April 24, 2014




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

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

Research Posters
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1. N. Tabatabaei, A. Mandelis,
Thermophotonic Radar Imaging of Turbid Media

2. Pradeep Kumar Raamana, Mirza Faisal Beg,
A Comprehensive Study of Differential Diagnosis among Alzheimer's Disease, Frontotemporal Disease and Healthy Aging

3. Evgeniy Lebed, Mei Young, Yifan Jian, Paul J. Mackenzie, Marinko V. Sarunic, Mirza Faisal Beg
Real time Compressive Sampling based FDOCT image acquisition and registration

Research Posters

  • Alex Martinez
    Simulation of Magnetic Resonance Imaging using Oscillatory Quadrature Methods
  • Evgeniy Lebed, Mei Young, Yifan Jian, Paul J. Mackenzie, Marinko V. Sarunic, Mirza Faisal Beg
    Real time Compressive Sampling based FDOCT image acquisition and registration

    Simulation of Magnetic Resonance Imaging using Oscillatory Quadratures Methods
    Alex Martinez
    University of Toronto

    Coauthors: Luca Antiga (Orobix Srl and Mario Negri Institute), David Steinman (University of Toronto)

    Magnetic resonance imaging (MRI) has become one of the leading modalities for non-invasive anatomical imaging. However, there are many independent parameters that control an MRI scan and many physical phenomena that affect the quality and accuracy of the acquired image. Studying the causes and effects of these phenomena is difficult, because MRI facility availability is scarce and operating time is costly. Computational simulation is MRI has become an attractive alternative, but can suffer from extensive simulation times. Moreover simulations are usually based on structured, Cartesian grids, which must be very dense in order to adequately resolve anatomically realistic objects.

    An alternative approach has been suggested in which the MRI signal equation, which represents the volumetric integration of a magnetized object modulated by a sinusoidally varying field, can be solved exactly over objects defined by an unstructured grid of linear tetrahedral elements [1]. If an object can be segmented into regions over which each a constant magnetization can be assumed, the signal for these regions can be converted, via the divergence theorem, into the result of a surface integration over linear triangles [2]. In either case, however, the number of simplexes, and hence the CPU time, required to resolve the curved boundaries of realistic objects, can be prohibitive.

    The present work focuses on the use of quadratic triangulations, which have been shown to offer significant reductions in the number of simplexes required to discretize complex objects [3], but which require numerical rather than exact integration of the signal equation. Due to the oscillatory terms in the signal equation, conventional Gaussian quadratures can be costly, as the number of points needed in each dimension is proportional to the maximum spatial frequency in the simulation. Instead, we consider here the novel use of highly oscillatory quadratures, for which the number of integration points decreases with increasing frequency. Specifically, in the numerical steepest descent (NSD) approach [4], the path between the integration limits is deformed using the method of stationary phase, but instead of trying to find an asymptotic estimate of the integral afterwards, the new integral is evaluated using Gaussian quadrature. This method can then be applied recursively for integrals of n dimensions.

    For a given number of integration points the NSD approach can be expected to yield lower errors compared to Gaussian quadrature. However, preliminary estimates suggest that each NSD quadrature point require 3-4 times the number of operations compared Gaussian quadrature. Moreover, NSD requires special handling for some combinations of simplex and spatial frequency orientations [4]. We intend to demonstrate whether the perceived benefits of oscillatory vs. conventional quadratures for simulating MRI are outweighed by these extra computational costs.


    Truscott KJ and Buonocore MH. Simulation of tagged MR images with linear tetrahedral solid elements. J Magn Reson Imaging 2001;14:336-340.

    Antiga L and Steinman DA. Efficient MRI simulation via integration of the signal equation over triangulated surfaces. Proc Int Soc Magn Reson Med 2008;16:489.

    Simedrea P, Antiga L, Steinman DA. FE-MRI: Simulation of MRI using arbitrary finite elements. Proc Int Soc Magn Reson Med 2006:14:2946.

    Huybrechs D and Vandewalle S. The construction of cubature rules for multivariate highly oscillatory integrals. Math Comp 2007; 76:1955
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    A Polyenergetic Iterative Reconstruction Framework for X-Ray Computerized Tomography
    Nargol Rezvani

    Department of Computer Science, University of Toronto
    Coauthors: D. A. Aruliah, Kenneth R. Jackson

    While most modern x-ray CT scanners rely on the well-known filtered back-projection (FBP) algorithm, the corresponding reconstructions can be corrupted by beam-hardening artifacts. These artifacts arise from the unrealistic physical assumption of monoenergetic x-ray beams. To compensate, we discretize an alternative model directly that accounts for differential absorption of polyenergetic x-ray photons. We present numerical reconstructions based on the associated nonlinear discrete formulation incorporating various iterative optimization frameworks.

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    Experimental framework to parameterize 3D MR image-based computer models of electrophysiology in heterogeneous infarcted porcine hearts
    Mihaela Pop
    Sunnybrook Research Institute, Toronto

    Coauthors: Maxime Sermesant (INRIA, France) Tommaso Mansi (Siemens Corporate Research, Princeton, USA) Sudip Ghate (Sunnybrook Research Institute, Toronto) Jean-Marc Peyrat (Siemens Molecular Imaging, Oxford, UK) Jen Berry (Sunnybrook Research Institute, Toronto) Beiping Qiang (Sunnybrook Research Institute, Toronto) Elliot McVeigh (Johns Hopkins University, USA) Eugene Crystal (Sunnybrook Research Institute, Toronto) Graham Wright (Sunnybrook Research Institute, Toronto)

    Mathematical modelling, high-resolution imaging and electrophysiology experiments are needed to better understand how tissue heterogeneities contribute to the genesis of arrhythmia in hearts with prior infarction (a major cause of sudden cardiac death). The purpose of this work was to globally parameterize a 3D magnetic resonance MR image-based computer model of electrophysiology (EP) constructed using a pre-clinical pig model of chronic infarct. The computer heart model was built from high-resolution ex-vivo 3D MRI scans. Diffusion weighted MRI was used to estimate myocardial anisotropy (i.e., fiber directions) and heterogeneities (healthy zone, dense scar and border zone, BZ). We used a simple mathematical model based on reaction-diffusion equations, and calculated the propagation of action potential (AP) after application of stimuli (with location and timing replicating precisely the stimulation protocol used in the experiment). Specifically, the mathematical parameters were globally fit by zone (i.e., the three zones derived from heterogeneous MRI maps); this step was performed using characteristics of AP waves measured ex-vivo (using 2D optical fluorescence imaging). Then, these fitted parameters were further used as input to the 3D computer model to replicate in-vivo EP studies, under pacing or arrhythmia induction. Our results showed a better agreement between experiments and simulations, when these customized parameters were used instead of literature values. Future work will focus on constructing the model from in-vivo MR images and translating the model into clinical applications.

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    Spatial clustering analysis of functional magnetic resonance imaging data
    Dinora Morales
    Universidad Politécnica de Madrid

    Coauthors: Concha Bielza, Pedro Larrañaga

    Functional magnetic resonance imaging (fMRI) allows the brain function detection by measuring hemodynamic changes related to neuronal activity given stimulus or task. The central problem in the analysis of fMRI is the reliable brain activated detection. One way is to compute a statistical map and the spatial dependence among voxels are making during inference form it. Clustering techniques have been applied to statistical map based on extent of activation cluster after intensity thresholding or taking into account contextual information clustering. In this paper we focus on the spatial information of fMRI to detect the brain activity taking into the spatial contiguity constraints using the neighbourhood expectation maximization algorithm with four and eight neighbourhood configurations. The neighbourhood expectation minimization algorithm was applied to Alzheimer's disease fMRI study.

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    Transient Wave Imaging
    Lili Guadarrama Bustos
    Laboratoire de Mathematiques, Universite Paris-Sud 11. France

    We study Elasticity imaging by the use of the acoustic radiation force of an ultrasonic focused beam to remotely generate mechanical vibrations in organs.We provide a solid mathematical foundation for this transient technique and design accurate methods for anomaly detection using transient measurements.

    We consider transient imaging in a non-dissipative medium. We develop anomaly reconstruction procedures that are based on rigorously established inner and outer time-domain asymptotic expansions of the perturbations in the transient measurements that are due to the presence of the anomaly.

    Using the outer asymptotic expansion, we design a time-reversal, Kirchhoff-, MUSIC- imaging technique for locating the anomaly. Based on such expansions, we propose an optimization problem for recovering geometric properties as well as the physical parameters of the anomaly.

    In the case of limited-view transient measurements, we construct Kirchhoff- and MUSIC- algorithms for imaging small anomalies. Our approach is based on averaging of the limited-view data, using weights constructed by the geometrical control method; It is quite robust with respect to perturbations of the non-accessible part of the boundary. Our main finding is that if one can construct accurately the geometric control then one can perform imaging with the same resolution using partial data as using complete data.

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    Synthetic Aperture Imaging in Acoustic Microscopy
    Golafsoun Ameri, Eric Strohm, Carl Kumaradas, Victor Yang

    Acoustic microscopy (AM) provides micro-meter resolution using a highly focused single-element transducer. A drawback in AM is a relatively small depth of filed, resulting in poor resolution outside the focus. Synthetic aperture (SA) image reconstruction techniques can be used to improve the image resolution throughout the field of view. SA mathematically synthesizes the effect of an array transducer and produces dynamic focusing and depth-independent resolution. SA reconstructions in both time domain (TD) and frequency domain (FD) were implemented and tested using simulated and experimental radio-frequency data from an acoustic microscope at 400 MHz. Lateral resolutions of the SA reconstructed images were better than those of conventional B-mode images. While both TD and FD algorithms improved the resolution, the FD algorithm had better resolution. In conclusion, FD-SA improves resolution in AM outside the focal region, at the expense of real-time imaging.

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Thermophotonic Radar Imaging of Turbid Media
by N. Tabatabaei*, A. Mandelis**

*Center for Advanced Diffusion-Wave Technologies (CADIFT), MIE Dept., University of Toronto, Toronto (Ontario), Canada M5S 3G8,
** Center for Advanced Diffusion-Wave Technologies (CADIFT), MIE Dept., University of Toronto, Toronto (Ontario), Canada M5S 3G8,

Lock-in thermography is an active thermographic method that incorporates quadrature demodulation to retrieve the amplitude and phase of the thermal-waves generated inside the sample either optically, acoustically or mechanically. The role of subsurface defects, in this case, is then to shift the thermal-wave centroid and therefore produce a contrast, both in amplitude and phase images, with respect to the intact areas. The significant difference of biological samples (turbid media) is that due to their translucency the infrared radiation emanating from them is governed by a coupled diffused-photon-density and thermal-wave field ("thermophotonics"), as opposed to purely thermal-wave field in opaque materials:
Optical field: ;

Thermal field:
The case of biological samples is a challenging case as these samples are usually translucent and do not effectively absorb the applied optical excitation. Even if they do, medical safety codes prevent researchers from applying high power excitation to these samples. As a result, the photothermal signals obtained from biological samples are generally poor in terms of signal-to-noise ratio (SNR). The intension of this poster presentation is to investigate the use of matched-filter Radar processing in the thermophotonic imaging of turbid media That is, the optical excitation is performed in a linear frequency modulated (chirped) or binary phase-coded manner and the infrared response from the sample is matched-filtered to the applied excitation according to the algorithm below:

One immediate outcome of such methodology is the ability to form depth-selective ( =constant) images rather than lock-in thermography's depth integrated images as well as maintaining higher SNR and axial resolution. The figure below compares the phase images obtained from a classic step-wedge sample inside a scattering phantom. The results clearly show the enhanced axial resolution of Radar imaging compared to that of the conventional lock-in imaging.

This poster presentation provides the analytical solution to the thermophotonic Radar problem of an absorber in a turbid medium and verifies the capabilities of the proposed methodology through detection of early dental caries in human teeth.

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Photoacoustic wave generation and signal-to-noise ratio modeling
Bahman Lashkari, and Andreas Mandelis
Center for Advanced Diffusion-Wave Technologies (CADIFT), Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, M5S 3G8, Canada

The generation of photoacoustic (PA) transients was modeled by employing a two dimensional axially symmetric solution in the frequency-domain. The frequency-domain solution facilitates the incorporation of the transducer dynamic and acoustic attenuation effects. In addition, the two- layer model automatically introduces the implementation of an arbitrary acoustic boundary condition. It has been shown that this solution asymptotically approaches the one-dimensional solution under specific conditions for beam spotsize and/or absorber size and minimum excitation frequency. The model has been used for both pulsed and continuous wave (CW) PA to predict the maximum signal and signal-to-noise ratio (SNR). In the CW PA, many parameters can be manipulated to increase the detected signal. The most important parameter is the frequency bandwidth of the excitation energy. The developed model predicts the optimum parameters to maximize the SNR. This analysis also provides a relative formulation depending on utilized parameters for the study of the performance of both modalities. This relative performance formulation demonstrates that by judicious selection of the chirped FD PA parameters, this method is capable of competing with the pulsed PA counterpart to generate superior SNR and resolution. The theoretical predictions were compared with experimental results achieved for both modalities using a dual-mode PA system.

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Assessing the Functional Significance of MEG Motor Cortex Gamma Oscillations Using Time-frequency Analysis
C. Liu1, W. Gaetz2, T.P.L. Roberts2, and H. Zhu1

1. Department of Mathematics and Statistics, York University, Toronto, ON, Canada
2. Lurie Family Foundation MEG Imaging Center, Department of Radiology, Children's Hospital of Philadelphia, Philadelphia, PA, United States

Gamma-band responses (40-90 Hz) are thought to represent a key neural signature of information processing in the human brain. Motor gamma band responses have also been observed for brief periods typically observed around movement onset, yet the functional significance of these responses remains unclear. In this study, we investigate the influence of task difficulty on the gamma-band motor cortex activity using the multi-source interference task (MSIT), a task designed in maximizing response interference. Due to huge variations of dynamic structures of brain functional activity, we propose an adaptive time-frequency analysis tool whose time-frequency resolution is adaptively adjusted to its analyzed signal; thus more accurate description of local signal characteristics can be obtained.
Fifteen right-handed subjects performed the MSIT. 80 control and 80 interference trials were recorded for each subject. Brain activity was recorded continuously using a 275 channel whole-head magnetoencephalography (MEG) (1200 samples/s). A differential minimum-variance beamformer algorithm was applied to identify the location of gamma-band (60-90 Hz) activity at the contralateral primary motor cortex (MIc). The proposed time-frequency analysis technique was applied to single trial MEG data from peak gamma-band locations. Gamma-band activity revealed in the time-frequency domain was compared for control and interference trials, and then for fast and slow trials, respectively.
Analysis results suggest that MIc gamma is significantly active for responses requiring relatively more processing time (slow vs. fast trials), and for tasks within the interference condition (interference vs. control trials). Anatomical connections between MI cortex and sub-thalamic nucleus (STN) are well known, and STN is also known to exhibit activity in gamma band. Thus, the current results may suggest enhanced MIc to STN communication with increasing task demands such as with the MSIT task.

Operator Independent Transcranial Doppler Ultrasound for Continuous Monitoring of Cerebral Vessels (poster image)
Lee B., Kumaradas JC, Yang V, Ryerson University

Continuous monitoring of the blood vessels 3-14 days after subarachnoid hemorrhage (SAH) from cerebral aneurysm rupture is imperative to assess the presence of vasospasms. Transcranial Doppler Ultrasound (TCD) can now be used for continuous monitoring of vasospasm. However, the use of TCD suffers from operator dependence requiring a skilled ultrasonographer to make doppler angle corrections. The aim of the research is to minimize the need of dedicated ultrasonographers for TCD monitoring of cerebral vasospasms. The 3D vascular structure of a phantom was obtained using binary skeletonization from 3D power Doppler images. The vascular structure was used in combination with angle independent pulsed Doppler to reconstruct the temporal blood velocity profiles at various parts of the vasculature. The results indicate the operator independent monitoring of cerebral vasospasm is possible.

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Real time Compressive Sampling based FDOCT image acquisition and registration
Evgeniy Lebed, Mei Young, Yifan Jian, Paul J. Mackenzie, Marinko V. Sarunic, Mirza Faisal Beg

Purpose Acquiring Fourier Domain Optical Coherence Tomography (FDOCT) at high speed is becoming an important problem in ophthalmic imaging. We present a medical imaging interpolation technique called Compressive Sampling (CS) for rapid volumetric acquisition of retina and Optic Nerve Head (ONH) in humans and in rodents.
Methods: The 3D volumes were acquired with a custom FDOCT system. A reduction in the acquisition time was implemented by modification of the scan pattern to acquire only a subset of the area (up to only 25%) using randomly spaced horizontal and vertical B-scans. Compressive sampling techniques were used to interpolate the missing data with high fidelity for scan time reductions of up to 73% on human ONH volumetric data.
Results: Reconstructions using the Compressive Sampling (CS) method were performed on sparsely acquired human retinal images. We show that it is possible to obtain several sparsely-acquired volumes in the same time that it would take to acquire a fully-sampled volume, and by means of non-rigid registration we obtain volumetric images that are potentially more preferential than the fully-sampled FDOCT images.
Conclusions: We demonstrated that Compressive Sampling can be used to reconstruct 3D FDOCT images with minimal degradation in quality. We showed that there is negligible effect on human retinal layers and on clinically relevant morphometric measurements of the human ONH. We also demonstrate that there is a significant reduction in motion artifacts when we sparsely sample the volume. The potential outcome of this work is a significant reduction in FDOCT image acquisition time for clinical volumetric imaging applications.

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A Comprehensive Study of Differential Diagnosis among Alzheimer's Disease, Frontotemporal Disease and Healthy Aging
Pradeep Kumar Raamana , Mirza Faisal Beg

Purpose: Alzheimer's disease (AD) and Frontotemporal dementia (FTD) are challenging to discriminate due to large overlap in clinical symptoms and the cognitive domains impaired. The NINCDS-ADRDA criteria for diagnosing probable AD have a sensitivity of 93% but a specificity of only 23% in distinguishing it from FTD as most patients with FTD also fulfilled NINCDS-ADRDA criteria for AD. Since pharmacologic treatments differ for AD and FTD, misdiagnosed patients will incur side effects for no benefit with important negative consequences. We present a comprehensive study in discriminating among Alzheimer's disease, Frontotemporal disease and Healthy Aging (HA) using various biomarkers.

Methods: The different biomarkers we compare and contrast are volumes, shape, and surface displacements of both hippocampi and lateral ventricles. The volumes and shape features are computed from the binary segmentations obtained via multi-atlas fusion of the segmentations from a cohort of a 30 FTD patients, 34 Probable AD patients and 14 age-matched controls.

Results: All the biomarkers are studied in a 3-class setting (AD, FTD and HA) using a fixed classifier to obtain the diagnostic value of these biomarkers in the context of differential diagnosis. To date, such a comprehensive study in a 3-class setting hasn't been published to the best of our knowledge. A highlight of this study is evidence of high diagnostic value of the ventricular degeneration, in shape and deformation, for the differential diagnosis of FTD, AD and HA. The results present a valuable insight into the discriminative power of different biomarkers studied here and demonstrate the potential of ventricular degeneration as biomarker in the differential diagnosis of FTD, AD and HA.

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