originally derived from the Navier-Stokes equation for the motion of a single magnetic particle subject to a magnetic gradient force is presented and validated. Displacement amplitudes for a spatially inhomogeneous and temporally sinusoidal force were measured as a function of force amplitude and Young's modulus, and the predicted linear and inverse relationships were confirmed in gelatin phantoms respectively with 3 out of 4 datasets exhibiting R2 ≥ 0.88. The mean absolute uncertainty between the predicted displacement magnitude and experimental results was 14%. These findings provide a means by which the performance of MMUS systems may be predicted to verify that systems are working to theoretical limits, and to compare results across laboratories.There is significant acoustic impedance contrast between the cortical bone and surrounding soft tissue, resulting in difficulty for ultrasound penetration into bone tissue with high frequency. It is challenging for the conventional pulse-echo modalities to give accurate cortical bone images using uniform sound velocity model. To overcome these limitations, an ultrasound imaging method called full-matrix Fourier-domain synthetic aperture based on velocity inversion (FM-FDSA-VI) was developed to provide accurate cortical bone images. The dual linear arrays were located on the upper and lower sides of the imaging region. After full-matrix acquisition with two identical linear array probes facing with each other, travel-time inversion was used to estimate the velocity distribution in advance. Then, full-matrix Fourier-domain synthetic aperture (FM-FDSA) imaging based on the estimated velocity model was applied twice to image the cortical bone, utilizing the data acquired from top and bottom linear array respectively. Finally, to further improve the image quality, the two images were merged to give the ultimate result. The performance of the method was verified by two simulated models and two bone phantoms (i.e., regularly and irregularly hollow bone phantom). The mean relative errors of estimated sound velocity in the region-of-interest (ROI) are all below 12%, and the mean errors of cortical section thickness are all less than 0.3 mm. Compared to the conventional synthetic aperture (SA) imaging, FM-FDSA-VI method is able to accurately image cortical bone with respect to the structure. Moreover, the result of irregular bone phantom was close to the image scanned by micro computed tomography (μCT) in terms of macro geometry and thickness. It is demonstrated that the proposed FM-FDSA-VI method is an efficient way for cortical bone ultrasonic imaging.Data truncation is a common problem in computed tomography (CT). Truncation causes cupping artifacts inside the field-of-view (FOV) and anatomical structures missing outside the FOV. Deep learning has achieved impressive results in CT reconstruction from limited data. However, its robustness is still a concern for clinical applications. Although the image quality of learning-based compensation schemes may be inadequate for clinical diagnosis, they can provide prior information for more accurate extrapolation than conventional heuristic extrapolation methods. With extrapolated projection, a conventional image reconstruction algorithm can be applied to obtain a final reconstruction. In this work, a general plug-and-play (PnP) method for truncation correction is proposed based on this idea, where various deep learning methods and conventional reconstruction algorithms can be plugged in. Such a PnP method integrates data consistency for measured data and learned prior image information for truncated data.  https://www.selleckchem.com/products/gdc-0084.html  This shows to have better robustness and interpretability than deep learning only. To demonstrate the efficacy of the proposed PnP method, two state-of-the-art deep learning methods, FBPConvNet and Pix2pixGAN, are investigated for truncation correction in cone-beam CT in noise-free and noisy cases. Their robustness is evaluated by showing false negative and false positive lesion cases. With our proposed PnP method, false lesion structures are corrected for both deep learning methods. For FBPConvNet, the root-mean-square error (RMSE) inside the FOV can be improved from 92HU to around 30HU by PnP in the noisy case. Pix2pixGAN solely achieves better image quality than FBPConvNet solely for truncation correction in general. PnP further improves the RMSE inside the FOV from 42HU to around 27HU for Pix2pixGAN. The efficacy of PnP is also demonstrated on real clinical head data.Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) method to approximate them. This instability arises in the presence of eigenvalues that are close to each other. This makes integrating eigendecomposition into deep networks difficult and often results in poor convergence, particularly when dealing with large matrices. While this can be mitigated by partitioning the data into small arbitrary groups, doing so has no theoretical basis and makes it impossible to exploit the full power of eigendecomposition. In previous work, we mitigated this using SVD during the forward pass and PI to compute the gradients during the backward pass. However, the iterative deflation procedure required to compute multiple eigenvectors using PI tends to accumulate errors and yield inaccurate gradients. Here, we show that the Taylor expansion of the SVD gradient is theoretically equivalent to the gradient obtained using PI without relying in practice on an iterative process and thus yields more accurate gradients.