April 16, 2014
January-August 2012
Thematic Program on Inverse Problems and Imaging

August 20-24, 2012
Industrial Problem-Solving Workshop on Medical Imaging

Organizers: Sean Bohun (UOIT),Michael Lynch (MITACS)
Huaxiong Huang (York), Nilima Nigam (SFU)
Mary Pugh (Toronto), Hongmei Zhu (York)
Proposed Problems
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Problem 1 Image Registration in the Presence of Discontinuities(presentation)
Presenters: Yonho Kim, Dustin Steinhauer, Karteek Popuri, Rolf Clackdoyle, Alvin Ihsani, Khaled Issa, Evgeniy Lebed
Image registration is one of the challenging problems in image processing and specifically medical imaging. Given two images taken, for example, at different times, and from different devices or perspectives, the goal is to determine a reasonable geometric transformation that aligns two images in a common frame of reference (full abstract).

Reference: Brain-Tumor Interaction Biophysical Models for Medical Image Registration
Deformable Registration of Brain Tumor Images

Problem 2. Rapid modeling of internal structures of deformable organs (i.e. liver) (presentation) Presenters: Bahram Marami, Iain Moyles
Edward Xishi Huang and James Drake
CIGITI, The Hospital for Sick Children

Accurate estimation of deformation of soft organ internal structures between two images acquired at different conditions. Boundary conditions: vessel curves and point landmarks

Cancer is one of the leading causes of death in the developed countries and the only major disease for which death rates are increasing. For example, the number of children who suffer from tumors has been increasing by about 0.6% per year. Although uncommon, cancer is the second leading cause of death in children.
Recent development of high intensity focused ultrasound (HIFU) thermal procedures has a great potential to provide a noninvasive alternative solution to tumor treatment, which is expected to replace many current invasive procedures for kids such as liver and kidney cancers. Although HIFU procedures provide advantages such as less trauma and side effects, their effectiveness are largely limited by the loss of direct vision. During the procedure, doctors have to rely on real-time image guidance for targeting treatment sites, sparing nearby normal tissues, and monitoring thermal dose delivery. Currently, real-time image guidance is limited by intra-operative low quality image and/or slow image acquisition process. High quality real-time image guidance is very challenging especially for deformable moving targets such as the liver, which involve large organ shift and deformation, and require dynamically steering HIFU beam to moving targets to improve treatment efficiency.
In order to improve image guidance, we need to map pre-treatment patient-specific deformable models and treatment plans to the patient to complement limited real-time imaging. Therefore, accurate deformation models of soft organs are an essential component for treatment planning, treatment delivery, and assessment of disease progression/regression.

Problem: Rapid modeling of internal structures of deformable organs (i.e. liver)
Our goal is to rapidly obtain 2D/3D models of deformable organs by estimating deformation using two images acquired at different conditions subject to multiple types of boundary conditions such as vessel curves and point landmarks. This problem may be formulated as deformation of elastic solid body, which can be solved by finite element methods (FEM).
Finite element method is one of deformable image registration techniques, aiming to find optimal geometric transformation of homologous points in two images. A typical FEM problem in deformable image registration is as follows: given tissue properties and boundary conditions extracted from two images, FEM optimizes an objective function such as energy in order to find the displacement/deformation field subject to boundary conditions.
However, due to measurement errors in tissue properties and boundary conditions, the accuracy and speed of conventional FEM methods is often limited when used for deformable image registration of two images, particularly for internal structures deep inside the organ. To address these problems, we need boundary conditions to include deep internal structure features such as centerlines of blood vessels and bifurcations of vessels. That is, we need different types of boundary conditions (i.e. curves of vessel centerlines and points of vessel bifurcations) to constrain the solution. This will ensure accurate alignment of internal structures deep inside organs.
After the curves of vessel centerlines are extracted from medical images, they can be represented by smooth differential B-Spline curves if it facilitates to solve this modeling problem. Extracted vessel trees can be further processed into curve segments with known end points.
One potential solution is that this deformation modeling can be formulated as a minimum energy problem subject to vessel curves and point landmarks.

Problem 1a: Modeling of internal structures with 2D images using vessel segments with both known end points.
Problem 1b: Same as 1 except only one known end point, free for another end point, i.e. it is possibly not equal for vessel lengths from two images due to imaging artifacts and extraction errors.
Problem 2: Modeling of internal structures with 3D images using vessel segments. It is easier to obtain more accurate curves and point landmarks from 3D images for validation in human subjects (2D problem is a simplified version).
Problem 3: Rapid 3D/4D modeling of deformable moving organs (i.e. liver)
Simultaneous estimation of deformation and tissue properties using multiple images acquired at different conditions
Boundary conditions: organ surface, 3D curves and 3D point landmarks
Acquisition of boundary conditions:
- Vessel centerlines: extracted from MR/CT images
- Branch points of vessels: extracted from MR/CT images
- (Organ surfaces: Segmented from MR/CT images or reconstructed from stereo video images for Problem 3.)

Accurate modeling of deformation of internal structures will improve the quality of image guided treatment procedures deep inside soft organs as these vessel structures provide a good reference to localize deep treatment targets.
After accurate modeling of deformation of internal structures, modeling of the whole deformable organ can be relatively easier to achieve using other techniques.
Accurate modeling of deformation of internal structures between two images acquired at different conditions will also be a fundamental step towards accurate 3D/4D modeling of deformable moving organs and intra-procedural image fusion.
Accurate models of deformable moving organs can facilitate treatment planning and map high quality patient-specific models/images to the patient. These models complement intra-operative images in order to improve outcomes of image guided treatment procedures.

Problem 3 Detecting current density vector coherent movement
Cerebral Diagnostics Canada Inc. (presentation.ppt)
Presenters: Sujanthan Sriskandarajah, Nataliya Portman, Alexandre Foucault, Dominique Brunet, Yousef Akhavan, Vavara Nika

I will describe the problem first in non-mathematical terms to clarify what we are trying to achieve and why. Then I will attempt to provide a mathematical frame work.

We want to be able to isolate current density signal patterns extracted from (electroencephalography) EEG and to measure small transient (often less than one quarter of one second) mental events in the brain such as little cognitions like what you mind does when you imagine the shape of a letter in the alphabet in your mind. If successful there are numerous ramifications for this for neuroscience. For example, it could help people communicate.

I, and many others, believe that these signals are hidden amongst the many EEG signals taken while a person performs the cognition. EEG itself plots voltage against time and, on its own, it is far too crude to find the type signals we are looking for. I believe this is because they are weak signals of low voltage that are coming from tiny areas of the brain and they are overshadowed (buried) among various larger signals.) For example it is known that there are special areas of the brain in which language aspects of vision and lettersare likely imagined.

We do source localization using an existing algorithm called eLoreta. This gives us a data set at each instant in time providing4 numbers for each voxel for each instant in time. The numbers are the x, y and z components and magnitude of the current density for each voxel. The voxels are in known positions.

When we make brain movies of these vectors we often see them dancing together. We use our imaging software to draw the vectors as lines radiating from the centre of each voxel. We can clearly see clusters of voxels. For example, voxels 2 and 3 are side by side at the bottom of the brain. In a given EEG recording they may be seen pivoting in unison about the midpoints of the voxels. At a given time instant within a given frequency band (e.g. 2-4 Hz brain activity) they may be seen pivoting about their center points in near perfect synchronicity the same movement
pattern. (This is a little hard to explain but easy to see in the movies.) Hence as the vector radiating out of one voxel shifts in the direction it is pointing, we might see the vector radiating out of the adjacent voxel shifting in almost exactly the same way.

What we need in the long run is a real time tool to colour code clusters and to make a list of the voxels that are members of a cluster at an instant in time. For example if there are 10 voxels in one cluster that are pivoting in one pattern then we need a colour assigned to all the vectors in group.

In the short run, before tackling the issue of real time, we need a post-processing method. Eventually we want this to be implemented in C++ because we want to make it part of our brain movie software bundle called DECI which is written in C++ and open GL.

Deci (Dynamic Electrical Cortical Imaging) is our software bundle. It can be made available through a free software research license. Data sets and sample movies are available to team members. This can be used to validate any new tool created by the team. If your tool works it will pick out the clusters of vectors we can see with our own eyes dancing together in the movies played with DECI.

Ideally, the math team needs to work in close association with computer programmers so that the project can culminate in a useful software tool that functions well and is well explained. In the future, once it works we plan to test it out by having people perform small cognitions, and they
seeing if the software can help us find things such as a cluster of vectors dancing together that are responsible for the cognition. This ambitious goal, if achieved, would be a great advance for neuroscience.

Mark Doidge MD, Aug. 1, 2012 and amended Aug. 6 2012

Problem 4 - Statistical models with tolerance for abnormalities
Shuo Li, GE Healthcare
(download) (presentation) Presentations: Craig Sinnamon, Anna Belkine, Berardo Galvao-Sousa

[1] M.M. Chakravarty, G. Bertrand, C.P. Hodge, A.F. Sadikot, and D.L. Collins, The creation of a brain atlas for image guided neurosurgery using serial histological data, Neuroimage 30 (2006), no. 2, 359-376.

[2] X. Zhou, T. Kitagawa, T. Hara, H. Fujita, X. Zhang, R. Yokoyama, H. Kondo, M. Kanematsu, and H. Hoshi, Constructing a probabilistic model for automated liver region segmentation using non-contrast x-ray torso ct images, Medical Image Computing and Computer-Assisted Intervention{MICCAI 2006 (2006), 856-863.

Problem 5 - Modelling human perception in clinical diagnosis
Shuo Li, GE Healthcare (download)

[1] G. Kong, D.L. Xu, and J.B. Yang, Clinical decision support systems: a review on knowledge representation and inference under uncertainties, International Journal of Computational Intelligence Systems 1 (2008), no. 2, 159-167

[2] V.M.C.A. Van Belle, B. Van Calster, D. Timmerman, T. Bourne, C. Bottomley, L. Valentin, P. Neven, S. Van Hu el, J.A.K. Suykens, and S. Boyd, A mathematical model for interpretable clinical

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