March  1, 2024




Conference on Mathematics of Medical Imaging
June 20-24, 2011
hosted by the Fields Institute
held at the University of Toronto

Organizing Committee:
Adrian Nachman , University of Toronto
Dhavide Aruliah, University of Ontario Institute of Technology
Hongmei Zhu, York University

Invited Plenary talks
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Invited plenary talks

Elsa Angelini Compressed Biological Imaging
Guillaume Bal Hybrid Inverse Problems and Internal Functionals
Charles L. Epstein New approaches to the numerical solution of Maxwell's Equations
Aaron Fenster Use of 3D Ultrasound Imaging in Diagnosis, Treatment and Research
Mathias Fink Multiwave Imaging and Elastography
Polina Golland Non-parametric Atlas-Based Segmentation of Highly Variable Anatomy
David Isaacson Problems in Electrical Impedance Imaging (talk cancelled)
Ender Konukoglu Personalizing Mathematical Models with Sparse Medical Data: Applications to Tumor Growth and Electrocardiophysiology
Jeremy Magland Processing strategies for real-time neurofeedback using fMRI
Anne Martel Assessing response of cancer to therapy using MRI
Dr Michael Miller Diffeomorpic Shape Momentum in Computational Anatomy and Neuroinformatics
Xavier Pennec Statistical Analysis on Manifolds in Medical Image Analysis
Justin Romberg A Survey of Compressed Sensing and Applications to Medical Imaging
Yoram Rudy Noninvasive Electrocardiographic Imaging (ECGI) of Cardiac Electrophysiology and Arrhythmia
John Schotland Physical Aspects of Hybrid Inverse Problems
Emil Sidky What does compressive sensing mean for X-ray CT and comparisons with its MRI application
Samuli Siltanen Low-dose three-dimensional X-ray imaging
Gunther Uhlmann Thermoacoustic tomography with a variable sound speed
Lihong V. Wang Photoacoustic Tomography: Ultrasonically Breaking through the Optical Diffusion Limit
Graham Wright MRI for Management of Ventricular Arrhythmias

Abstracts Invited plenary talks

Compressed Biological Imaging
Elsa Angelini
Institut Telecom, Telecom ParisTech
Coauthors: Jean-Christophe Olivo-Marin, Marcio Marim de Moraes, Michael Atlan, Yoann Le Montagner

Compressed sensing (CS) is a new sampling theory that was recently introduced for efficient acquisition of compressible signals. In the presented work, we have studied practical applications of the Fourier-based CS sampling theory for biological microscopy imaging, with two main contributions:

(i) Image denoising: microscopic images suffer from complex artifacts associated with noise and non-perfect illumination conditions. In fluorescence microscopy, noise and photobleaching degrade the quality of the image. In this work, we have exploited the CS theory as an image denoising tool, using multiple random undersampling in the Fourier domain and the Total Variation as a spatial sparsity prior. Compounding of images reconstructed from multiple sets of random measurements enforce spatial coherence of meaningful signal components and decorrelate noisy components. We have studied the relation between signal sparsity and noise reduction performance under different noise conditions. We have demonstrated on simulated and practical experiments on fluorescence microscopy that the proposed denoising framework provide images with similar or increased signal-to-noise ratio (SNR) compared to state of the art denoising methods while relying on a limited number of samples.

If Fourier-domain image point acquisitions were feasible, the proposed denoising could be used as a fast acquisition scheme which would enable to reduce exposition times, and reduce the photobleaching effects.

(ii) Compressed digital holographic microscopy: high data throughput is becoming increasingly important in microscopy, with high-resolution cameras (i.e. large numbers of samples per acquisition) and long observation times. The compressed sensing theory provides a framework to reconstruct images from fewer samples than traditional acquisition approaches. However, the very few measurements must be spread over a large field of view, which is difficult to achieve in conventional microscopy.

In a first experiment, we have proposed a computational scheme to perform fast temporal acquisitions of sequences of Fourier amplitude measures in optical Fourier imaging and estimate the missing phase information from spectra interpolation between few in-between complete keyframes. This approach was evaluated for high-frame rate imaging of moving cells.

In a second experiment, we have implemented a real CS acquisition scheme for digital holographic microscopy, acquiring a diffraction map of the optical field and recovering high quality images from as little as 7% of random measurements. The CS acquisition setup was successfully extended to high speed low-light single-shot off-axis holography.
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Hybrid Inverse Problems and Internal Functionals
Guillaume Bal
Columbia University

Hybrid inverse problems aim at combining the high contrast of one imaging modality (such as e.g. Electrical Impedance Tomography or Optical Tomography in medical imaging) with the high resolution of another modality (such as e.g. based on ultrasound or magnetic resonance). Mathematically, these problems often take the form of inverse problems with internal information. This talk will review several results of uniqueness and stability obtained recently in the field of hybrid inverse problems.
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New approaches to the numerical solution of Maxwell's Equations
Charles L. Epstein
University of Pennsylvania
Coauthors: Leslie Greengard (NYU) Michael O'Neil (NYU)

We develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in R^3. This representation leads to a coupled system of Fredholm integral equations of the second kind for four scalar densities supported on the material interface. Like the classical Muller equation, it has no spurious resonances. Unlike the classical approach, however, the representation does not suffer from low frequency breakdown. We earlier presented a similar method for the perfect conductor problem.
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Use of 3D Ultrasound Imaging in Diagnosis, Treatment and Research
Aaron Fenster
Robarts Research Institute

The last two decades have witnessed unprecedented developments of new imaging systems making use of 3D visualization. These new technologies have revolutionized diagnostic radiology, as they provide the clinician with information about the interior of the human body never before available. Ultrasound imaging is an important cost-effective technique used routinely in the management of a number of diseases. However, 2D viewing of 3D anatomy, using conventional ultrasound, limits our ability to quantify and visualize the anatomy and guide therapy, because multiple 2D images must be integrated mentally. This practice is inefficient, and leads to variability and incorrect diagnoses. Also, since the 2D ultrasound image represents a thin plane at an arbitrary angle in the body, reproduction of this plane at a later time is difficult.

Over the past 2 decades, investigators have addressed these limitations by developing 3D ultrasound techniques. In this paper we describe developments of 3D ultrasound imaging instrumentation and techniques for use in diagnosis and image-guided interventions. As ultrasound imaging is an interactive imaging modality, providing the physician with real-time visualization of anatomy and function, the development of image analysis and guidance tools is challenging. Typically, these tools require segmentation, classification, tracking and visualization of pathology and instruments to be executed in real-time, accurately, reproducibly and robustly. As an illustration of these needs, we will present some diagnostic and image-guided intervention applications that would benefit from these developments. Examples will be given for imaging various organs, such as the prostate, carotid arteries, and breast, and for the use in 3D ultrasound-guided prostate therapy. In addition, we describe analysis methods to be used for quantitative analysis of disease progression and regression.
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Multiwave Imaging and Elastography
Mathias Fink
Institut Langevin, ESPCI ParisTech, France

Interactions between different kinds of waves can yield images that beat the single-wave diffraction limit. Multiwave Imaging consists of combining two different waves-- one to provide contrast, another to provide spatial resolution - in order to build a new kind of image. Contrary to single-wave imaging that is always limited by the contrast and resolution properties of the wave that generated it, multiwave imaging provides a unique image of the most interesting contrast with the most interesting resolution. Multiwave imaging opens new avenues in medical imaging and a large interest for this approach is now emerging in geophysics and non-destructive testing.

We will describe the different potential interactions between waves that can give rise to multiwave imaging and we will emphasize the various multiwave approaches developed in the domain of medical imaging. Common to all these approaches, ultrasonic waves are almost always used as one of the wave to provide spatial resolution, while optical, electromagnetic or sonic shear waves provide the contrast. Among various multiwave techniques, we will mainly focus on photo-acoustic and shear wave imaging. Through various medical applications going from cancer diagnosis to cardiovascular imaging, we will emphasize the recent clinical successes of multiwave imaging.
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Non-parametric Atlas-Based Segmentation of Highly Variable Anatomy
Polina Golland, MIT
Coauthors: Michal Depa, Mert Sabuncu

We propose a non-parametric probabilistic model for automatic segmentation of medical images. The resulting inference algorithms register individual training images to the new image, transfer the segmentation labels and fuse them to obtain the final segmentation of the test subject. Our generative model yields previously proposed label fusion algorithms as special cases, but also leads to a new variant that aggregates evidence locally in determining the segmentation labels. We demonstrate the advantages of our approach in two clinical application: segmentation of neuroanatomical structures and segmentation of the left heart atrium whose shape varies significantly across the population.
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Problems in Electrical Impedance Imaging (Talk Canceled)
David Isaacson, Mathematical Sciences Department, Rensselaer Polytechnic Institute
Coauthors: J.C. Newell, and G. Saulnier

Electrical impedance imaging systems apply currents to the surface of a body and measure the resulting voltages. From this electromagnetic data an approximate reconstruction and display of the internal electrical properties of the body are made. We explain how this process leads to inverse boundary value problems for Maxwell's equations. Since the conductivity of hearts, and lungs change as blood enters and leaves these organs , impedance images can be used to monitor heart and lung function. Since the electrical properties of some cancers are different from surrounding normal tissues, electrical impedance spectroscopy may be used to help diagnose some cancers.

Images and movies of heart and lung function, as well as breast cancers, made with the RPI Adaptive current tomography systems will be shown. It will be explained how the analysis of spectral properties of the Dirichlet to Neumann map lead to the design of these adaptive current tomography systems.
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Personalizing Mathematical Models with Sparse Medical Data: Applications to Tumor Growth and Electrocardiophysiology
Ender Konukoglu
Microsoft Research Cambridge
Coauthors: Nicholas Ayache, Maxime Sermesant, Olivier Clatz, Bjoern H. Menze

Mathematical models for biophysical systems are crucial in understanding the underlying physiological dynamics as well as tailoring patient-specific treatment.One of the biggest challenges for biophysical models is the identification of patient-specific parameters and the personalized model. This talk will focus on the problem of parameter identification using sparse medical data. Challenges associated with the medical data will be demonstrated with two model problems, tumor growth and electrocardiophysiology, incorporating different types of data, i.e. MR images and cardiac mappings. Different techniques for dealing with sparse data will be presented including deterministic and probabilistic methods.
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Processing strategies for real-time neurofeedback using fMRI
Jeremy Magland
University of Pennsylvania
Coauthors: Anna Rose Childress

Functional magnetic resonance imaging (fMRI) is traditionally used as a probe for patterns of brain activity in response to instructed cognitive tasks and stimuli by averaging of the blood oxygenation level-dependent (BOLD) response over an entire scan session (usual 10-60 minutes). Recently, real-time feedback approaches have expanded fMRI from a brain probe to include potential brain interventions. However, real-time measurements and analyses require entirely different data processing techniques, because measurements must be made prospectively (on the fly) throughout the scan using only a subset of the acquired data. In this talk, we outline the challenges associated with performing real-time fMRI experiments, and describe the specific techniques we have found to be successful for providing meaningful and robust neurofeedback in real time.
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Assessing response of cancer to therapy using MRI
Anne Martel
Sunnybrook Health Sciences Centre, University of Toronto

Personalized medicine, the practice of tailoring medical therapies to the specific genetic and disease profiles of patients, represents a major shift from the epidemiologically based model of traditional medicine. This has lead to the development of novel new therapies for cancer, for example Herceptin for breast cancer and Gleevec for chronic myelogenous leukemia. Although this is an exciting development it poses several challenges to the clinician. These therapies are extremely expensive and are only designed to work on a subset of patients hence there is a pressing need for tools that can determine whether a therapy is effective early in the treatment regime.

Dynamic contrast-enhanced MRI (DCE-MRI) can provide valuable information about the efficacy of drug therapy. In addition to traditional measures of lesion size, it has been shown that DCE-MRI can provide important information about tumour function, for example by providing information about blood flow and permeability. In this talk I will give an overview of the role DCE-MRI has to play in monitoring response to therapy and outline some of the challenges involved in bringing this technology into routine clinical use. I will also describe some of the work done in my lab in the areas of quantitative analysis and image registration to address some of these challenges.
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Diffeomorpic Shape Momentum in Computational Anatomy and Neuroinformatics
Dr Michael Miller
Johns Hopkins University Center for Imaging Science

Over the past decade Computational Anatomy has been the study of structure and function in registered atlas coordinates.

Unlike Google Maps which has been based on the rigid motions with scale for aligning coordinate systems, the underlying "alignment" groups in CA are the infinite dimensional diffeomorphisms. For rigid motion angular momentum plays a parsimonious roll; in diffeomorphic motion the analogous roll is played by diffeomorphic shape momentum.

We present results from computational codes for generating diffeomorphic correspondences between anatomical coordinate systems and their encoding via diffeomorphic shape momentum. Statistics will be examined for quantifying probabilistic shape momentum representations of neuroanatomy at 1mm scale. As well we will present results on functional and structural neuroinformatics in populations of normals and diseased populations in registered atlas coordinates.
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Statistical Analysis on Manifolds in Medical Image Analysis
Xavier Pennec
INRIA, Asclepios team, Sophia-Antipolis, France

To analyze and model the biological variability of the human anatomy, the general method is to identify anatomically representative geometric features (points, tensors, curves, surfaces, volume transformations), and to describe and compare their statistical distribution in different populations. As these geometric features most often belong to manifolds that have no canonical Euclidean structure, we have to rely on more elaborated algorithmical bases.

I will first describe the Riemannian structure, which proves to be powerfull to develop a consistent framework for simple statistics on manifolds. It can be further extend to a complete computing framework on manifold-valued images. For instance, the choice of a convenient Riemannian metric on symmetric positive define matrices (SPD) allows to generalize consistently to fields of SPD matrices (e.g. DTI images) many important geometric data processing algorithms. This allows for instance to introduce anisotropic spatial priors in DTI estimation or to realize statistical models of the cardiac muscle fibers.

Then I will focus on statistics on deformations. The natural extension of the Riemannian framework is the use of right-invariant metrics on diffeomorphisms (often called LDDMM). When used on curves and surfaces modeled with geometric currents, the registration problem becomes finite-dimensional thanks to the representer theorem. An example application is the construction of a statistical model of the remodeling of the heart in rToF. For continuous images, however, the complexity remains very high. Dropping the metric, we propose to use the geodesics of the canonical Cartan connection (translates of one-parameter subgroups) for which very efficient algorithms exist. This log-demons framework will be illustrated with the individual and groupwise modeling of the morphological changes of the full brain in Alzheimer's disease.
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A Survey of Compressed Sensing and Applications to Medical Imaging
Justin Romberg
Georgia Tech

We will overview the fundamental results and recent theoretical trends in compressive sensing, and discuss current state-of-the-art models and algorithms for image reconstruction. We will present applications in medical imaging (including accelerated MRI and ultrasound), and discuss sparsity-based models being used for other imaging modalities and how they might apply to medical imaging.
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Noninvasive Electrocardiographic Imaging (ECGI) of Cardiac Electrophysiology and Arrhythmia
Yoram Rudy
Washington University in St Louis

A noninvasive imaging modality for cardiac electrophysiology and arrhythmias is not yet available for clinical application.Such modality could be used to identify patients at risk, provide accurate diagnosis and guide therapy. Standard noninvasive diagnostic techniques, such as the electrocardiogram (ECG) provide only low-resolution reflection of cardiac electrical activity on the body surface.
In my presentation, I will describe the application in humans of a new imaging modality called Electrocardiographic Imaging (ECGI) that noninvasively images cardiac electrical activity on the heart’s epicardial surface.
In ECGI, a multi-electrode vest (or strips) records 250 body-surface electrocardiograms; then, using geometrical information from a CT scan and an inverse solution to Laplace equation, electrical potentials, electrograms, activation sequences (isochrones) and repolarization patterns are reconstructed on the heart‘s surface.
I will show examples of imaged atrial and ventricular activation and ventricular repolarization in the normal heart and during cardiac arrhythmias.
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Physical Aspects of Hybrid Inverse Problems
John Schotland
University of Michigan

There is considerable interest in the development of optical methods for biomedical imaging. The mathematical problem consists of recovering the optical properties of a highly-scattering medium. This talk will review recent work on related inverse scattering problems for the radiative transport equation and efficient fast image reconstruction algorithms for large data sets. Numerical simulations and experimental data from model systems are used to illustrate the results.
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What does compressive sensing mean for X-ray CT and comparisons with its MRI application
Emil Sidky
University of Chicago

This talk will trace our attempts at understanding compressive sensing (CS) concepts in the context of X-ray computed tomography (CT) and translating CS ideas to realize sparse-data image reconstruction in CT.

The arrival of CS could not come at a more interesting time for CT. Research on iterative image reconstruction applied to actual CT systems has only recently begun due to the developments in computational technology that allow for data processing at the gigabyte level. From the application side, more and more CT exams are being prescribed and there is pressure to reduce dose to the patients as evidenced by the rapid deployment of "low-dose CT" products by the major CT manufacturers. The promise of sparse-data image reconstruction from CS may thus play an important role in these recent technological developments.

I will show results with actual CT data that seem to indicate that CS style optimization problems do indeed yield "high quality" images from sparse projection data. I will then point out various issues that arise in integrating iterative image reconstruction, in general, and CS methods, specifically, into CT systems. I will address questions such as: Which data model to use and how accurate does it have to be? Given that object functions are continuous, ...what is meant by object sparsity? ...what is sparse data and what is fully sampled data? How should we validate the new CS algorithms? These questions will be addressed for CT and comparisons made with MRI where the application of CS is more familiar.
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Low-dose three-dimensional X-ray imaging
Samuli Siltanen
University of Helsinki, Finland

A new kind of tomographic X-ray imaging modality is discussed, where the patient is radiated as little as possible while recovering enough three-dimensional information for the clinical task at hand. The input can be only a dozen projection images collected from different directions. Such sparse data typically represent limited-angle and local tomography configurations and lead to severely ill-posed reconstruction problems. This differs from traditional CT imaging, where a comprehensive data set is collected and the (only mildly ill-posed) reconstruction problem is solved using the classical filtered back-projection (FBP) algorithm. The incompleteness of sparse data violates the assumptions of FBP, leading to unacceptable reconstruction quality. However, statistical inversion methods can be used with sparse tomographic data. They yield clinically useful reconstructions, as demonstrated by real-data examples related to mammography, surgical imaging and dental imaging. Some of these methods have already entered commercial products: see
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Thermoacoustic tomography with a variable sound speed
Gunther Uhlmann
University of California irvine and University of Washington
Coauthors: Plamen Stefanov

We will discuss some recent results on termoacoustic tomography with a variable sound speed including the smooth case and the non-smooth one, the latter motivated by brain imaging. We will also present some numerical results based on the analytic reconstruction which is joint work with Jianliang Qian and Hongkai Zhao.
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Photoacoustic Tomography: Ultrasonically Breaking through the Optical Diffusion Limit
Lihong V. Wang
Washington University in St. Louis

We develop photoacoustic imaging technologies for in vivo early-cancer detection and functional or molecular imaging by physically combining non-ionizing electromagnetic and ultrasonic waves. Unlike ionizing x-ray radiation, non-ionizing electromagnetic waves—such as optical and radio waves—pose no health hazard and reveal new contrast mechanisms. Unfortunately, electromagnetic waves in the non-ionizing spectral region do not penetrate biological tissue in straight paths as x-rays do. Consequently, high-resolution tomography based on non-ionizing electromagnetic waves alone—such as confocal microscopy, two-photon microscopy, and optical coherence tomography—is limited to superficial imaging within approximately one optical transport mean free path (~1 mm in the skin) of the surface of scattering biological tissue. Ultrasonic imaging, on the contrary, provides good image resolution but has strong speckle artifacts as well as poor contrast in early-stage tumors. Ultrasound-mediated imaging modalities that combine electromagnetic and ultrasonic waves can synergistically overcome the above limitations. The hybrid modalities provide relatively deep penetration at high ultrasonic resolution and yield speckle-free images with high electromagnetic contrast.

In photoacoustic computed tomography, a pulsed broad laser beam illuminates the biological tissue to generate a small but rapid temperature rise, which leads to emission of ultrasonic waves due to thermoelastic expansion. The short-wavelength pulsed ultrasonic waves are then detected by unfocused ultrasonic transducers. High-resolution tomographic images of optical contrast are then formed through image reconstruction. Endogenous optical contrast can be used to quantify the concentration of total hemoglobin, the oxygen saturation of hemoglobin, and the concentration of melanin. Melanoma and other tumors have been imaged in vivo. Exogenous optical contrast can be used to provide molecular imaging and reporter gene imaging.

In photoacoustic microscopy, a pulsed laser beam is focused into the biological tissue to generate ultrasonic waves, which are then detected with a focused ultrasonic transducer to form a depth resolved 1D image. Raster scanning yields 3D high-resolution tomographic images. Super-depths beyond the optical diffusion limit have been reached with high spatial resolution.

Thermoacoustic tomography is similar to photoacoustic tomography except that low-energy microwave pulses, instead of laser pulses, are used. Although long-wavelength microwaves diffract rapidly, the short-wavelength microwave-induced ultrasonic waves provide high spatial resolution, which breaks through the microwave diffraction limit. Microwave contrast measures the concentrations of water and ions.

The annual conference on this topic has been doubling in size approximately every three years since 2003 and has become the largest in SPIE’s Photonics West as of 2009
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MRI for Management of Ventricular Arrhythmias
Graham Wright
Sunnybrook Health Sciences Centre, University of Toronto

Ventricular Arrhythmias are a major cause of sudden cardiac death. Magnetic resonance imaging (MRI) has the potential to identify those at greatest risk. In this presentation, current approaches to detection and treatment of ventricular arrhythmias as well as evidence of MRI’s potential clinical role are briefly reviewed. Emerging methods to better characterize the structural substrate of ventricular arrhythmia, notably scar and heterogeneous infarct, with MRI are presented . This characterization has been used to customize mathematical models of electrical propagation in the heart. The modeling results correspond well to experimental measurements of electrical activity in porcine hearts. Combining these tools with the development of MRI-compatible electrophysiology systems holds the promise of guiding ablation therapy to disrupt the arrhythmogenic substrate, yielding more effective solutions for patients at risk of life-threatening events.

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