Transcript Diapositivo 1
ATP Dynamics and Neuronal Activity: A Physiological Model for Brain Imaging
A. R. Gafaniz and J. Miguel Sanches
Institute for Systems and Robotics / Instituto Superior Técnico Lisboa, Portugal
Abstract
The relationship between Neuronal Activity (NA) and the HRF is the key issue in BOLD fMRI. Since the BOLD effect is weak and data is noisy, analyzing the information is difficult. So that, an accurate knowledge of the response of the BOLD signal to a localized neural stimulus is needed.
A physiologically-based linear model relating the ATP dynamics with the NA is presented, with the ultimate goal of modeling the relationship between blood oxygenation dynamics and the NA.
The Neuro-Metabolic Model (NMM) is tuned with physiological information. The critical elements involved in ATP dynamics are the Na/K-ATPase and the mitochondrion.
Problem Formulation
The proposed model describes the time-varying concentration of sodium, Na, potassium, K, and ATP.
intracellular The main processes that determine Na and K changes are: Na+ and K+ active transport by the Na/K-ATPase, Na+ and K+ diffusion, through LC and VGC, due to the electric field force and concentration gradient across the neuronal membrane.
ATP is expended by the Na/K-ATPase mostly to restore Na+ and K+
homeostasis,
that were degraded due to the NA, and is restored by the
mitochondria,
which is a regulator that continuously senses the ATP concentration inside the neuron and adjusts its activity in order to maintain ATP in a biological predefined reference level.
dNa
Na
V
3
pump
Na r
(
t
)
dt dK
K
V
2
pump
K r
(
t
)
dt Na
(
s
)
K
(
s
)
H G Na e
(
s
)
Na e Na e
(
s
)
Na e
G K e H K e
(
s
)
K
(
s
)
K e e
G r H r
(
s
)
R
(
s
) (
s
)
R
(
s
)
pump
Na
,
ATP r
(
t
)
pump
Na G r
(
s
)
ATP r
(
s
)
s
2
s
1 1
s
2 2
R
(
s
)
ATP d
(
s
) 1
ATP r
(
s
)
Na
(
s
)
s
Na
(
s
)
s ATP
(
s
)
s
2
s
Ref
(
s
) (
s s
2
s
)
Na
(
s
)
Experimental Results
Sustained Activation
vs
Repetitive Activation:
ATP
(
s
)
L R
(
s
)
Ref
(
s
)
L N
(
s
)
Na e
(
s
)
L K
(
s
)
K e
(
s
)
L r
(
s
)
R
(
s
)
ATP
(
s
)
L r
(
s
)
R
(
s
) (
s
2 1 1
s s
2 2 2
s
)(
s
2 3 3
s
4 )
p
1
p
3 3
L r
(
s
) (
s
p
) 2 ,
p
p
1
p
3 2 RecPad 2010 - 16th edition of the Portuguese Conference on Pattern Recognition, UTAD University, Vila Real city, October 29th