1. Electricity in the body
Prof. Dr. Moustafa Moustafa Mohamed Ahmed
Vice Dean
Faculty of Allied Medical Science
Pharos University
Alexandria
 Physics(GRPH-101)

2. Outcomes
By the end of the lecture, the students will Learn how to applied the basic concepts of electrical potential, current, resistance and capacitance to medical instruments and biological phenomena of nerve conduction

3. Body information transmission:
Electrical pulses through nerves
Brain  organs
Brain cells  brain cells

4. Nerve cells A nerve: bundle of nerve cells –neurons A neuron consists:
Cell body (soma): central core
Axon: long thin body
Dendrites: protuberances
Synapses: dendrites gaps to exchange information
Axon converts a stimulus, heart pulses, pressure, etc. to electrical form or receives an electrical stimulus from another neuron. The length and diameter of the axon vary according to its function. It can be as long as 1 m and typically ~ 0.02 mm in diameter. Some axons are wrapped around by Schwann cells, which form multilayered myelin sheath, reducing the membrane capacitance and increasing its electrical resistance. It allows a nerve pulse to travel farther without amplification, so that less metabolic energy is needed. The gap between successive Schwann cells is called the nodes of Ranvier, where the axon is in close contact with the surrounding interstitial fluid. It is at the nodes that the amplification of nerve pulses occurs in a myelinated nerve.

5. Cell models
K+, Ca+, Cl- ions caused the potential inside the axon to be 70 ~ 90 mV lower than outside
A stimulus causes the potential inside the axon to increase to ~ 110 mV thus is ~ 40 mV higher than outside
The raised potential rapidly decreases to its original value and the change in potential propagates alone the axon
The typical pulse propagation speed depends on axon types but is ~ 50 m/s
The duration of the pulse at any point on the axon is ~ 2x10-3 s

6. Resistance in a Metal Wire
resistance of a metal wire is directly proportional to its length, and inversely proportional to its cross-sectional area, A:
R – resistance (Ω)
ρ - resistivity(Ω m)
L – length (m)
A – cross sectional area (m2)

7. Nerve electric properties
What is R, R’, C?
Given the parameters in previous slide, what is R, R’, and C of an axon?

8. Axon resistance and capacitance
Leakage resistance:
For an unmyelinated axon, leakage resistance R’ is ~ 1% of axoplasm resistance, R, so most current entering an axon segment leaks out through the membrane walls in much less than 1 cm length (l=1cm in the above examples).

9. Nerve electric properties

10. Space parameter Space parameter, :  = 0.05 cm (unmyelinated axon)
 = 0.7 cm (myelinated axon)
Space parameter is the length that the axoplasm resistance, R, equals to the leakage resistance, R’.

11. The potential V0 in the fluid outside the cell is taken to be zero
The potential V0 in the fluid outside the cell is taken to be zero. The potential inside the axon is found to be 90 mV lower, so vi = -90 mV.
There is a potential difference across the membrane, so there must be small net charges ± Q on either side of the membrane. These can be calculated from Q =CV

12. Ionic concentration across cell membrane
From Q = CV and the resting potential V inside an axon is ~ 90 mV lower than outside, for C = 3.1x10^-9 F, the excess negative ions inside the cell is ~ 10 ppm (=10^-5).
Fig shows that Na+ concentration is much higher outside the axon, but the electrical field and diffusion process from concentration difference favors the transport of Na+ inside (Fig. 18.4). So there must be a continuous mechanism that brought back the Na+ against the electrical forces and concentration differences.
The K+ and Cl- ion flows are more complicated. The electric forces are opposite to the concentration differences. In a resting axon, the effect of K+ concentration difference exceeds that of the potential difference, and there is a net outward movement of K+ ions. The effect of Cl- concentration difference is exactly balanced by that of the resting potential difference. So there is no net movement of Cl- ions for a resting axon.

13. Forces effects on ions across the membrane
Diffusion force proportional to:
Membrane permeability
concentration difference (Co –Ci)
Electrical force (F=qE) proportional to:
Ionic charge (q)
Electric field (E)
Positive charge experience forces parallel to the field
Negative charge experience forces opposite to the field E + - +
Charge Motion + - +

14. Ionic motion across membrane
Concentration of Na+ is much higher outside the cell than inside.
Sodium ions will diffuse into the cell at a rate proportional to the Na+ concentration difference opposite Co – C1 and to the permeability of the membrane to Na+
There are more Cl- ions outside, so diffusion produces a net flow into the cell. However, the electric force on negative ions is to the field, so the electric filed withdraw some Cl- ions outward. *

15. Ionic motion across membrane

16. Equivalent potential difference
A potential that balances the ion flows due to concentration difference
Nernst equation:
Equilibrium occurs when the potential energy of one ion with charge q, q(vi – vo) is equal to the work required to transfer the ion to a region of higher concentration. This equilibrium potential can be determined by Nernst equation.
Example of Nernst equation: for potassium (K+), co=4, ci=155; KB = 1.38x10^-23; T=310; q=1.6x10^-19 => (vi-vo)=-98 mV. This value is larger than the resting potential of –90 mV. This means there is a net outward flow due to the concentration difference.
Similarly, the equilibrium potential difference for Na+ is +66 which is a positive value. So there is a large Na+ inward flow also due to concentration difference. The equilibrium potential difference for Cl- is –90 mV so there is no net Cl- flow.

17. Response to weak stimulus
Electrical stimulus
Weak: smaller than a critical threshold value (-50 mv).
The response of the axon is similar to that of an analog network of resistors and capacitors.
If a weak stimulus is applied at some point on the axon, no significant axon potential changes occur beyond a few millimeters from that point.
Strong: above the threshold level
produces a current pulse that travels the length of the axon without attenuation.

18. Axon & equivalent analog circuit
If we ignore those R’, v1 will be slowly charged to a potential equals to the EMF E with a time constant RC and v2 will be charged even slower to E with a time constant 2RC.
When R’ are considered, the potential v1 will be smaller than E, and v2 will be even smaller, and so on …

19. Axon & equivalent analog circuit

20. If the difference between the final and resting potentials at x = 0 is vd, then the difference at x is found to be:
V(x) =Vd e-x/λ
λ = Space parameter
V(x) = the difference between the potential at x and resting potentials at x = 0

21. Action potential
If the potential increase above the original action potential threshold (-50 mV),
shortly after this stimulus is applied, the axon potential at x suddenly increase and become positive, reaching a value as high as +50 mV.
The potential is gradually return to its resting value.
The shape and peak size of the action potential curve are independent of the strength stimulus or the distance x from the stimulus
the action potential is not proportional to the stimulus.

22. Na+ permeability suddenly increase by a factor of more than 1000.
In an myelinated axon, the action potential is accompanied by dramatic change in the permeability of the membrane to Na+ and K+.
Na+ permeability suddenly increase by a factor of more than 1000.
Causes a rapid influx of positive sodium ions, which changes the sign of V from negative to positive.
After about 0.3 ms,
Sodium influx diminishes.
Sodium permeability decrease toward its normal low level.
Potassium permeability gradually rises by about a factor of 30.
potassium ions now begin to flow rapidly out of the cell
V again become negative Vi (below the resting potential)
The Na- K pump does gradually reestablish the resting (Takes about 90 ms.)

23. Action potential
What’s the mechanism behind action potential propagation?
Amplification
Propagation without attenuation

24. Action potential propagation along an unmyelinated axon
(a) Resting state
b) An action potential pulse at point P
Propagation of an action potential in an unmyelinated axon. (a) Resting state. (b) An action potential pulse at point P. Positive ions then moves from P to Q and toward P from right outside of the axon. The +/- charges on either side of Q decreased, and the potential increases toward the action potential threshold. (c) Once the threshold is reached, the Na+ ions permeability suddenly increases (dashed arrows). The axon potential rises rapidly and becomes positive. (d) The action potential travels further to the right, and following an outflow of potassium ions (dashed arrows), the axon potential on the left segment has returned to a negative value close to the resting potential. The resting state potential and ionic concentrations are restored over a much longer period by the active Na-K pump.
Na+ ions permeability suddenly increases
The axon potential rises rapidly
and becomes positive.
(d) The action potential travels further to the right

25. Action potential propagation along a myelinated axon
At the nodes the membrane responds to an above-threshold stimulus similar in an unmyelinated axon, i.e., Na+ permeability increases rapidly, producing an influx of Na+ and the action potential pulse.
Because the gap between adjacent nodes is small (~ 1 mm) compared to the space parameter, (~ 7 mm), most of the current (positive ions) reaches the next node.
Unlike the unmyelinated axon, in a myelinated nerve, relatively few ions pass through the myelin sheath except at the node of Ranvier. At the nodes the membrane responds to an above-threshold stimulus similar in an unmyelinated axon, i.e., Na+ permeability increases rapidly, producing an influx of Na+ and the action potential pulse. Because the gap between adjacent nodes is small (~ 1 mm) compared to the space parameter, (~ 7 mm), most of the current (positive ions) reaches the next node.

26. Action potential propagation velocity
The velocity of propagation of an action potential between two nodes in myelinated axon is the distance X between two nodes divided by the time T

27. Questions
Complete
A myelinated axon is surrounded by
In resting state of an axon, there are far more ions on the outside than inside and far more ---- ions on the inside than outside
The Nernst equation relates the potential difference across a membrane to the equilibrium ratio of
The action potential involves a sudden increase in the membrane permeability to ---- ions
If radius of a myelinated axon is doubled, the velocity of axon potential changes by a factor of

28. Assignment for all students
Prepare a power point presentation about electrical activity of heart and recorded with Electrocardiograph

29. Recommended text books:
Experiments in Modern physics Advanced level physics Applied physics College physics Physics for Scientists and engineers