a catastrophe theory model for cognition declinedetritus.fundacioace.com/pub/talks/a catastrophe...

A Catastrophe Theory Model for Cognition DeclineThe Cognitive Network As Dependent on Metabolic Activity and

Synaptic Structure: A Trip through Cognitive Decline to Dementia

Oscar Sotolongo-Costa 1,2 L. M. Gaggero-Sager 1 F. Maestu 3

J. T. Becker 4 O. Sotolongo-Grau 5

1Departamento de Física, Facultad de Ciencias. Universidad Autónoma del Estado deMorelos. México

2”Henri Poincaré” Group of Complex Systems, University of Havana, Cuba

3Center for Biomedical Technology, Spain

4Department of Psychology, Department of Neurology, Department of Psychiatry, School ofMedicine, University of Pittsburgh, USA

5Fundació ACE. Institut Català de Neurociències Aplicades. Spain

OSG (Fundació ACE) Catastrophic Cognition Decline 1 / 19

Objective

Objective

• Find a simple mathematical model that describe the cognitivedecline through dementia


Introduction

The cognition network

• Well, first let us consider a spherical cow brain ...

Actually, this is just a topological problem

=⇒


Introduction


• Well, first let us consider a spherical cow brain ...Actually, this is just a topological problem

=⇒


Introduction


The neurons could be seen as the nodes of a network over thissurface. The links form the 3D body of the network.


Introduction


A cognition network is the network that is used to develop a specificcognitive function.


Introduction

The first law of thermodynamics

• For a closed system, in any process, the change in the internalenergy is considered due to a combination of heat added to thesystem and work done by the system

• For the mean cognition network, in any cognition process, thechange in metabolic activity is considered due to a combination ofthe metabolic losses and the cognition developed by the network


The model of cognition

Spending the energy

• The cognition is proportional to the correlation length of thenetwork (y )

• The metabolic activity (m) developed by the network isproportional to the network volume

• There is an amount of metabolic energy that is lost

m = m0 + ay3



Saving the energy

Brain network is a trade off between energetic cost and efficiency

Latticecheap,

inefficient

Complextrade off

Randomexpensive,

efficient



Saving the energy

• The network is organized as a complex network, gaining efficiencyand spending the energy as a smaller network of length y − y0

m = m0 + ay3−→ m = m0 + a (y − y0)3



Saving the energy

Several networks maintain the same nodes

Cognition network A Cognition network B



Saving the energy

Overlaping nodes also save energy

Networks overlap in the red marked nodes



Saving the energy

• Some nodes do not need to be fully maintained by a singlecognition network

• To characterize this phenomenon the synaptic overlap x is definedas a measure of the size of cortical connectivity hubs of the brain

• The amount of saved energy depends then on the volume of thenetwork that correspond to the shared cortical area

m = a (y − y0)3 + m0−byx2


Catastrophe theory model of cognition decline


m = m0 + a (y − y0)3 − byx2

Synaptic overlap

Metabolic activity

Co

gnit

ion




An important remark• The cognition is described only with the metabolic activity and

synaptic overlap but those are not necessarily the ultimatecauses, they are just useful parameters to describe the process



The cognition as function of metabolic activity

Co

gn

itio

n

Metabolic activity

healthy

dementia

after fall

maximum recovery

critical point

cata

stro

phic

fal

l

impairment

Cognition decline: As the metabolic activity decrease the cognition alsodecays




Co

gn

itio

n

Metabolic activity

healthy

dementia

after fall

maximum recovery

critical point

cata

stro

phic

fal

l

impairment

At some critical value the cognition outcome of the network suddenly drops tovery lower values, when this happens it is said that a catastrophe occurs




0

2

4

6

8

10

12

14

16

18

20

40 60 80 100 120 140

synapticoverlap

The critical fall point and the maximum level of recovery after the catastrophicfall depends on the synaptic overlap


Conclusions

Conclusions

• A very simple mathematical model for cognition decline has beenbuilt. Only two (measurable!) quantities are need in order todescribe the cognition decline process.

• Beyond its simplicity the model is capable of predict very complexphenomena.

• At some point of the cognitive decline a catastrophic fall intodementia occurs

• The possible therapies must be applied before this happens or thesubject recovery will be compromised

• The model predictions are compatible with known phenomena ascompensation or brain reorganization


Acknowledgments


a catastrophe theory model for cognition declinedetritus.fundacioace.com/pub/talks/a catastrophe...

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