NEUROINFORMATICS AND THE COMPLEXITY OF THE BRAIN AT THE MORPHOME 1MM SCALE

Michael I. Miller The Johns Hopkins University

August 2015 CCNS SAMSI 2015 Supported by NIH NINDS NIH NIMH NIH NIA NIH NIBIB NSF XSEDE • Motivate the Morphome Scale

• Pose the Model as an Orbit under

• Introduce Hamilton’s Principle for defining a Positioning System of information

• Look at our high throughput www.MRICloud.org

• Examine the Braak and Braak flow of neurodegeneration through the medial temporal lobe in dementia.

Rob pointed out that most of our work is derivative.

Ulf Grenander and I were highly influenced by D’Arcy Thompson’s On Growth and Form.

What I see as the Challenge for our JHU Community: Crossing Scales

JHU Multiscale Brainmaps

Electron Microscopy TI 1mm nano High Field 11.7T 250 mu

fMRI, DTI (3mm) Temporal

CLARITY mu

Two Photon Histology mu

nm micron mm SPATIAL Vogelstein & Miller The Human Brain: 10 Orders of Spatial Scale

Computational Medicine: Translating Models to Clinical Care Science Translation Winslow, Trayanova, Geman, Miller 2012 The Morphome Scale Reflects Growth, Atrophy, Aging and is Predictive of Cognitive Behavior fMRI Motor Cortex Somatosensory

DL: dorsolateral AL: anterior lateral PL: posterior lateral VL: ventral lateral MB Nebel, SE Joel, J Muschelli, AD Barber, BS Caffo, JJ Pekar & SH Mostofsky (2014). Disruption of functional organization within the primary motor cortex in children with autism. Human Brain Mapping, 35(2): 567-580. Prion-like Spread as General Mechanism in Neurodegenerative Diseases

--Brundin….Kopito Nature Reviews MCB 2010 Subcortical/Cortical Areas for Neurodegeneration

Mid sagittal view Anterior Cingulate Gyrus (ACG) Thalamus (TH)

Caudate (CA)

Putamen (PU)

Hippocampus (HC) Amygdala (AM) Entorhinal Cortex (ERC)

. Ratnanather, 20015 High field atlasing allows us to reconstruct the medial temporal lobe coordinates.

MEDIAL LATERAL

High field reconstruction: amygdala, hippocampus, ERC Frontiers in Bioengineering and Biotechnology, Network Neurodegeneration in Alzheimer’s disease via MRI based shape diffeomorphometry and high-field atlasing. Miller, et al.,2015 What are we up against at the Morphome Scale? • The brain: a collection of many curved coordinate systems (we can only go so far with voxels)

• Ideas from differential geometry must be important (signals and statistics on )

• The shift operator from time-series is replaced by transformations acting on spatial coordinates - the finite dimensional matrix groups and the infinite dimensional groups.

Matrix Rotation xx   + yy   cosθθ sin x     −sniθθ cos y  Diffeomorphisms are Generated as Flows φ − φ ()x XY φ 1  • 1 vx(φ ( )) φ ()x tt t •

x•

 φt = vt φt , φ0 = identity

vXt (x ),x∈ is a vector field 1 φ1 ()x = ∫+0 vt φt () x dt x Christensen, Rabbitt, Miller, 1996, Deformable Templates using Large Deformation Kinematics, IEEE Trans. Med. Imag. vx() vx() 0 6 vx12 ()

 0 6 12 φφt ()xv= tt ()x 1 φφ()x =x + ∫0 vtt () x dt

vx18 () vx24 ()24 vx29 ()29 We use diffeomorphisms to preserve correspondence across scales.

High Field 11.7T DTI Histology mu 250 mu

Mori & Miller How do we use this stuff to study populations? Integrating High Field Atlasing with Populations

Subject1 Subject2 Subject3

Controls Subject1

휙1 휙2 Population Template 휑 −1 휑

Disease Algebraic Orbit Model of CA - DTI Matrix Fractional Anisotropy, φ ⋅ MD diffusivity I 2 -4 Morphisms: ttmm/s (e10 )     group− action Structure - fMRI BOLD Preserving (% over baseline)

Transformations anatomy - Spectroscopy Metabolites Cr, Cho, NAA mM carries - PET %InjectDose/g or glucose metabolic rate physiology mg/100 g/min

Grenander and Miller,“Computational Anatomy: An Emerging Discipline”, Quarterly of Applied Mathematics, 1997. Miller and Qiu “Computational Functional Anatomy”, Neuroimage, Special Issue, 2008. Algebraic Orbit Model

Images IR:3 →, R ()ϕϕ I ⋅ I  I ϕ−1

IR :33→⋅ R ϕ I ( D ϕϕ I )−1 Vector fields  Jacobian DTI Tensors

33××33 TT T−1 IR :→⋅RI ϕ  (λλ11eeˆˆ1 + 222 ee ˆˆ + λ 333 ee ˆˆ ) φ

Deφφ1 De2 Deφ 3 eeˆ1 = , ˆˆ2 = , e3 = ‖‖‖‖Deφ11 Dφφ22e ‖ De ‖33

• “Positioning” information between coordinate systems is a basic problem in .

• The diffeomorphic flows “position information” by carrying the label maps .

• There are many admissable휙 ⋅ 퐼flows; this requires a least-action principle.

• Since the flows of CA carrying the label maps satisfy an Euler-equation for a least-action principle, we call it geodesic positioning.

Healthy Disease

Hamilton’s Principle, Diffeomorphometry & Coordinates Hamilton’s Principle of Least Action • Action Integral min , 1 푡 푡 휙 ∫0 퐿 휙 휙̇ 푑푑 퐿퐿퐿퐿퐿퐿퐿퐿퐿퐿 1 −1 2 • Euler-Lagrange equation for2 휙 ̇ diffeomorphism푡∘휙푡 푉 densities: (p has a density with respect to Lebesgue measure)

= 0 푑 푇 − 푝푡 − 퐷푣푡 ∘ 휙푡 푝푡 푑푑= , ( ) _

Miller, Trouve, Younes, Geodesics푡 Shooting for 푡Computational Anatomy, 2006, J. Math Imaging. 푣 ∫ 퐾 ⋅ 휙 푥 푝 � 푥 푑�

= 0 푑 푇 − 푝푡 − 퐷푣푡 ∘ 휙푡 푝푡 푑푑 Diffeomorphometry

• Least-action geodesic flows satisfy Euler. The “geodesic length” min | | gives the metric on the anatomical1 orbit.−1 0 ̇푡 푡 푉 ∫ 휙 ∘ 휙 푑푑 - The action on the orbit is “positioning”:

- The initial tangent space velocity of the 휙 ⋅ 퐼 = are “coordinates” in this Riemannian space. 0 0 푣 휙̇

Miller, Trouve, Younes, Geodesic Positioning and Diffeomorphometry, 2013, Technology. 28 Coordinates are determined by the metric, i.e. the law of motion of the geodesics.

Coordinates

π /2 (−+ 1, 1) Coordinates: Dense Image Matching

( ) = 퐼𝑎푎�푎 , 3 푝0 푥 퐷 휙 푥 퐼푡𝑡�푡푡 ∘ 휙 푥 − 퐼𝑎푎�푎 푥 푥 ∈ 푅

퐼푡𝑡�푡푡 Coordinates for positioning Human Anatomy are infinite dimensional. The initial vector field _0 is in a smooth (Sobolev space, two derivatives) and therefore푣 we can do statistics using Gaussian random field models.

We have reduced the millions of voxels to a parametric representation indexed to the templates. Neuroinformatics&BrainClouds in the NSF XSEDE Computational Anatomy Gateway

Application of Positioning

WWW.MRICLOUD.ORG

Brain Atlases

Brain GPS Cloud Database 10,000 Neuro Brain Cloud Pediatric Geriatric Machine Learning

Miller, Faria, Oishi, Mori, High Throughput Neuroinformatics”. Frontiers Neuroinfromatics,, 2013. 8/20/2015 HIGH THROUGHPUT PARSING

Superior parietal gyrus Superior frontal gyrus Middle frontal gyrus Inferior frontal gyrus Precentral gyrus Poscentral gyrus Angular gyrus Pre-cuneus gyrus Cuneus gyrus GPS Coordinates Lingual gyrus Modalities Atlas T1,T2,DWI, Amygdala Corticospinal tract Caudate Internal capsule PET, fMRI Globus Pallidum Thalamic radiation Hippocampus Corona radiatia Putamen Fornix Thalamus Superior longitudinal fasciculus Red Nucleus Inferior front-occipital fasciculus Substancia Nigra Corpus Callosum Hypothalamus External capsule Nucleus Accumbens Uncinate fasciculus Dentate Gyrus Miller, Faria, Oishi, Mori, High Throughput Neuroinformatics”. Frontiers Neuroinfromatics,, 2013. T1 Gray matter: Aging Flow of Atrophy in Medial Temporal Lobe Associated to Alzheimer’s Disease

The diffeomorphometry of temporal lobe structures in preclinical Alzheimer's disease , Neuroimage Clinical, Miller, Younes, Albert et al., 2013. Changepoint model in Alzheimer’s disease temporal lobe, Neuroimage Clinical, Younes, Albert, Miller, 2014. Frontiers in Bioengineering and Biotechnology, Network Neurodegeneration in Alzheimer’s disease via MRI based shape diffeomorphometry and high-field atlasing. Miller,et al.,2015 BIOCARD: Predictors of Cognitive Decline Among Normal Individuals Johns Hopkins, PI: Marilyn Albert

Almost all subjects were imaged before clinical symptom.

17 Symptomatic Subjects Scans x x x x x 50 Preclinical Subjects Scans x x x x

300 Control Subjects clinical Scans x x x x symptom time Integrating High Field Atlasing with Populations

Subject1 Subject2 Subject3

Controls Subject1

Population Template 휑 −1 휑

Disease

Generalized Linear Mixed-Effects Model

ysvj ( ):diffeomorphometry coordinate marker subject (s), image (j), coordinate (v)

=+++αα′ H0 : control yvj ( s ) v v age j () s NUIS noise icv, gender

′ H1 : disease yvj ( s )=++αα v ( v′ βv )agej ( s ) + NUIS + noise

(Mixed effect: noise across subjects >> noise within subject time-series)

H1 H0 Likelihood ratio test statistic SL vv = − L v is computed with P-values associated to test-statistic and family-wise error rates (FWER 5%) * calculated by evaluating the maximum SS maxv v

P-values computed using permutation sampling running until 10% accuracy with high probability. The maximum value S* is compared to the same computation a large number of times, for randomly assigned group labels. The p-value is the fraction of times the values of S* computed with true groups is larger than that obtained with permuted groups.

Family wise error rate plots of significant markers is calculated via permutation testing as well providing a conservative estimate of the set of markers on which the null hypothesis is not valid, defined by D= {v: S >q*} where q* is the 95 percentile of value over permutations v (Nichols and Hayasaka, 2003).

Medial Temporal Lobe:

AM, ERC, HI

20% Atrophy FWER 5% Braak & Braak

Lateral Sulcal region Frontiers in Bioengineering and Biotechnology, Network Neurodegeneration in Alzheimer’s disease via MRI based shape diffeomorphometry and high-field atlasing. Miller, et al.,2015

Frontiers in Bioengineering and Biotechnology, Network Neurodegeneration in Alzheimer’s disease via MRI based shape diffeomorphometry and high-field atlasing. Miller, et al.,2015 What is the progression of atrophy across the medial temporal lobe network?

Changepoint Model Estimate Changepoint Time Before Symptom

age changepoint symptom ∆

Generalized linear mixed effects model: mean-field at each vertex given by changepoint model. Changepoint model in Alzheimer’s disease temporal lobe, Neuroimage Clinical, Younes, Albert, Miller, 2014. Changepoint Model p-Value and Estimated Ordering

Amydala** Hippo ∆=2.6 +−1.75 ∆=2.8 ± 1.5 ∆ = 2.6+− 2.5 ∆=3.8 ± 2.5 ECR *** ∆=8.0± 2.5 ∆ = 9.0± 2.9

Changepoint model in Alzheimer’s disease temporal lobe, Neuroimage Clinical, Younes, Albert, Miller, 2014. Changepoint Model ERC 8-10 years < Hippocampus, Amygdala 3-5 years

Clinical Frontiers in Bioengineering and Biotechnology, Network Neurodegeneration in Alzheimer’s disease via MRI based shape diffeomorphometry and high-fieldSymptom atlasing. Miller, Time et al.,2015 Our Challenge Crossing Scales Thank-you