Computational Intelligence for Neurosciencecig.fi.upm.es/.../neuroscience_DS09_Porto.pdf · Computed Axial Tomography (CAT) Positron Emission Tomography (PET) Magnetic Res. Imaging

Intro PattRecog Simulation Optimization Conclusions

COMPUTATIONAL INTELLIGENCE

FOR NEUROSCIENCE

Concha Bielza, Pedro Larranaga

Departamento de Inteligencia ArtificialUniversidad Politecnica de Madrid

Discovery Science and Algorithmic Learning Theory - 2009Porto, October 3, 2009

C. Bielza, P. Larranaga Computational Intelligence for Neuroscience


Outline

1 Introduction

2 Pattern recognitionNeuroimaging-omicsClustering of neuronsClassification of neurons

3 Computer simulation of dendritic morphologyDendritic morphologySimulation models of dendritic morphologyComparing virtual and real cells

4 Parameter and structural optimization in neuronal and brain modelsCompartmental modelBrain networks

5 ConclusionsChallengingMore material



Outline

1 Introduction







Introduction


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Introduction


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Introduction


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Neuroscience

Neuroscience, the science of the brainGoal: understand the relationship between the physical brain and the functionalmind

—how we perceive, move, think, and remember

A principle: all behavior is an expression of neural activity

Involves answers to scientific fundamental questions:

How does the brain develop?Are specific mental processes located in specific brain regions?How do nerve cells in the brain communicate with one another?How do different patterns of interconnections give rise to differentperceptions and motor acts?How is communication between neurons modified by experience?How is it altered by diseases or drugs?



The human brain

Brain

real sagittal view

The most complex organ of our central nervous system and the most complexbiological structure known

Weight = 1.5kg, width = 140 mm, length = 167mm, height = 93mm

Consumes 20 % of total body oxygen

Stops growing at age 18



The human brain

Brain regions

regions lobes

Neuroanatomists distinguish main regions. Each has a complex internal structure

Left-right hemispheres covered by a thin layer of gray matter known as thecerebral cortex

Cerebral cortex, the most recently evolved region of the vertebrate brain, dividedinto four areas



The human brain

Brain areas: cerebral cortex

Some areas, such as the cortex and cerebellum, consist of layers, folded to fitwithin the available space

In mammals, neocortex: complex 6-layered structure, greatly enlarged inprimates, especially frontal lobe part (in humans, extreme enlargement).Concerned with the most evolved human behavior

Outermost=layer 1, innermost=layer 6



The human brain

Functions of each area (as currently understood)Medulla: sensory and motor functions

Cerebellum: fine motor coordination and body movement, posture, and balance(not needed, but it makes actions hesitant and clumsy)

Thalamus: acts as a switching center for nerve messages

Hypothalamus: control of sleep/wake cycles, eating and drinking, hormone

Hippocampus: involved in memory storage

Olfactory bulb: processes olfactory sensory signals



The human brain

Functions of cortex (as currently understood)

Occipital lobe: visual information

Temporal lobe: auditory signals, processing language, meaning of words

Parietal lobe: touch, taste, pressure, pain, temperature

Frontal lobe: motor activity, integration of muscle activity, speech, thought

Remaining parts associated with higher thought processes, planning, memory,personality and other human activities



The human brain

Brain at microscopic level

Composed of neurons, blood vessels, glial cells (supporting cells of the CNS)

Neuron is the basic structural and functional unit of the nervous system –neurondoctrine– (S. Ramon y Cajal, late 19th century)

Just 4 microns thick→ could fit 30,000 neurons on the head of a pin

∼100,000 million= 1011 interconnected neurons



The neuron

3 parts of a neuron

1 Dendrites receive info from another cell and transmit the message to soma2 Cell body (or soma) contains the nucleus, mitochondria and other organelles

typical of eukaryotic cells3 Axon conducts messages away to the next neuron via a specialized structure

–synapse–Axons fill most of the space in the brain→ >150,000 km in the human brain!!

Each neuron connected to 1,000 neighboring neurons

10,000 synaptic connections each→ 3 · 1014 synapses (adult) and 1015 (child)



The neuron

Variable in size and shapeNeurons are more varied than cells in any other part of the body



The neuron

Different shapes for different functions?

Pyramidal activate other neurons, sometimes making connections far away→ long axons to carry theelectrical impulses

Interneurons (e.g., chandelier, double bouquet, spiny stellate, basket cells) create network interactionsbetween neighboring neurons→ short dendrites and axons



The neuron

Synapse: junction between 2 neurons

Messages travel within the neuron as electrochemical impulses called actionpotentials, lasting less than a thousandth of a second at 1-100 m/s

Action potential arrives at a synapse and causes a chemical called aneurotransmitter, stored in small synaptic vesicles, to be released

Neurotransmitter binds to receptor molecules in the membrane of the target cell

Excitatory receptors (↑ rate of action potentials in the target cell) vs. inhibitory

Parkinson’s disease has a deficiency of the neurotransmitter dopamine. Alcoholweakens connections between neurons. Drugs such as caffeine, nicotine, heroin,cocaine, Prozac, act on some particular neurotransmitters



The neuron

SynapseYour brain generates nearly 25 watts of power while you’re awake, which isenough to light up a light bulb

—-See video



The neuron

Special parts involved in synapses: spines

Spines are found on the dendrites of most principal neurons in the brain

Synapses typically formed on dendritic spines (discovered by Ramon y Cajal)

Many different shapes too. Spines with strong synaptic contacts typically have alarge spine head

Dendritic spines are very “plastic”, i.e. change significantly in shape, volume, andnumber in small periods

Spine plasticity is implicated in motivation, learning, and memory

—-See video



Technology to help


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Technology to help


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Technology to help


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Observing the neurons

Optical (or light) microscope. Stain the tissue

Magnify image up to 2000 times Golgi’s method (1873) stains some cellsat random avoiding much overlap



Observing the neurons

Modern electron microscope

Magnify image up to 2 million times 3D from multiple 2D images



“Visualizing” mental activities from brain images

Electroencephalography (EEG): electrical activity directly

with electrodes predictive maps

Frequency analysis of the signals in the different bands to reveal patterns

Epilepsy, sleep disorders (narcolepsy), for completely paralysed users (ALS) tointeract with the environment through imaginary hand movement




Electrical activity indirectly

Computed Axial Tomography (CAT) Positron Emission Tomography (PET) Magnetic Res. Imaging (MRI)

Functional NIR Single Photon Emission Computed Functional MRI (fMRI)

Spectroscopy (fNIRS) Tomography (SPECT)




Electrical activity indirectly

fMRI fNIRS 3D (jazz) Integration

Changes in blood flow (SPECT, fMRI) or metabolic activity (PET).Reduced flow, less energy consumed = injured sites. Flow changes tocompensate for the increased metabolic demands of the area being used

Which brain structures are activated –structural info– and how –functional info–when performing different tasks (sound, movie, picture, press a button,improvising jazz...). Cognitive processes, causes of neuro-degenerative diseases

EEG: high temporal resolution (millisecond), but poor spatial resolution. fMRI:great 3D spatial resolution, but slow temporal resolution (seconds and minutes)→ Integrate methods

3D images —See 2 animations



Activate/inactivate genes...

in specific parts of the brain and see the effects

Identify which genes contribute to disorders and predict an individual’ssusceptibility

We can experiment with much simpler systems because many properties ofneurons are maintained across species



Efforts today?


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Efforts today?


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Efforts today?


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Reverse-engineer the brain

One of the 14 grand challenges for Engineeringthat will influence science and technology in the 21st century –National Academy ofEngineering in 2009, at the request of the NSF: http://www.engineeringchallenges.org

1 Make solar energy economical2 Provide energy from fusion3 Develop carbon sequestration methods4 Manage the nitrogen cycle5 Provide access to clean water6 Restore and improve urban infrastructure7 Advance health informatics8 Engineer better medicines9 Reverse-engineer the brain (the 4th in Internet votes)10 Prevent nuclear terror11 Secure cyberspace12 Enhance virtual reality13 Advance personalized learning14 Engineer the tools of scientific discovery




One of the 14 grand challengesEngineers and neuroscientists should work together

Brain and computers: devices for processing info, but differently (optimized fordifferent things: face recognition vs. many sums)

Using computers to study the brain: model groups of neurons or specific parts(eqns describing electrochemical activity)

...but not a realistic computational simulation of the entire nervous system tounderstand how brains perform computation

Attempts to build (powerful) computers that operate on brainlike principles,replicating its communication skills, but to date without success

Supercomputing designs inspired by brain-like connectivity (e.g. IBM Blue Gene)




One of the 14 grand challenges

Some advances: neural prostheses to restore damaged hearing (cochlearimplants), sight (artificial retinas), allow movement, communicationBCIs: read the thoughts of paralyzed patients and translate into commands likemoving a cursor on a computer screen



Blue Brain Project

Founded in 2005 by the Brain and Mind Institute of the Ecole Polytechnique inLausanne (Switzerland), directed by Henry Markram

An attempt to reverse-engineer the mammalian brain, in order to understandbrain function and dysfunction through detailed simulations

Between 1995 and 2005, Markram had mapped the types of neurons and theirconnections in a rat neocortical column, the smallest functional unit of theneocortex

In Dec’2006, the column was simulated (only 10,000 neurons; 60,000 in humans)

∼2 million columns in humans, 2mm tall

Markram predicts it to be built within the next 10 years



UPM+IC as partners of BBP

At the end of 2008, Universidad Politecnica de Madrid (UPM) and InstitutoCajal (IC) from the Spanish Research Council –subproject Cajal Blue Brain,till 2018

UPM, including Madrid Supercomputing and Visualization Center: data analysis,optimization and visualization

IC: morphology and function of neuronal cells

Cooperation from multiple disciplines: image analysis, machine learning,neuroscience, network analysis, high-performance computing...

Problems where machine learning can contribute –some already started(highlighted as green blocks during the talk)




At the end of 2008, Universidad Politecnica de Madrid (UPM) and InstitutoCajal (IC) from the Spanish Research Council –subproject Cajal Blue Brain,till 2018

UPM, including Madrid Supercomputing and Visualization Center: data analysis,optimization and visualization

IC: morphology and function of neuronal cells

Cooperation from multiple disciplines: image analysis, machine learning,neuroscience, network analysis, high-performance computing...

Problems where machine learning can contribute –some already started(highlighted as green blocks during the talk)




UPM IC



Computational intelligence

Supervised classification

X1 . . . Xn C(x (1), c(1)) x (1)

1 . . . x (1)n c(1)

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(x (N), c(N)) x (N)1 . . . x (N)

n c(N)

x (N+1) x (N+1)1 . . . x (N+1)

n ???

Unsupervised classification

X1 . . . Xn

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n




Supervised classification

X1 . . . Xn C(x (1), c(1)) x (1)

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. . . . . . . . .

(x (N), c(N)) x (N)1 . . . x (N)

n c(N)

x (N+1) x (N+1)1 . . . x (N+1)

n ???

Unsupervised classification

X1 . . . Xn

x (1) x (1)1 . . . x (1)

n. . . . . .

x (N) x (N)1 . . . x (N)

n




Discriminant analysis

Classification trees

Bayesian classifiers

K-nn classifiers

Logistic regression

Support vector machines

Bayesian networks

Artificial neural networks

Rule induction

Markov random fields

Clustering

Regularized linear regression

Feature subset selection

Optimization techniques

Simulation models

...




DifficultiesVariable C continuous or discrete

Variables X ’s too

Variable C is a vector

Noise in the data

2D and 3D data

Dynamic data

High-dim data (e.g. 105 voxels)

Much more variables than samples

Different scales: macrostructures (circuits, brain, CNS), microstructures (neuron,molecule)

Multimodal data: electrochemical, morphological, microarrays, neuroimaging...

Highly connected elements

High-processing requirements

Difficult to generalize (models for each subject?)



Ethics

Discovering how the brain works will offer rewards beyond building smartercomputers...

A world without pain and depressions

Reading others’ minds

A world without lies

Turn murderers into good people. Fuzzy frontiers. Difficult to program a brain tobe a banker or a robber⇒ [what is B. Madoff?]

Modify people’s brains. Make them to see things they in fact they don’t see.Delete selectively some traumatic memories [war experiences]

Alter children brains to influence their education, choosing their personality andprofessional vocation

Where to put the limits?



Ethics











Ethics











Ethics











Ethics











Ethics










Intro PattRecog Simulation Optimization Conclusions Neuroimaging -omics Clustering Classification

Outline

1 Introduction







Neuroimaging

Interdisciplinary field

Neuroimaging as an interdisciplinary field at the intersection of imageprocessing, computer science, physics, statistics and neurosciences

Investigate mental activities in healthy as well as in diseased situations

Two classes of images:Anatomical or structural images: Brain structures MRI and SPECTFunctional images: changes –measured directly (MEG) or indirectly (fMRI) and (PET)–in neuronalpopulation activity, provoked by sensory stimulations or during cognitive tasks

Topics

Introduction: Classes of images and examples of problems to be solved

PreprocessingVoxel (pixel) (set) selection. Region of interest (ROI)Dimensionality reduction via feature extractionDimensionality reduction via feature selection

ModelingDiscovering associationsUnsupervised classificationSupervised classificationRegression3D ultrastructure of the cortical column



Neuroimaging

Image. Voxels. Spatial. Temporal. Patients



Neuroimaging

Introduction. Examples of problems to be solved

Differential diagnosis between Alzheimer’s disease (AD)and frontotemporal dementia (FTD), the two most frequentneurodegenerative cognitive disorders

Diagnosis of early states of Alzheimer dis-ease

Separation of cocaine addicted subjectsversus non-drug controls subjects



Neuroimaging

Introduction. Examples of problems to be solved

Gender-related differentiation of the corpuscallosum based on discriminative morpho-metric characteristics between anatomicalbrain structures

Brain reading: classify patterns of fMRIactivation

Predicting activation of the brain afterhearing a word



Neuroimaging

Introduction. Difficulties in modeling

Few examples: 10 - 100

Many features: 104 - 105

Noise:

The scannerThe brainThe patient

Intra-variabilityInter-variability



Neuroimaging

Preprocessing

Spatial normalization because of variations of brain volume, shape and positionfrom one patient to another (Statistical Parametric Mapping Software (SPM2))

High dimensional data (e.g. in 3D images: 128 × 128 × n, where n is thenumber of slices)

Voxel (pixel) (set) selection. Region of interest (ROI)Dimensionality reduction via feature extractionDimensionality reduction via feature selection



Neuroimaging

Preprocessing. Univariate voxel selection. Where is the signal?



NeuroimagingPreprocessing. Univariate voxel selection

Suboptimal if correlation among voxels carries important information

Filter approaches: provide a ranking of voxels

t-test for detecting active voxels (Friston et al., 1995), scoring the voxel byits corresponding p-value (valid for a 2 class problem)F -test for classification problems with more than 2 class labelsNon-parametric tests (e.g. Mann-Whitney), after rejecting the assumptionof Gaussian densities with the Lilliefors test

Wrapper approaches: provide a ranking of voxels

Accuracy: scores the voxel by how accurately a classifier –based only onthe voxel– is able to predict correctly the examplesSearchlight accuracy: the same as accuracy but instead of using the datafrom a single voxel, we use the data from the voxel and its immediatelyadjacent neighbours in three dimensions

Multiple comparison criteria

From the ranking decide on how many of the top-ranked voxels to useMultiple testing problem: (a) adjusting by (Bonferroni (1936)) or by(Benjamini, Hochberg (1995)) corrections (b) controlling the fraction offalse positive rate (false discovery rate) (Genovesse et al. 2002)



NeuroimagingPreprocessing. Voxel sets and region of interest (ROI)

Voxel sets: Dynamic recursive partitioning (DRP) Kontos et al. (2009)

DRP partitions the two-dimensional image adaptively into progressivelysmaller subregions until statistically significant discriminative regions aredetected

By performing statistical tests on group of pixels rather than on individualpixels, the number of statistical tests is effectively reducedThe average value over the group of pixels becomes the value of thevariable (feature)

Region of interest (ROI)

ROIs as the result of the process of partitioning the digital image intomultiple segments (set of voxels (pixels))Feature value as the average of the values over the voxels (pixels) in suchROIClustering, edge detection, level set, watershed transformation, .....



Neuroimaging

Preprocessing. Dimensionality reduction via feature extraction

Ignore the class label

Principal Component Analysis (PCA) (Hansen et al. 1999): the Meigenvectors with largest eigenvalues of the covariance matrix (fMRIimages: n ≥ 104 and Σ size is n2)

Singular Value Decomposition (SVD) (Bai et al. 2007): Given Xn×m thedata set, obtain Zn×k and Wk×m with k << n such thatminZ ,W ||X − ZW ||2 where k is the rank of the approximation

Independent Component Analysis (ICA) (McKeown et al. 1998):



Neuroimaging

Preprocessing. Dimensionality reduction via feature extraction

Class label taken into account

Partial Least Squares (PLS) (McIntosh and Lobaugh, 2004) finds a linearmodel by projecting the predicted variables Yn×p and the observablevariables Xn×m to a new space (bilinear factor model). Given Xn×m andYn×p find T ,P,Q,E ,F such that:

X = TP t + E Y = TQt + F

where Tn×l is the factor matrix, and Pm×l , and Qp×l are the loadingmatrices. E and F are the error terms

Support Vector Decomposition Machine (SVDM) (Pereira and Gordon,2006):

minZ ,W ,Θ||X − ZW ||2 + f (Θ)

This objective trades reconstruction error (the first term) with a bound onclassification error (the second term)



Neuroimaging

Preprocessing. Dimensionality reduction via feature selection

Simulated Annealing (Yeh, Fu, 2005): more than 100,000 voxels

Recursive Feature Elimination (Li et al. (2007)): at each iteration, the worsefeature was identified and removed (SVM)

Fisher Criterion Score, Relief-F, Genetic Algorithms, Ensemble (Jim et al.(2009)): from 65,166 features to dozens (SVM)



Neuroimaging

Modelling

Gaussian naive Bayes: (Mitchell et al. 2004; Pereira et al., 2009; Zhang et al., 2005)

General linear model: (Bly, 2001; Friston et al., 1995)

Hidden Markov models: (Hojen-Gorensen et al., 1999)

Kernel logistic: (Horn et al., 2009)

k -nearest neighbor: (Fletcher-Heath et al., 2001; Haxby et al., 2001; Horn et al., 2009; Mitchell et al. 2004;Zhang et al., 2005)

Linear discriminant analysis: (Cox and Savoy, 2003; Horn et al., 2009; Pereira et al., 2009; Zhang et al.,2005)

Logistic regression: (Desco et al., 2001; Horn et al., 2009; Pererira et al., 2009)

Mixture of Gaussians (EM): (Desco et al., 2001; Tohka et al., 2007)

Multilayer perceptron: (Chaplot et al, 2006; El-Sayed et al., 2009; Horn et al., 2009)

Probabilistic graphical models: (Burge and Lane, 2007; Chen and Herskovits, 2007; Herkovits et al., 2004;Sun and Tang, 2009)

Sparse regression: (Carroll et al. 2009; Valdes-Sosa et al., 2005; van Gerven et al., 2009; Yamashita et al.,2008)

Support vector machine: (Chaplot et al., 2006; Cox and Savoy, 2003; El-Sayed et al., 2009; Horn et al.,2009; Jim et al., 2009; Li et al., 2007; Mitchell et al. 2004; Pereira et al., 2009; Zhang et al., 2005)



Neuroimaging

Discovering associations. Probabilistic graphical model (Burge and Lane 2007)

Bayesian network representing the relationships among ROIsNodes: groups of voxels together in a ROI (hierarchically related; activationas the average of voxel activation)Conditional probability tables: smoothing (small sample)Structure learning: Bayesian Dirichlet equivalence criteria (BDe)



NeuroimagingUnsupervised classification. Genetic algorithms for finite mixture models (Tohkaet al., 2007)

Overcome the dependency of the expectation-maximization (EM) algorithmregarding its initialization

Finite mixture model: Given xi ∈ Rd with i ∈ {1, ..., n}, n number of voxels

f (x|Θ) =K∑

j=1

πj fj (x|θj )

To find Θ the maximum likelihood estimation of Θ the following optimizationproblem has to be solved: Θ = arg maxΘL(x1, ..., xn|Θ)

The EM algorithm is an standard approach (trapped in local optima)

Genetic algorithms (GAs) with real code



Neuroimaging

Supervised classification. Comparing classifiers and classifier versusphysicians (Horn et al. 2009)

Automatic method for returning the probability that a patient suffers fromAlzheimer’s disease (AD) or frontotemporal dementia (FTD)

82 AD and 91 FTD patients characterized by 116 descriptors (average activity inROIs)

Single photon emission computed tomography (SPECT) images

Leave-one-out cross-validation



NeuroimagingRegression. Sparse Regression (Carroll et al. 2009)

2007 Pittsburgh Brain Activity Interpretation Competition (PBAIC)

fMRI data for the 33,000-35,000 voxels over 704 time points, 24 real-valuedresponse variables

Elastic net (Zou and Hastie, 2005): Lλ1,λ2= ||y− Xβ||22 + λ1||β||1 + λ2||β||22

LASSO (Tisbshirani, 1996): λ2 = 0Ridge regression (Hoerl and Kennard, 1970): λ1 = 0Ordinary linear regression: λ1 = 0 and λ2 = 0



Neuroimaging

3D ultrastructure of the cortical columnDecipher the wiring diagram and themap of connections at the synapticlevel of the cortical column

Electron microscopy 3D reconstructionmethods

A level of detail never reached before

Neuropil and synaptic connectivityUltrastructure of the neuropil: number and proportion of synapses; length,diameter and volume of axons, dendrites and glial; density of synaptic vesiclesper axon

Maps of synaptic connectivity: spatial distribution of synapses and spines;number of synapses per neuron —See 2 videos



Neuroimaging

Modelling. Performance versus interpretabilityPrediction performance of a model is a good measure ofmodel validityIn the sciences, interpretation remains key when applyingpredictive modeling techniquesPrediction accuracy alone does not guarantee validity



-omics

Genomics, proteomics, metabolomics. Integration of data-omics refers to Biology fields in which the objects of studyconforms a totalityGenomics (study of genome), proteomics (study ofproteome), metabolomics (study of metabolome)Neurological diseases: Alzheimer, Parkinson, Huntington,Amyotrophic Lateral Sclerosis, Creutzfeldt-Jakob...DNA microarrays, microRNA molecules, single nucleotidepolymorphisms, mass spectrometry, clinical data⇒Integrate them into a single research to study the possibleinfluences and interactions among them



-omics: Alzheimer’s disease (AD)

Alzheimer’s disease casesNeurological disorder primarily affecting the elderly that manifests throughmemory disorders, cognitive decline and loss of autonomy

17-20 million individuals affected worldwide

Every 70 seconds, someone develops Alzheimer’s

Alzheimer’s is the seventh-leading cause of death




Alzheimer’s studiesDNA microarrays: Guo et al. (2001), Lamb et al. (2006), Small et al. (2005), Konget al. (2009)

MicroRNA molecules: Lukiw et al. (2008), Wang et al. (2008)

Single nucleotide polymorphisms (SNP): Williams et al. (2009), Amouyel et al.(2009)

Mass spectrometry: Lewczuk et al. (2004), Lopez et al. (2005)

Clinical data (like Mini-Mental Status Examination score): Ray, Zhang (2009) withmicroarrays




Alzheimer’s studiesDNA microarrays: Guo et al. (2001), Lamb et al. (2006), Small et al. (2005), Konget al. (2009)

MicroRNA molecules: Lukiw et al. (2008), Wang et al. (2008)

Single nucleotide polymorphisms (SNP): Williams et al. (2009), Amouyel et al.(2009)

Mass spectrometry: Lewczuk et al. (2004), Lopez et al. (2005)

Clinical data (like Mini-Mental Status Examination score): Ray, Zhang (2009) withmicroarrays



-omics: Alzheimer’s disease

Genomics-AlzheimerGenetically complex and heterogeneous

Two types of neuropathologic lesions: (i) neurofibrillary degeneration fromintraneuronal accumulation of certain proteins; (ii) amyloid deposits fromextracellular accumulation of amyloid plaques, composed of Aβ peptides

Processes leading to form these lesions and their combined association with ADare not adequately understood

APOE on chromosome 19 is the only confirmed susceptibility locus for late-onsetAD (locus=specific location of a gene or DNA sequence on a chromosome)

Genes may have a role in more than 60 % of AD susceptibility and APOE mayaccount for as much as 50 % of this genetic susceptibility

More than 550 other genes proposed as candidates for AD susceptibility, but notconfirmed to have a role in AD pathogenesis




Genomics-AlzheimerGenetically complex and heterogeneous

Two types of neuropathologic lesions: (i) neurofibrillary degeneration fromintraneuronal accumulation of certain proteins; (ii) amyloid deposits fromextracellular accumulation of amyloid plaques, composed of Aβ peptides

Processes leading to form these lesions and their combined association with ADare not adequately understood

APOE on chromosome 19 is the only confirmed susceptibility locus for late-onsetAD (locus=specific location of a gene or DNA sequence on a chromosome)

Genes may have a role in more than 60 % of AD susceptibility and APOE mayaccount for as much as 50 % of this genetic susceptibility

More than 550 other genes proposed as candidates for AD susceptibility, but notconfirmed to have a role in AD pathogenesis




DNA microarraysSimultaneously measure thousands of gene expression levels

The most common although recent (2000) technology for AD studies




Microarrays: Kong et al. (2009)Extract the most informative features

⇒ 5 severe AD samples + 8 controls; 3,617 genes

⇒ PCA vs. ICA

⇒ Found 50 genes up-regulated and 37 down-regulated in severe AD

⇒ Unsupervised hierarchical clustering to validate the efficiency of ICA outputs todiscriminate controls and AD samples




Microarrays: Small et al. (2005)Microarrays as a powerful tool for isolating molecular differences betweenhealthy and diseased tissue, but with analytic challenges when applied to brain

Idea: generate microarray data selectively from the brain site most vulnerable toAD to maximice expression differences between AD and controls

Generate data also from a neighboring region relatively resistant to AD

Hippocampus is particularly vulnerable to AD (postmortem studies, fMRI data inliving subjects)

Regions: entorhinal cortex (EC) forms the main input to the hippocampus, themost vulnerable; dentate gyrus (DG), the most resistant




Microarrays: Small et al. (2005)Assume hypotheses: EC and DG are relevant regions and differences in ECbetween AD and controls are known to be age independent

Search for the variable(s) that best matches these hypotheses

Is some molecule differentially expressed in EC over DG, comparing AD tocontrols?

⇒ 6 diseased brains + 6 controls, obtained at autopsy⇒ 24 tissue samples

⇒ 7,610 molecules

⇒ Several ANOVA using group (AD vs. control), age (33-98 years old) andexpression levels (EC/DG)

⇒ Identified a molecule (VPS35) whose expression is abnormal in AD: it is reducedin the EC region (and it regulates Aβ peptide levels)

⇒ Validate the finding using cell culture studies




Microarrays: Small and us, 2009 In progress

Re-analyze the data differently to gain robustness (small sample size!)

Find out explicit new (or validate old) biological relationships and genes notpreviously reported

⇒ Learn a Bayesian network classifier (supervised classification task):Class={AD,control}. We use kDB structures

Naıve Bayes-based classifiers

Naıve Bayes - All variables

Selective naıve Bayes -Remove irrelevant var

Tree augmented naıveBayes - Tree with all var























C

X1 X4

X2 X3












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X2 X3












C

X1 X4

X2

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kDBExtension to allow a variable to have at most k parents (excluding the class)

Search of structure based on the (conditional) mutual information metric

0-dependence Bayesian classifier← naıve Bayes classifier1-dependence Bayesian classifier← tree augmented naıve Bayes(n − 1)-dependence Bayesian classifier← the complete Bayesianclassifier (no conditional independencies in the structure)

2DB





Induce many Bayesian classifiers by bootstrapping and assign confidence levelst to the arcs (# times each one must appear) to find robust gene interactions

Different confidence level t , different model Gt (from simple structures with a fewarcs when t ↑, to dense graphs when t ↓)⇒ Hierarchy of autoinclusive models G1 ⊇ G2 ⊇ ...Approach is a consensus feature selection on the final graph –gene interactionnetwork–

Consensus conclusions have shown to provide good results in microarray data

‘Robust arc identification’ algorithm (Armananzas et al, 2008)

Step 1. Repeat B times

Step 1.1. Randomly sample N instances with replacement

Step 1.2. Select an optimal feature subset and reduce the data set (CFS)

Step 1.3. Learn a kDB model

Step 2. Compute frequencies of all the included arcs out of the B models





Induce many Bayesian classifiers by bootstrapping and assign confidence levelst to the arcs (# times each one must appear) to find robust gene interactions

Different confidence level t , different model Gt (from simple structures with a fewarcs when t ↑, to dense graphs when t ↓)⇒ Hierarchy of autoinclusive models G1 ⊇ G2 ⊇ ...Approach is a consensus feature selection on the final graph –gene interactionnetwork–

Consensus conclusions have shown to provide good results in microarray data

‘Robust arc identification’ algorithm (Armananzas et al, 2008)

Step 1. Repeat B times

Step 1.1. Randomly sample N instances with replacement

Step 1.2. Select an optimal feature subset and reduce the data set (CFS)

Step 1.3. Learn a kDB model

Step 2. Compute frequencies of all the included arcs out of the B models



Reliable-kDB classifier –An example

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...700600500400

...100 <

...1





Gene-interaction network(s) of high reliability

⇒ 2 different analysis: EC-AD vs. EC-Control (12 samples, binary supervisedclassif problem) and EC-AD vs. EC-Control vs. DG-AD vs. DG-Control (24samples, multiclass)

⇒ k = 4,B = 10, 000, discretize into 3 intervals (up-regulated, down-regulated,baseline). t = 1, 000

⇒ 2 disconnected graphs. Genes related to neurological diseases: Huntington,Parkinson, bipolar disorder, depression→ related to AD? Some paper (2007) for Parkinson’s





Gene-interaction network(s) of high reliability

⇒ 2 different analysis: EC-AD vs. EC-Control (12 samples, binary supervisedclassif problem) and EC-AD vs. EC-Control vs. DG-AD vs. DG-Control (24samples, multiclass)

⇒ k = 4,B = 10, 000, discretize into 3 intervals (up-regulated, down-regulated,baseline). t = 1, 000

⇒ 2 disconnected graphs. Genes related to neurological diseases: Huntington,Parkinson, bipolar disorder, depression→ related to AD? Some paper (2007) for Parkinson’s




SNP (single-nucleotide polymorphism)A SNP is a DNA sequence variation occurring when a single nucleotide –A, T, C,or G– in the genome differs between members of a species (or between pairedchromosomes in an individual)

Example: 2 sequenced DNA fragments from different individuals, AAGGGA toAAGGAA, contain a difference at a single base-pair location




SNP: New markers published Sep’2009 Nature GeneticsIn addition to APOE locus, identify other loci associated with the risk oflate-onset AD

Williams et al. (2009):

529,218 SNPs involving 3,941 cases and 7,848 controlsCollections from UK, Germany, USATwo loci gave replicated evidence of association: CLU on chromosome 8(SNP rs11136000) and PICALM on chromosome 11 (SNP rs3851179)

Amouyel et al. (2009):

537,029 SNPs genotyped in 2,032 cases and 5,328 controlsCollections from France, Belgium, Finland, Italy and SpainLoci: CLU (SNPs rs2279590, rs11136000, rs9331888) and CR1 onchromosome 1 (SNPs rs6656401, rs3818361)

Information on age, sex, geographical region and disease status




SNP: New markers published Sep’2009 Nature Genetics

Chromosomalposition vs.− log10 P value

Threshold (redline) atP ≤ 9.4×10−10

with 13 SNPs

Filter FSS + logistic regression (which optional PCA to account for possiblepopulation stratification)

Additional and larger studies are required



Introduction

Golgi and Ramon y CajalNeuromorphology intensively studied after the discovery of Golgi method (Golgi,1873) named the black reaction (la reazione nera), allowing to see the entireneuron

Ramon y Cajal (1911) developed the neuron doctrine pointed out the variety ofpatterns of neurons depending on particular places and emitted hypothesis onthe role that could be played by particular forms

A better knowledge of the different neuronal populations that compose thisheterogeneous brain structure may therefore contribute to elucidating theirspecific role

Traditionally neuronal cell types have been classified using qualitative descriptorswith criteria that vary across investigators

In the recent decade several attempts to classify neurons quantitatively(objective classification) from multimodal information (physiological, molecular,morphological) have been developed



Introduction

Golgi and Ramon y Cajal



Introduction

Naming neuronsLorente de No (1938) qualitatively described classes ofinterneuronsRamon-Moliner (1958) defined types of neurons accordingto their dendritic arborisationsTyner (1975). The naming of neurons: applications oftaxonomic theory to the study of cellular populations. BrainBehaviour Evolution, 12, 75-96Rowe, Stone (1977). Naming the neurons. Classificationand naming of neurons of cat retinal ganglia cells. BrainBehaviour Evolution, 14, 185-216



Clustering methods for neurons

Neurolucida (morphological variables)



Clustering methods for neuronsNeurolucida (morphological variables)

DENDRITIC VARIABLES AXONAL VARIABLES SOMATIC VARIABLESnumber of dendrites axonal node total somatic perimeterdendritic node total total axonal length somatic areatotal dendritic length ratio of axonal length to surface somatic aspect ratioaverage length of dendrites highest order axon segment somatic compactnesstotal surface area of dendrites axonal torsion ratio somatic form factorratio of dendritic length to surface axonal planar angle ave somatic roundnessdendritic torsion ratio axonal planar angle stdv relative distance to piadendritic planar angle ave axonal local angle avedendritic planar angle stdv axonal local angle stdvdendritic local angle ave axonal spline angle avedendritic local angle stdv axonal spline angle stdvdendritic spline angle ave ave tortuosity of axonal segmentsdendritic spline angle stdv stdv of tortuosity of axonal segmentsave tortuosity of dendritic seg axonal segment length avestdv of tortuosity of dendritic seg axonal segment length stdvdendritic segment length ave ave tortuosity of axonal nodesdendritic segment length stdv stdv tortuosity of axonal nodesave tortuosity of dendritic nodes number axonal sholl sectionsstdv of tortuosity of dendritic nodes axonal sholl length at 100µmnumber of dendritic sholl sections axonal sholl length at 200µmdendritic sholl length at 50µm axonal sholl length at 300µmdendritic sholl length at 100µm axonal length density2dendritic sholl length at 150µm axonal node density2convex hull dendrite area convex hull axon areaconvex hull dendrite perimeter convex hull axon perimeterconvex hull dendrite volume convex hull axon volumeconvex hull dendrite surface area convex hull axon surface areahighest order dendritic segment k -dim axon (fractal analysis)k -dim dendrites (fractal analysis) total surface area of axon




NeuroMorpho.Org

Inventory of digitally reconstructed neurons

Morphological reconstructions are collected, published, and shared

Over two-dozen labs




NeuroMorpho.Org

CELL TYPE NUMBER CELL TYPE NUMBERAdapting Non-pyramidal cell 1 Amacrine cell 1Basket 64 Biploar 6Bitufted 47 Calbindin 18Calretinin 29 Chandelier 4Cholecystokinin 14 Climbing Fiber 2Cone 25 Dopamine 4DSCT 8 Double bouquet 9Ganglion 64 Granule 122Ia inhibitory 8 Large aspiny cell 146Lateral horn neuron 19 Martinotti 36Medium spiny 239 Modulated 12Motoneuron 100 Multipolar 29Neurogliaform 30 Neuropeptide Y 11NotReported 514 Parvalbumin 28Purkinje 10 Pyramidal 3316Relay 5 Renshaw 4Reticular 1 Somatostatin 33Stellate 33 Tangential 13Tripolar 25 Uniglomerular projection neuron 233Von economo 29




Main interneuron types of layers II-IV




State of the art methodsHierarchical clustering (Ward’s method + Euclideandistance)

Iterated cluster analysis

K -meansEM algorithm with Gaussian finite mixture




Hierarchical clustering (Ward’s method + Euclidean distance)

AUTHORS NEURONS CLUSTERS VARIABLES FSSCauli et al. (2000) 60 rat neocortical 3 clusters 14 electrophysiology NoPNAS interneurons Thorndike 9 cellular receptors

21 glutamate receptors





AUTHORS NEURONS CLUSTERS VARIABLES FSSKozloski et al. (2001) 15 mouse primary 4 clusters 18 morphological PCAScience visual cortex 11 selected

from layer 5 5 PCs



Clustering methods for neuronsHierarchical clustering (Ward’s method + Euclidean distance). Iterated clusteranalysis

AUTHORS NEURONS CLUSTERS VARIABLES FSSHelmstaedter et al. (2009) 39 interneurons 9 clusters 11: electrical + NoCerebral Cortex + 4 pyramidal Cutoff (4 pyramidal) dendrite +

from layer 2, 3 Weights random axonal



Clustering methods for neuronsHierarchical clustering (Ward’s method + Euclidean distance) and K -means

AUTHORS NEURONS CLUSTERS VARIABLES FSSKaragiannis et al. (2009) 200 NPY cells Hierarchical (6) 1 laminar location NoThe Journal of interneurons K -means (5) 10 molecularNeuroscience Silhouette 32 electrophy.





AUTHORS NEURONS CLUSTERS VARIABLES FSSWong et al. (2002) 36 drosophila 6 clusters 21 morpho. PCACell Protocerebrum 17 selec.

Pyramidal cells 7 PCsTsiola et al. (2003) 158 mouse primary 5 clusters 33 morpho. PCAThe Journal of Comparative visual cortex 14 selec.Neurology from layer 5 5 PCsHelmstaedter et al. (2009) 51 interneurons 4 clusters 5 morpho. NoCerebral Cortex layer 2,3 Thorndike axonal

rat cortexHelmstaedter et al. (2009) 64 interneurons 7 clusters 101 morpho. NoCerebral Cortex layer 2,3 validity dendritic

rat cortex 5 pyramidal

Tamas et al. (2003), Science

Karube et al. (2004), Journal of Neuroscience

Halabisky et al. (2006), Journal of Neurophysiology

Gallopin et al. (2006), Cerebral Cortex

David et al. (2007), Journal of Neuroscience

Andjelic et al. (2009), Journal of Neurophysiology



Clustering methods for neuronsHierarchical clustering + K -means + EM Gaussian finite-mixture. Guerra et al.(2009)

231 cells from cerebral cortex: 216 interneurons (13 of them Chandelier) + 15pyramidal (Columbia University)

Neurolucida: 67 variables

Chandelier and pyramidal used for validating the results

No feature subset selection

Hierarchical: Unable to group Chandelier neither pyramidal neurons

K -means: 12 of the Chandelier in the same group, the pyramidal no more than 3in the same group

EM: 12 of the Chandelier in the same group, 5 of the pyramidal in the same group

Feature subset selection: from 67 to 48 variables

Hierarchical: bad results with both types of cells

K -means: almost all Chandeliers in the same group, 8 of the pyramidal in thesame group

EM: all Chandeliers in the same group, 9 of the pyramidal in the same group



Supervised classification of neurons


It is expected that in the near future (with the help of electron microscopy) thenumber of neurons digitally reconstructed will increase

Helpful to have a supervised classification model to automatically classify theneurons

The two principal neuronal types of the cerebral cortex are:

Pyramidal cells (≈ 80 % of the total population)Interneurons (≈ 20 % of the total population): a heterogeneous group

The different approaches will be presented in two groups:

Supervised classification of neurons via clusteringSupervised classification of neurons via supervised methods




Supervised classification of neurons via clustering

AUTHORS CLASSES METHOD VARIABLES FSSBenavides et al. (2005) 90 (30× 3) pyramidal Hierarchical: 156 morphological PCACerebral Cortex Three cortical regions Ward’s method 11 features

Mouse neocortex Euclidean distance




Supervised classification of neurons via clustering

AUTHORS CLASSES METHOD VARIABLES FSSDumitriu et al. (2007) 39 interneurons Hierarchical: 98 morpho. + PCA:Cerebral Cortex 3 subtypes: Ward’s method 8 electr. 61 morpho.

PV, NPY, and SOM Euclidean distance 9 morpho. + 4 electr.




Supervised classification of neurons via supervised methods

AUTHORS CLASSES METHOD VARIABLES FSSMarin et al. (2002) 161 projection cells LDA 37 morpho. + 15 selectedCell 10 classes 40 repeated 5-cv 8 electr.

Error 7.8± 0.01




Supervised classification of neurons via superv. methods. Guerra et al. (2009)

Objective: Machine learning classification methods for discriminate betweeninterneurons and pyramidal cells

Database containing 327 cells (199 interneurons + 128 pyramidal) fromColumbia University

Each cell characterized with 65 morphological variables (29 dendritic variables,29 axonal variables, 7 somatic variables) from Neurolucida software

Algorithms for supervised classifications (Weka)

Hierarchical clustering (Ward’s method + Euclidean distance)Naive BayesClassification treek -nearest neighborsMulti-layer perceptronLogistic regression

Feature subset selection (FSS):

Multivariate filtering (correlation-based feature selection (CFS)) versuswrapperForward versus backward versus genetic algorithms




Supervised classification of neurons via superv. methods. Guerra et al. (2009)Validation: 10-cv

NO FSS #Hierarchical clustering 59.33 65Naive Bayes 80.73± 10.44 65Classification tree 84.40± 3.84 65k -nearest neighbors 83.18± 7.15 65Multi-layer perceptron (1) 87.46± 9.06 65Logistic regression 82.26± 7.36 65

MULTIVARIATE FILTERING (CFS)Forward # Backward # Genetic algorithms #

Hierarchical clustering 77.68 10 71.25 17 79.82 16Naive Bayes 79.82± 9.86 10 79.51± 9.74 17 80.43± 7.07 16Classification tree (2) 82.26± 7.17 9 88.07± 6.09 11 81.65± 7.24 6k -nearest neighbors 83.79± 9.55 10 84.71± 6.03 17 85.01± 5.60 16Multi-layer perceptron 82.57± 9.54 10 87.77± 6.36 17 82.26± 9.17 16Logistic regression 82.26± 9.82 10 85.63± 8.56 17 83.49± 9.45 16

WRAPPERForward # Backward # Genetic algorithms #

Naive Bayes (3) 87.16± 6.34 8 83.18± 9.12 50 83.49± 8.55 23Classification tree (4,5) 86.85± 5.29 7 87.16± 5.83 12 86.85± 4.72 13k -nearest neighbors (6,7) 89.30± 7.58 6 86.85± 6.26 51 87.46± 5.68 34Multi-layer perceptron (8,9) 88.07± 4.99 10 88.07± 8.27 61 87.46± 6.26 37Logistic regression (10,11) 85.63± 9.79 7 84.71± 7.54 59 91.13± 5.95 33


Intro PattRecog Simulation Optimization Conclusions Morphology Models Validation

Outline

1 Introduction







Computer simulation of dendritic morphology

Dendritic morphologyDendritic branching influenced by complex interaction of synaptic activity,intracellular transport, extracellularly initiated signaling cascades, membranetension and electrical activity

Tree shapes help determine both interconnectivity and functional roles ofneurons

How and why vastly different shapes arise is still largely unknown

Understanding how formed in the brain, learn about their normal function andwhy they are often malformed in neurological diseases or under the effects ofsome drugs (cocaine, morphine)




Dendritic morphologyNeurons typically grouped in morphological classes based on prominentgeometrical features of their arborizations

E.g.: uniform distribution in space (stellate), planar (retinal ganglion cells), orpolarized structure (basal and apical in pyramidal)

stellate retinal ganglion pyramidal Purkinje

Can be specific to location in the brain: pyramidal are different in hippocampusand neocortex, and within the cortex, in different lobes (occipital or prefrontal)and layers (II or V)

An extreme: only present in specific regions, like Purkinje cells in cerebellum

There are no 2 neurons with the same morphology, although there existbranching patterns

⇒ Anatomical characterization is statistical in nature




Computational modelingConstruct models that can simulate the huge variety of dendritic morphology

Synthetic neurons are generated within a virtual environment from amathematical-statistical model based on experimental measures collected fromreal traced cells

Simulated neurons should be indistinguishable (by statistical analysis or expertvisual inspection) from real cells

Steps1 Measure from real cells different parameters controlling branching behaviour2 Model these measures as statistical distributions3 Design a simulation model to account for all the parameters together and run it4 Compare formed virtual trees to reality




Computational modelingConstruct models that can simulate the huge variety of dendritic morphology

Synthetic neurons are generated within a virtual environment from amathematical-statistical model based on experimental measures collected fromreal traced cells

Simulated neurons should be indistinguishable (by statistical analysis or expertvisual inspection) from real cells

Steps1 Measure from real cells different parameters controlling branching behaviour2 Model these measures as statistical distributions3 Design a simulation model to account for all the parameters together and run it4 Compare formed virtual trees to reality




Data from real cellsDatabases at http://neuromorpho.org, with 5,500 neurons and animations

—-See animation

Own data




Parameters. Donohue and Ascoli (2008)5 basic parameters: branch pathlength, taper rate, daughter ratio,parent-daughter ratio and probability of bifurcating

With every basic parameter, 3 fundamental determinants are also measured toconstrain the sampling of basic parameters according to their location within thetree: branch order (N. of bifurcations towards soma), path distance from somaand branch radius




Parameters. Torben-Nielsen et al. (2008)Basic + emergent (coming from interaction between the basic) morphologicalproperties. E.g. total dendritic length emerges from the number of stems, stemlength and individual segment lengths




Probability distribution modelsDifferent hypotheses:

Basic parameters are uniformly distributed throughout the dendritic tree(Donohue et al, 2002)

Dendritic segments are built from sequences of units of constant diameter,and distributions of the lengths of units of similar diameter is independentof location within a dendritic tree (Lindsay et al, 2007)

Different dimensions of distributions (Lindsay et al, 2007):

Univariate distributions (marginal and conditional): diameter of the childconditioned on the parent diameterBivariate: joint distribution of the parent and child diametersTrivariate: parent, child and peer diameters



Computer simulation of dendritic morphologyProbability distribution models

Different distribution models:

Discrete (Donohue and Ascoli, 2005)

Gamma, Gaussian and uniform distributions (Donohue and Ascoli, 2008)

Kernel density estimators (Lindsay et al, 2007; Torben-Nielsen et al, 2008)

f (x) =1

nh

n∑i=1

K (x − xi

h)

x1, ..., xn the sampleh=bandwith→degree of smoothing(small=spiky=undersmoothing)

Gaussian: f (x) = 1nh√

2π

∑i exp

−(x−xi )2

2h2

Bivariate:f (x, y) = 1

nhx hy

∑ni=1 K (

x−xihx

)K (y−yi

hy)

Work in progressModels to capture interrelations between morphological properties?Bayesian networks



Computer simulation of dendritic morphologyProbability distribution models

Different distribution models:

Discrete (Donohue and Ascoli, 2005)

Gamma, Gaussian and uniform distributions (Donohue and Ascoli, 2008)

Kernel density estimators (Lindsay et al, 2007; Torben-Nielsen et al, 2008)

f (x) =1

nh

n∑i=1

K (x − xi

h)

x1, ..., xn the sampleh=bandwith→degree of smoothing(small=spiky=undersmoothing)

Gaussian: f (x) = 1nh√

2π

∑i exp

−(x−xi )2

2h2

Bivariate:f (x, y) = 1

nhx hy

∑ni=1 K (

x−xihx

)K (y−yi

hy)

Work in progressModels to capture interrelations between morphological properties?Bayesian networks




Simulation procedure

Donohue and Ascoli (2005) Torben-Nielsen et al. (2008)




A recent model: NETMORPH (Koene et al, 2009) (http://www.netmorph.org)

Neuronal outgrowth is a stochastic process, where at each time step, branchingand elongation probab, direction of outgrowth, branching angles and segmentdiameters are functions with some random element (e.g. branch prob dependson dist from the soma, baseline branch rate exponentially decreases)

We can simulate:

Models of dendritic morphologiesModels of axonal morphologies

pyramidal & basket axon




A recent model: NETMORPHWe can simulate:

Network developmentSynaptic connectivity: look for sites where axon and dendrite areseparated less than a given distance...connection diagrams, freq of synapses, 3D visualizations...




Comparing virtual and real cells: shape descriptorsMost commonly used method: Sholl’s analysis [Sholl, 1953], that uses std measures(length, surface area, number of branches...). Not orientation-sensitive

Or more sophisticated morphometrics related to branch patterns, defined in(Donohue and Ascoli, 2008)

Methods for orientation of the dendritic tree but losing important geometricinformation: “principal axes”, “circular orientation”, “cartesian grid density”(Uylings et al, 1986)

Fractal analysis to describe complexity of dendritic trees: do not discriminatebetween similar complexity but different spatial morphologies (Caserta et al, 1995)

Measure based on the Hausdorff distance, insensitive to outliers (also for 3Dstructures): connected and inconn parts are indistinguishable (Mizrahi et al, 2000)




Comparing virtual and real cells: dendrogramsTransform dendritic trees into dendrograms. Traditionally by hand. Now, e.g. withcomputer-vision techniques (segmentation based on curvature, edgedetection...) (Costa, 1999,2000)

Neuron Internal contours Skeleton

Dendrogram

(vertical width indicates width...)

But comparisons are qualitative and only capture some features of the structures




Comparing virtual and real cells: an explicit distance between topologies

Comparison measure based on tree-edit distance (comp sci) (Heumann, Wittum, 2009)

Represent the topology as a tree (root=soma), assign to each vertex labels(describing the geometry of the section), compute distance between 2 trees asthe minimal cost of a feasible sequence of edit-operations –substitution,insertion, deletion– that converts T1 into T2

Dist=3

High computational cost and nodes with single label (Gillette, Grefenstette, 2009)




Comparing virtual and real cells: clustering to validate this distance

Show that this distance D discriminates between different cell classes (a prioriknown)

Use matrix of distances D between every pair of cells and then ahierarchical-Ward clustering

Distinguish CA1 and CA3 pyramidal cells from hippocampus using volume for D:

Only 1 error


Intro PattRecog Simulation Optimization Conclusions Compartmental model Brain networks

Outline

1 Introduction







Optimization

Two examples of optimization problemsNeuronal parameter optimization in compartmentalneuronal modelStructural optimization in brain networks



Neuronal parameter optimization

Compartmental modelsCompartmental models,based on a circuitrepresentation of a neuron(Hodgkin and Huxley, 1952),describe the potential alongthe dendritic tree

The model is described by asystem of ordinarydifferential equations

The model is used toreplicate the response of areal neuron to a set ofsimple current stimuli




The optimization problem in compartmental modelsThe process of identifying sets of parameters that lead to adesired electrical activity pattern in a neuron or neuralnetwork model that is not fully constrained by experimentaldata (Printz, 2007)

Related questionsChoice of an objective function or goodness measure toevaluate the possible solutionsSelection of an appropriate optimization algorithm



Neuronal parameter optimizationObjective functions

Point-to-point comparison: based on thecomparison of the electrophysiological tracesprovided by the data and the model

Feature-based: (1) spike rate; (2) anaccommodation index; (3) latency to firstspike; (4) average AP overshoot; (5) averagedepth of after hyperpolarization (AHP); (6)average AP width

Multi-objective: several feature-based criteriaat the same time

Optimization algorithms

Hand tuning: Bhalla and Bower, 1993; Foster et al., 1993; Prinz et al., 2003

Gradient descent: Bhalla and Bower, 1993

Evolutionary algorithms: Achard and De Schutter, 2006; Gerken et al., 2006;Keren et al., 2005; Pettinen et al., 2006; Vanier and Bower, 1999; Taylor andEnoka, 2004; van Geit et al., 2008

Hybrid methods: van Geit et al., 2007




Hybrid method (van Geit et al., 2007)




Multi-objective (Druckmann et al., 2007)




GEneral NEural SImulation System (GENESIS) (Bower andBeeman, 1998)



Structural optimization in brain networks

Brain networksBrain activity can be modeled as a dynamical process acting on a network(DeLucia et al., 2005)

Each vertex of the structure represents an elementary component (brainareas, groups of neurons or individual cells)

Real and artificial brain networksThe network topology is a key element for understanding the behavior of theprocess

Based on real brain networks, similar artificial brain networks can be obtainedvia optimization

The artificial brain networks should satisfy some constraints identified in the realnetwork

The similarity is measured in terms of predefined topological characteristics(structural motifs and functional motifs)




Extraction of a real brain structural connectivity network




Optimization approachStructural optimization in brain networks implies theidentification of a network topology that:

satisfies a number of constraints identified in the real brainnetwork (same number of node degrees)is optimal with respect to measure(s) defined in the spaceof networks (structural motifs and functional motifs)

Multiobjective optimization under constraints




Structural motifs and functional motifsMotifs (Milo et al, 2002) as small network building blockswhich are defined by their size and interconnectionpatternsIt is possible (Sporns and Koetter, 2004) to gain insight intothe rules governing the structure of complex networks byinvestigating their composition from motifsStructural motifs as set of brain areas and pathways thatcan potentially engage in different patterns of interactionsFunctional motifs as specific combinations of nodes andconnections (contained in the structural motifs) that may beactivated in the course of neural information processing




Structural motifs and functional motifs

A “motif” is a connected graph consisting of M vertices and a set of edges (arcs) (maximally M2 − M fordirected graphs, minimally M − 1) forming a subgraph of a larger network

For M = 2, 3, 4, 5 the corresponding numbers of motif types are 2, 13, 199 and 9,365 (Harrary andPalmer, 1973)

A “structural motif” of size M is composed of a specific set of M vertices that are linked by edges (arcs). Thename structural because a larger network could be structurally assembled from a finite set of such motifs

As different edges (arcs) become functionally engaged, different “functional motifs” emerge within a singlestructural motif




Max. functional motifs and min. structural motifs (Spornsand Kotter, 2004)

Macaque visual cortex. Genetic algorithm.N = 30,K = 311. A: maximizing functionalmotifs. B: maximizing structural motifs

The results suggest the hypothesis thatbrain networks maximize the number offunctional motifs, while the repertoire ofstructural motifs remains small

Results are consistent with the hypothesisthat highly evolved neural architectures areorganized to:

maximize functional repertoires(maximizing the number of functionalmotifs)support highly efficient integration ofinformation (minimizing the number ofstructural motifs)




Non-dominated solutions learned in each run of the genetic algorithm (bluepoints) and absolute non-dominated solutions (red points) and original network(triangle)


Intro PattRecog Simulation Optimization Conclusions Challenging More material

Outline

1 Introduction







Computational intelligence for neuroscience

Neuroscience: challenging problems in modeling,simulation and optimization

Brain as the most complex organComputational intelligence

Pattern recognitionNeuroimaging-omicsClustering of neuronsClassification of neurons

Computer simulation of dendritic morphologyParameter and structural optimization in neuronal and brainnetworks



Computational intelligence in neuroscience

ChallengingUnderstanding the human brain will have profoundconsequences for technology, health and society (twobillion people on the planet affected by mental disorder)Reverse engineering the brain and the mind has deepphilosophical consequences in addition to its practicalimplicationsHow long will it take? Depends on resources, quality andquantity of researchers, coordination, computing speed,storage capacity, automated imaging systems, ... (amulti-decade effort)Most important outcome: computational neuroscientistsarmed with knowledge and tools to contribute in the futureof humanity



Relevant conferences

NIPS, INCFNeural Information Processing Systems (NIPS)

Key words: brain imaging, cognitive science and artificial intelligence,neuroscience2009 Workshops:

Connectivity inference in neuroimagingThe curse of dimensionality problem: How can the brain solve it?

Congress of Neuroinformatics (INCF)

The International Neuroinformatics Coordinating Facility (INCF) since2005 coordinates and fosters international activities for discovery andinnovation in neuroscience and related fields14 current member countries2009 Workshops:

Advances in the automatic analysis of multi-dim dataThe neuroinformatics of neural connectivityHigh performance computing and grid infrastructure forneuroinformatics applications



Relevant competitions

INCF, DIADEM, PBAICQuantitative Single-Neuron Modeling (INCF)

Predict the timing of every spike that a neuron emits with certain precisionhttp://www.incf.org/community/competitions/spike-time-prediction/2009

Digital Reconstruction of Axonal and Dendritic Morphology (DIADEM). Still open

Automatically reconstruct (3D) neuronal morphologies. Compare againstmanually supervised reconstructions using a well-defined metrichttp://diademchallenge.org/

Pittsburgh Brain Competition (PBAIC) http://pbc.lrdc.pitt.edu/

Fall 2009: applying data mining to map the “cables of the human brain”(∼300,000 fiber streamlines) into 20-50 cables or tracts. Still open



Relevant books

G. Ascoli (ed.) (2002) Computational Neuroanatomy: Principles and Methods,Humana Press

E. De Schutter (2003) Computational Neuroscience: Trends in Research 2003,Elsevier

R. Hecht-Nielsen, T. McKenna (2003) Computational Models for Neuroscience:Human Cortical Information Processing, Springer

P. Dayan, L.F. Abbott (2005) Theoretical Neuroscience: Computational andMathematical Modeling of Neural Systems, MIT



Relevant books

S. Koslow, S. Subramaniam (eds.) (2005) Databasing the Brain: From Data toKnowledge, Wiley

L. Benuskova, N. Kasabov (2007) Computational Neurogenetic Modeling,Springer

K. Doya, S. Ishii, A. Pouget, R. Rao (eds.) (2007) Bayesian Brain: ProbabilisticApproaches to Neural Coding, MIT

J. McBrewster, F. Miller, A. Vandome (2009) Mind Uploading: Artificial NeuralNetwork, Artificial Intelligence, Neuroinformatics, Computational Neuroscience.Alphascript Press



Relevant journals

Science

Nature

Neuroinformatics

Neurocomputing

BMC Neuroscience

Journal of Neuroscience Methods

Journal of Computational Neuroscience

Mathematical Biosciences

Frontiers in Neuroscience

Bioinformatics

PLoS Computational Biology

NeuroImage

Artificial Intelligence in Medicine

Pattern Recognition Letters




FOR NEUROSCIENCE

Concha Bielza, Pedro Larranaga

Departamento de Inteligencia ArtificialUniversidad Politecnica de Madrid

Discovery Science and Algorithmic Learning Theory - 2009Porto, October 3, 2009


Documents

Computational Intelligence for Neurosciencecig.fi.upm.es/.../neuroscience_DS09_Porto.pdf · Computed Axial Tomography (CAT) Positron Emission Tomography (PET) Magnetic Res. Imaging