Bias-reduced neural networks for parameter estimation in quantitative MRI.

PURPOSE: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. THEORY AND METHODS: We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. RESULTS: In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least-squares fitting, while state-of-the-art NNs show larger deviations. CONCLUSION: The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Sensitivity of unconstrained quantitative magnetization transfer MRI to Amyloid burden in preclinical Alzheimer's disease.

Introduction: Magnetization transfer MRI is sensitive to semi-solid macromolecules, including amyloid beta, and has been used to discriminate Alzheimer's disease (AD) patients from controls. Here, we utilize an unconstrained 2-pool quantitative MT (qMT) approach that quantifies the longitudinal relaxation rates of free water and semi-solids separately, and investigate its sensitivity to amyloid accumulation in preclinical subjects. Methods: We recruited 15 cognitively normal subjects, of which nine were amyloid positive by [ 18 F]Florbetaben PET. A 12 min qMT scan was used to estimate the unconstrained 2-pool qMT parameters. Group comparisons and correlations were analyzed at the lobar level. Results: The exchange rate and semi-solid pool's were sensitive to the amyloid concentration. The former finding is consistent with previous reports in clinical AD, but the latter is novel as its value is typically constrained. Discussion: qMT MRI may be a promising surrogate marker of amyloid beta without the need for contrast agents or radiotracers.

Bias-Reduced Neural Networks for Parameter Estimation in Quantitative MRI.

Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. Results: In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as non-linear least-squares fitting, while state-of-the-art NNs show larger deviations. Conclusion: The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Unconstrained quantitative magnetization transfer imaging: disentangling T1 of the free and semi-solid spin pools.

Since the inception of magnetization transfer (MT) imaging, it has been widely assumed that Henkelman's two spin pools have similar longitudinal relaxation times, which motivated many researchers to constrain them to each other. However, several recent publications reported a T1s of the semi-solid spin pool that is much shorter than T1f of the free pool. While these studies tailored experiments for robust proofs-of-concept, we here aim to quantify the disentangled relaxation processes on a voxel-by-voxel basis in a clinical imaging setting, i.e., with an effective resolution of 1.24mm isotropic and full brain coverage in 12min. To this end, we optimized a hybrid-state pulse sequence for mapping the parameters of an unconstrained MT model. We scanned four people with relapsing-remitting multiple sclerosis (MS) and four healthy controls with this pulse sequence and estimated T1f≈1.84s and T1s≈0.34s in healthy white matter. Our results confirm the reports that T1s≪T1f and we argue that this finding identifies MT as an inherent driver of longitudinal relaxation in brain tissue. Moreover, we estimated a fractional size of the semi-solid spin pool of m0s≈0.212, which is larger than previously assumed. An analysis of T1f in normal-appearing white matter revealed statistically significant differences between individuals with MS and controls.

Rapid quantitative magnetization transfer imaging: Utilizing the hybrid state and the generalized Bloch model.

PURPOSE: To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters. THEORY AND METHODS: We combine two recently proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi-solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two-pool model. We sparsely sample each time frame along this spin dynamics with a three-dimensional radial koosh-ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency. RESULTS: We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6-min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and longer relaxation times, consistent with previous reports. CONCLUSION: The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for efficient quantitative magnetization transfer imaging with few constraints on model parameters.

Cramér-Rao Bound Optimized Subspace Reconstruction in Quantitative MRI.

We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cramér-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps. To this end, we introduce an approximate compressed CRB based on orthogonalized versions of the signal's derivatives with respect to the model parameters. This approximation permits singular value decomposition (SVD)-based minimization of both the CRB and signal losses during compression. Compared to the traditional SVD approach, the proposed method better preserves the CRB across all biophysical parameters with negligible cost to the preserved signal energy, leading to reduced bias and variance of the parameter estimates in simulation. In vivo, improved accuracy and precision are observed in two quantitative neuroimaging applications, permitting the use of smaller basis sizes in subspace reconstruction and offering significant computational savings.

Dynamic fluence field modulation in computed tomography using multiple aperture devices.

A novel beam filter consisting of multiple aperture devices (MADs) has been developed for dynamic fluence field modulation (FFM) in CT. Each MAD achieves spatial modulation of x-ray through fine-scale, highly attenuating tungsten bars of varying widths and spacings. Moiré patterns produced by relative motions between two MADs provide versatile classes of modulation profiles. The dual-MAD filter can be designed to achieve specific classes of target profiles. The designed filter was manufactured through a laser-sintering process and integrated to an experimental imaging system that enables linear actuation of the MADs. Dynamic FFM was achieved through a combination of beam shape modulation (by relative MAD motion) and amplitude modulation (by view-dependent mAs). To correct for gains associated with the MADs, we developed an algorithm to account for possible focal spot changes during/between scans and spectral effects introduced by the MADs. We performed FFM designs for phantoms following two imaging objectives: (1) to achieve minimum mean variance in filtered backprojection (FBP) reconstruction, and (2) to flatten the fluence behind the phantom. Comparisons with conventional FFM strategies involving a static bowtie and pulse width modulation were performed. The dual-MAD filter produced modulation profiles closely matched with the design target, providing varying beam widths not achievable by the static bowtie. The entire range of modulation profiles was achieved by 0.373 mm of MAD displacement. The correction algorithm effectively alleviated ring artifacts as a result of MADs while preserving phantom details such as wires and tissue boundaries. Dynamic FFM enabled by the MADs were effective in achieving the imaging objectives and demonstrated superior FFM capabilities compared to the static bowtie. In an ellipse phantom, the FFM of objective 1 achieved the lowest mean variance in all cases investigated. The FFM of objective 2 produce nearly isotropic local noise power spectrum and homogeneous noise magnitude. The dual-MAD filter provides an effective tool for fluence control in CT to overcome limitations of conventional static bowties and to further enable patient-specific FFM studies for a wide range of dose and image quality objectives.

Implementation and Assessment of Dynamic Fluence Field Modulation with Multiple Aperture Devices.

This work reports experimental results of dynamic fluence field modulation (FFM) using a dual multiple aperture devices (MAD) system. MAD filters use Moiré patterns produced by relative motions between two sets of thin, highly attenuating tungsten bars of varying widths and spacings. Each MAD was affixed to a linear actuator and installed on an experimental cone-beam CT bench. Phantom-specific FFM profiles were designed based on a flatness and minimum mean variance objectives and realized through a combination of MAD translations and pulse width modulation at a constant tube current. To properly correct for gains associated with the MAD filters, a correction algorithm was designed to account for focal spot shifts during scanning, as well as spectral effects from incomplete blockage of x-rays by the tungsten bars. The FFM designs were demonstrated in an elliptical phantom (25.8×14.1 cm). Variance and noise power spectrum (NPS) analysis was performed on the resulting reconstructions. While conventionalgain correction produced reconstructions with high frequency ring artifacts in axial slices, the proposed correction algorithm effectively removed such artifacts while preserving phantom details. Fluence field designs for the elliptical phantom were achievedusing relative MAD motions over a 0.44 mm range, and measured beam profiles closely approximated the theoretically computed target profiles. The noise properties of the resulting reconstructions behave as expected: a flat detected fluence criterion yields nearly isotropic NPS and more homogeneous variance across the reconstruction as compared to an unmodulated scan; the minimum mean variance FFM results in lower mean variance compared to both the unmodulated and flat-field patterns at approximately matched total bare-beam fluence. These results suggest that a dual-MAD CT is an effective approach to provide fluence and image quality control and that can potentially accommodate a wide range of phantoms and design objectives.

Volume-of-interest CT imaging with dynamic beam filtering using multiple aperture devices.

Interior tomography is promising approach for retaining high quality CT images within a volume-of-interest (VOI) while reducing the total patient dose. A static collimating filter can only image a centered symmetric VOI, which requires careful patient positioning and may be suboptimal for many clinical applications. Multiple aperture devices (MADs) are an emerging technology based on sequential binary filters that can provide a wide range of fluence patterns that may be adjusted dynamically with relatively small motions. In this work, we introduce a general approach for VOI imaging using MAD-based fluence field modulation (FFM). Physical experiments using a CT test bench are conducted illustrating off-center x-ray beam control for imaging the spine in an abdominal phantom. Image quality and dose metrics are computed for both standard full-field CT and VOI CT. We find that the image quality within the VOI can be preserved for VOI CT with a significant drop in integral dose as compared with a standard full-field protocol.

Dynamic fluence field modulation for miscentered patients in computed tomography.

Traditional CT image acquisition uses bowtie filters to reduce dose, x-ray scatter, and detector dynamic range requirements. However, accurate patient centering within the bore of the CT scanner takes time and is often difficult to achieve precisely. Patient miscentering combined with a static bowtie filter can result in significant increases in dose, reconstruction noise, and CT number variations, and consequently raise overall exposure requirements. Approaches to estimate the patient position from scout scans and perform dynamic spatial beam filtration during acquisition are developed and applied in physical experiments on a CT test bench using different beam filtration strategies. While various dynamic beam modulation strategies have been developed, we focus on two approaches: (1) a simple approach using attenuation-based beam modulation using a translating bowtie filter and (2) dynamic beam modulation using multiple aperture devices (MADs)-an emerging beam filtration strategy based on binary filtration of the x-ray beam using variable width slits in a high-density beam blocker. Improved dose utilization and more consistent image performance with respect to an unmodulated baseline (static filter) are demonstrated for miscentered objects and dynamic beam filtration in physical experiments. For a homogeneous object miscentered by 4 cm, the dynamic filter reduced the maximum regional noise and dose penalties (compared with a centered object) from 173% to 16% and 42% to 14%, respectively, for a traditional bowtie, 29% to 8% and 24% to 15%, respectively, for a single MAD, and 275% to 11% and 56% to 18%, respectively, for a dual-MAD filter. The proposed methodology has the potential to relax patient centering requirements within the scanner, reduce setup time, and facilitate additional CT dose reduction.

Remote optimization of an ultracold atoms experiment by experts and citizen scientists.

We introduce a remote interface to control and optimize the experimental production of Bose-Einstein condensates (BECs) and find improved solutions using two distinct implementations. First, a team of theoreticians used a remote version of their dressed chopped random basis optimization algorithm (RedCRAB), and second, a gamified interface allowed 600 citizen scientists from around the world to participate in real-time optimization. Quantitative studies of player search behavior demonstrated that they collectively engage in a combination of local and global searches. This form of multiagent adaptive search prevents premature convergence by the explorative behavior of low-performing players while high-performing players locally refine their solutions. In addition, many successful citizen science games have relied on a problem representation that directly engaged the visual or experiential intuition of the players. Here we demonstrate that citizen scientists can also be successful in an entirely abstract problem visualization. This is encouraging because a much wider range of challenges could potentially be opened to gamification in the future.

The emergence of inequality in social groups: Network structure and institutions affect the distribution of earnings in cooperation games.

From small communities to entire nations and society at large, inequality in wealth, social status, and power is one of the most pervasive and tenacious features of the social world. What causes inequality to emerge and persist? In this study, we investigate how the structure and rules of our interactions can increase inequality in social groups. Specifically, we look into the effects of four structural conditions-network structure, network fluidity, reputation tracking, and punishment institutions-on the distribution of earnings in network cooperation games. We analyze 33 experiments comprising 96 experimental conditions altogether. We find that there is more inequality in clustered networks compared to random networks, in fixed networks compared to randomly rewired and strategically updated networks, and in groups with punishment institutions compared to groups without. Secondary analyses suggest that the reasons inequality emerges under these conditions may have to do with the fact that fixed networks allow exploitation of the poor by the wealthy and clustered networks foster segregation between the poor and the wealthy, while the burden of costly punishment falls onto the poor, leaving them poorer. Surprisingly, we do not find evidence that inequality is affected by reputation in a systematic way but this could be because reputation needs to play out in a particular network environment in order to have an effect. Overall, our findings suggest possible strategies and interventions to decrease inequality and mitigate its negative impact, particularly in the context of mid- and large-sized organizations and online communities.

Dynamic beam filtering for miscentered patients.

PURPOSE: Accurate centering of the patient within the bore of a CT scanner takes time and is often difficult to achieve precisely. Patient miscentering can result in significant dose and image noise penalties with the use of traditional bowtie filters. This work describes a system to dynamically position an x-ray beam filter during image acquisition to enable more consistent image performance and potentially lower dose needed for CT imaging. METHODS: We propose a new approach in which two orthogonal low-dose scout images are used to estimate a parametric model of the object describing its shape, size, and location within the field of view (FOV). This model is then used to compute an optimal filter motion profile by minimizing the variance of the expected detector fluence for each projection. Dynamic filtration was implemented on a cone-beam CT (CBCT) test bench using two different physical filters: 1) an aluminum bowtie and 2) a structured binary filter called a multiple aperture device (MAD). Dynamic filtration performance was compared to a static filter in studies of dose and reconstruction noise as a function of the degree of miscentering of a homogeneous water phantom. RESULTS: Estimated filter trajectories were found to be largely sinusoidal with an amplitude proportional to the amount of miscentering. Dynamic filtration demonstrated an improved ability to keep the spatial distribution of dose and reconstruction noise at baseline levels across varying levels of miscentering, reducing the maximum noise and dose deviation from 53% to 15% and 42% to 14% respectively for the bowtie filter, and 25% to 8% and 24% to 15% respectively for the MAD filter. CONCLUSION: Dynamic positioning of beam filters during acquisition improves dose utilization and image quality over static filters for miscentered patients. Such dynamic filters relax positioning requirements and have the potential to reduce set-up time and lower dose requirements.

Resilient cooperators stabilize long-run cooperation in the finitely repeated Prisoner's Dilemma.

Learning in finitely repeated games of cooperation remains poorly understood in part because their dynamics play out over a timescale exceeding that of traditional lab experiments. Here, we report results of a virtual lab experiment in which 94 subjects play up to 400 ten-round games of Prisoner's Dilemma over the course of twenty consecutive weekdays. Consistent with previous work, the typical round of first defection moves earlier for several days; however, this unravelling process stabilizes after roughly one week. Analysing individual strategies, we find that approximately 40% of players behave as resilient cooperators who avoid unravelling even at significant cost to themselves. Finally, using a standard learning model we predict that a sufficiently large minority of resilient cooperators can permanently stabilize unravelling among a majority of rational players. These results shed hopeful light on the long-term dynamics of cooperation, and demonstrate the importance of long-run experiments.

An Experimental Study of Team Size and Performance on a Complex Task.

The relationship between team size and productivity is a question of broad relevance across economics, psychology, and management science. For complex tasks, however, where both the potential benefits and costs of coordinated work increase with the number of workers, neither theoretical arguments nor empirical evidence consistently favor larger vs. smaller teams. Experimental findings, meanwhile, have relied on small groups and highly stylized tasks, hence are hard to generalize to realistic settings. Here we narrow the gap between real-world task complexity and experimental control, reporting results from an online experiment in which 47 teams of size ranging from n = 1 to 32 collaborated on a realistic crisis mapping task. We find that individuals in teams exerted lower overall effort than independent workers, in part by allocating their effort to less demanding (and less productive) sub-tasks; however, we also find that individuals in teams collaborated more with increasing team size. Directly comparing these competing effects, we find that the largest teams outperformed an equivalent number of independent workers, suggesting that gains to collaboration dominated losses to effort. Importantly, these teams also performed comparably to a field deployment of crisis mappers, suggesting that experiments of the type described here can help solve practical problems as well as advancing the science of collective intelligence.