1. 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society
ATP Consumption and Neural Electrical Activity: A Physiological Model for Brain Imaging Rita Gafaniz and J. Miguel Sanches
Institute for Systems and Robotics
Instituto Superior Técnico
Lisbon, Portugal
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

2. Motivation
The relation between neural electrical activity and oxygen consumption is the key issue in almost all brain image modalities.
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

3. Hemodynamic Response Function
ATP consumption versus
Electrical Activity
Energy Metabolism
e.g. Mitochondria and Glycolysis
BOLD
Membrane
Blood flow
Vasculature
O2, C02 & Glc
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

4. Goal
Practical, tractable and simultaneously accurate mathematical model to describe the relation between neural electrical activity and oxygen consumption is needed.
A physiologically-based mathematical model relating the electrical activity with the corresponding ATP consumption rate, ATPr, is proposed.
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

5. - + Model Na/K-ATPase (Pump) K leak channels (LC)
Na leak channels (LC)
Na Voltage Gated Channels (VGC)
K Voltage Gated Channels (VGC)
Mitochondria
Cellular Membrane +
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

6. Mathematical Formulation
Where Na is the concentration in the intracellular space
Na,K-ATPase Consumption Rate
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

7. Electrical Activity and Ionic Dynamics
Hodgkin-Huxley
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

8. A second order LTI system with a zero
Transfer Function
A second order LTI system with a zero
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

9. Pole-Zero Map One pole “almost” cancel with the zero
Imaginary Axis
Real Axis
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

10. First order approximation
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

11. Frequency response Response to a 100Hz impulse train of spikes
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

12. Results
f=250Hz = rad/sec
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

13. Results Sustained Activation vs Repetitive Activation
Input  mean value of the action potential sequence
Good agreement with the results published by [Aubert & Costalat (2002)]
Time constant
Consistent with experimental work for mammalian CNS neurons
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

14. Conclusions and future work
A physiological based model for the ATP expenditure as function of the electrical activity
A second order linear system with a zero.
Parameters tuned with data obtained from the literature.
Concordance with more complex models described in the literature.
Validation with more real data
Energy metabolism modeling
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

15. New Model
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

16. THANKS
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society