Components of Disparity Vergence Eye Movements: Application of Independent Component Analysis

IEEE Transactions On Biomedical EngineeringVolume 49, Number 8, August 2002

John L. Semmlow, Ph.D., Fellow, IEEEWeihong Yuan, Ph.D.

Presented by Joseph SaltzbartNeural Engineering BME 661

March 13, 2008

Table of Contents

• Background Material

• Methods

• Results

• Conclusion

• Supporting Material

Background Material

• Authors

• Disparity Vergence Eye Movements

• Linear Algebra

• Statistics

• Independent Component Analysis (ICA)

Authors

• John L. Semmlow, Ph.D.– Professor of Surgery at UMDNJ

Robert Wood Johnson Medical School

– Professor of Biomedical Engineering at Rutgers

– Fellow of IEEE– B.S. EE & Ph.D. from

University of Illinois– Thesis Advisor to Dr. Alvarez

John L. Semmlow, Ph.D.

• Current Research– Studies on the mechanics of the human lens using

magnetic resonance imaging and computer modeling

– The application of independent component analysis to determine control strategies for human eye movements

– The development of novel techniques such as opto-acoustic imaging.

John L. Semmlow, Ph.D.

• Recent Papers (Robert Wood Johnson)– Koretz JE, Stren, SA Strenk, LM Semmlow JL Scheimpflug and high-resolution

magnetic ressonance imaging. JOSA A 21:346-354, 2004 15005398.– Streank SA, Strenk LM, Semmlow JL DeMarco, JK Magnetic resonance

imaging study of the effects of age and accommodation on the human lens cross-sectional area. IOVS 45:539-45, 2004 14744896.

– Recent Papers (Rutgers)– Semmlow, JL, and Yuan, W, Adaptive Modification of Disparity Vergence

Components: An Independent Component Analysis study Investigative Ophthalmology and Vision Science (In Press).

– Yuan, W, Semmlow, JL, and Muller-Munoz, P, Model-Based Analysis of Dynamics in Vergence Adaptation IEEE Transactions Biomedical Engineering 48; 1402-1411 (2001).

– Strenk, S, Strenk L, and Semmlow, JL, High Resolution MRI Study of Circumlental Space in the Aging Eye Journal of Refractive Surgery 16 (2000).

Authors

• Weihong Yuan, Ph.D.– Research Assistant

Professor of Radiology at Cincinnati Children’s Hospital

– McLaurin Fellow in Pediatric Neurosurgery

– B.S. BME from Zhejiang University

– M.S. & Ph.D. from Rutgers University

Weihong Yuan, Ph.D.

• Special Interests– Diffusion tensor study pediatric patient with

hydrocephalus – Diffusion tensor imaging study of pediatric

supratentorial tumors – Diffusion tensor imaging study of children with

traumatic brain injury– Functional MRI study of pediatric patients with spina

bifida – fMRI/DTI study of epilepsy– Intra-operative neuroimaging

Weihong Yuan, Ph.D.

• Recent Papers– Yuan W, Holland SK, Schmithorst VJ, Walz NC, Cecil KM, Jones BV, Karunanayaka P,

Michaud L, S. Wade L. Diffusion Tensor MRI Reveals Persistent White Matter Damage after Traumatic Brain Injury Experienced During Preschool Years. (Accepted for publication).

– Holland SK, Vannest J, Mecoli M, Byars AW, Jacola LM, Karunanayaka PR, Schmithorst VJ, Yuan W, Plante E. Functional MRI of Language Development and Lateralization in Children. (accepted for publication).

– Yuan W, Holland SK, Cecil KM, Dietrich KN, Wessel SD, Altaye M, Hornung RW, Ris MD, Egelhoff JC, Lanphear BP.  The Impact of Early Childhood Lead Exposure on Brain Organization: An fMRI Study of Language Function. Pediatrics, 2006; 118(3):971-7.

– Yuan W, Szaflarski J, Schmithorst VJ, Schapiro M, Byars AW, Strawsburg RH, Holland SK. FMRI Shows Atypical Language Lateralization in Pediatric Epilepsy Patients. Epilepsia, 2006, 48(3):593-600.

– Zur KB, Holland SK, Yuan W, Choo DI. Functional magnetic resonance imaging: contemporary and future use. Curr Opin Otolaryngol Head Neck Surg. 2004; 12(5): 374-7.

Disparity Vergence Eye Movements

• Stimulus where the eye will rotate inward or outward to put the same object on the fovea.

• The motor response of disparity vergence is controlled by two components, a preprogrammed “transient” (fast) component and a feedback-controlled “sustained” (slow) component, which constitute the “dual mode” theory. Of particular importance are the timing and relative magnitudes of the two components since they are indicative of the mechanism used by the brain for their coordination and control.

Disparity Vergence Eye Movements

– Convergence is the inward turning of the eyes.

• Only convergence responses were used in the experiment.

– Divergence is the outward turning of the eyes.

• Dr. Alvarez’s Lab has Divergence Data.

Linear Algebra

• Vector (Wikipedia)• A spatial vector, or

simply vector, is a geometric object which has both a magnitude and a direction. A vector is frequently represented by a line segment connecting the initial point with the terminal point.

Linear Algebra

• Matrix (Wikipedia)– a matrix (plural matrices) is a

rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied. Matrices are used to describe linear equations, keep track of the coefficients of linear transformations and to record data that depend on multiple parameters.

Linear Algebra

• Inverse Matrix (Strang)– The Matrix A is invertible if there exists a matrix B

such that BA = I and AB = I. There is at most one such B, called the inverse of A and denoted by A-1.

– The matrix that leaves every vector unchanged is the identity matrix I.

I =

Linear Algebra

• Linearly Independent (Strang)– If only the trivial combination gives zero, so that c1v1+…+ckvk = 0

only happens when c1 = c2 = ck = 0, then the vectors v1,…,vk are linearly independent. Otherwise they are linearly dependent, and one of them is a linear combination of the others.

• Linear Transformations, Eigenvalues, and Eigenvectors (Wikipedia)– a vector may be thought of as an arrow. It has a length, called its

magnitude, and it points in some particular direction. A linear transformation may be considered to operate on a vector to change it, usually changing both its magnitude and its direction. An eigenvector of a given linear transformation is a vector which is multiplied by a constant called the eigenvalue during that transformation. The direction of the eigenvector is either unchanged by that transformation (for positive eigenvalues) or reversed (for negative eigenvalues).

Statistics

• Gaussian Distribution (Wikipedia)– The normal distribution, also called the Gaussian distribution, is an

important family of continuous probability distributions, applicable in many fields. Each member of the family may be defined by two parameters, location and scale: the mean ("average", μ) and variance (standard deviation squared) σ2, respectively.

– The importance of the normal distribution as a model of quantitative phenomena in the natural and behavioral sciences is due to the central limit theorem. Many psychological measurements and physical phenomena (like noise) can be approximated well by the normal distribution. While the mechanisms underlying these phenomena are often unknown, the use of the normal model can be theoretically justified by assuming that many small, independent effects are additively contributing to each observation.

StatisticsGaussian Distribution

Independent Component Analysis (ICA)

• Technique introduced by in the early 1980s by J. Heuralt, C. Jutten, and B. Ans.– Neurophysiological Phenomena

• Outputs ~ Two types of sensory signals (responses) measuring muscle contraction.

• Inputs ~ Angular position and velocity signals (components) of moving joint.

• Nervous System is somehow able to infer the position and velocity signals from the measured responses.

Independent Component Analysis (ICA)

• Cocktail Party Problem– “Imagine you're at a cocktail party. For you it is no problem to follow the

discussion of your neighbors, even if there are lots of other sound sources in the room: other discussions in English and in other languages, different kinds of music, etc.. You might even hear a siren from the passing-by police car.”

– “It is not known exactly how humans are able to separate the different sound sources. Independent Component Analysis is able to do it, if there are at least as many microphones or 'ears' in the room as there are different simultaneous sound sources.”

– “In this demo, you can select which sounds are present in your cocktail party. ICA will separate them without knowing anything about the different sound sources or the positions of the microphones.”

– http://www.cis.hut.fi/projects/ica/cocktail/cocktail_en.cgi

Independent Component Analysis (ICA)

• Definition– “ICA is a method for finding underlying factors

or components from multivariate (multidimensional) statistical data set.”

– “What distinguishes ICA from other methods is that it looks for components that are both statistically independent and nonguassian.”

– Independent Component Analysis

Independent Component Analysis (ICA)

• General Mathematical DefinitionIf, X = (x1(t), x2(t)……………………..xm(t)) and

S = (s1(t), s2(t)……………………....sn(t)) and A = is some unknown matrixWhere, 1) X is the output (response) vector, and

2) S is the component (source) vector which is linearly independent and non-gaussian, and

3) t is timeThen, X = A(S)Hence, ICA consists of estimating both the matrix A and S,

when we only observe X.

Independent Component Analysis (ICA)

• Linearly Noisy ICA– When assuming an uncorrelated Gaussian noise

n, then

X = AS + n

• Don’t Worry– Dr. Alvarez’s Lecture on Instrumentation,

Signals, and ICA– ICA Web sites

Independent Component Analysis (ICA)

• Superficially related to– Blind Source Separation– Factor Analysis– Principal Component Analysis

• Applications– Image Processing– Signal Processing (Vision Research, Telecom)– Brain Imaging (fMRI)– Econometrics– Image Feature Extraction

Methods

• Simulations vs. Subjects

• Instrumentation

• Independent Component Analysis

• ICA Evaluation, Compensation, and Model Simulations

• Principal Component Evaluation of the Number of Independent Components

Simulations vs. Subjects

• Simulations– 30 - 45 individual responses to vergence step stimuli to

determine accurate estimates of the two components: a preprogrammed transient component and a feedback-controlled “sustained” component.

• Subjects– Five people with normal uncorrected binocular vision.– No difficulty in performing the experiments.– At least 80 convergence responses were acquired due to

possibility of artifacts.• Saccades• Blinks

Simulations vs. Subjects

• Graph of Vergence (degrees) vs. Time

• 40 disparity vergence responses to a step change

Instrumentation

• Stimulus Apparatus– Target

• Two short 2° vertical lines viewed as a sterioscopic

• Manipulated to produce a 4° step change in vergence position

• Predictable amplitude, but randonmized onset to discourage prediction by the subject.

Instrumentation

• Eye Movement Monitor– Skalor (Model 6500)

• Calibration– Done on each response– Reponses sampled at 200 Hz

• Above Nyquist Frequency

Independent Component Analysis (ICA)

• Analytical method that isolates individual components from a linear mixture provided the components are nongaussian and sufficiently independent.

• Goal is to identify the linear mixing matrix.X = AS + Noise

• X includes m response vectors.• S includes n source (component) vectors.• Noise vector represents the disturbances in the form of

additive noise independent of the source vector S.• A is the linear mixing matrix.

Independent Component Analysis (ICA)

• Unmixing (Inverse) matrix U = A-1 is used to estimate the unobservable source vector S, where S = UX.

• Linear transformations of the data set are used to estimate the mixing matrix A by optimizing nongaussianity (related to statistical independence).

Independent Component Analysis (ICA)

• Assumptions– Vergence Responses

• Linearly Independent

• Nongaussian

– Neuronal Stimulus Induced Synchronization• Initially Dependent• Ultimately Independent (Synchronization diminishes)

Independent Component Analysis (ICA)

• Matrix Operations– Evaluation of Mixing Matrix A performed on the

latter diminished portion (independent) of the response.

– Unmixing matrix U applied to entire response to estimate the underlying motor components, the source vector S.

– Errors produced from initial synchronized portion of response were corrected in an algorithm.

Independent Component Analysis (ICA)

• ICA Software– MATLAB

• FastICA*• Jade

– Set to isolate two source components.– Amplitude scaling was adjusted by matching

the average vergence response.• Average vergence response equals the sum of the

two components.

ICA Evaluation, Compensation, and Model Simulations

• Dual-Component Model Simulations– Verified ICA was able to identify the

underlying control components.– Developed and evaluated the correction

algorithm for stimulus-induced loss of independence.

– Underlying control components are directly available as outputs.

ICA Evaluation, Compensation, and Model Simulations

• Model Parameters (7) Randomly Simulated Component Variability– Transient Component

• Onset Time• Pulse Width• Pulse Amplitude

– Sustained Component• Onset Time• Dynamics• Amplitude

– Motor Plant Time Constant

ICA Evaluation, Compensation, and Model Simulations

• Ensemble of 40 model simulated disparity vergence responses to a step change in stimulus.

• Ensemble standard deviations from experimental and simulated response ensembles shows that variability and its magnitude of simulated data is similar.

Principal Component Evaluation of the Number of Independent

Components• Selection of significant components in a

multivariate set– “Scree” plot

• Eigenvalues versus Number of Components.• Eigenvalues determined by MATLAB routine.• Breakpoint

– Flattening of the curve for eigenvalue numbers greater than three.

– Indicates that the data set contains only two uncorrelated sources.

Results

• Number of Components

• Simulation Results

• Experimental Results

Number of Components

• Scree plots for the five subjects and simulated data (upper left) are similar.

• Curves flattening above the second eigenvalue indicates subject data also consisted of two components.

Simulation Results

• Simulations provide the underlying components directly.

• Experimental conditions only measure the combined response.

• Figure 4A: Average delay between the transient and sustained component was 50 ms.

– Components identified by the ICA match the actual average component generated by the model.

• Figure 4B: Components activated simultaneously resulted in small errors in the initial segments attributable to the loss of independence between components.

• Figure 4C: Small errors were corrected by an algorithm.

• Correction algorithm was not required for the subject data due to an indicated greater independence between components.

Simulation Results

• Solid Lines– Components

identified by ICA

• Dashed Lines– Ensemble

Averages of the two components

• Thin dotted line– Overall response

average

Experimental Results

• Solid Lines– Component contributions identified by ICA from ensemble

disparity vergence response data of 5 subjects.

• Dashed Line– Average response computed from response data.

• Underlying components are similar– Initial portion of response is transient component that

decays to approximately zero at 600 – 800 ms.– Latter portion of response is dominated by sustained

component rising rapidly in the first 500 – 800 ms and rising more gradually in the remaining 1.5 s.

Experimental Results

Conclusion

• ICA identified both a transient and sustained component and their related dynamics.

• Component dynamics were similar in all five subjects.– Components were activated at the same time.– Sustained component dominated the latter

portion of the response as the transient component decayed to zero.

Conclusion

• Model simulation also identified both a transient and sustained component response.

• ICA confirmed the model but also provides stronger evidence for accurate representation of the vergence response since it requires fewer assumptions.

• However the model simulation can be applied to a single response whereas the ICA requires an ensemble response.

Conclusion

• ICA can extract the underlying components from ensemble data, but proceed with caution!– Correction necessary to compensate for

stimulus induced loss of independence from the initial segment of components in simulated data.

– Large artifacts are detrimental to the analysis.

Conclusion

• ICA Limitations– Applicable only to an ensemble of responses.– Estimates only of component averages.– For responses with large latency variations

compared with their dynamics, reduce the variability in the data.

– Noise contribution is assumed to be small.

Supporting Material

• John L. Semmlow, Ph.D.– http://biomedical.rutgers.edu/faculty.php?id=16– http://faculty.umdnj.edu/rwjms/Users/

semmlojo.asp

• Weihong Yuan– http://www.cincinnatichildrens.org/svc/alpha/

r/radiology/fs/fac/weihong-yuan.htm

Supporting Material

• Disparity Vergence Eye Movements– The Computational Brain, by Patricia Smith

Churchland, Terrence Joseph Sejnowski– Adler’s Physiology of the Eye, edited by

William M. Hart

Supporting Material

• Linear Algebra– Linear Algebra and Its Applications, by Gilbert

Strang

Supporting Material

• Independent Component Analysis (ICA)– http://www.cs.helsinki.fi/u/ahyvarin/

whatisica.shtml– Independent Component Analysis, by Juha

Karhunen, Aapo Hyvärinen, Erkki Oja