energy metabolism and neuronal activity: a physiological model for brain imaging
DESCRIPTION
FACULDADE DE MEDICINA Universidade de Lisboa. Energy Metabolism and Neuronal Activity: A Physiological Model for Brain Imaging. Ana Rita Laceiras Gafaniz 2 de Dezembro de 2010. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
ENERGY METABOLISM AND NEURONAL ACTIVITY: A PHYSIOLOGICAL MODEL FOR BRAIN IMAGING
Ana Rita Laceiras Gafaniz2 de Dezembro de 2010
FACULDADE DE MEDICINA
Universidade de Lisboa
2
INTRODUCTION Functional Magnetic Resonance Imaging (fMRI)
is a widely used method to detect the activated brain regions due to a stimulus application.
The Blood-Oxygenation-Level-Dependent (BOLD) signal is based on the well-established correlation between neuronal activity, energy metabolism and haemodynamics.
The BOLD effect is small and data is noisy, turning this inference problem a difficult task
An accurate knowledge of the Haemodynamic Response Function (HRF) to a localized neural stimulus is critical, in order to interpret the fMRI data confidently.
3
INTRODUCTION: MODEL DESIGN FOR THE HRF
Na,K-ATPase
4
MOTIVATION A Physiologically-Based Haemodynamic linear model for
the HRF (Afonso et al (2007))
the Brain Group modulates the brain cells CMRO2 and the vascular demand;
the Vessel Group modulates the summed effect of CBV and CBF vascular changes on the oxyHb/deoxyHb rate in and around blood vessels;
the Control Group for the systemic negative feedback control over vasodilation.
5
OBJECTIVES
Obtain a practical, tractable and simultaneously accurate mathematical model to describe the neuro-metabolic and neuro-vascular couplings that lead to the BOLD effect.
A physiologically-based lineal model describing the relation between the neuronal electrical activity and the ATP dynamics is proposed.
6
THE NEURO-METABOLIC MODEL:OVERVIEW
a) Na/K-ATPase; b) K+ leak channels; c) Na+ leak channels; d) Na+ Voltage Gated Channels; e) K+ Voltage Gated Channels; f) Mitochondria g) Cellular Membrane
SODIUM AND POTASSIUM DYNAMICS:ORDINARY DIFFERENTIAL EQUATIONS
Electrochemical gradient:Concentration gradient
Na/K-Pump:
dNaNaNa e
dKKK e
Electric field
dKKNaNa
dVV ee )(
Napump Ion transport
associated with theElectrical Activity
)(2
)(3
trVKdtdK
trVNadtdNa
Kpump
Napump
8
SODIUM AND POTASSIUM DYNAMICS:NEURONAL ELECTRICAL ACTIVITY
Hodgkin-Huxley
r(t)
depolarisation
hyperpolarisation
repolarisation
9
SODIUM AND POTASSIUM DYNAMICS:TRANSFER FUNCTIONS
)()()()()()()()()()(sRsHKsHNasHsKsRsGKsGNasGsNa
reKeN
reKeN
212
65
212
43
212
21
)(
)(
)(
ssssG
ssssG
ssssG
r
K
N
212
65
212
43
212
21
)(
)(
)(
ssssH
ssssH
ssssH
r
K
N
10
NEURONAL ELECTRICAL ACTIVITY AND ATP CONSUMPTION
)(sGr
)()(21
265 sR
ssssATPr
ATP Consumption Rate:
ATP Consumption:
ssATPsATP r
d)()(
)()( tNatATPr
11
THE MITOCHONDRIA
The mitochondria acts as a regulator, from a Control Theory perspective
With a type-I system, the steady-state error to the step is zero and it is finite to the ramp.
12
OVERALL NEURO-METABOLIC MODEL:NEURONAL ELECTRICAL ACTIVITY AND ATP DYNAMICS
The dynamic evolution of the intracellular concentration of ATP along the time results from the contribution of the ATP consumption, due to the Na,K-ATPase activity the ATP synthesis, by the mitochondrial activity
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ATP DYNAMICS:TRANSFER FUNCTIONS
)()()()()()()()()( sRsLsKsLsNasLsRefsLsATP reKeNR
))(()(
))(()(
))(()(
))(()(
432
212
12112
10
432
212
982
7
432
212
652
4
432
212
322
1
sssssssL
sssssssL
sssssssL
sssssssL
r
K
N
R
14
COEFFICIENTS ESTIMATION
The model parameters were obtained from the literature, or estimated when they were not available
Na(s) and K(s) coefficients
ATP(s) coefficients
15
RESULTS SUSTAINED ACTIVATION AND REPETITIVE ACTIVATION
Comparison with the results published by Aubert & Costalat (2002) (in blue)Time constant
spump 33Consistent with experimental work for mammalian CNS neurons
Hzf 100 Hzf 230
16
RESULTS SUSTAINED ACTIVATION AND REPETITIVE ACTIVATION
ATP dynamics: comparison with the results published by Aubert & Costalat (2002) (in blue)
Time constants30
17
POLE-ZERO (PZ) MAP
PZ from the Na/K-ATPase:
PZ from the mitochondria:
11 031.0 sradp
12 653.0 sradp
11 650.0 sradz
13 033.0 sradp
14 00.30 sradp
12 03.30 sradz
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OVERALL TRANSFER FUNCTION
p1 mainly depends on ρ, the Na/K-ATPase activity time constant
p3 derives from the time constant, τ, for ATP production by the mitochondria
42
31120
31
0 ,))((
)(
pppsps
sLr
24
24
2
3
2211
1
p
p
3
1
21 3
p
pSimplification using
the Taylor Series Expansion
19
OVERALL TRANSFER FUNCTION
31 pp
131
42
212
02
0320.02
,,)(
)(
radsppp
pps
sLr
)()(
1)(
)()()(
242
212
42
9
42
6
42
3
sRps
psK
sNasRefsATP
e
e
20
FREQUENCY RESPONSE
Response to a 100Hz impulse train of spikes
1032.0 radsc
21
CONCLUSIONS AND FUTURE WORK A physiologically-based model
representing the ATP dynamics as a function of the neuronal electrical activity was proposed
A second order linear system with no zeros
Model parameters tuned with data obtained from the literature.
Validation with real data Incorporate the Neuro-Metabolic Model in
a more general model describing the Haemodynamic Response Function
22
REFERENCES D. M. Afonso, J. M. Sanches, and M. H. Lauterbach, “Neural physiological modeling
towards a hemodynamic response function for fMRI,” in 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2007. IEEE International Conference of the Engineering in Medicine and Biology Society (EMBS), August 2007.
A. Aubert and R. Costalat, “A model of the coupling between electrical activity, metabolism, and hemodynamics: Application to the interpretation of functional neuroimaging,” Neuroimage, vol. 17, pp. 1162–1181, 2002.
S. Ogawa, T. M. Lee, A. R. Kay, and D.W. Tank, “Brain magnetic resonance imaging with contrast dependent on blood oxygenation,” in Proceedings of the National Academy of Sciences, S. U. H. Press, Ed., vol. 87. National Academy of Sciences, September 1990, pp. 9868–9872.
J. Malmivuo and R. Plonsey, Bioelectromagnetism, Principles and Applications of Bioelectric and Biomagnetic Fields. Oxford University Press, 1995.
M. F. Bear, B. W. Connors, and M. A. Paradiso, Neuroscience: Exploring the Brain. Williams & Wilkins, 1996.
A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and and its application to conduction and excitation in nerve,” Journal of Physiology (London), vol. 117, pp. 500–544, 1952.
M. D. Mann, “Control systems and homeostasis,” The Nervous System In Action, accessed at July 20, 2010. [Online]. Available: http://www.unmc.edu/physiology/Mann/mann2.html
D. Attwell and S. B. Laughlin, “An energy budget for signaling in the grey matter of the brain,” Journal of Cerebral Blood Flow & Metabolism, vol. 21, pp. 1133–1145, 2001.
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AKNOWLEDGEMENTS
Prof. João Sanches Prof. Patrícia Figueiredo Prof. Fernando Lopes da Silva Prof. João Miranda Lemos Nuno Santos André Gomes David Afonso