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

NEUROINFORMATICS AND THE COMPLEXITY OF THE BRAIN AT THE MORPHOME 1MM SCALE Michael I. Miller The Johns Hopkins University CCNS SAMSI 2015 August 2015

Supported by NIH NINDS NIH NIMH NIH NIA NIH NIBIB NSF XSEDE

Motivate the Morphome Scale Pose the Computational Anatomy Model as an Orbit under Diffeomorphisms Introduce Hamilton s Principle for defining a Geodesic 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 Temporal Electron Microscopy nano High Field 11.7T 250 mu TI 1mm fmri, DTI (3mm) CLARITY mu Two Photon Histology mu nm micron SPATIAL mm 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 Anterior Cingulate Gyrus (ACG) Mid sagittal view Thalamus (TH) Caudate (CA) Putamen (PU) Amygdala (AM) Hippocampus (HC) 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 manifolds) The shift operator from time-series is replaced by transformations acting on spatial coordinates - the finite dimensional matrix groups and the infinite dimensional diffeomorphism groups.

Matrix Group Rotation x x y y + cosθ sinθ x sn i θ cosθ y

Diffeomorphisms are Generated as Flows X φ Y 1 φ φ t ( x) t v ( φ ( x)) t φ ( x) 1 x φ v t t = v t φ t, φ 0 = identity ( x), x X is a vector field φ 1 1 0 ( x) = v ( x) dt + t φ t x Christensen, Rabbitt, Miller, 1996, Deformable Templates using Large Deformation Kinematics, IEEE Trans. Med. Imag.

v ( x) 0 v ( x) v ( x) 6 12 φ ( x) = v φ ( x) 0 6 12 φ t t t 1 ( x) = x + v φ ( x) dt 0 t t v ( x) v ( x) 18 24 v ( x) 29 24 29

We use diffeomorphisms to preserve correspondence across scales. High Field 11.7T 250 mu DTI Mori & Miller Histology mu

How do we use this stuff to study populations?

Integrating High Field Atlasing with Populations Subject1 Subject2 Subject3 Controls Subject1 φ φ 1 φ 1 φ 2 Population Template Disease

Algebraic Orbit Model of CA Morphisms: Structure Preserving Transformations φ t group action anatomy carries It physiology - DTI Matrix Fractional Anisotropy, MD diffusivity mm/s 2 (e10-4 ) - fmri BOLD (% over baseline) - Spectroscopy Metabolites Cr, Cho, NAA mm - PET %InjectDose/g or glucose metabolic rate 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 I : R R ( ϕ, I) ϕ I I ϕ 3 1 Vector fields I : R R ϕ I ( Dϕ I) ϕ 3 3 1 Jacobian DTI Tensors I : R R ϕ I ( λee ˆˆ + λ ee ˆˆ + λ ee ˆˆ ) φ 3 3 3 3 T T T 1 1 1 1 2 2 2 3 3 3 Dφe Dφe Dφe eˆ =, eˆ =, eˆ = 1 2 3 1 2 3 Dφ1e1 Dφ2e2 Dφ3e3

Positioning information between coordinate systems is a basic problem in Medical Imaging. The diffeomorphic flows position information by carrying the label maps φ I. There are many admissable flows; 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 L φ t, φ t φ 0 LLLLLLLLLL 1 2 φ t φ t 1 Euler-Lagrange equation for diffeomorphism densities: (p has a density with respect to Lebesgue measure) 1 2 V dd d dd p t Dv t T φ t p t = 0 v t = K, φ t (x) p_t x dd Miller, Trouve, Younes, Geodesics Shooting for Computational Anatomy, 2006, J. Math Imaging.

d dd p t Dv t T φ t p t = 0

Diffeomorphometry Least-action geodesic flows satisfy Euler. The geodesic length min φ 0 t φ 1 t V dd gives the metric on the anatomical orbit. - The action on the orbit is positioning : φ I - The initial tangent space velocity of the geodesics v 0 = φ 0 are coordinates in this Riemannian space. 1 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 1, /2 + 1)

Coordinates: Dense Image Matching I aaaaa p 0 (x) = D φ x I tttttt φ x I aaaaa x, x R 3 I tttttt

Coordinates for positioning Human Anatomy are infinite dimensional. The initial vector field v_0 is in a smooth Hilbert space (Sobolev space, two derivatives) and therefore 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 Cloud Database 10,000 Neuro Pediatric Geriatric Brain Cloud Brain GPS 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 Lingual gyrus Amygdala Caudate Globus Pallidum Hippocampus Putamen Thalamus Red Nucleus Substancia Nigra Hypothalamus Nucleus Accumbens Dentate Gyrus Atlas GPS Coordinates Corticospinal tract Internal capsule Thalamic radiation Corona radiatia Fornix Superior longitudinal fasciculus Inferior front-occipital fasciculus Corpus Callosum External capsule Uncinate fasciculus Miller, Faria, Oishi, Mori, High Throughput Neuroinformatics. Frontiers Neuroinfromatics,, 2013. Modalities T1,T2,DWI, PET, fmri

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. 50 Preclinical Subjects Scans x x x x 17 Symptomatic Subjects Scans x x x x x 300 Control Subjects Scans x x x x clinical symptom time

Integrating High Field Atlasing with Populations Subject1 Subject2 Subject3 Controls Subject1 φ φ 1 Population Template Disease

Generalized Linear Mixed-Effects Model y vj ( s): diffeomorphometry coordinate marker subject (s), image (j), coordinate (v) H 0 : control yvj ( s) = αv + α vage j ( s) + NUIS + noise icv, gender H : disease y ( s) = α + ( α + β ) age ( s) + NUIS + noise 1 vj v v v j (Mixed effect: noise across subjects >> noise within subject time-series)

S L L H 0 = 1 H Likelihood ratio test statistic v v v is computed with P-values associated to test-statistic and family-wise error rates (FWER 5%) * calculated by evaluating the maximum 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. S max v S v 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 * v is the 95 percentile of value over permutations (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 Hippo = 2.8 ± 1.5 = 3.8 ± 2.5 ERC *** = 8.0 ± 2.5 = 9.0 ± 2.9 Amydala ** = 2.6 + 1.75 = 2.6 + 2.5 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 Symptom Time Frontiers in Bioengineering and Biotechnology, Network Neurodegeneration in Alzheimer s disease via MRI based shape diffeomorphometry and high-field atlasing. Miller, et al.,2015

Our Challenge Crossing Scales

Thank-you