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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
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Objective
Objective
• Find a simple mathematical model that describe the cognitivedecline through dementia
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Introduction
The cognition network
• Well, first let us consider a spherical cow brain ...
Actually, this is just a topological problem
=⇒
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Introduction
The cognition network
• Well, first let us consider a spherical cow brain ...Actually, this is just a topological problem
=⇒
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Introduction
The cognition network
The neurons could be seen as the nodes of a network over thissurface. The links form the 3D body of the network.
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Introduction
The cognition network
A cognition network is the network that is used to develop a specificcognitive function.
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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
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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
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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
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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
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The model of cognition
Saving the energy
Brain network is a trade off between energetic cost and efficiency
Latticecheap,
inefficient
Complextrade off
Randomexpensive,
efficient
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The model of cognition
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
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The model of cognition
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
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The model of cognition
Saving the energy
Several networks maintain the same nodes
Cognition network A Cognition network B
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The model of cognition
Saving the energy
Overlaping nodes also save energy
Networks overlap in the red marked nodes
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The model of cognition
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
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The model of cognition
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
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Catastrophe theory model of cognition decline
The model of cognition
m = m0 + a (y − y0)3 − byx2
Synaptic overlap
Metabolic activity
Co
gnit
ion
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Catastrophe theory model of cognition decline
The model of cognition
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
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Catastrophe theory model of cognition decline
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
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Catastrophe theory model of cognition decline
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
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
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Catastrophe theory model of cognition decline
The cognition as function of metabolic activity
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
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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
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Acknowledgments
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