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Riccardo Lattanzi

Publications and source records attributed to Riccardo Lattanzi.

14 recordsLinked to original sources

Pixelwise Uncertainty Quantification of Accelerated MRI Reconstruction

Parallel imaging techniques reduce magnetic resonance imaging (MRI) scan time but image quality degrades as the acceleration factor increases. In clinical practice, conservative acceleration factors are chosen because no mechanism exists to automatically assess the diagnostic quality of undersampled reconstructions. This work introduces a general framework for pixel-wise uncertainty quantification in parallel MRI reconstructions, enabling automatic identification of unreliable regions without access to any ground-truth reference image. Our method integrates conformal quantile regression with image reconstruction methods to estimate statistically rigorous pixel-wise uncertainty intervals. We trained and evaluated our model on Cartesian undersampled brain and knee data obtained from the fastMRI dataset using acceleration factors ranging from 2 to 10. An end-to-end Variational Network was used for image reconstruction. Quantitative experiments demonstrate strong agreement between predicted uncertainty maps and true reconstruction error. Using our method, the corresponding Pearson correlation coefficient was higher than 90% at acceleration levels at and above four-fold; whereas it dropped to less than 70% when the uncertainty was computed using a simpler a heuristic notion (magnitude of the residual). Qualitative examples further show the uncertainty maps based on quantile regression capture the magnitude and spatial distribution of reconstruction errors across acceleration factors, with regions of elevated uncertainty aligning with pathologies and artifacts. The proposed framework enables evaluation of reconstruction quality without access to fully-sampled ground-truth reference images. It represents a step toward adaptive MRI acquisition protocols that may be able to dynamically balance scan time and diagnostic reliability.

eess.IV

Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.

quant-ph

Global Maxwell Tomography Using the Volume-Surface Integral Equation for Improved Estimation of Electrical Properties

Objective: Global Maxwell Tomography (GMT) is a noninvasive inverse optimization method for the estimation of electrical properties (EP) from magnetic resonance (MR) measurements. GMT uses the volume integral equation (VIE) in the forward problem and assumes that the sample has negligible effect on the coil currents. Consequently, GMT calculates the coil's incident fields with an initial EP distribution and keeps them constant for all optimization iterations. This can lead to erroneous reconstructions. This work introduces a novel version of GMT that replaces VIE with the volume-surface integral equation (VSIE), which recalculates the coil currents at every iteration based on updated EP estimates before computing the associated fields. Methods: We simulated an 8-channel transceiver coil array for 7 T brain imaging and reconstructed the EP of a realistic head model using VSIE-based GMT. We built the coil, collected experimental MR measurements, and reconstructed EP of a two-compartment phantom. Results: In simulations, VSIE-based GMT outperformed VIE-based GMT by at least 12% for both EP. In experiments, the relative difference with respect to probe-measured EP values in the inner (outer) compartment was 13% (26%) and 17% (33%) for the permittivity and conductivity, respectively. Conclusion: The use of VSIE over VIE enhances GMT's performance by accounting for the effect of the EP on the coil currents. Significance: VSIE-based GMT does not rely on an initial EP estimate, rendering it more suitable for experimental reconstructions compared to the VIE-based GMT.

cs.CE

PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networks

We propose Physics-Informed Fourier Networks for Electrical Properties (EP) Tomography (PIFON-EPT), a novel deep learning-based method for EP reconstruction using noisy and/or incomplete magnetic resonance (MR) measurements. Our approach leverages the Helmholtz equation to constrain two networks, responsible for the denoising and completion of the transmit fields, and the estimation of the object's EP, respectively. We embed a random Fourier features mapping into our networks to enable efficient learning of high-frequency details encoded in the transmit fields. We demonstrated the efficacy of PIFON-EPT through several simulated experiments at 3 and 7 tesla (T) MR imaging, and showed that our method can reconstruct physically consistent EP and transmit fields. Specifically, when only $20\%$ of the noisy measured fields were used as inputs, PIFON-EPT reconstructed the EP of a phantom with $\leq 5\%$ error, and denoised and completed the measurements with $\leq 1\%$ error. Additionally, we adapted PIFON-EPT to solve the generalized Helmholtz equation that accounts for gradients of EP between inhomogeneities. This yielded improved results at interfaces between different materials without explicit knowledge of boundary conditions. PIFON-EPT is the first method that can simultaneously reconstruct EP and transmit fields from incomplete noisy MR measurements, providing new opportunities for EPT research.

cs.LG

MR-Based Electrical Property Reconstruction Using Physics-Informed Neural Networks

Electrical properties (EP), namely permittivity and electric conductivity, dictate the interactions between electromagnetic waves and biological tissue. EP can be potential biomarkers for pathology characterization, such as cancer, and improve therapeutic modalities, such radiofrequency hyperthermia and ablation. MR-based electrical properties tomography (MR-EPT) uses MR measurements to reconstruct the EP maps. Using the homogeneous Helmholtz equation, EP can be directly computed through calculations of second order spatial derivatives of the measured magnetic transmit or receive fields $(B_{1}^{+}, B_{1}^{-})$. However, the numerical approximation of derivatives leads to noise amplifications in the measurements and thus erroneous reconstructions. Recently, a noise-robust supervised learning-based method (DL-EPT) was introduced for EP reconstruction. However, the pattern-matching nature of such network does not allow it to generalize for new samples since the network's training is done on a limited number of simulated data. In this work, we leverage recent developments on physics-informed deep learning to solve the Helmholtz equation for the EP reconstruction. We develop deep neural network (NN) algorithms that are constrained by the Helmholtz equation to effectively de-noise the $B_{1}^{+}$ measurements and reconstruct EP directly at an arbitrarily high spatial resolution without requiring any known $B_{1}^{+}$ and EP distribution pairs.

cs.LG

A hybrid volume-surface integral equation method for rapid electromagnetic simulations in MRI

Objective: We developed a hybrid volume surface integral equation (VSIE) method based on domain decomposition to perform fast and accurate magnetic resonance imaging (MRI) simulations that include both remote and local conductive elements. Methods: We separated the conductive surfaces present in MRI setups into two domains and optimized electromagnetic (EM) modeling for each case. Specifically, interactions between the body and EM waves originating from local radiofrequency (RF) coils were modeled with the precorrected fast Fourier transform, whereas the interactions with remote conductive surfaces (RF shield, scanner bore) were modeled with a novel cross tensor train-based algorithm. We compared the hybrid- VSIE with other VSIE methods for realistic MRI simulation setups. Results: The hybrid-VSIE was the only practical method for simulation using 1 mm voxel isotropic resolution (VIR). For 2 mm VIR, our method could be solved at least 23 times faster and required 760 times lower memory than traditional VSIE methods. Conclusion: The hybrid-VSIE demonstrated a marked improvement in terms of convergence times of the numerical EM simulation compared to traditional approaches in multiple realistic MRI scenarios. Significance: The efficiency of the novel hybrid-VSIE method could enable rapid simulations of complex and comprehensive MRI setups.

cs.CE

Compression of volume-surface integral equation matrices via Tucker decomposition for magnetic resonance applications

In this work, we propose a method for the compression of the coupling matrix in volume\hyp surface integral equation (VSIE) formulations. VSIE methods are used for electromagnetic analysis in magnetic resonance imaging (MRI) applications, for which the coupling matrix models the interactions between the coil and the body. We showed that these effects can be represented as independent interactions between remote elements in 3D tensor formats, and subsequently decomposed with the Tucker model. Our method can work in tandem with the adaptive cross approximation technique to provide fast solutions of VSIE problems. We demonstrated that our compression approaches can enable the use of VSIE matrices of prohibitive memory requirements, by allowing the effective use of modern graphical processing units (GPUs) to accelerate the arising matrix\hyp vector products. This is critical to enable numerical MRI simulations at clinical voxel resolutions in a feasible computation time. In this paper, we demonstrate that the VSIE matrix\hyp vector products needed to calculate the electromagnetic field produced by an MRI coil inside a numerical body model with $1$ mm$^3$ voxel resolution, could be performed in $\sim 33$ seconds in a GPU, after compressing the associated coupling matrix from $\sim 80$ TB to $\sim 43$ MB.

cs.CE

Magnetic-resonance-based electrical property mapping using Global Maxwell Tomography with an 8-channel head coil at 7 Tesla: a simulation study

Objective: Global Maxwell Tomography (GMT) is a recently introduced volumetric technique for noninvasive estimation of electrical properties (EP) from magnetic resonance measurements. Previous work evaluated GMT using ideal radiofrequency (RF) excitations. The aim of this simulation study was to assess GMT performance with a realistic RF coil. Methods: We designed a transmit-receive RF coil with $8$ decoupled channels for $7$T head imaging. We calculated the RF transmit field ($B_1^+$) inside heterogeneous head models for different RF shimming approaches, and used them as input for GMT to reconstruct EP for all voxels. Results: Coil tuning/decoupling remained relatively stable when the coil was loaded with different head models. Mean error in EP estimation changed from $7.5\%$ to $9.5\%$ and from $4.8\%$ to $7.2\%$ for relative permittivity and conductivity, respectively, when changing head model without re-tuning the coil. Results slightly improved when an SVD-based RF shimming algorithm was applied, in place of excitation with one coil at a time. Despite errors in EP, RF transmit field ($B_1^+$) and absorbed power could be predicted with less than $0.5\%$ error over the entire head. GMT could accurately detect a numerically inserted tumor. Conclusion: This work demonstrates that GMT can reliably reconstruct EP in realistic simulated scenarios using a tailored 8-channel RF coil design at $7$T. Future work will focus on construction of the coil and optimization of GMT's robustness to noise, to enable in-vivo GMT experiments. Significance: GMT could provide accurate estimations of tissue EP, which could be used as biomarkers and could enable patient-specific estimation of RF power deposition, which is an unsolved problem for ultra-high-field magnetic resonance imaging.

physics.med-ph

Magnetization Transfer in Magnetic Resonance Fingerprinting

Purpose: To study the effects of magnetization transfer (MT, in which a semisolid spin pool interacts with the free pool), in the context of magnetic resonance fingerprinting (MRF). Methods: Simulations and phantom experiments were performed to study the impact of MT on the MRF signal and its potential influence on T1 and T2 estimation. Subsequently, an MRF sequence implementing off-resonance MT pulses and a dictionary with an MT dimension by incorporating a two-pool model were used to estimate the fractional pool size in addition to the B1+, T1, and T2 values. The proposed method was evaluated in the human brain. Results: Simulations and phantom experiments showed that an MRF signal obtained from a cross-linked bovine serum sample is influenced by MT. Using a dictionary based on an MT model, a better match between simulations and acquired MR signals can be obtained (NRMSE 1.3% versus 4.7%). Adding off-resonance MT pulses can improve the differentiation of MT from T1 and T2. In-vivo results showed that MT affects the MRF signals from white matter (fractional pool-size ~16%) and gray matter (fractional pool-size ~10%). Furthermore, longer T1 (~1060 ms versus ~860 ms) and T2 values (~47 ms versus ~35 ms) can be observed in white matter if MT is accounted for. Conclusion: Our experiments demonstrated a potential influence of MT on the quantification of T1 and T2 with MRF. A model that encompasses MT effects can improve the accuracy of estimated relaxation parameters and allows quantification of the fractional pool size.

eess.IV

Optimized Quantification of Spin Relaxation Times in the Hybrid State

Purpose: The analysis of optimized spin ensemble trajectories for relaxometry in the hybrid state. Methods: First, we constructed visual representations to elucidate the differential equation that governs spin dynamics in hybrid state. Subsequently, numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for $T_1$-encoding, $T_2$-encoding, and their weighted sum, respectively, followed by a comparison of the Cramér-Rao bounds obtained with our optimized spin-trajectories, as well as Look-Locker and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. Results: After a nonrecurring inversion segment on the southern hemisphere of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern half of the sphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance $T_1$- and $T_2$-encoding still result in near optimal signal-to-noise efficiency. Thus, the second parameter can be encoded at virtually no extra cost. Conclusion: We provide insights regarding the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We find that joint acquisitions of $T_1$ and $T_2$ in the hybrid state are substantially more efficient than sequential encoding techniques.

physics.med-ph

The Optimality Principle for MR signal excitation and reception: New physical insights into ideal radiofrequency coil design

Purpose: Despite decades of collective experience, radiofrequency coil optimization for MR has remained a largely empirical process, with clear insight into what might constitute truly task-optimal, as opposed to merely 'good,' coil performance being difficult to come by. Here, a new principle, the Optimality Principle, is introduced, which allows one to predict, rapidly and intuitively, the form of optimal current patterns on any surface surrounding any arbitrary body. Theory: The Optimality Principle, in its simplest form, states that the surface current pattern associated with optimal transmit field or receive sensitivity at a point of interest (per unit current integrated over the surface) is a precise scaled replica of the tangential electric field pattern that would be generated on the surface by a precessing spin placed at that point. A more general perturbative formulation enables efficient calculation of the pattern modifications required to optimize signal-to-noise ratio in body-noise-dominated situations. Methods and Results: The unperturbed principle is validated numerically, and convergence of the perturbative formulation is explored in simple geometries. Current patterns and corresponding field patterns in a variety of concrete cases are then used to separate signal and noise effects in coil optimization, to understand the emergence of electric dipoles as strong performers at high frequency, and to highlight the importance of surface geometry in coil design. Conclusion: Like the Principle of Reciprocity from which it is derived, the Optimality Principle offers both a conceptual and a computational shortcut. In addition to providing quantitative targets for coil design, the Optimality Principle affords direct physical insight into the fundamental determinants of coil performance.

physics.ins-det

Hybrid-State Free Precession in Nuclear Magnetic Resonance

The dynamics of large spin-1/2 ensembles in the presence of a varying magnetic field are commonly described by the Bloch equation. Most magnetic field variations result in unintuitive spin dynamics, which are sensitive to small deviations in the driving field. Although simplistic field variations can produce robust dynamics, the captured information content is impoverished. Here, we identify adiabaticity conditions that span a rich experiment design space with tractable dynamics. These adiabaticity conditions trap the spin dynamics in a one-dimensional subspace. Namely, the dynamics is captured by the absolute value of the magnetization, which is in a transient state, while its direction adiabatically follows the steady state. We define the hybrid state as the co-existence of these two states and identify the polar angle as the effective driving force of the spin dynamics. As an example, we optimize this drive for robust and efficient quantification of spin relaxation times and utilize it for magnetic resonance imaging of the human brain.

physics.med-ph

Multicompartment Magnetic Resonance Fingerprinting

Magnetic resonance fingerprinting (MRF) is a technique for quantitative estimation of spin-relaxation parameters from magnetic-resonance data. Most current MRF approaches assume that only one tissue is present in each voxel, which neglects the tissue's microstructure, and may lead to artifacts in the recovered parameter maps at boundaries between tissues. In this work, we propose a multicompartment MRF model that accounts for the presence of multiple tissues per voxel. The model is fit to the data by iteratively solving a sparse linear inverse problem at each voxel, in order to express the magnetization signal as a linear combination of a few fingerprints in the precomputed dictionary. Thresholding-based methods commonly used for sparse recovery and compressed sensing do not perform well in this setting due to the high local coherence of the dictionary. Instead, we solve this challenging sparse-recovery problem by applying reweighted-l1-norm regularization, implemented using an efficient interior-point method. The proposed approach is validated with simulated data at different noise levels and undersampling factors, as well as with a controlled phantom imaging experiment on a clinical magnetic-resonance system.

physics.med-ph

Low Rank Alternating Direction Method of Multipliers Reconstruction for MR Fingerprinting

Purpose The proposed reconstruction framework addresses the reconstruction accuracy, noise propagation and computation time for Magnetic Resonance Fingerprinting (MRF). Methods Based on a singular value decomposition (SVD) of the signal evolution, MRF is formulated as a low rank inverse problem in which one image is reconstructed for each singular value under consideration. This low rank approximation of the signal evolution reduces the computational burden by reducing the number of Fourier transformations. Also, the low rank approximation improves the conditioning of the problem, which is further improved by extending the low rank inverse problem to an augmented Lagrangian that is solved by the alternating direction method of multipliers (ADMM). The root mean square error and the noise propagation are analyzed in simulations. For verification, in vivo examples are provided. Results The proposed low rank ADMM approach shows a reduced root mean square error compared to the original fingerprinting reconstruction, to a low rank approximation alone and to an ADMM approach without a low rank approximation. Incorporating sensitivity encoding allows for further artifact reduction. Conclusion The proposed reconstruction provides robust convergence, reduced computational burden and improved image quality compared to other MRF reconstruction approaches evaluated in this study.

physics.med-ph