
SCIENTIFIC PROGRAMS AND ACTIVITIES 

March 1, 2024  
Invited special session talks
Abstracts Special Session TalksCompressed Sensing in Cardiac MRI In this talk, we will discuss utility of compressed sensing (CS)
to accelerate image acquisition in cardiac MRI. A brief review of
the clinical needs, and the associated cardiac MRI scans will be
presented. Then, recent techniques for improving CS reconstruction
and their clinical applications in cardiac MRI will be discussed Reducing the data: Analysis of the role of vascular geometry
on the features of blood flow in curve vessels In recent years, numerical models using anatomical reconstruction techniques have generated a plethora of simulations of blood flow in threedimensional (3D) patientspecific geometries. These are usually performed in localised areas of the arterial system, although more recently within larger arterial networks. The motivation behind these studies is typically to determine distributions of flowrelated quantities (e.g. wall shear stress, WSS) due to their association with vascular disease. Such simulations provide insight into clinically relevant fluid dynamics, but unfortunately they often produce such large quantities of data that they are unlikely to be of practical use in a clinical setting.
Back to top Inadequate Sparse Data and Carbon Skeletons The first step in determining the structure of a new organic molecule is usually to determine the structure of the carbon skeleton. That is, which carbons are bonded to which other carbons. This can be determined by examining the 2d spectra produced by an INADEQUATE experiment, although doing so by eye is extremely difficult because the spectra are inherently very noisy, depending as they do on the rare occurrences of bonded carbon13s (which occur once per 10000 bonds). Various filtering and fitting methods have been applied to the signals, with some success. We propose a novel approach using variablesplitting, regularization in a sparse image subdomain, and penalty functions which embody a priori knowledge about the specturm determined by the likelihood of different bond patterns. Initial experimental results showed a 4fold reduction in experiment time is possible by using this method which can process much noisier data. Back to top Advances in photoacoustic tomography image reconstruction Photoacoustic tomography, also known as thermoacoustic tomography, is a rapidly emerging bioimaging modality that employs optical contrast and ultrasonic detection principles. In this talk, we describe recent advances in image reconstruction methods. Specifically, we will present iterative reconstruction methods that are based on accurate models of the measurement system and analytic methods for acoustically heterogeneous layered media. Back to top Quantitative PhotoAcoustic Tomography using Diffusion and Transport
Models The task in quantitative photoacoustic imaging (QPAT) is to recover the optical properties of an imaged region from a reconstructed photoacoustic image. Thus the data, considered as the product of the absorption coefficient and the light fluence, depends on both the absorption and the scattering properties in a nonlinear way. In this talk we apply modelbased inversions developed in diffuse optical tomography (DOT) to the QPAT problem. As the domain of photoacoustic images is relatively small scale, the differences between fluence models based on diffusion and radiative transport can become significant. In this talk we present simulations of QPAT absed on both models and discuss the differences. Back to top Novel Techniques for Multiscale Representations Multiscale analysis can give useful insight into various natural and manmade phenomena. In this talk, we will discuss some new techniques of multiscale analysis in the context of digital images. Nevertheless, the techniques presented are universal and can be applied to wide range of applications. Digital images can be thought of as sampled analogue signals. Images obtained from a camera could be noisy and blurry. Denoising and deblurring an image sometimes give rise to multiscale image representations, where we obtain different scales of the same image. We will talk about some historical background of the mathematical image processing methods and how they are interlinked with each other. I will then introduce two interesting types of integrodifferential equations (IDEs) which produce multiscale representations. These IDEs are motivated by the hierarchical decompositions of images. We will see their results and also some innovative variants of the IDEs. Back to top Wavefront Control and Optical Tomography of Scattering Media A number of experimental approaches such as Optical Coherence Tomography, Diffuse Tomography, acoustooptics etc. are used to image through scattering media. We will underline a number of their limits in term of resolution, depth and signal to noise ratio. In parallel a number of new approaches have emerged these last years that allow revisiting these techniques in order to improve their performances in term of contrast, resolution, speed etc. Then we will point few results that have been obtained using wavefront control in the space domain or in the time domain and discuss how these wavefront controls could help to enlarge the field of optical tomography. Back to top Some stability results for electric impedance tomography under
elastic deformation We consider electric impedance tomography under elastic perturbations,
where one tries to determine the conductivity in a bounded domain
from the knowledge of pairs of Dirichlet and Neumann data and from
their associated internal energy densities. In 2D, using a result
of Alessandrini and Nesi, one can show the injectivity and stability
of the map that associates the conductivity to the internal data
corresponding to 2 diffeomorphic imposed currents. In 3D, the situation
is more complex, and we only obtain a local result of uniqueness
and stability. [1] H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter, and M. Fink, Electrical impedance tomography by elastic deformation, SIAM J. APPL. MATH. Vol. 68, No. 6, pp. 15571573 (2008). [2] G. Bal, E. Bonnetier, F. Monard and F. Triki, Inverse diffusion from knowledge of power densities, submitted. [3] G. Bal and G. Uhlmann, Inverse diffusion theory for photoacoustics, Inverse Problems, 26(8) (2010), p. 085010. [4] Y. Capdeboscq, J. Fehrenbach, F. de Gournay, and O. Kavian, An optimal control approach to imaging by modification, SIAM Journal on Imaging Sciences, 2, pp. 10031030 (2009). Back to top The Role of Deformable Registration Algorithms in Adaptive Radiotherapy Advances in imaging and treatment planning have improved the precision and sophistication with which external beam radiation therapy can be planned. In addition, image guidance at the time of treatment delivery can improve the ability to accurately deliver this treatment. However, the information obtained from volumetric images at the time of treatment delivery has also provided information on the changes that can occur in the patient anatomy over the course of treatment, including weight loss, normal tissue response, and tumor response. These changes compromise the ability to accurately deliver the intended dose. In many cases, these changes can be substantial, warranting the need to generate a new treatment plan to ensure that the therapeutic intent is administered in the presence of these changes, termed ‘adaptive radiotherapy’. The infrastructure to enable adaptive radiotherapy in the clinical environment is not trivial. One key component is deformable registration, which enables mapping of the anatomy in the initial planning images with the image or images obtained over the course of treatment or at the time that the treatment adaptation is performed. Once the anatomical mapping is complete, dose accumulation can be performed. The results of the deformable registration become an important component linking the geometric states of the patient, and therefore ensuring that the mapping is accurate is critical. This presentation will review the key components of adaptive radiotherapy, specifically focusing on the role of deformable registration. A brief survey of the algorithms often used in the field will be provided. Results of a multiinstitution deformable registration accuracy study will be presented, highlighting the importance of algorithm implementation. Mathematical, phantom, and imagebased metrics to assess accuracy of the algorithms will be discussed. Back to top Quantitative Dynamic ContrastEnhanced MRI (DCEMRI) of Tumor
Angiogenesis Angiogenesis, the growth of new blood vessels, plays a critical role in tumor growth and metastasis. The morphology and function of tumor vessels, however, are distinct from healthy blood vessels. In general, tumor blood vessels are poorly formed, resulting in a chaotic vessel hierarchy with leaky endothelial linings, enlarged lumens, and poor perfusion, all of which contribute to an environment (e.g. hypoxic, high interstitial fluid pressure) that further drives malignant progression. Functional information on tumor vessels can, therefore, inform us on tumor biology, its progression and response to conventional chemo/radiotherapy or novel antiangiogenic therapies. As a noninvasive imaging modality, DCEMRI has been increasingly used over the last decade in the staging of patients with cancer and monitoring their therapeutic response. Quantitative DCEMRI, which extracts physiologically meaningful parameters (e.g. perfusion, vessel permeability, and cell packing), can further extend the role of MRI and potentially allow response prediction for patient selection and therapy planning, as well as elucidate the biological effects of new therapeutic developments. We will describe the current stateoftheart in DCEMRI technology, the requirements for robust and reliable quantitation, and recent advances that will enable clinical implementation of quantitative DCEMRI for cancer management. Back to top Use of adaptive beamformers in MEG source modeling Neuromagnetic inverse solutions involve determining the distribution of electrical activity within the brain that contributes to the magnetic field recorded by sensors outside of the head. Solutions to such inverse problems are nonunique and highly underdetermined. Traditional approaches to this problem model the underlying neural generators as combinations of discrete point sources (dipole fitting) or as distributed current solutions (e.g., minimumnorm). These approaches can be limited by crosstalk between multiple brain sources, or the presence of interference sources that are not included in the forward models. An alternative approach is to construct 3dimensional source images from a lattice of spatial filters based on adaptive (minimumvariance) beamforming. This method minimizes crosstalk between sources based on the observed correlation between signals measured across the array of detectors, and is thus ideally suited to modern wholehead MEG systems that consist of a hundred or more recording channels distributed over the head. I will review current beamforming approaches used in MEG source analysis, and describe some of the advantages and disadvantages of this source modeling approach. I will also show examples of the application of a spatiotemporal beamforming algorithm developed in our lab at SickKids in both clinical and basic studies of human brain function. Back to top Quantitative Perfusion Estimation from Two Photon Fluorescence
Microscopy Microvasculature Maps OBJECTIVE: Many models have been proposed to explain the relationship
between neural activity and hemodynamic parameters but in their
present forms these models fail to provide a detailed understanding
of the neurovascular coupling on the micron scale. Our laboratory
has been recently using two photon fluorescence microscopy (2PFM)
to image the 3D vascular network close to the epicenter of neural
activity elicited by somatosensory stimulation and quantitatively
analyzing the 3D vascular morphology to deduce dynamic changes in
the cerebral blood volume across the vascular tree. The current
work estimates cerebral blood flow and perfusion from the 3D geometry
and a 2D time series tracking the bolus passage of an injected fluorescent
dextran. Back to top DataDriven Measurement and Removal of Physiological Noise in
BOLD fMRI BOLD fMRI is an invaluable tool for measuring correlates of brain function; however, this technique is limited by a relatively poor ContrasttoNoiseRatio, making it difficult to obtain robust, accurate measurements. One of the principal confounds of fMRI is physiological noise, including the effects of respiration and pulsatile bloodflow, which exhibit complex, undersampled temporal structure in standard fMRI. In addition, physiological noise is often nonorthogonal to the neuronallylinked BOLD response, presenting a significant challenge in separating subjectderived signal and noise. In this talk, we present a multivariate, datadriven procedure for estimating physiological noise in fMRI data, based on physiologicallyderived constraints. This method identifies high frequency, autocorrelated noise sources with reproducible spatial structure, using an adaptation of Canonical Correlation Analysis, in a splithalf resampling framework. The technique is able to identify a physiological noise subspace with vascularlinked spatial structure, and an intrinsic dimensionality that is task and subjectdependent. In addition, we demonstrate that subjects with higher variance in respiratory and cardiac rates generally require a higherdimensional subspace to optimize the detection of physiological noise in fMRI. This technique may be used to remove the physiological noise component from fMRI data, which increases spatial reproducibility and prediction accuracy of analyses. These results provide novel information about the structure of physiological noise in BOLD fMRI, as well as a principled method of removing physiological artifact. Back to top Random walks for deformable image registration I will present a novel discrete optimization formulation of deformable image registration, that can be solved by the random walker (RW) framework. The space of deformations is discretized and the image registration problem is formulated as a Gaussian MRF where continuous labels correspond to the probability of a point having a certain discrete deformation. The interaction (regularization) term of the corresponding MRF energy is convex and image dependent, thus being able to accommodate different types of tissue elasticity. This formulation results in a fast algorithm that can easily accommodate a large number of displacement labels, has provable robustness to noise, and a global solution. We experimentally demonstrate the validity of our formulation on synthetic and real medical data. Back to top Characterizing neural representation with multivariate pattern
analysis of fMRI data A traditional functional MRI experiment aims to identify the brain regions recruited by some cognitive function. To best identify regions activated in the majority of volunteers, data are typically spatially smoothed with a kernel of diameter 12cm and statistics subsequently performed on single voxels in a mass univariate regime. In a new approach of rapidly increasing popularity, multivariate (or multivoxel) pattern analysis (MVPA), a measure is taken of the consistency of the relationship between cognitive state and the pattern of activity across a local brain region within an individual. Data are typically not smoothed and it is not assumed that all voxels will be positively activated (some may carry information by deactivating). Group analyses are then performed on statistics that summarize the extent of representation of a given aspect of the cognitive state within a local region, and power is not reduced if the patterns of activity that signal these states are quite distinct in different volunteers. This method is often more sensitive than conventional fMRI, and is capable of distinguishing much more finely differentiated mental states. The method will be illustrated with examples from studies of auditory and visual memory and object recognition. Back to top Electrical Impedance Tomography: 3D reconstructions using scattering
transforms In late 1980s, the theoretical foundation of a direct quantitative method for Electrical Impedance Tomography was formulated (J. Sylvester, G. Uhlmann, R. G. Novikov, A. Nachman) and successfully implemented in the 2D case (S. Siltanen, J. Mueller, D. Isaacson) and in the 3D case for radial symmetric conductivities (J. Bikowski, K. Knudsen, J. Mueller). The method is based on the reformulation of the electrical potential equation as a Schrödinger equation and the reconstruction algorithm makes use of ideas from inverse scattering theory. The measurements are modelled by the DirichlettoNeumann map, which, roughly speaking, contains the measurement of currents at electrodes when voltages are imposed. The main difficulty in the inverse problem of recovering a conductivity from the knowledge of the DirichlettoNeumann map (Calderón problem) is the illposedness of the problem, a difficulty the reconstruction algorithm inherits. When not treated carefully, even small measurement errors can lead to aberrant reconstructions. In this talk, we propose to show the feasibility and relative efficiency of a 3D implementation of the algorithm for general conductivities in the unit ball, with a reasonable computation time. First, the reconstruction algorithm and its possible simplifications obtained by approximation, will be introduced. After briefly presenting the implementation, the reconstructions for numerical phantoms will be showed and the obtained resolution for the different simplifications will be discussed. Back to top 3D Anatomical Structure Localization We propose a method for the automatic localization of complex anatomical
structures using interest points derived from Random Forests and
matching based on discrete optimization. During training landmarks
are annotated in a set of example volumes. A sparse elastic model
encodes the geometric constraints of the landmarks. A Random Forest
classifier learns the local appearance around the landmarks based
on Haarlike 3D descriptors. Back to top Joint Segmentation and Deformable Registration of Fractured
Vertebrae Using a Synthesis of the Expectation Maximization and
Belief Propagation Algorithms A new surgical procedure aims to restore the height of damaged
vertebral bodies that have suffered a compression fracture as a
result of severe trauma. A computational method is needed to assess
the efficacy of the procedure by automatically measuring the change
in shape of the vertebral bodies in CT scans taken before and afterward. Back to top Mathematical Methods for Breast Image Registration Dynamic contrast enhanced magnetic resonance imaging (DCEMRI)
provides a very high sensitivity for the detection of breast cancer
and a sharp delineation of breast lesions. In the first part of
this talk, we present an efficient numerical methodology for automated
simultaneous registration and intensity correction of DCEMRI series.
The model separates the intensity correction term from the images
being registered in a regularized expression. A joint objective
functional is formed for which the corresponding Hessian and Jacobian
is computed and employed in a multilevel GaussNewton minimization
approach. Back to top Numerical aspects of piline reconstruction algorithms in tomography We investigate algorithms of filtered backprojection type that are based on piline inversion formulas such as Katsevich's inversion formula in two and three dimensions. The location of a characteristic artifact is identified and related to the region of backprojection as well as the support of the backprojected derivative. An application to data alignment is presented and some advantages of piline reconstruction algorithms are pointed out. Back to top Potential for Compressed Sensing in Clinical MR Imaging Magnetic resonance (MR) is a commonly used method for acquiring crosssectional (tomographic) images through the human body. Most large medical centre across Canada have one or more, heavily utilized, MR scanners. Unlike computed tomography (CT – a modality that forms tomographic images from collected projection xray images), MR uses radiowaves and magnetic fields to ‘image’ hydrogen in the body and thus does not expose patients to ionizing radiation. Drawbacks to MR imaging include the need to operationally tradeoff resolution, signaltonoise (SNR) and total acquisition times. Clinically useful MR examinations require a sufficiently lengthy total acquisition time in order to achieve resolution or SNR targets. Most clinical MR imaging uses a linear image reconstruction methodology (typically based on the Fourier transform). Compressed sensing is a recently proposed reconstruction methodology that can partially decouple the relationship between resolution, SNR and total acquisition time, provided specific conditions are met. The principle condition is that the reconstructed image, or a representation of it in another domain, must have sparsity. An increasing number of theoretical, phantom and patientbased studies are beginning to investigate the application of compressed sensing in MR imaging. This presentation reviews when it may be possible to decouple the relationship between resolution, SNR and total acquisition time, and overviews some of the applications currently under investigation. It will also discuss current limitations relating to the iterative nature and slowness of the compressed sensing Back to top Use of 3D GraphTheoretic Approaches in the Segmentation of
Ophthalmic Structures Threedimensional graphtheoretic techniques, such as graph cuts and the LayeredOptimalGraphImageSegmentationofMultipleObjectsandSurfaces (LOGISMOS) approach, are becoming increasingly popular for segmenting threedimensional structures within medical images. Such approaches enable globally optimal (with respect to a cost function) segmentations of 3D objects to be achieved in polynomial time. Furthermore, approaches such as LOGISMOS enable the simultaneous optimal detection of multiple surfaces in volumetric images, which is important in many medical image segmentation applications for which interrelationships between surfaces and objects are important. The first part of this talk reviews the theory behind the LOGISMOS approach and presents an overview of a number of applications. The second part of this talk discusses some of the ophthalmic applications in greater depth, such as the simultaneous segmentation of multiple layers of the retina within spectraldomain optical coherence tomography volumes. Back to top A Scale Consistent Approach to Image Completion Most patch based algorithms for completing missing parts of images fill in the absent regions by copying patches from the known part of the image into the unknown part, somewhat like plastic surgery. The criterion for deciding which patch to copy is compatibility of the copied patch with the vicinity of the region being completed. In this research we propose introducing a new dimension to this compatibility criterion, namely, scale. The patch is thus chosen by evaluating its consistency with respect to a hierarchy of smoothed (less detailed) versions of the image, as well as its surroundings in the current version. Applied recursively, this approach results in a multiscale framework that is shown to yield a dramatic improvement in the robustness of patch based image completion. Back to top MagnetoHemoDynamics in MRI devices In presence of a high magnetic field (typically in a MRI device), the blood flow in the aorta induces an electrical potential which is responsible for an increase of the Twave in the electrocardiogram (ECG). This phenomenon may perturb ECGgated medical imaging. The aim of this study is to reproduce this experimental observation through computer simulations. The model consists of three components: magnetohydrodynamics (MHD) in the aorta, bidomain equations in the heart and electrical diffusion in the rest of the body. These models are strongly coupled together and solved with finite elements. Some numerical results without and with a magnetic field are presented and discussed. Back to top The use of multivariate methods for the analysis of fMRI studies
of cognition In this talk I will discuss the motivation for why a scientist interested in the brain mechanisms underlying cognition would want to use multivariate methods for analyzing functional neuroimaging datasets. This will be followed by presentation of one particular multivariate method, Partial Least Squares (PLS), and some examples of how PLS can be used to answer questions about cognition. These will include descriptions of how we assess brain activity differences across cognitive tasks and groups (e.g., young vs. older adults), functional connectivity of specific brain regions, and relations between brain measures and behaviour. Back to top Universal Models for Targeted Image Segmentation Traditional image segmentation methods have the goal of localizing all objects which are present in an image. In contrast, many medical imaging applications of image segmentation seek to localize a particular object within an image. Unfortunately, the design of these targeted image segmentation algorithms is often very specific to the particular object and acquisition device, which requires a new algorithm design for each targeted segmentation application. I will discuss progress toward creating a universal segmentation algorithm that can successfully find any target object in any image when sufficient targeting information has been supplied. Back to top Multiscale patientspecific modeling of brain blood flow Realistic simulations of thrombus formation in intracranial aneurysms require resolution of the macro (centimeter) scale as well as the micro and submicron scale flow features. In this talk we will review some mathematical models and computational approaches we have developed over the last few years for multiscale blood flow simulations. We will also present new simulation results of platelets aggregation in a patientspecific model of intracranial aneurysm. The simulation has been carried out using patientspecific geometry and with high spatiotemporal resolution on 131, 074 processors of BlueGene/P supercomputer. To resolve the macro and micro scale flow features we have coupled two parallel codes: NEKTAR  a highorder spectral element parallel NavierStokes solver, and DPDLAMMPS – a coarsegrained molecular dynamics solver based on the dissipative particle dynamics method. Back to top Inverse Problems for multisource experiments Many parameter estimation problems involve with a parameterdependant PDEs with multiple right hand sides. The computational cost and memory requirements of such problems increases linearly with the number of right hand sides. For many applications this is the main bottleneck of the computation. In this work we show that problems with multiple right hand sides can be reformulated as stochastic optimization problems that are much cheaper to solve. We discuss the solution methodology and use the direct current resistivity as a model problem to show the effectiveness of our approach. Back to top An Algorithm's Journey Through Government, Academia, and Industry I will discuss the progression of a simple algorithm that has value in government, academia and industrial positions I have held or currently hold. I will focus on the metrics that define value in all three of these knowledgebuilding arenas. Back to top Inversion of the Attenuated Ray Transform We discuss some recent progress in obtaining closed form inversion formulae for the attenuated ray transform on nontrivial families of curves in 2dimensional space. Some novel formulae are discussed whose derivation rely on complexanalytic methods. This work arose initially from the nuclear medical diagnostic modality SPECT and arises in electrical impedance tomography. Back to top Some results on the attenuated ray transform We present some novel explicit filtered backprojection (FBP) type inversion formulae for the attenuated xray transform over curves in the twodimensional unit disc in cases of known transmission coefficient. The formulae we present involve complexification of the vector fields generating the photon transport in the medium. This tomographic problem is useful in the nuclear medical imaging modality SPECT and has also arisen in the problem of determining the interior permittivity and permeability parameters of a conductive body from external Maxwell measurements. Back to top Optimal design in medical inversion In the quest for improving inversion capabilities design, vast attention has been devoted to effective solution of the problem under various regularization configurations. Nevertheless, questions such as optimal configuration of data acquisition or more generally any other controllable parameters of the apparatus and process (e.g. regularization) were mostly overlooked. While design for wellposed problems has been extensively studied in the past years, very little consideration has been givento its illposed counterpart. This stands in contrast to the fact that many reallife problems we challenge are of such nature. In this talk we shall describe some of the intrinsic difficulties associated with design for illposed inverse problems, lay out a coherent formulation to address them and finally demonstrate the importance of design for medical imaging problems. Back to top Functional Imaging of Cancer Using ContrastEnhanced Ultrasound Contrast enhanced ultrasound imaging offers a unique method to quantify the microvascular haemodynamics of tissue and cancers. This is achieved by exploiting the ability of the contrast agent (microbubbles) to be disrupted and preferentially detected with contrast specific imaging techniques. The procedure, known as DisruptionReplenishment, uses a clinical ultrasound system to disrupt the freely flowing microbubbles within the imaging scan plane with a short burst of high intensity ultrasound. This creates a regional ‘void’ of tracer that will refill at a rate dependent upon the flow velocity, morphology, and blood volume of the feeding vasculature. In order to extract useful information from the timeintensity refill curves, we have developed a generalized model of replenishment that accounts for the details of the flow system under study (i.e. velocity distribution, fluid volume, vascular structure etc.) in addition to the influence of the ultrasound system used to make the measurement and its interaction with the circulating microbubble population. The model is used to generate parameterenhanced radiological images of the microcirculation from which a variety of quantitative statistics can be calculated and used to monitor cancer therapy. In relation to a clinical antiangiogenic trial for renal cell carcinoma, we have shown that microbubble dynamics can be used to selectively filter small vessel flow from large vessel flow in order to isolate the microvessels that might be preferentially targeted by antiangiogenic treatments. Back to top Electrical impedance tomography with two electrodes Electrical impedance tomography is a noninvasive imaging technique for recovering the conductivity distribution inside a body from boundary measurements of current and voltage. In this talk, we consider impedance tomography in the special case that the measurements are carried out with two electrodes that can be moved along the boundary of the (twodimensional) object of interest. Two different types of data are considered: The backscatter data is obtained by using a small probe consisting of two electrodes for driving currents and measuring voltage differences subsequently at various neighboring locations on the boundary of the object. The sweep data is gathered by fixing the location of one electrode and measuring the voltage difference required for maintaining a unit current as a function of the position of the other. A reconstruction algorithm for locating conductivity inhomogeneities in homogeneous background from such data sets is introduced and tested numerically. Back to top Confidence Regions and Means of Random Sets using Oriented Distance
Functions Image analysis frequently deals with shape estimation and image reconstruction. The objects of interest in these problems may be thought of as random sets, and one is interested in fi nding a representative, or expected, set. We consider a definition of set expectation using oriented distance functions and study the properties of the associated empirical set. Conditions are given such that the empirical average is consistent, and a method to calculate a confidence region for the expected set is introduced. The proposed methodology was motivated by the problem of skinboundary reconstruction in a mammogram image, and we illustrate our methods in this setting. Back to top Predicting Treatment Efficacy by Quantitative MRI via a Bayesian
Joint Model The prognosis for patients with highgrade gliomas is poor, with a median survival of one year. Treatment efficacy is typically assessed three to four months post therapy. However, our colleagues hypothesize that quantitative MRI can assess treatment efficacy three weeks after therapy starts, thereby allowing salvage treatments to begin earlier. The purpose of this work is to build a predictive model of treatment efficacy using qMRI data and to assess its performance. The outcome is oneyear survival status. We propose a joint, twostage Bayesian model. In stage I, we smooth the image data with a multivariate spatiotemporal pairwise difference prior. In stage II, summary statistics from stage I enter a generalized nonlinear model (GNLM) as predictors of survival status. We use the probit link and a multivariate adaptive regression spline basis. Through model performance comparisons we find that we are able to acheive higher overall correct classification rates by accounting for the spatiotemporal correlation in the images and by allowing for a more complex and flexible decision boundary provided by the GNLM. Back to top Rewards and Challenges in Adoption of Diagnostically Acceptable
Irreversible Compression As the increasing volume and size of medical images offsets the decreasing cost of storage, and as the implementation of regional Digital Images repositories allows access to exams region wide, there is a need for lossy compression to speed image transmission on limited bandwidth and save on storage costs. Compression ratios have been recommended for approved compression methods JPEG and JPEG2000 in National Standards but there are still quality issues to be solved to allow for large scale adoption and implementation of Diagnostically Acceptable Irreversible Compression. Back to top Detecting small changes in the brain with structural MRI While the investigation of anatomy in studies of brain development and neurological or neuropsychiatric disorders is older than the field of brain imaging itself, recent studies have shown that even subtle differences due to learning can be detected using modern imaging hardware and sophisticated image processing techniques. In this talk I will present methods on how to analyze structural imaging data for detecting subtle alterations in neuroanatomy, with a particular focus on registration based techniques. Applications to both human and mouse data as well as simulated results will be discussed. Back to top Mathematics of Cardiac Image Segmentation and Registration Major recent advances in the mathematics have led to great improvement in the automated cardiac segmentation and registration methods. Different real time and practical tools have been invented to handle the complexity in cardiac images especial in Magnetic Resonance Images. With the focus on the applied math and its application, a short review will be presented followed by an intensive discussion on the future development by leveraging the strength of advanced mathematics. Back to top System compression: theory and application Data in large quantity such as image or video data may be compressed to reduce its quantity for efficient storage and transmission. High efficiency lossy data compression is realized by locating and eliminating the redundancy, or say unessential elements, of the data set. Similarly, a linear system in large volume can be compressed through locating and eliminating its unessential elements  linear equations. The notion of system compression (SC) is related to compressed sensing (CS). One major difference between CS and SC is the requirement of randomness. CS paradigm emphasizes on randomness. Partial samples are randomly taken from the whole signal. As a result, the performance of reconstruction is random too. Reconstruction failures often occur. By contrast, in SC paradigm, partial samples are selectively taken from whole signal, in correspondence with the formation of system matrix, so that the matrix have certain desirable mathematical properties which may guarantee the stable success of signal reconstruction. Back to top Automated Analysis of Infarct Heterogeneity on Delayed Enhancement
Magnetic Resonance Images This presentation introduces an automated infarct heterogeneity
analysis method for cardiac delayed enhancement magnetic resonance
images(DEMRI). Delayed enhancement magnetic resonance imaging (DEMRI)
is an imaging method for identifying myocardial infarct (MI). Two
popular methods for determining the threshold values for the infarct
core and gray zones on IRGRE images have been proposed previously:
standard deviation(SD) method and fullwidth at halfmaximum (FWHM)
method. For both methods, three contours are necessary: epicardial,
endocardial and remote healthy myocardium region. Manual drawing
of these contours is time consuming and suffers from high interobserver
and intraobserver variability. Back to top Active B1 Imaging Using Polar Decomposition Method A novel way of measuring the radiofrequency B1 field is presented.
It uses an MRI based method called Polar Decomposition Radiofrequency
Current Density Imaging (PDRFCDI). Unlike the conventional B1 mapping
techniques that only measure the magnitude of B1, the proposed approach
also measures the phase of B1. Back to top Resistor networks and optimal grids for electrical impedance
tomography with partial boundary measurements We present methods to solve the partial data Electrical Impedance Tomography (EIT) problem numerically. Our methods regularize the problem by using sparse representations of the unknown conductivity on adaptive finite volume grids known as the optimal grids. The discretized problem is reduced to solving the discrete inverse problems for resistor networks. Two distinct approaches implementing this strategy are presented. The first approach uses the results for the full data EIT with circular resistor networks. The optimal grids for such networks are essentially one dimensional objects, which can be computed explicitly. We solve the partial data problem by reducing it to the full data case using the theory of extremal quasiconformal mappings. The second approach is based on pyramidal resistor networks. The optimal grids in this case are computed using the sensitivity analysis of both the continuum and the discrete EIT problems. Numerical results show two main advantages of our approaches compared to the traditional optimizationbased methods. First, the inversion based on resistor networks is much faster than any iterative algorithm. Second, we are able to reconstruct the conductivities of ultra high contrast, which usually presents a challenge to inversion methods. Back to top The biomedical photoacoustic radar imager: Principles, signaltonoise
ratio, contrast and resolution The talk will present the photoacoustic (PA) imaging (chirped) radar (or sonar) with respect to physical and instrumentation/signal generation and processing principles. A review of experimental and theoretical results obtained in our laboratory will demonstrate the instrumental capabilities for specific PA tissue imaging applications. Distinct features of the PA radar include excellent signaltonoise ratio and efficiently suppressed baselines compared to pulsed laser sources, underscoring the high potential of this technique for depthselective imaging of deep lying tissue chromophores. Our results demonstrate that submillimeter depthselective photoacoustic imaging can be achieved without nanosecond pulsed laser systems by appropriate modulation of a continuous laser source and a signal processing algorithm adapted to specific parameters of the photoacoustic response. Furthermore, imaging contrast will be compared with the pulsed laser method. The application of nonlinear frequency modulation instead of the standard linear frequency chirps was investigated and its effects on signal to noise ratio (SNR), contrast and image resolution will be discussed. In addition to the image produced by the amplitude of the crosscorrelation between input and detected signals, the phase of the correlation signal was used as a filter of the PA amplitude combined with linear or nonlinear frequency chirps. It was demonstrated that the phase signal can effectively filter the amplitude image and greatly improve its contrast. The experimental results with a highfrequency transducer exhibit more than 10 and 8 times contrast enhancement using nonlinear and linear chirps, respectively. Concomitant improvements in SNR and image resolution were also observed. Back to top Wall stress and flow dynamics in abdominal aortic aneurysms Abdominal aortic aneurysms (AAA) are characterized by the dilation of the aorta associated with degradation of the vessel wall. The natural history, in the absence of treatment, is the progressive enlargement of the aneurysm and eventually its rupture, an event that carries a very high mortality (up to 90%). In the clinical practice, physicians are faced with deciding between elective repair and conservative management of the disease without a reliable predictor of rupture risk. The most common threshold value used to recommend surgical repair is an AAA transverse diameter larger than 5.5 cm. However, smaller aneurysms can and do occasionally rupture. In recent years, several studies have used finite element models to investigate the biomechanical determinants of AAA rupture. Peak wall stress appears to be a major factor, in addition to the thickness of the wall, its stiffness and the thickness of the intraluminal thrombus. Finite element models are widely used to estimate the wall stresses in an aneurysm; however, there does not seem to be universal agreement on the simulation strategy to adopt; dry (without the presence of fluid), fluidonly as well as fluidstructure interaction approaches have been used. Moreover, the approaches differ significantly with respect to the boundary conditions applied. We tested different simulation strategies: dry static, dry dynamic, and fluidstructure interaction. For the boundary conditions, we considered fixed ends only, the presence of an external pressure that mimics the abdominal cavity and the direct structural representation of the organs surrounding the aorta. We report a comparison of the different simulation strategies and recommendations to develop a simulation strategy that best estimates the stresses in the aorta in the presence of an aneurysm. Back to top Viscoelastic models for tissue: Theoretical results for the
forward problem We consider viscoelastic models that have the property of finite propagation speed and frequency dependent wave speeds. We establish theoretical properties for these systems in 3D. We also discuss plane strain and plane stress approximating systems in 2D. Back to top Application of independent component analysis (ICA) to identify
and separate tumor arterial input function (AIF) in dynamic contrast
enhancedMRI Investigating image intensity change in each pixel in dynamic contrast enhanced (DCE)MRI data enables separation of its various tissue types based on their differences in contrast uptake. Pharmacokinetic (PK) modeling of tumor tissue is commonly used to extract physiological parameters (i.e. Ktrans and ve) from the concentrationtime curves of the contrast agent in different spaces. In a two compartmental PK model the concentrationtime curve of the feeding blood vessels or arterial input function (AIF) is required. This intravascular signal is inseparable from the signal from the extravascular extracellular space (EES) due to low resolution of the data and other imaging issues such as partial volume effect and intravoxel dephasing. Since direct measurement of these quantities is not possible in the tumor, some assumptions are made to approximate these concentration curves. Independent component analysis (ICA) has the potential to separate the AIF from the DCEMRI of the tumor. We have performed a validation study using tissue mimicking phantoms and invivo VX2 tumors in a rabbit model to assess the performance of ICA in separating tumor AIF. The results demonstrated the efficiency of the ICA in identifying and separating the tumor AIF in DCEMRI which may lead to more accurate measurement of PK parameters. Back to top Fast and accurate HARDI and its application to neurological
diagnosis The advent of diffusion MRI (dMRI) has led to the development of
qualitatively new methods of interrogating the white matter of the
brain. High angular resolution diffusion imaging (HARDI) constitutes
a particularly important instance of dMRI, which offers a more accurate
delineation of local diffusion patterns as compared to diffusion
tensor imaging, while having considerably milder acquisition requirements
as compared to the case of diffusion spectral imaging. Unfortunately,
the clinical value of HARDI still remains limited, mainly because
of the problem of prohibitively long acquisition times required
to complete HARDI scans. Moreover, as the acquisition of HARDI data
requires repetitive measurements from the same volume of interest
using a number of diffusionencoding gradients, the problem of acquisition
times is known to aggravate with an increase in their number. Back to top Conductivity imaging in the presence of perfectly conducting
and insulating inclusions from one interior measurement We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field J. We prove that the conductivity outside the inclusions, and the shape and position of the perfectly conducting and insulating inclusions are uniquely determined by the magnitude of the current generated by imposing a given boundary voltage. We also establish a connection between the above problem and the uniqueness of the minimizers of weighted least gradient problem F(u)=?Wa?u with u?W=f. Back to top Visualization and Quantification of Blood Flow in the Human
Aorta. From in vivo 4D Phase Contrast MRI to SubjectSpecific Computational
Hemodynamics The human aorta is the major vessel that transports blood pumped by the left ventricle to the systemic circulation. The complex hemodynamics that are observed in the human aorta partially originate in the complicated geometry. The other reason for the observed complexity is that the thoracic aorta is the site in the healthy cardiovascular system where laminarturbulent transitional flows are present. There is substantial evidence that aortic segments that appear to be exposed to abnormal flow are more prone to the onset and development of vascular pathology. In the past, the majority of the studies on the subject focused primarily on wall shear stress (WSS)based descriptors as quantitative indicators of disturbed flow. Only recently the interest in the role played by the bulk flow, in particular by the onset and decay of helical patterns in the pathophysiology of the human aorta has grown dramatically. This is the consequence of the emerging awareness that aortic hemodynamics, an intricate process that involves a continuous reorganization of bulk flow structures, could play a primary role in the optimization of fluid transport processes in the cardiovascular system, aimed at obtaining efficient perfusion, in the regulation/alteration of mass transfer and in being atheroprotective/susceptible. In the last decades, the PC MRI technique has become the prevalent imaging technique for noninvasive and detailed in vivo quantification of the aortic flow, allowing for the possibility of acquiring timedependent data sets that are necessary to perform reliable and local hemodynamic characterization. Due to its features, PC MRI has provided insight into the hemodynamics of the aorta in humans, where it has been used to illustrate clinical physiopathological findings. However, two main limitations arise from using PCMRI measurements to fully characterize the aortic flow. The first one is that 4D flow patterns may be overlooked if only visualization tools are used. All of the in vivo observations of aortic flow topologies associated with common physiological and pathological findings that are available in the literature are based on qualitative visual evaluation, and the mechanistic role that these emerging flow features play in aorta hemodynamics remains unclear. Aiming to overcome this limitation, we present the results of in
vivo helical flow quantification in ostensibly healthy human aortas,
performed employing 4D PCMRI. Our study is aimed at identifying
common characteristics in healthy aortic flow topology in terms
of its helical content. Technically, a method for helical flow quantification,
which has been developed to reveal the global organization of blood
flow, was applied to the datasets from healthy volunteers, making
use of tools developed for computational fluid dynamics. In particular,
we mapped the patterns of the transient flowin the human aortic
arch in detail and quantified helical structures. This quantitative
approach allowed us to rank the behavior of flowing blood and identify
emerging physiological bulk flow features. Moreover, here we also present our findings about e the influence of assumptions regarding the velocity profile at the inlet section of ascending aorta, incorporating the 4D PCMRI measured velocity profiles within the computational models. The final aim is to describe the impact of different strategies in combining measured BCs on WSS and, by identifying proper sets of BCs, eliminate a potential source of errors and uncertainties in blood flow simulations in human aortic arch. Back to top Imaging and Localizing Neural Sources from MEG Data Magnetoencephalography (MEG) measures the extremely weak quasistatic magnetic field outside the scalp generated by neural activity within the brain; electroencephalography (EEG) measures the scalp potentials from the same activity. The forward problem is the calculation of the external fields given an elemental source within the brain, for which the solution is analytic for spheres and more generally solved using numerical methods for tessellated shapes. Because the fields are nearly static, the forward models are specializations of the Newtonian potential measured from a distance, and therefore the inverse solution is ambiguous, without the imposition of strong models. In practice, the fields are measured at a few hundred sites about the upper hemisphere of the head, in the presence of substantial environmental and biological noise, and sampling rates and filtering protocols restrict the bandwidth to about 100 Hz, recorded on the order of ten minutes. Magnetic resonance images are used as anatomical basis sets on which to project most of the present day functional solutions. We review the basics of the acquisition systems and forward modeling, then focus on the inverse modeling approaches used to process these large spatiotemporal data matrices. Back to top Functional connectivity exploration with the Potts and random
cluster models Exploratory analysis based on clustering methods may elucidate
interconnectivity in brain responses associated to complex activation
paradigms such as epileptic seizures and drug studies. We have used
a method based on the Potts model clustering and the random cluster
model to find interconnected regions under the restingstate and
fingertapping paradigms. One key advantage of our method is its
ability to consider spatial constraints of the data through prior
graph edges. We are also exploring the use of the Potts model to
modulate the false discovery rate of active voxels. Potts model
clustering is a powerful kernelbased clustering method. We have
built on the work of Blatt, Wiseman and Domany (1996) who, borrowing
from known algorithms in physics, used Potts models as a general
tool for data clustering. One of the crucial steps in Potts model
clustering is the estimation of the temperature of the Potts density.
We present a Bayesian version of our model based on a prior for
the temperature derived from random graph theory. Back to top Determining a Flow Profile from MultiScale Phase Contrast Angiographic
MRI Data Magnetic Resonance Imaging (MRI) detects changes of magnetic spin of nuclei (mostly protons) through the application of external magnetic fields. Changes of spin depend foremost on the density of water, but also on the local chemical environment and the motion of the tissue. Phase Contrast Angiography (PCA) uses changes resulting from balanced spatially linear variations in magnetic field strength to produce variations in the angle of the magnetization proportional to the velocity. As the field variation increases, so too does the sensitivity of the data to changes in velocity, however higher variations cause the angle of the spinning protons to wrap around making it impossible to differentiate the signals of fast and slow spinning protons because of aliasing in the velocity dimension. When formulated as an objective function, we have to choose between a convex objective with a very shallow minimum (and resulting uncertainty in the presence of noisy data) or nonconvex objective with multiple narrow minima, effectively converting some of the uncertainty into discrete uncertainty resulting from the multiple minima. Conceptually, we propose to combine a series of data recruited from low and high field variation experiments, the lower field variation data can be used to guide the solver in detecting the true densities and velocities from the results of the high field variation data. Concretely, we will show how this information can be combined into a family of objectives which can be solved using a continuation approach. Additionally, a priori information about the properties of blood and its flow pattern is used to regularize the problem and further reduce the inaccuracies caused by noise. Back to top The Modelling of Biological Growth: a Pattern Theoretic Approach This presentation will take you for a journey from the beginnings of computational anatomy to mathematical representations of biological laws of growth. I will explore evolution and the power of mathematical ideas that allow biologically meaningful interpretation and understanding of images of natural shapes. More precisely, I will focus on a pattern theoretic model for a biological growth called GRID (Growth as Random Iterated Diffeomorphisms). It was first introduced by Dr. Ulf Grenander in 2005 in response to the need to study growth and development of human anatomy based on a sequence of images. The GRID model represents a modification of growth models employed in the field of computational anatomy, acknowledging that diffeomorphic transformations induced by growth are dependent on genetic controls within an organism. The genetic control is expressed by a probability law which governs spatialtemporal patterns of cell decisions (cell division/death, enlargement) in such a way that the image of an initial organism becomes continuously transformed into the image of a grown organism. I will then demonstrate the GRIDbased inference algorithm developed in my doctoral thesis that automatically estimates growth characteristics of an organism directly from image data. An example of larval growth of the Drosophila wind disc as seen in confocal micrographs of Wingless gene expression patterns will be considered. Overall, with implementation of the GRID model one can gain a new insight into the growthinduced shape generation process as controlled by the genes. Namely, one can reveal spatialtemporal patterns of intensity of cell divisions hidden deeper in given observations of growth. Back to top Numerical solution of inverse Helmholtz problems with interior
data We investigate numerically an inverse problem of the Helmholtz equation where the objective is to reconstruct both the refractive index and absorption coefficient from interior energy data. It is wellknown that one set of interior data is enough to reconstruct one of the coefficients. We show here numerically that with data collected from carefullychosen multiple set of illuminations, one can reconstruct both coefficients stably. Back to top Optimized modelbased undersampling and reconstruction for dynamic
MRI based on support splitting. Application to phase contrast MRI
carotid blood flow imaging. Traditional approaches to accelerated dynamic MRI (UNFOLD, kt
BLAST, PARADIGM) are based on kt lattice sampling. The underlying
signal model is that most pixels in the MRimage are (nearly) static
while only one or a few regions of interest (ROI) are dynamic. In
the yf domain (Fourier dual of the kt domain) this model is a
special case of sparse model insofar as y locations not corresponding
to the ROIs have zero content for nonzero f. When the kt lattice
sampling strategy is optimized for a particular yf support  estimated
e.g. using training data  high quality reconstructions can be
obtained. However, since kt lattice sampling corresponds to tiling
in the yf domain, the achievable acceleration factor is limited
by the packability of the support. Back to top Spectral Xray Imaging  Implications for Attenuation and Scatterbased
Tomography. Recent development of solidstate xray high resolution imaging arrays that provide xray photon count and discriminate photon energies are becoming available for microCT and likely for clinical CT in the near future. This has implications for reducing image noise down to the photon count level and for elimination of beam hardening artifacts. This also has potential for expanding the imaging repertoire by providing multienergy discrimination of various naturally occurring (e.g.,calcium, iodine, iron) and purposely introduced (e.g.,gadolinium, barium, gold) elements as well as increased contrast of soft tissues by virtue of coherent scatter imaging which can be achieved at one angle (instead of the usual range of angles) to the illuminating xray beam. This presentation will include some examples of these capabilities as well as the challenges presented by the detector characteristics and image processing involved. REFERENCES 1. Jakubek J. Semiconductor Pixel detectors and their applications in life sciences. Journal of Instrumentation 2009;4: 118. DOI: 10.1088/17480221/4/03/P03013. 2. Roessl E, Proksa R. Kedge imaging in xray computed tomography using multibin photon counting detectors. Physics in Medicine and Biology 2007;52(15):46794696. 3. Frey EC, Wang X, Du Y, Taguchi K, Xu J, Tsui BMQW. Investigation of the use of photon counting xray detectors with energy discrimination for material decomposition in microcomputed tomography. Medical Imaging 2007: Physics of Med Imaging. Proc of SPIE 2007;65100:65100A1—65100A11. 4. Butzer JS, Butler APH, Bones BJ, Cook N, L Tlustos L. Medipix Imaging – Evaluation of data sets with PCA. IEEE 2008;9781424425822/08. 5. Butler APH, Anderson NG, Tipples R, Cook N, Watts R, Meyer J, Bell AJ, Melzer TR, Butler PH. Biomedical Xray imaging with spectroscopic pixel detectors. Nucl Instr and Methods in Physics Res A. 2008;591(1):141146. 6. Eaker DR, Jorgensen SM, Butler APH, Ritman EL. Tomographic imaging of coherent xray scatter momentum transfer distribution using spectral xray detection and polycapillary optic.Proc. SPIE, Developments in Xray Tomography VII 7804:78041O1—78041O7, 2010. Back to top Identifying brain networks of coherent oscillations with MEG Applying beamformer source analysis to the neuromagnetic signal recorded with magnetoencephalography (MEG) results in a four dimensional data set of brain activity in space and time. MEG has highest resolution in the time domain and the signal can be described by time series of activities at a set of discrete sources within the brain volume. Synchrony between oscillations at different brain areas, measured as coherence, has been suggested as a mechanism of connectivity within wide range networks. However, corticocortical coherence is compromised by the limited spatial resolution of the source analysis. This presentation introduces first a method for separating eventrelated coherence from apparent coherence resulting from spatial filtering and second a test for signal detection based on circular statistics. The principle of the method is demonstrated with MonteCarlo simulations, and the detection of event related coherence is applied to human MEG data. In healthy young participants, listening to rhythmic auditory stimuli during MEG recording, we identified a brain network involving auditory and sensorimotor areas. The interpretation is that synchronous beta oscillations play a role in auditorymotor integration, facilitating auditory cued rhythmic movements. Back to top Imaging conductivity changes deep in the brain Many existing techniques for imaging brain function or processes are restricted to imaging surface or peripheral changes. We have recently proposed and tested methods for imaging conductivity changes as a result of activity. We have found that these techniques are robust and feasible for imaging deep changes. In this talk I will give examples of applications and approaches we have used thus far, and outline strategies for future improvements. Back to top A Novel Iterative Thresholding Algorithm for Compressed Sensing
Reconstruction of Quantitative MRI Parameters from Insufficient
Data Quantification of MR parameters using analytical models of MRI signal often offers a unique and important perspective onto tissue micro environment compared to the traditional visualization of human anatomy by MRI. Examples of quantitative MRI (qMRI) techniques are T1 and T2 relaxometry and methods based on diffusion weighting contrast. The estimation of qMRI parameters requires acquisition of multiple datasets at different values of pulse sequence parameters (control parameters). As a result, quantitative MRI typically incurs a severalfold increase in scan time compared with conventional imaging. Quantitative MRI offers an additional, parametric, dimension, similar to time variable in dynamic imaging. The standard twostep qMRI procedure reconstructs images for each value of the control parameter separately and then fits them to a model equation. Such an approach fails to exploit dependencies between images in the parametric dimension which are implied by the underlying physical model, hence, it does not utilize fully the power of a priori knowledge. Several methods making use of the physical model and resulting interimage dependencies in the parametric dimension were proposed so far to accelerate quantitative measurements. Unfortunately, many of them lack robustness in practical imaging situations where imaging artifacts and deviation from anticipated analytical model may be significant. We propose a novel algorithm that utilizes knowledge of physical signal model within compressed sensing framework for robust accelerated quantitative MRI. The algorithm was demonstrated with T2/T1 relaxometry data and provided significant imaging acceleration. Back to top Computational tools for microwave imaging – some finite
element aspects High contrast in electrical permittivity and conductivity motivates
the investigation of electromagnetic methods for medical imaging,
for instance for breast cancer detection. A straightforward approach
to modelling the spatial distribution of these parameters is the
assumption of piecewise constant values, defined on a moderately
fine tessellation of the volume under investigation by hexahedra
or tetrahedra. We study here the solution of the 3D forward problem
for monofrequency microwave tomography using finite elements, based
on the above mentioned tessellation. Furthermore, we seek to reconstruct
the spatial distribution of permittivity and conductivity of an
overparameterized model by a regularised output least squares approach.
Our model assumption, piecewise constant coefficients, allows for
simplifications of the forward solver which eventually lead to an
overall faster imaging algorithm. The model assumption also requires
special care when the regularisation operator is derived for unstructured
meshes within the finite element framework. The Physical Basis of RF Electrical Properties Contrast Imaging
by MRI MRI is unique in its ability to quantify and map RF magnetic fields in vivo at the Larmor frequency, but the simplified signal equation is a product of left(LCP) and right(RCP) circularly polarized RF magnetic field terms. The possibility of creating contrast from the radio frequency electrical properties of tissue by MRI was first proposed and demonstrated almost two decades ago. In recent years, the focus has turned to creating quantitative images of RF conductivity and permittivity of tissue using a variety of approximations, and even an estimation of the RF power. To recover these properties, the Helmholtz equation is analyzed
in terms of LCP and RCP terms, but MRI RF field mapping can only
map a transmit field (LCP) relative to an implicit receive (RCP)
field. To estimate vector field components, the zero divergence
of magnetic fields must be used, and approximations for a dominant
Bo directed RF electric field/current density may be needed based
on RF coil/antenna geometry. Simplified pulse sequences that use
only phase information for conductivity, or amplitude information
for permittivity become possible when certain expanded Helmholtz
terms can be neglected. Finally, most field analysis uses spatial
derivative operations, but it is also possible to build in the field
equations using a simplified form of the Kottler integral equations.
This presentation will provide an overview of these approximations
and future directions for reconstruction and contrast generation
of RF electrical properties by MRI. Inverse Problems in Medical Imaging: Electrical Property Imaging
using MRI Last two decades, much researches in biomedical imaging area deal with electromagnetic or mechanical property imaging instead of anatomical imaging since they manifest structural and pathological conditions of the tissue providing valuable diagnostic information. The corresponding objectives are in visualizing crosssectional image reconstructions of admittivity, susceptibility, shear modulus distributions inside the human body. This talk focuses on electrical property imaging modalities which require interdisciplinary research incorporating mathematical theories, inverse problems and image reconstruction algorithms, image processing (denoising, segmentation, compressed sensing), numerical analysis and error estimates, MR physics and experimental techniques.To achieve these objectives, we need to set up a mathematical framework using the constitutive relation, related physical principles, and available measurement techniques, and it must be taken into account the wellposedness and uncertainties in boundary conditions and material characterizations. It is often necessary to make various simplifications of reality with sacrificing physical details so that the simplified model is manageable and holds key information to be aimed. In this talk, we briefly discuss these issues from its mathematical framework to human experiments via error analysis. Back to top Transport studies of patient specific hemodynamics: Methods
of modeling and characterization This talk will focus on the study of advectionrelated processes in cardiovascular flow. It is widely accepted that local blood flow conditions can greatly influence the development and progression of many vascular diseases. Furthermore, proper diagnosis of flow conditions can be essential in properly assessing vascular disease progression, or evaluating different treatment options. Major obstacles in this area of research include being able to obtain realistic and relevant blood flow information (modeling), and being able to comprehend the complex, transportrelated processes at work (characterization). We will discuss a framework that notably combines a dynamical systems approach to studying transport, with computational fluid dynamics and medical imaging, to obtain unique insights into blood transport problems. This framework takes a unique perspective to understanding blood flow, by shifting the paradigm from a “shearcentric” view of hemodynamics to a more complete appreciation and understanding of the biomechanical aspects of blood flow, while providing the tools needed to make such understandings possible. Back to top Advancements in Radiation Therapy Treatment Planning and Optimization Cancer is a leading cause of disability and mortality affecting
the lives of many Canadians. Ionizing radiation is a potent therapeutic
agent and its role in treating cancer was established and applied
almost immediately after the discovery of xrays. Radiation therapy
has been an important option in the control of cancer for over one
hundred years. Every so often, advancements in engineering, computation,
medical imaging, treatment planning, and control theory have converged
to change how we view radiation therapy. From technological shifts,
important concepts have emerged, including intensitymodulation,
and imageguidance. Contemporary radiation therapy strategies build
on these concepts, and now are applied within an extensive framework
of machines and computing resources supporting teamwork among staff
highly trained in a number of medical and technical specialties. Back to top Growth Dynamics in the Mouse The mouse as a model organism provides tremendous opportunities for learning the functions of genes and for constructing complex models of human diseases. Morphology, as revealed by 3D imaging, has proven particularly sensitive for dectecting abnomal phenotypes caused by genetic mutations in inbred mice and therefore provides a means to infer gene function. However, the interpretation of these data can be complex as phenotypic differences manifest as perturbations to the normal developmental trajectory. Moreover, the resolution limitations of current in vivo imaging technologies motivate one to infer populationbased growth dynamics from crosssectional rather than longitudinal data. In this presentation, we examine computational approaches to infer growth dynamics in the embryonic and immature mouse as well as in the microcirculation of the murine placenta. Back to top Moving the best ideas from 1985’s constrained reconstruction
techniques into 2011’s compressed sensing reconstruction With the recent availability of efficient algorithms for nonlinear optimizations, there has been an explosion of interest in applying compressive sensing (CS) techniques in various engineering applications. A key concept behind MR compressed sensing is the gathering of reduced kspace data sets. This concept can be traced back to superresolution reconstruction (SR) algorithms of 1985 which were an attempt to improve upon the even earlier techniques of partial Fourier transform reconstruction. In this paper, we demonstrate how many successful processes and validation technique from superresolution can be adapted to compressed sensing reconstruction to considerable advantage. We examine (i) the importance of ensuring that the simulated data used to validate and tune CS algorithms matches the characteristics of experimental data and (ii) techniques to improve the appearance of CS images used for diagnostic purposes. We propose the adaption of two existing SR techniques for use in CS reconstruction (iii) by using a kspace approach to generating a sparser data set by modeling the edges of the data rather the data itself, and (iv) combining the TERA SR algorithm with CS’s sparse sampling regime to remove issues surrounding the truncation of kspace data. Back to top In vivo imaging of cerebral hemodynamics with two photon fluorescence
microscopy The present talk will discuss our recent work on the assessment of stimulation induced changes in the brain microvascular network in vivo. We employ time series two photon laser scanning microscopy data of the microvessels in the primary somatosensory cortex of anesthetized rodents during electrical stimulation of the forepaw. A semiautomated, multiscale, model based algorithm is employed for segmentation of the intravascular space over time, followed by generalized linear modeling to evaluate the spatiotemporal pattern of changes in vessels calibers elicited in this vascular bed by the functional stimulus. We observe a highly heterogeneous changes in the capillaries, with the preponderance of dilatations occurring on the level of cortical penetrating vessels. Consistent with mesoscopic modalities, net response is that of dilatation, with peak radii changes of 5into neurovascular network reactivity. Back to top Advanced Signal Processing for NonInvasive Medical Diagnostic
System Applications Introduction: The material of this presentation emerged from the
author’s most recent investigations in implementing defense
oriented research from sonar and radar system applications into
noninvasive medical diagnostic R&D to address difficult diagnostic
problems and delivery of health care in very remote areas. Thus,
this material bring together some of the most recent theoretical
developments on advanced signal processing; in order to provide
a glimpse on how modern technology can be applied to the development
of current and next generation real time medical diagnostic systems.
The first part will focus on advances in digital signal processing
algorithms and on their implementation in PCbased computing architectures
that can provide the ability to produce real time systems that have
capabilities far exceeding those of a few years ago. It included
also a generic concept for implementing successfully adaptive schemes
with nearinstantaneous convergence in 2dimensional (2D) and 3dimensional
(3D) array of sensors, such as planar, circular, cylindrical and
spherical arrays of sensors. The second part focuses on the emerging
medical technologies in the areas of noninvasive tomography imaging,
monitoring vital signs and addresses topics on recent advances on
image segmentation, registration and fusion techniques for 3D/4D
ultrasound and other tomography imaging modalities. 1) a 32x32 sensor planar array ultrasound probe with a fully digital data acquisition peripheral; 2) a portable ultrasound computing architecture consisting of a cluster of DSPs and CPUs; 3) adaptive 3D beamforming algorithms with volumetric visualization, including fusion and automated segmentation capabilities; and 4) the implementation of a decisionsupport process to provide
automated diagnostic capabilities for noninvasively detecting internal
injuries and facilitate image guided surgery. Back to top A Novel Method for Motion Correction in Cardiac MRI Highquality magnetic resonance images (MRI) typically require
data acquisitions lasting anywhere from several seconds to several
minutes. Over this time period, significant physiologic motion may
occur. In cardiac imaging, motion is caused by both the beating
of the heart, as well as respiration. As a result of this motion,
the heart will be in different positions at different times in the
scan. This will cause inconsistencies in the data; giving rise to
errors in the images reconstructed from this data. Back to top FrequencyDomain Photoacoustics: Specifics of Signal Processing
and Image Reconstruction It was demonstrated that spatiallyresolved photoacoustic (PA) imaging can be accomplished using relatively long intensitymodulated laser excitation as opposed to shortpulse imaging mode. Although this method is very attractive for design of portable clinical instrumentation, it requires different approach to signal detection and image reconstruction. This presentation discusses problems of the frequencydomain PA technique and possible solutions pertinent to spatiallyresolved imaging of optical contrast in biological tissues. Back to top Uncertainty quantification in resistor network inversion We present a method for finding the electrical conductivity in a domain from electrical measurements at the boundary. Our method consists of two steps. In the first step we find a resistor network that fits the data and then we estimate the conductivity from the resistors by interpreting the network as a finite volumes discretization of the problem. We show through a Monte Carlo study that our discretization of the conductivity reduces the uncertainty in the reconstructions, as compared to a conventional discretization. We review recent developments on extensions of resistor network inversion to other setups in two dimensions. Back to top The clinical and basic significance of studying fluctuations
of brain coordinated activity Experimental evidence and considerations about the basic and clinical implications of the study of the variability in brain signals will be presented. More specifically, most of the presentation will centre on the possible usefulness of the quantification of spatiotemporal variability of the brain synchronization patterns in patient prognosis after traumatic brain injury, in finding precursors of seizures in epileptiform activity, and in classifying (diagnosing?) subjects with autism. Some general considerations of more theoretical nature will be discussed, specifically related to the upper or lower bounds to the variability in nervous system activity for the individual to be adaptable and viable, and the relation to pathologies. Back to top Application of Temporally Constrained Compressed Sensing for
High Spatial and Temporal Resolution Magnetic Resonance Imaging Many clinical applications necessitate a limited scan time for dynamic MRI acquisition, e.g. due to breath hold or contrast passage. This often restricts attainable spatial and temporal resolution, limiting potential diagnostic or research applications. To reconstruct significantly undersampled time frames at clinically desired spatial/temporal resolution a number of approaches have been proposed, including compressed sensing (CS). CS reconstruction from incomplete data relies on the assumption that the underlying signal has a sparse representation in some basis. Typically, CS utilizes spatial sparsity of the image itself or its discrete gradient. However, in timeresolved imaging, the level of spatial sparsity may not be sufficient to support the required high accelerations, leading to residual artifacts and loss of spatial resolution. We will discuss a way to use spatiotemporal correlations in the image series as a means to achieve high accelerations without loss of spatial resolution / SNR and without compromising waveform fidelity. We evaluate the performance of the proposed temporally constrained compressed sensing approach in such clinical applications as contrastenhanced intracranial angiography and cardiac perfusion imaging. Back to top An Integrated Morphology+CFD Statistical Investigation of Parent
Vessel in Cerebral Aneurysms It is widely accepted that hemodynamics plays a relevant role in initiation, progression and eventually rupture of brain aneurysms.Several works actually point out how the geometry and consequently the blood flow in the aneurysm are related to the evolution of this pathology. However, the underlying mechanism need still to be identified and explained. The accomplishment of this task is anticipated to detect possible morphological indexes to be used for a prognostic purpose. Geometrical landmarks could support the decision making of doctors that need to decide whether it is convenient to operate or not. In this talk we give a contribution in this direction with two distinctive features, one refers to the specific subject of our investigation, the other one to the data analysis methods adopted. 1) The focus of our study is on the geometry of the vessel hosting
the aneurysm rather than on the sac itself. With "data" here we mean both geometry and fluid dynamics.
In particular, under the category of geometrical features we consider
different quantities of the parent vessels (e.g. radius, curvature,
tortuosity); hemodynamical quantities are in particular the Wall
Shear Stress (WSS) along the parent vessel and its axial gradient.
These quantities are regarded as stochastic functions of the axial
coordinate along the vessel. To extract patterns from such a heterogeneous
aggregate of informations we resorted to an advanced statistical
technique, the Functional Principal Component Analysis (FPCA). This
method allows to identify the part of the data set relevant for
our purpose, which is the correlation to the rupture. In this talk I will address these steps and present results obtained following this approach on a data set (52 patients) collected at the Hospital Ca' Granda, Niguarda in Milan (Italy), whithin the collaborative framework called ANEURISK, granted by the Politecnico di Milano Foundation with the support of SIEMENS Medical Solutions, Italy. The results identify possible landmarks for the assessment of a rupture risk index.This research is partially supported by The Brain Aneurysm Foundation in the framework of the project "Computational and Statistical Analysis of Brain Aneurysm Morphology&Hemodynamics". Back to top 4D ImageBased CFD Simulation of a Compliant Blood Vessel Numerical simulation of fluidstructure interaction (FSI) in the
arterial system is a challenging and time consuming procedure because
of the intrinsic heterogeneous nature of the problem. Moreover,
in patientspecific simulations, modeling of the vascular structure
requires parameter identification still difficult to accomplish.
On the other hand, new imaging devices provide time sequences of
the moving vessel of interest. When one is interested only in the
blood dynamics in the compliant vessel, a possible alternative to
the full fluidstructure interaction simulation is to track the
vessel displacement from the images and then to solve the fluid
problem in the moving domain reconstructed accordingly. We present
an example of this imagebased technique. We describe the steps
necessary for this approach (image acquisition and 3D geometric
reconstruction, motion tracking, computational fluid dynamics (CFD)
simulation) and present some results referring to an aortic arch
and a validation of the proposed technique vs. a traditional FSI
simulation in a carotid bifurcation. Back to top Sparse Sampling of Velocity MRI The standard MRI is being used to image objects at rest. In addition to standard MRI images, which measure tissues at rest, Phase Contrast MRI can be used to quantify the motion of blood and tissue in the human body. The current method used in Phase Contrast MRI is time consuming. The development of new trajectories has minimized imaging time, but creates subsampling errors. The proposed method uses regularization of velocities and proton densities to eliminate errors arising from kspace undersampling. Back to top Analyzing Diffusion MRI Based "Connectivity" for Diagnosis The talk will present a brief overview of diffusion imaging (tensor and higher order models). It will cover various issues involved in analyzing diffusion data with the aim of conducting large population studies as well as creating markers of "connectivity" from the population that best characterize the pathology. The talk will briefly discuss statistical and machine learning methods employed in such studies. Back to top From imaging and hemodynamic data to patientspecific simulations
of Glenn to Fontan conversion Singleventricle defects are a class of congenital heart diseases that leave the child with only one operational pump, requiring the systemic and the pulmonary circulations to be placed in series through several operations performed during young childhood. The last procedure (the Fontan palliation) artificially connects both venae cavae to the pulmonary arteries, which improves oxygeneration of the child at the cost of blood flowing passively into the lungs. Numerical simulations may be used to investigate the nature of the flow and its connection to postoperative failures and sources of morbidity. However they heavily rely on boundary condition prescrip tion. We present our recent work on predictive patientspecific modeling of the Fontan conversion. Patientspecific preoperative models are developed based on clinical data. Results include a sensitivity analysis of several hemodynamics factors to the input data. In addition, previous studies have demonstrated that the geometry plays an important role in Fontan hemodynamics. A novel Yshaped design was recently proposed to improve upon traditional designs, and results showed promising hemodynamics. In this study, we show how geometry and boundary conditions affect the performance of these virtual surgical designs. In particular, we investigate if and how the inferior vena cava flow (which contains an important biological factor) can be optimally distributed amoung both lungs. We also present an outlook on how multiscale simulations can be predictive. Numerical issues related to patientspecific simulations will be briefly discussed. Back to top Radio Frequency Current Density Imaging with a 180Degree Sample
Rotation Biological tissues are generally conductive and knowing the current distribution in these tissues is of great importance in theoretical and practical biomedical applications. Based on magnetic resonance imaging (MRI), radio frequency current density imaging (RFCDI) measures current density distributions at the Larmor frequency of the magnetic resonance (MR) imager. RFCDI computes the applied Larmor frequency current density, J, from the noninvasively measured magnetic field, H, produced by J. However, the previous method for RF current density reconstruction could only compute one component of J. Moreover, this reconstruction required an assumption about H, which may be easily violated in biomedical applications. We propose a new reconstruction method for RFCDI to fully reconstruct all three components of J without relying on any assumption of H. The central idea of our approach is to rotate the sample by 180 degrees in the horizontal plane to collect adequate MR data to compute one component of J. Furthermore, this approach can be extended to reconstruct the other two components of J by one additional sample orientation in the horizontal plane. Using simulations and experiments, we have demonstrated for the first time the feasibility of imaging the magnitude and phase of all components of a radio frequency current density vector field. In addition, the reconstruction of the complex conductivity of biological tissues becomes possible due to measurement of the complete H vector field. Back to top fMRI Signal Processing Methods for Brain Connectivity Modeling There have been revolutions in neuroimaging technologies that can noninvasively probe the brain at different temporal and spatial scales, such as functional MRI (fMRI) and electroencephalogram (EEG). With the recent revolution in fMRI neuroimaging techniques, there is greater recognition of the vital role signal processing techniques can play for modeling brain connectivity. While there has been significant progress, there are still a number of challenges associated with inferring brain connectivity from fMRI signals that require special exploration. In this talk, we focus on developing novel, fundamental signal processing and graphical models for accurately inferring brain connectivity from fMRI data by addressing key challenges, including sparsity, error control in learning network structures and group analysis to deal with intersubject variability. A real fMRI case study in Parkinson's disease suggests that the proposed brain connectivity modeling approach demonstrated relative normalization of brain connectivity due to Ldopa medication. Back to top A SemiDefinite, Nonlinear Model for Optimizing kSpace Sample
Separation in Parallel Magnetic Resonance Imaging Parallel MRI, in which Fourier (kSpace) is regularly undersampled, is critical for imaging speed. In our approach, a semidefinite model is built to optimize the pattern of regular data sampling to minimize noise in the reconstructed image. To solve the model, a bilevel strategy is applied. Back to top Ultrasound methods to image the electrical/electrokinetic properties
of biomaterials We propose a novel method to combine ultrasound and electromagnetic waves to image and characterize tissues by further investigating a new effect: the physiologicallevel Electricfield Induced Mechanical Changes (EIMC) in soft tissues (Doganay and Xu, JASAEL V128, P261267, 2010). We found that the application of a DC or a lowfrequency AC electric field (at physiologically safe levels) to various types of soft biological tissues can induce mechanical changes, including strain and deformation, in the samples. We have also shown that the EIMC can be monitored by commercial ultrasound instruments. Our preliminary results have suggested that EIMC is an electrokinetic phenomenon (motion of particles and fluids under the influence of an electric field) and is related to the fixed charge density in the sample. Although electrokinetic phenomena have been widely studied in solutions, gelatin, cell cultures, and some special tissues such as cartilage (due to the large fixed charge density in these tissues’ extracellular matrix), it is the first time that the electrokinetic phenomena have been observed and imaged both from the inside and at the surface of various soft tissues. EIMC depends on the chemical composition and conductivity of the samples. Therefore, EIMCbased imaging methods have the potential to measure the electric/electrokinetic properties of biological tissues noninvasively. Back to top Compressive MUSIC for diffuse optical tomography using joint
sparsity Diffuse optical tomography (DOT) is a sensitive and relatively lowcost imaging modality that reconstructs optical properties of a highly scattering medium. However, due to the diffusive nature of light propagation, the problem is severely illconditioned and highly nonlinear. Even though nonlinear iterative methods have been commonly used, they are computationally expensive especially for three dimensional imaging geometry. Recently, compressed sensing theory has provided a systematic understanding of high resolution reconstruction of sparse objects in many imaging problems; hence, the goal of this paper is to extend the theory to the diffuse optical tomography problem. The main contributions of this paper are to formulate the imaging problem as a joint sparse recovery problem in a compressive sensing framework and to propose a novel noniterative and exact inversion algorithm that achieves the l0 optimality as the rank of measurement increases to the unknown sparsity level. The algorithm is based on the recently discovered generalized MUSIC criterion, which exploits the advantages of both compressive sensing and array signal processing. A theoretical criterion for optimizing the imaging geometry is provided, and simulation results confirm that the new algorithm outperforms the existing algorithms and reliably reconstructs the optical inhomogeneities when we assume that the optical background is known to a reasonable accuracy. Back to top A RegistrationBased Atlas Propagation Framework for Automatic
Whole Heart Segmentation Extracting anatomical information of the heart can be important for the development of new clinical application, as well as the planning and guidance of cardiac interventional procedures. To avoid inter and intraobserver variability of manual delineation, it is highly desirable to develop an automatic segmentation method such as from cardiac MRI. However, automating this process is complicated, particularly by the large shape variation of the heart between subjects. To achieve this goal, we employ a registrationbased atlas propagation framework where a novel technique, locally affine registration method, is proposed to tackle the challenge of large shape variations. Locally affine registration method (LARM) is an attractive registration alternative for applications where a single global affine transformation cannot provide enough accuracy, while a nonrigid registration would incorrectly affect the local topology, such as due to the large shape variability of the heart anatomy. In the automatic whole heart segmentation framework, LARM globally deforms the heart image but locally maintains the shape of the predefined substructures, such as the four chambers and the major vessels. Such an approach is able to avoid local optima during the optimization of the global transformation and eventually provides a good initialization of substructures for the followup nonrigid registration to achieve an accurate and robust refinement. The talk will also show a validation study where 37 pathological MR data were used and some extension works. Back to main index 
