Question

A) Estimate how much energy is required to transmit one action potential along the axon 20 cm long of radius 20 μm . The thickness of the membrane is about 10−8 and the dielectric constant is about 3. [Hint: the energy to transmit one pulse is equivalent to the energy stored by charging the axon capacitance].

B) What minimum average power is required for 104 neurons each transmitting 100 pulses per second?

Answer 1

Given that :

length of the axon, L = 20 cm = 0.2 m

radius of the axon, r = 20 x 10^-6 m

thickness of the membrane, t = 10^-8

dielectric constant, k = 3

(A) The energy is required to transmit one action potential along the axon which is given as :

E = (1/2) [k ₀ A t]                                                            { eq.1 }

where, A = area of the axon = 2rL

inserting the values in above eq.

E = (0.5) [(3) (8.85 x 10^-12 C²/Nm²) 2 (3.14) (20 x 10^-6 m) (0.2 m)] (10^-8)

E = 333.4 x 10^-20 J

E = 3.34 x 10^-18 J

(b) minimum average power required which will be given as :

P = E / t

P = (3.34 x 10^-18 J) 10⁴ / (100 sec)

P = 3.34 x 10^-16 W