# Research Portal

### My research interest spans across multiple disciplines but it is rooted in concrete problems especially in computational, mathematical and statistical aspects of medical imaging. My first research focus was on diffusion tensor imaging and the research has resulted in more accurate estimate of the diffusion tensor (see Refs.[4,5] and the book chapter) and better uncertainty quantification of fiber directions (see Refs.[8,11]). My research on MR signal and noise analysis has also been quite fruitful and has resulted in a novel fixed point formula for characterizing the underlying signal-to-noise ratio (SNR) of MR images (see Ref.[3]), a new technique called PIESNO for simultaneously identifying noise-only pixels and estimating the noise level in MR images (see Ref.[15]) and a novel signal-transformational framework for breaking the noise floor (see Ref.[13]), which have been successfully applied to other MR techniques, see Ref.[24] and Ref.[30]. My occasional meandering to other related research areas resulted in the first 3D analytical MRI phantom in the Fourier domain (see Ref.[9]); the phantom was based on the 3D version of the well-known Shepp-Logan phantom in the image domain. My recent research efforts on optimal acquisition designs for Diffusion MRI (see Refs.[23,25]) and 3D radial MRI (Refs[.25,26]) have led to among other things the development of the first deterministic approach to generating nearly uniform antipodally symmetric (in light of Ref.[29], mirror-symmetric) points on the unit sphere (see Refs[22,23], and its first applications outside of MRI were in Astrophysics, Optics, Quantum Information) and the development of pseudometrically constrained centroidal Voronoi tessellations for generating large-scale uniform antipodally symmetric points on the unit sphere suitable for 3D radial MRI applications (Ref.[26] and the link here). I also developed other models of uniform distribution of points on the sphere Ref.[29], which shares similarity with the 2D Wigner crystal or the 2D system of charged particles in the circular parabolic potential well . Recently, I took another good look at ways for analyzing diffusion tensor imaging data and developed a single-subject analytic framework based on measures derived from the elliptical cone of uncertainty, see Ref.[34]. A nice off-shoot from this research was a new and efficient tool for computing the exact p-value of Wilcoxon-Mann-Whitney test, see the site for more details.

### Publications:

**Book Chapters**

Özarslan E, Koay CG, Basser PJ. Simple harmonic oscillator based reconstruction and estimation for one-dimensional q-space magnetic resonance (1D-SHORE). *Excursions in Harmonic Analysis**: The February Fourier Talks at the Norbert Wiener Center*, ed. Andrews TD, Balan R, Benedetto JJ, Czaja W, and Okoudjou KA, New York: Springer, 2013, Volume 2, 373–400.

Koay CG.* Least squares approaches to diffusion tensor estimation*. In Derek K. Jones, PhD (Ed.), *Diffusion MRI: Theory, Methods, and Applications.* Oxford University Press, 2010. (ISBN 0195369777). Preprint copy is available.

**Selected Journal Articles**

[36] Yeh PH, Koay CG, Wang B, Morissette J, Sham E, Senseney J, Joy D, Kubli A, Yeh CH, Eskay V, Liu W, French LM, Oakes TR, Riedy G, Ollinger J. *Compromised Neurocircuitry in Chronic Blast-Related Mild Traumatic Brain Injury*. Human Brain Mapping 2017; 38(1):352-369.

[35] Hutchinson EB, Avram AV, Irfanoglu MO, Koay CG, Barnett AS, Komlosh ME, Özarslan E, Schwerin SC, Juliano SL and Pierpaoli C. *Analysis of the effects of noise, DWI sampling, and value of assumed parameters in diffusion MRI models*. Magnetic Resonance in Medicine 2017; 78(5):1767-1780.

[34] Koay CG, Yeh P-H, Ollinger JM, İrfanoğlu MO, Pierpaoli C, Basser PJ, Oakes TR, Riedy G. *Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI): A framework for single-subject analysis in diffusion tensor imaging*. NeuroImage 2016; 126: 151-163. DOI: 10.1016/j.neuroimage.2015.11.046 arXiv:1510.02934 Software: TOADDI and Wilcoxon-Mann-Whitney p-value computation

[33] Lewis CM, Hurley SA, Meyerand ME, Koay CG. *Data-driven optimized flip angle selection for T1 estimation from spoiled gradient echo acquisitions*. Magnetic Resonance in Medicine 2016; 3(76): 792–802.

[32] Hosseinbor AP, Chung MK, Koay CG, Schaefer SM, van Reekum CM, Schmitz LP, Sutterer M, Alexander AL and Davidson RJ. *4D Hyperspherical Harmonic (HyperSPHARM) Representation of Surface Anatomy: A Holistic Treatment of Multiple Disconnected Anatomical Structures*. Medical Image Analysis 2015; 22: 89-101.

[31] Hoy AR, Koay CG, Kecskemeti SR, Alexander AL. *Optimization of a Free Water Elimination Two-Compartment Model for Diffusion Tensor Imaging*. NeuroImage 2014; 103: 323-333.

[30] Bai R, Koay CG, Hutchinson EB, Basser PJ. *A framework for accurate determination of the T2-distribution from multiple echo magnitude MRI images*. Journal of Magnetic Resonance 2014; 244: 53–63.

[29] Koay CG. *Distributing points uniformly on the unit sphere under a mirror reflection symmetry constraint*. Journal of Computational Science 2014; 5: 696-700. arXiv:1403.3851 Software/Data

[28] Koay CG, Özarslan E. *Conceptual foundations of diffusion in magnetic resonance*. Concepts in Magnetic Resonance Part A 2013; 42: 116–129. [Preprint copy]

[27] Özarslan E, Koay CG, Shepherd TM, Komlosh ME, İrfanoğlu MO, Pierpaoli C, and Basser PJ. *Mean Apparent Propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure*. NeuroImage 2013; 78: 16-32.

[26] Koay CG. *Pseudometrically Constrained Centroidal Voronoi Tessellations: Generating uniform antipodally symmetric points on the unit sphere with a novel acceleration strategy and its applications to diffusion and 3D radial MRI*. Magnetic Resonance in Medicine 2014; 71: 723-734. (Published online 11 March 2013). [ Software/Data , Figures in high resolutions: Figure 5 and Figure 6, Presentation].

[25] Koay CG, Özarslan E, Johnson KM, Meyerand ME. *Sparse and optimal acquisition design for diffusion MRI and beyond*. Medical Physics 2012; 39(5): 2499-2511. Software

[24] Özarslan E, Shepherd TM, Koay CG, Blackband SJ, Basser PJ.* Temporal scaling characteristics of diffusion as a new MRI contrast: Findings in rat hippocampus*. NeuroImage 2012; 60 (2):1380-1393.

[23] Koay CG, Hurley SA, Meyerand ME. *Extremely efficient and deterministic approach to generating optimal ordering of diffusion MRI measurements*. Medical Physics 2011; 38 (8): 4795-4801. Software

[22] Koay CG. *A simple scheme for generating nearly uniform distribution of antipodally symmetric points on the unit sphere*. Journal of Computational Science 2011; 2: 377-381. Software

[21] Koay CG. *Analytically exact spiral scheme for generating uniformly distributed points on the unit sphere*

. Journal of Computational Science 2011; 2: 88-91. Software

[20] Özarslan E, Shemesh N, Koay CG, Cohen Y and Basser PJ. *Nuclear magnetic resonance characterization of general compartment size distributions*. New Journal of Physics 2011; 015010 (1-17).

[19] Walker L, Chang LC, Koay CG, Sharma N, Cohen L, Verma R and Pierpaoli C. *Effects of physiological noise in population analysis of diffusion tensor MRI data*. NeuroImage 2011; 54(2): 1168-1177.

[18] Nevo U, Özarslan E, Komlosh ME, Koay CG, Sarlls JE and Basser PJ. *A system and mathematical framework to model shear flow effects in biomedical DW-imaging and spectroscopy*. NMR in Biomedicine 2010; 23(7): 734-744.

[17] İrfanoğlu MO, Koay CG, Pajevic S, Machiraju R, and Basser PJ. *Diffusion tensor field registration in the presence of uncertainty*. *MICCAI* 2009; Part I, LNCS 5761:181–189

[16] Özarslan E, Koay CG and Basser PJ. *Remarks on q-space MR propagator in partially restricted, axially-symmetric, and isotropic environments*. Magnetic Resonance Imaging 2009; 27(6): 834-44.

[15] Koay CG, Özarslan E and Pierpaoli C.* Probabilistic Identification and Estimation of Noise (PIESNO)*: *A self-consistent approach and its applications in MRI*. Journal of Magnetic Resonance 2009; 199: 94-103. PIESNO Website.

[14] Koay CG. *On the six-dimensional orthogonal tensor representation of the rotation in three dimensions: A simplified approach*. Mechanics of Materials. 2009; 41: 951-953. [NOTE: Thanks to Dr. M Okan Irfanoglu for pointing out the typo: R_{43} in Equation (14) should be Sqrt(2) Q_{13}Q_{23} not Sqrt(2) Q_{13}Q_{22}.]

[13] Koay CG, Özarslan E and Basser PJ. *A signal transformational framework for breaking the noise floor and its applications in MRI*. Journal of Magnetic Resonance 2009; 197: 108-119. STF Website.

[12] Chang LC, Koay CG, Basser PJ and Pierpaoli C. *Linear least-squares method for unbiased estimation of* *T _{1}*

*from SPGR signals*. Magnetic Resonance in Medicine 2008; 60(2): 496-501.

[11] Koay CG, Nevo U, Chang LC, Pierpaoli C and Basser PJ. *The elliptical cone of uncertainty and its normalized measures in diffusion tensor imaging*. IEEE Transactions on Medical Imaging 2008; 27(6): 834-846. Software

[10] Freidlin RZ, Özarslan E, Komlosh ME, Chang LC, Koay CG, Jones DK and Basser PJ. *Parsimonious model selection for tissue segmentation and classification applications: A study using simulated and experimental DTI data*. IEEE Transactions on Medical Imaging 2007; 26(11): 1576-1584.

[9] Koay CG, Sarlls JE and Özarslan E. *Three dimensional analytical magnetic resonance imaging phantom in the Fourier domain*. Magnetic Resonance in Medicine. 2007; 58: 430-436. Software.

[8] Koay CG, Chang LC, Pierpaoli C and Basser PJ. *Error propagation framework for diffusion tensor imaging via diffusion tensor representations*. IEEE Transactions on Medical Imaging 2007; 26(8): 1017-1034. Erratum in 2007; 26(10): 1424. Preprint copy is available.

[7] McMillan KM, Rogers BP, Koay CG, Laird AR, Price RR and Meyerand ME. *An objective method for combining multi-parametric MRI datasets to characterize malignant tumors*. Medical Physics. 2007; 34(3): 1053-1061.

[6] Chang LC, Koay CG, Pierpaoli C and Basser PJ. *The variance of estimated DTI-derived parameters via first-order perturbation methods*. Magnetic Resonance in Medicine. 2007; 57: 141-149.

[5] Koay CG, Chang LC, Carew JD, Pierpaoli C and Basser PJ. *A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging*. Journal of Magnetic Resonance 2006; 182: 115-125. Software

[4] Koay CG, Carew JD, Alexander AL, Basser PJ and Meyerand ME. *Investigation of anomalous estimates of some tensor-derived quantities in diffusion tensor imaging*. Magnetic Resonance in Medicine. 2006; 55: 930-936. Software

[3] Koay CG and Basser PJ. *Analytically exact correction scheme for signal extraction from noisy magnitude MR signals*. Journal of Magnetic Resonance 2006; 179: 317-322. Software

[2] Crescimanno M, Koay CG, Peterson R and Walsworth R. *Analytical estimate of the critical velocity for vortex pair creation in trapped Bose condensates*. Physics Review A. 2000; 62 (6): 063612.

[1] Crescimanno M, Koay CG and Peterson R. *Limits to sympathetic evaporative cooling of a two-component Fermi gas*. Physics Review A. 2000; 61 (5): 053602.

**PhD Thesis**

Koay CG. *Advances in data analysis of diffusion tensor imaging* (Paperback). ProQuest (UMI), 2006. ISBN 9780542283062.

I am the principal developer of **HI**GHLY **SP**ECIFIC BUT **E**DGILY **E**FFECTIVE **D**ATA-PROCESSING (**HI-SPEED**) SOFTWARE PACKETS (http://sites.google.com/site/hispeedpackets). A poster showcasing the HI-SPEED software packets was presented at the 2009 ISMRM Educational Session, click here to download the poster. The site also contains several brief notes on various topics related to my research. Although the core routines of HI-SPEED are written in Java, special interfaces to these routines in other programming languages such as IDL, MATLAB and Mathematica are also available.

**Selected Presentation Slides**:

[1]. Workshop on Biomedical Image Analysis and Algorithms (There was a typo on slide #12 in the original version, which is available through the website of the Norbert Wiener Center. The correct version is made available on this site. Here is the link )

[2]. PIESNO

[4]. Computation and Informatics in Biology and Medicine Seminar.

**Selected Published Abstracts:**

[1] Koay CG, Alexander AL, Meyerand ME. (2011) New strategy for registering DW and non-DW images via tensor estimation metric. In *Proc. Intl. Soc. Mag. Reson. Med.* 19. p. 3893.

[2] Koay CG, Pierpaoli C, and Basser PJ. (2010) A new Mahalanobis distance measure for clustering of fiber tracts. In *Proc. Intl. Soc. Mag. Reson. Med.* 18. p. 4012.

[3] Koay CG, Chang LC, Deoni S, and Pierpaoli C. (2007) An Optimal Framework for T1 Estimation in An SPGR Acquisition. In *Proc. Intl. Soc. Mag. Reson. Med.* 15. p. 1794.

**Expository notes**:

[1] Euler's Theorem on the Axis of a Rotation: A Journey through Physics, Geometry, Algebra and Analysis.

### Contact Info:

Email: cgkoay AT uwalumni DOT com (replace "AT" with "@" and "DOT" with "." )

**NOTE:** My primary focus at this time is on teaching, especially at the secondary school level. I am currently a math teacher at Instilling Goodness and Developing Virtue Boys School (igdvs.org).