Jacob White

• Massachusetts Institute of Technology

High static field MR scanners can produce human tissue images of astounding clarity, but rely on high frequency electromagnetic radiation that generates complicated in-tissue field patterns that are patient-specific and potentially harmful. Many such scanners use parallel transmitters to better control field patterns, but then adjust the transmitte...

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 electrom...

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 electromagn...

The cover image is based on the Research Article Improving D‐2‐hydroxyglutarate MR spectroscopic imaging in mutant isocitrate dehydrogenase glioma patients with multiplexed RF‐receive/B0‐shim array coils at 3 T by Bernhard Strasser et al., https://doi.org/10.1002/nbm.4621.

Purpose To demonstrate, through numerical simulations, novel designs of spatially selective radiofrequency (RF) excitations of the fetal brain by both a restricted 2D slice and 3D inner‐volume selection. These designs exploit a single‐channel RF pulse, conventional gradient fields, and the spatially non‐linear ΔB0 fields of a multi‐coil shim array,...

Purpose To test an integrated “AC/DC” array approach at 7T, where B0 inhomogeneity poses an obstacle for functional imaging, diffusion‐weighted MRI, MR spectroscopy, and other applications. Methods A close‐fitting 7T 31‐channel (31‐ch) brain array was constructed and tested using combined Rx and ΔB0 shim channels driven by a set of rapidly switcha...

MR spectroscopic imaging (MRSI) noninvasively maps the metabolism of human brains. In particular, the imaging of D-2-hydroxyglutarate (2HG) produced by glioma isocitrate dehydrogenase (IDH) mutations has become a key application in neuro-oncology. However, the performance of full field-of-view MRSI is limited by B0 spatial nonuniformity and lipid a...

We propose a memory compression scheme for the coupling matrices appearing in volume-surface integral equation formulations. When there is some distance between the surface and the volumetric scatterers, the low-rank properties of the coupling matrix, allow us to reshape it into a set of four-dimensional tensors, which can be heavily compressed wit...

In this work, we propose a method for the compression of the coupling matrix in volume-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 ca...

Global Maxwell Tomography (GMT) is a recently introduced technique that estimates tissue electrical properties from magnetic resonance measurements by solving an inverse scattering problem. In this work, we propose a new implementation of GMT that uses a Projected Newton method to minimize the cost function, instead of the quasi-Newton method emplo...

The volume-surface integral equation (VSIE) method is used for rapid and accurate simulations of electromagnetic fields in magnetic resonance imaging. For the case of a 7T array and a numerical head phantom, we constructed the VSIE coupling matrix that models the interactions between the coil and the scatterer. We reshaped the columns of the matrix...

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 effec...

To reach its potential as an emerging technology platform, integrated silicon photonics needs accompanying design-for-manufacturability (DFM) methods and tools to assist the design of silicon photonic devices and circuits. Here, we explore spatial sampling in adjoint-based methods for analysis of the sensitivity of photonic components against key f...

VoxCap, a fast Fourier transform (FFT)-accelerated and Tucker-enhanced integral equation simulator for capacitance extraction of voxelized structures, is proposed. The VoxCap solves the surface integral equations (SIEs) for the conductor and dielectric surfaces with three key attributes that make the VoxCap highly CPU and memory-efficient for the c...

Metabolic imaging of the human brain by in-vivo magnetic resonance spectroscopic imaging (MRSI) can non-invasively probe neurochemistry in healthy and disease conditions. MRSI at ultra-high field (≥ 7 T) provides increased sensitivity for fast high-resolution metabolic imaging, but comes with technical challenges due to non-uniform B0 field. Here,...

Purpose We propose a fast, patient‐specific workflow for on‐line specific absorption rate (SAR) supervision. An individualized electromagnetic model is created while the subject is on the table, followed by rapid SAR estimates for that individual. Our goal is an improved correspondence between the patient and model, reducing reliance on general ana...

Electrical properties (EP) can be retrieved from magnetic resonance measurements. We employed numerical simulations to investigate the use of convolutional neural networks (CNN) as a tensor-to-tensor translation between transmit magnetic field pattern ( b1+ ) and EP distribution for simple tissue-mimicking phantoms. Given the volumetric nature of t...

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. Meth...

VoxCap, a fast Fourier transform (FFT)-accelerated and Tucker-enhanced integral equation simulator for capacitance extraction of voxelized structures, is proposed. The VoxCap solves the surface integral equations (SIEs) for conductor and dielectric surfaces with three key attributes that make the VoxCap highly CPU and memory efficient for the capac...

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. Meth...

Functional magnetic resonance imaging (fMRI) in monkeys is important for bridging the gap between invasive animal brain studies and non-invasive human brain studies. To resolve the finer functional structure of the monkey brain, ultra-high-field (UHF) MR is essential, and high-performance, close-fitting RF receive coils are typically desired to ful...

The discrete dipole approximation (DDA) is a popular numerical method for electromagnetic scattering calculations. The standard DDA formulation involves the uniform discretization of the underlying volume integral equation, leading to a linear system of convolution form. This permits a matrix-vector product to be performed with O(nlogn) complexity...

While access to a laboratory MRI system is ideal for teaching MR physics as well as many aspects of signal processing, providing multiple MRI scanners can be prohibitively expensive for educational settings. To address this need, we developed a small, low-cost, open-interface tabletop MRI scanner for academic use. We constructed and tested 20 of th...

We simulated a Global Maxwell Tomography experiment for the estimation of electrical properties in a numerical tissue-mimicking phantom using a decoupled 8 channel radiofrequency coil designed for 7 Tesla magnetic resonance scanners. The goal of this work was to investigate whether the orthogonality of the coil’s transmit fields (b1+ measurements)...

We simulated a Global Maxwell Tomography experiment for the estimation of electrical properties in a numerical tissue-mimicking phantom using a decoupled 8 channel radiofrequency coil designed for 7 Tesla magnetic resonance scanners. The goal of this work was to investigate whether the orthogonality of the coil's transmit fields (b1+ measurements)...

Recently, the volume integral equation (VIE) approach has been proposed as an efficient simulation tool for silicon photonics applications [J. Lightw. Technol. 36, 3765 (2018)JLTEDG0733-872410.1109/JLT.2018.2842054]. However, for the high-frequency and strong-contrast problems arising in photonics, the convergence of iterative solvers for the solut...

With the rising demand for integrated silicon photonics as a technology platform, it becomes crucial to provide variation-aware models and design for manufacturability (DFM) methods to inform the design of silicon photonic devices and circuits. In this paper, we demonstrate the application of the adjoint method to estimating the sensitivity of phot...

Objective: In this paper, we introduce Global Maxwell Tomography (GMT), a novel, volumetric technique that estimates electric conductivity and permittivity by solving an inverse scattering problem based on magnetic resonance measurements. Methods: GMT relies on a fast volume integral equation solver, MARIE, for the forward path and a novel regul...

The discrete dipole approximation (DDA) is a popular numerical method for calculating the scattering properties of atmospheric ice crystals. The standard DDA formulation involves the uniform discretization of the underlying volume integral equation, leading to a linear system with a block-Toeplitz Toeplitz-block matrix. This structure permits a mat...

Recently, the volume integral equation (VIE) approach has been proposed as an efficient simulation tool for silicon photonics applications [J. Lightw. Technol. 36, 3765 (2018)]. However, for the high-frequency and strong contrast problems arising in photonics, the convergence of iterative solvers for the solution of the linear system can be extreme...

In vivo access to electrical properties (EP) of biological tissues is a challenging problem that has tantalized scientists for decades. Non-invasive cross-sectional mapping of electrical conductivity and permittivity could be useful for tissue characterization and provide novel biomarkers for pathologies, including cancer. Furthermore, knowledge of...

We consider the sequence acceleration problem for the alternating direction method of multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex quadratic objectives, which frequently arise as the Newton subproblem of interior-point methods. Within this context, the ADMM update equations are linear, the iterates are...

This paper describes the implementation and performance of adiabatic absorbing layers in an FFT-accelerated volume integral equation (VIE) method for simulating truncated nanophotonics structures. At the truncation sites, we place absorbing regions in which the conductivity is increased gradually in order to minimize reflections. In the continuous...

This paper describes the implementation and performance of adiabatic absorbing layers in an FFT-accelerated volume integral equation (VIE) method for simulating truncated nanophotonics structures. At the truncation sites, we place absorbing regions in which the conductivity is increased gradually in order to minimize reflections. In the continuous...

VoxHenry, a fast Fourier transform (FFT)-accelerated integral-equation-based simulator for extracting frequency-dependent inductances and resistances of structures discretized by voxels, is presented. VoxHenry shares many features with the popular inductance extractor, FastHenry. Just like FastHenry, VoxHenry solves a combination of the electric vo...

Background: Bistable behaviors are prevalent in cell signaling and can be modeled by ordinary differential equations (ODEs) with kinetic parameters. A bistable switch has recently been found to regulate the activation of transforming growth factor-β1 (TGF-β1) in the context of liver fibrosis, and an ordinary differential equation (ODE) model was p...

Purpose: We introduce a method for calculation of the ultimate specific absorption rate (SAR) amplification factors (uSAF) in non-uniform body models. The uSAF is the greatest possible SAF achievable by any hyperthermia (HT) phased array for a given frequency, body model and target heating volume. Methods: First, we generate a basis-set of solut...

Purpose: We compute the ultimate signal-to-noise ratio (uSNR) and G-factor (uGF) in a realistic head model from 0.5 to 21 Tesla. Methods: We excite the head model and a uniform sphere with a large number of electric and magnetic dipoles placed at 3 cm from the object. The resulting electromagnetic fields are computed using an ultrafast volume in...

High penetrations of distributed renewables can dramatically increase uncertainty in the transmission system, making small-signal stability verification far more challenging. In this paper, we examine the impact of generating 30% of the power in the IEEE 118 bus test network with 118 distributed renewable sources, and show the inadequacy of samplin...

The uptake of high penetrations of renewable energy in microgrids is curtailed by concerns that their intermittency may cause the system to become unstable. The classic approach of small-signal stability analysis may lead to overly optimistic conclusions, because it implicitly assumes that the intermittency is small-signal in nature. Instead, LMI t...

A new, MR-based algorithm for the estimation of electrical properties (permittivity and conductivity) is presented. The algorithm is based on a volume integral equation formulation that represents scatterers in terms of equivalent currents. Set up as an unconstrained optimization problem, the algorithm iterates over estimates of electrical properti...

The rate of electric-field-driven transport across ion-selective membranes can exceed the limit predicted by Nernst (the limiting current), and encouraging this “overlimiting” phenomenon can improve efficiency in many electrochemical systems. Overlimiting behavior is the result of electroconvectively induced vortex formation near membrane surfaces,...

We consider the solution of linear saddle-point problems, using the alternating direction method-of-multipliers (ADMM) as a preconditioner for the generalized minimum residual method (GMRES). We show, using theoretical bounds and empirical results, that ADMM is made remarkably insensitive to the parameter choice with Krylov subspace acceleration. W...

A fast frequency domain, full-wave electromagnetic simulation method is introduced for the analysis of MRI coils loaded with realistic human body models. The approach is based on integral equation methods decomposed into two domains: 1) the RF coil array and shield, and 2) the human body region where the load is placed. The analysis of multiple coi...

This paper investigates the generalized minimum residual method (GMRES) in its ability to accelerate the convergence of the alternating direction method-of-multipliers (ADMM). We provide evidence that ADMM-GMRES can consistently converge to an $\epsilon$-accurate solution for a $\kappa$-conditioned problem in $O(\kappa^{1/4}\log\epsilon^{-1})$ iter...

The dynamic behaviors of signaling pathways can provide clues to pathway mechanisms. In cancer cells, excessive phosphorylation and activation of the Akt pathway is responsible for cell survival advantages. In normal cells, serum stimulation causes brief peaks of extremely high Akt phosphorylation before reaching a moderate steady-state. Previous m...

Rapidly diversifying technology and declining computational costs are popularizing technologically flexible simulation and verification techniques, even at some cost in performance. This paper investigates a data-driven, sampling-based approach for computing substrate Green's functions, which is more technology flexible than specialized layered med...

Dampers are widely used in power electronics to damp resonances, in order to reduce device stress, power loss, and electromagnetic interference. In this paper we formulate the damping problem so as to expose the fundamental tradeoff between damping amplitude peaks and minimizing power dissipation, and then use a constrained optimization approach to...

We describe some preliminary results on a fluctuating volume-current formulation of non-equilibrium fluctuations in inhomogeneous media. The proposed framework generalizes the recently developed power formulas for volume integral equation formulations, in order to facilitate applications including radiative heat transfer, Casimir forces, and fluore...

We describe an adapted robust control technique for analyzing microgrid stability under the uncertainty of renewable sources and loads. Two realistic case studies are presented to demonstrate the method's effectiveness as a tool for system design and analysis. Results show that the method is able to provide a non-trivial lower bound for the minimum...

We describe a fluctuating volume–current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88, 054305] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forc...

A fast numerical method is presented for the simulation of complicated 3-D structures, such as inductors constructed from Litz or stranded wires, above or sandwiched between the planar lossy magnetic media. Making use of its smoothness, the quasi-static multilayer Green's function is numerically computed using finite differences, and its source hei...

A stable volume integral equation formulation based on equivalent volumetric currents is presented for modeling electromagnetic scattering of highly inhomogeneous dielectric objects. The proposed formulation is numerically solved by means of Galerkin method of moments on uniform grids, allowing for acceleration of the matrix–vector products associa...

A simple scheme for compressing the tensors arising in FFT-volume integral equation formulations is reported. The proposed solution is based on the Tucker model and the algorithm originally developed by De Lathauwer et al. [1]. A representative example from the EM analysis of human body models is used to demonstrate the effectiveness of the method;...

We present simple and stable formulas for computing power (including absorbed/radiated, scattered and extinction power) in current-based volume integral equation formulations. The proposed formulas are given in terms of vector-matrix-vector products of quantities found solely in the associated linear system. In addition to their efficiency, the der...

We consider model-order reduction of systems occurring in electromagnetic scattering problems, where the inputs are current distributions operating in the presence of a scatterer, and the outputs are their corresponding scattered fields. Using the singular-value decomposition (SVD), we formally derive minimal-order models for such systems. We then...

The TGF-β/Smad signaling system decreases its activity through strong negative regulation. Several molecular mechanisms of negative regulation have been published, but the relative impact of each mechanism on the overall system is unknown. In this work, we used computational and experimental methods to assess multiple negative regulatory effects on...

The losses of realistic litz wires are characterized while explicitly accounting for their construction, using a procedure that computes the current-driven and magnetic-field-driven copper losses using fast numerical simulations. We present a case study that examines loss variation in one- and two-level litz wires as a function of twisting pitch, o...

We present a generic technique, automated by computer-algebra systems and available as open-source software \cite{scuff-em}, for efficient numerical evaluation of a large family of singular and nonsingular 4-dimensional integrals over triangle-product domains, such as those arising in the boundary-element method (BEM) of computational electromagnet...

This paper describes a new distributed algorithm for the consensus control of a group of agents connected via a communication network where the states of the agents lie within individually-defined constraints. It considers the case where the state of each agent is a scalar in an undirected network with no communication delays and uses the edge weig...

We propose a methodology for the fast analysis of the EM fields generated by the transmit radio-frequency coils when operating in the presence of realistic human body models (RHBM). This work is driven by the need of fast and accurate specific absorption rate (SAR) prediction and coil design analysis in the context of high-field Magnetic Resonance...

A simple transformation of the Galerkin inner products arising in the numerical solution of volume integral equation formulations with piece-wise constant functions is presented. Making use of some simple steps, we derive integrals of reduced dimensionality and smoother kernels, amenable to standard cubatures developed for surface integral equation...

Typically, biological models fitted to experimental data suffer from significant parameter uncertainty, which can lead to inaccurate or uncertain predictions. One school of thought holds that accurate estimation of the true parameters of a biological system is inherently problematic. Recent work, however, suggests that optimal experimental design t...

A simulator includes an analysis module for extracting a state-space model of response of a physical system to an input from a frequency-domain representation thereof, using a SVD, and singular vectors thereof, of a Loewner matrix derived from the frequency-domain representation, and a simulator module for simulating the response of the physical sy...

An FFT-volume integral equation formulation based on equivalent polarization currents is presented for the analysis of inhomogeneous dielectric objects. The Galerkin discretization scheme used herein incorporates piecewise constant functions and results into well-posed systems even for scatterers of high contrast. Moreover, the original 6-D (volume...

Cell signaling pathways and metabolic networks are often modeled using ordinary differential equations (ODEs) to represent the production/consumption of molecular species over time. Regardless whether a model is built de novo or adapted from previous models, there is a need to estimate kinetic rate constants based on time-series experimental measur...

6.002x is the first electronic circuits course to be taught online to tens of thousands of students. The goal of the 6.002x experiment was to explore ways to use computer assisted instruction to surpass the quality of traditional residential teaching. By providing superior on-line content delivery and assessment, we hope to both be able to educate...

Motivation: Computational models of biological signalling networks, based on ordinary differential equations (ODEs), have generated many insights into cellular dynamics, but the model-building process typically requires estimating rate parameters based on experimentally observed concentrations. New proteomic methods can measure concentrations for a...

The theory and methods of linear model order reduction (MOR) have matured in recent decades. Accordingly, MOR research has been turning to nonlinear systems, such as those encountered in coupled partial differential equations (PDEs) models of microelectromechanical systems (MEMS). This chapter focuses on reduction methods based on state projection....

Electrical impedance myography (EIM) is a technique for the evaluation of neuromuscular diseases, including amyotrophic lateral sclerosis and muscular dystrophy. In this study, we evaluated how alterations in the size and conductivity of muscle and thickness of subcutaneous fat impact the EIM data, with the aim of identifying an optimized electrode...

Motivation: TRAIL has been widely studied for the ability to kill cancer cells selectively, but its clinical usefulness has been hindered by the development of resistance. Multiple compounds have been identified that sensitize cancer cells to TRAIL-induced apoptosis. The drug LY303511 (LY30), combined with TRAIL, caused synergistic (greater than a...

We present a systematic, multiscale, fully detailed numerical modeling for dynamics of fluid flow and ion transport covering Ohmic, limiting, and overlimiting current regimes in conductance of ion-selective membrane. By numerically solving the Poisson-Nernst-Planck-Navier-Stokes equations, it is demonstrated that the electroconvective instability,...

Transforming growth factor-β1 (TGF-β1) is a potent regulator of extracellular matrix production, wound healing, differentiation, and immune response, and is implicated in the progression of fibrotic diseases and cancer. Extracellular activation of TGF-β1 from its latent form provides spatiotemporal control over TGF-β1 signaling, but the current und...

This paper presents a new method for the efficient numerical computation of Casimir interactions between objects of arbitrary geometries, composed of materials with arbitrary frequency-dependent electrical properties. Our method formulates the Casimir effect as an interaction between effective electric and magnetic current distributions on the surf...

Fibrotic diseases are often caused by chronic injuries, and are characterized by pathological over-activation of certain stages of wound healing, particularly extracellular matrix secretion. Matrix secretion is driven by the fibrotic cytokine TGF-β1 (transforming growth factorβ1), which is secreted by cells as a latent complex, and must be activate...

A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and testing points is a major issue that is addressed by the proposed scheme, in the context of the 2D Laplace equation...

Plasmin (PLS) and urokinase-type plasminogen activator (UPA) are ubiquitous proteases that regulate the extracellular environment. Although they are secreted in inactive forms, they can activate each other through proteolytic cleavage. This mutual interplay creates the potential for complex dynamics, which we investigated using mathematical modelin...

We extend a recently introduced method for computing Casimir forces between arbitrarily shaped metallic objects [M. T. H. Reid , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.040401 103 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our o...

We present a few modifications that stabilize nonlinear reduced order models generated by discrete empirical interpolation methods. We combine a different approach to linearization with a multipoint stabilization technique. The examples used to demonstrate our method's effectiveness are a nonlinear transmission line, a micromachined switch, and a n...

Computing parametric sensitivities for oscillators has a now well-understood subtlety associated with the indeterminacy of phase. A less universal, but still vexing, subtlety arises when an oscillator is described by a system of differential equations with “hidden” conservation constraints (HCC’s); defined as weighted sums of state variables that a...

Fast surface integral equation (SIE) methods seem to be ideal for simulating 3-D nanophotonic devices, as such devices generate fields in both the interior device volume and in the infinite exterior domain. SIE methods were originally developed for computing scattering from structures with finite surfaces, and since SIE methods automatically repres...

Motivation: Modeling biological signaling networks using ordinary differential equations (ODEs) has proven to be a powerful technique for generating insight into cellular dynamics, but it typically requires estimating rate parameters based on experimentally observed concentrations. New measurement methods can measure concentrations for all molecula...

We present a few modifications that stabilize nonlinear reduced order models generated by discrete empirical interpolation methods. We combine a different approach to linearization with a multipoint stabilization technique. The examples used to demonstrate our method's effectiveness are a nonlinear transmission line, a micromachined switch, and a n...

Many numerical techniques developed for analyzing circuits can be “recycled”—that is, they can be used to analyze mass-action kinetics (MAK) models of biological processes. But the recycling must be judicious, as the differences in behavior between typical circuits and typical MAK models can impact a numerical technique’s accuracy and efficiency. I...

We show how to compute Casimir forces at nonzero temperatures with time-domain electromagnetic simulations, for example using a finite-difference time-domain (FDTD) method. Compared to our previous zero-temperature time-domain method, only a small modification is required, but we explain that some care is required to properly capture the zero-frequ...

Contains reports on five research projects.